Matrix/0000755000175100001440000000000012272020333011526 5ustar hornikusersMatrix/TODO0000644000175100001440000003442512256112203012226 0ustar hornikusers##-*- mode: org -*- * *Urgent* in some sense --------------------------------------------------- ** TODO M[] indexing should work (but with a warning: use *dense*!) ** TODO src/CHOLMOD/MatrixOps/cholmod_symmetry.c is "cool" and fast; Definitely should use it for solve() {it seems MATLAB does}; alternatively also is_sym() [in src/cs_utils.c], see below. ** TODO diagonalMatrix inherits from sparseMatrix, *BUT* "ddiMatrix" does not inherit from "dsparseMatrix", nor does "ldiMatrix" from "lparseMatrix". Seems an undesirable inconsistency. Try changing setClass("ddiMatrix", contains = c("diagonalMatrix", "dMatrix")) to setClass("ddiMatrix", contains = c("diagonalMatrix", "dsparseMatrix")) ** TODO Look at Paul Bailey's problem -- CHOLMOD error (even seg.fault for him) --> ~/R/MM/Pkg-ex/Matrix/sparseOrderedLogit.R ** TODO BunchKaufman()'s result is not really useful yet {but it is used on C level e.g. for solve(). Should define expand() method or similar, see man/BunchKaufman-methods.Rd and R/dsyMatrix.R (at end). ** TODO src/cs_utils.c : I think is_sym() [only used in Matrix_cs_to_SEXP()] can be made sped up: leave the for loops, as soon as is_lower == is_upper == 0. * New smallish ideas, relatively urgent for MM ----------------------------- ** DONE generalize new "indMatrix" class, to allow 0 repetitions of some samples, i.e., columns of all 0 s. It's mathematically more natural --> typically will be useful. ** TODO cor() and cov() at least for y=NULL ("no y"). -> ~/R/MM/Pkg-ex/Matrix/cor_sparse-propos.R <- http://stackoverflow.com/questions/5888287/ ** TODO Investigate the "band changing (and getting) ideas 'band<-' etc, from Jeremy D Silver, per posts to R-devel on Aug.26,2011 {MM: ~/R/MM/Pkg-ex/Matrix/bands-Jeremy_Silver-ex.R } ** TODO FIXME(2) and (3) in R/products.R: t(.Call(Csparse_dense_*)) ** TODO cbind2() / rbind2() for sparseMatrices: dimnames propagation should happen in C, see R/bind2.R and src/Csparse.c (Csparse_horzcat etc). ** TODO use getOption("Matrix.quiet") in more places [--> less messages/warnings] ** TODO Check for DimNames propagation in coercion and other operations. Done for (%*%, crossprod, tcrossprod). ** TODO Report the problem in the Linux ldexp manual page. The second and third calls in the Synopsis should be to ldexpf and ldexpl. ** TODO provide methods for "dspMatrix" and "dppMatrix"! 2012-07: mostly(?) DONE, with Ops, etc, also pack() / unpack() ** TODO combine the C functions for multiplication by special forms and solution wrt special forms by using a 'right' argument and a 'classed' argument. [done with dgeMatrix_matrix_mm(); not yet for other classes; and for _crossprod()] ** DONE Cache '@factors' components also from R, e.g., for "Tsparse.." via .set.factors() ** TODO chol() and Cholesky() caching unfinished: the *name* [Ss][Pp][Dd]Cholesky depends on (perm, LDL, super) arguments: *** DONE .chkName.CHM(name, perm, LDL, super) and .CHM.factor.name() *** TODO use the above ** TODO partly DONE; new arg 'cache=FALSE': allow cache=FALSE to disable the caching * Generalization of Existing Classes and Methods --------------------------- ** TODO "Math2" , "Math", "Arith": keep triangular and symmetric Matrices when appropriate: particularly desirable for "Math2": round(), signif() ** TODO For triangular matrices, ensure the four rules of "triangular matrix algebra" (Golub+Van Loan 1996, 3.1.8, p.93)" *** DONE since 2008-03-06 for Csparse *** DONE since 2010-07-23 for %*% *** TODO e.g. for %*% ** TODO "d" <-> "l" coercion for all "[TCR]" sparse matrices is really trivial: "d" -> "l" : drops the 'x' slot "l" -> "d" : construct an 'x' slot of all '1' We currently have many of these conversions explicitly, e.g. setAs("dsTMatrix", "lsTMatrix", function(from) new("lsTMatrix", i = from@i, j = from@j, uplo = from@uplo, Dim = from@Dim, Dimnames = from@Dimnames)) but I would rather want to automatically construct all these coercion methods at once by a ``method constructor'', i.e., for all "dsparse*" -> "lsparse*" and vice versa. How can one do this {in a documented way} ? ** TODO Think of constructing setAs(...) calls automatically in order to basically enable all ``sensible'' as(fromMatrix, toMatrix) calls, possibly using canCoerce(.) ** TODO When we have a packed matrix, it's a waste to go through "full" to "sparse": ==> implement setAs("dspMatrix", "sparseMatrix") setAs("dppMatrix", "sparseMatrix") setAs("dtpMatrix", "sparseMatrix") and the same for "lsp" , "ltp" and "nsp" , "ntp" ! ** TODO tcrossprod(x, y) : do provide methods for y != NULL calling Lapack's DGEMM for "dense" [2005-12-xx: done for dgeMatrix at least] ** TODO Factorizations: LU done; also Schur() for *sparse* Matrices. ** TODO use .Call(Csparse_drop, M, tol) in more places, both with 'tol = 0.' to drop "values that happen to be 0" and for zapsmall() methods for Csparse* ** TODO implement .Call(Csparse_scale, ....) interfacing to cholmod_scale() in src/CHOLMOD/Include/cholmod_matrixops.h : for another function specifically for multiplying a cholmod_sparse object by a diagonal matrix. Use it in %*% and [t]crossprod methods. ** TODO make sure *all* group methods have (maybe "bail-out") setMethod for "Matrix". e.g. zapsmall() fails "badly" ** TODO rbind2(, ) does not work (e.g. , ) ** TODO %*% {also in crossprod/tcrossprod} currently always returns , since --> Csparse_dense_prod --> cholmod_sdmult and that does only return dense. When the sparse matrix is very sparse, i.e. has many rows with only zero entries, it would make much sense to return sparse. ** TODO ! loses symmetry, both for dense and sparse matrices. !M where M is "sparseMatrix", currently always gives dense. This only makes sense when M is ``really sparse''. ** TODO diag(m) <- val currently automatically works via m[cbind(i,i)] <- val This (`[<-` method) is now "smart" for diagonalMatrix, but needs also to be for triangularMatrix, and probably also "dense*general*Matrix" since the above currently goes via "matrix" and back instead of using the 'x' slot directly; in particular, the triangular* "class property" is lost! [current ??] ** TODO The "[<-" now uses src/t_Csparse_subassign.c and no longer explodes memory. *However* it is still too slow when the replacment region is large. * Cholesky(), chol() etc --------------------------------------------------- ** chol() should ``work'': proper result or "good" error message. (mostly done ?) ** example(Cholesky, echo=FALSE) ; cm <- chol(mtm); str(cm); str(mtm) shows that chol() does not seem to make use of an already present factorization and rather uses one with more '0' in x slot. ** examples for solve( Cholesky(.), b, system = c("A", "LDLt"....)) probably rather in man/CHMfactor-class.Rd than man/Cholesky.Rd ** LDL() looks relatively easy; via "tCsparse_diag()" {diagonal entries of *triangular* Csparse} --> see comment in determinant() in R/dsCMatrix.R, will give faster determinant ** Allow Cholesky(A,..) when A is not symmetric *AND* we really _mean_ to factorize AA' ( + beta * I) ** update(Cholesky(..), *): make *also* use of the possibility to update with non-symmetric A and then AA' + mult * I is really meant. .updateCHMfactor() ## allows that already(?) ** TODO add examples (and tests!) for update(, ..) and Cholesky(......, Imult), also tests for hidden {hence no examples} ldetL2up() { R/CHMfactor.R }; see ex in man/wrld_1deg.Rd MM: See e.g. ~/R/MM/Pkg-ex/Matrix/CholUpdate.R -- for solve(, ) ** TODO implement fast diag() via calling new src/Csparse.c's diag_tC_ptr() . - diag_tC_ptr() functionality now exported via R/dsCMatrix.R .diag.dsC() : the name is silly, but functionality nice. See (hidden) example in man/Cholesky.Rd ** TODO chol() gives "temporarily disabled" but should give the *symbolic* factorization; similarly Cholesky(.) is not enabled * "Basic" new functionality -- "nice to have" (non-urgent) ----------------- ** TODO tr(A %*% B) {and even tr(A %*% B %*% C) ...} are also needed frequently in some computations {conditional normal distr. ...}. Since this can be done faster than by sum(diag(A %*% B)) even for traditional matrices, e.g. sum(A * t(B)) or {even faster for "full" mat} crossprod(as.vector(A), as.vector(B)) and even more so for, e.g. %*% {used in Soeren's 'gR' computations}, we should also provide a generic and methods. ** TODO diag(A %*% B) might look like a "generalization" of tr(A %*% B), but as the above tricks show, is not really. Still, it's well worth to provide diag.prod(A, B): Well, if A %*% B is square, diag(A %*% B) === colSums(t(A) * B) and we should probably teach people about that ! ** TODO eigen() should become generic, and get a method at least for diagonal, but also for symmetric -> dsyMatrix [LAPACK dsyev() uses UPLO !], but also simply for dgeMatrix (without going via tradition matrices). What about Sparse? There's fill-in, but it may still be sensible, e.g. mlist <- list(1, 2:3, diag(x=5:3), 27, cbind(1,3:6), 100:101) ee <- eigen(tcrossprod(bdiag(lapply(mlist, as.matrix)))) Matrix( signif(ee$vectors, 3) ) * Everything else aka "Miscellaneous" -------------------------------------- ** qr.R(qr(x)) may differ for the "same" matrix, depending on it being sparse or dense: "qr.R() may differ from qr.R() because of permutations" This is not really acceptable and currently influences rcond() as well. ** facmul() has no single method defined; it looks like a good idea though (instead of the infamous qr.qy, qr.qty,.... functions) ** TODO symmpart() and skewpart() for *sparse* matrices still use (x +/- t(x))/2 and could be made more efficient. Consider going via asTuniq() or something very close to .Arith.Csparse() in R/Ops.R For a traditional "matrix" object, we should speedup, using C code .. ** TODO many setAs(*, "[dl]..Matrix") are still needed, as long as e.g. replCmat() uses as_CspClass() and drop0(.) which itself call as_CspClass() quite a bit. --> try to replace these by as(*, "CsparseMatrix"); forceSymmetric, etc. ** writeMM(obj, file=stdout()) creates file "1" since file is silently assumed to be a string, i.e. cannot be a connection. An R (instead of C) version should be pretty simple, and would work with connections automatically ["lsparse" become either "real" or "pattern", "depending if they have NAs or not]. ** o still works via sparse in some cases, but could return in the same cases where o does. ** look at solve.QP.compact() in \pkg{quadprog} and how to do that using our sparse matrices. Maybe this needs to be re-implemented using CHOLMOD routines. ** We allow "over-allocated" (i,x)-slots for CsparseMatrix objects, as per Csparse_validate() and the tests in tests/validObj.R. This is as in CHOLMOD/CSparse, where nzmax (>= .@p[n]) corresponds to length(.@i), and makes sense e.g. for M[.,.] <- v assignments which could allocate in chunks and would not need to re-allocate anything in many cases. HOWEVER, replCmat() in R/Csparse.R is still far from making use of that. ** TODO advertize rbind2() / cbind2() and (rather?) rBind() / cBind() ------ ----- in all vignettes / talks / ... !! People erronously try rbind/cbind see that they don't work and then reinvent the wheel! --> Consider using the new 'dotMethods' functionality to define cbind() and rbind() versions that work with Matrix. The "Rmpfr" package does that now. ** TODO In all(M1 == M2) for sparse large matrices M1, M2 (e.g. M2 <- M1 !), the intermediate 'M1 == M2' typically is dense, hence potentially using humongous amount of memory. We should/could devise something like allCompare(M1, M2, `==`) which would remain sparse in all its computations. -------- ** Reconsider the linkages in the include files for the SuiteSparse packages. It may be better simply to add all the src//Include directories to the include path for all compilations. I don't think there is a big overhead. Right now we need to modify the include file src/SPQR/Include/SuiteSparseQR_C.h so that it does not expect to have src/UFsparse and src/CHOLMOD/Include on the include path. Maybe just those two should be added to the include path. ** (systematically check that LAPACK-calling functions check for 0-dimensional input themselves; LAPACK gives an integer error code) ** the f[,5762] <- thisCol now go via Csparse_subassign() call ... [ in tests/indexing.R ]. Still would be nice to be able to use abIndex (see replTmat in R/Tsparse.R) ** {IS THIS CURRENT?} Sept. 2009: Subject: chol2inv() |-> solve() when testing and documenting chol2inv(), I found that it's pretty simple to also define a method for "CHMfactor" objects, namely simply the solve(*, Diagonal(.) "A") method. This is not particularly exciting, and also does *not*, I think help for defining a chol2inv() method for *sparse* (upper) triangular matrices. ** sort(, partial=..), needed, for mean(*, trim = .) or median(). Note that defining xtfrm() does not "help" (as sort() then goes via dense index). See "mean" in R/Matrix.R ** TODO rcond() for square currently goes via *dense* -- BAD -- can we go via qr() in any case? In some cases, e.g. lmer()'s "Lambda" (block triangular, small blocks) rcond(L) := 1 / (norm(L) * norm(solve(L))) is simple {and remains sparse, as solve(L) is still block triangular} ** TODO How can we ensure that inst/include/cholmod.h remains correct and equivalent to src/CHOLMOD/Include/cholmod_core.h and siblings ??? {currently need to do this manually (Emacs M-x compare-windows) for the typedefs} ** finalize and activate the new *unused* code in src/t_sparseVector.c ** check all uses of alloca()/Alloca() in src/*.[ch] ensuring that the *size* allocated cannot grow with the vector/matrix/nnzero sizes of the input. [see the change needed in svn r2770 in src/dtCMatrix.c !] Matrix/po/0000755000175100001440000000000012271765426012166 5ustar hornikusersMatrix/po/update-me.sh0000755000175100001440000000164112131725455014401 0ustar hornikusers#!/bin/sh # #__>> Keep in sync with ~/R/Pkgs/cluster/po/update-me.sh <<__ # ## Script for updating package-specific *.pot files ## written such that it should work for any package # R=${R:-R} thisdir=`dirname $0` ; cd $thisdir; thisdir=`pwd` echo 'preliminary thisdir='$thisdir pkgDIR=`dirname $thisdir` pkg=`basename $pkgDIR` echo ' --> pkgDIR='$pkgDIR' ; pkg='$pkg # echo ''; echo '## FIXME ## use new Scheme from R 3.0.x on' # cd `$R RHOME`/po # make pkg-update PKG=$pkg PKGDIR=$pkgDIR echo "require('tools'); update_pkg_po('$pkgDIR')" | $R --slave ## -------------------------------- as of R 3.0.0 echo 'end{make pkg-update}' ; echo '' echo 'Test with (e.g.)' echo ' LANGUAGE=de R --no-environ --no-save' ; echo '' echo 'and then something like' echo ' Matrix(1:6, 2,3) %*% Matrix(1:4, 2)'; echo '' echo 'Commit with something like' echo " svn ci -m'translation updates' po inst/po"; echo '' Matrix/po/R-Matrix.pot0000644000175100001440000003457212256121033014347 0ustar hornikusersmsgid "" msgstr "" "Project-Id-Version: Matrix 1.1-1\n" "POT-Creation-Date: 2013-12-23 21:27\n" "PO-Revision-Date: YEAR-MO-DA HO:MI+ZONE\n" "Last-Translator: FULL NAME \n" "Language-Team: LANGUAGE \n" "MIME-Version: 1.0\n" "Content-Type: text/plain; charset=CHARSET\n" "Content-Transfer-Encoding: 8bit\n" msgid "invalid 'mod': %s" msgstr "" msgid "not-yet-implemented method for %s(<%s>).\n ->> Ask the package authors to implement the missing feature." msgstr "" msgid "not-yet-implemented method for %s(<%s>, <%s>).\n ->> Ask the package authors to implement the missing feature." msgstr "" msgid "'x' is not positive definite -- chol() undefined." msgstr "" msgid "Matrices must have same dimensions in %s" msgstr "" msgid "non-conformable matrix dimensions in %s" msgstr "" msgid "dimnames [%d] mismatch in %s" msgstr "" msgid "Matrices must have same number of rows in %s" msgstr "" msgid "Matrices must have same number of columns in %s" msgstr "" msgid "[[ suppressing %d column names %s ... ]]" msgstr "" msgid "[[ suppressing %d column names %s ]]" msgstr "" msgid "'x' must be \"sparseMatrix\"" msgstr "" msgid "not yet implemented for class %s" msgstr "" msgid "not a triangular matrix" msgstr "" msgid "not a symmetric matrix; consider forceSymmetric() or symmpart()" msgstr "" msgid "not yet implemented for matrix with typeof %s" msgstr "" msgid "not yet implemented for %s" msgstr "" msgid "general Matrix class not yet implemented for %s" msgstr "" msgid "arguments %s are disregarded in\n %s" msgstr "" msgid "Quadratic matrix '%s' (=: A) is not formally\n\tsymmetric. Will be treated as\tA A'" msgstr "" msgid "'update' must be logical or '+' or '-'; 'C' a matrix, and 'L' a \"CHMfactor\"" msgstr "" msgid "update must be TRUE/FALSE or '+' or '-'" msgstr "" msgid "Matrix-internal error in [i,,d]; please report" msgstr "" msgid "nothing to replace with" msgstr "" msgid "number of items to replace is not a multiple of replacement length" msgstr "" msgid "too many replacement values" msgstr "" msgid "i1[1] == 0 ==> C-level verbosity will not happen!" msgstr "" msgid "using\t \"old code\" part in Csparse subassignment" msgstr "" msgid "Cholesky() -> *symbolic* factorization -- not yet implemented" msgstr "" msgid "Not a valid format" msgstr "" msgid "'file' must be a character string or connection" msgstr "" msgid "Invalid storage type: %s" msgstr "" msgid "Only numeric sparse matrices allowed" msgstr "" msgid "Invalid storage format: %s" msgstr "" msgid "Invalid assembled indicator: %s" msgstr "" msgid "file is not a MatrixMarket file" msgstr "" msgid "type '%s' not recognized" msgstr "" msgid "representation '%s' not recognized" msgstr "" msgid "element type '%s' not recognized" msgstr "" msgid "symmetry form '%s' not recognized" msgstr "" msgid "readMM(): row\t values 'i' are not in 1:nr" msgstr "" msgid "readMM(): column values 'j' are not in 1:nc" msgstr "" msgid "symmetry form 'skew-symmetric' not yet implemented for reading" msgstr "" msgid "symmetry form 'hermitian' not yet implemented for reading" msgstr "" msgid "symmetry form '%s' is not yet implemented" msgstr "" msgid "element type 'complex' not yet implemented" msgstr "" msgid "'%s()' is not yet implemented for element type '%s'" msgstr "" msgid "'%s()' is not yet implemented for representation '%s'" msgstr "" msgid "trimmed mean of 'sparseVector' -- suboptimally using as.numeric(.)" msgstr "" msgid "'V' is not a square matrix" msgstr "" msgid "diag(.) had 0 or NA entries; non-finite result is doubtful" msgstr "" msgid "invalid dimnames given for %s object" msgstr "" msgid "dimnames(.) <- NULL: translated to \ndimnames(.) <- list(NULL,NULL) <==> unname(.)" msgstr "" msgid "'nrow', 'ncol', etc, are disregarded when 'data' is \"Matrix\" already" msgstr "" msgid "invalid 'data'" msgstr "" msgid "'nrow', 'ncol', etc, are disregarded for matrix 'data'" msgstr "" msgid "complex matrices not yet implemented in Matrix package" msgstr "" msgid "using slow kronecker() method" msgstr "" msgid "Cholesky(A) called for 'A' of class \"%s\";\n\t it is currently defined for sparseMatrix only; consider using chol() instead" msgstr "" msgid "'lag' and 'differences' must be integers >= 1" msgstr "" msgid "programming error: min() should have dispatched w/ 1st arg much earlier" msgstr "" msgid "invalid or not-yet-implemented 'Matrix' subsetting" msgstr "" msgid "[ ] : .M.sub.i.logical() maybe inefficient" msgstr "" msgid "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.logical)?" msgstr "" msgid "m[ ]: inefficiently indexing single elements" msgstr "" msgid "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.2col)?" msgstr "" msgid ".M.sub.i.2col(): 'i' has no integer column number;\n should never happen; please report" msgstr "" msgid "such indexing must be by logical or 2-column numeric matrix" msgstr "" msgid ".M.repl.i.2col(): 'i' has no integer column number;\n should never happen; please report" msgstr "" msgid ".M.repl.i.2col(): drop 'matrix' case ..." msgstr "" msgid "negative values are not allowed in a matrix subscript" msgstr "" msgid "NAs are not allowed in subscripted assignments" msgstr "" msgid "m[ ] <- v: inefficiently treating single elements" msgstr "" msgid "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' ?" msgstr "" msgid "RHS 'value' (class %s) matches 'ANY', but must match matrix class %s" msgstr "" msgid "not-yet-implemented 'Matrix[<-' method" msgstr "" msgid "inefficient method used for \"- e1\"" msgstr "" msgid " %s %s is undefined" msgstr "" msgid "internal bug in \"Compare\" method (Cmp.Mat.atomic); please report" msgstr "" msgid "Cmp.Mat.atomic() should not be called for diagonalMatrix" msgstr "" msgid "Matrices must have same number of rows for arithmetic" msgstr "" msgid "number of rows are not compatible for %s" msgstr "" msgid "length of 2nd arg does not match dimension of first" msgstr "" msgid "length of 1st arg does not match dimension of 2nd" msgstr "" msgid "internal bug in \"Logic\" method (Logic.Mat.atomic); please report" msgstr "" msgid "Logic.Mat.atomic() should not be called for diagonalMatrix" msgstr "" msgid "vector too long in Matrix - vector operation" msgstr "" msgid "longer object length\n\tis not a multiple of shorter object length" msgstr "" msgid "%s %s is undefined" msgstr "" msgid "longer object length" msgstr "" msgid "is not a multiple of shorter object length" msgstr "" msgid "dim [product %d] do not match the length of object [%d]" msgstr "" msgid "invalid class: %s" msgstr "" msgid "not-yet-implemented coercion to \"TsparseMatrix\"" msgstr "" msgid "you cannot mix negative and positive indices" msgstr "" msgid "index larger than maximal %d" msgstr "" msgid "'NA' indices are not (yet?) supported for sparse Matrices" msgstr "" msgid "logical subscript too long (%d, should be %d)" msgstr "" msgid "no 'dimnames[[.]]': cannot use character indexing" msgstr "" msgid "invalid character indexing" msgstr "" msgid "Matrix-internal error in [i,,d]; please report" msgstr "" msgid "FIXME: NOT YET FINISHED IMPLEMENTATION" msgstr "" msgid "internal bug: missing 'i' in replTmat(): please report" msgstr "" msgid "[ ] indexing not allowed: forgot a \",\" ?" msgstr "" msgid "internal bug: matrix 'i' in replTmat(): please report" msgstr "" msgid "x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced; NA |--> TRUE." msgstr "" msgid "x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced." msgstr "" msgid "x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced NA |--> TRUE." msgstr "" msgid "x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced." msgstr "" msgid "x[.,.] <- val : x being coerced from Tsparse* to CsparseMatrix" msgstr "" msgid "nargs() = %d should never happen; please report." msgstr "" msgid "row indices must be <= nrow(.) which is %d" msgstr "" msgid "column indices must be <= ncol(.) which is %d" msgstr "" msgid "'force' must be (coercable to) TRUE or FALSE" msgstr "" msgid "invalid (to - from)/by in seq(.)" msgstr "" msgid "wrong sign in 'by' argument" msgstr "" msgid "'by' argument is much too small" msgstr "" msgid "length must be non-negative number" msgstr "" msgid "too many arguments" msgstr "" msgid "c(,..) of different kinds, coercing all to 'rleDiff'" msgstr "" msgid "[i] is not yet implemented" msgstr "" msgid "all() is not yet implemented" msgstr "" msgid "sum() is not yet implemented" msgstr "" msgid "prod() is not yet implemented" msgstr "" msgid "not yet implemented" msgstr "" msgid "x / 0 for an x with sign-change\n no longer representable as 'rleDiff'" msgstr "" msgid " --> is not yet implemented" msgstr "" msgid " --> is not yet implemented" msgstr "" msgid "'diagonals' matrix must have %d columns (= length(k) )" msgstr "" msgid "'diagonals' must have the same length (%d) as 'k'" msgstr "" msgid "for symmetric band matrix, only specify upper or lower triangle\n hence, all k must have the same sign" msgstr "" msgid "the %d-th (sub)-diagonal (k = %d) is too short; filling with NA's" msgstr "" msgid "'A' must be a square matrix" msgstr "" msgid "must either specify 'A' or the functions 'A.x' and 'At.x'" msgstr "" msgid "when 'A' is specified, 'A.x' and 'At.x' are disregarded" msgstr "" msgid "not converged in %d iterations" msgstr "" msgid "hit a cycle (1) -- stop iterations" msgstr "" msgid "hit a cycle (2) -- stop iterations" msgstr "" msgid "not enough new vecs -- stop iterations" msgstr "" msgid "\"dMatrix\" object with NAs cannot be coerced to \"nMatrix\"" msgstr "" msgid "diagonalMatrix in .dense2C() -- should never happen, please report!" msgstr "" msgid "undefined method for class %s" msgstr "" msgid "dim(.) value must be numeric of length 2" msgstr "" msgid "dimensions don't match the number of cells" msgstr "" msgid "invalid nargs()= %d" msgstr "" msgid "LU computationally singular: ratio of extreme entries in |diag(U)| = %9.4g" msgstr "" msgid "cannot coerce non-symmetric \"dgTMatrix\" to \"dsCMatrix\" class" msgstr "" msgid "the matrix is not triangular" msgstr "" msgid "'lwd' must be NULL or non-negative numeric" msgstr "" msgid "'x' has invalid data type" msgstr "" msgid "length(x) must be either 1 or #{cols}" msgstr "" msgid "some arguments are not matrices" msgstr "" msgid "%s kind not yet implemented" msgstr "" msgid "non-square matrix" msgstr "" msgid "matrix with non-zero off-diagonals cannot be coerced to \"diagonalMatrix\"" msgstr "" msgid "matrix is not diagonal" msgstr "" msgid "Internal bug: nargs()=%d; please report" msgstr "" msgid "chol() is undefined for diagonal matrix with negative entries" msgstr "" msgid "non-matching dimensions" msgstr "" msgid "incompatible matrix dimensions" msgstr "" msgid "intermediate 'r' is of type %s" msgstr "" msgid "not yet implemented .. please report" msgstr "" msgid "not a positive definite matrix" msgstr "" msgid "as(.,\"dsCMatrix\") is deprecated (since 2008); do use as(., \"symmetricMatrix\")" msgstr "" msgid "inefficient coercion (lost triangularity); please report" msgstr "" msgid "coercion to \"indMatrix\" only works from integer numeric" msgstr "" msgid "coercion from list(i1,...,ik, d) to \"indMatrix\" failed.\n All entries must be integer valued and the number of columns, d, not smaller\n than the maximal index i*." msgstr "" msgid "not a skinny matrix" msgstr "" msgid "the number of non-zero entries differs from nrow(.)" msgstr "" msgid "must have exactly one non-zero entry per row" msgstr "" msgid "kronecker method must use default 'FUN'" msgstr "" msgid "replacing \"indMatrix\" entries is not allowed, as rarely sensible" msgstr "" msgid "\"lMatrix\" object with NAs cannot be coerced to \"nMatrix\"" msgstr "" msgid "Matrix seems negative semi-definite" msgstr "" msgid "'nearPD()' did not converge in %d iterations" msgstr "" msgid "cannot coerce 'NA's to \"nsparseMatrix\"" msgstr "" msgid "temporarily disabled" msgstr "" msgid "coercion to \"pMatrix\" only works from integer numeric" msgstr "" msgid "not a square matrix" msgstr "" msgid "not-yet-implemented method for <%s> %%*%% <%s>" msgstr "" msgid "rankMatrix(, method = '%s') coerces to dense matrix.\n Probably should rather use method = 'qr' !?" msgstr "" msgid "rankMatrix(x, method='qr'): computing t(x) as nrow(x) < ncol(x)" msgstr "" msgid "model frame and formula mismatch in model.matrix()" msgstr "" msgid "variable '%s' converted to a factor" msgstr "" msgid "invalid 'contrasts.arg' argument" msgstr "" msgid "variable '%s' is absent, its contrast will be ignored" msgstr "" msgid "only 2-dimensional tables can be directly coerced to sparse matrices" msgstr "" msgid "exactly one of 'i', 'j', or 'p' must be missing from call" msgstr "" msgid "'p' must be a non-decreasing vector (0, ...)" msgstr "" msgid "NA's in (i,j) are not allowed" msgstr "" msgid "symmetric matrix must be square" msgstr "" msgid "length(i) is not a multiple of length(x)" msgstr "" msgid "only square matrices can be used as incidence matrices for graphs" msgstr "" msgid "Matrix-internal error in [i,,d]; please report" msgstr "" msgid "invalid 'col.names' string: %s" msgstr "" msgid "logic programming error in printSpMatrix2(), please report" msgstr "" msgid "invalid 'type'" msgstr "" msgid "rcond(.) via sparse -> dense coercion" msgstr "" msgid "'V' is not a *square* matrix" msgstr "" msgid "qr.R() may differ from qr.R() because of permutations. Possibly use our qrR() instead" msgstr "" msgid "cannot coerce 'NA's to \"nsparseVector\"" msgstr "" msgid "'x' must inherit from \"sparseVector\"" msgstr "" msgid "'ncol' must be >= 0" msgstr "" msgid "'nrow' must be >= 0" msgstr "" msgid "Must specify 'nrow' when 'symmetric' is true" msgstr "" msgid "'nrow' and 'ncol' must be the same when 'symmetric' is true" msgstr "" msgid "'x' must have length nrow^2 when 'symmetric' is true" msgstr "" msgid "'ncol' is not a factor of length(x)" msgstr "" msgid "'nrow' is not a factor of length(x)" msgstr "" msgid "Class %s is not yet implemented" msgstr "" msgid "index must be numeric, logical or sparseVector for indexing sparseVectors" msgstr "" msgid "'times >= 0' is required" msgstr "" msgid "(un)packing only applies to dense matrices, class(x)='%s'" msgstr "" msgid "'x' is not symmetric nor triangular" msgstr "" Matrix/po/de.po0000644000175100001440000007421412256121033013105 0ustar hornikusers# Translation of matrix to German # Copyright (C) 2001-2012 The R Foundation # This file is distributed under the same license as the matrix package. # Chris Leick , 2009-2011. # Detlef Steuer , 2012. msgid "" msgstr "" "Project-Id-Version: R 2.15.2 / matrix 1.0-10\n" "Report-Msgid-Bugs-To: \n" "POT-Creation-Date: 2013-12-23 21:27+0100\n" "PO-Revision-Date: 2012-10-01 15:33+0200\n" "Last-Translator: Chris Leick \n" "Language-Team: German \n" "Language: de\n" "MIME-Version: 1.0\n" "Content-Type: text/plain; charset=UTF-8\n" "Content-Transfer-Encoding: 8bit\n" "Plural-Forms: nplurals=2; plural=(n != 1);\n" #: CHMfactor.c:14 #, c-format msgid "cholmod_change_factor failed with status %d" msgstr "cholmod_change_factor mit Status %d fehlgeschlagen" #: CHMfactor.c:30 CHMfactor.c:60 msgid "system argument is not valid" msgstr "Systemargument ist nicht gültig" #: CHMfactor.c:47 #, c-format msgid "cholmod_updown() returned %d" msgstr "cholmod_updown() gab Fehlerkode %d zurück" # http://www.matheboard.de/archive/160705/thread.html #: CHMfactor.c:97 #, c-format msgid "diagonal element %d of Cholesky factor is missing" msgstr "Diagonalelement %d des Choleskyfaktors fehlt" #: CHMfactor.c:135 #, c-format msgid "cholmod_factorize_p failed: status %d, minor %d of ncol %d" msgstr "cholmod_factorize_p fehlgeschlagen: Status %d, Minor %d von ncol %d" #: CHMfactor.c:140 msgid "cholmod_change_factor failed" msgstr "cholmod_change_factor fehlgeschlagen" #: Csparse.c:55 msgid "Csparse_sort(x): x is not a valid (apart from sorting) CsparseMatrix" msgstr "" #: Csparse.c:73 msgid "slot p must have length = nrow(.) + 1" msgstr "Slot p muss Länge = nrow(.) + 1 haben" #: Csparse.c:75 msgid "first element of slot p must be zero" msgstr "erstes Element von Slot p muss Null sein" #: Csparse.c:78 msgid "last element of slot p must match length of slots j and x" msgstr "" "letztes Element von Slot p muss eine zu den Slots j und x passende Länge " "haben" #: Csparse.c:81 msgid "all column indices must be between 0 and ncol-1" msgstr "Alle Spaltenindizes müssen zwischen 0 und ncol-1 liegen" #: Csparse.c:86 msgid "slot p must be non-decreasing" msgstr "Slot p darf nicht abnehmend sein" #: Csparse.c:97 msgid "slot j is not increasing inside a column" msgstr "Slot j ist nicht zunehmend innerhalb einer Spalte" #: Csparse.c:99 msgid "slot j is not *strictly* increasing inside a column" msgstr "Slot j ist nicht *strikt* zunehmend innerhalb einer Spalte" #: Csparse.c:144 msgid "not a 'n.CMatrix'" msgstr "keine 'n.CMatrix'" #: Csparse.c:145 msgid "not a CsparseMatrix" msgstr "keine CsparseMatrix" #: Csparse.c:172 #, c-format msgid "nz2Csparse(): invalid/non-implemented r_kind = %d" msgstr "nz2Csparse(): ungültiges/nicht implementiertes r_kind = %d" #: Csparse.c:221 msgid "Nonsymmetric matrix in Csparse_symmetric_to_general" msgstr "Unsymmetrische Matrix in Csparse_symmetric_to_general" #: Csparse.c:232 msgid "Csparse_general_to_symmetric(): matrix is not square!" msgstr "Csparse_general_to_symmetric(): Matrix ist nicht quadratisch." #: Csparse.c:423 msgid "Csparse_crossprod(): error return from cholmod_aat()" msgstr "Csparse_crossprod(): Fehler von cholmod_aat() zurückgegeben" #: Csparse.c:455 msgid "cholmod_drop() failed" msgstr "cholmod_drop() fehlgeschlagen" #: Csparse.c:568 msgid "Index i must be NULL or integer" msgstr "Index i muss NULL oder eine Ganzzahl sein" #: Csparse.c:570 msgid "Index j must be NULL or integer" msgstr "Index j muss NULL oder eine Ganzzahl sein" #: Csparse.c:612 #, c-format msgid "failure to open file \"%s\" for writing" msgstr "Öffnen von Datei »%s« zum Schreiben fehlgeschlagen" #: Csparse.c:616 msgid "cholmod_write_sparse returned error code" msgstr "cholmod_write_sparse gab Fehlerkode zurück" #: Csparse.c:689 #, c-format msgid "%s = '%s' (back-permuted) is experimental" msgstr "%s = »%s« (zurückgetauscht) ist experimentell" #: Csparse.c:699 msgid "diag_tC(): invalid 'resultKind'" msgstr "diag_tC(): »resultKind« ungültig" #: Csparse.c:760 #, c-format msgid "negative vector lengths not allowed: np = %d, nnz = %d" msgstr "negative Vektorlänge ist nicht erlaubt: np = %d, nnz = %d" #: Csparse.c:765 msgid "exactly 1 of 'i', 'j' or 'p' must be NULL" msgstr "exakt 1 von »i«, »j« oder »p« muss NULL sein" #: Csparse.c:767 #, c-format msgid "np = %d, must be zero when p is NULL" msgstr "np = %d, muss Null sein, wenn p NULL ist" #: Csparse.c:770 #, c-format msgid "p[0] = %d, should be zero" msgstr "p[0] = %d, sollte Null sein" #: Csparse.c:773 msgid "p must be non-decreasing" msgstr "p darf nicht abnehmend sein" #: Csparse.c:789 #, c-format msgid "Inconsistent dimensions: np = 0 and nnz = %d" msgstr "Inkonsistente Dimensionen: np = 0 und nnz = %d" #: Csparse.c:797 #, c-format msgid "invalid row index at position %d" msgstr "ungültiger Zeilenindex an Position %d" #: Csparse.c:804 #, c-format msgid "invalid column index at position %d" msgstr "ungültiger Spaltenindex an Position %d" #: Csparse.c:814 #, c-format msgid "strlen of cls argument = %d, should be 8" msgstr "strlen des cls-Arguments = %d, sollte 8 sein" #: Csparse.c:816 #, c-format msgid "cls = \"%s\" does not end in \"CMatrix\"" msgstr "cls = »%s« endet nicht in »CMatrix«" #: Csparse.c:826 #, c-format msgid "cls = \"%s\" must begin with 'd', 'l' or 'n'" msgstr "cls = »%s« muss mit »d«, »l« oder »n« beginnen" #: Csparse.c:829 msgid "Only 'g'eneral sparse matrix types allowed" msgstr "Nur »g«enerelle dünn besetzte Matrixtypen erlaubt" #: Csparse.c:857 msgid "code not yet written for cls = \"lgCMatrix\"" msgstr "Kode noch nicht für cls = »lgCMatrix« geschrieben" #: Mutils.c:14 Mutils.c:33 #, c-format msgid "argument type[1]='%s' must be a one-letter character string" msgstr "Argument type[1]=»%s« muss eine Zeichenkette aus einem Buchstaben sein" #: Mutils.c:22 #, c-format msgid "argument type[1]='%s' must be one of 'M','1','O','I','F' or 'E'" msgstr "" "Argument type[1]=»%s« muss eins aus »M«, »1«, »O«, »I«, »F« oder »E« sein" #: Mutils.c:39 #, c-format msgid "argument type[1]='%s' must be one of '1','O', or 'I'" msgstr "Argument type[1]=»%s« eins aus »1«, »O« oder »I« sein" #: Mutils.c:50 Mutils.c:66 msgid "object must be a named, numeric vector" msgstr "Objekt muss ein benannter numerischer Vektor sein" #: Mutils.c:113 Mutils.c:137 msgid "'factors' slot must be a named list" msgstr "»faktors«-Slot muss eine benannte Liste sein" #: Mutils.c:257 #, c-format msgid "'%s' slot must have length 1" msgstr "Slot »%s« muss die Länge 1 haben" #: Mutils.c:261 #, c-format msgid "'%s' must have string length 1" msgstr "»%s« muss die Zeichenkettenlänge 1 haben" #: Mutils.c:268 #, c-format msgid "'%s' must be in '%s'" msgstr "»%s« muss in »%s« sein" #: Mutils.c:287 msgid "'s1' and 's2' must be \"character\" vectors" msgstr "»s1« und »s2« müssen »character«-Vektoren sein" #: Mutils.c:309 msgid "length of x slot != prod(Dim)" msgstr "Länge von x-Slot != prod(Dim)" #: Mutils.c:330 Mutils.c:356 msgid "'uplo' must be UPP or LOW" msgstr "»uplo« muss UPP oder LOW sein" #: Mutils.c:643 #, c-format msgid "invalid class '%s' to dup_mMatrix_as_geMatrix" msgstr "ungültige Klasse »%s« für dup_mMatrix_as_geMatrix" #: Mutils.c:763 #, c-format msgid "unexpected ctype = %d in dup_mMatrix_as_geMatrix" msgstr "unerwartetes ctype = %d in dup_mMatrix_as_geMatrix" #: Mutils.c:794 #, c-format msgid "invalid class '%s' to dup_mMatrix_as_dgeMatrix" msgstr "ungültige Klasse »%s« für dup_mMatrix_as_dgeMatrix" #: Mutils.c:840 msgid "Argument ij must be 2-column integer matrix" msgstr "Argument ij muss eine zweispaltige Ganzzahlmatrix sein" #: Mutils.c:856 msgid "subscript 'i' out of bounds in M[ij]" msgstr "Subskript »i« außerhalb des Bereichs in M[ij]" #: Mutils.c:858 msgid "subscript 'j' out of bounds in M[ij]" msgstr "Subskript »j« außerhalb des Bereichs in M[ij]" #: Mutils.c:897 msgid "i and j must be integer vectors of the same length" msgstr "i und j müssen Ganzzahlvektoren mit der gleichen Länge sein" #: Mutils.c:983 msgid "'data' must be of a vector type" msgstr "" #: Mutils.c:990 #, c-format msgid "invalid '%s' argument" msgstr "" #: Mutils.c:997 Mutils.c:1005 msgid "non-numeric matrix extent" msgstr "" #: Mutils.c:1000 msgid "invalid 'nrow' value (too large or NA)" msgstr "" #: Mutils.c:1002 msgid "invalid 'nrow' value (< 0)" msgstr "" #: Mutils.c:1008 msgid "invalid 'ncol' value (too large or NA)" msgstr "" #: Mutils.c:1010 msgid "invalid 'ncol' value (< 0)" msgstr "" #: Mutils.c:1028 #, c-format msgid "" "data length [%d] is not a sub-multiple or multiple of the number of rows [%d]" msgstr "" #: Mutils.c:1031 #, c-format msgid "" "data length [%d] is not a sub-multiple or multiple of the number of columns " "[%d]" msgstr "" #: Mutils.c:1034 msgid "data length exceeds size of matrix" msgstr "" #: Mutils.c:1040 msgid "too many elements specified" msgstr "" #: Mutils.c:1127 Mutils.c:1160 #, fuzzy msgid "Argument must be numeric-like atomic vector" msgstr "Argument y muss numerisch oder ganzzahlig sein" #: Tsparse.c:20 msgid "lengths of slots i and j must match" msgstr "Längen der Slots i und j müssen passen" #: Tsparse.c:23 msgid "slot Dim must have length 2" msgstr "Slot Dim muss die Länge 2 haben" #: Tsparse.c:27 msgid "" "all row indices (slot 'i') must be between 0 and nrow-1 in a TsparseMatrix" msgstr "" "alle Zeilenindizes (slot 'i') müssen in TsparseMatrix zwischen 0 und nrow-1 " "liegen" #: Tsparse.c:29 msgid "" "all column indices (slot 'j') must be between 0 and ncol-1 in a TsparseMatrix" msgstr "" "Alle Spaltenindizes (slot 'j') müssen in TsparseMatrix zwischen 0 und ncol-1 " "liegen" #: chm_common.c:74 msgid "Argument rho must be an environment" msgstr "Argument rho muss eine Umgebung sein" #: chm_common.c:237 msgid "invalid class of object to as_cholmod_sparse" msgstr "ungültige Klasse des Objektes zu as_cholmod_sparse" #: chm_common.c:239 msgid "invalid object passed to as_cholmod_sparse" msgstr "ungültige Objekt an Klasse as_cholmod_sparse übergeben" #: chm_common.c:266 msgid "in_place cholmod_sort returned an error code" msgstr "in_place cholmod_sort gab einen Fehlerkode zurück" #: chm_common.c:272 msgid "cholmod_sort returned an error code" msgstr "cholmod_sort gab einen Fehlerkode zurück" #: chm_common.c:353 msgid "chm_sparse_to_SEXP(, *): invalid 'Rkind' (real kind code)" msgstr "chm_sparse_to_SEXP(, *): ungültiges »Rkind« (echter Artkode)" #: chm_common.c:361 msgid "unknown xtype in cholmod_sparse object" msgstr "unbekannter xtype in Objekt cholmod_sparse" #: chm_common.c:390 chm_common.c:585 chm_common.c:820 chm_common.c:870 msgid "complex sparse matrix code not yet written" msgstr "Kode für komplexe dünn besetzte Matrizen noch nicht geschrieben" #: chm_common.c:395 chm_common.c:590 msgid "Symmetric and triangular both set" msgstr "Symmetrisch und dreieckig sind beide gesetzt" #: chm_common.c:435 msgid "invalid class of object to as_cholmod_triplet" msgstr "ungültige Klasse des Objektes zu as_cholmod_triplet" #: chm_common.c:459 msgid "as_cholmod_triplet(): could not reallocate for internal diagU2N()" msgstr "as_cholmod_triplet(): konnte für internes diagU2N() nicht reallozieren" #: chm_common.c:557 msgid "unknown xtype in cholmod_triplet object" msgstr "unbekannter xtype in Objekt cholmod_triplet" #: chm_common.c:636 msgid "invalid class of object to as_cholmod_dense" msgstr "ungültige Klasse des Objektes zu as_cholmod_dense" #: chm_common.c:706 #, c-format msgid "Cholmod error '%s' at file %s, line %d" msgstr "Cholmod-Fehler '%s' bei Datei %s, Zeile %d" #: chm_common.c:710 #, c-format msgid "Cholmod warning '%s' at file %s, line %d" msgstr "Cholmod-Warnung '%s' bei Datei %s, Zeile %d" #: chm_common.c:739 #, c-format msgid "Unable to initialize cholmod: error code %d" msgstr "cholmod kann nicht initialisiert werden: Fehlerkode %d" #: chm_common.c:786 msgid "unknown 'Rkind'" msgstr "»Rkind« unbekannt" #: chm_common.c:793 chm_common.c:856 msgid "unknown xtype" msgstr "unbekannter xtype" #: chm_common.c:826 chm_common.c:879 msgid "code for cholmod_dense with holes not yet written" msgstr "Kode für cholmod_dense mit Löchern noch nicht geschrieben" #: chm_common.c:875 msgid "don't know if a dense pattern matrix makes sense" msgstr "es ist nicht klar, ob eine dicht besetzte Mustermatrix sinnvoll ist" #: chm_common.c:942 msgid "invalid class of object to as_cholmod_factor" msgstr "ungültige Klasse des Objektes zu as_cholmod_factor" #: chm_common.c:956 msgid "Supernodal LDL' decomposition not available" msgstr "Superknoten-LDL'-Zerlegung nicht verfügbar" #: chm_common.c:958 msgid "Supernodal/simplicial class inconsistent with type flags" msgstr "Superknoten-/simpliziale Klasse inkonstent mit Typkennzeichen" #: chm_common.c:976 msgid "Number of supernodes must be positive when is_super is TRUE" msgstr "Anzahl der Superknoten muss positiv sein, wenn is_super TRUE ist" #: chm_common.c:979 msgid "Lengths of super and pi must be equal" msgstr "Längen von super und pi müssen gleich sein" #: chm_common.c:983 msgid "Lengths of super and px must be equal" msgstr "Längen von super und px müssen gleich sein" #: chm_common.c:996 msgid "failure in as_cholmod_factor" msgstr "Misserfolg in as_cholmod_factor" #: chm_common.c:1024 msgid "CHOLMOD factorization was unsuccessful" msgstr "CHOLMOD-Faktorzerlegung war nicht erfolgreich" #: chm_common.c:1037 #, c-format msgid "f->xtype of %d not recognized" msgstr "f->xtype von %d nicht erkannt" #: chm_common.c:1102 #, c-format msgid "chm_diagN2U(): nrow=%d, ncol=%d" msgstr "chm_diagN2U(= k (%d)" msgstr "falsches zyklisches Linksverschieben, j (%d) >= k (%d)" #: dense.c:31 #, c-format msgid "incorrect left cyclic shift, j (%d) < 0" msgstr "falsches zyklisches Linksverschieben, j (%d) < 0" #: dense.c:33 #, c-format msgid "incorrect left cyclic shift, k (%d) > ldx (%d)" msgstr "falsches zyklisches Linksverschieben, k (%d) > ldx (%d)" #: dense.c:78 msgid "Unknown error in getGivens" msgstr "Unbekannter Fehler in getGivens" #: dense.c:90 dense.c:106 dense.c:139 msgid "X must be a numeric (double precision) matrix" msgstr "X muss eine numerische (doppelte Genauigkeit) Matrix sein" #: dense.c:111 dense.c:144 msgid "y must be a numeric (double precision) matrix" msgstr "y muss eine numerische (doppelte Genauigkeit) Matrix sein" #: dense.c:115 dense.c:148 #, c-format msgid "number of rows in y (%d) does not match number of rows in X (%d)" msgstr "" "Anzahl der Zeilen in y (%d) passt nicht zur Anzahl der Zeilen in X (%d)" # http://de.wikipedia.org/wiki/LAPACK #: dense.c:126 #, c-format msgid "Lapack routine dposv returned error code %d" msgstr "Lapack-Routine dposv gab Fehlerkode %d zurück" #: dense.c:159 #, c-format msgid "First call to Lapack routine dgels returned error code %d" msgstr "Erster Aufruf der Lapack-Routine dgels gab Fehlerkode %d zurück" #: dense.c:166 #, c-format msgid "Second call to Lapack routine dgels returned error code %d" msgstr "Zweiter Aufruf der Lapack-Routine dgels gab Fehlerkode %d zurück" #: dense.c:179 msgid "X must be a real (numeric) matrix" msgstr "X muss eine echte (numerische) Matrix sein" #: dense.c:180 #, c-format msgid "tol, given as %g, must be non-negative" msgstr "tol, als %g gegeben, darf nicht negativ sein" #: dense.c:181 #, c-format msgid "tol, given as %g, must be <= 1" msgstr "tol, als %g gegeben, muss <= 1 sein" #: dense.c:205 #, c-format msgid "First call to dgeqrf returned error code %d" msgstr "Erster Aufruf von dgeqrf gab Fehlerkode %d zurück" #: dense.c:211 #, c-format msgid "Second call to dgeqrf returned error code %d" msgstr "Zweiter Aufruf von dgeqrf gab Fehlerkode %d zurück" #: dense.c:216 dense.c:236 #, c-format msgid "Lapack routine dtrcon returned error code %d" msgstr "Lapack-Routine dtrcon gab Fehlerkode %d zurück" #: dense.c:285 #, c-format msgid "Lower band %d > upper band %d" msgstr "Unteres Band %d > oberes Band %d" #: dense.c:354 msgid "ddense_to_symmetric(): matrix is not square!" msgstr "ddense_to_symmetric(): Matrix ist nicht quadratisch." #: dense.c:365 #, c-format msgid "matrix is not symmetric [%d,%d]" msgstr "Matrix ist nicht symmetrisch [%d,%d]" #: dense.c:413 msgid "matrix is not square! (symmetric part)" msgstr "Matrix ist nicht quadratisch. (symmetrischer Teil)" #: dense.c:457 msgid "matrix is not square! (skew-symmetric part)" msgstr "Matrix ist nicht quadratisch. (schief-symmetrischer Teil)" #: dgCMatrix.c:17 msgid "lengths of slots 'i' and 'x' must match" msgstr "Längen der Slots »i« und »x« müssen passen" #: dgCMatrix.c:29 msgid "lengths of slots 'j' and 'x' must match" msgstr "Längen der Slots »j« und »x« müssen passen" #: dgCMatrix.c:51 #, c-format msgid "invalid class(x) '%s' in compressed_to_TMatrix(x)" msgstr "ungültige class(x) »%s« in compressed_to_TMatrix(x)" #: dgCMatrix.c:85 #, c-format msgid "invalid class(x) '%s' in R_to_CMatrix(x)" msgstr "ungültige class(x) »%s« in R_to_CMatrix(x)" #: dgCMatrix.c:155 msgid "dgCMatrix_lusol requires a square, non-empty matrix" msgstr "dgCMatrix_lusol benötigt eine quadratische, nicht leere Matrix" #: dgCMatrix.c:157 dgCMatrix.c:183 dgCMatrix.c:437 dgCMatrix.c:470 #: dgeMatrix.c:422 dpoMatrix.c:91 dpoMatrix.c:116 dppMatrix.c:80 #: dspMatrix.c:78 dsyMatrix.c:85 dtCMatrix.c:90 dtCMatrix.c:106 dtrMatrix.c:98 msgid "Dimensions of system to be solved are inconsistent" msgstr "Dimensionen des Systems, das gelöst werden soll, sind inkonsistent" #: dgCMatrix.c:159 msgid "cs_lusol failed" msgstr "cs_lusol fehlgeschlagen" #: dgCMatrix.c:180 msgid "dgCMatrix_qrsol(., order) needs order in {0,..,3}" msgstr "dgCMatrix_qrsol(., Anordnung) benötigt Anordnung in {0,..,3}" #: dgCMatrix.c:189 #, c-format msgid "dgCMatrix_qrsol(<%d x %d>-matrix) requires a 'tall' rectangular matrix" msgstr "" "dgCMatrix_qrsol(<%d x %d>-Matrix) benötigt eine »lange« rechteckige Matrix" #: dgCMatrix.c:200 msgid "cs_qrsol() failed inside dgCMatrix_qrsol()" msgstr "cs_qrsol() innerhalb dgCMatrix_qrsol() fehlgeschlagen" #: dgCMatrix.c:219 msgid "A must have #{rows} >= #{columns}" msgstr "A muss #{rows} >= #{columns} haben" #: dgCMatrix.c:224 msgid "cs_sqr failed" msgstr "cs_sqr fehlgeschlagen" #: dgCMatrix.c:229 msgid "cs_qr failed" msgstr "cs_qr fehlgeschlagen" #: dgCMatrix.c:292 msgid "SuiteSparseQR_C_QR returned an error code" msgstr "SuiteSparseQR_C_QR gab einen Fehlerkode zurück" #: dgCMatrix.c:336 msgid "LU decomposition applies only to square matrices" msgstr "LU-Zerlegung ist nur bei quadratischen Matrizen anwendbar" #: dgCMatrix.c:345 msgid "cs_lu(A) failed: near-singular A (or out of memory)" msgstr "" "cs_lu(A) fehlgeschlagen: near-Singuläres A (oder außerhalb des Speichers)" #: dgCMatrix.c:405 msgid "dgCMatrix_matrix_solve(.., sparse=TRUE) not yet implemented" msgstr "" #: dgCMatrix.c:468 msgid "dgCMatrix_cholsol requires a 'short, wide' rectangular matrix" msgstr "dgCMatrix_cholsol benötigt eine »short, wide«-rechteckige Matrix" #: dgCMatrix.c:476 msgid "cholmod_sdmult error (rhs)" msgstr "cholmod_sdmult-Fehler (rhs)" #: dgCMatrix.c:479 #, c-format msgid "cholmod_factorize failed: status %d, minor %d from ncol %d" msgstr "cholmod_factorize fehlgeschlagen: Status %d, Minor %d von ncol %d" #: dgCMatrix.c:483 #, c-format msgid "cholmod_solve (CHOLMOD_A) failed: status %d, minor %d from ncol %d" msgstr "" "cholmod_solve (CHOLMOD_A) fehlgeschlagen: Status %d, Minor %d von ncol %d" #: dgCMatrix.c:500 msgid "cholmod_sdmult error (resid)" msgstr "cholmod_sdmult-Fehler (resid)" #: dgTMatrix.c:15 msgid "lengths of slots i and x must match" msgstr "Längen der Slots i und x müssen zusammen passen" #: dgTMatrix.c:56 #, c-format msgid "Cannot coerce to too large *geMatrix with %.0f entries" msgstr "Kann nicht in eine große *geMatrix mit %.0f Einträgen umwandeln" #: dgeMatrix.c:10 msgid "Dim slot must have length 2" msgstr "Dim-Slot muss die Länge 2 haben" #: dgeMatrix.c:14 msgid "Negative value in Dim" msgid_plural "Negative values in Dim" msgstr[0] "Negativer Wert in Dim" msgstr[1] "Negative Werte in Dim" #: dgeMatrix.c:18 msgid "x slot must be numeric \"double\"" msgstr "x-Slot muss ein numerisch »double« sein" #: dgeMatrix.c:31 msgid "factors slot must be named list" msgstr "Faktoren-Slot muss eine benannte Liste sein" #: dgeMatrix.c:69 msgid "rcond requires a square, non-empty matrix" msgstr "rcond benötigt eine quadratische, nicht leere Matrix" #: dgeMatrix.c:126 dgeMatrix.c:183 #, c-format msgid "Dimensions of x and y are not compatible for %s" msgstr "Dimensionen von x und y sind nicht kompatibel für %s" #: dgeMatrix.c:165 msgid "Argument y must be numeric or integer" msgstr "Argument y muss numerisch oder ganzzahlig sein" #: dgeMatrix.c:306 msgid "Cannot factor a matrix with zero extents" msgstr "Eine Matrix mit Umfang Null kann nicht berücksichtigt werden" #: dgeMatrix.c:316 dpoMatrix.c:42 dppMatrix.c:36 dspMatrix.c:181 #, c-format msgid "Lapack routine %s returned error code %d" msgstr "Lapack-Routine %s gab einen Fehlerkode %d zurück" #: dgeMatrix.c:318 #, c-format msgid "Exact singularity detected during LU decomposition: %s, i=%d." msgstr "Exakte Singularität während LU-Zerlegung entdeckt: %s, i=%d." #: dgeMatrix.c:340 msgid "Determinant requires a square matrix" msgstr "Determinante benötigt eine quadratische Matrix" #: dgeMatrix.c:382 msgid "Solve requires a square matrix" msgstr "Auflösen benötigt eine quadratische Matrix" #: dgeMatrix.c:395 #, c-format msgid "error [%d] from Lapack 'dgecon()'" msgstr "Fehler [%d] von Lapack-'dgecon()'" #: dgeMatrix.c:397 #, c-format msgid "" "Lapack dgecon(): system computationally singular, reciprocal condition " "number = %g" msgstr "" "Lapack-dgecon(): System rechnerisch singulär, reziproke Bedingungsnummer = %g" #: dgeMatrix.c:407 msgid "Lapack routine dgetri: system is exactly singular" msgstr "Lapack-Routine dgetri: System ist exakt singulär" #: dgeMatrix.c:427 msgid "Lapack routine dgetrs: system is exactly singular" msgstr "Lapack-Routine dgetrs:: System ist exakt singulär" #: dgeMatrix.c:446 dgeMatrix.c:468 dspMatrix.c:152 dsyMatrix.c:122 #: dtrMatrix.c:122 msgid "Matrices are not conformable for multiplication" msgstr "Matrizen sind nicht für Multiplikation konform" #: dgeMatrix.c:569 msgid "Matrix exponential requires square, non-null matrix" msgstr "Exponentielle Matrix benötigt eine quadratische Matrix ungleich Null" #: dgeMatrix.c:586 dgeMatrix.c:588 #, c-format msgid "dgeMatrix_exp: LAPACK routine dgebal returned %d" msgstr "dgeMatrix_exp: LAPACK-Routine dgebal gab %d zurück" #: dgeMatrix.c:626 #, c-format msgid "dgeMatrix_exp: dgetrf returned error code %d" msgstr "dgeMatrix_exp: dgetrf gab Fehlerkode %d zurück" #: dgeMatrix.c:628 #, c-format msgid "dgeMatrix_exp: dgetrs returned error code %d" msgstr "dgeMatrix_exp: dgetrs gab Fehlerkode %d zurück" #: dgeMatrix.c:701 msgid "dgeMatrix_Schur: argument x must be a non-null square matrix" msgstr "" "dgeMatrix_Schur: Argument x muss eine quadratische Matrix ungleich Null sein" #: dgeMatrix.c:712 msgid "dgeMatrix_Schur: first call to dgees failed" msgstr "dgeMatrix_Schur: Erster Aufruf von dgees fehlgeschlagen" #: dgeMatrix.c:720 #, c-format msgid "dgeMatrix_Schur: dgees returned code %d" msgstr "dgeMatrix_Schur: dgees gab Fehlerkode %d zurück" #: dpoMatrix.c:12 msgid "dpoMatrix is not positive definite" msgstr "dpoMatrix ist nicht positiv definit" #: dpoMatrix.c:39 dppMatrix.c:33 #, c-format msgid "the leading minor of order %d is not positive definite" msgstr "der führende Minor der Ordnung %d ist nicht positiv definit" #: dpoMatrix.c:93 msgid "Cannot solve() for matrices with zero extents" msgstr "solve() für Matrizen mit Umfang Null nicht möglich" #: dpoMatrix.c:114 msgid "Argument b must be a numeric matrix" msgstr "Argument b muss eine numerische Matrix sein" #: dsCMatrix.c:25 msgid "chm_factor_name(): did not get string of length 11" msgstr "" #: dsCMatrix.c:99 msgid "" "Cholesky factorization failed; unusually, please report to Matrix-authors" msgstr "" "Cholesky-Faktorisierung fehlgeschlagen; ungewöhnlich, bitte an Matrix-" "authors melden!" #: dsCMatrix.c:105 msgid "internal_chm_factor: Cholesky factorization failed" msgstr "internal_chm_factor: Cholesky-Faktorisierung fehlgeschlagen" #: dsCMatrix.c:241 msgid "Non-symmetric matrix passed to dsCMatrix_to_dgTMatrix" msgstr "Nicht symmetrische Matrix an dsCMatrix_to_dgTMatrix übergeben" #: dspMatrix.c:13 dtpMatrix.c:17 msgid "Incorrect length of 'x' slot" msgstr "Falsche Länge von »x«-Slot" #: dsyMatrix.c:7 dtrMatrix.c:10 msgid "'Dim' slot has length less than two" msgstr "»Dim«-Slot hat eine Länge kleiner zwei" #: dsyMatrix.c:9 dtrMatrix.c:12 msgid "Matrix is not square" msgstr "Matrix ist nicht quadratisch" #: dsyMatrix.c:158 #, c-format msgid "Lapack routine dsytrf returned error code %d" msgstr "Lapack-Routine dsytrf gab Fehlerkode %d zurück" #: dtCMatrix.c:28 dtCMatrix.c:63 dtTMatrix.c:24 msgid "uplo='U' must not have sparse entries below the diagonal" msgstr "" "uplo=»U« darf keine dünn besetzten Einträge unterhalb der Diagonale haben" #: dtCMatrix.c:34 dtCMatrix.c:69 dtTMatrix.c:29 msgid "uplo='L' must not have sparse entries above the diagonal" msgstr "" "uplo=»L« darf keine dünn besetzten Einträge unterhalb der Diagonale haben" #: dtpMatrix.c:124 dtpMatrix.c:152 dtpMatrix.c:183 #, c-format msgid "Dimensions of a (%d,%d) and b (%d,%d) do not conform" msgstr "Dimensionen von a (%d,%d) und b (%d,%d) sind nicht konform" #: dtpMatrix.c:131 msgid "right=TRUE is not yet implemented __ FIXME" msgstr "" #: dtrMatrix.c:120 msgid "dtrMatrix must be square" msgstr "dtrMatrix muss quadratisch sein" #: dtrMatrix.c:160 msgid "dtrMatrices in %*% must have matching (square) dim." msgstr "dtrMatrix in %*% muss quadratisch mit passender Dimension sein" #: dtrMatrix.c:247 msgid "cannot set diag() as long as 'diag = \"U\"'" msgstr "kann diag() nicht setzen solange 'diag = \"U\"'" #: dtrMatrix.c:268 msgid "cannot add diag() as long as 'diag = \"U\"'" msgstr "kann diag() nicht hinzufügen solange 'diag = \"U\"'" #: init.c:359 msgid "missing 'Matrix' namespace: should never happen" msgstr "fehlender 'Matrix'-Namensraum: Sollte niemals vorkommen" #: init.c:370 msgid "Matrix namespace not determined correctly" msgstr "Matrix-Namensraum nicht korrekt bestimmt" #: lgCMatrix.c:58 msgid "A must be a logical matrix" msgstr "A muss eine logische Matrix sein" #: sparseQR.c:13 msgid "length(p) must match nrow(V)" msgstr "length(p) muss zu nrow(V) passen" #: sparseQR.c:15 #, fuzzy msgid "length(beta) must match ncol(V)" msgstr "length(beta) muss zu nrow(V) passen" #: sparseQR.c:18 msgid "length(q) must be zero or ncol(R)" msgstr "length(q) muss null oder ncol(R) sein" #: sparseQR.c:46 #, c-format msgid "sparseQR_Qmult(): nrow(y) = %d != %d = nrow(V)" msgstr "" #: sparseQR.c:121 sparseQR.c:159 sparseQR.c:195 #, c-format msgid "%s(): structurally rank deficient case: possibly WRONG zeros" msgstr "" #: t_Csparse_subassign.c:144 msgid "invalid class of 'x' in Csparse_subassign()" msgstr "ungültige Klasse von 'x' in Csparse_subassign()" #: t_Csparse_subassign.c:146 msgid "invalid class of 'value' in Csparse_subassign()" msgstr "ungültige Klasse von 'value' in Csparse_subassign()" #: t_Csparse_subassign.c:189 #, fuzzy, c-format msgid "x[] <- val: val is coerced to logical for \"%s\" x" msgstr "x[] <- val: val muss logisch sein für \"%s\" x" #: t_Csparse_subassign.c:194 #, fuzzy, c-format msgid "" "x[] <- val: val should be integer or logical, is coerced to integer, for \"%s" "\" x" msgstr "x[] <- val: val muss ganzzahlig oder logisch sein für \"%s\" x" #: t_Csparse_subassign.c:201 msgid "programming error in Csparse_subassign() should never happen" msgstr "Fehler in Csparse_subassign(); sollte niemals vorkommen" #~ msgid "slot p must have length = ncol(.) + 1" #~ msgstr "Slot p muss Länge = ncol(.) + 1 haben" #~ msgid "last element of slot p must match length of slots i and x" #~ msgstr "" #~ "letztes Element von Slot p muss eine zu den Slots i und x passende Länge " #~ "haben" #~ msgid "all row indices must be between 0 and nrow-1" #~ msgstr "alle Zeilenindizes müssen zwischen 0 und nrow-1 liegen" #~ msgid "" #~ "slot i is not *strictly* increasing inside a column (even after " #~ "cholmod_l_sort)" #~ msgstr "" #~ "Slot i ist nicht *strikt* zunehmend innerhalb einer Spalte (sogar nach " #~ "cholmod_l_sort)" #~ msgid "row indices are not sorted within columns" #~ msgstr "Zeilenindizes sind nicht innerhalb von Spalten sortiert" #~ msgid "slot i is not *strictly* increasing inside a column" #~ msgstr "Slot i ist nicht *strikt* zunehmend innerhalb einer Spalte" #~ msgid "Dimensions of system are inconsistent" #~ msgstr "Dimensionen des Systems sind inkonsistent" #~ msgid "could not find correct environment; please report!" #~ msgstr "korrekte Umgebung konnte nicht gefunden werden. Bitte berichten!" #~ msgid "previous CHOLMOD factorization was unsuccessful" #~ msgstr "frühere CHOLMOD Faktorisierung war nicht erfolgreich" #~ msgid "Negative value(s) in Dim" #~ msgstr "Negative(r) Wert(e) in Dim" #~ msgid "cs_qrsol failed" #~ msgstr "cs_qrsol fehlgeschlagen" #~ msgid "p[np] = %d != nnz = %d" #~ msgstr "p[np] = %d != nnz = %d" #~ msgid "ncol(V) != ncol(R)" #~ msgstr "ncol(V) != ncol(R)" Matrix/po/Matrix.pot0000644000175100001440000004605512256121033014147 0ustar hornikusers# SOME DESCRIPTIVE TITLE. # Copyright (C) YEAR THE PACKAGE'S COPYRIGHT HOLDER # This file is distributed under the same license as the PACKAGE package. # FIRST AUTHOR , YEAR. # #, fuzzy msgid "" msgstr "" "Project-Id-Version: Matrix 1.1-1\n" "Report-Msgid-Bugs-To: \n" "POT-Creation-Date: 2013-12-23 21:27+0100\n" "PO-Revision-Date: YEAR-MO-DA HO:MI+ZONE\n" "Last-Translator: FULL NAME \n" "Language-Team: LANGUAGE \n" "Language: \n" "MIME-Version: 1.0\n" "Content-Type: text/plain; charset=CHARSET\n" "Content-Transfer-Encoding: 8bit\n" "Plural-Forms: nplurals=INTEGER; plural=EXPRESSION;\n" #: CHMfactor.c:14 #, c-format msgid "cholmod_change_factor failed with status %d" msgstr "" #: CHMfactor.c:30 CHMfactor.c:60 msgid "system argument is not valid" msgstr "" #: CHMfactor.c:47 #, c-format msgid "cholmod_updown() returned %d" msgstr "" #: CHMfactor.c:97 #, c-format msgid "diagonal element %d of Cholesky factor is missing" msgstr "" #: CHMfactor.c:135 #, c-format msgid "cholmod_factorize_p failed: status %d, minor %d of ncol %d" msgstr "" #: CHMfactor.c:140 msgid "cholmod_change_factor failed" msgstr "" #: Csparse.c:55 msgid "Csparse_sort(x): x is not a valid (apart from sorting) CsparseMatrix" msgstr "" #: Csparse.c:73 msgid "slot p must have length = nrow(.) + 1" msgstr "" #: Csparse.c:75 msgid "first element of slot p must be zero" msgstr "" #: Csparse.c:78 msgid "last element of slot p must match length of slots j and x" msgstr "" #: Csparse.c:81 msgid "all column indices must be between 0 and ncol-1" msgstr "" #: Csparse.c:86 msgid "slot p must be non-decreasing" msgstr "" #: Csparse.c:97 msgid "slot j is not increasing inside a column" msgstr "" #: Csparse.c:99 msgid "slot j is not *strictly* increasing inside a column" msgstr "" #: Csparse.c:144 msgid "not a 'n.CMatrix'" msgstr "" #: Csparse.c:145 msgid "not a CsparseMatrix" msgstr "" #: Csparse.c:172 #, c-format msgid "nz2Csparse(): invalid/non-implemented r_kind = %d" msgstr "" #: Csparse.c:221 msgid "Nonsymmetric matrix in Csparse_symmetric_to_general" msgstr "" #: Csparse.c:232 msgid "Csparse_general_to_symmetric(): matrix is not square!" msgstr "" #: Csparse.c:423 msgid "Csparse_crossprod(): error return from cholmod_aat()" msgstr "" #: Csparse.c:455 msgid "cholmod_drop() failed" msgstr "" #: Csparse.c:568 msgid "Index i must be NULL or integer" msgstr "" #: Csparse.c:570 msgid "Index j must be NULL or integer" msgstr "" #: Csparse.c:612 #, c-format msgid "failure to open file \"%s\" for writing" msgstr "" #: Csparse.c:616 msgid "cholmod_write_sparse returned error code" msgstr "" #: Csparse.c:689 #, c-format msgid "%s = '%s' (back-permuted) is experimental" msgstr "" #: Csparse.c:699 msgid "diag_tC(): invalid 'resultKind'" msgstr "" #: Csparse.c:760 #, c-format msgid "negative vector lengths not allowed: np = %d, nnz = %d" msgstr "" #: Csparse.c:765 msgid "exactly 1 of 'i', 'j' or 'p' must be NULL" msgstr "" #: Csparse.c:767 #, c-format msgid "np = %d, must be zero when p is NULL" msgstr "" #: Csparse.c:770 #, c-format msgid "p[0] = %d, should be zero" msgstr "" #: Csparse.c:773 msgid "p must be non-decreasing" msgstr "" #: Csparse.c:789 #, c-format msgid "Inconsistent dimensions: np = 0 and nnz = %d" msgstr "" #: Csparse.c:797 #, c-format msgid "invalid row index at position %d" msgstr "" #: Csparse.c:804 #, c-format msgid "invalid column index at position %d" msgstr "" #: Csparse.c:814 #, c-format msgid "strlen of cls argument = %d, should be 8" msgstr "" #: Csparse.c:816 #, c-format msgid "cls = \"%s\" does not end in \"CMatrix\"" msgstr "" #: Csparse.c:826 #, c-format msgid "cls = \"%s\" must begin with 'd', 'l' or 'n'" msgstr "" #: Csparse.c:829 msgid "Only 'g'eneral sparse matrix types allowed" msgstr "" #: Csparse.c:857 msgid "code not yet written for cls = \"lgCMatrix\"" msgstr "" #: Mutils.c:14 Mutils.c:33 #, c-format msgid "argument type[1]='%s' must be a one-letter character string" msgstr "" #: Mutils.c:22 #, c-format msgid "argument type[1]='%s' must be one of 'M','1','O','I','F' or 'E'" msgstr "" #: Mutils.c:39 #, c-format msgid "argument type[1]='%s' must be one of '1','O', or 'I'" msgstr "" #: Mutils.c:50 Mutils.c:66 msgid "object must be a named, numeric vector" msgstr "" #: Mutils.c:113 Mutils.c:137 msgid "'factors' slot must be a named list" msgstr "" #: Mutils.c:257 #, c-format msgid "'%s' slot must have length 1" msgstr "" #: Mutils.c:261 #, c-format msgid "'%s' must have string length 1" msgstr "" #: Mutils.c:268 #, c-format msgid "'%s' must be in '%s'" msgstr "" #: Mutils.c:287 msgid "'s1' and 's2' must be \"character\" vectors" msgstr "" #: Mutils.c:309 msgid "length of x slot != prod(Dim)" msgstr "" #: Mutils.c:330 Mutils.c:356 msgid "'uplo' must be UPP or LOW" msgstr "" #: Mutils.c:643 #, c-format msgid "invalid class '%s' to dup_mMatrix_as_geMatrix" msgstr "" #: Mutils.c:763 #, c-format msgid "unexpected ctype = %d in dup_mMatrix_as_geMatrix" msgstr "" #: Mutils.c:794 #, c-format msgid "invalid class '%s' to dup_mMatrix_as_dgeMatrix" msgstr "" #: Mutils.c:840 msgid "Argument ij must be 2-column integer matrix" msgstr "" #: Mutils.c:856 msgid "subscript 'i' out of bounds in M[ij]" msgstr "" #: Mutils.c:858 msgid "subscript 'j' out of bounds in M[ij]" msgstr "" #: Mutils.c:897 msgid "i and j must be integer vectors of the same length" msgstr "" #: Mutils.c:983 msgid "'data' must be of a vector type" msgstr "" #: Mutils.c:990 #, c-format msgid "invalid '%s' argument" msgstr "" #: Mutils.c:997 Mutils.c:1005 msgid "non-numeric matrix extent" msgstr "" #: Mutils.c:1000 msgid "invalid 'nrow' value (too large or NA)" msgstr "" #: Mutils.c:1002 msgid "invalid 'nrow' value (< 0)" msgstr "" #: Mutils.c:1008 msgid "invalid 'ncol' value (too large or NA)" msgstr "" #: Mutils.c:1010 msgid "invalid 'ncol' value (< 0)" msgstr "" #: Mutils.c:1028 #, c-format msgid "" "data length [%d] is not a sub-multiple or multiple of the number of rows [%d]" msgstr "" #: Mutils.c:1031 #, c-format msgid "" "data length [%d] is not a sub-multiple or multiple of the number of columns " "[%d]" msgstr "" #: Mutils.c:1034 msgid "data length exceeds size of matrix" msgstr "" #: Mutils.c:1040 msgid "too many elements specified" msgstr "" #: Mutils.c:1127 Mutils.c:1160 msgid "Argument must be numeric-like atomic vector" msgstr "" #: Tsparse.c:20 msgid "lengths of slots i and j must match" msgstr "" #: Tsparse.c:23 msgid "slot Dim must have length 2" msgstr "" #: Tsparse.c:27 msgid "" "all row indices (slot 'i') must be between 0 and nrow-1 in a TsparseMatrix" msgstr "" #: Tsparse.c:29 msgid "" "all column indices (slot 'j') must be between 0 and ncol-1 in a TsparseMatrix" msgstr "" #: chm_common.c:74 msgid "Argument rho must be an environment" msgstr "" #: chm_common.c:237 msgid "invalid class of object to as_cholmod_sparse" msgstr "" #: chm_common.c:239 msgid "invalid object passed to as_cholmod_sparse" msgstr "" #: chm_common.c:266 msgid "in_place cholmod_sort returned an error code" msgstr "" #: chm_common.c:272 msgid "cholmod_sort returned an error code" msgstr "" #: chm_common.c:353 msgid "chm_sparse_to_SEXP(, *): invalid 'Rkind' (real kind code)" msgstr "" #: chm_common.c:361 msgid "unknown xtype in cholmod_sparse object" msgstr "" #: chm_common.c:390 chm_common.c:585 chm_common.c:820 chm_common.c:870 msgid "complex sparse matrix code not yet written" msgstr "" #: chm_common.c:395 chm_common.c:590 msgid "Symmetric and triangular both set" msgstr "" #: chm_common.c:435 msgid "invalid class of object to as_cholmod_triplet" msgstr "" #: chm_common.c:459 msgid "as_cholmod_triplet(): could not reallocate for internal diagU2N()" msgstr "" #: chm_common.c:557 msgid "unknown xtype in cholmod_triplet object" msgstr "" #: chm_common.c:636 msgid "invalid class of object to as_cholmod_dense" msgstr "" #: chm_common.c:706 #, c-format msgid "Cholmod error '%s' at file %s, line %d" msgstr "" #: chm_common.c:710 #, c-format msgid "Cholmod warning '%s' at file %s, line %d" msgstr "" #: chm_common.c:739 #, c-format msgid "Unable to initialize cholmod: error code %d" msgstr "" #: chm_common.c:786 msgid "unknown 'Rkind'" msgstr "" #: chm_common.c:793 chm_common.c:856 msgid "unknown xtype" msgstr "" #: chm_common.c:826 chm_common.c:879 msgid "code for cholmod_dense with holes not yet written" msgstr "" #: chm_common.c:875 msgid "don't know if a dense pattern matrix makes sense" msgstr "" #: chm_common.c:942 msgid "invalid class of object to as_cholmod_factor" msgstr "" #: chm_common.c:956 msgid "Supernodal LDL' decomposition not available" msgstr "" #: chm_common.c:958 msgid "Supernodal/simplicial class inconsistent with type flags" msgstr "" #: chm_common.c:976 msgid "Number of supernodes must be positive when is_super is TRUE" msgstr "" #: chm_common.c:979 msgid "Lengths of super and pi must be equal" msgstr "" #: chm_common.c:983 msgid "Lengths of super and px must be equal" msgstr "" #: chm_common.c:996 msgid "failure in as_cholmod_factor" msgstr "" #: chm_common.c:1024 msgid "CHOLMOD factorization was unsuccessful" msgstr "" #: chm_common.c:1037 #, c-format msgid "f->xtype of %d not recognized" msgstr "" #: chm_common.c:1102 #, c-format msgid "chm_diagN2U(): nrow=%d, ncol=%d" msgstr "" #: chm_common.c:1145 #, c-format msgid "chm_diagN2U(x, uploT = %d): uploT should be +- 1" msgstr "" #: cs_utils.c:37 msgid "csp_eye argument n must be positive" msgstr "" #: cs_utils.c:68 msgid "invalid class of 'x' in Matrix_as_cs(a, x)" msgstr "" #: cs_utils.c:126 cs_utils.c:170 cs_utils.c:185 cs_utils.c:205 cs_utils.c:218 #, c-format msgid "invalid class of object to %s" msgstr "" #: cs_utils.c:139 #, c-format msgid "cs matrix not compatible with class '%s'" msgstr "" #: cs_utils.c:242 cs_utils.c:261 #, c-format msgid "Inappropriate class cl='%s' in Matrix_css_to_SEXP(S, cl, ..)" msgstr "" #: cs_utils.c:287 cs_utils.c:306 #, c-format msgid "Inappropriate class cl='%s' in Matrix_csn_to_SEXP(S, cl, ..)" msgstr "" #: dense.c:29 #, c-format msgid "incorrect left cyclic shift, j (%d) >= k (%d)" msgstr "" #: dense.c:31 #, c-format msgid "incorrect left cyclic shift, j (%d) < 0" msgstr "" #: dense.c:33 #, c-format msgid "incorrect left cyclic shift, k (%d) > ldx (%d)" msgstr "" #: dense.c:78 msgid "Unknown error in getGivens" msgstr "" #: dense.c:90 dense.c:106 dense.c:139 msgid "X must be a numeric (double precision) matrix" msgstr "" #: dense.c:111 dense.c:144 msgid "y must be a numeric (double precision) matrix" msgstr "" #: dense.c:115 dense.c:148 #, c-format msgid "number of rows in y (%d) does not match number of rows in X (%d)" msgstr "" #: dense.c:126 #, c-format msgid "Lapack routine dposv returned error code %d" msgstr "" #: dense.c:159 #, c-format msgid "First call to Lapack routine dgels returned error code %d" msgstr "" #: dense.c:166 #, c-format msgid "Second call to Lapack routine dgels returned error code %d" msgstr "" #: dense.c:179 msgid "X must be a real (numeric) matrix" msgstr "" #: dense.c:180 #, c-format msgid "tol, given as %g, must be non-negative" msgstr "" #: dense.c:181 #, c-format msgid "tol, given as %g, must be <= 1" msgstr "" #: dense.c:205 #, c-format msgid "First call to dgeqrf returned error code %d" msgstr "" #: dense.c:211 #, c-format msgid "Second call to dgeqrf returned error code %d" msgstr "" #: dense.c:216 dense.c:236 #, c-format msgid "Lapack routine dtrcon returned error code %d" msgstr "" #: dense.c:285 #, c-format msgid "Lower band %d > upper band %d" msgstr "" #: dense.c:354 msgid "ddense_to_symmetric(): matrix is not square!" msgstr "" #: dense.c:365 #, c-format msgid "matrix is not symmetric [%d,%d]" msgstr "" #: dense.c:413 msgid "matrix is not square! (symmetric part)" msgstr "" #: dense.c:457 msgid "matrix is not square! (skew-symmetric part)" msgstr "" #: dgCMatrix.c:17 msgid "lengths of slots 'i' and 'x' must match" msgstr "" #: dgCMatrix.c:29 msgid "lengths of slots 'j' and 'x' must match" msgstr "" #: dgCMatrix.c:51 #, c-format msgid "invalid class(x) '%s' in compressed_to_TMatrix(x)" msgstr "" #: dgCMatrix.c:85 #, c-format msgid "invalid class(x) '%s' in R_to_CMatrix(x)" msgstr "" #: dgCMatrix.c:155 msgid "dgCMatrix_lusol requires a square, non-empty matrix" msgstr "" #: dgCMatrix.c:157 dgCMatrix.c:183 dgCMatrix.c:437 dgCMatrix.c:470 #: dgeMatrix.c:422 dpoMatrix.c:91 dpoMatrix.c:116 dppMatrix.c:80 #: dspMatrix.c:78 dsyMatrix.c:85 dtCMatrix.c:90 dtCMatrix.c:106 dtrMatrix.c:98 msgid "Dimensions of system to be solved are inconsistent" msgstr "" #: dgCMatrix.c:159 msgid "cs_lusol failed" msgstr "" #: dgCMatrix.c:180 msgid "dgCMatrix_qrsol(., order) needs order in {0,..,3}" msgstr "" #: dgCMatrix.c:189 #, c-format msgid "dgCMatrix_qrsol(<%d x %d>-matrix) requires a 'tall' rectangular matrix" msgstr "" #: dgCMatrix.c:200 msgid "cs_qrsol() failed inside dgCMatrix_qrsol()" msgstr "" #: dgCMatrix.c:219 msgid "A must have #{rows} >= #{columns}" msgstr "" #: dgCMatrix.c:224 msgid "cs_sqr failed" msgstr "" #: dgCMatrix.c:229 msgid "cs_qr failed" msgstr "" #: dgCMatrix.c:292 msgid "SuiteSparseQR_C_QR returned an error code" msgstr "" #: dgCMatrix.c:336 msgid "LU decomposition applies only to square matrices" msgstr "" #: dgCMatrix.c:345 msgid "cs_lu(A) failed: near-singular A (or out of memory)" msgstr "" #: dgCMatrix.c:405 msgid "dgCMatrix_matrix_solve(.., sparse=TRUE) not yet implemented" msgstr "" #: dgCMatrix.c:468 msgid "dgCMatrix_cholsol requires a 'short, wide' rectangular matrix" msgstr "" #: dgCMatrix.c:476 msgid "cholmod_sdmult error (rhs)" msgstr "" #: dgCMatrix.c:479 #, c-format msgid "cholmod_factorize failed: status %d, minor %d from ncol %d" msgstr "" #: dgCMatrix.c:483 #, c-format msgid "cholmod_solve (CHOLMOD_A) failed: status %d, minor %d from ncol %d" msgstr "" #: dgCMatrix.c:500 msgid "cholmod_sdmult error (resid)" msgstr "" #: dgTMatrix.c:15 msgid "lengths of slots i and x must match" msgstr "" #: dgTMatrix.c:56 #, c-format msgid "Cannot coerce to too large *geMatrix with %.0f entries" msgstr "" #: dgeMatrix.c:10 msgid "Dim slot must have length 2" msgstr "" #: dgeMatrix.c:14 msgid "Negative value in Dim" msgid_plural "Negative values in Dim" msgstr[0] "" msgstr[1] "" #: dgeMatrix.c:18 msgid "x slot must be numeric \"double\"" msgstr "" #: dgeMatrix.c:31 msgid "factors slot must be named list" msgstr "" #: dgeMatrix.c:69 msgid "rcond requires a square, non-empty matrix" msgstr "" #: dgeMatrix.c:126 dgeMatrix.c:183 #, c-format msgid "Dimensions of x and y are not compatible for %s" msgstr "" #: dgeMatrix.c:165 msgid "Argument y must be numeric or integer" msgstr "" #: dgeMatrix.c:306 msgid "Cannot factor a matrix with zero extents" msgstr "" #: dgeMatrix.c:316 dpoMatrix.c:42 dppMatrix.c:36 dspMatrix.c:181 #, c-format msgid "Lapack routine %s returned error code %d" msgstr "" #: dgeMatrix.c:318 #, c-format msgid "Exact singularity detected during LU decomposition: %s, i=%d." msgstr "" #: dgeMatrix.c:340 msgid "Determinant requires a square matrix" msgstr "" #: dgeMatrix.c:382 msgid "Solve requires a square matrix" msgstr "" #: dgeMatrix.c:395 #, c-format msgid "error [%d] from Lapack 'dgecon()'" msgstr "" #: dgeMatrix.c:397 #, c-format msgid "" "Lapack dgecon(): system computationally singular, reciprocal condition " "number = %g" msgstr "" #: dgeMatrix.c:407 msgid "Lapack routine dgetri: system is exactly singular" msgstr "" #: dgeMatrix.c:427 msgid "Lapack routine dgetrs: system is exactly singular" msgstr "" #: dgeMatrix.c:446 dgeMatrix.c:468 dspMatrix.c:152 dsyMatrix.c:122 #: dtrMatrix.c:122 msgid "Matrices are not conformable for multiplication" msgstr "" #: dgeMatrix.c:569 msgid "Matrix exponential requires square, non-null matrix" msgstr "" #: dgeMatrix.c:586 dgeMatrix.c:588 #, c-format msgid "dgeMatrix_exp: LAPACK routine dgebal returned %d" msgstr "" #: dgeMatrix.c:626 #, c-format msgid "dgeMatrix_exp: dgetrf returned error code %d" msgstr "" #: dgeMatrix.c:628 #, c-format msgid "dgeMatrix_exp: dgetrs returned error code %d" msgstr "" #: dgeMatrix.c:701 msgid "dgeMatrix_Schur: argument x must be a non-null square matrix" msgstr "" #: dgeMatrix.c:712 msgid "dgeMatrix_Schur: first call to dgees failed" msgstr "" #: dgeMatrix.c:720 #, c-format msgid "dgeMatrix_Schur: dgees returned code %d" msgstr "" #: dpoMatrix.c:12 msgid "dpoMatrix is not positive definite" msgstr "" #: dpoMatrix.c:39 dppMatrix.c:33 #, c-format msgid "the leading minor of order %d is not positive definite" msgstr "" #: dpoMatrix.c:93 msgid "Cannot solve() for matrices with zero extents" msgstr "" #: dpoMatrix.c:114 msgid "Argument b must be a numeric matrix" msgstr "" #: dsCMatrix.c:25 msgid "chm_factor_name(): did not get string of length 11" msgstr "" #: dsCMatrix.c:99 msgid "" "Cholesky factorization failed; unusually, please report to Matrix-authors" msgstr "" #: dsCMatrix.c:105 msgid "internal_chm_factor: Cholesky factorization failed" msgstr "" #: dsCMatrix.c:241 msgid "Non-symmetric matrix passed to dsCMatrix_to_dgTMatrix" msgstr "" #: dspMatrix.c:13 dtpMatrix.c:17 msgid "Incorrect length of 'x' slot" msgstr "" #: dsyMatrix.c:7 dtrMatrix.c:10 msgid "'Dim' slot has length less than two" msgstr "" #: dsyMatrix.c:9 dtrMatrix.c:12 msgid "Matrix is not square" msgstr "" #: dsyMatrix.c:158 #, c-format msgid "Lapack routine dsytrf returned error code %d" msgstr "" #: dtCMatrix.c:28 dtCMatrix.c:63 dtTMatrix.c:24 msgid "uplo='U' must not have sparse entries below the diagonal" msgstr "" #: dtCMatrix.c:34 dtCMatrix.c:69 dtTMatrix.c:29 msgid "uplo='L' must not have sparse entries above the diagonal" msgstr "" #: dtpMatrix.c:124 dtpMatrix.c:152 dtpMatrix.c:183 #, c-format msgid "Dimensions of a (%d,%d) and b (%d,%d) do not conform" msgstr "" #: dtpMatrix.c:131 msgid "right=TRUE is not yet implemented __ FIXME" msgstr "" #: dtrMatrix.c:120 msgid "dtrMatrix must be square" msgstr "" #: dtrMatrix.c:160 msgid "dtrMatrices in %*% must have matching (square) dim." msgstr "" #: dtrMatrix.c:247 msgid "cannot set diag() as long as 'diag = \"U\"'" msgstr "" #: dtrMatrix.c:268 msgid "cannot add diag() as long as 'diag = \"U\"'" msgstr "" #: init.c:359 msgid "missing 'Matrix' namespace: should never happen" msgstr "" #: init.c:370 msgid "Matrix namespace not determined correctly" msgstr "" #: lgCMatrix.c:58 msgid "A must be a logical matrix" msgstr "" #: sparseQR.c:13 msgid "length(p) must match nrow(V)" msgstr "" #: sparseQR.c:15 msgid "length(beta) must match ncol(V)" msgstr "" #: sparseQR.c:18 msgid "length(q) must be zero or ncol(R)" msgstr "" #: sparseQR.c:46 #, c-format msgid "sparseQR_Qmult(): nrow(y) = %d != %d = nrow(V)" msgstr "" #: sparseQR.c:121 sparseQR.c:159 sparseQR.c:195 #, c-format msgid "%s(): structurally rank deficient case: possibly WRONG zeros" msgstr "" #: t_Csparse_subassign.c:144 msgid "invalid class of 'x' in Csparse_subassign()" msgstr "" #: t_Csparse_subassign.c:146 msgid "invalid class of 'value' in Csparse_subassign()" msgstr "" #: t_Csparse_subassign.c:189 #, c-format msgid "x[] <- val: val is coerced to logical for \"%s\" x" msgstr "" #: t_Csparse_subassign.c:194 #, c-format msgid "" "x[] <- val: val should be integer or logical, is coerced to integer, for \"%s" "\" x" msgstr "" #: t_Csparse_subassign.c:201 msgid "programming error in Csparse_subassign() should never happen" msgstr "" Matrix/po/pl.po0000644000175100001440000015644512256121033013137 0ustar hornikusersmsgid "" msgstr "" "Project-Id-Version: Matrix 1.0-9\n" "Report-Msgid-Bugs-To: \n" "POT-Creation-Date: 2013-12-23 21:27+0100\n" "PO-Revision-Date: 2012-08-22 08:17+0100\n" "Last-Translator: Łukasz Daniel \n" "Language-Team: Łukasz Daniel \n" "Language: pl_PL\n" "MIME-Version: 1.0\n" "Content-Type: text/plain; charset=UTF-8\n" "Content-Transfer-Encoding: 8bit\n" "Plural-Forms: nplurals=3; plural=(n==1 ? 0 : n%10>=2 && n%10<=4 && (n%100<10 " "|| n%100>=20) ? 1 : 2)\n" "X-Poedit-SourceCharset: iso-8859-1\n" # Recommended/Matrix/src/CHMfactor.c: 14 # error(_("cholmod_change_factor failed with status %d"), c.status) #: CHMfactor.c:14 #, c-format msgid "cholmod_change_factor failed with status %d" msgstr "'cholmod_change_factor' nie powiódł się zwracając status %d" # Recommended/Matrix/src/CHMfactor.c: 30 # error(_("system argument is not valid")) # Recommended/Matrix/src/CHMfactor.c: 60 # error(_("system argument is not valid")) #: CHMfactor.c:30 CHMfactor.c:60 msgid "system argument is not valid" msgstr "argument systemowy nie jest poprawny" #: CHMfactor.c:47 #, c-format msgid "cholmod_updown() returned %d" msgstr "cholmod_updown() zwróciło %d" # Recommended/Matrix/src/CHMfactor.c: 97 # error(_("diagonal element %d of Cholesky factor is missing"), j) #: CHMfactor.c:97 #, c-format msgid "diagonal element %d of Cholesky factor is missing" msgstr "brakuje elementu diagonalnego %d czynnika Cholesky'ego" # Recommended/Matrix/src/CHMfactor.c: 135 # error(_("cholmod_factorize_p failed: status %d, minor %d of ncol %d"), # c.status, f->minor, f->n) #: CHMfactor.c:135 #, c-format msgid "cholmod_factorize_p failed: status %d, minor %d of ncol %d" msgstr "" "'cholmod_factorize_p' nie powiódł się: status %d, minor %d liczba kolumn %d" # Recommended/Matrix/src/CHMfactor.c: 140 # error(_("cholmod_change_factor failed")) #: CHMfactor.c:140 msgid "cholmod_change_factor failed" msgstr "'cholmod_change_factor' nie powiódł się" #: Csparse.c:55 msgid "Csparse_sort(x): x is not a valid (apart from sorting) CsparseMatrix" msgstr "" # Recommended/Matrix/src/Csparse.c: 117 # (_("slot p must have length = nrow(.) + 1")) #: Csparse.c:73 msgid "slot p must have length = nrow(.) + 1" msgstr "gniazdo 'p' musi mieć długość = nrow(.) + 1" # Recommended/Matrix/src/Csparse.c: 60 # (_("first element of slot p must be zero")) # Recommended/Matrix/src/Csparse.c: 119 # (_("first element of slot p must be zero")) #: Csparse.c:75 msgid "first element of slot p must be zero" msgstr "pierwszy element gniazda 'p' musi być zerem" # Recommended/Matrix/src/Csparse.c: 122 # (_("last element of slot p must match length of slots j and x")) #: Csparse.c:78 msgid "last element of slot p must match length of slots j and x" msgstr "" "ostatni element gniazda 'p' musi zgadzać się długością z gniazdem 'j' oraz " "'x'" # Recommended/Matrix/src/Csparse.c: 125 # (_("all column indices must be between 0 and ncol-1")) #: Csparse.c:81 msgid "all column indices must be between 0 and ncol-1" msgstr "wszystkie indeksy kolumn muszą być pomiędzy 0 a 'ncol-1'" # Recommended/Matrix/src/Csparse.c: 71 # (_("slot p must be non-decreasing")) # Recommended/Matrix/src/Csparse.c: 130 # (_("slot p must be non-decreasing")) #: Csparse.c:86 msgid "slot p must be non-decreasing" msgstr "gniazdo 'p' musi być niemalejące" # Recommended/Matrix/src/Csparse.c: 141 # (_("slot j is not increasing inside a column")) #: Csparse.c:97 msgid "slot j is not increasing inside a column" msgstr "gniazdo 'j' nie jest rosnące wewnątrz kolumny" # Recommended/Matrix/src/Csparse.c: 143 # (_("slot j is not *strictly* increasing inside a column")) #: Csparse.c:99 msgid "slot j is not *strictly* increasing inside a column" msgstr "gniazdo 'j' nie jest *ściśle* rosnące wewnątrz kolumny" # Recommended/Matrix/src/Csparse.c: 188 # error(_("not a 'n.CMatrix'")) #: Csparse.c:144 msgid "not a 'n.CMatrix'" msgstr "to nie jest 'n.CMatrix'" # Recommended/Matrix/src/Csparse.c: 189 # error(_("not a CsparseMatrix")) #: Csparse.c:145 msgid "not a CsparseMatrix" msgstr "to nie jest 'CsparseMatrix'" # Recommended/Matrix/src/Csparse.c: 216 # error(_("nz2Csparse(): invalid/non-implemented r_kind = %d"), # r_kind) #: Csparse.c:172 #, c-format msgid "nz2Csparse(): invalid/non-implemented r_kind = %d" msgstr "nz2Csparse(): niepoprawny/niezaimplementowany 'r_kind = %d'" # Recommended/Matrix/src/Csparse.c: 261 # error(_("Nonsymmetric matrix in Csparse_symmetric_to_general")) #: Csparse.c:221 msgid "Nonsymmetric matrix in Csparse_symmetric_to_general" msgstr "Niesymetryczna macierz w 'Csparse_symmetric_to_general'" #: Csparse.c:232 msgid "Csparse_general_to_symmetric(): matrix is not square!" msgstr "Csparse_general_to_symmetric(): macierz nie jest kwadratowa!" # Recommended/Matrix/src/Csparse.c: 459 # error(_("Csparse_crossprod(): error return from cholmod_aat()")) #: Csparse.c:423 msgid "Csparse_crossprod(): error return from cholmod_aat()" msgstr "Csparse_crossprod(): błąd zwrócony z 'cholmod_aat()'" # Recommended/Matrix/src/Csparse.c: 491 # error(_("cholmod_drop() failed")) #: Csparse.c:455 msgid "cholmod_drop() failed" msgstr "'cholmod_drop()' nie powiódł się" # Recommended/Matrix/src/Csparse.c: 603 # error(_("Index i must be NULL or integer")) #: Csparse.c:568 msgid "Index i must be NULL or integer" msgstr "Indeks 'i' musi być wartością NULL lub być liczbą całkowitą" # Recommended/Matrix/src/Csparse.c: 605 # error(_("Index j must be NULL or integer")) #: Csparse.c:570 msgid "Index j must be NULL or integer" msgstr "Indeks 'j' musi być wartością NULL lub być liczbą całkowitą" # Recommended/Matrix/src/Csparse.c: 647 # error(_("failure to open file \"%s\" for writing"), # CHAR(asChar(fname))) #: Csparse.c:612 #, c-format msgid "failure to open file \"%s\" for writing" msgstr "nie udało się otworzyć pliku '%s' do zapisu" # Recommended/Matrix/src/Csparse.c: 651 # error(_("cholmod_write_sparse returned error code")) #: Csparse.c:616 msgid "cholmod_write_sparse returned error code" msgstr "'cholmod_write_sparse' zwrócił kod błędu" #: Csparse.c:689 #, c-format msgid "%s = '%s' (back-permuted) is experimental" msgstr "%s = '%s' (wstecznie permutowany) jest eksperymentalny" # Recommended/Matrix/src/Csparse.c: 734 # error(_("diag_tC(): invalid 'resultKind'")) #: Csparse.c:699 msgid "diag_tC(): invalid 'resultKind'" msgstr "diag_tC(): niepoprawny 'resultKind'" # Recommended/Matrix/src/Csparse.c: 795 # error(_("negative vector lengths not allowed: np = %d, nnz = %d"), # np, nnz) #: Csparse.c:760 #, c-format msgid "negative vector lengths not allowed: np = %d, nnz = %d" msgstr "ujemne długości wektora nie są dozwolone: np = %d, nnz = %d" # Recommended/Matrix/src/Csparse.c: 800 # error(_("exactly 1 of 'i', 'j' or 'p' must be NULL")) #: Csparse.c:765 msgid "exactly 1 of 'i', 'j' or 'p' must be NULL" msgstr "dokładnie jeden z 'i', 'j' lub 'p' musi być wartością NULL" # Recommended/Matrix/src/Csparse.c: 802 # error(_("np = %d, must be zero when p is NULL"), np) #: Csparse.c:767 #, c-format msgid "np = %d, must be zero when p is NULL" msgstr "np = %d, musi wynosić zero gdy 'p' ma wartość NULL" # Recommended/Matrix/src/Csparse.c: 805 # error(_("p[0] = %d, should be zero"), p[0]) #: Csparse.c:770 #, c-format msgid "p[0] = %d, should be zero" msgstr "'p[0] = %d', powinno być zero" # Recommended/Matrix/src/Csparse.c: 808 # error(_("p must be non-decreasing")) #: Csparse.c:773 msgid "p must be non-decreasing" msgstr "'p' musi być niemalejące" # Recommended/Matrix/src/Csparse.c: 824 # error(_("Inconsistent dimensions: np = 0 and nnz = %d"), # nnz) #: Csparse.c:789 #, c-format msgid "Inconsistent dimensions: np = 0 and nnz = %d" msgstr "Niespójne wymiary: 'np = 0' oraz 'nnz = %d'" # Recommended/Matrix/src/Csparse.c: 832 # error(_("invalid row index at position %d"), ii) #: Csparse.c:797 #, c-format msgid "invalid row index at position %d" msgstr "niepoprawny indeks wiersza na pozycji %d" # Recommended/Matrix/src/Csparse.c: 839 # error(_("invalid column index at position %d"), jj) #: Csparse.c:804 #, c-format msgid "invalid column index at position %d" msgstr "niepoprawny indeks kolumny na pozycji %d" # Recommended/Matrix/src/Csparse.c: 849 # error(_("strlen of cls argument = %d, should be 8"), strlen(cls)) #: Csparse.c:814 #, c-format msgid "strlen of cls argument = %d, should be 8" msgstr "długość argumentu 'cls = %d', powinna wynosić 8" # Recommended/Matrix/src/Csparse.c: 851 # error(_("cls = \"%s\" does not end in \"CMatrix\""), cls) #: Csparse.c:816 #, c-format msgid "cls = \"%s\" does not end in \"CMatrix\"" msgstr "'cls = \"%s\"' nie kończy się w 'CMatrix'" # Recommended/Matrix/src/Csparse.c: 861 # error(_("cls = \"%s\" must begin with 'd', 'l' or 'n'"), cls) #: Csparse.c:826 #, c-format msgid "cls = \"%s\" must begin with 'd', 'l' or 'n'" msgstr "'cls = \"%s\"' musi rozpoczynać się od 'd', 'l' lub 'n'" # Recommended/Matrix/src/Csparse.c: 864 # error(_("Only 'g'eneral sparse matrix types allowed")) #: Csparse.c:829 msgid "Only 'g'eneral sparse matrix types allowed" msgstr "Tylko ogólne ('g') typy rzadkich macierzy są dozwolone" # Recommended/Matrix/src/Csparse.c: 892 # error(_("code not yet written for cls = \"lgCMatrix\"")) #: Csparse.c:857 msgid "code not yet written for cls = \"lgCMatrix\"" msgstr "kod dla 'cls = \"lgCMatrix\"' nie został jeszcze napisany" # Recommended/Matrix/src/Mutils.c: 15 # error( # _("argument type[1]='%s' must be a one-letter character string"), # typstr) # Recommended/Matrix/src/Mutils.c: 34 # error( # _("argument type[1]='%s' must be a one-letter character string"), # typstr) #: Mutils.c:14 Mutils.c:33 #, c-format msgid "argument type[1]='%s' must be a one-letter character string" msgstr "argument type[1]='%s' musi być jednoliterowym łańcuchem tekstowym" # Recommended/Matrix/src/Mutils.c: 24 # error(_("argument type[1]='%s' must be one of 'M','1','O','I','F' or 'E'"), # typstr) #: Mutils.c:22 #, c-format msgid "argument type[1]='%s' must be one of 'M','1','O','I','F' or 'E'" msgstr "argument type[1]='%s' musi być jednym z 'M','1','O','I','F' lub 'E'" # Recommended/Matrix/src/Mutils.c: 41 # error(_("argument type[1]='%s' must be one of '1','O', or 'I'"), # typstr) #: Mutils.c:39 #, c-format msgid "argument type[1]='%s' must be one of '1','O', or 'I'" msgstr "argument type[1]='%s' musi być jednym z '1','O', lub 'I'" # Recommended/Matrix/src/Mutils.c: 53 # error(_("object must be a named, numeric vector")) # Recommended/Matrix/src/Mutils.c: 69 # error(_("object must be a named, numeric vector")) #: Mutils.c:50 Mutils.c:66 msgid "object must be a named, numeric vector" msgstr "obiekt musi być nazwanym wektorem liczbowym" # Recommended/Matrix/src/Mutils.c: 116 # error(_("'factors' slot must be a named list")) # Recommended/Matrix/src/Mutils.c: 136 # error(_("'factors' slot must be a named list")) #: Mutils.c:113 Mutils.c:137 msgid "'factors' slot must be a named list" msgstr "gniazdo 'factors' musi być nazwaną listą" # Recommended/Matrix/src/Mutils.c: 244 # _("'%s' slot must have length 1") #: Mutils.c:257 #, c-format msgid "'%s' slot must have length 1" msgstr "gniazdo '%s' musi mieć długość 1" # Recommended/Matrix/src/Mutils.c: 248 # SPRINTF(buf, _("'%s' must have string length 1"), nm); #: Mutils.c:261 #, c-format msgid "'%s' must have string length 1" msgstr "'%s' musi mieć łańcuch długości 1" # Recommended/Matrix/src/Mutils.c: 255 # SPRINTF(buf, _("'%s' must be in '%s'"), nm, vals); #: Mutils.c:268 #, c-format msgid "'%s' must be in '%s'" msgstr "'%s' musi być w '%s'" # Recommended/Matrix/src/Mutils.c: 274 # error(_("'s1' and 's2' must be \"character\" vectors")) #: Mutils.c:287 msgid "'s1' and 's2' must be \"character\" vectors" msgstr "'s1' oraz 's2' muszą być wektorami tekstowymi" # Recommended/Matrix/src/Mutils.c: 296 # (_("length of x slot != prod(Dim)")) #: Mutils.c:309 msgid "length of x slot != prod(Dim)" msgstr "długość gniazda 'x' != prod(Dim)" # Recommended/Matrix/src/Mutils.c: 317 # error(_("'uplo' must be UPP or LOW")) # Recommended/Matrix/src/Mutils.c: 343 # error(_("'uplo' must be UPP or LOW")) #: Mutils.c:330 Mutils.c:356 msgid "'uplo' must be UPP or LOW" msgstr "'uplo' musi być UPP lub LOW" # Recommended/Matrix/src/Mutils.c: 630 # error(_("invalid class '%s' to dup_mMatrix_as_geMatrix"), # class_P(A)) #: Mutils.c:643 #, c-format msgid "invalid class '%s' to dup_mMatrix_as_geMatrix" msgstr "niepoprawna klasa '%s' przekazana do 'dup_mMatrix_as_geMatrix'" # Recommended/Matrix/src/Mutils.c: 750 # error(_("unexpected ctype = %d in dup_mMatrix_as_geMatrix"), ctype) #: Mutils.c:763 #, c-format msgid "unexpected ctype = %d in dup_mMatrix_as_geMatrix" msgstr "nieoczekiwany 'ctype = %d' w 'dup_mMatrix_as_geMatrix'" # Recommended/Matrix/src/Mutils.c: 781 # error(_("invalid class '%s' to dup_mMatrix_as_dgeMatrix"), # class_P(A)) #: Mutils.c:794 #, c-format msgid "invalid class '%s' to dup_mMatrix_as_dgeMatrix" msgstr "niepoprawna klasa '%s' przekazana do 'dup_mMatrix_as_dgeMatrix'" # Recommended/Matrix/src/Mutils.c: 827 # error(_("Argument ij must be 2-column integer matrix")) #: Mutils.c:840 msgid "Argument ij must be 2-column integer matrix" msgstr "Argument 'ij' musi być 2-kolumnową macierzą liczb całkowitych" # Recommended/Matrix/src/Mutils.c: 843 # error(_("subscript 'i' out of bounds in M[ij]")) #: Mutils.c:856 msgid "subscript 'i' out of bounds in M[ij]" msgstr "indeks 'i' poza zakresem w 'M[ij]'" # Recommended/Matrix/src/Mutils.c: 845 # error(_("subscript 'j' out of bounds in M[ij]")) #: Mutils.c:858 msgid "subscript 'j' out of bounds in M[ij]" msgstr "indeks 'j' poza zakresem w 'M[ij]'" # Recommended/Matrix/src/Mutils.c: 884 # error(_("i and j must be integer vectors of the same length")) #: Mutils.c:897 msgid "i and j must be integer vectors of the same length" msgstr "" "'i' oraz 'j' muszą być wektorami liczb całkowitych o tej samej długości" #: Mutils.c:983 msgid "'data' must be of a vector type" msgstr "" #: Mutils.c:990 #, c-format msgid "invalid '%s' argument" msgstr "" #: Mutils.c:997 Mutils.c:1005 msgid "non-numeric matrix extent" msgstr "" #: Mutils.c:1000 msgid "invalid 'nrow' value (too large or NA)" msgstr "" #: Mutils.c:1002 msgid "invalid 'nrow' value (< 0)" msgstr "" #: Mutils.c:1008 msgid "invalid 'ncol' value (too large or NA)" msgstr "" #: Mutils.c:1010 msgid "invalid 'ncol' value (< 0)" msgstr "" #: Mutils.c:1028 #, c-format msgid "" "data length [%d] is not a sub-multiple or multiple of the number of rows [%d]" msgstr "" #: Mutils.c:1031 #, c-format msgid "" "data length [%d] is not a sub-multiple or multiple of the number of columns " "[%d]" msgstr "" #: Mutils.c:1034 msgid "data length exceeds size of matrix" msgstr "" #: Mutils.c:1040 msgid "too many elements specified" msgstr "" #: Mutils.c:1127 Mutils.c:1160 #, fuzzy msgid "Argument must be numeric-like atomic vector" msgstr "Argument 'y' musi być liczbą lub rzeczywistą lub całkowitą" # Recommended/Matrix/src/Tsparse.c: 20 # (_("lengths of slots i and j must match")) #: Tsparse.c:20 msgid "lengths of slots i and j must match" msgstr "długość gniazd 'i' oraz 'j' musi się zgadzać" # Recommended/Matrix/src/Tsparse.c: 23 # (_("slot Dim must have length 2")) #: Tsparse.c:23 msgid "slot Dim must have length 2" msgstr "gniazdo 'Dim' musi mieć długość 2" # Recommended/Matrix/src/Tsparse.c: 27 # (_("all row indices (slot 'i') must be between 0 and nrow-1 in a TsparseMatrix")) #: Tsparse.c:27 msgid "" "all row indices (slot 'i') must be between 0 and nrow-1 in a TsparseMatrix" msgstr "" "wszystkie indeksy wierszy (gniazdo 'i') muszą być pomiędzy 0 a 'nrow-1' w " "'TsparseMatrix'" # Recommended/Matrix/src/Tsparse.c: 29 # (_("all column indices (slot 'j') must be between 0 and ncol-1 in a TsparseMatrix")) #: Tsparse.c:29 msgid "" "all column indices (slot 'j') must be between 0 and ncol-1 in a TsparseMatrix" msgstr "" "wszystkie indeksy kolumn (gniazdo 'j') muszą być pomiędzy 0 a 'ncol-1' w " "'TsparseMatrix'" # Recommended/Matrix/src/chm_common.c: 67 # error(_("Argument rho must be an environment")) #: chm_common.c:74 msgid "Argument rho must be an environment" msgstr "Argument 'rho' musi być środowiskiem" # Recommended/Matrix/src/chm_common.c: 230 # error(_("invalid class of object to as_cholmod_sparse")) #: chm_common.c:237 msgid "invalid class of object to as_cholmod_sparse" msgstr "niepoprawna klasa obiektu przekazanego do 'as_cholmod_sparse'" # Recommended/Matrix/src/chm_common.c: 232 # error(_("invalid object passed to as_cholmod_sparse")) #: chm_common.c:239 msgid "invalid object passed to as_cholmod_sparse" msgstr "niepoprawny obiekt przekazany do 'as_cholmod_sparse'" # Recommended/Matrix/src/chm_common.c: 259 # error(_("in_place cholmod_sort returned an error code")) #: chm_common.c:266 msgid "in_place cholmod_sort returned an error code" msgstr "'in_place cholmod_sort' zwrócił kod błędu" # Recommended/Matrix/src/chm_common.c: 265 # error(_("cholmod_sort returned an error code")) #: chm_common.c:272 msgid "cholmod_sort returned an error code" msgstr "'cholmod_sort' zwrócił kod błędu" # Recommended/Matrix/src/chm_common.c: 339 # error(_("chm_sparse_to_SEXP(, *): invalid 'Rkind' (real kind code)")) #: chm_common.c:353 msgid "chm_sparse_to_SEXP(, *): invalid 'Rkind' (real kind code)" msgstr "chm_sparse_to_SEXP(, *): niepoprawny 'Rkind' (kod 'real kind')" # Recommended/Matrix/src/chm_common.c: 345 # error(_("unknown xtype in cholmod_sparse object")) #: chm_common.c:361 msgid "unknown xtype in cholmod_sparse object" msgstr "nieznany 'xtype' w obiekcie 'cholmod_sparse'" # Recommended/Matrix/src/chm_common.c: 373 # error(_("complex sparse matrix code not yet written")) # Recommended/Matrix/src/chm_common.c: 560 # error(_("complex sparse matrix code not yet written")) # Recommended/Matrix/src/chm_common.c: 786 # error(_("complex sparse matrix code not yet written")) # Recommended/Matrix/src/chm_common.c: 826 # error(_("complex sparse matrix code not yet written")) #: chm_common.c:390 chm_common.c:585 chm_common.c:820 chm_common.c:870 msgid "complex sparse matrix code not yet written" msgstr "kod dla zespolonych rzadkich macierzy nie został jeszcze napisany" # Recommended/Matrix/src/chm_common.c: 377 # error(_("Symmetric and triangular both set")) # Recommended/Matrix/src/chm_common.c: 564 # error(_("Symmetric and triangular both set")) #: chm_common.c:395 chm_common.c:590 msgid "Symmetric and triangular both set" msgstr "Ustawiono: symetryczny oraz trójkątny" # Recommended/Matrix/src/chm_common.c: 418 # error(_("invalid class of object to as_cholmod_triplet")) #: chm_common.c:435 msgid "invalid class of object to as_cholmod_triplet" msgstr "niepoprawna klasa obiektu przekazanego do 'as_cholmod_triplet'" # Recommended/Matrix/src/chm_common.c: 442 # error(_("as_cholmod_triplet(): could not reallocate for internal diagU2N()" # )) #: chm_common.c:459 msgid "as_cholmod_triplet(): could not reallocate for internal diagU2N()" msgstr "" "as_cholmod_triplet(): nie można ponownie przydzielić dla wewnętrznego " "'diagU2N()'" # Recommended/Matrix/src/chm_common.c: 533 # error(_("unknown xtype in cholmod_triplet object")) #: chm_common.c:557 msgid "unknown xtype in cholmod_triplet object" msgstr "nieznany 'xtype' w obiekcie 'cholmod_triplet'" # Recommended/Matrix/src/chm_common.c: 610 # error(_("invalid class of object to as_cholmod_dense")) #: chm_common.c:636 msgid "invalid class of object to as_cholmod_dense" msgstr "niepoprawna klasa obiektu przekazanego do 'as_cholmod_dense'" # Recommended/Matrix/src/chm_common.c: 680 # error(_("Cholmod error '%s' at file %s, line %d"), message, file, line) #: chm_common.c:706 #, c-format msgid "Cholmod error '%s' at file %s, line %d" msgstr "Błąd 'cholmod' '%s' w pliku %s, linia %d" # Recommended/Matrix/src/chm_common.c: 684 # warning(_("Cholmod warning '%s' at file %s, line %d"), # message, file, line) #: chm_common.c:710 #, c-format msgid "Cholmod warning '%s' at file %s, line %d" msgstr "Ostrzeżenie 'cholmod' '%s' w pliku %s, linia %d" # Recommended/Matrix/src/chm_common.c: 713 # error(_("Unable to initialize cholmod: error code %d"), res) #: chm_common.c:739 #, c-format msgid "Unable to initialize cholmod: error code %d" msgstr "Nie można zainicjować 'cholmod': kod błędu %d" # Recommended/Matrix/src/chm_common.c: 754 # error(_("unknown 'Rkind'")) #: chm_common.c:786 msgid "unknown 'Rkind'" msgstr "nieznany 'Rkind'" # Recommended/Matrix/src/chm_common.c: 760 # error(_("unknown xtype")) # Recommended/Matrix/src/chm_common.c: 819 # error(_("unknown xtype")) #: chm_common.c:793 chm_common.c:856 msgid "unknown xtype" msgstr "nieznany 'xtype'" # Recommended/Matrix/src/chm_common.c: 789 # error(_("code for cholmod_dense with holes not yet written")) # Recommended/Matrix/src/chm_common.c: 831 # error(_("code for cholmod_dense with holes not yet written")) #: chm_common.c:826 chm_common.c:879 msgid "code for cholmod_dense with holes not yet written" msgstr "kod dla 'cholmod_dense' z dziurami nie jest jeszcze napisany" # Recommended/Matrix/src/chm_common.c: 828 # error(_("don't know if a dense pattern matrix makes sense")) #: chm_common.c:875 msgid "don't know if a dense pattern matrix makes sense" msgstr "nie wiadomo, czy gęsty wzrór macierzy ma sens" # Recommended/Matrix/src/chm_common.c: 872 # error(_("invalid class of object to as_cholmod_factor")) #: chm_common.c:942 msgid "invalid class of object to as_cholmod_factor" msgstr "niepoprawna klasa obiektu przekazanego do 'as_cholmod_factor'" # Recommended/Matrix/src/chm_common.c: 886 # error(_("Supernodal LDL' decomposition not available")) #: chm_common.c:956 msgid "Supernodal LDL' decomposition not available" msgstr "Dekompozycja 'supernodal LDL' nie jest dostępna" # Recommended/Matrix/src/chm_common.c: 888 # error(_("Supernodal/simplicial class inconsistent with type flags")) #: chm_common.c:958 msgid "Supernodal/simplicial class inconsistent with type flags" msgstr "klasa supernodal/simplicial niespójna z flagami typów" # Recommended/Matrix/src/chm_common.c: 906 # error(_("Number of supernodes must be positive when is_super is TRUE")) #: chm_common.c:976 msgid "Number of supernodes must be positive when is_super is TRUE" msgstr "Liczba super węzłów musi być dodadnia gdy 'is_super' ma wartość TRUE" # Recommended/Matrix/src/chm_common.c: 909 # error(_("Lengths of super and pi must be equal")) #: chm_common.c:979 msgid "Lengths of super and pi must be equal" msgstr "Długości 'super' oraz 'pi' muszą być równe" # Recommended/Matrix/src/chm_common.c: 913 # error(_("Lengths of super and px must be equal")) #: chm_common.c:983 msgid "Lengths of super and px must be equal" msgstr "Długości 'super' oraz 'px' muszą być równe" # Recommended/Matrix/src/chm_common.c: 926 # error(_("failure in as_cholmod_factor")) #: chm_common.c:996 msgid "failure in as_cholmod_factor" msgstr "niepowodzenie w 'as_cholmod_factor'" # Recommended/Matrix/src/chm_common.c: 954 # error(_("CHOLMOD factorization was unsuccessful")) #: chm_common.c:1024 msgid "CHOLMOD factorization was unsuccessful" msgstr "Faktoryzacja 'CHOLMOD' nie powiodła się" # Recommended/Matrix/src/chm_common.c: 967 # error(_("f->xtype of %d not recognized"), f->xtype) #: chm_common.c:1037 #, c-format msgid "f->xtype of %d not recognized" msgstr "'f->xtype' dla %d nie został rozpoznany" # Recommended/Matrix/src/chm_common.c: 1032 # error(_("chm_diagN2U(): nrow=%d, ncol=%d"), # n, chx->ncol) #: chm_common.c:1102 #, c-format msgid "chm_diagN2U(): nrow=%d, ncol=%d" msgstr "chm_diagN2U(): nrow=%d, ncol=%d" # Recommended/Matrix/src/chm_common.c: 1075 # error(_("chm_diagN2U(x, uploT = %d): uploT should be +- 1"), uploT) #: chm_common.c:1145 #, c-format msgid "chm_diagN2U(x, uploT = %d): uploT should be +- 1" msgstr "chm_diagN2U(x, uploT = %d): 'uploT' powinien wynosić +/- 1" # Recommended/Matrix/src/cs_utils.c: 37 # error(_("csp_eye argument n must be positive")) #: cs_utils.c:37 msgid "csp_eye argument n must be positive" msgstr "argument 'n' w 'csp_eye' musi być dodatni" # Recommended/Matrix/src/cs_utils.c: 68 # error(_("invalid class of 'x' in Matrix_as_cs(a, x)")) #: cs_utils.c:68 msgid "invalid class of 'x' in Matrix_as_cs(a, x)" msgstr "niepoprawna klasa 'x' w 'Matrix_as_cs(a, x)'" # Recommended/Matrix/src/cs_utils.c: 127 # error(_("invalid class of object to %s"), "Matrix_cs_to_SEXP") # Recommended/Matrix/src/cs_utils.c: 171 # error(_("invalid class of object to %s"), "Matrix_as_css") # Recommended/Matrix/src/cs_utils.c: 186 # error(_("invalid class of object to %s"), "Matrix_as_css") # Recommended/Matrix/src/cs_utils.c: 206 # error(_("invalid class of object to %s"), "Matrix_as_csn") # Recommended/Matrix/src/cs_utils.c: 219 # error(_("invalid class of object to %s"), "Matrix_as_csn") #: cs_utils.c:126 cs_utils.c:170 cs_utils.c:185 cs_utils.c:205 cs_utils.c:218 #, c-format msgid "invalid class of object to %s" msgstr "niepoprawna klasa obiektu przekazanego do '%s'" # Recommended/Matrix/src/cs_utils.c: 140 # error(_("cs matrix not compatible with class '%s'"), valid[ctype]) #: cs_utils.c:139 #, c-format msgid "cs matrix not compatible with class '%s'" msgstr "'cs matrix' nie jest zgodne z klasą '%s'" # Recommended/Matrix/src/cs_utils.c: 243 # error(_("Inappropriate class cl='%s' in Matrix_css_to_SEXP(S, cl, ..)"), # cl) # Recommended/Matrix/src/cs_utils.c: 262 # error(_("Inappropriate class cl='%s' in Matrix_css_to_SEXP(S, cl, ..)"), # cl) #: cs_utils.c:242 cs_utils.c:261 #, c-format msgid "Inappropriate class cl='%s' in Matrix_css_to_SEXP(S, cl, ..)" msgstr "Niepoprawna klasa cl='%s' w 'Matrix_css_to_SEXP(S, cl, ..)'" # Recommended/Matrix/src/cs_utils.c: 288 # error(_("Inappropriate class cl='%s' in Matrix_csn_to_SEXP(S, cl, ..)"), # cl) # Recommended/Matrix/src/cs_utils.c: 307 # error(_("Inappropriate class cl='%s' in Matrix_csn_to_SEXP(S, cl, ..)"), # cl) #: cs_utils.c:287 cs_utils.c:306 #, c-format msgid "Inappropriate class cl='%s' in Matrix_csn_to_SEXP(S, cl, ..)" msgstr "Niepoprawna klasa cl='%s' w 'Matrix_csn_to_SEXP(S, cl, ..)'" # Recommended/Matrix/src/dense.c: 29 # error(_("incorrect left cyclic shift, j (%d) >= k (%d)"), j, k) #: dense.c:29 #, c-format msgid "incorrect left cyclic shift, j (%d) >= k (%d)" msgstr "niepoprawne lewe cykliczne przesunięcie, j (%d) >= k (%d)" # Recommended/Matrix/src/dense.c: 31 # error(_("incorrect left cyclic shift, j (%d) < 0"), j, k) #: dense.c:31 #, c-format msgid "incorrect left cyclic shift, j (%d) < 0" msgstr "niepoprawne lewe cykliczne przesunięcie, j (%d) < 0" # Recommended/Matrix/src/dense.c: 33 # error(_("incorrect left cyclic shift, k (%d) > ldx (%d)"), k, ldx) #: dense.c:33 #, c-format msgid "incorrect left cyclic shift, k (%d) > ldx (%d)" msgstr "niepoprawne lewe cykliczne przesunięcie, k (%d) > ldx (%d)" # Recommended/Matrix/src/dense.c: 78 # error(_("Unknown error in getGivens")) #: dense.c:78 msgid "Unknown error in getGivens" msgstr "Nieznany błąd w 'getGivens'" # Recommended/Matrix/src/dense.c: 90 # error(_("X must be a numeric (double precision) matrix")) # Recommended/Matrix/src/dense.c: 106 # error(_("X must be a numeric (double precision) matrix")) # Recommended/Matrix/src/dense.c: 139 # error(_("X must be a numeric (double precision) matrix")) #: dense.c:90 dense.c:106 dense.c:139 msgid "X must be a numeric (double precision) matrix" msgstr "'X' musi być macierzą liczbową (o podwójnej precyzji)" # Recommended/Matrix/src/dense.c: 111 # error(_("y must be a numeric (double precision) matrix")) # Recommended/Matrix/src/dense.c: 144 # error(_("y must be a numeric (double precision) matrix")) #: dense.c:111 dense.c:144 msgid "y must be a numeric (double precision) matrix" msgstr "'y' musi być macierzą liczbową (o podwójnej precyzji)" # Recommended/Matrix/src/dense.c: 114 # error(_( # "number of rows in y (%d) does not match number of rows in X (%d)"), # ydims[0], n) # Recommended/Matrix/src/dense.c: 147 # error(_( # "number of rows in y (%d) does not match number of rows in X (%d)"), # ydims[0], n) #: dense.c:115 dense.c:148 #, c-format msgid "number of rows in y (%d) does not match number of rows in X (%d)" msgstr "liczba wierszy w 'y' (%d) nie zgadza się z liczbą wierszy w 'X' (%d)" # Recommended/Matrix/src/dense.c: 126 # error(_("Lapack routine dposv returned error code %d"), info) #: dense.c:126 #, c-format msgid "Lapack routine dposv returned error code %d" msgstr "procedura Lapack 'dposv' zwróciła kod błędu %d" # Recommended/Matrix/src/dense.c: 159 # error(_("First call to Lapack routine dgels returned error code %d"), # info) #: dense.c:159 #, c-format msgid "First call to Lapack routine dgels returned error code %d" msgstr "Pierwsze wywołanie procedury Lapack 'dgels' zwróciło kod błędu %d" # Recommended/Matrix/src/dense.c: 166 # error(_("Second call to Lapack routine dgels returned error code %d"), # info) #: dense.c:166 #, c-format msgid "Second call to Lapack routine dgels returned error code %d" msgstr "Drugie wywołanie procedury Lapack 'dgels' zwróciło kod błędu %d" # Recommended/Matrix/src/dense.c: 179 # error(_("X must be a real (numeric) matrix")) #: dense.c:179 msgid "X must be a real (numeric) matrix" msgstr "'X' musi być rzeczywistą (liczbową) macierzą" # Recommended/Matrix/src/dense.c: 180 # error(_("tol, given as %g, must be non-negative"), tol) #: dense.c:180 #, c-format msgid "tol, given as %g, must be non-negative" msgstr "'tol', podane jako %g, musi być nieujemne" # Recommended/Matrix/src/dense.c: 181 # error(_("tol, given as %g, must be <= 1"), tol) #: dense.c:181 #, c-format msgid "tol, given as %g, must be <= 1" msgstr "'tol', podane jako %g, musi być <= 1" # Recommended/Matrix/src/dense.c: 205 # error(_("First call to dgeqrf returned error code %d"), info) #: dense.c:205 #, c-format msgid "First call to dgeqrf returned error code %d" msgstr "Pierwsze wywołanie 'dgeqrf' zwróciło kod błędu %d" # Recommended/Matrix/src/dense.c: 211 # error(_("Second call to dgeqrf returned error code %d"), info) #: dense.c:211 #, c-format msgid "Second call to dgeqrf returned error code %d" msgstr "Drugie wywołanie 'dgeqrf' zwróciło kod %d" # Recommended/Matrix/src/dense.c: 216 # error(_("Lapack routine dtrcon returned error code %d"), info) # Recommended/Matrix/src/dense.c: 236 # error(_("Lapack routine dtrcon returned error code %d"), info) #: dense.c:216 dense.c:236 #, c-format msgid "Lapack routine dtrcon returned error code %d" msgstr "Procedura Lapack 'dtrcon' zwróciła kod błędu %d" # Recommended/Matrix/src/dense.c: 285 # error(_("Lower band %d > upper band %d"), k1, k2) #: dense.c:285 #, c-format msgid "Lower band %d > upper band %d" msgstr "Niższe pasmo %d > górne pasmo %d" # Recommended/Matrix/src/dense.c: 356 # error(_("ddense_to_symmetric(): matrix is not square!")) #: dense.c:354 msgid "ddense_to_symmetric(): matrix is not square!" msgstr "ddense_to_symmetric(): macierz nie jest kwadratowa!" # Recommended/Matrix/src/dense.c: 364 # error(_("matrix is not symmetric [%d,%d]"), i+1, j+1) #: dense.c:365 #, c-format msgid "matrix is not symmetric [%d,%d]" msgstr "macierz nie jest symetryczna [%d,%d]" # Recommended/Matrix/src/dense.c: 412 # error(_("matrix is not square! (symmetric part)")) #: dense.c:413 msgid "matrix is not square! (symmetric part)" msgstr "macierz nie jest kwadratowa! (część symetryczna)" # Recommended/Matrix/src/dense.c: 456 # error(_("matrix is not square! (skew-symmetric part)")) #: dense.c:457 msgid "matrix is not square! (skew-symmetric part)" msgstr "macierz nie jest kwadratowa! (część skośno-symetryczna)" # Recommended/Matrix/src/dgCMatrix.c: 17 # (_("lengths of slots 'i' and 'x' must match")) #: dgCMatrix.c:17 msgid "lengths of slots 'i' and 'x' must match" msgstr "długość gniazd 'i' oraz 'x' musi się zgadzać" # Recommended/Matrix/src/dgCMatrix.c: 29 # (_("lengths of slots 'j' and 'x' must match")) #: dgCMatrix.c:29 msgid "lengths of slots 'j' and 'x' must match" msgstr "długość gniazd 'j' oraz 'x' musi się zgadzać" # Recommended/Matrix/src/dgCMatrix.c: 51 # error(_("invalid class(x) '%s' in compressed_to_TMatrix(x)"), ncl) #: dgCMatrix.c:51 #, c-format msgid "invalid class(x) '%s' in compressed_to_TMatrix(x)" msgstr "niepoprawne 'class(x)' '%s' w 'compressed_to_TMatrix(x)'" # Recommended/Matrix/src/dgCMatrix.c: 85 # error(_("invalid class(x) '%s' in R_to_CMatrix(x)"), ncl) #: dgCMatrix.c:85 #, c-format msgid "invalid class(x) '%s' in R_to_CMatrix(x)" msgstr "niepoprawne 'class(x)' '%s' w 'R_to_CMatrix(x)'" # Recommended/Matrix/src/dgCMatrix.c: 155 # error(_("dgCMatrix_lusol requires a square, non-empty matrix")) #: dgCMatrix.c:155 msgid "dgCMatrix_lusol requires a square, non-empty matrix" msgstr "'dgCMatrix_lusol' wymaga kwadratowej, niepustej macierzy" # Recommended/Matrix/src/dtCMatrix.c: 90 # error(_("Dimensions of system to be solved are inconsistent")) # Recommended/Matrix/src/dtCMatrix.c: 106 # error(_("Dimensions of system to be solved are inconsistent")) # Recommended/Matrix/src/dppMatrix.c: 80 # error(_("Dimensions of system to be solved are inconsistent")) # Recommended/Matrix/src/dtrMatrix.c: 98 # error(_("Dimensions of system to be solved are inconsistent")) # Recommended/Matrix/src/dgeMatrix.c: 422 # error(_("Dimensions of system to be solved are inconsistent")) # Recommended/Matrix/src/dgCMatrix.c: 157 # error(_("Dimensions of system to be solved are inconsistent")) # Recommended/Matrix/src/dgCMatrix.c: 183 # error(_("Dimensions of system to be solved are inconsistent")) # Recommended/Matrix/src/dgCMatrix.c: 429 # error(_("Dimensions of system to be solved are inconsistent")) # Recommended/Matrix/src/dgCMatrix.c: 462 # error(_("Dimensions of system to be solved are inconsistent")) # Recommended/Matrix/src/dspMatrix.c: 78 # error(_("Dimensions of system to be solved are inconsistent")) # Recommended/Matrix/src/dsyMatrix.c: 85 # error(_("Dimensions of system to be solved are inconsistent")) # Recommended/Matrix/src/dpoMatrix.c: 91 # error(_("Dimensions of system to be solved are inconsistent")) # Recommended/Matrix/src/dpoMatrix.c: 116 # error(_("Dimensions of system to be solved are inconsistent")) #: dgCMatrix.c:157 dgCMatrix.c:183 dgCMatrix.c:437 dgCMatrix.c:470 #: dgeMatrix.c:422 dpoMatrix.c:91 dpoMatrix.c:116 dppMatrix.c:80 #: dspMatrix.c:78 dsyMatrix.c:85 dtCMatrix.c:90 dtCMatrix.c:106 dtrMatrix.c:98 msgid "Dimensions of system to be solved are inconsistent" msgstr "Wymiary systemu, który ma być rozwiązany, są niespójne" # Recommended/Matrix/src/dgCMatrix.c: 159 # error(_("cs_lusol failed")) #: dgCMatrix.c:159 msgid "cs_lusol failed" msgstr "'cs_lusol' nie powiódł się" # Recommended/Matrix/src/dgCMatrix.c: 180 # error(_("dgCMatrix_qrsol(., order) needs order in {0,..,3}")) #: dgCMatrix.c:180 msgid "dgCMatrix_qrsol(., order) needs order in {0,..,3}" msgstr "" "'dgCMatrix_qrsol(., order)' potrzebuje zmiennej 'order' ze zbioru {0,..,3}" # Recommended/Matrix/src/dgCMatrix.c: 189 # error(_("dgCMatrix_qrsol(<%d x %d>-matrix) requires a 'tall' rectangular matrix"), # xc->m, xc->n) #: dgCMatrix.c:189 #, c-format msgid "dgCMatrix_qrsol(<%d x %d>-matrix) requires a 'tall' rectangular matrix" msgstr "" "'dgCMatrix_qrsol(macierz <%d x %d>)' wymaga długiej prostokątnej macierzy" # Recommended/Matrix/src/dgCMatrix.c: 200 # error(_("cs_qrsol() failed inside dgCMatrix_qrsol()")) #: dgCMatrix.c:200 msgid "cs_qrsol() failed inside dgCMatrix_qrsol()" msgstr "'cs_qrsol()' nie powiódł się wewnątrz 'dgCMatrix_qrsol()'" # Recommended/Matrix/src/dgCMatrix.c: 226 # error(_("A must have #{rows} >= #{columns}")) #: dgCMatrix.c:219 msgid "A must have #{rows} >= #{columns}" msgstr "'A' musi mieć liczbę wierszy >= liczba kolumn" # Recommended/Matrix/src/dgCMatrix.c: 229 # error(_("cs_sqr failed")) #: dgCMatrix.c:224 msgid "cs_sqr failed" msgstr "'cs_sqr' nie powiódł się" # Recommended/Matrix/src/dgCMatrix.c: 231 # error(_("cs_qr failed")) #: dgCMatrix.c:229 msgid "cs_qr failed" msgstr "'cs_qr' nie powiódł się" # Recommended/Matrix/src/dgCMatrix.c: 297 # error(_("SuiteSparseQR_C_QR returned an error code")) #: dgCMatrix.c:292 msgid "SuiteSparseQR_C_QR returned an error code" msgstr "'SuiteSparseQR_C_QR' zwrócił kod błędu" # Recommended/Matrix/src/dgCMatrix.c: 341 # error(_("LU decomposition applies only to square matrices")) #: dgCMatrix.c:336 msgid "LU decomposition applies only to square matrices" msgstr "dekompozycja LU stosuje się tylko do macierzy kwadratowych" # Recommended/Matrix/src/dgCMatrix.c: 350 # error(_("cs_lu(A) failed: near-singular A (or out of memory)")) #: dgCMatrix.c:345 msgid "cs_lu(A) failed: near-singular A (or out of memory)" msgstr "" "'cs_lu(A)' nie powiódł się: 'A' jest bliskie osobliwości (lub brak pamięci)" #: dgCMatrix.c:405 msgid "dgCMatrix_matrix_solve(.., sparse=TRUE) not yet implemented" msgstr "" # Recommended/Matrix/src/dgCMatrix.c: 460 # error(_("dgCMatrix_cholsol requires a 'short, wide' rectangular matrix")) #: dgCMatrix.c:468 msgid "dgCMatrix_cholsol requires a 'short, wide' rectangular matrix" msgstr "" "'dgCMatrix_cholsol' wymaga krótkiej lub szerokiej macierzy prostokątnej" # Recommended/Matrix/src/dgCMatrix.c: 468 # error(_("cholmod_sdmult error (rhs)")) #: dgCMatrix.c:476 msgid "cholmod_sdmult error (rhs)" msgstr "błąd 'cholmod_sdmult' (prawa strona)" # Recommended/Matrix/src/dgCMatrix.c: 471 # error(_("cholmod_factorize failed: status %d, minor %d from ncol %d"), # c.status, L->minor, L->n) #: dgCMatrix.c:479 #, c-format msgid "cholmod_factorize failed: status %d, minor %d from ncol %d" msgstr "" "'cholmod_factorize' nie powiódł się: status %d, minor %d z liczbą kolumn %d" # Recommended/Matrix/src/dgCMatrix.c: 475 # error(_("cholmod_solve (CHOLMOD_A) failed: status %d, minor %d from ncol %d"), # c.status, L->minor, L->n) #: dgCMatrix.c:483 #, c-format msgid "cholmod_solve (CHOLMOD_A) failed: status %d, minor %d from ncol %d" msgstr "" "'cholmod_solve (CHOLMOD_A)' nie powiódł się: status %d, minor %d z liczbą " "kolumn %d" # Recommended/Matrix/src/dgCMatrix.c: 492 # error(_("cholmod_sdmult error (resid)")) #: dgCMatrix.c:500 msgid "cholmod_sdmult error (resid)" msgstr "błąd 'cholmod_sdmult' (reszta)" # Recommended/Matrix/src/dgTMatrix.c: 15 # (_("lengths of slots i and x must match")) #: dgTMatrix.c:15 msgid "lengths of slots i and x must match" msgstr "długość gniazd 'i' oraz 'x' musi się zgadzać" # Recommended/Matrix/src/dgTMatrix.c: 56 # error(_("Cannot coerce to too large *geMatrix with %.0f entries"), len) #: dgTMatrix.c:56 #, c-format msgid "Cannot coerce to too large *geMatrix with %.0f entries" msgstr "Nie można przekształcić do dużego *geMatrix z %.0f wpisami" # Recommended/Matrix/src/dgeMatrix.c: 10 # (_("Dim slot must have length 2")) #: dgeMatrix.c:10 msgid "Dim slot must have length 2" msgstr "gniazdo 'dim' musi mieć długość 2" # Recommended/Matrix/src/dgeMatrix.c: 13 # ngettext("Matrix", # "Negative value in Dim", # "Negative values in Dim", # (m*n > 0) ? 2 : 1) #: dgeMatrix.c:14 msgid "Negative value in Dim" msgid_plural "Negative values in Dim" msgstr[0] "Ujemna wartość w 'Dim'" msgstr[1] "Ujemne wartości w 'Dim'" msgstr[2] "Ujemne wartości w 'Dim'" # Recommended/Matrix/src/dgeMatrix.c: 18 # (_("x slot must be numeric \"double\"")) #: dgeMatrix.c:18 msgid "x slot must be numeric \"double\"" msgstr "gniazdo 'x' musi być liczbą typu 'double'" # Recommended/Matrix/src/dgeMatrix.c: 31 # (_("factors slot must be named list")) #: dgeMatrix.c:31 msgid "factors slot must be named list" msgstr "gniazdo czynników musi być nazwaną listą" # Recommended/Matrix/src/dgeMatrix.c: 69 # error(_("rcond requires a square, non-empty matrix")) #: dgeMatrix.c:69 msgid "rcond requires a square, non-empty matrix" msgstr "'rcond' wymaga kwadratowej, niepustej macierzy" # Recommended/Matrix/src/dgeMatrix.c: 126 # error(_("Dimensions of x and y are not compatible for %s"), # tr ? "tcrossprod" : "crossprod") # Recommended/Matrix/src/dgeMatrix.c: 183 # error(_("Dimensions of x and y are not compatible for %s"), # tr ? "tcrossprod" : "crossprod") #: dgeMatrix.c:126 dgeMatrix.c:183 #, c-format msgid "Dimensions of x and y are not compatible for %s" msgstr "Wymiary 'x' oraz 'y' nie są zgodne dla '%s'" #: dgeMatrix.c:165 msgid "Argument y must be numeric or integer" msgstr "Argument 'y' musi być liczbą lub rzeczywistą lub całkowitą" # Recommended/Matrix/src/dgeMatrix.c: 306 # error(_("Cannot factor a matrix with zero extents")) #: dgeMatrix.c:306 msgid "Cannot factor a matrix with zero extents" msgstr "Nie można faktoryzować macierzy o zerowym stopniu" # Recommended/Matrix/src/dppMatrix.c: 36 # error(_("Lapack routine %s returned error code %d"), "dpptrf", info) # Recommended/Matrix/src/dgeMatrix.c: 316 # error(_("Lapack routine %s returned error code %d"), "dgetrf", info) # Recommended/Matrix/src/dspMatrix.c: 181 # error(_("Lapack routine %s returned error code %d"), "dsptrf", info) # Recommended/Matrix/src/dpoMatrix.c: 42 # error(_("Lapack routine %s returned error code %d"), "dpotrf", info) #: dgeMatrix.c:316 dpoMatrix.c:42 dppMatrix.c:36 dspMatrix.c:181 #, c-format msgid "Lapack routine %s returned error code %d" msgstr "Procedura Lapack '%s' zwróciła kod błędu %d" # Recommended/Matrix/src/dgeMatrix.c: 318 # warning(_("Exact singularity detected during LU decomposition: %s, i=%d."), # "U[i,i]=0", info) #: dgeMatrix.c:318 #, c-format msgid "Exact singularity detected during LU decomposition: %s, i=%d." msgstr "Wykryto dokładną osobliwość podczas dekompozycji LU: %s, i=%d." # Recommended/Matrix/src/dgeMatrix.c: 340 # error(_("Determinant requires a square matrix")) #: dgeMatrix.c:340 msgid "Determinant requires a square matrix" msgstr "Wyznacznik wymaga aby macierz była kwadratowa" # Recommended/Matrix/src/dgeMatrix.c: 382 # error(_("Solve requires a square matrix")) #: dgeMatrix.c:382 msgid "Solve requires a square matrix" msgstr "'Solve' wymaga kwadratowej macierzy" # Recommended/Matrix/src/dgeMatrix.c: 395 # error(_("error [%d] from Lapack 'dgecon()'"), info) #: dgeMatrix.c:395 #, c-format msgid "error [%d] from Lapack 'dgecon()'" msgstr "błąd [%d] z procedury Lapack 'dgecon()'" # Recommended/Matrix/src/dgeMatrix.c: 397 # error(_("Lapack dgecon(): system computationally singular, reciprocal condition number = %g"), # rcond) #: dgeMatrix.c:397 #, c-format msgid "" "Lapack dgecon(): system computationally singular, reciprocal condition " "number = %g" msgstr "" "Lapack dgecon(): system obliczeniowo osobliwy, numer obustronnego stanu = %g" # Recommended/Matrix/src/dgeMatrix.c: 407 # error(_("Lapack routine dgetri: system is exactly singular")) #: dgeMatrix.c:407 msgid "Lapack routine dgetri: system is exactly singular" msgstr "procedura Lapack 'dgetri': system jest ściśle osobliwy" # Recommended/Matrix/src/dgeMatrix.c: 427 # error(_("Lapack routine dgetrs: system is exactly singular")) #: dgeMatrix.c:427 msgid "Lapack routine dgetrs: system is exactly singular" msgstr "procedura Lapack 'dgetrs': system jest ściśle osobliwy" # Recommended/Matrix/src/dtrMatrix.c: 122 # error(_("Matrices are not conformable for multiplication")) # Recommended/Matrix/src/dgeMatrix.c: 446 # error(_("Matrices are not conformable for multiplication")) # Recommended/Matrix/src/dgeMatrix.c: 468 # error(_("Matrices are not conformable for multiplication")) # Recommended/Matrix/src/dspMatrix.c: 152 # error(_("Matrices are not conformable for multiplication")) # Recommended/Matrix/src/dsyMatrix.c: 122 # error(_("Matrices are not conformable for multiplication")) #: dgeMatrix.c:446 dgeMatrix.c:468 dspMatrix.c:152 dsyMatrix.c:122 #: dtrMatrix.c:122 msgid "Matrices are not conformable for multiplication" msgstr "Macierze nie są dostosowane do przemnożenia" # Recommended/Matrix/src/dgeMatrix.c: 569 # error(_("Matrix exponential requires square, non-null matrix")) #: dgeMatrix.c:569 msgid "Matrix exponential requires square, non-null matrix" msgstr "Eksponencjowanie macierzy wymaga kwadratowej, niepustej macierzy" # Recommended/Matrix/src/dgeMatrix.c: 586 # error(_("dgeMatrix_exp: LAPACK routine dgebal returned %d"), j) # Recommended/Matrix/src/dgeMatrix.c: 588 # error(_("dgeMatrix_exp: LAPACK routine dgebal returned %d"), j) #: dgeMatrix.c:586 dgeMatrix.c:588 #, c-format msgid "dgeMatrix_exp: LAPACK routine dgebal returned %d" msgstr "dgeMatrix_exp: procedura LAPACK 'dgebal' zwróciła %d" # Recommended/Matrix/src/dgeMatrix.c: 626 # error(_("dgeMatrix_exp: dgetrf returned error code %d"), j) #: dgeMatrix.c:626 #, c-format msgid "dgeMatrix_exp: dgetrf returned error code %d" msgstr "dgeMatrix_exp: 'dgetrf' zwrócił kod błędu %d" # Recommended/Matrix/src/dgeMatrix.c: 628 # error(_("dgeMatrix_exp: dgetrs returned error code %d"), j) #: dgeMatrix.c:628 #, c-format msgid "dgeMatrix_exp: dgetrs returned error code %d" msgstr "dgeMatrix_exp: 'dgetrs' zwrócił kod błędu %d" # Recommended/Matrix/src/dgeMatrix.c: 689 # error(_("dgeMatrix_Schur: argument x must be a non-null square matrix")) #: dgeMatrix.c:701 msgid "dgeMatrix_Schur: argument x must be a non-null square matrix" msgstr "dgeMatrix_Schur: argument 'x' musi być niepustą macierzą kwadratową" # Recommended/Matrix/src/dgeMatrix.c: 698 # error(_("dgeMatrix_Schur: first call to dgees failed")) #: dgeMatrix.c:712 msgid "dgeMatrix_Schur: first call to dgees failed" msgstr "dgeMatrix_Schur: pierwsze wywołanie 'dgees' nie powiodło się" # Recommended/Matrix/src/dgeMatrix.c: 706 # error(_("dgeMatrix_Schur: dgees returned code %d"), info) #: dgeMatrix.c:720 #, c-format msgid "dgeMatrix_Schur: dgees returned code %d" msgstr "dgeMatrix_Schur: 'dgees' zwrócił kod %d" # Recommended/Matrix/src/dpoMatrix.c: 12 # (_("dpoMatrix is not positive definite")) #: dpoMatrix.c:12 msgid "dpoMatrix is not positive definite" msgstr "'dpoMatrix' nie jest dodatnio określone" # Recommended/Matrix/src/dppMatrix.c: 33 # error(_("the leading minor of order %d is not positive definite"), # info) # Recommended/Matrix/src/dpoMatrix.c: 39 # error(_("the leading minor of order %d is not positive definite"), # info) #: dpoMatrix.c:39 dppMatrix.c:33 #, c-format msgid "the leading minor of order %d is not positive definite" msgstr "wiodący minor rzędu %d nie jest dodatnio określony" # Recommended/Matrix/src/dpoMatrix.c: 93 # error(_("Cannot solve() for matrices with zero extents")) #: dpoMatrix.c:93 msgid "Cannot solve() for matrices with zero extents" msgstr "Nie można wykonać 'solve()' dla macierzy o zerowym stopniu" # Recommended/Matrix/src/dpoMatrix.c: 114 # error(_("Argument b must be a numeric matrix")) #: dpoMatrix.c:114 msgid "Argument b must be a numeric matrix" msgstr "Argument 'b' musi być macierzą liczbową" #: dsCMatrix.c:25 msgid "chm_factor_name(): did not get string of length 11" msgstr "" # Recommended/Matrix/src/dsCMatrix.c: 71 # error(_("Cholesky factorization failed; unusually, please report to Matrix-authors")) #: dsCMatrix.c:99 msgid "" "Cholesky factorization failed; unusually, please report to Matrix-authors" msgstr "" "faktoryzacja Cholesky'ego nie powiodła się; nietypowo, proszę zgłosić raport " "autorom pakietu Matrix" # Recommended/Matrix/src/dsCMatrix.c: 77 # error(_("internal_chm_factor: Cholesky factorization failed")) #: dsCMatrix.c:105 msgid "internal_chm_factor: Cholesky factorization failed" msgstr "internal_chm_factor: faktoryzacja Cholesky'ego nie powiodła się" # Recommended/Matrix/src/dsCMatrix.c: 213 # error(_("Non-symmetric matrix passed to dsCMatrix_to_dgTMatrix")) #: dsCMatrix.c:241 msgid "Non-symmetric matrix passed to dsCMatrix_to_dgTMatrix" msgstr "Niesymetryczna macierz przekazana do 'dsCMatrix_to_dgTMatrix'" # Recommended/Matrix/src/dtpMatrix.c: 17 # (_("Incorrect length of 'x' slot")) # Recommended/Matrix/src/dspMatrix.c: 13 # (_("Incorrect length of 'x' slot")) #: dspMatrix.c:13 dtpMatrix.c:17 msgid "Incorrect length of 'x' slot" msgstr "Niepoprawna długość gniazda 'x'" # Recommended/Matrix/src/dtrMatrix.c: 10 # (_("'Dim' slot has length less than two")) # Recommended/Matrix/src/dsyMatrix.c: 7 # (_("'Dim' slot has length less than two")) #: dsyMatrix.c:7 dtrMatrix.c:10 msgid "'Dim' slot has length less than two" msgstr "gniazdo 'Dim' ma długość mniejszą niż dwa" # Recommended/Matrix/src/dtrMatrix.c: 12 # (_("Matrix is not square")) # Recommended/Matrix/src/dsyMatrix.c: 9 # (_("Matrix is not square")) #: dsyMatrix.c:9 dtrMatrix.c:12 msgid "Matrix is not square" msgstr "Macierz nie jest kwadratowa" # Recommended/Matrix/src/dsyMatrix.c: 158 # error(_("Lapack routine dsytrf returned error code %d"), info) #: dsyMatrix.c:158 #, c-format msgid "Lapack routine dsytrf returned error code %d" msgstr "procedura Lapack 'dsytrf' zwróciła kod błędu %d" # Recommended/Matrix/src/dtCMatrix.c: 28 # (_("uplo='U' must not have sparse entries below the diagonal")) # Recommended/Matrix/src/dtCMatrix.c: 63 # (_("uplo='U' must not have sparse entries below the diagonal")) # Recommended/Matrix/src/dtTMatrix.c: 24 # (_("uplo='U' must not have sparse entries below the diagonal")) #: dtCMatrix.c:28 dtCMatrix.c:63 dtTMatrix.c:24 msgid "uplo='U' must not have sparse entries below the diagonal" msgstr "uplo='U' nie może mieć rzadkich wpisów poniżej diagonali" # Recommended/Matrix/src/dtCMatrix.c: 34 # (_("uplo='L' must not have sparse entries above the diagonal")) # Recommended/Matrix/src/dtCMatrix.c: 69 # (_("uplo='L' must not have sparse entries above the diagonal")) # Recommended/Matrix/src/dtTMatrix.c: 29 # (_("uplo='L' must not have sparse entries above the diagonal")) #: dtCMatrix.c:34 dtCMatrix.c:69 dtTMatrix.c:29 msgid "uplo='L' must not have sparse entries above the diagonal" msgstr "uplo='L' nie może mieć rzadkich wpisów powyżej diagonali" # Recommended/Matrix/src/dtpMatrix.c: 120 # error(_("Dimensions of a (%d,%d) and b (%d,%d) do not conform"), # xDim[0], xDim[1], yDim[0], yDim[1]) # Recommended/Matrix/src/dtpMatrix.c: 141 # error(_("Dimensions of a (%d,%d) and b (%d,%d) do not conform"), # aDim[0], aDim[1], bDim[0], bDim[1]) # Recommended/Matrix/src/dtpMatrix.c: 164 # error(_("Dimensions of a (%d,%d) and b (%d,%d) do not conform"), # xDim[0], xDim[1], yDim[0], yDim[1]) #: dtpMatrix.c:124 dtpMatrix.c:152 dtpMatrix.c:183 #, c-format msgid "Dimensions of a (%d,%d) and b (%d,%d) do not conform" msgstr "Wymiary 'a' (%d,%d) oraz 'b' (%d,%d) nie pokrywają się" #: dtpMatrix.c:131 msgid "right=TRUE is not yet implemented __ FIXME" msgstr "" # Recommended/Matrix/src/dtrMatrix.c: 120 # error(_("dtrMatrix must be square")) #: dtrMatrix.c:120 msgid "dtrMatrix must be square" msgstr "'dtrMatrix' musi być kwadratowa" # Recommended/Matrix/src/dtrMatrix.c: 160 # error(_("dtrMatrices in %*% must have matching (square) dim.")) #: dtrMatrix.c:160 msgid "dtrMatrices in %*% must have matching (square) dim." msgstr "'dtrMatrices' w %*% muszą mieć pasujące (kwadratowe) wymiary." #: dtrMatrix.c:247 msgid "cannot set diag() as long as 'diag = \"U\"'" msgstr "nie można ustawić 'diag()' dopóki 'diag = \"U\"'" #: dtrMatrix.c:268 msgid "cannot add diag() as long as 'diag = \"U\"'" msgstr "nie można dodać 'diag()' dopóki 'diag = \"U\"'" # Recommended/Matrix/src/init.c: 342 # error(_("missing 'Matrix' namespace: should never happen")) #: init.c:359 msgid "missing 'Matrix' namespace: should never happen" msgstr "brakuje przestrzeni nazw 'Matrix': nie powinno się wydarzyć" # Recommended/Matrix/src/init.c: 353 # error(_("Matrix namespace not determined correctly")) #: init.c:370 msgid "Matrix namespace not determined correctly" msgstr "przestrzeń nazw macierzy nie została poprawnie określona" # Recommended/Matrix/src/lgCMatrix.c: 58 # error(_("A must be a logical matrix")) #: lgCMatrix.c:58 msgid "A must be a logical matrix" msgstr "'A' musi być macierzą logiczną" # Recommended/Matrix/src/sparseQR.c: 14 # (_("length(p) must match nrow(V)")) #: sparseQR.c:13 msgid "length(p) must match nrow(V)" msgstr "'length(p)' musi zgadzać się z 'nrow(V)'" # Recommended/Matrix/src/sparseQR.c: 16 # (_("length(beta) must match nrow(V)")) #: sparseQR.c:15 #, fuzzy msgid "length(beta) must match ncol(V)" msgstr "'length(beta)' musi zgadzać się z 'nrow(V)'" # Recommended/Matrix/src/sparseQR.c: 18 # (_("length(q) must be zero or ncol(R)")) #: sparseQR.c:18 msgid "length(q) must be zero or ncol(R)" msgstr "'length(q)' musi wynosić zero lub 'sncol(R)'" #: sparseQR.c:46 #, c-format msgid "sparseQR_Qmult(): nrow(y) = %d != %d = nrow(V)" msgstr "" #: sparseQR.c:121 sparseQR.c:159 sparseQR.c:195 #, c-format msgid "%s(): structurally rank deficient case: possibly WRONG zeros" msgstr "" # Recommended/Matrix/src/t_Csparse_subassign.c: 144 # error(_("invalid class of 'x' in Csparse_subassign()")) #: t_Csparse_subassign.c:144 msgid "invalid class of 'x' in Csparse_subassign()" msgstr "niepoprawna klasa 'x' w 'Csparse_subassign()'" # Recommended/Matrix/src/t_Csparse_subassign.c: 146 # error(_("invalid class of 'value' in Csparse_subassign()")) #: t_Csparse_subassign.c:146 msgid "invalid class of 'value' in Csparse_subassign()" msgstr "niepoprawna klasa 'value' w 'Csparse_subassign()'" # Recommended/Matrix/src/t_Csparse_subassign.c: 189 # warning(_("x[] <- val: val must be logical for \"%s\" x"), # valid_cM[ctype_x]) #: t_Csparse_subassign.c:189 #, fuzzy, c-format msgid "x[] <- val: val is coerced to logical for \"%s\" x" msgstr "x[] <- val: 'val' musi być wartością logiczną dla '%s' 'x'" # Recommended/Matrix/src/t_Csparse_subassign.c: 194 # error(_("x[] <- val: val must be integer or logical for \"%s\" x"), # valid_cM[ctype_x]) #: t_Csparse_subassign.c:194 #, fuzzy, c-format msgid "" "x[] <- val: val should be integer or logical, is coerced to integer, for \"%s" "\" x" msgstr "" "x[] <- val: 'val' musi być liczbą całkowitą lub wartością logiczną dla '%s' " "'x'" # Recommended/Matrix/src/t_Csparse_subassign.c: 201 # error(_("programming error in Csparse_subassign() should never happen")) #: t_Csparse_subassign.c:201 msgid "programming error in Csparse_subassign() should never happen" msgstr "błąd programowy w 'Csparse_subassign()' nie powinien się wydarzyć" # Recommended/Matrix/src/Csparse.c: 58 # (_("slot p must have length = ncol(.) + 1")) #~ msgid "slot p must have length = ncol(.) + 1" #~ msgstr "gniazdo 'p' musi mieć długość = ncol(.) + 1" # Recommended/Matrix/src/Csparse.c: 63 # (_("last element of slot p must match length of slots i and x")) #~ msgid "last element of slot p must match length of slots i and x" #~ msgstr "" #~ "ostatni element gniazda 'p' musi zgadzać się długością z gniazd 'i' oraz " #~ "'x'" # Recommended/Matrix/src/Csparse.c: 66 # (_("all row indices must be between 0 and nrow-1")) #~ msgid "all row indices must be between 0 and nrow-1" #~ msgstr "wszystkie indeksy wierszy muszą być pomiędzy 0 a 'nrow-1'" # Recommended/Matrix/src/Csparse.c: 92 # (_("slot i is not *strictly* increasing inside a column (even after cholmod_l_sort)")) #~ msgid "" #~ "slot i is not *strictly* increasing inside a column (even after " #~ "cholmod_l_sort)" #~ msgstr "" #~ "gniazdo 'i' nie jest *ściśle* rosnące wewnątrz kolumny (nawet po " #~ "zastosowaniu 'cholmod_l_sort')" # Recommended/Matrix/src/Csparse.c: 95 # (_("row indices are not sorted within columns")) #~ msgid "row indices are not sorted within columns" #~ msgstr "indeksy wierszy nie są posortowane wewnątrz kolumn" # Recommended/Matrix/src/Csparse.c: 98 # (_("slot i is not *strictly* increasing inside a column")) #~ msgid "slot i is not *strictly* increasing inside a column" #~ msgstr "gniazdo 'i' nie jest *ściśle* rosnące wewnątrz kolumny" # Recommended/Matrix/src/sparseQR.c: 45 # error(_("Dimensions of system are inconsistent")) #~ msgid "Dimensions of system are inconsistent" #~ msgstr "Wymiary systemu nie są spójne" #~ msgid "could not find correct environment; please report!" #~ msgstr "nie można znaleźć prawidłowego środowiska; proszę zgłosić raport!" Matrix/po/R-de.po0000644000175100001440000007341212256121033013303 0ustar hornikusers# Translation of R-matrix to German # Copyright (C) 2001 The R Foundation # This file is distributed under the same license as the matrix package. # Chris Leick , 2009. # Detlef Steuer , 2012. msgid "" msgstr "" "Project-Id-Version: R 2.15.2 / matrix 1.0-10\n" "Report-Msgid-Bugs-To: bugs.r-project.org\n" "POT-Creation-Date: 2013-12-23 21:27\n" "PO-Revision-Date: 2012-10-01 15:38+0200\n" "Last-Translator: Chris Leick \n" "Language-Team: German \n" "Language: de\n" "MIME-Version: 1.0\n" "Content-Type: text/plain; charset=UTF-8\n" "Content-Transfer-Encoding: 8bit\n" "Plural-Forms: nplurals=2; plural=(n != 1);\n" #, fuzzy msgid "invalid 'mod': %s" msgstr "ungültiges 'mod':" msgid "" "not-yet-implemented method for %s(<%s>).\n" " ->> Ask the package authors to implement the missing feature." msgstr "" "noch nicht implementierte Methode für %s(<%s>).\n" " ->> Bitten Sie die Autoren des Pakets, diese fehlende Funktion zu " "implementieren." msgid "" "not-yet-implemented method for %s(<%s>, <%s>).\n" " ->> Ask the package authors to implement the missing feature." msgstr "" "noch nicht implementierte Methode für %s(<%s>, <%s>).\n" " ->> Bitten Sie die Autoren des Pakets, diese fehlende Funktion zu " "implementieren." msgid "'x' is not positive definite -- chol() undefined." msgstr "'x' ist nicht positiv definit -- chol() undefiniert." msgid "Matrices must have same dimensions in %s" msgstr "Matrizen müssen in %s die gleichen Dimensionen haben" msgid "non-conformable matrix dimensions in %s" msgstr "nicht konforme Matrixdimensionen in %s" msgid "dimnames [%d] mismatch in %s" msgstr "dimnames [%d] passen nicht in %s" msgid "Matrices must have same number of rows in %s" msgstr "Matrizen müssen die gleiche Anzahl Zeilen in %s haben" msgid "Matrices must have same number of columns in %s" msgstr "Matrizen müssen die gleiche Anzahl Spalten in %s haben" # erstes %s Spaltennamen zweites %s "..." oder "" #, fuzzy msgid "[[ suppressing %d column names %s ... ]]" msgstr "[[ %d Spaltennamen %s%s werden unterdrückt ]]" # erstes %s Spaltennamen zweites %s "..." oder "" #, fuzzy msgid "[[ suppressing %d column names %s ]]" msgstr "[[ %d Spaltennamen %s%s werden unterdrückt ]]" #, fuzzy msgid "'x' must be \"sparseMatrix\"" msgstr "'x' muss sparseMatrix sein" #, fuzzy msgid "not yet implemented for class %s" msgstr "noch nicht für Klasse implementiert" msgid "not a triangular matrix" msgstr "keine Dreiecksmatrix" msgid "not a symmetric matrix; consider forceSymmetric() or symmpart()" msgstr "" "keine symmetrische Matrix. Erwägen Sie forceSymmetric() oder symmpart()" #, fuzzy msgid "not yet implemented for matrix with typeof %s" msgstr "noch nicht implementiert für Matrix mit typeof" #, fuzzy msgid "not yet implemented for %s" msgstr "noch nicht implementiert für" #, fuzzy msgid "general Matrix class not yet implemented for %s" msgstr "generelle Matrixklasse noch nicht implementiert für" #, fuzzy msgid "" "arguments %s are disregarded in\n" " %s" msgstr "werden nicht berücksichtigt in" msgid "" "Quadratic matrix '%s' (=: A) is not formally\n" "\tsymmetric. Will be treated as\tA A'" msgstr "" "Die quadratische Matrix '%s' (=: A) ist formal\n" " nicht symmetrisch. Wird behandelt wie A A'" msgid "" "'update' must be logical or '+' or '-'; 'C' a matrix, and 'L' a \"CHMfactor\"" msgstr "" "'update' muss entweder boolesch, '+' oder '-' sein; 'C' eine Matrix\n" "und 'L' ein \"CHMfactor\"" msgid "update must be TRUE/FALSE or '+' or '-'" msgstr "update muss entweder TRUE/FALSE, '+' oder '-' sein" msgid "Matrix-internal error in [i,,d]; please report" msgstr "Matrixinterner Fehler in [i,,d]. Bitte berichten" msgid "nothing to replace with" msgstr "nichts zu ersetzen mit" msgid "number of items to replace is not a multiple of replacement length" msgstr "" "Anzahl der zu ersetzenden Elemente ist kein Vielfaches der Austauschlänge" msgid "too many replacement values" msgstr "zu viele Austauschwerte" msgid "i1[1] == 0 ==> C-level verbosity will not happen!" msgstr "i1[1] == 0 ==> C-Ebene wird nicht detailliert sein!" msgid "using\t \"old code\" part in Csparse subassignment" msgstr "benutzt wird\t 'alter Kode'-Teil in Csparse-Unterzuweisung" msgid "" "Cholesky() -> *symbolic* factorization -- not yet implemented" msgstr "" "Cholesky() -> *symbolische* Faktorisierung – noch nicht " "implementiert" msgid "Not a valid format" msgstr "Kein gültiges Format" msgid "'file' must be a character string or connection" msgstr "'file' muss eine Zeichenkette oder Verbindung sein" #, fuzzy msgid "Invalid storage type: %s" msgstr "Falscher Speichertyp:" msgid "Only numeric sparse matrices allowed" msgstr "Nur dünn besetzte Matrizen erlaubt" #, fuzzy msgid "Invalid storage format: %s" msgstr "Ungültiges Speicherformat:" #, fuzzy msgid "Invalid assembled indicator: %s" msgstr "Ungültig zusammengesetzter Indikator:" msgid "file is not a MatrixMarket file" msgstr "Datei ist keine MatrixMarket-Datei" msgid "type '%s' not recognized" msgstr "Typ '%s' nicht erkannt" msgid "representation '%s' not recognized" msgstr "Repräsentation '%s' nicht erkannt" msgid "element type '%s' not recognized" msgstr "Elementtyp '%s' nicht erkannt" msgid "symmetry form '%s' not recognized" msgstr "Symmetrieform '%s' nicht erkannt" msgid "readMM(): row\t values 'i' are not in 1:nr" msgstr "readMM(): Zeile\t Werte 'i' sind nicht in 1:nr" msgid "readMM(): column values 'j' are not in 1:nc" msgstr "readMM(): Spalte\t Werte 'j' sind nicht in 1:nc" msgid "symmetry form 'skew-symmetric' not yet implemented for reading" msgstr "Symmetrieform 'skew-symmetric' noch nicht zum Lesen implementiert" msgid "symmetry form 'hermitian' not yet implemented for reading" msgstr "Symmetrieform 'hermitian' noch nicht zum Lesen implementiert" msgid "symmetry form '%s' is not yet implemented" msgstr "Symmetrieform '%s' noch nicht implementiert" msgid "element type 'complex' not yet implemented" msgstr "Elementtyp 'complex' noch nicht implementiert" msgid "'%s()' is not yet implemented for element type '%s'" msgstr "'%s()' ist noch nicht für Elementtyp '%s' implementiert" msgid "'%s()' is not yet implemented for representation '%s'" msgstr "'%s()' ist noch nicht implementiert für Darstellung '%s'" msgid "trimmed mean of 'sparseVector' -- suboptimally using as.numeric(.)" msgstr "" "getrimmter Mittelwert von 'sparseVector' – suboptimalerweise wird as.numeric" "(.) benutzt" msgid "'V' is not a square matrix" msgstr "'V' ist keine quadratische Matrix" msgid "diag(.) had 0 or NA entries; non-finite result is doubtful" msgstr "" "diag(.) hatte 0 oder NA Einträge. Nicht-endliches Ergebnis ist zweifelhaft" #, fuzzy msgid "invalid dimnames given for %s object" msgstr "ungültige dimnames für Objekt '%s' gegeben" #, fuzzy msgid "" "dimnames(.) <- NULL: translated to \n" "dimnames(.) <- list(NULL,NULL) <==> unname(.)" msgstr "dimnames(.) <- list(NULL,NULL) <==> unname(.)" msgid "'nrow', 'ncol', etc, are disregarded when 'data' is \"Matrix\" already" msgstr "" "'nrow', 'ncol', etc werden nicht berücksichtigt, wenn 'data' bereits " "'Matrix' ist" msgid "invalid 'data'" msgstr "ungültiges 'data'" msgid "'nrow', 'ncol', etc, are disregarded for matrix 'data'" msgstr "'nrow', 'ncol', etc werden nicht für Matrix 'data' berücksichtigt" msgid "complex matrices not yet implemented in Matrix package" msgstr "komplexe Matrizen noch nicht im Matrixpaket implementiert" msgid "using slow kronecker() method" msgstr "langsame kronecker()-Methode wird benutzt" msgid "" "Cholesky(A) called for 'A' of class \"%s\";\n" "\t it is currently defined for sparseMatrix only; consider using chol() " "instead" msgstr "" "Cholesky(A) für 'A' der Klasse \"%s\" aufgerufen;\n" "\t es ist derzeit nur für sparseMatrix definiert; erwägen Sie, chol() zu " "benutzen " msgid "'lag' and 'differences' must be integers >= 1" msgstr "'lag' und 'differences' müssen Ganzzahlen >=1 sein" msgid "programming error: min() should have dispatched w/ 1st arg much earlier" msgstr "" "Programmierfehler: min() ohne erstes Argument hätte eher abgefangen\n" "sein müssen" msgid "invalid or not-yet-implemented 'Matrix' subsetting" msgstr "ungültige oder noch nicht implementierte 'Matrix'-Untermenge" msgid "[ ] : .M.sub.i.logical() maybe inefficient" msgstr "[ ] : .M.sub.i.logical() könnte ineffizient sein" msgid "" "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.logical)?" msgstr "" "nargs() = %d. Irrelevante ungültige Argumente innerhalb '[ .. ]' (i.logical)?" msgid "m[ ]: inefficiently indexing single elements" msgstr "m[ ]: ineffiziente Indexierung einzelner Elemente" msgid "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.2col)?" msgstr "" "nargs() = %d. Irrelevante ungültige Argumente innerhalb '[ .. ]' (i.2col)?" #, fuzzy msgid "" ".M.sub.i.2col(): 'i' has no integer column number;\n" " should never happen; please report" msgstr ".M.sub.i.2col(): 'i' hat keine ganzzahlige Spaltennummer." msgid "such indexing must be by logical or 2-column numeric matrix" msgstr "" "solche Indexierung muss von logischer oder 2-spaltig numerischer Matrix sein" #, fuzzy msgid "" ".M.repl.i.2col(): 'i' has no integer column number;\n" " should never happen; please report" msgstr ".M.repl.i.2col(): 'i' hat keine ganzzahlige Spaltennummer." msgid ".M.repl.i.2col(): drop 'matrix' case ..." msgstr ".M.repl.i.2col(): 'matrix'-Fall weglassen ..." msgid "negative values are not allowed in a matrix subscript" msgstr "negative Werte sind in einer Matrix-Subskript nicht erlaubt" msgid "NAs are not allowed in subscripted assignments" msgstr "NAs sind in indexierten Anweisungen nicht erlaubt" msgid "m[ ] <- v: inefficiently treating single elements" msgstr "m[ ] <- v: Einzelne Elemente ineffizient behandelt" msgid "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' ?" msgstr "nargs() = %d. Irrelevante ungültige Argumente innerhalb '[ .. ]'?" msgid "RHS 'value' (class %s) matches 'ANY', but must match matrix class %s" msgstr "" "RHS 'value' (Klasse %s) passt zu 'ANY', muss aber zur Matrixklasse %s passen" msgid "not-yet-implemented 'Matrix[<-' method" msgstr "noch nicht implementierte 'Matrix[<-'-Methode" msgid "inefficient method used for \"- e1\"" msgstr "ineffiziente Methode für '- e1' benutzt" #, fuzzy msgid " %s %s is undefined" msgstr " ist undefiniert" msgid "internal bug in \"Compare\" method (Cmp.Mat.atomic); please report" msgstr "" "interner Fehler in der \"Compare\"-Methode (Cmp.Mat.atomic). Bitte berichten" msgid "Cmp.Mat.atomic() should not be called for diagonalMatrix" msgstr "Cmp.Mat.atomic() sollte nicht für diagonalMatrix aufgerufen werden" msgid "Matrices must have same number of rows for arithmetic" msgstr "Matrizen müssen für Arithmetik die gleiche Anzahl Zeilen haben" #, fuzzy msgid "number of rows are not compatible for %s" msgstr "Anzahl der Zeilen ist nicht kompatibel für" msgid "length of 2nd arg does not match dimension of first" msgstr "Länge des zweiten Arguments passt nicht zur Dimension des ersten" msgid "length of 1st arg does not match dimension of 2nd" msgstr "Länge des ersten arg passt nicht zur Dimension des zweiten" msgid "internal bug in \"Logic\" method (Logic.Mat.atomic); please report" msgstr "" "interner Fehler in der \"Logic\"-Methode (.Logic.Mat.atomic). Bitte berichten" msgid "Logic.Mat.atomic() should not be called for diagonalMatrix" msgstr "Logic.mat.atomic() sollte für diagonalMatrix nicht aufgerufen werden" msgid "vector too long in Matrix - vector operation" msgstr "Vektor zu lang in der Matrix - Vektor Operation" msgid "" "longer object length\n" "\tis not a multiple of shorter object length" msgstr "" "längere Objektlänge\n" "\tist kein Vielfaches der kürzeren Objektlänge" #, fuzzy msgid "%s %s is undefined" msgstr " ist undefiniert" msgid "longer object length" msgstr "längere Objektlänge" msgid "is not a multiple of shorter object length" msgstr "ist kein Vielfaches der kürzeren Objektlänge" msgid "dim [product %d] do not match the length of object [%d]" msgstr "dim [produkt %d] passt nicht zur Länge des Objekts [%d]" #, fuzzy msgid "invalid class: %s" msgstr "ungültige Klasse:" msgid "not-yet-implemented coercion to \"TsparseMatrix\"" msgstr "noch nicht implementierte Typumwandlung zu 'TsparseMatrix'" msgid "you cannot mix negative and positive indices" msgstr "Sie können positive und negative Indizes nicht mischen" #, fuzzy msgid "index larger than maximal %d" msgstr "Index größer als maximal" msgid "'NA' indices are not (yet?) supported for sparse Matrices" msgstr "" "'NA'-Indizes werden (noch?) nicht für dünn besetzte Matrizen unterstützt" msgid "logical subscript too long (%d, should be %d)" msgstr "logisches Subskript zu lang (%d, sollte %d sein)" msgid "no 'dimnames[[.]]': cannot use character indexing" msgstr "keine 'dimnames[[.]]': Zeichenindexierung kann nicht benutzt werden" msgid "invalid character indexing" msgstr "ungültige Zeichenindexierung" msgid "Matrix-internal error in [i,,d]; please report" msgstr "Matrixinterner Fehler in [i,,d]; Bitte berichten" msgid "FIXME: NOT YET FINISHED IMPLEMENTATION" msgstr "ZU ERLEDIGEN: NOCH NICHT ABGESCHLOSSENE IMPLEMENTIERUNG" msgid "internal bug: missing 'i' in replTmat(): please report" msgstr "interner Fehler: Fehlendes 'i' in replTmat(): Bitte berichten" msgid "[ ] indexing not allowed: forgot a \",\" ?" msgstr "[ ] Indexierung nicht erlaubt: Ein ',' vergessen?" msgid "internal bug: matrix 'i' in replTmat(): please report" msgstr "interner Fehler: Matrix 'i' in replTmat(): Bitte berichten" #, fuzzy msgid "" "x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced; NA |--> TRUE." msgstr "" "x[.] <- val: x ist \"%s\", val nicht in {TRUE, FALSE} wird umgewandelt%s" #, fuzzy msgid "x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced." msgstr "" "x[.] <- val: x ist \"%s\", val nicht in {TRUE, FALSE} wird umgewandelt%s" #, fuzzy msgid "" "x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced NA |--> TRUE." msgstr "" "x[.,.] <- val: x ist \"%s\", val nicht in {TRUE, FALSE} wird umgewandelt%s" #, fuzzy msgid "x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced." msgstr "" "x[.,.] <- val: x ist \"%s\", val nicht in {TRUE, FALSE} wird umgewandelt%s" msgid "x[.,.] <- val : x being coerced from Tsparse* to CsparseMatrix" msgstr "x[.,.] <- val : x wird von Tsparse* in CsparseMatrix umgewandelt" msgid "nargs() = %d should never happen; please report." msgstr "nargs() = %d sollte niemals vorkommen. Bitte berichten." #, fuzzy msgid "row indices must be <= nrow(.) which is %d" msgstr "Zeilenindizes müssen <= nrow(.) sein. Dies ist" #, fuzzy msgid "column indices must be <= ncol(.) which is %d" msgstr "Spaltenindizes müssen <= ncol(.) sein. Dies ist" msgid "'force' must be (coercable to) TRUE or FALSE" msgstr "'force' muss (mindestens umwandelbar nach) TRUE oder FALSE sein" msgid "invalid (to - from)/by in seq(.)" msgstr "unzulässiges (to - from)/by in seq(.)" msgid "wrong sign in 'by' argument" msgstr "falsches Vorzeichen im Argument 'by'" msgid "'by' argument is much too small" msgstr "Argument 'by' ist zu klein" msgid "length must be non-negative number" msgstr "Länge muss eine nicht negative Zahl sein" msgid "too many arguments" msgstr "zu viele Argumente" msgid "c(,..) of different kinds, coercing all to 'rleDiff'" msgstr "" "c(,..) von unterschiedlichen Arten, alle werden in 'rleDiff' " "umgewandelt" msgid "[i] is not yet implemented" msgstr "[i] ist noch nicht implementiert" msgid "all() is not yet implemented" msgstr "all() ist noch nicht implementiert" msgid "sum() is not yet implemented" msgstr "sum() ist noch nicht implementiert" msgid "prod() is not yet implemented" msgstr "prod() ist noch nicht implementiert" msgid "not yet implemented" msgstr "noch nicht implementiert" #, fuzzy msgid "" "x / 0 for an x with sign-change\n" " no longer representable as 'rleDiff'" msgstr "x / 0 für ein x mit Vorzeichenwechsel" msgid " --> is not yet implemented" msgstr " --> ist noch nicht implementiert" msgid " --> is not yet implemented" msgstr " --> ist noch nicht implementiert" msgid "'diagonals' matrix must have %d columns (= length(k) )" msgstr "'diagonals'-Matrix muss %d Spalten haben (= length(k) )" msgid "'diagonals' must have the same length (%d) as 'k'" msgstr "'diagonals' muss die gleiche Länge (%d) wie 'k' haben" msgid "" "for symmetric band matrix, only specify upper or lower triangle\n" " hence, all k must have the same sign" msgstr "" "geben Sie für symmetrische Bandmatrizen nur oberes oder unteres Dreieck an.\n" " deshalb müssen alle k dasselbe Vorzeichen haben." msgid "the %d-th (sub)-diagonal (k = %d) is too short; filling with NA's" msgstr "die %d-te (Unter)-Diagonale (k = %d) ist zu kurz und wird mit NA aufgefüllt" msgid "'A' must be a square matrix" msgstr "'A' muss eine quadratische Matrix sein" msgid "must either specify 'A' or the functions 'A.x' and 'At.x'" msgstr "muss entweder 'A' angeben oder die Funktionen 'A.x' und 'At.x'" msgid "when 'A' is specified, 'A.x' and 'At.x' are disregarded" msgstr "wenn 'A' angegeben wurde, werden 'A.x' und 'At.x' nicht berücksichtigt" msgid "not converged in %d iterations" msgstr "nicht konvergiert in %d Iterationsschritten" msgid "hit a cycle (1) -- stop iterations" msgstr "auf einen Zyklus getroffen (1) – Iterationen stoppen" msgid "hit a cycle (2) -- stop iterations" msgstr "auf einen Zyklus getroffen (2) – Iterationen stoppen" msgid "not enough new vecs -- stop iterations" msgstr "nicht genügend neue Vektoren – Iterationen stoppen" msgid "\"dMatrix\" object with NAs cannot be coerced to \"nMatrix\"" msgstr "" "\"dMatrix\"-Objekt mit NAs kann nicht in \"nMatrix\" umgewandelt werden" msgid "diagonalMatrix in .dense2C() -- should never happen, please report!" msgstr "" "diagonalMatrix in .dense2C() -- sollte niemals vorkommen. Bitte berichten." #, fuzzy msgid "undefined method for class %s" msgstr "undefinierte Methode für Klasse" msgid "dim(.) value must be numeric of length 2" msgstr "dim(.)-Wert muss numerisch sein und von die Länge 2 haben" msgid "dimensions don't match the number of cells" msgstr "Dimensionen passen nicht zur Anzahl der Zellen" #, fuzzy msgid "invalid nargs()= %d" msgstr "ungültige nargs()=" msgid "" "LU computationally singular: ratio of extreme entries in |diag(U)| = %9.4g" msgstr "" "Die LU Zerlegung ist computational singulär; Quotient der extremen Elemente von |diag(U)| = %9.4g" #, fuzzy msgid "cannot coerce non-symmetric \"dgTMatrix\" to \"dsCMatrix\" class" msgstr "" "nicht symmetrische dgTMatrix kann nicht zu dsCMatrix umgewandelt werden" msgid "the matrix is not triangular" msgstr "die Matrix ist nicht dreieckig" msgid "'lwd' must be NULL or non-negative numeric" msgstr "'lwd' muss NULL oder nicht negativ numerisch sein" msgid "'x' has invalid data type" msgstr "'x' hat ungültigen Datentyp" msgid "length(x) must be either 1 or #{cols}" msgstr "length(x) muss 1 oder #{cols} sein" msgid "some arguments are not matrices" msgstr "einige Argumente sind keine Matrizen" #, fuzzy msgid "%s kind not yet implemented" msgstr "'-Art noch nicht implementiert" msgid "non-square matrix" msgstr "nicht quadratische Matrix" #, fuzzy msgid "" "matrix with non-zero off-diagonals cannot be coerced to \"diagonalMatrix\"" msgstr "" "Matrix mit Nichtdiagonalelementen ungleich null kann nicht in \"diagonalMatrix\" " "umgewandelt werden" msgid "matrix is not diagonal" msgstr "Matrix ist nicht diagonal" msgid "Internal bug: nargs()=%d; please report" msgstr "Interner Fehler: nargs()=%d; bitte melden" msgid "chol() is undefined for diagonal matrix with negative entries" msgstr "chol() ist undefiniert für diagonale Matrix mit negativen Einträgen" msgid "non-matching dimensions" msgstr "nicht passende Dimensionen" msgid "incompatible matrix dimensions" msgstr "inkompatible Matrixdimensionen" msgid "intermediate 'r' is of type %s" msgstr "Zwischenergebnis 'r' ist vom Typ %s" msgid "not yet implemented .. please report" msgstr "noch nicht implementiert ... bitte melden" msgid "not a positive definite matrix" msgstr "keine positiv definite Matrix" #, fuzzy msgid "" "as(.,\"dsCMatrix\") is deprecated (since 2008); do use as(., " "\"symmetricMatrix\")" msgstr "" "as(.,'dsCMatrix') ist missbilligt. Benutzen Sie as(., 'symmetricMatrix')" msgid "inefficient coercion (lost triangularity); please report" msgstr "ineffiziente Umwandlung (verlorene Dreieckigkeit). Bitte berichten" #, fuzzy msgid "coercion to \"indMatrix\" only works from integer numeric" msgstr "Umwandlung zu \"indMatrix\" funktioniert nur von ganzzahligen numerischen Vektoren" msgid "" "coercion from list(i1,...,ik, d) to \"indMatrix\" failed.\n" " All entries must be integer valued and the number of columns, d, not " "smaller\n" " than the maximal index i*." msgstr "" "Umwandlung von list(i1,...,ik, d) zu \"indMatrix\" gescheitert.\n" " Alle Elemente müssen ganzzahlig sein und die Anzahl Spalten, d, nicht kleiner\n" " als der maximale Index i*." msgid "not a skinny matrix" msgstr "keine lange (\"skinny\") Matrix" msgid "the number of non-zero entries differs from nrow(.)" msgstr "die Anzahl der Nicht-Null-Einträge weicht von nrow(.) ab" msgid "must have exactly one non-zero entry per row" msgstr "muss genau einen Nicht-Null-Eintrag pro Zeile haben" msgid "kronecker method must use default 'FUN'" msgstr "kronecker-Methode muss Standard 'FUN' benutzen" msgid "replacing \"indMatrix\" entries is not allowed, as rarely sensible" msgstr "" "Ersetzen von \"indMatrix\"-Einträgen ist nicht erlaubt, da selten sinnvoll" msgid "\"lMatrix\" object with NAs cannot be coerced to \"nMatrix\"" msgstr "'lMatrix'-Objekt mit NAs kann nicht zu 'nMatrix' umgewandelt werden" msgid "Matrix seems negative semi-definite" msgstr "Matrix scheint negativ semidefinit zu sein" #, fuzzy msgid "'nearPD()' did not converge in %d iterations" msgstr "nearPD() näherte sich nicht an in" msgid "cannot coerce 'NA's to \"nsparseMatrix\"" msgstr "'NA's können nicht in \"nsparseMatrix\" umgewandelt werden" msgid "temporarily disabled" msgstr "zeitweise ausgeschaltet" #, fuzzy msgid "coercion to \"pMatrix\" only works from integer numeric" msgstr "Umwandlung zu 'pMatrix' funktioniert nur von ganzzahlig numerisch" msgid "not a square matrix" msgstr "keine quadratische Matrix" msgid "not-yet-implemented method for <%s> %%*%% <%s>" msgstr "noch nicht implementierte Methode für <%s> %%*%% <%s>" msgid "" "rankMatrix(, method = '%s') coerces to dense matrix.\n" " Probably should rather use method = 'qr' !?" msgstr "" msgid "rankMatrix(x, method='qr'): computing t(x) as nrow(x) < ncol(x)" msgstr "rankMatrix(x, method='qr'): t(x) berechnet, da nrow(x) < ncol(x)" msgid "model frame and formula mismatch in model.matrix()" msgstr "Model-Frame und Formel passen nicht zusammen in model.matrix()" msgid "variable '%s' converted to a factor" msgstr "Variable '%s' konvertiert in einen Faktor" msgid "invalid 'contrasts.arg' argument" msgstr "unzulässiges 'contrasts.arg' Argument" msgid "variable '%s' is absent, its contrast will be ignored" msgstr "Variable '%s' fehlt, ihr Kontrast wird irgnoriert" msgid "only 2-dimensional tables can be directly coerced to sparse matrices" msgstr "" "nur 2-dimensionale Tabellen könne direkt in eine dünn besetzte Matrix\n" "umgewandelt werden" msgid "exactly one of 'i', 'j', or 'p' must be missing from call" msgstr "exakt eins von 'i', 'j' oder 'p' muss vom Aufruf fehlen" msgid "'p' must be a non-decreasing vector (0, ...)" msgstr "'p' muss ein nicht abnehmender Vektor (0, ...) sein" msgid "NA's in (i,j) are not allowed" msgstr "NAs sind in (i,j) nicht erlaubt" msgid "symmetric matrix must be square" msgstr "symmetrische Matrix muss quadratisch sein" msgid "length(i) is not a multiple of length(x)" msgstr "length(i) ist kein Vielfaches von length(x)" msgid "only square matrices can be used as incidence matrices for graphs" msgstr "" "nur quadratische Matrizen können als Inzidenzmatrizen für Graphen benutzt " "werden" msgid "Matrix-internal error in [i,,d]; please report" msgstr "Matrixinterner Fehler in [i,,d]. Bitte berichten" #, fuzzy msgid "invalid 'col.names' string: %s" msgstr "ungültige 'col.names'-Zeichenkette:" msgid "logic programming error in printSpMatrix2(), please report" msgstr "logischer Programmierungsfehler in printSpMatrix2(), bitte berichten" msgid "invalid 'type'" msgstr "ungültiger 'type'" msgid "rcond(.) via sparse -> dense coercion" msgstr "rcond(.) über Umwandlung dünn besetzt -> dicht besetzt" msgid "'V' is not a *square* matrix" msgstr "'V' ist keine *quadratische* Matrix" #, fuzzy msgid "" "qr.R() may differ from qr.R() because of permutations. " "Possibly use our qrR() instead" msgstr "" "qr.R() könnte von qr.R() aufgrund von Permutationen abweichen" msgid "cannot coerce 'NA's to \"nsparseVector\"" msgstr "Kann NAs nicht in 'nsparseVector' umwandeln" msgid "'x' must inherit from \"sparseVector\"" msgstr "'x' muss von \"sparseVector\" geerbt sein" msgid "'ncol' must be >= 0" msgstr "'ncol' muss >= 0 sein" msgid "'nrow' must be >= 0" msgstr "'nrow' muss >= 0 sein" msgid "Must specify 'nrow' when 'symmetric' is true" msgstr "'nrow' muss angegeben werden, wenn 'symmetric' auf true gesetzt ist" msgid "'nrow' and 'ncol' must be the same when 'symmetric' is true" msgstr "" "'nrow' und 'ncol' müssen gleich sein, wenn 'symmetric' auf true gesetzt ist" msgid "'x' must have length nrow^2 when 'symmetric' is true" msgstr "'x' muss die Länge nrow^2, wenn 'symmetric' auf true gesetzt ist" msgid "'ncol' is not a factor of length(x)" msgstr "'ncol' ist kein Faktor der length(x)" msgid "'nrow' is not a factor of length(x)" msgstr "'nrow' ist kein Faktor der length(x)" #, fuzzy msgid "Class %s is not yet implemented" msgstr "Klasse '%s' noch nicht implementiert" msgid "" "index must be numeric, logical or sparseVector for indexing sparseVectors" msgstr "" "Index muss numerisch, logisch oder sparseVector sein, um sparseVector zu " "indizieren" msgid "'times >= 0' is required" msgstr "'times >= 0' wird benötigt" msgid "(un)packing only applies to dense matrices, class(x)='%s'" msgstr "" "(ent)packen ist nur für dicht besetzte Matrizen anwendbar, class(x)='%s'" msgid "'x' is not symmetric nor triangular" msgstr "'x' ist weder symmetrisch noch in Dreiecksform" #~ msgid "duplicate ij-entries in 'Matrix[ ij ] <- value'; using last" #~ msgstr "" #~ "doppelte ij-Einträge in 'Matrix[ IJ ] <- value'. Letzter wird benutzt" #, fuzzy #~ msgid "method %s not applicable for qr() result class %s" #~ msgstr "Methode '%s' nicht nutzbar für das qr() Ergebniss der Klasse '%s'" #, fuzzy #~ msgid "too large index i > n = %d" #~ msgstr "zu großer Index i > n =" #~ msgid "," #~ msgstr "," #~ msgid "..." #~ msgstr "..." #~ msgid "arguments" #~ msgstr "Argumente" #~ msgid ")$" #~ msgstr ")$" #~ msgid "^list\\(" #~ msgstr "^list\\\\(" #~ msgid "dimnames(.) <- NULL: translated to" #~ msgstr "dimnames(.) <- NULL: übersetzt zu" #~ msgid "in Summary(, .): %s(<%s>, <%s>%s)" #~ msgstr "in Summary(, .): %s(<%s>, <%s>%s)" #~ msgid ", ..." #~ msgstr ", ..." #~ msgid "should never happen; please report" #~ msgstr "Sollte niemals vorkommen. Bitte berichten." #~ msgid "" #~ msgstr "" #~ msgid "(0) is undefined" #~ msgstr "(0) ist undefiniert" #~ msgid "(0)" #~ msgstr "(0)" #~ msgid "no longer representable as 'rleDiff'" #~ msgstr "nicht länger als 'rleDiff' darstellbar" #~ msgid "hence, all k must have the same sign" #~ msgstr "daher müssen alle k das Zeichen haben" #~ msgid "too short; filling with NA's" #~ msgstr "zu kurz. Wird mit NAs gefüllt" #~ msgid "iterations" #~ msgstr "Iterationen" #~ msgid "'" #~ msgstr "'" #~ msgid "; please report" #~ msgstr ". Bitte berichten" #~ msgid "type '" #~ msgstr "Typ '" #~ msgid "representation '" #~ msgstr "Entsprechung '" #~ msgid "element type '" #~ msgstr "Elementtyp '" #~ msgid "symmetry form '" #~ msgstr "symmetrische Form '" #~ msgid "numeric()" #~ msgstr "numeric()" #~ msgid "must supply either 'formula' or 'data'" #~ msgstr "entweder 'formula' oder 'data' muss angegeben werden" #~ msgid "'formula' missing or incorrect" #~ msgstr "'formula' fehlt oder ist falsch" #~ msgid "interactions are not allowed" #~ msgstr "Wechselwirkungen sind nicht erlaubt" #~ msgid "xtabs(*, sparse=TRUE) applies only to two-way tables" #~ msgstr "xtabs(*, sparse=TRUE) liefert nur wechselseitige Tabellen" #~ msgid "cbind2() method for (%s,%s) not-yet defined" #~ msgstr "cbind2()-Methode für (%s,%s) noch nicht definiert" #~ msgid "not yet implemented for packed class" #~ msgstr "noch nicht für gepackte Klasse implementiert" #~ msgid "numeric(0)" #~ msgstr "numeric(0)" #~ msgid "'NA's coerced to 'FALSE' in coercion to logical sparse" #~ msgstr "'NA's zu 'FALSE' umwandeln in Umwandlung zu logisch dünne besetzt" #~ msgid "crossprod(x) calculated as x %*% x for sparse, symmetric x" #~ msgstr "" #~ "crossprod(x) berechnete als x %*% x für dünn besetztes,symmetrisches x" #~ msgid "tcrossprod(x) calculated as x %*% x for sparse, symmetric x" #~ msgstr "" #~ "tcrossprod(x) berechnete als x %*% x für dünn besetztes,symmetrisches x" #~ msgid "(j,p) --> RsparseMatrix : not yet implemented" #~ msgstr "(j,p) --> RsparseMatrix : Noch nicht implementiert" #~ msgid "unknown method" #~ msgstr "unbekannte Methode" #~ msgid "indexing out of range 0:" #~ msgstr "Indexierung außerhalb des Bereichs 0:" #~ msgid "nargs() =" #~ msgstr "nargs() =" #~ msgid "nrow * ncol < length(x)" #~ msgstr "'nrow' * ncol < length(x)" #~ msgid "nrow * ncol != length(x)" #~ msgstr "'nrow' * ncol != length(x)" Matrix/po/R-en@quot.po0000644000175100001440000006244212124340341014326 0ustar hornikusers# All this catalog "translates" are quotation characters. # The msgids must be ASCII and therefore cannot contain real quotation # characters, only substitutes like grave accent (0x60), apostrophe (0x27) # and double quote (0x22). These substitutes look strange; see # http://www.cl.cam.ac.uk/~mgk25/ucs/quotes.html # # This catalog translates grave accent (0x60) and apostrophe (0x27) to # left single quotation mark (U+2018) and right single quotation mark (U+2019). # It also translates pairs of apostrophe (0x27) to # left single quotation mark (U+2018) and right single quotation mark (U+2019) # and pairs of quotation mark (0x22) to # left double quotation mark (U+201C) and right double quotation mark (U+201D). # # When output to an UTF-8 terminal, the quotation characters appear perfectly. # When output to an ISO-8859-1 terminal, the single quotation marks are # transliterated to apostrophes (by iconv in glibc 2.2 or newer) or to # grave/acute accent (by libiconv), and the double quotation marks are # transliterated to 0x22. # When output to an ASCII terminal, the single quotation marks are # transliterated to apostrophes, and the double quotation marks are # transliterated to 0x22. # msgid "" msgstr "" "Project-Id-Version: R 2.15.3\n" "Report-Msgid-Bugs-To: bugs.r-project.org\n" "POT-Creation-Date: 2013-03-26 16:27\n" "PO-Revision-Date: 2013-03-26 16:27\n" "Last-Translator: Automatically generated\n" "Language-Team: none\n" "MIME-Version: 1.0\n" "Content-Type: text/plain; charset=UTF-8\n" "Content-Transfer-Encoding: 8bit\n" "Language: en\n" "Plural-Forms: nplurals=2; plural=(n != 1);\n" msgid "invalid 'mod': %s" msgstr "invalid ‘mod’: %s" msgid "" "not-yet-implemented method for %s(<%s>).\n" " ->> Ask the package authors to implement the missing feature." msgstr "" "not-yet-implemented method for %s(<%s>).\n" " ->> Ask the package authors to implement the missing feature." msgid "" "not-yet-implemented method for %s(<%s>, <%s>).\n" " ->> Ask the package authors to implement the missing feature." msgstr "" "not-yet-implemented method for %s(<%s>, <%s>).\n" " ->> Ask the package authors to implement the missing feature." msgid "'x' is not positive definite -- chol() undefined." msgstr "‘x’ is not positive definite -- chol() undefined." msgid "Matrices must have same dimensions in %s" msgstr "Matrices must have same dimensions in %s" msgid "non-conformable matrix dimensions in %s" msgstr "non-conformable matrix dimensions in %s" msgid "dimnames [%d] mismatch in %s" msgstr "dimnames [%d] mismatch in %s" msgid "Matrices must have same number of rows in %s" msgstr "Matrices must have same number of rows in %s" msgid "Matrices must have same number of columns in %s" msgstr "Matrices must have same number of columns in %s" msgid "[[ suppressing %d column names %s ... ]]" msgstr "[[ suppressing %d column names %s ... ]]" msgid "[[ suppressing %d column names %s ]]" msgstr "[[ suppressing %d column names %s ]]" msgid "'x' must be \"sparseMatrix\"" msgstr "‘x’ must be \"sparseMatrix\"" msgid "not yet implemented for class %s" msgstr "not yet implemented for class %s" msgid "not a triangular matrix" msgstr "not a triangular matrix" msgid "not yet implemented for matrix with typeof %s" msgstr "not yet implemented for matrix with typeof %s" msgid "not yet implemented for %s" msgstr "not yet implemented for %s" msgid "general Matrix class not yet implemented for %s" msgstr "general Matrix class not yet implemented for %s" msgid "" "arguments %s are disregarded in\n" " %s" msgstr "" "arguments %s are disregarded in\n" " %s" msgid "" "Quadratic matrix '%s' (=: A) is not formally\n" "\tsymmetric. Will be treated as\tA A'" msgstr "" "Quadratic matrix ‘%s’ (=: A) is not formally\n" "\tsymmetric. Will be treated as\tA A'" msgid "" "'update' must be logical or '+' or '-'; 'C' a matrix, and 'L' a \"CHMfactor\"" msgstr "" "‘update’ must be logical or ‘+’ or ‘-’; ‘C’ a matrix, and ‘L’ a \"CHMfactor\"" msgid "update must be TRUE/FALSE or '+' or '-'" msgstr "update must be TRUE/FALSE or ‘+’ or ‘-’" msgid "not a symmetric matrix; consider forceSymmetric() or symmpart()" msgstr "not a symmetric matrix; consider forceSymmetric() or symmpart()" msgid "Matrix-internal error in [i,,d]; please report" msgstr "Matrix-internal error in [i,,d]; please report" msgid "nothing to replace with" msgstr "nothing to replace with" msgid "number of items to replace is not a multiple of replacement length" msgstr "number of items to replace is not a multiple of replacement length" msgid "too many replacement values" msgstr "too many replacement values" msgid "i1[1] == 0 ==> C-level verbosity will not happen!" msgstr "i1[1] == 0 ==> C-level verbosity will not happen!" msgid "using\t \"old code\" part in Csparse subassignment" msgstr "using\t \"old code\" part in Csparse subassignment" msgid "" "Cholesky() -> *symbolic* factorization -- not yet implemented" msgstr "" "Cholesky() -> *symbolic* factorization -- not yet implemented" msgid "Not a valid format" msgstr "Not a valid format" msgid "'file' must be a character string or connection" msgstr "‘file’ must be a character string or connection" msgid "Invalid storage type: %s" msgstr "Invalid storage type: %s" msgid "Only numeric sparse matrices allowed" msgstr "Only numeric sparse matrices allowed" msgid "Invalid storage format: %s" msgstr "Invalid storage format: %s" msgid "Invalid assembled indicator: %s" msgstr "Invalid assembled indicator: %s" msgid "file is not a MatrixMarket file" msgstr "file is not a MatrixMarket file" msgid "type '%s' not recognized" msgstr "type ‘%s’ not recognized" msgid "representation '%s' not recognized" msgstr "representation ‘%s’ not recognized" msgid "element type '%s' not recognized" msgstr "element type ‘%s’ not recognized" msgid "symmetry form '%s' not recognized" msgstr "symmetry form ‘%s’ not recognized" msgid "readMM(): row\t values 'i' are not in 1:nr" msgstr "readMM(): row\t values ‘i’ are not in 1:nr" msgid "readMM(): column values 'j' are not in 1:nc" msgstr "readMM(): column values ‘j’ are not in 1:nc" msgid "symmetry form 'skew-symmetric' not yet implemented for reading" msgstr "symmetry form ‘skew-symmetric’ not yet implemented for reading" msgid "symmetry form 'hermitian' not yet implemented for reading" msgstr "symmetry form ‘hermitian’ not yet implemented for reading" msgid "symmetry form '%s' is not yet implemented" msgstr "symmetry form ‘%s’ is not yet implemented" msgid "element type 'complex' not yet implemented" msgstr "element type ‘complex’ not yet implemented" msgid "'%s()' is not yet implemented for element type '%s'" msgstr "‘%s()’ is not yet implemented for element type ‘%s’" msgid "'%s()' is not yet implemented for representation '%s'" msgstr "‘%s()’ is not yet implemented for representation ‘%s’" msgid "trimmed mean of 'sparseVector' -- suboptimally using as.numeric(.)" msgstr "trimmed mean of ‘sparseVector’ -- suboptimally using as.numeric(.)" msgid "'V' is not a square matrix" msgstr "‘V’ is not a square matrix" msgid "diag(.) had 0 or NA entries; non-finite result is doubtful" msgstr "diag(.) had 0 or NA entries; non-finite result is doubtful" msgid "invalid dimnames given for %s object" msgstr "invalid dimnames given for %s object" msgid "" "dimnames(.) <- NULL: translated to \n" "dimnames(.) <- list(NULL,NULL) <==> unname(.)" msgstr "" "dimnames(.) <- NULL: translated to \n" "dimnames(.) <- list(NULL,NULL) <==> unname(.)" msgid "'nrow', 'ncol', etc, are disregarded when 'data' is \"Matrix\" already" msgstr "'nrow', ‘ncol’, etc, are disregarded when ‘data’ is \"Matrix\" already" msgid "invalid 'data'" msgstr "invalid ‘data’" msgid "'nrow', 'ncol', etc, are disregarded for matrix 'data'" msgstr "'nrow', ‘ncol’, etc, are disregarded for matrix ‘data’" msgid "complex matrices not yet implemented in Matrix package" msgstr "complex matrices not yet implemented in Matrix package" msgid "using slow kronecker() method" msgstr "using slow kronecker() method" msgid "" "Cholesky(A) called for 'A' of class \"%s\";\n" "\t it is currently defined for sparseMatrix only; consider using chol() " "instead" msgstr "" "Cholesky(A) called for ‘A’ of class \"%s\";\n" "\t it is currently defined for sparseMatrix only; consider using chol() " "instead" msgid "'lag' and 'differences' must be integers >= 1" msgstr "‘lag’ and ‘differences’ must be integers >= 1" msgid "programming error: min() should have dispatched w/ 1st arg much earlier" msgstr "" "programming error: min() should have dispatched w/ 1st arg much earlier" msgid "invalid or not-yet-implemented 'Matrix' subsetting" msgstr "invalid or not-yet-implemented ‘Matrix’ subsetting" msgid "[ ] : .M.sub.i.logical() maybe inefficient" msgstr "[ ] : .M.sub.i.logical() maybe inefficient" msgid "" "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.logical)?" msgstr "" "nargs() = %d. Extraneous illegal arguments inside ‘[ .. ]’ (i.logical)?" msgid "m[ ]: inefficiently indexing single elements" msgstr "m[ ]: inefficiently indexing single elements" msgid "" ".M.sub.i.2col(): 'i' has no integer column number;\n" " should never happen; please report" msgstr "" ".M.sub.i.2col(): ‘i’ has no integer column number;\n" " should never happen; please report" msgid "such indexing must be by logical or 2-column numeric matrix" msgstr "such indexing must be by logical or 2-column numeric matrix" msgid "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.2col)?" msgstr "nargs() = %d. Extraneous illegal arguments inside ‘[ .. ]’ (i.2col)?" msgid "" ".M.repl.i.2col(): 'i' has no integer column number;\n" " should never happen; please report" msgstr "" ".M.repl.i.2col(): ‘i’ has no integer column number;\n" " should never happen; please report" msgid ".M.repl.i.2col(): drop 'matrix' case ..." msgstr ".M.repl.i.2col(): drop ‘matrix’ case ..." msgid "negative values are not allowed in a matrix subscript" msgstr "negative values are not allowed in a matrix subscript" msgid "NAs are not allowed in subscripted assignments" msgstr "NAs are not allowed in subscripted assignments" msgid "m[ ] <- v: inefficiently treating single elements" msgstr "m[ ] <- v: inefficiently treating single elements" msgid "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' ?" msgstr "nargs() = %d. Extraneous illegal arguments inside ‘[ .. ]’ ?" msgid "RHS 'value' (class %s) matches 'ANY', but must match matrix class %s" msgstr "RHS ‘value’ (class %s) matches ‘ANY’, but must match matrix class %s" msgid "not-yet-implemented 'Matrix[<-' method" msgstr "not-yet-implemented ‘Matrix[<-’ method" msgid "inefficient method used for \"- e1\"" msgstr "inefficient method used for \"- e1\"" msgid " %s %s is undefined" msgstr " %s %s is undefined" msgid "internal bug in \"Compare\" method (Cmp.Mat.atomic); please report" msgstr "internal bug in \"Compare\" method (Cmp.Mat.atomic); please report" msgid "Cmp.Mat.atomic() should not be called for diagonalMatrix" msgstr "Cmp.Mat.atomic() should not be called for diagonalMatrix" msgid "Matrices must have same number of rows for arithmetic" msgstr "Matrices must have same number of rows for arithmetic" msgid "number of rows are not compatible for %s" msgstr "number of rows are not compatible for %s" msgid "length of 2nd arg does not match dimension of first" msgstr "length of 2nd arg does not match dimension of first" msgid "length of 1st arg does not match dimension of 2nd" msgstr "length of 1st arg does not match dimension of 2nd" msgid "internal bug in \"Logic\" method (Logic.Mat.atomic); please report" msgstr "internal bug in \"Logic\" method (Logic.Mat.atomic); please report" msgid "Logic.Mat.atomic() should not be called for diagonalMatrix" msgstr "Logic.Mat.atomic() should not be called for diagonalMatrix" msgid "vector too long in Matrix - vector operation" msgstr "vector too long in Matrix - vector operation" msgid "" "longer object length\n" "\tis not a multiple of shorter object length" msgstr "" "longer object length\n" "\tis not a multiple of shorter object length" msgid "%s %s is undefined" msgstr "%s %s is undefined" msgid "longer object length" msgstr "longer object length" msgid "is not a multiple of shorter object length" msgstr "is not a multiple of shorter object length" msgid "dim [product %d] do not match the length of object [%d]" msgstr "dim [product %d] do not match the length of object [%d]" msgid "invalid class: %s" msgstr "invalid class: %s" msgid "not-yet-implemented coercion to \"TsparseMatrix\"" msgstr "not-yet-implemented coercion to \"TsparseMatrix\"" msgid "'NA' indices are not (yet?) supported for sparse Matrices" msgstr "‘NA’ indices are not (yet?) supported for sparse Matrices" msgid "you cannot mix negative and positive indices" msgstr "you cannot mix negative and positive indices" msgid "index larger than maximal %d" msgstr "index larger than maximal %d" msgid "logical subscript too long (%d, should be %d)" msgstr "logical subscript too long (%d, should be %d)" msgid "no 'dimnames[[.]]': cannot use character indexing" msgstr "no ‘dimnames[[.]]’: cannot use character indexing" msgid "invalid character indexing" msgstr "invalid character indexing" msgid "Matrix-internal error in [i,,d]; please report" msgstr "Matrix-internal error in [i,,d]; please report" msgid "FIXME: NOT YET FINISHED IMPLEMENTATION" msgstr "FIXME: NOT YET FINISHED IMPLEMENTATION" msgid "internal bug: missing 'i' in replTmat(): please report" msgstr "internal bug: missing ‘i’ in replTmat(): please report" msgid "[ ] indexing not allowed: forgot a \",\" ?" msgstr "[ ] indexing not allowed: forgot a \",\" ?" msgid "internal bug: matrix 'i' in replTmat(): please report" msgstr "internal bug: matrix ‘i’ in replTmat(): please report" msgid "x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced NA |--> TRUE." msgstr "" "x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced NA |--> TRUE." msgid "x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced." msgstr "x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced." msgid "" "x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced NA |--> TRUE." msgstr "" "x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced NA |--> TRUE." msgid "x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced." msgstr "x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced." msgid "x[.,.] <- val : x being coerced from Tsparse* to CsparseMatrix" msgstr "x[.,.] <- val : x being coerced from Tsparse* to CsparseMatrix" msgid "nargs() = %d should never happen; please report." msgstr "nargs() = %d should never happen; please report." msgid "row indices must be <= nrow(.) which is %d" msgstr "row indices must be <= nrow(.) which is %d" msgid "column indices must be <= ncol(.) which is %d" msgstr "column indices must be <= ncol(.) which is %d" msgid "duplicate ij-entries in 'Matrix[ ij ] <- value'; using last" msgstr "duplicate ij-entries in ‘Matrix[ ij ] <- value’; using last" msgid "'force' must be (coercable to) TRUE or FALSE" msgstr "‘force’ must be (coercable to) TRUE or FALSE" msgid "invalid (to - from)/by in seq(.)" msgstr "invalid (to - from)/by in seq(.)" msgid "wrong sign in 'by' argument" msgstr "wrong sign in ‘by’ argument" msgid "'by' argument is much too small" msgstr "‘by’ argument is much too small" msgid "length must be non-negative number" msgstr "length must be non-negative number" msgid "too many arguments" msgstr "too many arguments" msgid "c(,..) of different kinds, coercing all to 'rleDiff'" msgstr "c(,..) of different kinds, coercing all to ‘rleDiff’" msgid "[i] is not yet implemented" msgstr "[i] is not yet implemented" msgid "all() is not yet implemented" msgstr "all() is not yet implemented" msgid "sum() is not yet implemented" msgstr "sum() is not yet implemented" msgid "prod() is not yet implemented" msgstr "prod() is not yet implemented" msgid "not yet implemented" msgstr "not yet implemented" msgid "" "x / 0 for an x with sign-change\n" " no longer representable as 'rleDiff'" msgstr "" "x / 0 for an x with sign-change\n" " no longer representable as ‘rleDiff’" msgid " --> is not yet implemented" msgstr " --> is not yet implemented" msgid " --> is not yet implemented" msgstr " --> is not yet implemented" msgid "'diagonals' matrix must have %d columns (= length(k) )" msgstr "‘diagonals’ matrix must have %d columns (= length(k) )" msgid "'diagonals' must have the same length (%d) as 'k'" msgstr "‘diagonals’ must have the same length (%d) as ‘k’" msgid "" "for symmetric band matrix, only specify upper or lower triangle\n" " hence, all k must have the same sign" msgstr "" "for symmetric band matrix, only specify upper or lower triangle\n" " hence, all k must have the same sign" msgid "the %d-th (sub)-diagonal (k = %d) is too short; filling with NA's" msgstr "the %d-th (sub)-diagonal (k = %d) is too short; filling with NA's" msgid "'A' must be a square matrix" msgstr "‘A’ must be a square matrix" msgid "must either specify 'A' or the functions 'A.x' and 'At.x'" msgstr "must either specify ‘A’ or the functions ‘A.x’ and ‘At.x’" msgid "when 'A' is specified, 'A.x' and 'At.x' are disregarded" msgstr "when ‘A’ is specified, ‘A.x’ and ‘At.x’ are disregarded" msgid "not converged in %d iterations" msgstr "not converged in %d iterations" msgid "hit a cycle (1) -- stop iterations" msgstr "hit a cycle (1) -- stop iterations" msgid "hit a cycle (2) -- stop iterations" msgstr "hit a cycle (2) -- stop iterations" msgid "not enough new vecs -- stop iterations" msgstr "not enough new vecs -- stop iterations" msgid "\"dMatrix\" object with NAs cannot be coerced to \"nMatrix\"" msgstr "\"dMatrix\" object with NAs cannot be coerced to \"nMatrix\"" msgid "diagonalMatrix in .dense2C() -- should never happen, please report!" msgstr "diagonalMatrix in .dense2C() -- should never happen, please report!" msgid "undefined method for class %s" msgstr "undefined method for class %s" msgid "dim(.) value must be numeric of length 2" msgstr "dim(.) value must be numeric of length 2" msgid "dimensions don't match the number of cells" msgstr "dimensions don't match the number of cells" msgid "invalid nargs()= %d" msgstr "invalid nargs()= %d" msgid "cannot coerce non-symmetric \"dgTMatrix\" to \"dsCMatrix\" class" msgstr "cannot coerce non-symmetric \"dgTMatrix\" to \"dsCMatrix\" class" msgid "the matrix is not triangular" msgstr "the matrix is not triangular" msgid "'lwd' must be NULL or non-negative numeric" msgstr "‘lwd’ must be NULL or non-negative numeric" msgid "'x' has invalid data type" msgstr "‘x’ has invalid data type" msgid "length(x) must be either 1 or #{cols}" msgstr "length(x) must be either 1 or #{cols}" msgid "some arguments are not matrices" msgstr "some arguments are not matrices" msgid "%s kind not yet implemented" msgstr "%s kind not yet implemented" msgid "non-square matrix" msgstr "non-square matrix" msgid "" "matrix with non-zero off-diagonals cannot be coerced to \"diagonalMatrix\"" msgstr "" "matrix with non-zero off-diagonals cannot be coerced to \"diagonalMatrix\"" msgid "matrix is not diagonal" msgstr "matrix is not diagonal" msgid "Internal bug: nargs()=%d; please report" msgstr "Internal bug: nargs()=%d; please report" msgid "chol() is undefined for diagonal matrix with negative entries" msgstr "chol() is undefined for diagonal matrix with negative entries" msgid "non-matching dimensions" msgstr "non-matching dimensions" msgid "incompatible matrix dimensions" msgstr "incompatible matrix dimensions" msgid "intermediate 'r' is of type %s" msgstr "intermediate ‘r’ is of type %s" msgid "not yet implemented .. please report" msgstr "not yet implemented .. please report" msgid "not a positive definite matrix" msgstr "not a positive definite matrix" msgid "" "as(.,\"dsCMatrix\") is deprecated (since 2008); do use as(., " "\"symmetricMatrix\")" msgstr "" "as(.,\"dsCMatrix\") is deprecated (since 2008); do use as(., " "\"symmetricMatrix\")" msgid "inefficient coercion (lost triangularity); please report" msgstr "inefficient coercion (lost triangularity); please report" msgid "kronecker method must use default 'FUN'" msgstr "kronecker method must use default ‘FUN’" msgid "\"lMatrix\" object with NAs cannot be coerced to \"nMatrix\"" msgstr "\"lMatrix\" object with NAs cannot be coerced to \"nMatrix\"" msgid "Matrix seems negative semi-definite" msgstr "Matrix seems negative semi-definite" msgid "'nearPD()' did not converge in %d iterations" msgstr "‘nearPD()’ did not converge in %d iterations" msgid "cannot coerce 'NA's to \"nsparseMatrix\"" msgstr "cannot coerce 'NA's to \"nsparseMatrix\"" msgid "temporarily disabled" msgstr "temporarily disabled" msgid "coercion to \"pMatrix\" only works from integer numeric" msgstr "coercion to \"pMatrix\" only works from integer numeric" msgid "not a square matrix" msgstr "not a square matrix" msgid "the number of non-zero entries differs from nrow(.)" msgstr "the number of non-zero entries differs from nrow(.)" msgid "must have exactly one non-zero entry per row" msgstr "must have exactly one non-zero entry per row" msgid "replacing \"pMatrix\" entries is not allowed, as rarely sensible" msgstr "replacing \"pMatrix\" entries is not allowed, as rarely sensible" msgid "not-yet-implemented method for <%s> %%*%% <%s>" msgstr "not-yet-implemented method for <%s> %%*%% <%s>" msgid "method %s not applicable for qr() result class %s" msgstr "method %s not applicable for qr() result class %s" msgid "model frame and formula mismatch in model.matrix()" msgstr "model frame and formula mismatch in model.matrix()" msgid "variable '%s' converted to a factor" msgstr "variable ‘%s’ converted to a factor" msgid "invalid 'contrasts.arg' argument" msgstr "invalid ‘contrasts.arg’ argument" msgid "variable '%s' is absent, its contrast will be ignored" msgstr "variable ‘%s’ is absent, its contrast will be ignored" msgid "only 2-dimensional tables can be directly coerced to sparse matrices" msgstr "only 2-dimensional tables can be directly coerced to sparse matrices" msgid "exactly one of 'i', 'j', or 'p' must be missing from call" msgstr "exactly one of ‘i’, ‘j’, or ‘p’ must be missing from call" msgid "'p' must be a non-decreasing vector (0, ...)" msgstr "‘p’ must be a non-decreasing vector (0, ...)" msgid "NA's in (i,j) are not allowed" msgstr "NA's in (i,j) are not allowed" msgid "symmetric matrix must be square" msgstr "symmetric matrix must be square" msgid "length(i) is not a multiple of length(x)" msgstr "length(i) is not a multiple of length(x)" msgid "only square matrices can be used as incidence matrices for graphs" msgstr "only square matrices can be used as incidence matrices for graphs" msgid "Matrix-internal error in [i,,d]; please report" msgstr "Matrix-internal error in [i,,d]; please report" msgid "invalid 'col.names' string: %s" msgstr "invalid ‘col.names’ string: %s" msgid "logic programming error in printSpMatrix2(), please report" msgstr "logic programming error in printSpMatrix2(), please report" msgid "invalid 'type'" msgstr "invalid ‘type’" msgid "rcond(.) via sparse -> dense coercion" msgstr "rcond(.) via sparse -> dense coercion" msgid "'V' is not a *square* matrix" msgstr "‘V’ is not a *square* matrix" msgid "" "qr.R() may differ from qr.R() because of permutations. " "Possibly use our qrR() instead" msgstr "" "qr.R() may differ from qr.R() because of permutations. " "Possibly use our qrR() instead" msgid "cannot coerce 'NA's to \"nsparseVector\"" msgstr "cannot coerce 'NA's to \"nsparseVector\"" msgid "'x' must inherit from \"sparseVector\"" msgstr "‘x’ must inherit from \"sparseVector\"" msgid "'ncol' must be >= 0" msgstr "‘ncol’ must be >= 0" msgid "'nrow' must be >= 0" msgstr "‘nrow’ must be >= 0" msgid "Must specify 'nrow' when 'symmetric' is true" msgstr "Must specify ‘nrow’ when ‘symmetric’ is true" msgid "'nrow' and 'ncol' must be the same when 'symmetric' is true" msgstr "‘nrow’ and ‘ncol’ must be the same when ‘symmetric’ is true" msgid "'x' must have length nrow^2 when 'symmetric' is true" msgstr "‘x’ must have length nrow^2 when ‘symmetric’ is true" msgid "'ncol' is not a factor of length(x)" msgstr "‘ncol’ is not a factor of length(x)" msgid "'nrow' is not a factor of length(x)" msgstr "‘nrow’ is not a factor of length(x)" msgid "Class %s is not yet implemented" msgstr "Class %s is not yet implemented" msgid "too large index i > n = %d" msgstr "too large index i > n = %d" msgid "" "index must be numeric, logical or sparseVector for indexing sparseVectors" msgstr "" "index must be numeric, logical or sparseVector for indexing sparseVectors" msgid "'times >= 0' is required" msgstr "‘times >= 0’ is required" msgid "(un)packing only applies to dense matrices, class(x)='%s'" msgstr "(un)packing only applies to dense matrices, class(x)='%s'" msgid "'x' is not symmetric nor triangular" msgstr "‘x’ is not symmetric nor triangular" Matrix/po/en@quot.po0000644000175100001440000007241712124340341014132 0ustar hornikusers# English translations for R package. # Copyright (C) 2013 The R Core Team # This file is distributed under the same license as the R package. # Automatically generated, 2013. # # All this catalog "translates" are quotation characters. # The msgids must be ASCII and therefore cannot contain real quotation # characters, only substitutes like grave accent (0x60), apostrophe (0x27) # and double quote (0x22). These substitutes look strange; see # http://www.cl.cam.ac.uk/~mgk25/ucs/quotes.html # # This catalog translates grave accent (0x60) and apostrophe (0x27) to # left single quotation mark (U+2018) and right single quotation mark (U+2019). # It also translates pairs of apostrophe (0x27) to # left single quotation mark (U+2018) and right single quotation mark (U+2019) # and pairs of quotation mark (0x22) to # left double quotation mark (U+201C) and right double quotation mark (U+201D). # # When output to an UTF-8 terminal, the quotation characters appear perfectly. # When output to an ISO-8859-1 terminal, the single quotation marks are # transliterated to apostrophes (by iconv in glibc 2.2 or newer) or to # grave/acute accent (by libiconv), and the double quotation marks are # transliterated to 0x22. # When output to an ASCII terminal, the single quotation marks are # transliterated to apostrophes, and the double quotation marks are # transliterated to 0x22. # msgid "" msgstr "" "Project-Id-Version: R 2.15.3\n" "Report-Msgid-Bugs-To: bugs.r-project.org\n" "POT-Creation-Date: 2013-03-26 16:27+0100\n" "PO-Revision-Date: 2013-03-26 16:27+0100\n" "Last-Translator: Automatically generated\n" "Language-Team: none\n" "Language: en\n" "MIME-Version: 1.0\n" "Content-Type: text/plain; charset=UTF-8\n" "Content-Transfer-Encoding: 8bit\n" "Plural-Forms: nplurals=2; plural=(n != 1);\n" #: CHMfactor.c:14 #, c-format msgid "cholmod_change_factor failed with status %d" msgstr "cholmod_change_factor failed with status %d" #: CHMfactor.c:30 CHMfactor.c:60 msgid "system argument is not valid" msgstr "system argument is not valid" #: CHMfactor.c:47 #, c-format msgid "cholmod_updown() returned %d" msgstr "cholmod_updown() returned %d" #: CHMfactor.c:97 #, c-format msgid "diagonal element %d of Cholesky factor is missing" msgstr "diagonal element %d of Cholesky factor is missing" #: CHMfactor.c:135 #, c-format msgid "cholmod_factorize_p failed: status %d, minor %d of ncol %d" msgstr "cholmod_factorize_p failed: status %d, minor %d of ncol %d" #: CHMfactor.c:140 msgid "cholmod_change_factor failed" msgstr "cholmod_change_factor failed" #: Csparse.c:58 msgid "slot p must have length = ncol(.) + 1" msgstr "slot p must have length = ncol(.) + 1" #: Csparse.c:60 Csparse.c:119 msgid "first element of slot p must be zero" msgstr "first element of slot p must be zero" #: Csparse.c:63 msgid "last element of slot p must match length of slots i and x" msgstr "last element of slot p must match length of slots i and x" #: Csparse.c:66 msgid "all row indices must be between 0 and nrow-1" msgstr "all row indices must be between 0 and nrow-1" #: Csparse.c:71 Csparse.c:130 msgid "slot p must be non-decreasing" msgstr "slot p must be non-decreasing" #: Csparse.c:92 msgid "" "slot i is not *strictly* increasing inside a column (even after " "cholmod_l_sort)" msgstr "" "slot i is not *strictly* increasing inside a column (even after " "cholmod_l_sort)" #: Csparse.c:95 msgid "row indices are not sorted within columns" msgstr "row indices are not sorted within columns" #: Csparse.c:98 msgid "slot i is not *strictly* increasing inside a column" msgstr "slot i is not *strictly* increasing inside a column" #: Csparse.c:117 msgid "slot p must have length = nrow(.) + 1" msgstr "slot p must have length = nrow(.) + 1" #: Csparse.c:122 msgid "last element of slot p must match length of slots j and x" msgstr "last element of slot p must match length of slots j and x" #: Csparse.c:125 msgid "all column indices must be between 0 and ncol-1" msgstr "all column indices must be between 0 and ncol-1" #: Csparse.c:141 msgid "slot j is not increasing inside a column" msgstr "slot j is not increasing inside a column" #: Csparse.c:143 msgid "slot j is not *strictly* increasing inside a column" msgstr "slot j is not *strictly* increasing inside a column" #: Csparse.c:188 msgid "not a 'n.CMatrix'" msgstr "not a ‘n.CMatrix’" #: Csparse.c:189 msgid "not a CsparseMatrix" msgstr "not a CsparseMatrix" #: Csparse.c:216 #, c-format msgid "nz2Csparse(): invalid/non-implemented r_kind = %d" msgstr "nz2Csparse(): invalid/non-implemented r_kind = %d" #: Csparse.c:261 msgid "Nonsymmetric matrix in Csparse_symmetric_to_general" msgstr "Nonsymmetric matrix in Csparse_symmetric_to_general" #: Csparse.c:272 msgid "Csparse_general_to_symmetric(): matrix is not square!" msgstr "Csparse_general_to_symmetric(): matrix is not square!" #: Csparse.c:463 msgid "Csparse_crossprod(): error return from cholmod_aat()" msgstr "Csparse_crossprod(): error return from cholmod_aat()" #: Csparse.c:495 msgid "cholmod_drop() failed" msgstr "cholmod_drop() failed" #: Csparse.c:608 msgid "Index i must be NULL or integer" msgstr "Index i must be NULL or integer" #: Csparse.c:610 msgid "Index j must be NULL or integer" msgstr "Index j must be NULL or integer" #: Csparse.c:652 #, c-format msgid "failure to open file \"%s\" for writing" msgstr "failure to open file \"%s\" for writing" #: Csparse.c:656 msgid "cholmod_write_sparse returned error code" msgstr "cholmod_write_sparse returned error code" #: Csparse.c:729 #, c-format msgid "%s = '%s' (back-permuted) is experimental" msgstr "%s = ‘%s’ (back-permuted) is experimental" #: Csparse.c:739 msgid "diag_tC(): invalid 'resultKind'" msgstr "diag_tC(): invalid ‘resultKind’" #: Csparse.c:800 #, c-format msgid "negative vector lengths not allowed: np = %d, nnz = %d" msgstr "negative vector lengths not allowed: np = %d, nnz = %d" #: Csparse.c:805 msgid "exactly 1 of 'i', 'j' or 'p' must be NULL" msgstr "exactly 1 of ‘i’, ‘j’ or ‘p’ must be NULL" #: Csparse.c:807 #, c-format msgid "np = %d, must be zero when p is NULL" msgstr "np = %d, must be zero when p is NULL" #: Csparse.c:810 #, c-format msgid "p[0] = %d, should be zero" msgstr "p[0] = %d, should be zero" #: Csparse.c:813 msgid "p must be non-decreasing" msgstr "p must be non-decreasing" #: Csparse.c:829 #, c-format msgid "Inconsistent dimensions: np = 0 and nnz = %d" msgstr "Inconsistent dimensions: np = 0 and nnz = %d" #: Csparse.c:837 #, c-format msgid "invalid row index at position %d" msgstr "invalid row index at position %d" #: Csparse.c:844 #, c-format msgid "invalid column index at position %d" msgstr "invalid column index at position %d" #: Csparse.c:854 #, c-format msgid "strlen of cls argument = %d, should be 8" msgstr "strlen of cls argument = %d, should be 8" #: Csparse.c:856 #, c-format msgid "cls = \"%s\" does not end in \"CMatrix\"" msgstr "cls = \"%s\" does not end in \"CMatrix\"" #: Csparse.c:866 #, c-format msgid "cls = \"%s\" must begin with 'd', 'l' or 'n'" msgstr "cls = \"%s\" must begin with ‘d’, ‘l’ or ‘n’" #: Csparse.c:869 msgid "Only 'g'eneral sparse matrix types allowed" msgstr "Only 'g'eneral sparse matrix types allowed" #: Csparse.c:897 msgid "code not yet written for cls = \"lgCMatrix\"" msgstr "code not yet written for cls = \"lgCMatrix\"" #: Mutils.c:14 Mutils.c:33 #, c-format msgid "argument type[1]='%s' must be a one-letter character string" msgstr "argument type[1]='%s' must be a one-letter character string" #: Mutils.c:22 #, c-format msgid "argument type[1]='%s' must be one of 'M','1','O','I','F' or 'E'" msgstr "argument type[1]='%s' must be one of ‘M’,'1','O','I','F' or ‘E’" #: Mutils.c:39 #, c-format msgid "argument type[1]='%s' must be one of '1','O', or 'I'" msgstr "argument type[1]='%s' must be one of ‘1’,'O', or ‘I’" #: Mutils.c:50 Mutils.c:66 msgid "object must be a named, numeric vector" msgstr "object must be a named, numeric vector" #: Mutils.c:113 Mutils.c:133 msgid "'factors' slot must be a named list" msgstr "‘factors’ slot must be a named list" #: Mutils.c:241 #, c-format msgid "'%s' slot must have length 1" msgstr "‘%s’ slot must have length 1" #: Mutils.c:245 #, c-format msgid "'%s' must have string length 1" msgstr "‘%s’ must have string length 1" #: Mutils.c:252 #, c-format msgid "'%s' must be in '%s'" msgstr "‘%s’ must be in ‘%s’" #: Mutils.c:271 msgid "'s1' and 's2' must be \"character\" vectors" msgstr "‘s1’ and ‘s2’ must be \"character\" vectors" #: Mutils.c:293 msgid "length of x slot != prod(Dim)" msgstr "length of x slot != prod(Dim)" #: Mutils.c:314 Mutils.c:340 msgid "'uplo' must be UPP or LOW" msgstr "‘uplo’ must be UPP or LOW" #: Mutils.c:627 #, c-format msgid "invalid class '%s' to dup_mMatrix_as_geMatrix" msgstr "invalid class ‘%s’ to dup_mMatrix_as_geMatrix" #: Mutils.c:747 #, c-format msgid "unexpected ctype = %d in dup_mMatrix_as_geMatrix" msgstr "unexpected ctype = %d in dup_mMatrix_as_geMatrix" #: Mutils.c:778 #, c-format msgid "invalid class '%s' to dup_mMatrix_as_dgeMatrix" msgstr "invalid class ‘%s’ to dup_mMatrix_as_dgeMatrix" #: Mutils.c:824 msgid "Argument ij must be 2-column integer matrix" msgstr "Argument ij must be 2-column integer matrix" #: Mutils.c:840 msgid "subscript 'i' out of bounds in M[ij]" msgstr "subscript ‘i’ out of bounds in M[ij]" #: Mutils.c:842 msgid "subscript 'j' out of bounds in M[ij]" msgstr "subscript ‘j’ out of bounds in M[ij]" #: Mutils.c:881 msgid "i and j must be integer vectors of the same length" msgstr "i and j must be integer vectors of the same length" #: Mutils.c:967 msgid "'data' must be of a vector type" msgstr "‘data’ must be of a vector type" #: Mutils.c:974 #, c-format msgid "invalid '%s' argument" msgstr "invalid ‘%s’ argument" #: Mutils.c:981 Mutils.c:989 msgid "non-numeric matrix extent" msgstr "non-numeric matrix extent" #: Mutils.c:984 msgid "invalid 'nrow' value (too large or NA)" msgstr "invalid ‘nrow’ value (too large or NA)" #: Mutils.c:986 msgid "invalid 'nrow' value (< 0)" msgstr "invalid ‘nrow’ value (< 0)" #: Mutils.c:992 msgid "invalid 'ncol' value (too large or NA)" msgstr "invalid ‘ncol’ value (too large or NA)" #: Mutils.c:994 msgid "invalid 'ncol' value (< 0)" msgstr "invalid ‘ncol’ value (< 0)" #: Mutils.c:1012 #, c-format msgid "" "data length [%d] is not a sub-multiple or multiple of the number of rows [%d]" msgstr "" "data length [%d] is not a sub-multiple or multiple of the number of rows [%d]" #: Mutils.c:1015 #, c-format msgid "" "data length [%d] is not a sub-multiple or multiple of the number of columns " "[%d]" msgstr "" "data length [%d] is not a sub-multiple or multiple of the number of columns " "[%d]" #: Mutils.c:1018 msgid "data length exceeds size of matrix" msgstr "data length exceeds size of matrix" #: Mutils.c:1024 msgid "too many elements specified" msgstr "too many elements specified" #: Tsparse.c:20 msgid "lengths of slots i and j must match" msgstr "lengths of slots i and j must match" #: Tsparse.c:23 msgid "slot Dim must have length 2" msgstr "slot Dim must have length 2" #: Tsparse.c:27 msgid "" "all row indices (slot 'i') must be between 0 and nrow-1 in a TsparseMatrix" msgstr "" "all row indices (slot ‘i’) must be between 0 and nrow-1 in a TsparseMatrix" #: Tsparse.c:29 msgid "" "all column indices (slot 'j') must be between 0 and ncol-1 in a TsparseMatrix" msgstr "" "all column indices (slot ‘j’) must be between 0 and ncol-1 in a TsparseMatrix" #: chm_common.c:67 msgid "Argument rho must be an environment" msgstr "Argument rho must be an environment" #: chm_common.c:230 msgid "invalid class of object to as_cholmod_sparse" msgstr "invalid class of object to as_cholmod_sparse" #: chm_common.c:232 msgid "invalid object passed to as_cholmod_sparse" msgstr "invalid object passed to as_cholmod_sparse" #: chm_common.c:259 msgid "in_place cholmod_sort returned an error code" msgstr "in_place cholmod_sort returned an error code" #: chm_common.c:265 msgid "cholmod_sort returned an error code" msgstr "cholmod_sort returned an error code" #: chm_common.c:346 msgid "chm_sparse_to_SEXP(, *): invalid 'Rkind' (real kind code)" msgstr "chm_sparse_to_SEXP(, *): invalid ‘Rkind’ (real kind code)" #: chm_common.c:354 msgid "unknown xtype in cholmod_sparse object" msgstr "unknown xtype in cholmod_sparse object" #: chm_common.c:383 chm_common.c:578 chm_common.c:813 chm_common.c:860 msgid "complex sparse matrix code not yet written" msgstr "complex sparse matrix code not yet written" #: chm_common.c:388 chm_common.c:583 msgid "Symmetric and triangular both set" msgstr "Symmetric and triangular both set" #: chm_common.c:428 msgid "invalid class of object to as_cholmod_triplet" msgstr "invalid class of object to as_cholmod_triplet" #: chm_common.c:452 msgid "as_cholmod_triplet(): could not reallocate for internal diagU2N()" msgstr "as_cholmod_triplet(): could not reallocate for internal diagU2N()" #: chm_common.c:550 msgid "unknown xtype in cholmod_triplet object" msgstr "unknown xtype in cholmod_triplet object" #: chm_common.c:629 msgid "invalid class of object to as_cholmod_dense" msgstr "invalid class of object to as_cholmod_dense" #: chm_common.c:699 #, c-format msgid "Cholmod error '%s' at file %s, line %d" msgstr "Cholmod error ‘%s’ at file %s, line %d" #: chm_common.c:703 #, c-format msgid "Cholmod warning '%s' at file %s, line %d" msgstr "Cholmod warning ‘%s’ at file %s, line %d" #: chm_common.c:732 #, c-format msgid "Unable to initialize cholmod: error code %d" msgstr "Unable to initialize cholmod: error code %d" #: chm_common.c:779 msgid "unknown 'Rkind'" msgstr "unknown ‘Rkind’" #: chm_common.c:786 chm_common.c:851 msgid "unknown xtype" msgstr "unknown xtype" #: chm_common.c:819 chm_common.c:869 msgid "code for cholmod_dense with holes not yet written" msgstr "code for cholmod_dense with holes not yet written" #: chm_common.c:865 msgid "don't know if a dense pattern matrix makes sense" msgstr "don't know if a dense pattern matrix makes sense" #: chm_common.c:910 msgid "invalid class of object to as_cholmod_factor" msgstr "invalid class of object to as_cholmod_factor" #: chm_common.c:924 msgid "Supernodal LDL' decomposition not available" msgstr "Supernodal LDL' decomposition not available" #: chm_common.c:926 msgid "Supernodal/simplicial class inconsistent with type flags" msgstr "Supernodal/simplicial class inconsistent with type flags" #: chm_common.c:944 msgid "Number of supernodes must be positive when is_super is TRUE" msgstr "Number of supernodes must be positive when is_super is TRUE" #: chm_common.c:947 msgid "Lengths of super and pi must be equal" msgstr "Lengths of super and pi must be equal" #: chm_common.c:951 msgid "Lengths of super and px must be equal" msgstr "Lengths of super and px must be equal" #: chm_common.c:964 msgid "failure in as_cholmod_factor" msgstr "failure in as_cholmod_factor" #: chm_common.c:992 msgid "CHOLMOD factorization was unsuccessful" msgstr "CHOLMOD factorization was unsuccessful" #: chm_common.c:1005 #, c-format msgid "f->xtype of %d not recognized" msgstr "f->xtype of %d not recognized" #: chm_common.c:1070 #, c-format msgid "chm_diagN2U(): nrow=%d, ncol=%d" msgstr "chm_diagN2U(): nrow=%d, ncol=%d" #: chm_common.c:1113 #, c-format msgid "chm_diagN2U(x, uploT = %d): uploT should be +- 1" msgstr "chm_diagN2U(x, uploT = %d): uploT should be +- 1" #: cs_utils.c:37 msgid "csp_eye argument n must be positive" msgstr "csp_eye argument n must be positive" #: cs_utils.c:68 msgid "invalid class of 'x' in Matrix_as_cs(a, x)" msgstr "invalid class of ‘x’ in Matrix_as_cs(a, x)" #: cs_utils.c:126 cs_utils.c:170 cs_utils.c:185 cs_utils.c:205 cs_utils.c:218 #, c-format msgid "invalid class of object to %s" msgstr "invalid class of object to %s" #: cs_utils.c:139 #, c-format msgid "cs matrix not compatible with class '%s'" msgstr "cs matrix not compatible with class ‘%s’" #: cs_utils.c:242 cs_utils.c:261 #, c-format msgid "Inappropriate class cl='%s' in Matrix_css_to_SEXP(S, cl, ..)" msgstr "Inappropriate class cl='%s' in Matrix_css_to_SEXP(S, cl, ..)" #: cs_utils.c:287 cs_utils.c:306 #, c-format msgid "Inappropriate class cl='%s' in Matrix_csn_to_SEXP(S, cl, ..)" msgstr "Inappropriate class cl='%s' in Matrix_csn_to_SEXP(S, cl, ..)" #: dense.c:29 #, c-format msgid "incorrect left cyclic shift, j (%d) >= k (%d)" msgstr "incorrect left cyclic shift, j (%d) >= k (%d)" #: dense.c:31 #, c-format msgid "incorrect left cyclic shift, j (%d) < 0" msgstr "incorrect left cyclic shift, j (%d) < 0" #: dense.c:33 #, c-format msgid "incorrect left cyclic shift, k (%d) > ldx (%d)" msgstr "incorrect left cyclic shift, k (%d) > ldx (%d)" #: dense.c:78 msgid "Unknown error in getGivens" msgstr "Unknown error in getGivens" #: dense.c:90 dense.c:106 dense.c:139 msgid "X must be a numeric (double precision) matrix" msgstr "X must be a numeric (double precision) matrix" #: dense.c:111 dense.c:144 msgid "y must be a numeric (double precision) matrix" msgstr "y must be a numeric (double precision) matrix" #: dense.c:115 dense.c:148 #, c-format msgid "number of rows in y (%d) does not match number of rows in X (%d)" msgstr "number of rows in y (%d) does not match number of rows in X (%d)" #: dense.c:126 #, c-format msgid "Lapack routine dposv returned error code %d" msgstr "Lapack routine dposv returned error code %d" #: dense.c:159 #, c-format msgid "First call to Lapack routine dgels returned error code %d" msgstr "First call to Lapack routine dgels returned error code %d" #: dense.c:166 #, c-format msgid "Second call to Lapack routine dgels returned error code %d" msgstr "Second call to Lapack routine dgels returned error code %d" #: dense.c:179 msgid "X must be a real (numeric) matrix" msgstr "X must be a real (numeric) matrix" #: dense.c:180 #, c-format msgid "tol, given as %g, must be non-negative" msgstr "tol, given as %g, must be non-negative" #: dense.c:181 #, c-format msgid "tol, given as %g, must be <= 1" msgstr "tol, given as %g, must be <= 1" #: dense.c:205 #, c-format msgid "First call to dgeqrf returned error code %d" msgstr "First call to dgeqrf returned error code %d" #: dense.c:211 #, c-format msgid "Second call to dgeqrf returned error code %d" msgstr "Second call to dgeqrf returned error code %d" #: dense.c:216 dense.c:236 #, c-format msgid "Lapack routine dtrcon returned error code %d" msgstr "Lapack routine dtrcon returned error code %d" #: dense.c:285 #, c-format msgid "Lower band %d > upper band %d" msgstr "Lower band %d > upper band %d" #: dense.c:354 msgid "ddense_to_symmetric(): matrix is not square!" msgstr "ddense_to_symmetric(): matrix is not square!" #: dense.c:365 #, c-format msgid "matrix is not symmetric [%d,%d]" msgstr "matrix is not symmetric [%d,%d]" #: dense.c:413 msgid "matrix is not square! (symmetric part)" msgstr "matrix is not square! (symmetric part)" #: dense.c:457 msgid "matrix is not square! (skew-symmetric part)" msgstr "matrix is not square! (skew-symmetric part)" #: dgCMatrix.c:17 msgid "lengths of slots 'i' and 'x' must match" msgstr "lengths of slots ‘i’ and ‘x’ must match" #: dgCMatrix.c:29 msgid "lengths of slots 'j' and 'x' must match" msgstr "lengths of slots ‘j’ and ‘x’ must match" #: dgCMatrix.c:51 #, c-format msgid "invalid class(x) '%s' in compressed_to_TMatrix(x)" msgstr "invalid class(x) ‘%s’ in compressed_to_TMatrix(x)" #: dgCMatrix.c:85 #, c-format msgid "invalid class(x) '%s' in R_to_CMatrix(x)" msgstr "invalid class(x) ‘%s’ in R_to_CMatrix(x)" #: dgCMatrix.c:155 msgid "dgCMatrix_lusol requires a square, non-empty matrix" msgstr "dgCMatrix_lusol requires a square, non-empty matrix" #: dgCMatrix.c:157 dgCMatrix.c:183 dgCMatrix.c:430 dgCMatrix.c:463 #: dgeMatrix.c:422 dpoMatrix.c:91 dpoMatrix.c:116 dppMatrix.c:80 #: dspMatrix.c:78 dsyMatrix.c:85 dtCMatrix.c:90 dtCMatrix.c:106 dtrMatrix.c:98 msgid "Dimensions of system to be solved are inconsistent" msgstr "Dimensions of system to be solved are inconsistent" #: dgCMatrix.c:159 msgid "cs_lusol failed" msgstr "cs_lusol failed" #: dgCMatrix.c:180 msgid "dgCMatrix_qrsol(., order) needs order in {0,..,3}" msgstr "dgCMatrix_qrsol(., order) needs order in {0,..,3}" #: dgCMatrix.c:189 #, c-format msgid "dgCMatrix_qrsol(<%d x %d>-matrix) requires a 'tall' rectangular matrix" msgstr "dgCMatrix_qrsol(<%d x %d>-matrix) requires a ‘tall’ rectangular matrix" #: dgCMatrix.c:200 msgid "cs_qrsol() failed inside dgCMatrix_qrsol()" msgstr "cs_qrsol() failed inside dgCMatrix_qrsol()" #: dgCMatrix.c:225 msgid "A must have #{rows} >= #{columns}" msgstr "A must have #{rows} >= #{columns}" #: dgCMatrix.c:230 msgid "cs_sqr failed" msgstr "cs_sqr failed" #: dgCMatrix.c:235 msgid "cs_qr failed" msgstr "cs_qr failed" #: dgCMatrix.c:298 msgid "SuiteSparseQR_C_QR returned an error code" msgstr "SuiteSparseQR_C_QR returned an error code" #: dgCMatrix.c:342 msgid "LU decomposition applies only to square matrices" msgstr "LU decomposition applies only to square matrices" #: dgCMatrix.c:351 msgid "cs_lu(A) failed: near-singular A (or out of memory)" msgstr "cs_lu(A) failed: near-singular A (or out of memory)" #: dgCMatrix.c:461 msgid "dgCMatrix_cholsol requires a 'short, wide' rectangular matrix" msgstr "dgCMatrix_cholsol requires a ‘short, wide’ rectangular matrix" #: dgCMatrix.c:469 msgid "cholmod_sdmult error (rhs)" msgstr "cholmod_sdmult error (rhs)" #: dgCMatrix.c:472 #, c-format msgid "cholmod_factorize failed: status %d, minor %d from ncol %d" msgstr "cholmod_factorize failed: status %d, minor %d from ncol %d" #: dgCMatrix.c:476 #, c-format msgid "cholmod_solve (CHOLMOD_A) failed: status %d, minor %d from ncol %d" msgstr "cholmod_solve (CHOLMOD_A) failed: status %d, minor %d from ncol %d" #: dgCMatrix.c:493 msgid "cholmod_sdmult error (resid)" msgstr "cholmod_sdmult error (resid)" #: dgTMatrix.c:15 msgid "lengths of slots i and x must match" msgstr "lengths of slots i and x must match" #: dgTMatrix.c:56 #, c-format msgid "Cannot coerce to too large *geMatrix with %.0f entries" msgstr "Cannot coerce to too large *geMatrix with %.0f entries" #: dgeMatrix.c:10 msgid "Dim slot must have length 2" msgstr "Dim slot must have length 2" #: dgeMatrix.c:14 msgid "Negative value in Dim" msgid_plural "Negative values in Dim" msgstr[0] "Negative value in Dim" msgstr[1] "Negative values in Dim" #: dgeMatrix.c:18 msgid "x slot must be numeric \"double\"" msgstr "x slot must be numeric \"double\"" #: dgeMatrix.c:31 msgid "factors slot must be named list" msgstr "factors slot must be named list" #: dgeMatrix.c:69 msgid "rcond requires a square, non-empty matrix" msgstr "rcond requires a square, non-empty matrix" #: dgeMatrix.c:126 dgeMatrix.c:183 #, c-format msgid "Dimensions of x and y are not compatible for %s" msgstr "Dimensions of x and y are not compatible for %s" #: dgeMatrix.c:165 msgid "Argument y must be numeric or integer" msgstr "Argument y must be numeric or integer" #: dgeMatrix.c:306 msgid "Cannot factor a matrix with zero extents" msgstr "Cannot factor a matrix with zero extents" #: dgeMatrix.c:316 dpoMatrix.c:42 dppMatrix.c:36 dspMatrix.c:181 #, c-format msgid "Lapack routine %s returned error code %d" msgstr "Lapack routine %s returned error code %d" #: dgeMatrix.c:318 #, c-format msgid "Exact singularity detected during LU decomposition: %s, i=%d." msgstr "Exact singularity detected during LU decomposition: %s, i=%d." #: dgeMatrix.c:340 msgid "Determinant requires a square matrix" msgstr "Determinant requires a square matrix" #: dgeMatrix.c:382 msgid "Solve requires a square matrix" msgstr "Solve requires a square matrix" #: dgeMatrix.c:395 #, c-format msgid "error [%d] from Lapack 'dgecon()'" msgstr "error [%d] from Lapack ‘dgecon()’" #: dgeMatrix.c:397 #, c-format msgid "" "Lapack dgecon(): system computationally singular, reciprocal condition " "number = %g" msgstr "" "Lapack dgecon(): system computationally singular, reciprocal condition " "number = %g" #: dgeMatrix.c:407 msgid "Lapack routine dgetri: system is exactly singular" msgstr "Lapack routine dgetri: system is exactly singular" #: dgeMatrix.c:427 msgid "Lapack routine dgetrs: system is exactly singular" msgstr "Lapack routine dgetrs: system is exactly singular" #: dgeMatrix.c:446 dgeMatrix.c:468 dspMatrix.c:152 dsyMatrix.c:122 #: dtrMatrix.c:122 msgid "Matrices are not conformable for multiplication" msgstr "Matrices are not conformable for multiplication" #: dgeMatrix.c:569 msgid "Matrix exponential requires square, non-null matrix" msgstr "Matrix exponential requires square, non-null matrix" #: dgeMatrix.c:586 dgeMatrix.c:588 #, c-format msgid "dgeMatrix_exp: LAPACK routine dgebal returned %d" msgstr "dgeMatrix_exp: LAPACK routine dgebal returned %d" #: dgeMatrix.c:626 #, c-format msgid "dgeMatrix_exp: dgetrf returned error code %d" msgstr "dgeMatrix_exp: dgetrf returned error code %d" #: dgeMatrix.c:628 #, c-format msgid "dgeMatrix_exp: dgetrs returned error code %d" msgstr "dgeMatrix_exp: dgetrs returned error code %d" #: dgeMatrix.c:701 msgid "dgeMatrix_Schur: argument x must be a non-null square matrix" msgstr "dgeMatrix_Schur: argument x must be a non-null square matrix" #: dgeMatrix.c:712 msgid "dgeMatrix_Schur: first call to dgees failed" msgstr "dgeMatrix_Schur: first call to dgees failed" #: dgeMatrix.c:720 #, c-format msgid "dgeMatrix_Schur: dgees returned code %d" msgstr "dgeMatrix_Schur: dgees returned code %d" #: dpoMatrix.c:12 msgid "dpoMatrix is not positive definite" msgstr "dpoMatrix is not positive definite" #: dpoMatrix.c:39 dppMatrix.c:33 #, c-format msgid "the leading minor of order %d is not positive definite" msgstr "the leading minor of order %d is not positive definite" #: dpoMatrix.c:93 msgid "Cannot solve() for matrices with zero extents" msgstr "Cannot solve() for matrices with zero extents" #: dpoMatrix.c:114 msgid "Argument b must be a numeric matrix" msgstr "Argument b must be a numeric matrix" #: dsCMatrix.c:71 msgid "" "Cholesky factorization failed; unusually, please report to Matrix-authors" msgstr "" "Cholesky factorization failed; unusually, please report to Matrix-authors" #: dsCMatrix.c:77 msgid "internal_chm_factor: Cholesky factorization failed" msgstr "internal_chm_factor: Cholesky factorization failed" #: dsCMatrix.c:213 msgid "Non-symmetric matrix passed to dsCMatrix_to_dgTMatrix" msgstr "Non-symmetric matrix passed to dsCMatrix_to_dgTMatrix" #: dspMatrix.c:13 dtpMatrix.c:17 msgid "Incorrect length of 'x' slot" msgstr "Incorrect length of ‘x’ slot" #: dsyMatrix.c:7 dtrMatrix.c:10 msgid "'Dim' slot has length less than two" msgstr "‘Dim’ slot has length less than two" #: dsyMatrix.c:9 dtrMatrix.c:12 msgid "Matrix is not square" msgstr "Matrix is not square" #: dsyMatrix.c:158 #, c-format msgid "Lapack routine dsytrf returned error code %d" msgstr "Lapack routine dsytrf returned error code %d" #: dtCMatrix.c:28 dtCMatrix.c:63 dtTMatrix.c:24 msgid "uplo='U' must not have sparse entries below the diagonal" msgstr "uplo='U' must not have sparse entries below the diagonal" #: dtCMatrix.c:34 dtCMatrix.c:69 dtTMatrix.c:29 msgid "uplo='L' must not have sparse entries above the diagonal" msgstr "uplo='L' must not have sparse entries above the diagonal" #: dtpMatrix.c:120 dtpMatrix.c:141 dtpMatrix.c:164 #, c-format msgid "Dimensions of a (%d,%d) and b (%d,%d) do not conform" msgstr "Dimensions of a (%d,%d) and b (%d,%d) do not conform" #: dtrMatrix.c:120 msgid "dtrMatrix must be square" msgstr "dtrMatrix must be square" #: dtrMatrix.c:160 msgid "dtrMatrices in %*% must have matching (square) dim." msgstr "dtrMatrices in %*% must have matching (square) dim." #: dtrMatrix.c:247 msgid "cannot set diag() as long as 'diag = \"U\"'" msgstr "cannot set diag() as long as ‘diag = \"U\"’" #: dtrMatrix.c:268 msgid "cannot add diag() as long as 'diag = \"U\"'" msgstr "cannot add diag() as long as ‘diag = \"U\"’" #: init.c:350 msgid "missing 'Matrix' namespace: should never happen" msgstr "missing ‘Matrix’ namespace: should never happen" #: init.c:361 msgid "Matrix namespace not determined correctly" msgstr "Matrix namespace not determined correctly" #: lgCMatrix.c:58 msgid "A must be a logical matrix" msgstr "A must be a logical matrix" #: sparseQR.c:13 msgid "length(p) must match nrow(V)" msgstr "length(p) must match nrow(V)" #: sparseQR.c:15 msgid "length(beta) must match ncol(V)" msgstr "length(beta) must match ncol(V)" #: sparseQR.c:18 msgid "length(q) must be zero or ncol(R)" msgstr "length(q) must be zero or ncol(R)" #: sparseQR.c:46 #, c-format msgid "sparseQR_Qmult(): nrow(y) = %d != %d = nrow(V)" msgstr "sparseQR_Qmult(): nrow(y) = %d != %d = nrow(V)" #: sparseQR.c:121 sparseQR.c:159 sparseQR.c:195 #, c-format msgid "%s(): structurally rank deficient case: possibly WRONG zeros" msgstr "%s(): structurally rank deficient case: possibly WRONG zeros" #: t_Csparse_subassign.c:144 msgid "invalid class of 'x' in Csparse_subassign()" msgstr "invalid class of ‘x’ in Csparse_subassign()" #: t_Csparse_subassign.c:146 msgid "invalid class of 'value' in Csparse_subassign()" msgstr "invalid class of ‘value’ in Csparse_subassign()" #: t_Csparse_subassign.c:189 #, c-format msgid "x[] <- val: val must be logical for \"%s\" x" msgstr "x[] <- val: val must be logical for \"%s\" x" #: t_Csparse_subassign.c:194 #, c-format msgid "x[] <- val: val must be integer or logical for \"%s\" x" msgstr "x[] <- val: val must be integer or logical for \"%s\" x" #: t_Csparse_subassign.c:201 msgid "programming error in Csparse_subassign() should never happen" msgstr "programming error in Csparse_subassign() should never happen" Matrix/po/R-pl.po0000644000175100001440000016174412256121033013334 0ustar hornikusersmsgid "" msgstr "" "Project-Id-Version: Matrix 1.0-9\n" "Report-Msgid-Bugs-To: bugs.r-project.org\n" "POT-Creation-Date: 2013-12-23 21:27\n" "PO-Revision-Date: 2012-08-22 08:17+0100\n" "Last-Translator: Łukasz Daniel \n" "Language-Team: Łukasz Daniel \n" "Language: pl_PL\n" "MIME-Version: 1.0\n" "Content-Type: text/plain; charset=UTF-8\n" "Content-Transfer-Encoding: 8bit\n" "Plural-Forms: nplurals=3; plural=(n==1 ? 0 : n%10>=2 && n%10<=4 && (n%100<10 " "|| n%100>=20) ? 1 : 2)\n" "X-Poedit-SourceCharset: iso-8859-1\n" # Recommended/Matrix/R/Matrix.R: 202 # stop("invalid 'data'") #, fuzzy msgid "invalid 'mod': %s" msgstr "niepoprawne 'mod':" # Recommended/Matrix/R/Auxiliaries.R: 39 # stop(gettextf('not-yet-implemented method for %s(<%s>).\n # >> Ask the package authors to implement the missing feature.', fun, cl), # call. = FALSE) msgid "" "not-yet-implemented method for %s(<%s>).\n" " ->> Ask the package authors to implement the missing feature." msgstr "" "metoda jeszcze niezaimplementowana dla %s(<%s>).\n" " ->> Poproś autorów pakietu o zaimplementowanie brakującej funkcjonalności." # Recommended/Matrix/R/Auxiliaries.R: 43 # stop(gettextf('not-yet-implemented method for %s(<%s>, <%s>).\n # >> Ask the package authors to implement the missing feature.', # fun, cl1, cl2), call. = FALSE) msgid "" "not-yet-implemented method for %s(<%s>, <%s>).\n" " ->> Ask the package authors to implement the missing feature." msgstr "" "metoda jeszcze niezaimplementowana dla %s(<%s>, <%s>).\n" " ->> Poproś autorów pakietu o zaimplementowanie brakującej funkcjonalności." # Recommended/Matrix/R/dsparseMatrix.R: 11 # stop("'x' is not positive definite -- chol() undefined.") # Recommended/Matrix/R/Auxiliaries.R: 130 # stop("'x' is not positive definite -- chol() undefined.") msgid "'x' is not positive definite -- chol() undefined." msgstr "'x' nie jest dodatnio określone -- nieokreślony 'chol()'." # Recommended/Matrix/R/Auxiliaries.R: 203 # stop(gettextf("Matrices must have same dimensions in %s", # deparse(sys.call(sys.parent()))), # call. = FALSE) msgid "Matrices must have same dimensions in %s" msgstr "Macierze muszą mieć te same wymiary w %s" # Recommended/Matrix/R/Auxiliaries.R: 230 # stop(gettextf("non-conformable matrix dimensions in %s", # deparse(sys.call(sys.parent()))), # call. = FALSE) msgid "non-conformable matrix dimensions in %s" msgstr "niezgodne wymiary macierzy w %s" # Recommended/Matrix/R/Auxiliaries.R: 251 # warning(gettextf("dimnames [%d] mismatch in %s", j, # deparse(sys.call(sys.parent()))), # call. = FALSE) msgid "dimnames [%d] mismatch in %s" msgstr "niezgodność nazw wymiarów [%d] w %s" # Recommended/Matrix/R/Auxiliaries.R: 266 # stop(gettextf("Matrices must have same number of rows in %s", # deparse(sys.call(sys.parent()))), # call. = FALSE) msgid "Matrices must have same number of rows in %s" msgstr "Macierze muszą mieć tę samą liczbę wierszy w %s" # Recommended/Matrix/R/Auxiliaries.R: 277 # stop(gettextf("Matrices must have same number of columns in %s", # deparse(sys.call(sys.parent()))), # call. = FALSE) msgid "Matrices must have same number of columns in %s" msgstr "Macierze muszą mieć tę samą liczbę kolumn w %s" # Recommended/Matrix/R/Auxiliaries.R: 338 # message(sprintf(" [[ suppressing %d column names %s%s ]]", nc, # paste(sQuote(cn[1:min(3, lc)]), collapse = ", "), # if(lc > 3) " ..." else "")) #, fuzzy msgid "[[ suppressing %d column names %s ... ]]" msgstr "[[ zmniejszanie %d nazw kolumn %s%s ]]" # Recommended/Matrix/R/Auxiliaries.R: 338 # message(sprintf(" [[ suppressing %d column names %s%s ]]", nc, # paste(sQuote(cn[1:min(3, lc)]), collapse = ", "), # if(lc > 3) " ..." else "")) #, fuzzy msgid "[[ suppressing %d column names %s ]]" msgstr "[[ zmniejszanie %d nazw kolumn %s%s ]]" # Recommended/Matrix/R/Auxiliaries.R: 475 # stop("'x' must be sparseMatrix") #, fuzzy msgid "'x' must be \"sparseMatrix\"" msgstr "'x' musi być klasy 'sparseMatrix'" # Recommended/Matrix/R/Auxiliaries.R: 595 # stop("not yet implemented for class ", class.x) #, fuzzy msgid "not yet implemented for class %s" msgstr "jeszcze niezaimplementowane dla klasy" # Recommended/Matrix/R/ldenseMatrix.R: 74 # stop("not a triangular matrix") # Recommended/Matrix/R/Auxiliaries.R: 759 # stop("not a triangular matrix") # Recommended/Matrix/R/Auxiliaries.R: 990 # stop("not a triangular matrix") # Recommended/Matrix/R/ndenseMatrix.R: 86 # stop("not a triangular matrix") msgid "not a triangular matrix" msgstr "to nie jest macierz trójkątną" # Recommended/Matrix/R/dsyMatrix.R: 8 # stop("not a symmetric matrix; consider forceSymmetric() or symmpart()") # Recommended/Matrix/R/ldenseMatrix.R: 65 # stop("not a symmetric matrix; consider forceSymmetric() or symmpart()") # Recommended/Matrix/R/dgTMatrix.R: 37 # stop("not a symmetric matrix; consider forceSymmetric() or symmpart()") # Recommended/Matrix/R/Csparse.R: 71 # stop("not a symmetric matrix; consider forceSymmetric() or symmpart()") # Recommended/Matrix/R/ndenseMatrix.R: 77 # stop("not a symmetric matrix; consider forceSymmetric() or symmpart()") msgid "not a symmetric matrix; consider forceSymmetric() or symmpart()" msgstr "" "to nie jest macierz symetryczna; rozważ 'forceSymmetric()' lub 'symmpart()'" # Recommended/Matrix/R/Auxiliaries.R: 775 # stop("not yet implemented for matrix w/ typeof ", typeof(x)) # Recommended/Matrix/R/Auxiliaries.R: 788 # stop("not yet implemented for matrix w/ typeof ", typeof(x)) #, fuzzy msgid "not yet implemented for matrix with typeof %s" msgstr "jeszcze niezaimplementowana dla macierzy z typem" #, fuzzy msgid "not yet implemented for %s" msgstr "jeszcze nie jest zaimplementowana dla" # Recommended/Matrix/R/Auxiliaries.R: 860 # stop("general Matrix class not yet implemented for ", # class(x)) #, fuzzy msgid "general Matrix class not yet implemented for %s" msgstr "ogólna klasa 'Matrix' jeszcze nie jest zaimplementowana dla" #, fuzzy msgid "" "arguments %s are disregarded in\n" " %s" msgstr "zostały odrzucone w" msgid "" "Quadratic matrix '%s' (=: A) is not formally\n" "\tsymmetric. Will be treated as\tA A'" msgstr "" "Macierz kwadratowa '%s' (=: A) nie jest formalnie\n" "\tsymetryczna. Będzie traktowana jako\tA A'" msgid "" "'update' must be logical or '+' or '-'; 'C' a matrix, and 'L' a \"CHMfactor\"" msgstr "" "'update' musi być wartością logiczną lub '+' lub '-'; 'C' musi być macierzą, " "oraz 'L' musi być obiektem klasy 'CHMfactor'" msgid "update must be TRUE/FALSE or '+' or '-'" msgstr "'update' musi wynosić TRUE/FALSE lub '+' lub '-'" # Recommended/Matrix/R/Csparse.R: 184 # stop("Matrix-internal error in [i,,d]; please report") msgid "Matrix-internal error in [i,,d]; please report" msgstr "" "błąd wewnętrzny w pakiecie 'Matrix' w '[i,,d]'; proszę zgłosić " "raport" # Recommended/Matrix/R/sparseVector.R: 488 # stop("nothing to replace with") # Recommended/Matrix/R/Csparse.R: 238 # stop("nothing to replace with") # Recommended/Matrix/R/Tsparse.R: 400 # stop("nothing to replace with") # Recommended/Matrix/R/Tsparse.R: 651 # stop("nothing to replace with") msgid "nothing to replace with" msgstr "nic do zastąpienia" # Recommended/Matrix/R/sparseVector.R: 493 # stop("number of items to replace is not a multiple of replacement length") # Recommended/Matrix/R/Csparse.R: 243 # stop("number of items to replace is not a multiple of replacement length") # Recommended/Matrix/R/Matrix.R: 710 # warning("number of items to replace is not a multiple of replacement length") # Recommended/Matrix/R/Tsparse.R: 366 # warning("number of items to replace is not a multiple of replacement length") # Recommended/Matrix/R/Tsparse.R: 405 # stop("number of items to replace is not a multiple of replacement length") # Recommended/Matrix/R/Tsparse.R: 655 # warning("number of items to replace is not a multiple of replacement length") msgid "number of items to replace is not a multiple of replacement length" msgstr "" "liczba pozycji do zastąpienia nie jest wielokrotnością długości elementu " "zastępującego" # Recommended/Matrix/R/sparseVector.R: 520 # stop("too many replacement values") # Recommended/Matrix/R/Csparse.R: 245 # stop("too many replacement values") # Recommended/Matrix/R/Tsparse.R: 495 # stop("too many replacement values") msgid "too many replacement values" msgstr "zbyt dużo wartości zamieniających" # Recommended/Matrix/R/Csparse.R: 282 # warning("i1[1] == 0 ==> C-level verbosity will not happen!") msgid "i1[1] == 0 ==> C-level verbosity will not happen!" msgstr "i1[1] == 0 ==> tryb 'verbose' poziomu C nie zostanie wykonany!" msgid "using\t \"old code\" part in Csparse subassignment" msgstr "używanie\t części 'old code' w przypisaniu w 'Csparse'" # Recommended/Matrix/R/Csparse.R: 498 # stop("Cholesky() -> *symbolic* factorization -- not yet implemented") msgid "" "Cholesky() -> *symbolic* factorization -- not yet implemented" msgstr "" "Cholesky() -> *symboliczna* faktoryzacja -- jeszcze " "niezaimplementowana" # Recommended/Matrix/R/HBMM.R: 13 # stop("Not a valid format") msgid "Not a valid format" msgstr "Niepoprawny format" # Recommended/Matrix/R/HBMM.R: 33 # stop("'file' must be a character string or connection") # Recommended/Matrix/R/HBMM.R: 82 # stop("'file' must be a character string or connection") msgid "'file' must be a character string or connection" msgstr "'file' musi być łańcuchem tekstowym lub połączeniem" # Recommended/Matrix/R/HBMM.R: 47 # stop(paste("Invalid storage type:", t1)) #, fuzzy msgid "Invalid storage type: %s" msgstr "Niepoprawny typ przechowywania:" # Recommended/Matrix/R/HBMM.R: 48 # stop("Only numeric sparse matrices allowed") msgid "Only numeric sparse matrices allowed" msgstr "Dozwolone są jedynie liczbowe rzadkie macierze" # Recommended/Matrix/R/HBMM.R: 51 # stop(paste("Invalid storage format:", t2)) #, fuzzy msgid "Invalid storage format: %s" msgstr "Niepoprawny format przechowywania:" # Recommended/Matrix/R/HBMM.R: 53 # stop(paste("Invalid assembled indicator:", t3)) #, fuzzy msgid "Invalid assembled indicator: %s" msgstr "Niepoprawnie złożony wskaźnik:" # Recommended/Matrix/R/HBMM.R: 91 # stop("file is not a MatrixMarket file") msgid "file is not a MatrixMarket file" msgstr "plik nie jest plikiem typu 'MatrixMarket'" # Recommended/Matrix/R/HBMM.R: 93 # stop("type '", typ, "' not recognized") # Recommended/Matrix/R/HBMM.R: 95 # stop("representation '", repr, "' not recognized") # Recommended/Matrix/R/HBMM.R: 98 # stop("element type '", elt, "' not recognized") # Recommended/Matrix/R/HBMM.R: 101 # stop("symmetry form '", sym, "' not recognized") msgid "type '%s' not recognized" msgstr "typ '%s' nie został rozpoznany" # Recommended/Matrix/R/HBMM.R: 93 # stop("type '", typ, "' not recognized") # Recommended/Matrix/R/HBMM.R: 95 # stop("representation '", repr, "' not recognized") # Recommended/Matrix/R/HBMM.R: 98 # stop("element type '", elt, "' not recognized") # Recommended/Matrix/R/HBMM.R: 101 # stop("symmetry form '", sym, "' not recognized") msgid "representation '%s' not recognized" msgstr "reprezentacja '%s' nie została rozpoznana" # Recommended/Matrix/R/HBMM.R: 93 # stop("type '", typ, "' not recognized") # Recommended/Matrix/R/HBMM.R: 95 # stop("representation '", repr, "' not recognized") # Recommended/Matrix/R/HBMM.R: 98 # stop("element type '", elt, "' not recognized") # Recommended/Matrix/R/HBMM.R: 101 # stop("symmetry form '", sym, "' not recognized") msgid "element type '%s' not recognized" msgstr "element typu '%s' nie został rozpoznany" # Recommended/Matrix/R/HBMM.R: 140 # stop(gettextf("symmetry form '%s' is not yet implemented", sym)) # Recommended/Matrix/R/HBMM.R: 167 # stop(gettextf("symmetry form '%s' is not yet implemented", sym)) msgid "symmetry form '%s' not recognized" msgstr "forma symetryczna '%s' nie została rozpoznana" msgid "readMM(): row\t values 'i' are not in 1:nr" msgstr "readMM(): wartości wiersza 'i' nie są w przedziale 1:nr" # Recommended/Matrix/R/HBMM.R: 109 # stop("readMM(): column values 'j' are not in 1:nc", call.=FALSE) msgid "readMM(): column values 'j' are not in 1:nc" msgstr "readMM(): wartości kolumny 'j' nie są w przedziale 1:nc" # Recommended/Matrix/R/HBMM.R: 130 # stop("symmetry form 'skew-symmetric' not yet implemented for reading") # Recommended/Matrix/R/HBMM.R: 157 # stop("symmetry form 'skew-symmetric' not yet implemented for reading") msgid "symmetry form 'skew-symmetric' not yet implemented for reading" msgstr "" "forma symetryczna 'skew-symmetric' nie jest jeszcze zaimplementowana na " "potrzeby odczytu" # Recommended/Matrix/R/HBMM.R: 137 # stop("symmetry form 'hermitian' not yet implemented for reading") # Recommended/Matrix/R/HBMM.R: 164 # stop("symmetry form 'hermitian' not yet implemented for reading") msgid "symmetry form 'hermitian' not yet implemented for reading" msgstr "" "forma symetryczna 'hermitian' nie jest jeszcze zaimplementowana na potrzeby " "odczytu" # Recommended/Matrix/R/HBMM.R: 140 # stop(gettextf("symmetry form '%s' is not yet implemented", sym)) # Recommended/Matrix/R/HBMM.R: 167 # stop(gettextf("symmetry form '%s' is not yet implemented", sym)) msgid "symmetry form '%s' is not yet implemented" msgstr "forma symetryczna '%s' nie jest jeszcze zaimplementowana" # Recommended/Matrix/R/HBMM.R: 171 # stop("element type 'complex' not yet implemented") msgid "element type 'complex' not yet implemented" msgstr "typ elementu 'complex' nie jest jeszcze zaimplementowany" # Recommended/Matrix/R/HBMM.R: 174 # stop(gettextf("'%s()' is not yet implemented for element type '%s'", # "readMM", elt)) msgid "'%s()' is not yet implemented for element type '%s'" msgstr "'%s()' nie jest jeszcze zaimplementowany dla typu '%s' elementu" # Recommended/Matrix/R/HBMM.R: 178 # stop(gettextf("'%s()' is not yet implemented for representation '%s'", # "readMM", repr)) msgid "'%s()' is not yet implemented for representation '%s'" msgstr "'%s()' nie jest jeszcze zaimplementowane dla reprezentacji '%s'" # Recommended/Matrix/R/Matrix.R: 71 # warning("trimmed mean of 'sparseVector' -- suboptimally using as.numeric(.)") msgid "trimmed mean of 'sparseVector' -- suboptimally using as.numeric(.)" msgstr "" "przycięta średnia 'sparseVector' -- optymalnie używając 'as.numeric(.)'" # Recommended/Matrix/R/Matrix.R: 90 # stop("'V' is not a square matrix") msgid "'V' is not a square matrix" msgstr "'V' nie jest macierzą kwadratową" # Recommended/Matrix/R/Matrix.R: 93 # warning("diag(.) had 0 or NA entries; non-finite result is doubtful") # Recommended/Matrix/R/sparseMatrix.R: 753 # warning("diag(.) had 0 or NA entries; non-finite result is doubtful") msgid "diag(.) had 0 or NA entries; non-finite result is doubtful" msgstr "'diag(.)' posiadało wpisy 0 lub NA; nieskończony wynik jest wątpliwy" # Recommended/Matrix/R/Matrix.R: 139 # stop(gettextf("invalid dimnames given for '%s' object", class(x))) #, fuzzy msgid "invalid dimnames given for %s object" msgstr "podano niepoprawne nazwy wymiarów dla obiektu '%s'" # Recommended/Matrix/R/Matrix.R: 149 # message("dimnames(.) <- NULL: translated to \n # "dimnames(.) <- list(NULL,NULL) <==> unname(.)") #, fuzzy msgid "" "dimnames(.) <- NULL: translated to \n" "dimnames(.) <- list(NULL,NULL) <==> unname(.)" msgstr "dimnames(.) <- list(NULL,NULL) <==> unname(.)" # Recommended/Matrix/R/Matrix.R: 182 # warning("'nrow', 'ncol', etc, are disregarded when 'data' is \"Matrix\" already") msgid "'nrow', 'ncol', etc, are disregarded when 'data' is \"Matrix\" already" msgstr "" "'nrow', 'ncol', itd., nie są uwzględniane gdy 'data' ma już typ 'Matrix'" # Recommended/Matrix/R/Matrix.R: 202 # stop("invalid 'data'") msgid "invalid 'data'" msgstr "niepoprawne 'data'" # Recommended/Matrix/R/Matrix.R: 216 # warning("'nrow', 'ncol', etc, are disregarded for matrix 'data'") msgid "'nrow', 'ncol', etc, are disregarded for matrix 'data'" msgstr "'nrow', 'ncol', itd., są nieuwzględniane dla 'data' typu macierzowego" # Recommended/Matrix/R/Matrix.R: 243 # stop("complex matrices not yet implemented in Matrix package") msgid "complex matrices not yet implemented in Matrix package" msgstr "macierze zespolone nie są jeszcze zaimplementowane w pakiecie 'Matrix'" # Recommended/Matrix/R/Matrix.R: 303 # warning("using slow kronecker() method") # Recommended/Matrix/R/Matrix.R: 310 # warning("using slow kronecker() method") msgid "using slow kronecker() method" msgstr "używanie powolnej metody 'kronecker()'" # Recommended/Matrix/R/Matrix.R: 327 # stop(gettextf("Cholesky(A) called for 'A' of class \"%s\";\n # it is currently defined for sparseMatrix only; consider using chol() instead", # class(A)), call. = FALSE) msgid "" "Cholesky(A) called for 'A' of class \"%s\";\n" "\t it is currently defined for sparseMatrix only; consider using chol() " "instead" msgstr "" "metoda 'Cholesky(A)' poprosiła o 'A' klasy '%s';\n" "\t aktualnie jest ona zdefiniowana jedynie dla klasy 'sparseMatrix'; rozważ " "w zamian użycie 'metodychol()'" # Recommended/Matrix/R/Matrix.R: 395 # stop("'lag' and 'differences' must be integers >= 1") msgid "'lag' and 'differences' must be integers >= 1" msgstr "'lag' oraz 'differences' muszą być liczbami całkowitymi >= 1" msgid "programming error: min() should have dispatched w/ 1st arg much earlier" msgstr "" "błąd programistyczny: 'min()' powinno zostać wysłane z pierwszym argumentem " "znacznie wcześniej" # Recommended/Matrix/R/Matrix.R: 555 # stop("invalid or not-yet-implemented 'Matrix' subsetting") msgid "invalid or not-yet-implemented 'Matrix' subsetting" msgstr "niepoprawne lub jeszcze niezaimplementowane podstawienie 'Matrix'" # Recommended/Matrix/R/Matrix.R: 566 # message("[ ] : .M.sub.i.logical() maybe inefficient") msgid "[ ] : .M.sub.i.logical() maybe inefficient" msgstr "[ ] : '.M.sub.i.logical()' może być niewydajne" # Recommended/Matrix/R/Matrix.R: 582 # stop(gettextf( # "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.logical)?", # nA)) msgid "" "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.logical)?" msgstr "" "nargs() = %d. Obce nielegalne argumenty wewnątrz '[ .. ]' (i.logical)?" # Recommended/Matrix/R/Matrix.R: 637 # message("m[ ]: inefficiently indexing single elements") msgid "m[ ]: inefficiently indexing single elements" msgstr "m[ ]: nieefektywne indeksowanie pojedynczych elementów" # Recommended/Matrix/R/Matrix.R: 667 # stop(gettextf( # "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.2col)?", # nA)) msgid "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.2col)?" msgstr "nargs() = %d. Obce nielegalne argumenty wewnątrz '[ .. ]' (i.2col)?" # Recommended/Matrix/R/Matrix.R: 656 # stop(".M.sub.i.2col(): 'i' has no integer column number;\n # "should never happen; please report") #, fuzzy msgid "" ".M.sub.i.2col(): 'i' has no integer column number;\n" " should never happen; please report" msgstr ".M.sub.i.2col(): 'i' posiada niecałkowitą liczbę kolumn;" # Recommended/Matrix/R/Matrix.R: 661 # stop("such indexing must be by logical or 2-column numeric matrix") # Recommended/Matrix/R/Matrix.R: 693 # stop("such indexing must be by logical or 2-column numeric matrix") # Recommended/Matrix/R/Tsparse.R: 636 # stop("such indexing must be by logical or 2-column numeric matrix") msgid "such indexing must be by logical or 2-column numeric matrix" msgstr "" "takie indeksowanie musi być wykonane poprzez macierz logiczną lub 2-" "kolumnową macierz liczbową" # Recommended/Matrix/R/Matrix.R: 690 # stop(".M.repl.i.2col(): 'i' has no integer column number;\n # "should never happen; please report") #, fuzzy msgid "" ".M.repl.i.2col(): 'i' has no integer column number;\n" " should never happen; please report" msgstr ".M.repl.i.2col(): 'i' posiada niecałkowitą liczbę kolumn;" # Recommended/Matrix/R/Matrix.R: 695 # message(".M.repl.i.2col(): drop 'matrix' case ...") msgid ".M.repl.i.2col(): drop 'matrix' case ..." msgstr ".M.repl.i.2col(): zrzuć przypadek 'matrix' ..." # Recommended/Matrix/R/Matrix.R: 701 # stop("negative values are not allowed in a matrix subscript") # Recommended/Matrix/R/Tsparse.R: 639 # stop("negative values are not allowed in a matrix subscript") msgid "negative values are not allowed in a matrix subscript" msgstr "ujemne wartości nie są dozwolone w indeksach macierzy" # Recommended/Matrix/R/Matrix.R: 703 # stop("NAs are not allowed in subscripted assignments") # Recommended/Matrix/R/Tsparse.R: 641 # stop("NAs are not allowed in subscripted assignments") msgid "NAs are not allowed in subscripted assignments" msgstr "wartości NA nie są dozwolone w indeksowanych przypisaniach" # Recommended/Matrix/R/Matrix.R: 716 # message("m[ ] <- v: inefficiently treating single elements") msgid "m[ ] <- v: inefficiently treating single elements" msgstr "m[ ] <- v: nieefektywne traktowanie pojedynczych elementów" # Recommended/Matrix/R/Matrix.R: 722 # stop(gettextf( # "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' ?", # nA)) msgid "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' ?" msgstr "nargs() = %d. Obce nielegalne argumenty wewnątrz '[ .. ]' ?" # Recommended/Matrix/R/Matrix.R: 795 # stop(gettextf( # "RHS 'value' (class %s) matches 'ANY', but must match matrix class %s", # class(value), class(x))) msgid "RHS 'value' (class %s) matches 'ANY', but must match matrix class %s" msgstr "" "prawa strona 'value' (klasa %s) pasuje do 'ANY', a musi pasować do klasy " "macierzy '%s'" # Recommended/Matrix/R/Matrix.R: 798 # stop("not-yet-implemented 'Matrix[<-' method") msgid "not-yet-implemented 'Matrix[<-' method" msgstr "jeszcze niezaimplementowana metoda 'Matrix[<-'" # Recommended/Matrix/R/Ops.R: 35 # warning("inefficient method used for \"- e1\"") msgid "inefficient method used for \"- e1\"" msgstr "nieefektywna metoda użyta dla '- e1'" # Recommended/Matrix/R/Ops.R: 1153 # stop(class(e2),"(0) ",.Generic," is undefined") #, fuzzy msgid " %s %s is undefined" msgstr " nie jest określone" # Recommended/Matrix/R/Ops.R: 172 # stop("internal bug in \"Compare\" method (Cmp.Mat.atomic); please report") msgid "internal bug in \"Compare\" method (Cmp.Mat.atomic); please report" msgstr "" "błąd wewnętrzny w metodzie 'Compare' (Cmp.Mat.atomic); proszę zgłosić raport" msgid "Cmp.Mat.atomic() should not be called for diagonalMatrix" msgstr "'Cmp.Mat.atomic()' nie powinien być wywołany dla 'diagonalMatrix'" # Recommended/Matrix/R/Ops.R: 426 # stop("Matrices must have same number of rows for arithmetic") msgid "Matrices must have same number of rows for arithmetic" msgstr "" "Macierze muszą mieć tę samą liczbę wierszy jeśli mają być przeprowadzane " "działania arytmetyczne" # Recommended/Matrix/R/Ops.R: 442 # stop("number of rows are not compatible for ", .Generic) #, fuzzy msgid "number of rows are not compatible for %s" msgstr "liczba wierszy nie jest zgodna dla" # Recommended/Matrix/R/Ops.R: 453 # stop ("length of 2nd arg does not match dimension of first") # Recommended/Matrix/R/Ops.R: 507 # stop ("length of 2nd arg does not match dimension of first") msgid "length of 2nd arg does not match dimension of first" msgstr "długość drugiego argumentu nie zgadza się z wymiarem pierwszego" # Recommended/Matrix/R/Ops.R: 465 # stop ("length of 1st arg does not match dimension of 2nd") # Recommended/Matrix/R/Ops.R: 538 # stop ("length of 1st arg does not match dimension of 2nd") msgid "length of 1st arg does not match dimension of 2nd" msgstr "długość pierwszego argumentu nie zgadza się z wymiarem drugiego" msgid "internal bug in \"Logic\" method (Logic.Mat.atomic); please report" msgstr "" "błąd wewnętrzny w metodzie 'Logic' (.Logic.Mat.atomic); proszę zgłosić raport" msgid "Logic.Mat.atomic() should not be called for diagonalMatrix" msgstr "'Logic.Mat.atomic()' nie powinien być wywołany dla 'diagonalMatrix'" msgid "vector too long in Matrix - vector operation" msgstr "" # Recommended/Matrix/R/abIndex.R: 467 # warning("longer object length\n # is not a multiple of shorter object length") msgid "" "longer object length\n" "\tis not a multiple of shorter object length" msgstr "" "długość dłuższego obiektu\n" "\tnie jest wielokrotnością długości krótszego obiektu" # Recommended/Matrix/R/Ops.R: 1153 # stop(class(e2),"(0) ",.Generic," is undefined") #, fuzzy msgid "%s %s is undefined" msgstr " nie jest określone" # Matrix/R/abIndex.R: 467 # warning("longer object length\n # is not a multiple of shorter object length") # Recommended/Matrix/R/Ops.R: 1494 # warning("longer object length\n # ", # "is not a multiple of shorter object length") # Recommended/Matrix/R/Ops.R: 1587 # warning("longer object length\n # ", # "is not a multiple of shorter object length") # Recommended/Matrix/R/Ops.R: 1614 # warning("longer object length\n # ", # "is not a multiple of shorter object length") msgid "longer object length" msgstr "długość dłuższego obiektu" # Matrix/R/abIndex.R: 467 # warning("longer object length\n # is not a multiple of shorter object length") # Recommended/Matrix/R/Ops.R: 1494 # warning("longer object length\n # ", # "is not a multiple of shorter object length") # Recommended/Matrix/R/Ops.R: 1587 # warning("longer object length\n # ", # "is not a multiple of shorter object length") # Recommended/Matrix/R/Ops.R: 1614 # warning("longer object length\n # ", # "is not a multiple of shorter object length") msgid "is not a multiple of shorter object length" msgstr "nie jest wielokrotnością długości krótszego obiektu" # Recommended/Matrix/R/Ops.R: 1578 # stop(sprintf( # "dim [product %d] do not match the length of object [%d]", # n1, n2)) # Recommended/Matrix/R/Ops.R: 1605 # stop(sprintf( # "dim [product %d] do not match the length of object [%d]", # n2, n1)) msgid "dim [product %d] do not match the length of object [%d]" msgstr "wymiar [produkt %d] nie zgadza się z długością obiektu [%d]" # Recommended/Matrix/R/Rsparse.R: 32 # stop("invalid class:", cl) # Recommended/Matrix/R/Rsparse.R: 59 # stop("invalid class:", cl) #, fuzzy msgid "invalid class: %s" msgstr "niepoprawna klasa:" # Recommended/Matrix/R/Tsparse.R: 8 # stop("not-yet-implemented coercion to \"TsparseMatrix\"") msgid "not-yet-implemented coercion to \"TsparseMatrix\"" msgstr "jeszcze niezaimplementowane przekształcenie na 'TsparseMatrix'" # Recommended/Matrix/R/sparseVector.R: 357 # stop("you cannot mix negative and positive indices") # Recommended/Matrix/R/sparseVector.R: 424 # stop("you cannot mix negative and positive indices") # Recommended/Matrix/R/Tsparse.R: 126 # stop("you cannot mix negative and positive indices") msgid "you cannot mix negative and positive indices" msgstr "nie można mieszać ujemnych oraz dodatnich indeksów" # Recommended/Matrix/R/Tsparse.R: 130 # stop("index larger than maximal ",n) #, fuzzy msgid "index larger than maximal %d" msgstr "indeks dłuższy niż maksymalny możliwy" # Recommended/Matrix/R/Tsparse.R: 123 # stop("'NA' indices are not (yet?) supported for sparse Matrices") msgid "'NA' indices are not (yet?) supported for sparse Matrices" msgstr "indeksy 'NA' nie są (jeszcze?) wspierane dla rzadkich macierzy" # Recommended/Matrix/R/Tsparse.R: 138 # stop(gettextf("logical subscript too long (%d, should be %d)", # length(i), n)) msgid "logical subscript too long (%d, should be %d)" msgstr "indeks logiczny jest zbyt długi (%d, powinien być %d)" # Recommended/Matrix/R/Tsparse.R: 144 # stop("no 'dimnames[[.]]': cannot use character indexing") msgid "no 'dimnames[[.]]': cannot use character indexing" msgstr "brak 'dimnames[[.]]': nie można używać indeksowania tekstowego" # Recommended/Matrix/R/Tsparse.R: 146 # stop("invalid character indexing") msgid "invalid character indexing" msgstr "niepoprawne tekstowe indeksowanie" # Recommended/Matrix/R/Tsparse.R: 207 # stop("Matrix-internal error in [i,,d]; please report") msgid "Matrix-internal error in [i,,d]; please report" msgstr "" "błąd wewnętrzny pakiecie 'Matrix' w '[i,,d]'; proszę zgłosić raport" # Recommended/Matrix/R/Tsparse.R: 257 # stop("FIXME: NOT YET FINISHED IMPLEMENTATION") msgid "FIXME: NOT YET FINISHED IMPLEMENTATION" msgstr "FIXME: JESZCZE NIEZAKOŃCZONA IMPLEMENTACJA" # Recommended/Matrix/R/Tsparse.R: 310 # stop("internal bug: missing 'i' in replTmat(): please report") msgid "internal bug: missing 'i' in replTmat(): please report" msgstr "błąd wewnętrzny: brakuje 'i' w 'replTmat()': proszę zgłosić raport" # Recommended/Matrix/R/Tsparse.R: 312 # stop("[ ] indexing not allowed: forgot a \",\" ?") msgid "[ ] indexing not allowed: forgot a \",\" ?" msgstr "indeksowanie [ ] nie jest dozwolone: zapomniałeś ',' ?" # Recommended/Matrix/R/Tsparse.R: 314 # stop("internal bug: matrix 'i' in replTmat(): please report") msgid "internal bug: matrix 'i' in replTmat(): please report" msgstr "wewnętrzny błąd: macierz 'i' w 'replTmat()': proszę zgłosić raport" # Recommended/Matrix/R/Tsparse.R: 344 # warning(gettextf("x[.] <- val: x is \"%s\", val not in {TRUE, FALSE} is coerced%s.", # clx, if(iNA) " NA |--> TRUE" else "")) #, fuzzy msgid "" "x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced; NA |--> TRUE." msgstr "" "x[.] <- wartość: 'x' to '%s', wartość nie w zakresie {TRUE, FALSE} zostaje " "przekształcona %s." # Recommended/Matrix/R/Tsparse.R: 344 # warning(gettextf("x[.] <- val: x is \"%s\", val not in {TRUE, FALSE} is coerced%s.", # clx, if(iNA) " NA |--> TRUE" else "")) #, fuzzy msgid "x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced." msgstr "" "x[.] <- wartość: 'x' to '%s', wartość nie w zakresie {TRUE, FALSE} zostaje " "przekształcona %s." # Recommended/Matrix/R/Tsparse.R: 500 # warning(gettextf("x[.,.] <- val: x is \"%s\", val not in {TRUE, FALSE} is coerced%s.", # clx, if(iNA) " NA |--> TRUE" else "")) #, fuzzy msgid "" "x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced NA |--> TRUE." msgstr "" "x[.,.] <- wartość: 'x' to '%s', wartość nie w zakresie {TRUE, FALSE} zostaje " "przekształcona %s." # Recommended/Matrix/R/Tsparse.R: 500 # warning(gettextf("x[.,.] <- val: x is \"%s\", val not in {TRUE, FALSE} is coerced%s.", # clx, if(iNA) " NA |--> TRUE" else "")) #, fuzzy msgid "x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced." msgstr "" "x[.,.] <- wartość: 'x' to '%s', wartość nie w zakresie {TRUE, FALSE} zostaje " "przekształcona %s." # Recommended/Matrix/R/Tsparse.R: 527 # gettextf("x[.,.] <- val : x being coerced from Tsparse* to CsparseMatrix") msgid "x[.,.] <- val : x being coerced from Tsparse* to CsparseMatrix" msgstr "" "x[.,.] <- wartość : 'x' zostaje przekształcone z 'Tsparse*' na " "'CsparseMatrix'" # Recommended/Matrix/R/Matrix.R: 768 # stop(gettextf("nargs() = %d should never happen; please report.", nA)) # Recommended/Matrix/R/Matrix.R: 780 # stop(gettextf("nargs() = %d should never happen; please report.", nA)) # Recommended/Matrix/R/Tsparse.R: 622 # stop(gettextf("nargs() = %d should never happen; please report.", nA)) msgid "nargs() = %d should never happen; please report." msgstr "'nargs() = %d' nie powinno się wydarzyć; proszę zgłosić raport." # Recommended/Matrix/R/Tsparse.R: 667 # stop("row indices must be <= nrow(.) which is ", nr) #, fuzzy msgid "row indices must be <= nrow(.) which is %d" msgstr "indeksy wiersza muszą być <= 'nrow(.)' który wynosi" # Recommended/Matrix/R/Tsparse.R: 668 # stop("column indices must be <= ncol(.) which is ", nc) #, fuzzy msgid "column indices must be <= ncol(.) which is %d" msgstr "indeksy kolumn muszą być <= 'ncol(.)' który wynosi" # Recommended/Matrix/R/abIndex.R: 13 # stop("'force' must be (coercable to) TRUE or FALSE") msgid "'force' must be (coercable to) TRUE or FALSE" msgstr "'force' musi być (przekształcalne do) TRUE lub FALSE" # Recommended/Matrix/R/abIndex.R: 164 # stop("invalid (to - from)/by in seq(.)") msgid "invalid (to - from)/by in seq(.)" msgstr "niepoprawne '(to - from)/by' w 'seq(.)'" # Recommended/Matrix/R/abIndex.R: 167 # stop("wrong sign in 'by' argument") msgid "wrong sign in 'by' argument" msgstr "niepoprawny znak w argumencie 'by'" # Recommended/Matrix/R/abIndex.R: 169 # stop("'by' argument is much too small") msgid "'by' argument is much too small" msgstr "argument 'by' jest znacznie za mały" # Recommended/Matrix/R/abIndex.R: 179 # stop("length must be non-negative number") msgid "length must be non-negative number" msgstr "długość musi być nieujemną liczbą" # Recommended/Matrix/R/abIndex.R: 200 # stop("too many arguments") msgid "too many arguments" msgstr "zbyt wiele argumentów" # Recommended/Matrix/R/abIndex.R: 288 # warning("c(,..) of different kinds, coercing all to 'rleDiff'") msgid "c(,..) of different kinds, coercing all to 'rleDiff'" msgstr "" "'c(,..)' różnych rodzajów, przekształcanie wszystkich do 'rleDiff'" # Recommended/Matrix/R/abIndex.R: 347 # stop("[i] is not yet implemented") msgid "[i] is not yet implemented" msgstr "'[i]' nie jest jeszcze zaimplementowane" # Recommended/Matrix/R/abIndex.R: 425 # stop("all() is not yet implemented") msgid "all() is not yet implemented" msgstr "'all()' nie jest jeszcze zaimplementowane" # Recommended/Matrix/R/abIndex.R: 431 # stop("sum() is not yet implemented") msgid "sum() is not yet implemented" msgstr "'sum()' nie jest jeszcze zaimplementowane" # Recommended/Matrix/R/abIndex.R: 434 # stop("prod() is not yet implemented") msgid "prod() is not yet implemented" msgstr "'prod()' nie jest jeszcze zaimplementowane" # Recommended/Matrix/R/abIndex.R: 462 # stop("not yet implemented") # Recommended/Matrix/R/sparseMatrix.R: 665 # stop("not yet implemented") msgid "not yet implemented" msgstr "jeszcze niezaimplementowane" # Recommended/Matrix/R/abIndex.R: 520 # warning("x / 0 for an x with sign-change\n # "no longer representable as 'rleDiff'") #, fuzzy msgid "" "x / 0 for an x with sign-change\n" " no longer representable as 'rleDiff'" msgstr "x / 0 dla ' x' ze zmianą znaku" # Recommended/Matrix/R/abIndex.R: 697 # stop(" --> is not yet implemented") msgid " --> is not yet implemented" msgstr " --> nie jest jeszcze zaimplementowane" # Recommended/Matrix/R/abIndex.R: 702 # stop(" --> is not yet implemented") msgid " --> is not yet implemented" msgstr " --> nie jest jeszcze zaimplementowane" # Recommended/Matrix/R/bandSparse.R: 26 # stop(gettextf("'diagonals' matrix must have %d columns (= length(k) )", # len.k)) msgid "'diagonals' matrix must have %d columns (= length(k) )" msgstr "macierz 'diagonals' musi mieć %d kolumn (= length(k) )" # Recommended/Matrix/R/bandSparse.R: 32 # stop(gettextf("'diagonals' must have the same length (%d) as 'k'", # len.k)) msgid "'diagonals' must have the same length (%d) as 'k'" msgstr "'diagonals' musi mieć tę samą długość (%d) co 'k'" # Recommended/Matrix/R/bandSparse.R: 38 # stop("for symmetric band matrix, only specify upper or lower triangle", # "\n # hence, all k must have the same sign") #, fuzzy msgid "" "for symmetric band matrix, only specify upper or lower triangle\n" " hence, all k must have the same sign" msgstr "" "dla symetrycznej macierzy wstęgowej, określ jedynie górny oraz dolny trójkąt" # Recommended/Matrix/R/bandSparse.R: 67 # warning(sprintf("the %d-th (sub)-diagonal (k = %d) is %s", # s, kk, "too short; filling with NA's")) #, fuzzy msgid "the %d-th (sub)-diagonal (k = %d) is too short; filling with NA's" msgstr "(pod)-diagonala %d (k = %d) jest %s" # Recommended/Matrix/R/condest.R: 74 # stop("'A' must be a square matrix") # Recommended/Matrix/R/condest.R: 194 # stop("'A' must be a square matrix") msgid "'A' must be a square matrix" msgstr "'A' musi być macierzą kwadratową" # Recommended/Matrix/R/condest.R: 186 # stop("must either specify 'A' or the functions 'A.x' and 'At.x'") msgid "must either specify 'A' or the functions 'A.x' and 'At.x'" msgstr "potrzeba określić 'A' lub funkcje 'A.x' oraz 'At.x'" # Recommended/Matrix/R/condest.R: 188 # warning("when 'A' is specified, 'A.x' and 'At.x' are disregarded") msgid "when 'A' is specified, 'A.x' and 'At.x' are disregarded" msgstr "gdy 'A' jest określone, 'A.x' oraz 'At.x' są odrzucane" # Recommended/Matrix/R/condest.R: 234 # warning("not converged in ",iter.max," iterations") #, fuzzy msgid "not converged in %d iterations" msgstr "nie uzbieżnił się w" # Recommended/Matrix/R/condest.R: 249 # message("hit a cycle (1) -- stop iterations") msgid "hit a cycle (1) -- stop iterations" msgstr "natrafiona na cykl (1) -- zatrzymywanie iteracji" # Recommended/Matrix/R/condest.R: 283 # message("hit a cycle (2) -- stop iterations") msgid "hit a cycle (2) -- stop iterations" msgstr "natrafiona na cykl (2) -- zatrzymywanie iteracji" # Recommended/Matrix/R/condest.R: 300 # message("not enough new vecs -- stop iterations") msgid "not enough new vecs -- stop iterations" msgstr "zbyt mało nowych wektorów -- zatrzymywanie iteracji" # Recommended/Matrix/R/dMatrix.R: 22 # stop("\"dMatrix\" object with NAs cannot be coerced to \"nMatrix\"") msgid "\"dMatrix\" object with NAs cannot be coerced to \"nMatrix\"" msgstr "" "obiekt 'dMatrix' z wartościami NA nie może zostać przekształcony w 'nMatrix'" # Recommended/Matrix/R/denseMatrix.R: 30 # stop("diagonalMatrix in .dense2C() -- should never happen, please report!") msgid "diagonalMatrix in .dense2C() -- should never happen, please report!" msgstr "" "'diagonalMatrix' w '.dense2C()' -- nie powinno nigdy się wydarzyć, proszę " "zgłosić raport!" # Recommended/Matrix/R/denseMatrix.R: 36 # stop("undefined method for class ", cl) #, fuzzy msgid "undefined method for class %s" msgstr "niezdefiniowana metoda dla klasy" # Recommended/Matrix/R/sparseVector.R: 279 # stop("dim(.) value must be numeric of length 2") # Recommended/Matrix/R/denseMatrix.R: 71 # stop("dim(.) value must be numeric of length 2") # Recommended/Matrix/R/sparseMatrix.R: 700 # stop("dim(.) value must be numeric of length 2") msgid "dim(.) value must be numeric of length 2" msgstr "wartości 'dim(.)' muszą być liczbami o długości 2" # Recommended/Matrix/R/sparseVector.R: 281 # stop("dimensions don't match the number of cells") # Recommended/Matrix/R/denseMatrix.R: 73 # stop("dimensions don't match the number of cells") # Recommended/Matrix/R/sparseMatrix.R: 702 # stop("dimensions don't match the number of cells") msgid "dimensions don't match the number of cells" msgstr "wymiary nie zgadzają się z liczbą komórek" # Recommended/Matrix/R/denseMatrix.R: 101 # stop("invalid nargs()= ",na) # Recommended/Matrix/R/denseMatrix.R: 164 # stop("invalid nargs()= ",na) #, fuzzy msgid "invalid nargs()= %d" msgstr "niepoprawne nargs()=" msgid "" "LU computationally singular: ratio of extreme entries in |diag(U)| = %9.4g" msgstr "" # Recommended/Matrix/R/dgTMatrix.R: 20 # stop("cannot coerce non-symmetric dgTMatrix to dsCMatrix class") #, fuzzy msgid "cannot coerce non-symmetric \"dgTMatrix\" to \"dsCMatrix\" class" msgstr "" "nie można przekształcić niesymetrycznej macierzy klasy 'dgTMatrix' na klasę " "'dsCMatrix'" # Recommended/Matrix/R/dgTMatrix.R: 44 # stop("the matrix is not triangular") msgid "the matrix is not triangular" msgstr "macierz nie jest trójkątna" # Recommended/Matrix/R/dgTMatrix.R: 108 # stop("'lwd' must be NULL or non-negative numeric") msgid "'lwd' must be NULL or non-negative numeric" msgstr "'lwd' musi mieć wartość NULL lub być nieujemną liczbą" # Recommended/Matrix/R/diagMatrix.R: 29 # stop("'x' has invalid data type") msgid "'x' has invalid data type" msgstr "'x' posiada niepoprawny typ danych" # Recommended/Matrix/R/diagMatrix.R: 54 # stop("length(x) must be either 1 or #{cols}") msgid "length(x) must be either 1 or #{cols}" msgstr "'length(x)' musi wynosić 1 lub #{kolumn}" # Recommended/Matrix/R/diagMatrix.R: 92 # stop("some arguments are not matrices") msgid "some arguments are not matrices" msgstr "niektóre argumenty nie są macierzami" # Recommended/Matrix/R/diagMatrix.R: 216 # stop("'", kind,"' kind not yet implemented") #, fuzzy msgid "%s kind not yet implemented" msgstr "' nie jest jeszcze zaimplementowany" # Recommended/Matrix/R/diagMatrix.R: 326 # stop("non-square matrix") # Recommended/Matrix/R/diagMatrix.R: 346 # stop("non-square matrix") msgid "non-square matrix" msgstr "niekwadratowa macierz" # Recommended/Matrix/R/diagMatrix.R: 328 # stop("matrix with non-zero off-diagonals cannot be coerced to diagonalMatrix") #, fuzzy msgid "" "matrix with non-zero off-diagonals cannot be coerced to \"diagonalMatrix\"" msgstr "" "macierz z niezerowaymi wartościami pozadiagonalnymi nie może zostać " "przekształcona w na obiekt klasy 'diagonalMatrix'" # Recommended/Matrix/R/diagMatrix.R: 347 # stop("matrix is not diagonal") msgid "matrix is not diagonal" msgstr "macierz nie jest diagonalna" # Recommended/Matrix/R/diagMatrix.R: 407 # stop("Internal bug: nargs()=",na,"; please report") #, fuzzy msgid "Internal bug: nargs()=%d; please report" msgstr "Błąd wewnętrzny: nargs()=" # Recommended/Matrix/R/diagMatrix.R: 500 # stop("chol() is undefined for diagonal matrix with negative entries") msgid "chol() is undefined for diagonal matrix with negative entries" msgstr "" "'chol()' jest nieokreślona dla macierzy diagonalnych z ujemnymi wpisami" # Recommended/Matrix/R/diagMatrix.R: 558 # stop("non-matching dimensions") # Recommended/Matrix/R/diagMatrix.R: 571 # stop("non-matching dimensions") # Recommended/Matrix/R/diagMatrix.R: 587 # stop("non-matching dimensions") # Recommended/Matrix/R/diagMatrix.R: 599 # stop("non-matching dimensions") # Recommended/Matrix/R/diagMatrix.R: 630 # stop("non-matching dimensions") # Recommended/Matrix/R/diagMatrix.R: 648 # stop("non-matching dimensions") msgid "non-matching dimensions" msgstr "niezgodne wymiary" # Recommended/Matrix/R/diagMatrix.R: 716 # stop("incompatible matrix dimensions") msgid "incompatible matrix dimensions" msgstr "niezgodne wymiary macierzy" # Recommended/Matrix/R/diagMatrix.R: 751 # stop("intermediate 'r' is of type", typeof(r)) #, fuzzy msgid "intermediate 'r' is of type %s" msgstr "pośrednie 'r' jest typu" # Recommended/Matrix/R/diagMatrix.R: 768 # stop("not yet implemented .. please report") msgid "not yet implemented .. please report" msgstr "jeszcze niezaimplementowane .. proszę zgłosić raport" # Recommended/Matrix/R/dsyMatrix.R: 94 # stop("not a positive definite matrix") # Recommended/Matrix/R/dppMatrix.R: 27 # stop("not a positive definite matrix") msgid "not a positive definite matrix" msgstr "to nie jest dodatnio określona macierz" # Recommended/Matrix/R/dsCMatrix.R: 6 # warning("as(.,\"dsCMatrix\") is deprecated; do use as(., \"symmetricMatrix\")") #, fuzzy msgid "" "as(.,\"dsCMatrix\") is deprecated (since 2008); do use as(., " "\"symmetricMatrix\")" msgstr "" "'as(.,\"dsCMatrix\")' jest przestarzałe; używaj 'as(., \"symmetricMatrix\")'" # Recommended/Matrix/R/dtpMatrix.R: 14 # warning("inefficient coercion (lost triangularity); please report") msgid "inefficient coercion (lost triangularity); please report" msgstr "" "nieefektywne przekształcenie (utracono trójkątność); proszę zgłosić raport" # Recommended/Matrix/R/indMatrix.R: 15 # stop("coercion to 'indMatrix' only works from integer numeric") #, fuzzy msgid "coercion to \"indMatrix\" only works from integer numeric" msgstr "przekształcenie na 'indMatrix' działa jedynie dla liczb całkowitych" msgid "" "coercion from list(i1,...,ik, d) to \"indMatrix\" failed.\n" " All entries must be integer valued and the number of columns, d, not " "smaller\n" " than the maximal index i*." msgstr "" # Recommended/Matrix/R/pMatrix.R: 47 # stop("not a square matrix") #, fuzzy msgid "not a skinny matrix" msgstr "to nie jest macierz kwadratowa" # Recommended/Matrix/R/pMatrix.R: 49 # stop("the number of non-zero entries differs from nrow(.)") msgid "the number of non-zero entries differs from nrow(.)" msgstr "liczba niezerowych wpisów różni się od 'nrow(.)'" # Recommended/Matrix/R/pMatrix.R: 55 # stop("must have exactly one non-zero entry per row") msgid "must have exactly one non-zero entry per row" msgstr "potrzeba mieć dokładnie jeden niezerowy wpis na wiersz" # Recommended/Matrix/R/kronecker.R: 37 # stop("kronecker method must use default 'FUN'") # Recommended/Matrix/R/kronecker.R: 55 # stop("kronecker method must use default 'FUN'") msgid "kronecker method must use default 'FUN'" msgstr "metoda kroneckera musi użyć domyślnej 'FUN'" # Recommended/Matrix/R/pMatrix.R: 147 # stop('replacing "pMatrix" entries is not allowed, as rarely sensible') msgid "replacing \"indMatrix\" entries is not allowed, as rarely sensible" msgstr "" "zastępowanie wpisów w 'indMatrix' jest niedozwolone, ponieważ jest to rzadko " "sensowne" # Recommended/Matrix/R/lMatrix.R: 8 # stop("\"lMatrix\" object with NAs cannot be coerced to \"nMatrix\"") msgid "\"lMatrix\" object with NAs cannot be coerced to \"nMatrix\"" msgstr "" "obiekt 'lMatrix' z wartościami NA nie może zostać przekształcony na 'nMatrix'" # Recommended/Matrix/R/nearPD.R: 50 # stop("Matrix seems negative semi-definite") msgid "Matrix seems negative semi-definite" msgstr "Macierz wydaje się być ujemnie określona" # Recommended/Matrix/R/nearPD.R: 77 # warning("nearPD() did not converge in ", iter, " iterations") #, fuzzy msgid "'nearPD()' did not converge in %d iterations" msgstr "'nearPD()' nie uzbieżnił się w" # Recommended/Matrix/R/ngTMatrix.R: 24 # stop("cannot coerce 'NA's to \"nsparseMatrix\"") msgid "cannot coerce 'NA's to \"nsparseMatrix\"" msgstr "nie można przekształcić wartości 'NA' na 'nsparseMatrix'" # Recommended/Matrix/R/nsCMatrix.R: 58 # stop("temporarily disabled") msgid "temporarily disabled" msgstr "tymczasowo niedostępne" # Recommended/Matrix/R/pMatrix.R: 15 msgid "coercion to \"pMatrix\" only works from integer numeric" msgstr "przekształcenie na 'pMatrix' działa jedynie dla liczb całkowitych" # Recommended/Matrix/R/pMatrix.R: 47 # stop("not a square matrix") msgid "not a square matrix" msgstr "to nie jest macierz kwadratowa" # Recommended/Matrix/R/products.R: 186 # stop(gettextf('not-yet-implemented method for <%s> %%*%% <%s>', # class(x), class(y))) msgid "not-yet-implemented method for <%s> %%*%% <%s>" msgstr "jeszcze niezaimplementowana metoda dla <%s> %%*%% <%s>" msgid "" "rankMatrix(, method = '%s') coerces to dense matrix.\n" " Probably should rather use method = 'qr' !?" msgstr "" msgid "rankMatrix(x, method='qr'): computing t(x) as nrow(x) < ncol(x)" msgstr "" # Recommended/Matrix/R/spModels.R: 113 # stop("model frame and formula mismatch in model.matrix()") msgid "model frame and formula mismatch in model.matrix()" msgstr "niezgodność ramki modelu oraz formuły w 'model.matrix()'" # Recommended/Matrix/R/spModels.R: 125 # warning(gettextf("variable '%s' converted to a factor", i), # domain = NA) msgid "variable '%s' converted to a factor" msgstr "zmienna '%s' została zamieniona na czynnik" # Recommended/Matrix/R/spModels.R: 138 # stop("invalid 'contrasts.arg' argument") msgid "invalid 'contrasts.arg' argument" msgstr "niepoprawny argument 'contrasts.arg'" # Recommended/Matrix/R/spModels.R: 141 # warning(gettextf("variable '%s' is absent, its contrast will be ignored", nn), # domain = NA) msgid "variable '%s' is absent, its contrast will be ignored" msgstr "zmienna '%s' jest nieobecna, jej kontrast zostanie zignorowany" # Recommended/Matrix/R/sparseMatrix.R: 13 # stop("only 2-dimensional tables can be directly coerced to sparse matrices") msgid "only 2-dimensional tables can be directly coerced to sparse matrices" msgstr "" "jedynie 2-wymiarowe tablice mogą zostać bezpośrednio przekształcone w " "rzadkie macierze" # Recommended/Matrix/R/sparseMatrix.R: 44 # stop("exactly one of 'i', 'j', or 'p' must be missing from call") msgid "exactly one of 'i', 'j', or 'p' must be missing from call" msgstr "dokłanie jeden z 'i', 'j', lub 'p' musi być nieobecny w wywołaniu" # Recommended/Matrix/R/sparseMatrix.R: 48 # stop("'p' must be a non-decreasing vector (0, ...)") msgid "'p' must be a non-decreasing vector (0, ...)" msgstr "'p' musi być niemalejącym wektorem (0, ...)" # Recommended/Matrix/R/sparseMatrix.R: 58 # stop("NA's in (i,j) are not allowed") msgid "NA's in (i,j) are not allowed" msgstr "wartości NA w (i,j) nie są dozwolone" # Recommended/Matrix/R/sparseMatrix.R: 67 # stop("symmetric matrix must be square") msgid "symmetric matrix must be square" msgstr "macierz symetryczna musi być kwadratowa" # Recommended/Matrix/R/sparseMatrix.R: 79 # warning("length(i) is not a multiple of length(x)") msgid "length(i) is not a multiple of length(x)" msgstr "'length(i)' nie jest wielokrotnością 'length(x)'" # Recommended/Matrix/R/sparseMatrix.R: 198 # stop("only square matrices can be used as incidence matrices for graphs") msgid "only square matrices can be used as incidence matrices for graphs" msgstr "" "jedynie kwadratowe macierze mogą zostać użyte jako macierz incydencji dla " "grafów" # Recommended/Matrix/R/sparseMatrix.R: 240 # stop("Matrix-internal error in [i,,d]; please report") msgid "Matrix-internal error in [i,,d]; please report" msgstr "" "błąd wewnętrzny pakietu 'Matrix' w '[i,,d]'; proszę zgłosić raport" # Recommended/Matrix/R/sparseMatrix.R: 371 # stop("invalid 'col.names' string: ", cn) #, fuzzy msgid "invalid 'col.names' string: %s" msgstr "niepoprawny łańcuch 'col.names':" # Recommended/Matrix/R/sparseMatrix.R: 598 # stop("logic programming error in printSpMatrix2(), please report") msgid "logic programming error in printSpMatrix2(), please report" msgstr "błąd logiczny programu w 'printSpMatrix2()', proszę zgłosić raport" # Recommended/Matrix/R/sparseMatrix.R: 720 # stop("invalid 'type'") msgid "invalid 'type'" msgstr "niepoprawny 'type'" # Recommended/Matrix/R/sparseMatrix.R: 737 # warning("rcond(.) via sparse -> dense coercion") msgid "rcond(.) via sparse -> dense coercion" msgstr "'rcond(.)' poprzez przekształcenie rzadkie -> gęste" # Recommended/Matrix/R/sparseMatrix.R: 748 # stop("'V' is not a *square* matrix") msgid "'V' is not a *square* matrix" msgstr "'V' nie jest macierzą *kwadratową*" # Recommended/Matrix/R/sparseQR.R: 10 # warning("qr.R() may differ from qr.R() because of permutations") #, fuzzy msgid "" "qr.R() may differ from qr.R() because of permutations. " "Possibly use our qrR() instead" msgstr "" "'qr.R()' może różnić się od 'qr.R()' z powodu permutacji" # Recommended/Matrix/R/sparseVector.R: 53 # stop("cannot coerce 'NA's to \"nsparseVector\"") msgid "cannot coerce 'NA's to \"nsparseVector\"" msgstr "nie można przekształcić wartości 'NA' na 'nsparseVector'" # Recommended/Matrix/R/sparseVector.R: 216 # stop("'x' must inherit from \"sparseVector\"") msgid "'x' must inherit from \"sparseVector\"" msgstr "'x' musi dziedziczyć z klasy 'sparseVector'" # Recommended/Matrix/R/sparseVector.R: 218 # stop("'ncol' must be >= 0") msgid "'ncol' must be >= 0" msgstr "'ncol' musi być >= 0" # Recommended/Matrix/R/sparseVector.R: 220 # stop("'nrow' must be >= 0") msgid "'nrow' must be >= 0" msgstr "'nrow' musi być >= 0" msgid "Must specify 'nrow' when 'symmetric' is true" msgstr "" msgid "'nrow' and 'ncol' must be the same when 'symmetric' is true" msgstr "" msgid "'x' must have length nrow^2 when 'symmetric' is true" msgstr "" # Recommended/Matrix/R/sparseVector.R: 228 # warning("'ncol' is not a factor of length(x)") msgid "'ncol' is not a factor of length(x)" msgstr "'ncol' nie jest czynnikiem długości 'length(x)'" # Recommended/Matrix/R/sparseVector.R: 232 # warning("'nrow' is not a factor of length(x)") msgid "'nrow' is not a factor of length(x)" msgstr "'nrow' nie jest czynnikiem długości 'length(x)'" # Recommended/Matrix/R/HBMM.R: 140 # stop(gettextf("symmetry form '%s' is not yet implemented", sym)) # Recommended/Matrix/R/HBMM.R: 167 # stop(gettextf("symmetry form '%s' is not yet implemented", sym)) #, fuzzy msgid "Class %s is not yet implemented" msgstr "forma symetryczna '%s' nie jest jeszcze zaimplementowana" # Recommended/Matrix/R/sparseVector.R: 377 # stop("index must be numeric, logical or sparseVector for indexing sparseVectors") msgid "" "index must be numeric, logical or sparseVector for indexing sparseVectors" msgstr "" "indeks musi być typem liczbowym, logicznym lub obiektem klasy 'sparseVector' " "na potrzeby indeksowania obiektów klasy 'sparseVector'" # Recommended/Matrix/R/sparseVector.R: 703 # stop("'times >= 0' is required") msgid "'times >= 0' is required" msgstr "wymagane jest 'times >= 0'" msgid "(un)packing only applies to dense matrices, class(x)='%s'" msgstr "(roz)pakowanie stosuje się jedynie do gęstych macierzy, class(x)='%s'" # Recommended/Matrix/R/dgTMatrix.R: 44 # stop("the matrix is not triangular") msgid "'x' is not symmetric nor triangular" msgstr "'x' nie jest macierzą symetryczną ani trójkątną" # Recommended/Matrix/R/Tsparse.R: 725 # warning("duplicate ij-entries in 'Matrix[ ij ] <- value'; using last") #~ msgid "duplicate ij-entries in 'Matrix[ ij ] <- value'; using last" #~ msgstr "" #~ "powtórzone wpisy 'ij' w 'Matrix[ ij ] <- value'; używanie ostatniego" # Recommended/Matrix/R/rankMatrix.R: 63 # stop(gettextf( # "method '%s' not applicable for qr() result class '%s'", # method, class(q.r)[1])) #, fuzzy #~ msgid "method %s not applicable for qr() result class %s" #~ msgstr "metoda '%s' nie ma zastosowania dla wyniku 'qr()' o klasie '%s'" # Recommended/Matrix/R/sparseVector.R: 361 # stop("too large index i > n =",n) #, fuzzy #~ msgid "too large index i > n = %d" #~ msgstr "zbyt duży indeks i > n =" # Recommended/Matrix/R/Auxiliaries.R: 338 # message(sprintf(" [[ suppressing %d column names %s%s ]]", nc, # paste(sQuote(cn[1:min(3, lc)]), collapse = ", "), # if(lc > 3) " ..." else "")) #~ msgid "," #~ msgstr "," # Recommended/Matrix/R/Auxiliaries.R: 338 # message(sprintf(" [[ suppressing %d column names %s%s ]]", nc, # paste(sQuote(cn[1:min(3, lc)]), collapse = ", "), # if(lc > 3) " ..." else "")) #~ msgid "..." #~ msgstr "..." #~ msgid "arguments" #~ msgstr "argumenty" #~ msgid ")$" #~ msgstr ")$" #~ msgid "^list\\(" #~ msgstr "^list\\(" # Recommended/Matrix/R/Matrix.R: 149 # message("dimnames(.) <- NULL: translated to \n # "dimnames(.) <- list(NULL,NULL) <==> unname(.)") #~ msgid "dimnames(.) <- NULL: translated to" #~ msgstr "dimnames(.) <- NULL: przetłumaczono na" #~ msgid "in Summary(, .): %s(<%s>, <%s>%s)" #~ msgstr "w 'Summary(, .)': %s(<%s>, <%s>%s)" #~ msgid ", ..." #~ msgstr ", ..." # Recommended/Matrix/R/Matrix.R: 656 # stop(".M.sub.i.2col(): 'i' has no integer column number;\n # "should never happen; please report") # Recommended/Matrix/R/Matrix.R: 690 # stop(".M.repl.i.2col(): 'i' has no integer column number;\n # "should never happen; please report") #~ msgid "should never happen; please report" #~ msgstr "nie powinno się wydarzyć; proszę zgłosić raport" # Recommended/Matrix/R/Ops.R: 134 # stop(" ",.Generic," ", class(e2),"(0) is undefined") # Recommended/Matrix/R/Ops.R: 638 # stop(" ",.Generic," ", class(e2),"(0) is undefined") # Recommended/Matrix/R/Ops.R: 1122 # stop(" ",.Generic," ", class(e2),"(0) is undefined") #~ msgid "" #~ msgstr "" # Recommended/Matrix/R/Ops.R: 134 # stop(" ",.Generic," ", class(e2),"(0) is undefined") # Recommended/Matrix/R/Ops.R: 638 # stop(" ",.Generic," ", class(e2),"(0) is undefined") # Recommended/Matrix/R/Ops.R: 1122 # stop(" ",.Generic," ", class(e2),"(0) is undefined") #~ msgid "(0) is undefined" #~ msgstr "(0) jest nieokreślone" # Recommended/Matrix/R/Ops.R: 1153 # stop(class(e2),"(0) ",.Generic," is undefined") #~ msgid "(0)" #~ msgstr "(0)" # Recommended/Matrix/R/abIndex.R: 520 # warning("x / 0 for an x with sign-change\n # "no longer representable as 'rleDiff'") #~ msgid "no longer representable as 'rleDiff'" #~ msgstr "nie jest już dłużej reprezentowalna jako 'rleDiff'" # Recommended/Matrix/R/bandSparse.R: 38 # stop("for symmetric band matrix, only specify upper or lower triangle", # "\n # hence, all k must have the same sign") #~ msgid "hence, all k must have the same sign" #~ msgstr "tak, więc wszystkie 'k' muszą mieć ten sam znak" # Recommended/Matrix/R/bandSparse.R: 67 # warning(sprintf("the %d-th (sub)-diagonal (k = %d) is %s", # s, kk, "too short; filling with NA's")) #~ msgid "too short; filling with NA's" #~ msgstr "zbyt krótka; wypełnianie wartościami NA" # Recommended/Matrix/R/condest.R: 234 # warning("not converged in ",iter.max," iterations") # Recommended/Matrix/R/nearPD.R: 77 # warning("nearPD() did not converge in ", iter, " iterations") #~ msgid "iterations" #~ msgstr "iteracjach" # Recommended/Matrix/R/diagMatrix.R: 216 # stop("'", kind,"' kind not yet implemented") #~ msgid "'" #~ msgstr "rodzaj '" # Recommended/Matrix/R/diagMatrix.R: 407 # stop("Internal bug: nargs()=",na,"; please report") #~ msgid "; please report" #~ msgstr "; proszę zgłosić raport" Matrix/inst/0000755000175100001440000000000012271765426012525 5ustar hornikusersMatrix/inst/po/0000755000175100001440000000000012271765426013143 5ustar hornikusersMatrix/inst/po/pl/0000755000175100001440000000000012271765426013556 5ustar hornikusersMatrix/inst/po/pl/LC_MESSAGES/0000755000175100001440000000000012271765426015343 5ustar hornikusersMatrix/inst/po/pl/LC_MESSAGES/Matrix.mo0000644000175100001440000005452112256121033017132 0ustar hornikusers$, 0)1[p##)8!S#u+#%&66(m-I&(54^5$4 2?/r=9+<F<, *0JR{(11)+[,,%%-/K3{),53Q;*:,'T)s+8!+$P-k!M/ J9;4?A5)w)20?/o+:: DaB|#( $) *N 1y * * (!3*!^! n!*{! !#!,!="3C"1w"F"<"'-#+U#0#,#,# $1,$0^$"$3$$!$)!%K%i%%%%$%2%,$&'Q&-y&.&2&. '-8'/f'+'*''+ (,7(,d(-(((1(#)*>) i)9)))!)'!*'I*#q*#*+*&* +/,+6\+++$+@+1,&Q,x,,<,),-3.-(b--%-(-$-$.B.6_..&.0. / /&+/'R/8z/8//- 0:06'2^2&t2$2.2+2/3K3!h3/3*3A3&'4?N4)4>434<+5hh5*5057-6<e6.6%686;07,l7B7F76#8;Z8;8,8"8B"9Be9;9L9/1:8a:8:2:3;3:;/n;/;";-;@<`<;|<J<==7A=Jy=8=D=,B>#o>*>0>7>''?1O??9?0?[ @;f@\@D@9DAD~ATA/B1HB6zB;BDB*2C?]C#COCND `D&DWD$E%E,DE)qE7E<E8FBIF)FPFG%G=@G~G*G3GIG8CHJ|HKHGI)[I?I6I0I0-J#^J6J/J(J@K SK)tK>K(K,L#3L.WL,LLL-M4.M:cM;MAM?N>\N1N-N,N.(O<WO=O=O>P/OP8P(P4P(QS?Q#Q*Q-Q1R1BR1tR1R;R3S$HS=mS>SST5TFTT;T,TUUE>U.U%U:U/V"DV/gV3V"V"V$W56W%lW*W6WWX,X-CX<qX<X+X9YLN~+K^.e12#W&%"(F|!jrJ} Uxc9o\qwtzBl0$,sy:/E8@ dZfG{ n7>QX*;ASM=TR`3CpOk[ ) mg-5 ?aHbD6I<4Vuh]vP'Y_i%s = '%s' (back-permuted) is experimental'%s' must be in '%s''%s' must have string length 1'%s' slot must have length 1'Dim' slot has length less than two'factors' slot must be a named list's1' and 's2' must be "character" vectors'uplo' must be UPP or LOWA must be a logical matrixA must have #{rows} >= #{columns}Argument b must be a numeric matrixArgument ij must be 2-column integer matrixArgument rho must be an environmentArgument y must be numeric or integerCHOLMOD factorization was unsuccessfulCannot coerce to too large *geMatrix with %.0f entriesCannot factor a matrix with zero extentsCannot solve() for matrices with zero extentsCholesky factorization failed; unusually, please report to Matrix-authorsCholmod error '%s' at file %s, line %dCholmod warning '%s' at file %s, line %dCsparse_crossprod(): error return from cholmod_aat()Csparse_general_to_symmetric(): matrix is not square!Determinant requires a square matrixDim slot must have length 2Dimensions of a (%d,%d) and b (%d,%d) do not conformDimensions of system to be solved are inconsistentDimensions of x and y are not compatible for %sExact singularity detected during LU decomposition: %s, i=%d.First call to Lapack routine dgels returned error code %dFirst call to dgeqrf returned error code %dInappropriate class cl='%s' in Matrix_csn_to_SEXP(S, cl, ..)Inappropriate class cl='%s' in Matrix_css_to_SEXP(S, cl, ..)Inconsistent dimensions: np = 0 and nnz = %dIncorrect length of 'x' slotIndex i must be NULL or integerIndex j must be NULL or integerLU decomposition applies only to square matricesLapack dgecon(): system computationally singular, reciprocal condition number = %gLapack routine %s returned error code %dLapack routine dgetri: system is exactly singularLapack routine dgetrs: system is exactly singularLapack routine dposv returned error code %dLapack routine dsytrf returned error code %dLapack routine dtrcon returned error code %dLengths of super and pi must be equalLengths of super and px must be equalLower band %d > upper band %dMatrices are not conformable for multiplicationMatrix exponential requires square, non-null matrixMatrix is not squareMatrix namespace not determined correctlyNegative value in DimNegative values in DimNon-symmetric matrix passed to dsCMatrix_to_dgTMatrixNonsymmetric matrix in Csparse_symmetric_to_generalNumber of supernodes must be positive when is_super is TRUEOnly 'g'eneral sparse matrix types allowedSecond call to Lapack routine dgels returned error code %dSecond call to dgeqrf returned error code %dSolve requires a square matrixSuiteSparseQR_C_QR returned an error codeSupernodal LDL' decomposition not availableSupernodal/simplicial class inconsistent with type flagsSymmetric and triangular both setUnable to initialize cholmod: error code %dUnknown error in getGivensX must be a numeric (double precision) matrixX must be a real (numeric) matrixall column indices (slot 'j') must be between 0 and ncol-1 in a TsparseMatrixall column indices must be between 0 and ncol-1all row indices (slot 'i') must be between 0 and nrow-1 in a TsparseMatrixargument type[1]='%s' must be a one-letter character stringargument type[1]='%s' must be one of '1','O', or 'I'argument type[1]='%s' must be one of 'M','1','O','I','F' or 'E'as_cholmod_triplet(): could not reallocate for internal diagU2N()cannot add diag() as long as 'diag = "U"'cannot set diag() as long as 'diag = "U"'chm_diagN2U(): nrow=%d, ncol=%dchm_diagN2U(x, uploT = %d): uploT should be +- 1chm_sparse_to_SEXP(, *): invalid 'Rkind' (real kind code)cholmod_change_factor failedcholmod_change_factor failed with status %dcholmod_drop() failedcholmod_factorize failed: status %d, minor %d from ncol %dcholmod_factorize_p failed: status %d, minor %d of ncol %dcholmod_sdmult error (resid)cholmod_sdmult error (rhs)cholmod_solve (CHOLMOD_A) failed: status %d, minor %d from ncol %dcholmod_sort returned an error codecholmod_updown() returned %dcholmod_write_sparse returned error codecls = "%s" does not end in "CMatrix"cls = "%s" must begin with 'd', 'l' or 'n'code for cholmod_dense with holes not yet writtencode not yet written for cls = "lgCMatrix"complex sparse matrix code not yet writtencs matrix not compatible with class '%s'cs_lu(A) failed: near-singular A (or out of memory)cs_lusol failedcs_qr failedcs_qrsol() failed inside dgCMatrix_qrsol()cs_sqr failedcsp_eye argument n must be positiveddense_to_symmetric(): matrix is not square!dgCMatrix_cholsol requires a 'short, wide' rectangular matrixdgCMatrix_lusol requires a square, non-empty matrixdgCMatrix_qrsol(., order) needs order in {0,..,3}dgCMatrix_qrsol(<%d x %d>-matrix) requires a 'tall' rectangular matrixdgeMatrix_Schur: argument x must be a non-null square matrixdgeMatrix_Schur: dgees returned code %ddgeMatrix_Schur: first call to dgees faileddgeMatrix_exp: LAPACK routine dgebal returned %ddgeMatrix_exp: dgetrf returned error code %ddgeMatrix_exp: dgetrs returned error code %ddiag_tC(): invalid 'resultKind'diagonal element %d of Cholesky factor is missingdon't know if a dense pattern matrix makes sensedpoMatrix is not positive definitedtrMatrices in %*% must have matching (square) dim.dtrMatrix must be squareerror [%d] from Lapack 'dgecon()'exactly 1 of 'i', 'j' or 'p' must be NULLf->xtype of %d not recognizedfactors slot must be named listfailure in as_cholmod_factorfailure to open file "%s" for writingfirst element of slot p must be zeroi and j must be integer vectors of the same lengthin_place cholmod_sort returned an error codeincorrect left cyclic shift, j (%d) < 0incorrect left cyclic shift, j (%d) >= k (%d)incorrect left cyclic shift, k (%d) > ldx (%d)internal_chm_factor: Cholesky factorization failedinvalid class '%s' to dup_mMatrix_as_dgeMatrixinvalid class '%s' to dup_mMatrix_as_geMatrixinvalid class of 'value' in Csparse_subassign()invalid class of 'x' in Csparse_subassign()invalid class of 'x' in Matrix_as_cs(a, x)invalid class of object to %sinvalid class of object to as_cholmod_denseinvalid class of object to as_cholmod_factorinvalid class of object to as_cholmod_sparseinvalid class of object to as_cholmod_tripletinvalid class(x) '%s' in R_to_CMatrix(x)invalid class(x) '%s' in compressed_to_TMatrix(x)invalid column index at position %dinvalid object passed to as_cholmod_sparseinvalid row index at position %dlast element of slot p must match length of slots j and xlength of x slot != prod(Dim)length(p) must match nrow(V)length(q) must be zero or ncol(R)lengths of slots 'i' and 'x' must matchlengths of slots 'j' and 'x' must matchlengths of slots i and j must matchlengths of slots i and x must matchmatrix is not square! (skew-symmetric part)matrix is not square! (symmetric part)matrix is not symmetric [%d,%d]missing 'Matrix' namespace: should never happennegative vector lengths not allowed: np = %d, nnz = %dnot a 'n.CMatrix'not a CsparseMatrixnp = %d, must be zero when p is NULLnumber of rows in y (%d) does not match number of rows in X (%d)nz2Csparse(): invalid/non-implemented r_kind = %dobject must be a named, numeric vectorp must be non-decreasingp[0] = %d, should be zeroprogramming error in Csparse_subassign() should never happenrcond requires a square, non-empty matrixslot Dim must have length 2slot j is not *strictly* increasing inside a columnslot j is not increasing inside a columnslot p must be non-decreasingslot p must have length = nrow(.) + 1strlen of cls argument = %d, should be 8subscript 'i' out of bounds in M[ij]subscript 'j' out of bounds in M[ij]system argument is not validthe leading minor of order %d is not positive definitetol, given as %g, must be <= 1tol, given as %g, must be non-negativeunexpected ctype = %d in dup_mMatrix_as_geMatrixunknown 'Rkind'unknown xtypeunknown xtype in cholmod_sparse objectunknown xtype in cholmod_triplet objectuplo='L' must not have sparse entries above the diagonaluplo='U' must not have sparse entries below the diagonalx slot must be numeric "double"y must be a numeric (double precision) matrixProject-Id-Version: Matrix 1.0-9 Report-Msgid-Bugs-To: POT-Creation-Date: 2013-12-23 21:27+0100 PO-Revision-Date: 2012-08-22 08:17+0100 Last-Translator: Łukasz Daniel Language-Team: Łukasz Daniel Language: pl_PL MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Plural-Forms: nplurals=3; plural=(n==1 ? 0 : n%10>=2 && n%10<=4 && (n%100<10 || n%100>=20) ? 1 : 2) X-Poedit-SourceCharset: iso-8859-1 %s = '%s' (wstecznie permutowany) jest eksperymentalny'%s' musi być w '%s''%s' musi mieć łańcuch długości 1gniazdo '%s' musi mieć długość 1gniazdo 'Dim' ma długość mniejszą niż dwagniazdo 'factors' musi być nazwaną listą's1' oraz 's2' muszą być wektorami tekstowymi'uplo' musi być UPP lub LOW'A' musi być macierzą logiczną'A' musi mieć liczbę wierszy >= liczba kolumnArgument 'b' musi być macierzą liczbowąArgument 'ij' musi być 2-kolumnową macierzą liczb całkowitychArgument 'rho' musi być środowiskiemArgument 'y' musi być liczbą lub rzeczywistą lub całkowitąFaktoryzacja 'CHOLMOD' nie powiodła sięNie można przekształcić do dużego *geMatrix z %.0f wpisamiNie można faktoryzować macierzy o zerowym stopniuNie można wykonać 'solve()' dla macierzy o zerowym stopniufaktoryzacja Cholesky'ego nie powiodła się; nietypowo, proszę zgłosić raport autorom pakietu MatrixBłąd 'cholmod' '%s' w pliku %s, linia %dOstrzeżenie 'cholmod' '%s' w pliku %s, linia %dCsparse_crossprod(): błąd zwrócony z 'cholmod_aat()'Csparse_general_to_symmetric(): macierz nie jest kwadratowa!Wyznacznik wymaga aby macierz była kwadratowagniazdo 'dim' musi mieć długość 2Wymiary 'a' (%d,%d) oraz 'b' (%d,%d) nie pokrywają sięWymiary systemu, który ma być rozwiązany, są niespójneWymiary 'x' oraz 'y' nie są zgodne dla '%s'Wykryto dokładną osobliwość podczas dekompozycji LU: %s, i=%d.Pierwsze wywołanie procedury Lapack 'dgels' zwróciło kod błędu %dPierwsze wywołanie 'dgeqrf' zwróciło kod błędu %dNiepoprawna klasa cl='%s' w 'Matrix_csn_to_SEXP(S, cl, ..)'Niepoprawna klasa cl='%s' w 'Matrix_css_to_SEXP(S, cl, ..)'Niespójne wymiary: 'np = 0' oraz 'nnz = %d'Niepoprawna długość gniazda 'x'Indeks 'i' musi być wartością NULL lub być liczbą całkowitąIndeks 'j' musi być wartością NULL lub być liczbą całkowitądekompozycja LU stosuje się tylko do macierzy kwadratowychLapack dgecon(): system obliczeniowo osobliwy, numer obustronnego stanu = %gProcedura Lapack '%s' zwróciła kod błędu %dprocedura Lapack 'dgetri': system jest ściśle osobliwyprocedura Lapack 'dgetrs': system jest ściśle osobliwyprocedura Lapack 'dposv' zwróciła kod błędu %dprocedura Lapack 'dsytrf' zwróciła kod błędu %dProcedura Lapack 'dtrcon' zwróciła kod błędu %dDługości 'super' oraz 'pi' muszą być równeDługości 'super' oraz 'px' muszą być równeNiższe pasmo %d > górne pasmo %dMacierze nie są dostosowane do przemnożeniaEksponencjowanie macierzy wymaga kwadratowej, niepustej macierzyMacierz nie jest kwadratowaprzestrzeń nazw macierzy nie została poprawnie określonaUjemna wartość w 'Dim'Ujemne wartości w 'Dim'Ujemne wartości w 'Dim'Niesymetryczna macierz przekazana do 'dsCMatrix_to_dgTMatrix'Niesymetryczna macierz w 'Csparse_symmetric_to_general'Liczba super węzłów musi być dodadnia gdy 'is_super' ma wartość TRUETylko ogólne ('g') typy rzadkich macierzy są dozwoloneDrugie wywołanie procedury Lapack 'dgels' zwróciło kod błędu %dDrugie wywołanie 'dgeqrf' zwróciło kod %d'Solve' wymaga kwadratowej macierzy'SuiteSparseQR_C_QR' zwrócił kod błęduDekompozycja 'supernodal LDL' nie jest dostępnaklasa supernodal/simplicial niespójna z flagami typówUstawiono: symetryczny oraz trójkątnyNie można zainicjować 'cholmod': kod błędu %dNieznany błąd w 'getGivens''X' musi być macierzą liczbową (o podwójnej precyzji)'X' musi być rzeczywistą (liczbową) macierząwszystkie indeksy kolumn (gniazdo 'j') muszą być pomiędzy 0 a 'ncol-1' w 'TsparseMatrix'wszystkie indeksy kolumn muszą być pomiędzy 0 a 'ncol-1'wszystkie indeksy wierszy (gniazdo 'i') muszą być pomiędzy 0 a 'nrow-1' w 'TsparseMatrix'argument type[1]='%s' musi być jednoliterowym łańcuchem tekstowymargument type[1]='%s' musi być jednym z '1','O', lub 'I'argument type[1]='%s' musi być jednym z 'M','1','O','I','F' lub 'E'as_cholmod_triplet(): nie można ponownie przydzielić dla wewnętrznego 'diagU2N()'nie można dodać 'diag()' dopóki 'diag = "U"'nie można ustawić 'diag()' dopóki 'diag = "U"'chm_diagN2U(): nrow=%d, ncol=%dchm_diagN2U(x, uploT = %d): 'uploT' powinien wynosić +/- 1chm_sparse_to_SEXP(, *): niepoprawny 'Rkind' (kod 'real kind')'cholmod_change_factor' nie powiódł się'cholmod_change_factor' nie powiódł się zwracając status %d'cholmod_drop()' nie powiódł się'cholmod_factorize' nie powiódł się: status %d, minor %d z liczbą kolumn %d'cholmod_factorize_p' nie powiódł się: status %d, minor %d liczba kolumn %dbłąd 'cholmod_sdmult' (reszta)błąd 'cholmod_sdmult' (prawa strona)'cholmod_solve (CHOLMOD_A)' nie powiódł się: status %d, minor %d z liczbą kolumn %d'cholmod_sort' zwrócił kod błęducholmod_updown() zwróciło %d'cholmod_write_sparse' zwrócił kod błędu'cls = "%s"' nie kończy się w 'CMatrix''cls = "%s"' musi rozpoczynać się od 'd', 'l' lub 'n'kod dla 'cholmod_dense' z dziurami nie jest jeszcze napisanykod dla 'cls = "lgCMatrix"' nie został jeszcze napisanykod dla zespolonych rzadkich macierzy nie został jeszcze napisany'cs matrix' nie jest zgodne z klasą '%s''cs_lu(A)' nie powiódł się: 'A' jest bliskie osobliwości (lub brak pamięci)'cs_lusol' nie powiódł się'cs_qr' nie powiódł się'cs_qrsol()' nie powiódł się wewnątrz 'dgCMatrix_qrsol()''cs_sqr' nie powiódł sięargument 'n' w 'csp_eye' musi być dodatniddense_to_symmetric(): macierz nie jest kwadratowa!'dgCMatrix_cholsol' wymaga krótkiej lub szerokiej macierzy prostokątnej'dgCMatrix_lusol' wymaga kwadratowej, niepustej macierzy'dgCMatrix_qrsol(., order)' potrzebuje zmiennej 'order' ze zbioru {0,..,3}'dgCMatrix_qrsol(macierz <%d x %d>)' wymaga długiej prostokątnej macierzydgeMatrix_Schur: argument 'x' musi być niepustą macierzą kwadratowądgeMatrix_Schur: 'dgees' zwrócił kod %ddgeMatrix_Schur: pierwsze wywołanie 'dgees' nie powiodło siędgeMatrix_exp: procedura LAPACK 'dgebal' zwróciła %ddgeMatrix_exp: 'dgetrf' zwrócił kod błędu %ddgeMatrix_exp: 'dgetrs' zwrócił kod błędu %ddiag_tC(): niepoprawny 'resultKind'brakuje elementu diagonalnego %d czynnika Cholesky'egonie wiadomo, czy gęsty wzrór macierzy ma sens'dpoMatrix' nie jest dodatnio określone'dtrMatrices' w %*% muszą mieć pasujące (kwadratowe) wymiary.'dtrMatrix' musi być kwadratowabłąd [%d] z procedury Lapack 'dgecon()'dokładnie jeden z 'i', 'j' lub 'p' musi być wartością NULL'f->xtype' dla %d nie został rozpoznanygniazdo czynników musi być nazwaną listąniepowodzenie w 'as_cholmod_factor'nie udało się otworzyć pliku '%s' do zapisupierwszy element gniazda 'p' musi być zerem'i' oraz 'j' muszą być wektorami liczb całkowitych o tej samej długości'in_place cholmod_sort' zwrócił kod błęduniepoprawne lewe cykliczne przesunięcie, j (%d) < 0niepoprawne lewe cykliczne przesunięcie, j (%d) >= k (%d)niepoprawne lewe cykliczne przesunięcie, k (%d) > ldx (%d)internal_chm_factor: faktoryzacja Cholesky'ego nie powiodła sięniepoprawna klasa '%s' przekazana do 'dup_mMatrix_as_dgeMatrix'niepoprawna klasa '%s' przekazana do 'dup_mMatrix_as_geMatrix'niepoprawna klasa 'value' w 'Csparse_subassign()'niepoprawna klasa 'x' w 'Csparse_subassign()'niepoprawna klasa 'x' w 'Matrix_as_cs(a, x)'niepoprawna klasa obiektu przekazanego do '%s'niepoprawna klasa obiektu przekazanego do 'as_cholmod_dense'niepoprawna klasa obiektu przekazanego do 'as_cholmod_factor'niepoprawna klasa obiektu przekazanego do 'as_cholmod_sparse'niepoprawna klasa obiektu przekazanego do 'as_cholmod_triplet'niepoprawne 'class(x)' '%s' w 'R_to_CMatrix(x)'niepoprawne 'class(x)' '%s' w 'compressed_to_TMatrix(x)'niepoprawny indeks kolumny na pozycji %dniepoprawny obiekt przekazany do 'as_cholmod_sparse'niepoprawny indeks wiersza na pozycji %dostatni element gniazda 'p' musi zgadzać się długością z gniazdem 'j' oraz 'x'długość gniazda 'x' != prod(Dim)'length(p)' musi zgadzać się z 'nrow(V)''length(q)' musi wynosić zero lub 'sncol(R)'długość gniazd 'i' oraz 'x' musi się zgadzaćdługość gniazd 'j' oraz 'x' musi się zgadzaćdługość gniazd 'i' oraz 'j' musi się zgadzaćdługość gniazd 'i' oraz 'x' musi się zgadzaćmacierz nie jest kwadratowa! (część skośno-symetryczna)macierz nie jest kwadratowa! (część symetryczna)macierz nie jest symetryczna [%d,%d]brakuje przestrzeni nazw 'Matrix': nie powinno się wydarzyćujemne długości wektora nie są dozwolone: np = %d, nnz = %dto nie jest 'n.CMatrix'to nie jest 'CsparseMatrix'np = %d, musi wynosić zero gdy 'p' ma wartość NULLliczba wierszy w 'y' (%d) nie zgadza się z liczbą wierszy w 'X' (%d)nz2Csparse(): niepoprawny/niezaimplementowany 'r_kind = %d'obiekt musi być nazwanym wektorem liczbowym'p' musi być niemalejące'p[0] = %d', powinno być zerobłąd programowy w 'Csparse_subassign()' nie powinien się wydarzyć'rcond' wymaga kwadratowej, niepustej macierzygniazdo 'Dim' musi mieć długość 2gniazdo 'j' nie jest *ściśle* rosnące wewnątrz kolumnygniazdo 'j' nie jest rosnące wewnątrz kolumnygniazdo 'p' musi być niemalejącegniazdo 'p' musi mieć długość = nrow(.) + 1długość argumentu 'cls = %d', powinna wynosić 8indeks 'i' poza zakresem w 'M[ij]'indeks 'j' poza zakresem w 'M[ij]'argument systemowy nie jest poprawnywiodący minor rzędu %d nie jest dodatnio określony'tol', podane jako %g, musi być <= 1'tol', podane jako %g, musi być nieujemnenieoczekiwany 'ctype = %d' w 'dup_mMatrix_as_geMatrix'nieznany 'Rkind'nieznany 'xtype'nieznany 'xtype' w obiekcie 'cholmod_sparse'nieznany 'xtype' w obiekcie 'cholmod_triplet'uplo='L' nie może mieć rzadkich wpisów powyżej diagonaliuplo='U' nie może mieć rzadkich wpisów poniżej diagonaligniazdo 'x' musi być liczbą typu 'double''y' musi być macierzą liczbową (o podwójnej precyzji)Matrix/inst/po/pl/LC_MESSAGES/R-Matrix.mo0000644000175100001440000005101212256121033017321 0ustar hornikusers,< 8 8 6+3b9 $6D1{/,- *8#c#6D ,O|K1#-$Q9v(0$ 0/:`Ix8^&:(/"5R,#887K.$QDZ4%=&8&_=56:1Cl7(*< Y*z9"""1EwI8"@<@}56 +L[ j2*'",1O3(%:-?m@=8 : 2Q 9 , 0 E!Hb!=!5!1"'Q"y""""?"#&.#U#$i#&#/#h#nN$.$$B%DG%A%&%G%%=&+c&)&@&"&';='%y'')'!'9 (>E(((3(((B)\)'u)0))#)5*7F*~*>*,*+P-QQ-?-?-##.?G.$.".$.7.7,/8d/6/?/;01P00100G0K(1-t111">2;a242,2G2/G3;w313;3@!4Sb44CU5+5E5* 6366hj646+7U47S7Q7&08<W88/8]8W59@929O:<Q:<:H:D;GY;G;^;?H<6<-<&<(=8==Dv=)=0=0>>G>>>R'?%z?R?S?HG@H@$@@A'$A!LAAnA8A.A'BC@BCB2B)BG%C7mCCXCGDCeDD;D5E87EDpEEEHE=DF7FAFFG.G'DGlGLG G5G/H7KH.H?HHtI6I3J]GJZJTK3UKcK5K9#L9]LXL*L&MbBM2M(M8N.:NSiNXNO.O4KOO$OKOP1(P8ZP'P+P>P8&Q"_QQQ5Q6 x/ -^l:h,) vR1Y3}i+4U>u@BS[* 8#s`kDeaPL{|pT HG2bnZt<f'!"7(z0Adm;KMNI5.WOEF&X_VQ\$o] cg%=9ywrqJCj?~"dMatrix" object with NAs cannot be coerced to "nMatrix""lMatrix" object with NAs cannot be coerced to "nMatrix"'%s()' is not yet implemented for representation '%s''%s()' is not yet implemented for element type '%s''A' must be a square matrix'NA' indices are not (yet?) supported for sparse Matrices'V' is not a *square* matrix'V' is not a square matrix'by' argument is much too small'diagonals' matrix must have %d columns (= length(k) )'diagonals' must have the same length (%d) as 'k''file' must be a character string or connection'force' must be (coercable to) TRUE or FALSE'lag' and 'differences' must be integers >= 1'lwd' must be NULL or non-negative numeric'ncol' is not a factor of length(x)'ncol' must be >= 0'nrow' is not a factor of length(x)'nrow' must be >= 0'nrow', 'ncol', etc, are disregarded for matrix 'data''nrow', 'ncol', etc, are disregarded when 'data' is "Matrix" already'p' must be a non-decreasing vector (0, ...)'times >= 0' is required'update' must be logical or '+' or '-'; 'C' a matrix, and 'L' a "CHMfactor"'x' has invalid data type'x' is not positive definite -- chol() undefined.'x' is not symmetric nor triangular'x' must inherit from "sparseVector"(un)packing only applies to dense matrices, class(x)='%s'.M.repl.i.2col(): drop 'matrix' case ... --> is not yet implemented[i] is not yet implemented --> is not yet implemented[ ] : .M.sub.i.logical() maybe inefficientCholesky() -> *symbolic* factorization -- not yet implementedCholesky(A) called for 'A' of class "%s"; it is currently defined for sparseMatrix only; consider using chol() insteadCmp.Mat.atomic() should not be called for diagonalMatrixFIXME: NOT YET FINISHED IMPLEMENTATIONLogic.Mat.atomic() should not be called for diagonalMatrixMatrices must have same dimensions in %sMatrices must have same number of columns in %sMatrices must have same number of rows for arithmeticMatrices must have same number of rows in %sMatrix seems negative semi-definiteMatrix-internal error in [i,,d]; please reportMatrix-internal error in [i,,d]; please reportMatrix-internal error in [i,,d]; please reportNA's in (i,j) are not allowedNAs are not allowed in subscripted assignmentsNot a valid formatOnly numeric sparse matrices allowedQuadratic matrix '%s' (=: A) is not formally symmetric. Will be treated as A A'RHS 'value' (class %s) matches 'ANY', but must match matrix class %s[ ] indexing not allowed: forgot a "," ?all() is not yet implementedc(,..) of different kinds, coercing all to 'rleDiff'cannot coerce 'NA's to "nsparseMatrix"cannot coerce 'NA's to "nsparseVector"chol() is undefined for diagonal matrix with negative entriescoercion to "pMatrix" only works from integer numericcomplex matrices not yet implemented in Matrix packagediag(.) had 0 or NA entries; non-finite result is doubtfuldiagonalMatrix in .dense2C() -- should never happen, please report!dim [product %d] do not match the length of object [%d]dim(.) value must be numeric of length 2dimensions don't match the number of cellsdimnames [%d] mismatch in %selement type '%s' not recognizedelement type 'complex' not yet implementedexactly one of 'i', 'j', or 'p' must be missing from callfile is not a MatrixMarket filehit a cycle (1) -- stop iterationshit a cycle (2) -- stop iterationsi1[1] == 0 ==> C-level verbosity will not happen!incompatible matrix dimensionsindex must be numeric, logical or sparseVector for indexing sparseVectorsinefficient coercion (lost triangularity); please reportinefficient method used for "- e1"internal bug in "Compare" method (Cmp.Mat.atomic); please reportinternal bug in "Logic" method (Logic.Mat.atomic); please reportinternal bug: matrix 'i' in replTmat(): please reportinternal bug: missing 'i' in replTmat(): please reportinvalid 'contrasts.arg' argumentinvalid 'data'invalid 'type'invalid (to - from)/by in seq(.)invalid character indexinginvalid or not-yet-implemented 'Matrix' subsettingis not a multiple of shorter object lengthkronecker method must use default 'FUN'length must be non-negative numberlength of 1st arg does not match dimension of 2ndlength of 2nd arg does not match dimension of firstlength(i) is not a multiple of length(x)length(x) must be either 1 or #{cols}logic programming error in printSpMatrix2(), please reportlogical subscript too long (%d, should be %d)longer object lengthlonger object length is not a multiple of shorter object lengthm[ ] <- v: inefficiently treating single elementsm[ ]: inefficiently indexing single elementsmatrix is not diagonalmodel frame and formula mismatch in model.matrix()must either specify 'A' or the functions 'A.x' and 'At.x'must have exactly one non-zero entry per rownargs() = %d should never happen; please report.nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.2col)?nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.logical)?nargs() = %d. Extraneous illegal arguments inside '[ .. ]' ?negative values are not allowed in a matrix subscriptno 'dimnames[[.]]': cannot use character indexingnon-conformable matrix dimensions in %snon-matching dimensionsnon-square matrixnot a positive definite matrixnot a square matrixnot a symmetric matrix; consider forceSymmetric() or symmpart()not a triangular matrixnot enough new vecs -- stop iterationsnot yet implementednot yet implemented .. please reportnot-yet-implemented 'Matrix[<-' methodnot-yet-implemented coercion to "TsparseMatrix"not-yet-implemented method for %s(<%s>). ->> Ask the package authors to implement the missing feature.not-yet-implemented method for %s(<%s>, <%s>). ->> Ask the package authors to implement the missing feature.not-yet-implemented method for <%s> %%*%% <%s>nothing to replace withnumber of items to replace is not a multiple of replacement lengthonly 2-dimensional tables can be directly coerced to sparse matricesonly square matrices can be used as incidence matrices for graphsprod() is not yet implementedprogramming error: min() should have dispatched w/ 1st arg much earlierrcond(.) via sparse -> dense coercionreadMM(): column values 'j' are not in 1:ncreadMM(): row values 'i' are not in 1:nrreplacing "indMatrix" entries is not allowed, as rarely sensiblerepresentation '%s' not recognizedsome arguments are not matricessuch indexing must be by logical or 2-column numeric matrixsum() is not yet implementedsymmetric matrix must be squaresymmetry form '%s' is not yet implementedsymmetry form '%s' not recognizedsymmetry form 'hermitian' not yet implemented for readingsymmetry form 'skew-symmetric' not yet implemented for readingtemporarily disabledthe matrix is not triangularthe number of non-zero entries differs from nrow(.)too many argumentstoo many replacement valuestrimmed mean of 'sparseVector' -- suboptimally using as.numeric(.)type '%s' not recognizedupdate must be TRUE/FALSE or '+' or '-'using "old code" part in Csparse subassignmentusing slow kronecker() methodvariable '%s' converted to a factorvariable '%s' is absent, its contrast will be ignoredwhen 'A' is specified, 'A.x' and 'At.x' are disregardedwrong sign in 'by' argumentx[.,.] <- val : x being coerced from Tsparse* to CsparseMatrixyou cannot mix negative and positive indicesProject-Id-Version: Matrix 1.0-9 Report-Msgid-Bugs-To: bugs.r-project.org POT-Creation-Date: 2013-12-23 21:27 PO-Revision-Date: 2012-08-22 08:17+0100 Last-Translator: Łukasz Daniel Language-Team: Łukasz Daniel Language: pl_PL MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Plural-Forms: nplurals=3; plural=(n==1 ? 0 : n%10>=2 && n%10<=4 && (n%100<10 || n%100>=20) ? 1 : 2) X-Poedit-SourceCharset: iso-8859-1 obiekt 'dMatrix' z wartościami NA nie może zostać przekształcony w 'nMatrix'obiekt 'lMatrix' z wartościami NA nie może zostać przekształcony na 'nMatrix''%s()' nie jest jeszcze zaimplementowane dla reprezentacji '%s''%s()' nie jest jeszcze zaimplementowany dla typu '%s' elementu'A' musi być macierzą kwadratowąindeksy 'NA' nie są (jeszcze?) wspierane dla rzadkich macierzy'V' nie jest macierzą *kwadratową*'V' nie jest macierzą kwadratowąargument 'by' jest znacznie za małymacierz 'diagonals' musi mieć %d kolumn (= length(k) )'diagonals' musi mieć tę samą długość (%d) co 'k''file' musi być łańcuchem tekstowym lub połączeniem'force' musi być (przekształcalne do) TRUE lub FALSE'lag' oraz 'differences' muszą być liczbami całkowitymi >= 1'lwd' musi mieć wartość NULL lub być nieujemną liczbą'ncol' nie jest czynnikiem długości 'length(x)''ncol' musi być >= 0'nrow' nie jest czynnikiem długości 'length(x)''nrow' musi być >= 0'nrow', 'ncol', itd., są nieuwzględniane dla 'data' typu macierzowego'nrow', 'ncol', itd., nie są uwzględniane gdy 'data' ma już typ 'Matrix''p' musi być niemalejącym wektorem (0, ...)wymagane jest 'times >= 0''update' musi być wartością logiczną lub '+' lub '-'; 'C' musi być macierzą, oraz 'L' musi być obiektem klasy 'CHMfactor''x' posiada niepoprawny typ danych'x' nie jest dodatnio określone -- nieokreślony 'chol()'.'x' nie jest macierzą symetryczną ani trójkątną'x' musi dziedziczyć z klasy 'sparseVector'(roz)pakowanie stosuje się jedynie do gęstych macierzy, class(x)='%s'.M.repl.i.2col(): zrzuć przypadek 'matrix' ... --> nie jest jeszcze zaimplementowane'[i]' nie jest jeszcze zaimplementowane --> nie jest jeszcze zaimplementowane[ ] : '.M.sub.i.logical()' może być niewydajneCholesky() -> *symboliczna* faktoryzacja -- jeszcze niezaimplementowanametoda 'Cholesky(A)' poprosiła o 'A' klasy '%s'; aktualnie jest ona zdefiniowana jedynie dla klasy 'sparseMatrix'; rozważ w zamian użycie 'metodychol()''Cmp.Mat.atomic()' nie powinien być wywołany dla 'diagonalMatrix'FIXME: JESZCZE NIEZAKOŃCZONA IMPLEMENTACJA'Logic.Mat.atomic()' nie powinien być wywołany dla 'diagonalMatrix'Macierze muszą mieć te same wymiary w %sMacierze muszą mieć tę samą liczbę kolumn w %sMacierze muszą mieć tę samą liczbę wierszy jeśli mają być przeprowadzane działania arytmetyczneMacierze muszą mieć tę samą liczbę wierszy w %sMacierz wydaje się być ujemnie określonabłąd wewnętrzny w pakiecie 'Matrix' w '[i,,d]'; proszę zgłosić raportbłąd wewnętrzny pakiecie 'Matrix' w '[i,,d]'; proszę zgłosić raportbłąd wewnętrzny pakietu 'Matrix' w '[i,,d]'; proszę zgłosić raportwartości NA w (i,j) nie są dozwolonewartości NA nie są dozwolone w indeksowanych przypisaniachNiepoprawny formatDozwolone są jedynie liczbowe rzadkie macierzeMacierz kwadratowa '%s' (=: A) nie jest formalnie symetryczna. Będzie traktowana jako A A'prawa strona 'value' (klasa %s) pasuje do 'ANY', a musi pasować do klasy macierzy '%s'indeksowanie [ ] nie jest dozwolone: zapomniałeś ',' ?'all()' nie jest jeszcze zaimplementowane'c(,..)' różnych rodzajów, przekształcanie wszystkich do 'rleDiff'nie można przekształcić wartości 'NA' na 'nsparseMatrix'nie można przekształcić wartości 'NA' na 'nsparseVector''chol()' jest nieokreślona dla macierzy diagonalnych z ujemnymi wpisamiprzekształcenie na 'pMatrix' działa jedynie dla liczb całkowitychmacierze zespolone nie są jeszcze zaimplementowane w pakiecie 'Matrix''diag(.)' posiadało wpisy 0 lub NA; nieskończony wynik jest wątpliwy'diagonalMatrix' w '.dense2C()' -- nie powinno nigdy się wydarzyć, proszę zgłosić raport!wymiar [produkt %d] nie zgadza się z długością obiektu [%d]wartości 'dim(.)' muszą być liczbami o długości 2wymiary nie zgadzają się z liczbą komórekniezgodność nazw wymiarów [%d] w %selement typu '%s' nie został rozpoznanytyp elementu 'complex' nie jest jeszcze zaimplementowanydokłanie jeden z 'i', 'j', lub 'p' musi być nieobecny w wywołaniuplik nie jest plikiem typu 'MatrixMarket'natrafiona na cykl (1) -- zatrzymywanie iteracjinatrafiona na cykl (2) -- zatrzymywanie iteracjii1[1] == 0 ==> tryb 'verbose' poziomu C nie zostanie wykonany!niezgodne wymiary macierzyindeks musi być typem liczbowym, logicznym lub obiektem klasy 'sparseVector' na potrzeby indeksowania obiektów klasy 'sparseVector'nieefektywne przekształcenie (utracono trójkątność); proszę zgłosić raportnieefektywna metoda użyta dla '- e1'błąd wewnętrzny w metodzie 'Compare' (Cmp.Mat.atomic); proszę zgłosić raportbłąd wewnętrzny w metodzie 'Logic' (.Logic.Mat.atomic); proszę zgłosić raportwewnętrzny błąd: macierz 'i' w 'replTmat()': proszę zgłosić raportbłąd wewnętrzny: brakuje 'i' w 'replTmat()': proszę zgłosić raportniepoprawny argument 'contrasts.arg'niepoprawne 'data'niepoprawny 'type'niepoprawne '(to - from)/by' w 'seq(.)'niepoprawne tekstowe indeksowanieniepoprawne lub jeszcze niezaimplementowane podstawienie 'Matrix'nie jest wielokrotnością długości krótszego obiektumetoda kroneckera musi użyć domyślnej 'FUN'długość musi być nieujemną liczbądługość pierwszego argumentu nie zgadza się z wymiarem drugiegodługość drugiego argumentu nie zgadza się z wymiarem pierwszego'length(i)' nie jest wielokrotnością 'length(x)''length(x)' musi wynosić 1 lub #{kolumn}błąd logiczny programu w 'printSpMatrix2()', proszę zgłosić raportindeks logiczny jest zbyt długi (%d, powinien być %d)długość dłuższego obiektudługość dłuższego obiektu nie jest wielokrotnością długości krótszego obiektum[ ] <- v: nieefektywne traktowanie pojedynczych elementówm[ ]: nieefektywne indeksowanie pojedynczych elementówmacierz nie jest diagonalnaniezgodność ramki modelu oraz formuły w 'model.matrix()'potrzeba określić 'A' lub funkcje 'A.x' oraz 'At.x'potrzeba mieć dokładnie jeden niezerowy wpis na wiersz'nargs() = %d' nie powinno się wydarzyć; proszę zgłosić raport.nargs() = %d. Obce nielegalne argumenty wewnątrz '[ .. ]' (i.2col)?nargs() = %d. Obce nielegalne argumenty wewnątrz '[ .. ]' (i.logical)?nargs() = %d. Obce nielegalne argumenty wewnątrz '[ .. ]' ?ujemne wartości nie są dozwolone w indeksach macierzybrak 'dimnames[[.]]': nie można używać indeksowania tekstowegoniezgodne wymiary macierzy w %sniezgodne wymiaryniekwadratowa macierzto nie jest dodatnio określona macierzto nie jest macierz kwadratowato nie jest macierz symetryczna; rozważ 'forceSymmetric()' lub 'symmpart()'to nie jest macierz trójkątnązbyt mało nowych wektorów -- zatrzymywanie iteracjijeszcze niezaimplementowanejeszcze niezaimplementowane .. proszę zgłosić raportjeszcze niezaimplementowana metoda 'Matrix[<-'jeszcze niezaimplementowane przekształcenie na 'TsparseMatrix'metoda jeszcze niezaimplementowana dla %s(<%s>). ->> Poproś autorów pakietu o zaimplementowanie brakującej funkcjonalności.metoda jeszcze niezaimplementowana dla %s(<%s>, <%s>). ->> Poproś autorów pakietu o zaimplementowanie brakującej funkcjonalności.jeszcze niezaimplementowana metoda dla <%s> %%*%% <%s>nic do zastąpienialiczba pozycji do zastąpienia nie jest wielokrotnością długości elementu zastępującegojedynie 2-wymiarowe tablice mogą zostać bezpośrednio przekształcone w rzadkie macierzejedynie kwadratowe macierze mogą zostać użyte jako macierz incydencji dla grafów'prod()' nie jest jeszcze zaimplementowanebłąd programistyczny: 'min()' powinno zostać wysłane z pierwszym argumentem znacznie wcześniej'rcond(.)' poprzez przekształcenie rzadkie -> gęstereadMM(): wartości kolumny 'j' nie są w przedziale 1:ncreadMM(): wartości wiersza 'i' nie są w przedziale 1:nrzastępowanie wpisów w 'indMatrix' jest niedozwolone, ponieważ jest to rzadko sensownereprezentacja '%s' nie została rozpoznananiektóre argumenty nie są macierzamitakie indeksowanie musi być wykonane poprzez macierz logiczną lub 2-kolumnową macierz liczbową'sum()' nie jest jeszcze zaimplementowanemacierz symetryczna musi być kwadratowaforma symetryczna '%s' nie jest jeszcze zaimplementowanaforma symetryczna '%s' nie została rozpoznanaforma symetryczna 'hermitian' nie jest jeszcze zaimplementowana na potrzeby odczytuforma symetryczna 'skew-symmetric' nie jest jeszcze zaimplementowana na potrzeby odczytutymczasowo niedostępnemacierz nie jest trójkątnaliczba niezerowych wpisów różni się od 'nrow(.)'zbyt wiele argumentówzbyt dużo wartości zamieniającychprzycięta średnia 'sparseVector' -- optymalnie używając 'as.numeric(.)'typ '%s' nie został rozpoznany'update' musi wynosić TRUE/FALSE lub '+' lub '-'używanie części 'old code' w przypisaniu w 'Csparse'używanie powolnej metody 'kronecker()'zmienna '%s' została zamieniona na czynnikzmienna '%s' jest nieobecna, jej kontrast zostanie zignorowanygdy 'A' jest określone, 'A.x' oraz 'At.x' są odrzucaneniepoprawny znak w argumencie 'by'x[.,.] <- wartość : 'x' zostaje przekształcone z 'Tsparse*' na 'CsparseMatrix'nie można mieszać ujemnych oraz dodatnich indeksówMatrix/inst/po/en@quot/0000755000175100001440000000000012271765426014556 5ustar hornikusersMatrix/inst/po/en@quot/LC_MESSAGES/0000755000175100001440000000000012271765426016343 5ustar hornikusersMatrix/inst/po/en@quot/LC_MESSAGES/Matrix.mo0000644000175100001440000005604012256121033020130 0ustar hornikusers%| )<;x## )1[u!#++#.%R&x6(-I-&w(45D2$w42/ =P9+<<1,n0R)(|11+ ,5,b%%/3)])r,53;3*o:,)!+K8w!+-!GMi/J;24n?A)% )O 2y 0 2 ?!P!+m!!:!:!%"B"B]"#""("$ #*/#1Z#*#*#(#3 $?$ O$*\$ $#$P$M %"X%,{%=%3%;&1V&F&<&' '+4'0`',',''1 (0=("n(3((!())*)H)h)%)$)2),*'0*-X*.*2***&+@+&[+.+-+/++,*;,f,+,,,,,- -(8-1a-#-*- -9.=.[.{.!.'.'.# /#./+R/&~////6/,0F0X0$l0@010&1+1D1<^1)1*113 2(@2i2%2.2(2$3$*3O36l33&330464 F4&T4'{484845055Of5-5X5-=7<k77"7 7' 8#18'U81}888!8# 9+.9+Z9#9%9&969(.:-W:I:*:,:4';5\;D;$;;4<2M</<=<9<+(=@T=@=,= >$>D>0d>R>(>1?1C?+u?,?,?%?%!@G@/e@3@@)@,A55A3kA;A.A: B,EBrB)B+B8B! C+BCnC-C!CQC/+DN[D?DDD[/EAE-E-E2)F0\F2FCFG+!GMG:cG:GGGBH#THxH(H$H6H1I*LI*wI,I3IJ J* J KJ#YJP}JMJ"K,?KAlK3K;K1LJPL<L'L+M0,M,]M,M#M1M0 N">N3aNN%N5N O(OHO%eO$O2O,O'P-8P.fP2PPP*Q,Q*KQ2vQ1Q3Q/R.?RnR+R,R,R-S,@S5mS#S*S S9TMTkTT!T/T/T#*U#NU+rU&UU3U6VPVjVV$V@V1V&,WSWlW<W)W*WX34X(hXX%X.X(Y(-Y(VYY6YY&YZ05ZfZ zZ&Z'Z<Z<[Q[0q[O[-[I8lp~=#E5 J(L];k9M}+{`1&n$!>s,A)m@uU:/zW-<q ?rTv" GKB[Z'.|Q4o XN3PD_H6 d*^S%w\RfjYiC2gFyta0xb7h OcVe%s = '%s' (back-permuted) is experimental%s(): structurally rank deficient case: possibly WRONG zeros'%s' must be in '%s''%s' must have string length 1'%s' slot must have length 1'Dim' slot has length less than two'data' must be of a vector type'factors' slot must be a named list's1' and 's2' must be "character" vectors'uplo' must be UPP or LOWA must be a logical matrixA must have #{rows} >= #{columns}Argument b must be a numeric matrixArgument ij must be 2-column integer matrixArgument must be numeric-like atomic vectorArgument rho must be an environmentArgument y must be numeric or integerCHOLMOD factorization was unsuccessfulCannot coerce to too large *geMatrix with %.0f entriesCannot factor a matrix with zero extentsCannot solve() for matrices with zero extentsCholesky factorization failed; unusually, please report to Matrix-authorsCholmod error '%s' at file %s, line %dCholmod warning '%s' at file %s, line %dCsparse_crossprod(): error return from cholmod_aat()Csparse_general_to_symmetric(): matrix is not square!Csparse_sort(x): x is not a valid (apart from sorting) CsparseMatrixDeterminant requires a square matrixDim slot must have length 2Dimensions of a (%d,%d) and b (%d,%d) do not conformDimensions of system to be solved are inconsistentDimensions of x and y are not compatible for %sExact singularity detected during LU decomposition: %s, i=%d.First call to Lapack routine dgels returned error code %dFirst call to dgeqrf returned error code %dInappropriate class cl='%s' in Matrix_csn_to_SEXP(S, cl, ..)Inappropriate class cl='%s' in Matrix_css_to_SEXP(S, cl, ..)Inconsistent dimensions: np = 0 and nnz = %dIncorrect length of 'x' slotIndex i must be NULL or integerIndex j must be NULL or integerLU decomposition applies only to square matricesLapack dgecon(): system computationally singular, reciprocal condition number = %gLapack routine %s returned error code %dLapack routine dgetri: system is exactly singularLapack routine dgetrs: system is exactly singularLapack routine dposv returned error code %dLapack routine dsytrf returned error code %dLapack routine dtrcon returned error code %dLengths of super and pi must be equalLengths of super and px must be equalLower band %d > upper band %dMatrices are not conformable for multiplicationMatrix exponential requires square, non-null matrixMatrix is not squareMatrix namespace not determined correctlyNegative value in DimNegative values in DimNon-symmetric matrix passed to dsCMatrix_to_dgTMatrixNonsymmetric matrix in Csparse_symmetric_to_generalNumber of supernodes must be positive when is_super is TRUEOnly 'g'eneral sparse matrix types allowedSecond call to Lapack routine dgels returned error code %dSecond call to dgeqrf returned error code %dSolve requires a square matrixSuiteSparseQR_C_QR returned an error codeSupernodal LDL' decomposition not availableSupernodal/simplicial class inconsistent with type flagsSymmetric and triangular both setUnable to initialize cholmod: error code %dUnknown error in getGivensX must be a numeric (double precision) matrixX must be a real (numeric) matrixall column indices (slot 'j') must be between 0 and ncol-1 in a TsparseMatrixall column indices must be between 0 and ncol-1all row indices (slot 'i') must be between 0 and nrow-1 in a TsparseMatrixargument type[1]='%s' must be a one-letter character stringargument type[1]='%s' must be one of '1','O', or 'I'argument type[1]='%s' must be one of 'M','1','O','I','F' or 'E'as_cholmod_triplet(): could not reallocate for internal diagU2N()cannot add diag() as long as 'diag = "U"'cannot set diag() as long as 'diag = "U"'chm_diagN2U(): nrow=%d, ncol=%dchm_diagN2U(x, uploT = %d): uploT should be +- 1chm_factor_name(): did not get string of length 11chm_sparse_to_SEXP(, *): invalid 'Rkind' (real kind code)cholmod_change_factor failedcholmod_change_factor failed with status %dcholmod_drop() failedcholmod_factorize failed: status %d, minor %d from ncol %dcholmod_factorize_p failed: status %d, minor %d of ncol %dcholmod_sdmult error (resid)cholmod_sdmult error (rhs)cholmod_solve (CHOLMOD_A) failed: status %d, minor %d from ncol %dcholmod_sort returned an error codecholmod_updown() returned %dcholmod_write_sparse returned error codecls = "%s" does not end in "CMatrix"cls = "%s" must begin with 'd', 'l' or 'n'code for cholmod_dense with holes not yet writtencode not yet written for cls = "lgCMatrix"complex sparse matrix code not yet writtencs matrix not compatible with class '%s'cs_lu(A) failed: near-singular A (or out of memory)cs_lusol failedcs_qr failedcs_qrsol() failed inside dgCMatrix_qrsol()cs_sqr failedcsp_eye argument n must be positivedata length [%d] is not a sub-multiple or multiple of the number of columns [%d]data length [%d] is not a sub-multiple or multiple of the number of rows [%d]data length exceeds size of matrixddense_to_symmetric(): matrix is not square!dgCMatrix_cholsol requires a 'short, wide' rectangular matrixdgCMatrix_lusol requires a square, non-empty matrixdgCMatrix_matrix_solve(.., sparse=TRUE) not yet implementeddgCMatrix_qrsol(., order) needs order in {0,..,3}dgCMatrix_qrsol(<%d x %d>-matrix) requires a 'tall' rectangular matrixdgeMatrix_Schur: argument x must be a non-null square matrixdgeMatrix_Schur: dgees returned code %ddgeMatrix_Schur: first call to dgees faileddgeMatrix_exp: LAPACK routine dgebal returned %ddgeMatrix_exp: dgetrf returned error code %ddgeMatrix_exp: dgetrs returned error code %ddiag_tC(): invalid 'resultKind'diagonal element %d of Cholesky factor is missingdon't know if a dense pattern matrix makes sensedpoMatrix is not positive definitedtrMatrices in %*% must have matching (square) dim.dtrMatrix must be squareerror [%d] from Lapack 'dgecon()'exactly 1 of 'i', 'j' or 'p' must be NULLf->xtype of %d not recognizedfactors slot must be named listfailure in as_cholmod_factorfailure to open file "%s" for writingfirst element of slot p must be zeroi and j must be integer vectors of the same lengthin_place cholmod_sort returned an error codeincorrect left cyclic shift, j (%d) < 0incorrect left cyclic shift, j (%d) >= k (%d)incorrect left cyclic shift, k (%d) > ldx (%d)internal_chm_factor: Cholesky factorization failedinvalid '%s' argumentinvalid 'ncol' value (< 0)invalid 'ncol' value (too large or NA)invalid 'nrow' value (< 0)invalid 'nrow' value (too large or NA)invalid class '%s' to dup_mMatrix_as_dgeMatrixinvalid class '%s' to dup_mMatrix_as_geMatrixinvalid class of 'value' in Csparse_subassign()invalid class of 'x' in Csparse_subassign()invalid class of 'x' in Matrix_as_cs(a, x)invalid class of object to %sinvalid class of object to as_cholmod_denseinvalid class of object to as_cholmod_factorinvalid class of object to as_cholmod_sparseinvalid class of object to as_cholmod_tripletinvalid class(x) '%s' in R_to_CMatrix(x)invalid class(x) '%s' in compressed_to_TMatrix(x)invalid column index at position %dinvalid object passed to as_cholmod_sparseinvalid row index at position %dlast element of slot p must match length of slots j and xlength of x slot != prod(Dim)length(beta) must match ncol(V)length(p) must match nrow(V)length(q) must be zero or ncol(R)lengths of slots 'i' and 'x' must matchlengths of slots 'j' and 'x' must matchlengths of slots i and j must matchlengths of slots i and x must matchmatrix is not square! (skew-symmetric part)matrix is not square! (symmetric part)matrix is not symmetric [%d,%d]missing 'Matrix' namespace: should never happennegative vector lengths not allowed: np = %d, nnz = %dnon-numeric matrix extentnot a 'n.CMatrix'not a CsparseMatrixnp = %d, must be zero when p is NULLnumber of rows in y (%d) does not match number of rows in X (%d)nz2Csparse(): invalid/non-implemented r_kind = %dobject must be a named, numeric vectorp must be non-decreasingp[0] = %d, should be zeroprogramming error in Csparse_subassign() should never happenrcond requires a square, non-empty matrixright=TRUE is not yet implemented __ FIXMEslot Dim must have length 2slot j is not *strictly* increasing inside a columnslot j is not increasing inside a columnslot p must be non-decreasingslot p must have length = nrow(.) + 1sparseQR_Qmult(): nrow(y) = %d != %d = nrow(V)strlen of cls argument = %d, should be 8subscript 'i' out of bounds in M[ij]subscript 'j' out of bounds in M[ij]system argument is not validthe leading minor of order %d is not positive definitetol, given as %g, must be <= 1tol, given as %g, must be non-negativetoo many elements specifiedunexpected ctype = %d in dup_mMatrix_as_geMatrixunknown 'Rkind'unknown xtypeunknown xtype in cholmod_sparse objectunknown xtype in cholmod_triplet objectuplo='L' must not have sparse entries above the diagonaluplo='U' must not have sparse entries below the diagonalx slot must be numeric "double"x[] <- val: val is coerced to logical for "%s" xx[] <- val: val should be integer or logical, is coerced to integer, for "%s" xy must be a numeric (double precision) matrixProject-Id-Version: Matrix 1.1-1 Report-Msgid-Bugs-To: POT-Creation-Date: 2013-12-23 21:27+0100 PO-Revision-Date: 2013-12-23 21:27+0100 Last-Translator: Automatically generated Language-Team: none Language: en MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Plural-Forms: nplurals=2; plural=(n != 1); %s = ‘%s’ (back-permuted) is experimental%s(): structurally rank deficient case: possibly WRONG zeros‘%s’ must be in ‘%s’‘%s’ must have string length 1‘%s’ slot must have length 1‘Dim’ slot has length less than two‘data’ must be of a vector type‘factors’ slot must be a named list‘s1’ and ‘s2’ must be "character" vectors‘uplo’ must be UPP or LOWA must be a logical matrixA must have #{rows} >= #{columns}Argument b must be a numeric matrixArgument ij must be 2-column integer matrixArgument must be numeric-like atomic vectorArgument rho must be an environmentArgument y must be numeric or integerCHOLMOD factorization was unsuccessfulCannot coerce to too large *geMatrix with %.0f entriesCannot factor a matrix with zero extentsCannot solve() for matrices with zero extentsCholesky factorization failed; unusually, please report to Matrix-authorsCholmod error ‘%s’ at file %s, line %dCholmod warning ‘%s’ at file %s, line %dCsparse_crossprod(): error return from cholmod_aat()Csparse_general_to_symmetric(): matrix is not square!Csparse_sort(x): x is not a valid (apart from sorting) CsparseMatrixDeterminant requires a square matrixDim slot must have length 2Dimensions of a (%d,%d) and b (%d,%d) do not conformDimensions of system to be solved are inconsistentDimensions of x and y are not compatible for %sExact singularity detected during LU decomposition: %s, i=%d.First call to Lapack routine dgels returned error code %dFirst call to dgeqrf returned error code %dInappropriate class cl=‘%s’ in Matrix_csn_to_SEXP(S, cl, ..)Inappropriate class cl=‘%s’ in Matrix_css_to_SEXP(S, cl, ..)Inconsistent dimensions: np = 0 and nnz = %dIncorrect length of ‘x’ slotIndex i must be NULL or integerIndex j must be NULL or integerLU decomposition applies only to square matricesLapack dgecon(): system computationally singular, reciprocal condition number = %gLapack routine %s returned error code %dLapack routine dgetri: system is exactly singularLapack routine dgetrs: system is exactly singularLapack routine dposv returned error code %dLapack routine dsytrf returned error code %dLapack routine dtrcon returned error code %dLengths of super and pi must be equalLengths of super and px must be equalLower band %d > upper band %dMatrices are not conformable for multiplicationMatrix exponential requires square, non-null matrixMatrix is not squareMatrix namespace not determined correctlyNegative value in DimNegative values in DimNon-symmetric matrix passed to dsCMatrix_to_dgTMatrixNonsymmetric matrix in Csparse_symmetric_to_generalNumber of supernodes must be positive when is_super is TRUEOnly ‘g’eneral sparse matrix types allowedSecond call to Lapack routine dgels returned error code %dSecond call to dgeqrf returned error code %dSolve requires a square matrixSuiteSparseQR_C_QR returned an error codeSupernodal LDL' decomposition not availableSupernodal/simplicial class inconsistent with type flagsSymmetric and triangular both setUnable to initialize cholmod: error code %dUnknown error in getGivensX must be a numeric (double precision) matrixX must be a real (numeric) matrixall column indices (slot ‘j’) must be between 0 and ncol-1 in a TsparseMatrixall column indices must be between 0 and ncol-1all row indices (slot ‘i’) must be between 0 and nrow-1 in a TsparseMatrixargument type[1]=‘%s’ must be a one-letter character stringargument type[1]=‘%s’ must be one of ‘1’,‘O’, or ‘I’argument type[1]=‘%s’ must be one of ‘M’,‘1’,‘O’,‘I’,‘F’ or ‘E’as_cholmod_triplet(): could not reallocate for internal diagU2N()cannot add diag() as long as ‘diag = "U"’cannot set diag() as long as ‘diag = "U"’chm_diagN2U(): nrow=%d, ncol=%dchm_diagN2U(x, uploT = %d): uploT should be +- 1chm_factor_name(): did not get string of length 11chm_sparse_to_SEXP(, *): invalid ‘Rkind’ (real kind code)cholmod_change_factor failedcholmod_change_factor failed with status %dcholmod_drop() failedcholmod_factorize failed: status %d, minor %d from ncol %dcholmod_factorize_p failed: status %d, minor %d of ncol %dcholmod_sdmult error (resid)cholmod_sdmult error (rhs)cholmod_solve (CHOLMOD_A) failed: status %d, minor %d from ncol %dcholmod_sort returned an error codecholmod_updown() returned %dcholmod_write_sparse returned error codecls = "%s" does not end in "CMatrix"cls = "%s" must begin with ‘d’, ‘l’ or ‘n’code for cholmod_dense with holes not yet writtencode not yet written for cls = "lgCMatrix"complex sparse matrix code not yet writtencs matrix not compatible with class ‘%s’cs_lu(A) failed: near-singular A (or out of memory)cs_lusol failedcs_qr failedcs_qrsol() failed inside dgCMatrix_qrsol()cs_sqr failedcsp_eye argument n must be positivedata length [%d] is not a sub-multiple or multiple of the number of columns [%d]data length [%d] is not a sub-multiple or multiple of the number of rows [%d]data length exceeds size of matrixddense_to_symmetric(): matrix is not square!dgCMatrix_cholsol requires a ‘short, wide’ rectangular matrixdgCMatrix_lusol requires a square, non-empty matrixdgCMatrix_matrix_solve(.., sparse=TRUE) not yet implementeddgCMatrix_qrsol(., order) needs order in {0,..,3}dgCMatrix_qrsol(<%d x %d>-matrix) requires a ‘tall’ rectangular matrixdgeMatrix_Schur: argument x must be a non-null square matrixdgeMatrix_Schur: dgees returned code %ddgeMatrix_Schur: first call to dgees faileddgeMatrix_exp: LAPACK routine dgebal returned %ddgeMatrix_exp: dgetrf returned error code %ddgeMatrix_exp: dgetrs returned error code %ddiag_tC(): invalid ‘resultKind’diagonal element %d of Cholesky factor is missingdon't know if a dense pattern matrix makes sensedpoMatrix is not positive definitedtrMatrices in %*% must have matching (square) dim.dtrMatrix must be squareerror [%d] from Lapack ‘dgecon()’exactly 1 of ‘i’, ‘j’ or ‘p’ must be NULLf->xtype of %d not recognizedfactors slot must be named listfailure in as_cholmod_factorfailure to open file "%s" for writingfirst element of slot p must be zeroi and j must be integer vectors of the same lengthin_place cholmod_sort returned an error codeincorrect left cyclic shift, j (%d) < 0incorrect left cyclic shift, j (%d) >= k (%d)incorrect left cyclic shift, k (%d) > ldx (%d)internal_chm_factor: Cholesky factorization failedinvalid ‘%s’ argumentinvalid ‘ncol’ value (< 0)invalid ‘ncol’ value (too large or NA)invalid ‘nrow’ value (< 0)invalid ‘nrow’ value (too large or NA)invalid class ‘%s’ to dup_mMatrix_as_dgeMatrixinvalid class ‘%s’ to dup_mMatrix_as_geMatrixinvalid class of ‘value’ in Csparse_subassign()invalid class of ‘x’ in Csparse_subassign()invalid class of ‘x’ in Matrix_as_cs(a, x)invalid class of object to %sinvalid class of object to as_cholmod_denseinvalid class of object to as_cholmod_factorinvalid class of object to as_cholmod_sparseinvalid class of object to as_cholmod_tripletinvalid class(x) ‘%s’ in R_to_CMatrix(x)invalid class(x) ‘%s’ in compressed_to_TMatrix(x)invalid column index at position %dinvalid object passed to as_cholmod_sparseinvalid row index at position %dlast element of slot p must match length of slots j and xlength of x slot != prod(Dim)length(beta) must match ncol(V)length(p) must match nrow(V)length(q) must be zero or ncol(R)lengths of slots ‘i’ and ‘x’ must matchlengths of slots ‘j’ and ‘x’ must matchlengths of slots i and j must matchlengths of slots i and x must matchmatrix is not square! (skew-symmetric part)matrix is not square! (symmetric part)matrix is not symmetric [%d,%d]missing ‘Matrix’ namespace: should never happennegative vector lengths not allowed: np = %d, nnz = %dnon-numeric matrix extentnot a ‘n.CMatrix’not a CsparseMatrixnp = %d, must be zero when p is NULLnumber of rows in y (%d) does not match number of rows in X (%d)nz2Csparse(): invalid/non-implemented r_kind = %dobject must be a named, numeric vectorp must be non-decreasingp[0] = %d, should be zeroprogramming error in Csparse_subassign() should never happenrcond requires a square, non-empty matrixright=TRUE is not yet implemented __ FIXMEslot Dim must have length 2slot j is not *strictly* increasing inside a columnslot j is not increasing inside a columnslot p must be non-decreasingslot p must have length = nrow(.) + 1sparseQR_Qmult(): nrow(y) = %d != %d = nrow(V)strlen of cls argument = %d, should be 8subscript ‘i’ out of bounds in M[ij]subscript ‘j’ out of bounds in M[ij]system argument is not validthe leading minor of order %d is not positive definitetol, given as %g, must be <= 1tol, given as %g, must be non-negativetoo many elements specifiedunexpected ctype = %d in dup_mMatrix_as_geMatrixunknown ‘Rkind’unknown xtypeunknown xtype in cholmod_sparse objectunknown xtype in cholmod_triplet objectuplo=‘L’ must not have sparse entries above the diagonaluplo=‘U’ must not have sparse entries below the diagonalx slot must be numeric "double"x[] <- val: val is coerced to logical for "%s" xx[] <- val: val should be integer or logical, is coerced to integer, for "%s" xy must be a numeric (double precision) matrixMatrix/inst/po/en@quot/LC_MESSAGES/R-Matrix.mo0000644000175100001440000006237112256121033020333 0ustar hornikusers% 8!8Z6369R61/M,}-*#',;;h#6D,XK1#6Z4u$9W (aV0$.0S:Ix 8&'*JeJ~:(/-5],#887V,.$Q@D4( $5%Z#M=&0 &W <~ = 7!5!- "67":n"C"7"(%#*N#y#T# #* $97$q$e$/$"'%"J%1m%%%I%8%&"^&&@&@&5"'6X'' '''' ' (;($M(r(2(*('(" )1/)3a)()%):)-*M*@b*=*8*+H1+2z+9+,+0,EE,H,=,5-1H-'z------?.S.k.&..$.. /-&/&T//{/h/n0.00B0( 1D61A{1&1G1e,2v2? 3%I3+o3)3@3"4*)4T4;t4%44)4! 59B5>|55A563/6c6v6B666' 7047e7#757,77 8B8O^8>8I8<79:t9H9,97%:8];8;;;><;F<<=< <=# =:D=9=3=0=5>.T>'>>0>G>'cIc< d:HdHd,d:er{f}CXUuz&~1SO4g*A NcDB< 0vomx[W).t='(dlbjTP%]Zs^ - `I2G+;!pE /QF$nqV #"a\_>Hh85w7kMKyi|YR6?,3@J9L"dMatrix" object with NAs cannot be coerced to "nMatrix""lMatrix" object with NAs cannot be coerced to "nMatrix"%s %s is undefined%s kind not yet implemented'%s()' is not yet implemented for representation '%s''%s()' is not yet implemented for element type '%s''A' must be a square matrix'NA' indices are not (yet?) supported for sparse Matrices'V' is not a *square* matrix'V' is not a square matrix'by' argument is much too small'diagonals' matrix must have %d columns (= length(k) )'diagonals' must have the same length (%d) as 'k''file' must be a character string or connection'force' must be (coercable to) TRUE or FALSE'lag' and 'differences' must be integers >= 1'lwd' must be NULL or non-negative numeric'ncol' is not a factor of length(x)'ncol' must be >= 0'nearPD()' did not converge in %d iterations'nrow' and 'ncol' must be the same when 'symmetric' is true'nrow' is not a factor of length(x)'nrow' must be >= 0'nrow', 'ncol', etc, are disregarded for matrix 'data''nrow', 'ncol', etc, are disregarded when 'data' is "Matrix" already'p' must be a non-decreasing vector (0, ...)'times >= 0' is required'update' must be logical or '+' or '-'; 'C' a matrix, and 'L' a "CHMfactor"'x' has invalid data type'x' is not positive definite -- chol() undefined.'x' is not symmetric nor triangular'x' must be "sparseMatrix"'x' must have length nrow^2 when 'symmetric' is true'x' must inherit from "sparseVector"(un)packing only applies to dense matrices, class(x)='%s'.M.repl.i.2col(): 'i' has no integer column number; should never happen; please report.M.repl.i.2col(): drop 'matrix' case ....M.sub.i.2col(): 'i' has no integer column number; should never happen; please report %s %s is undefined --> is not yet implemented[i] is not yet implemented --> is not yet implemented[ ] : .M.sub.i.logical() maybe inefficientCholesky() -> *symbolic* factorization -- not yet implementedCholesky(A) called for 'A' of class "%s"; it is currently defined for sparseMatrix only; consider using chol() insteadClass %s is not yet implementedCmp.Mat.atomic() should not be called for diagonalMatrixFIXME: NOT YET FINISHED IMPLEMENTATIONInternal bug: nargs()=%d; please reportInvalid assembled indicator: %sInvalid storage format: %sInvalid storage type: %sLU computationally singular: ratio of extreme entries in |diag(U)| = %9.4gLogic.Mat.atomic() should not be called for diagonalMatrixMatrices must have same dimensions in %sMatrices must have same number of columns in %sMatrices must have same number of rows for arithmeticMatrices must have same number of rows in %sMatrix seems negative semi-definiteMatrix-internal error in [i,,d]; please reportMatrix-internal error in [i,,d]; please reportMatrix-internal error in [i,,d]; please reportMust specify 'nrow' when 'symmetric' is trueNA's in (i,j) are not allowedNAs are not allowed in subscripted assignmentsNot a valid formatOnly numeric sparse matrices allowedQuadratic matrix '%s' (=: A) is not formally symmetric. Will be treated as A A'RHS 'value' (class %s) matches 'ANY', but must match matrix class %s[ ] indexing not allowed: forgot a "," ?[[ suppressing %d column names %s ... ]][[ suppressing %d column names %s ]]all() is not yet implementedarguments %s are disregarded in %sas(.,"dsCMatrix") is deprecated (since 2008); do use as(., "symmetricMatrix")c(,..) of different kinds, coercing all to 'rleDiff'cannot coerce 'NA's to "nsparseMatrix"cannot coerce 'NA's to "nsparseVector"cannot coerce non-symmetric "dgTMatrix" to "dsCMatrix" classchol() is undefined for diagonal matrix with negative entriescoercion from list(i1,...,ik, d) to "indMatrix" failed. All entries must be integer valued and the number of columns, d, not smaller than the maximal index i*.coercion to "indMatrix" only works from integer numericcoercion to "pMatrix" only works from integer numericcolumn indices must be <= ncol(.) which is %dcomplex matrices not yet implemented in Matrix packagediag(.) had 0 or NA entries; non-finite result is doubtfuldiagonalMatrix in .dense2C() -- should never happen, please report!dim [product %d] do not match the length of object [%d]dim(.) value must be numeric of length 2dimensions don't match the number of cellsdimnames [%d] mismatch in %sdimnames(.) <- NULL: translated to dimnames(.) <- list(NULL,NULL) <==> unname(.)element type '%s' not recognizedelement type 'complex' not yet implementedexactly one of 'i', 'j', or 'p' must be missing from callfile is not a MatrixMarket filefor symmetric band matrix, only specify upper or lower triangle hence, all k must have the same signgeneral Matrix class not yet implemented for %shit a cycle (1) -- stop iterationshit a cycle (2) -- stop iterationsi1[1] == 0 ==> C-level verbosity will not happen!incompatible matrix dimensionsindex larger than maximal %dindex must be numeric, logical or sparseVector for indexing sparseVectorsinefficient coercion (lost triangularity); please reportinefficient method used for "- e1"intermediate 'r' is of type %sinternal bug in "Compare" method (Cmp.Mat.atomic); please reportinternal bug in "Logic" method (Logic.Mat.atomic); please reportinternal bug: matrix 'i' in replTmat(): please reportinternal bug: missing 'i' in replTmat(): please reportinvalid 'col.names' string: %sinvalid 'contrasts.arg' argumentinvalid 'data'invalid 'mod': %sinvalid 'type'invalid (to - from)/by in seq(.)invalid character indexinginvalid class: %sinvalid dimnames given for %s objectinvalid nargs()= %dinvalid or not-yet-implemented 'Matrix' subsettingis not a multiple of shorter object lengthkronecker method must use default 'FUN'length must be non-negative numberlength of 1st arg does not match dimension of 2ndlength of 2nd arg does not match dimension of firstlength(i) is not a multiple of length(x)length(x) must be either 1 or #{cols}logic programming error in printSpMatrix2(), please reportlogical subscript too long (%d, should be %d)longer object lengthlonger object length is not a multiple of shorter object lengthm[ ] <- v: inefficiently treating single elementsm[ ]: inefficiently indexing single elementsmatrix is not diagonalmatrix with non-zero off-diagonals cannot be coerced to "diagonalMatrix"model frame and formula mismatch in model.matrix()must either specify 'A' or the functions 'A.x' and 'At.x'must have exactly one non-zero entry per rownargs() = %d should never happen; please report.nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.2col)?nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.logical)?nargs() = %d. Extraneous illegal arguments inside '[ .. ]' ?negative values are not allowed in a matrix subscriptno 'dimnames[[.]]': cannot use character indexingnon-conformable matrix dimensions in %snon-matching dimensionsnon-square matrixnot a positive definite matrixnot a skinny matrixnot a square matrixnot a symmetric matrix; consider forceSymmetric() or symmpart()not a triangular matrixnot converged in %d iterationsnot enough new vecs -- stop iterationsnot yet implementednot yet implemented .. please reportnot yet implemented for %snot yet implemented for class %snot yet implemented for matrix with typeof %snot-yet-implemented 'Matrix[<-' methodnot-yet-implemented coercion to "TsparseMatrix"not-yet-implemented method for %s(<%s>). ->> Ask the package authors to implement the missing feature.not-yet-implemented method for %s(<%s>, <%s>). ->> Ask the package authors to implement the missing feature.not-yet-implemented method for <%s> %%*%% <%s>nothing to replace withnumber of items to replace is not a multiple of replacement lengthnumber of rows are not compatible for %sonly 2-dimensional tables can be directly coerced to sparse matricesonly square matrices can be used as incidence matrices for graphsprod() is not yet implementedprogramming error: min() should have dispatched w/ 1st arg much earlierqr.R() may differ from qr.R() because of permutations. Possibly use our qrR() insteadrankMatrix(, method = '%s') coerces to dense matrix. Probably should rather use method = 'qr' !?rankMatrix(x, method='qr'): computing t(x) as nrow(x) < ncol(x)rcond(.) via sparse -> dense coercionreadMM(): column values 'j' are not in 1:ncreadMM(): row values 'i' are not in 1:nrreplacing "indMatrix" entries is not allowed, as rarely sensiblerepresentation '%s' not recognizedrow indices must be <= nrow(.) which is %dsome arguments are not matricessuch indexing must be by logical or 2-column numeric matrixsum() is not yet implementedsymmetric matrix must be squaresymmetry form '%s' is not yet implementedsymmetry form '%s' not recognizedsymmetry form 'hermitian' not yet implemented for readingsymmetry form 'skew-symmetric' not yet implemented for readingtemporarily disabledthe %d-th (sub)-diagonal (k = %d) is too short; filling with NA'sthe matrix is not triangularthe number of non-zero entries differs from nrow(.)too many argumentstoo many replacement valuestrimmed mean of 'sparseVector' -- suboptimally using as.numeric(.)type '%s' not recognizedundefined method for class %supdate must be TRUE/FALSE or '+' or '-'using "old code" part in Csparse subassignmentusing slow kronecker() methodvariable '%s' converted to a factorvariable '%s' is absent, its contrast will be ignoredvector too long in Matrix - vector operationwhen 'A' is specified, 'A.x' and 'At.x' are disregardedwrong sign in 'by' argumentx / 0 for an x with sign-change no longer representable as 'rleDiff'x[.,.] <- val : x being coerced from Tsparse* to CsparseMatrixx[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced NA |--> TRUE.x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced.x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced.x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced; NA |--> TRUE.you cannot mix negative and positive indicesProject-Id-Version: Matrix 1.1-1 POT-Creation-Date: 2013-12-23 21:27 PO-Revision-Date: 2013-12-23 21:27 Last-Translator: Automatically generated Language-Team: none MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Language: en Plural-Forms: nplurals=2; plural=(n != 1); "dMatrix" object with NAs cannot be coerced to "nMatrix""lMatrix" object with NAs cannot be coerced to "nMatrix"%s %s is undefined%s kind not yet implemented‘%s()’ is not yet implemented for representation ‘%s’‘%s()’ is not yet implemented for element type ‘%s’‘A’ must be a square matrix‘NA’ indices are not (yet?) supported for sparse Matrices‘V’ is not a *square* matrix‘V’ is not a square matrix‘by’ argument is much too small‘diagonals’ matrix must have %d columns (= length(k) )‘diagonals’ must have the same length (%d) as ‘k’‘file’ must be a character string or connection‘force’ must be (coercable to) TRUE or FALSE‘lag’ and ‘differences’ must be integers >= 1‘lwd’ must be NULL or non-negative numeric‘ncol’ is not a factor of length(x)‘ncol’ must be >= 0‘nearPD()’ did not converge in %d iterations‘nrow’ and ‘ncol’ must be the same when ‘symmetric’ is true‘nrow’ is not a factor of length(x)‘nrow’ must be >= 0‘nrow’, ‘ncol’, etc, are disregarded for matrix ‘data’‘nrow’, ‘ncol’, etc, are disregarded when ‘data’ is "Matrix" already‘p’ must be a non-decreasing vector (0, ...)‘times >= 0’ is required‘update’ must be logical or ‘+’ or ‘-’; ‘C’ a matrix, and ‘L’ a "CHMfactor"‘x’ has invalid data type‘x’ is not positive definite -- chol() undefined.‘x’ is not symmetric nor triangular‘x’ must be "sparseMatrix"‘x’ must have length nrow^2 when ‘symmetric’ is true‘x’ must inherit from "sparseVector"(un)packing only applies to dense matrices, class(x)=‘%s’.M.repl.i.2col(): ‘i’ has no integer column number; should never happen; please report.M.repl.i.2col(): drop ‘matrix’ case ....M.sub.i.2col(): ‘i’ has no integer column number; should never happen; please report %s %s is undefined --> is not yet implemented[i] is not yet implemented --> is not yet implemented[ ] : .M.sub.i.logical() maybe inefficientCholesky() -> *symbolic* factorization -- not yet implementedCholesky(A) called for ‘A’ of class "%s"; it is currently defined for sparseMatrix only; consider using chol() insteadClass %s is not yet implementedCmp.Mat.atomic() should not be called for diagonalMatrixFIXME: NOT YET FINISHED IMPLEMENTATIONInternal bug: nargs()=%d; please reportInvalid assembled indicator: %sInvalid storage format: %sInvalid storage type: %sLU computationally singular: ratio of extreme entries in |diag(U)| = %9.4gLogic.Mat.atomic() should not be called for diagonalMatrixMatrices must have same dimensions in %sMatrices must have same number of columns in %sMatrices must have same number of rows for arithmeticMatrices must have same number of rows in %sMatrix seems negative semi-definiteMatrix-internal error in [i,,d]; please reportMatrix-internal error in [i,,d]; please reportMatrix-internal error in [i,,d]; please reportMust specify ‘nrow’ when ‘symmetric’ is trueNA's in (i,j) are not allowedNAs are not allowed in subscripted assignmentsNot a valid formatOnly numeric sparse matrices allowedQuadratic matrix ‘%s’ (=: A) is not formally symmetric. Will be treated as A A'RHS ‘value’ (class %s) matches ‘ANY’, but must match matrix class %s[ ] indexing not allowed: forgot a "," ?[[ suppressing %d column names %s ... ]][[ suppressing %d column names %s ]]all() is not yet implementedarguments %s are disregarded in %sas(.,"dsCMatrix") is deprecated (since 2008); do use as(., "symmetricMatrix")c(,..) of different kinds, coercing all to ‘rleDiff’cannot coerce ‘NA’s to "nsparseMatrix"cannot coerce ‘NA’s to "nsparseVector"cannot coerce non-symmetric "dgTMatrix" to "dsCMatrix" classchol() is undefined for diagonal matrix with negative entriescoercion from list(i1,...,ik, d) to "indMatrix" failed. All entries must be integer valued and the number of columns, d, not smaller than the maximal index i*.coercion to "indMatrix" only works from integer numericcoercion to "pMatrix" only works from integer numericcolumn indices must be <= ncol(.) which is %dcomplex matrices not yet implemented in Matrix packagediag(.) had 0 or NA entries; non-finite result is doubtfuldiagonalMatrix in .dense2C() -- should never happen, please report!dim [product %d] do not match the length of object [%d]dim(.) value must be numeric of length 2dimensions don't match the number of cellsdimnames [%d] mismatch in %sdimnames(.) <- NULL: translated to dimnames(.) <- list(NULL,NULL) <==> unname(.)element type ‘%s’ not recognizedelement type ‘complex’ not yet implementedexactly one of ‘i’, ‘j’, or ‘p’ must be missing from callfile is not a MatrixMarket filefor symmetric band matrix, only specify upper or lower triangle hence, all k must have the same signgeneral Matrix class not yet implemented for %shit a cycle (1) -- stop iterationshit a cycle (2) -- stop iterationsi1[1] == 0 ==> C-level verbosity will not happen!incompatible matrix dimensionsindex larger than maximal %dindex must be numeric, logical or sparseVector for indexing sparseVectorsinefficient coercion (lost triangularity); please reportinefficient method used for "- e1"intermediate ‘r’ is of type %sinternal bug in "Compare" method (Cmp.Mat.atomic); please reportinternal bug in "Logic" method (Logic.Mat.atomic); please reportinternal bug: matrix ‘i’ in replTmat(): please reportinternal bug: missing ‘i’ in replTmat(): please reportinvalid ‘col.names’ string: %sinvalid ‘contrasts.arg’ argumentinvalid ‘data’invalid ‘mod’: %sinvalid ‘type’invalid (to - from)/by in seq(.)invalid character indexinginvalid class: %sinvalid dimnames given for %s objectinvalid nargs()= %dinvalid or not-yet-implemented ‘Matrix’ subsettingis not a multiple of shorter object lengthkronecker method must use default ‘FUN’length must be non-negative numberlength of 1st arg does not match dimension of 2ndlength of 2nd arg does not match dimension of firstlength(i) is not a multiple of length(x)length(x) must be either 1 or #{cols}logic programming error in printSpMatrix2(), please reportlogical subscript too long (%d, should be %d)longer object lengthlonger object length is not a multiple of shorter object lengthm[ ] <- v: inefficiently treating single elementsm[ ]: inefficiently indexing single elementsmatrix is not diagonalmatrix with non-zero off-diagonals cannot be coerced to "diagonalMatrix"model frame and formula mismatch in model.matrix()must either specify ‘A’ or the functions ‘A.x’ and ‘At.x’must have exactly one non-zero entry per rownargs() = %d should never happen; please report.nargs() = %d. Extraneous illegal arguments inside ‘[ .. ]’ (i.2col)?nargs() = %d. Extraneous illegal arguments inside ‘[ .. ]’ (i.logical)?nargs() = %d. Extraneous illegal arguments inside ‘[ .. ]’ ?negative values are not allowed in a matrix subscriptno ‘dimnames[[.]]’: cannot use character indexingnon-conformable matrix dimensions in %snon-matching dimensionsnon-square matrixnot a positive definite matrixnot a skinny matrixnot a square matrixnot a symmetric matrix; consider forceSymmetric() or symmpart()not a triangular matrixnot converged in %d iterationsnot enough new vecs -- stop iterationsnot yet implementednot yet implemented .. please reportnot yet implemented for %snot yet implemented for class %snot yet implemented for matrix with typeof %snot-yet-implemented ‘Matrix[<-’ methodnot-yet-implemented coercion to "TsparseMatrix"not-yet-implemented method for %s(<%s>). ->> Ask the package authors to implement the missing feature.not-yet-implemented method for %s(<%s>, <%s>). ->> Ask the package authors to implement the missing feature.not-yet-implemented method for <%s> %%*%% <%s>nothing to replace withnumber of items to replace is not a multiple of replacement lengthnumber of rows are not compatible for %sonly 2-dimensional tables can be directly coerced to sparse matricesonly square matrices can be used as incidence matrices for graphsprod() is not yet implementedprogramming error: min() should have dispatched w/ 1st arg much earlierqr.R() may differ from qr.R() because of permutations. Possibly use our qrR() insteadrankMatrix(, method = ‘%s’) coerces to dense matrix. Probably should rather use method = ‘qr’ !?rankMatrix(x, method=‘qr’): computing t(x) as nrow(x) < ncol(x)rcond(.) via sparse -> dense coercionreadMM(): column values ‘j’ are not in 1:ncreadMM(): row values ‘i’ are not in 1:nrreplacing "indMatrix" entries is not allowed, as rarely sensiblerepresentation ‘%s’ not recognizedrow indices must be <= nrow(.) which is %dsome arguments are not matricessuch indexing must be by logical or 2-column numeric matrixsum() is not yet implementedsymmetric matrix must be squaresymmetry form ‘%s’ is not yet implementedsymmetry form ‘%s’ not recognizedsymmetry form ‘hermitian’ not yet implemented for readingsymmetry form ‘skew-symmetric’ not yet implemented for readingtemporarily disabledthe %d-th (sub)-diagonal (k = %d) is too short; filling with NA'sthe matrix is not triangularthe number of non-zero entries differs from nrow(.)too many argumentstoo many replacement valuestrimmed mean of ‘sparseVector’ -- suboptimally using as.numeric(.)type ‘%s’ not recognizedundefined method for class %supdate must be TRUE/FALSE or ‘+’ or ‘-’using "old code" part in Csparse subassignmentusing slow kronecker() methodvariable ‘%s’ converted to a factorvariable ‘%s’ is absent, its contrast will be ignoredvector too long in Matrix - vector operationwhen ‘A’ is specified, ‘A.x’ and ‘At.x’ are disregardedwrong sign in ‘by’ argumentx / 0 for an x with sign-change no longer representable as ‘rleDiff’x[.,.] <- val : x being coerced from Tsparse* to CsparseMatrixx[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced NA |--> TRUE.x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced.x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced.x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced; NA |--> TRUE.you cannot mix negative and positive indicesMatrix/inst/po/de/0000755000175100001440000000000012271765426013533 5ustar hornikusersMatrix/inst/po/de/LC_MESSAGES/0000755000175100001440000000000012271765426015320 5ustar hornikusersMatrix/inst/po/de/LC_MESSAGES/Matrix.mo0000644000175100001440000005351212256121033017106 0ustar hornikusers$, 0)1[p##)8!S#u+#%&66(m-I&(54^5$4 2?/r=9+<F<, *0JR{(11)+[,,%%-/K3{),53Q;*:,'T)s+8!+$P-k!M/ J9;4?A5)w)20?/o+:: DaB|#( $) *N 1y * * (!3*!^! n!*{! !#!,!="3C"1w"F"<"'-#+U#0#,#,# $1,$0^$"$3$$!$)!%K%i%%%%$%2%,$&'Q&-y&.&2&. '-8'/f'+'*''+ (,7(,d(-(((1(#)*>) i)9)))!)'!*'I*#q*#*+*&* +/,+6\+++$+@+1,&Q,x,,<,),-3.-(b--%-(-$-$.B.6_..&.0. / /&+/'R/8z/8//- 0:0012+2#H2)l2.2522 3"<3+_363$3/3-4AE4=444V4*Q5+|5<5=5/#6 S6:t6C656>)7@h727?7?8.\88)8)898N79191929.:0L:/}:,:,: ;/(;EX;;(;+;><5O<@<4<A<3==,q=/=+===,8>6e>>9>*>T!?8v?S?H@=L@W@G@2*A-]A9A2AEA$>B2cBBABCB:CXCItC)C*C+D'?D6gD;D4DAE,QEK~EEE5E-F$CF4hFCF?F=!GM_GLG0G7+H3cH/H0H#H,ICII#I>II!J22JeJ+JJ5J(K=.K2lK0K6K7L;?L6{L5L4L0M1NM$M2M3M3 N4@N-uN6N'N8O&;OObOO O%O0P0IP(zP1P9P2Q$BQ7gQ:QQQ(RG)R;qR1RRR8S5PS S:S1S T&5T,\T0T0T T< U#IU,mU2UUU*U+VMJVMV)V9WLN~+K^.e12#W&%"(F|!jrJ} Uxc9o\qwtzBl0$,sy:/E8@ dZfG{ n7>QX*;ASM=TR`3CpOk[ ) mg-5 ?aHbD6I<4Vuh]vP'Y_i%s = '%s' (back-permuted) is experimental'%s' must be in '%s''%s' must have string length 1'%s' slot must have length 1'Dim' slot has length less than two'factors' slot must be a named list's1' and 's2' must be "character" vectors'uplo' must be UPP or LOWA must be a logical matrixA must have #{rows} >= #{columns}Argument b must be a numeric matrixArgument ij must be 2-column integer matrixArgument rho must be an environmentArgument y must be numeric or integerCHOLMOD factorization was unsuccessfulCannot coerce to too large *geMatrix with %.0f entriesCannot factor a matrix with zero extentsCannot solve() for matrices with zero extentsCholesky factorization failed; unusually, please report to Matrix-authorsCholmod error '%s' at file %s, line %dCholmod warning '%s' at file %s, line %dCsparse_crossprod(): error return from cholmod_aat()Csparse_general_to_symmetric(): matrix is not square!Determinant requires a square matrixDim slot must have length 2Dimensions of a (%d,%d) and b (%d,%d) do not conformDimensions of system to be solved are inconsistentDimensions of x and y are not compatible for %sExact singularity detected during LU decomposition: %s, i=%d.First call to Lapack routine dgels returned error code %dFirst call to dgeqrf returned error code %dInappropriate class cl='%s' in Matrix_csn_to_SEXP(S, cl, ..)Inappropriate class cl='%s' in Matrix_css_to_SEXP(S, cl, ..)Inconsistent dimensions: np = 0 and nnz = %dIncorrect length of 'x' slotIndex i must be NULL or integerIndex j must be NULL or integerLU decomposition applies only to square matricesLapack dgecon(): system computationally singular, reciprocal condition number = %gLapack routine %s returned error code %dLapack routine dgetri: system is exactly singularLapack routine dgetrs: system is exactly singularLapack routine dposv returned error code %dLapack routine dsytrf returned error code %dLapack routine dtrcon returned error code %dLengths of super and pi must be equalLengths of super and px must be equalLower band %d > upper band %dMatrices are not conformable for multiplicationMatrix exponential requires square, non-null matrixMatrix is not squareMatrix namespace not determined correctlyNegative value in DimNegative values in DimNon-symmetric matrix passed to dsCMatrix_to_dgTMatrixNonsymmetric matrix in Csparse_symmetric_to_generalNumber of supernodes must be positive when is_super is TRUEOnly 'g'eneral sparse matrix types allowedSecond call to Lapack routine dgels returned error code %dSecond call to dgeqrf returned error code %dSolve requires a square matrixSuiteSparseQR_C_QR returned an error codeSupernodal LDL' decomposition not availableSupernodal/simplicial class inconsistent with type flagsSymmetric and triangular both setUnable to initialize cholmod: error code %dUnknown error in getGivensX must be a numeric (double precision) matrixX must be a real (numeric) matrixall column indices (slot 'j') must be between 0 and ncol-1 in a TsparseMatrixall column indices must be between 0 and ncol-1all row indices (slot 'i') must be between 0 and nrow-1 in a TsparseMatrixargument type[1]='%s' must be a one-letter character stringargument type[1]='%s' must be one of '1','O', or 'I'argument type[1]='%s' must be one of 'M','1','O','I','F' or 'E'as_cholmod_triplet(): could not reallocate for internal diagU2N()cannot add diag() as long as 'diag = "U"'cannot set diag() as long as 'diag = "U"'chm_diagN2U(): nrow=%d, ncol=%dchm_diagN2U(x, uploT = %d): uploT should be +- 1chm_sparse_to_SEXP(, *): invalid 'Rkind' (real kind code)cholmod_change_factor failedcholmod_change_factor failed with status %dcholmod_drop() failedcholmod_factorize failed: status %d, minor %d from ncol %dcholmod_factorize_p failed: status %d, minor %d of ncol %dcholmod_sdmult error (resid)cholmod_sdmult error (rhs)cholmod_solve (CHOLMOD_A) failed: status %d, minor %d from ncol %dcholmod_sort returned an error codecholmod_updown() returned %dcholmod_write_sparse returned error codecls = "%s" does not end in "CMatrix"cls = "%s" must begin with 'd', 'l' or 'n'code for cholmod_dense with holes not yet writtencode not yet written for cls = "lgCMatrix"complex sparse matrix code not yet writtencs matrix not compatible with class '%s'cs_lu(A) failed: near-singular A (or out of memory)cs_lusol failedcs_qr failedcs_qrsol() failed inside dgCMatrix_qrsol()cs_sqr failedcsp_eye argument n must be positiveddense_to_symmetric(): matrix is not square!dgCMatrix_cholsol requires a 'short, wide' rectangular matrixdgCMatrix_lusol requires a square, non-empty matrixdgCMatrix_qrsol(., order) needs order in {0,..,3}dgCMatrix_qrsol(<%d x %d>-matrix) requires a 'tall' rectangular matrixdgeMatrix_Schur: argument x must be a non-null square matrixdgeMatrix_Schur: dgees returned code %ddgeMatrix_Schur: first call to dgees faileddgeMatrix_exp: LAPACK routine dgebal returned %ddgeMatrix_exp: dgetrf returned error code %ddgeMatrix_exp: dgetrs returned error code %ddiag_tC(): invalid 'resultKind'diagonal element %d of Cholesky factor is missingdon't know if a dense pattern matrix makes sensedpoMatrix is not positive definitedtrMatrices in %*% must have matching (square) dim.dtrMatrix must be squareerror [%d] from Lapack 'dgecon()'exactly 1 of 'i', 'j' or 'p' must be NULLf->xtype of %d not recognizedfactors slot must be named listfailure in as_cholmod_factorfailure to open file "%s" for writingfirst element of slot p must be zeroi and j must be integer vectors of the same lengthin_place cholmod_sort returned an error codeincorrect left cyclic shift, j (%d) < 0incorrect left cyclic shift, j (%d) >= k (%d)incorrect left cyclic shift, k (%d) > ldx (%d)internal_chm_factor: Cholesky factorization failedinvalid class '%s' to dup_mMatrix_as_dgeMatrixinvalid class '%s' to dup_mMatrix_as_geMatrixinvalid class of 'value' in Csparse_subassign()invalid class of 'x' in Csparse_subassign()invalid class of 'x' in Matrix_as_cs(a, x)invalid class of object to %sinvalid class of object to as_cholmod_denseinvalid class of object to as_cholmod_factorinvalid class of object to as_cholmod_sparseinvalid class of object to as_cholmod_tripletinvalid class(x) '%s' in R_to_CMatrix(x)invalid class(x) '%s' in compressed_to_TMatrix(x)invalid column index at position %dinvalid object passed to as_cholmod_sparseinvalid row index at position %dlast element of slot p must match length of slots j and xlength of x slot != prod(Dim)length(p) must match nrow(V)length(q) must be zero or ncol(R)lengths of slots 'i' and 'x' must matchlengths of slots 'j' and 'x' must matchlengths of slots i and j must matchlengths of slots i and x must matchmatrix is not square! (skew-symmetric part)matrix is not square! (symmetric part)matrix is not symmetric [%d,%d]missing 'Matrix' namespace: should never happennegative vector lengths not allowed: np = %d, nnz = %dnot a 'n.CMatrix'not a CsparseMatrixnp = %d, must be zero when p is NULLnumber of rows in y (%d) does not match number of rows in X (%d)nz2Csparse(): invalid/non-implemented r_kind = %dobject must be a named, numeric vectorp must be non-decreasingp[0] = %d, should be zeroprogramming error in Csparse_subassign() should never happenrcond requires a square, non-empty matrixslot Dim must have length 2slot j is not *strictly* increasing inside a columnslot j is not increasing inside a columnslot p must be non-decreasingslot p must have length = nrow(.) + 1strlen of cls argument = %d, should be 8subscript 'i' out of bounds in M[ij]subscript 'j' out of bounds in M[ij]system argument is not validthe leading minor of order %d is not positive definitetol, given as %g, must be <= 1tol, given as %g, must be non-negativeunexpected ctype = %d in dup_mMatrix_as_geMatrixunknown 'Rkind'unknown xtypeunknown xtype in cholmod_sparse objectunknown xtype in cholmod_triplet objectuplo='L' must not have sparse entries above the diagonaluplo='U' must not have sparse entries below the diagonalx slot must be numeric "double"y must be a numeric (double precision) matrixProject-Id-Version: R 2.15.2 / matrix 1.0-10 Report-Msgid-Bugs-To: POT-Creation-Date: 2013-12-23 21:27+0100 PO-Revision-Date: 2012-10-01 15:33+0200 Last-Translator: Chris Leick Language-Team: German Language: de MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Plural-Forms: nplurals=2; plural=(n != 1); %s = »%s« (zurückgetauscht) ist experimentell»%s« muss in »%s« sein»%s« muss die Zeichenkettenlänge 1 habenSlot »%s« muss die Länge 1 haben»Dim«-Slot hat eine Länge kleiner zwei»faktors«-Slot muss eine benannte Liste sein»s1« und »s2« müssen »character«-Vektoren sein»uplo« muss UPP oder LOW seinA muss eine logische Matrix seinA muss #{rows} >= #{columns} habenArgument b muss eine numerische Matrix seinArgument ij muss eine zweispaltige Ganzzahlmatrix seinArgument rho muss eine Umgebung seinArgument y muss numerisch oder ganzzahlig seinCHOLMOD-Faktorzerlegung war nicht erfolgreichKann nicht in eine große *geMatrix mit %.0f Einträgen umwandelnEine Matrix mit Umfang Null kann nicht berücksichtigt werdensolve() für Matrizen mit Umfang Null nicht möglichCholesky-Faktorisierung fehlgeschlagen; ungewöhnlich, bitte an Matrix-authors melden!Cholmod-Fehler '%s' bei Datei %s, Zeile %dCholmod-Warnung '%s' bei Datei %s, Zeile %dCsparse_crossprod(): Fehler von cholmod_aat() zurückgegebenCsparse_general_to_symmetric(): Matrix ist nicht quadratisch.Determinante benötigt eine quadratische MatrixDim-Slot muss die Länge 2 habenDimensionen von a (%d,%d) und b (%d,%d) sind nicht konformDimensionen des Systems, das gelöst werden soll, sind inkonsistentDimensionen von x und y sind nicht kompatibel für %sExakte Singularität während LU-Zerlegung entdeckt: %s, i=%d.Erster Aufruf der Lapack-Routine dgels gab Fehlerkode %d zurückErster Aufruf von dgeqrf gab Fehlerkode %d zurückUnangemessene Klasse cl=»%s« in Matrix_csn_to_SEXP(S, cl, ..)Unangemessene Klasse cl=»%s« in Matrix_css_to_SEXP(S, cl, ..)Inkonsistente Dimensionen: np = 0 und nnz = %dFalsche Länge von »x«-SlotIndex i muss NULL oder eine Ganzzahl seinIndex j muss NULL oder eine Ganzzahl seinLU-Zerlegung ist nur bei quadratischen Matrizen anwendbarLapack-dgecon(): System rechnerisch singulär, reziproke Bedingungsnummer = %gLapack-Routine %s gab einen Fehlerkode %d zurückLapack-Routine dgetri: System ist exakt singulärLapack-Routine dgetrs:: System ist exakt singulärLapack-Routine dposv gab Fehlerkode %d zurückLapack-Routine dsytrf gab Fehlerkode %d zurückLapack-Routine dtrcon gab Fehlerkode %d zurückLängen von super und pi müssen gleich seinLängen von super und px müssen gleich seinUnteres Band %d > oberes Band %dMatrizen sind nicht für Multiplikation konformExponentielle Matrix benötigt eine quadratische Matrix ungleich NullMatrix ist nicht quadratischMatrix-Namensraum nicht korrekt bestimmtNegativer Wert in DimNegative Werte in DimNicht symmetrische Matrix an dsCMatrix_to_dgTMatrix übergebenUnsymmetrische Matrix in Csparse_symmetric_to_generalAnzahl der Superknoten muss positiv sein, wenn is_super TRUE istNur »g«enerelle dünn besetzte Matrixtypen erlaubtZweiter Aufruf der Lapack-Routine dgels gab Fehlerkode %d zurückZweiter Aufruf von dgeqrf gab Fehlerkode %d zurückAuflösen benötigt eine quadratische MatrixSuiteSparseQR_C_QR gab einen Fehlerkode zurückSuperknoten-LDL'-Zerlegung nicht verfügbarSuperknoten-/simpliziale Klasse inkonstent mit TypkennzeichenSymmetrisch und dreieckig sind beide gesetztcholmod kann nicht initialisiert werden: Fehlerkode %dUnbekannter Fehler in getGivensX muss eine numerische (doppelte Genauigkeit) Matrix seinX muss eine echte (numerische) Matrix seinAlle Spaltenindizes (slot 'j') müssen in TsparseMatrix zwischen 0 und ncol-1 liegenAlle Spaltenindizes müssen zwischen 0 und ncol-1 liegenalle Zeilenindizes (slot 'i') müssen in TsparseMatrix zwischen 0 und nrow-1 liegenArgument type[1]=»%s« muss eine Zeichenkette aus einem Buchstaben seinArgument type[1]=»%s« eins aus »1«, »O« oder »I« seinArgument type[1]=»%s« muss eins aus »M«, »1«, »O«, »I«, »F« oder »E« seinas_cholmod_triplet(): konnte für internes diagU2N() nicht reallozierenkann diag() nicht hinzufügen solange 'diag = "U"'kann diag() nicht setzen solange 'diag = "U"'chm_diagN2U(, *): ungültiges »Rkind« (echter Artkode)cholmod_change_factor fehlgeschlagencholmod_change_factor mit Status %d fehlgeschlagencholmod_drop() fehlgeschlagencholmod_factorize fehlgeschlagen: Status %d, Minor %d von ncol %dcholmod_factorize_p fehlgeschlagen: Status %d, Minor %d von ncol %dcholmod_sdmult-Fehler (resid)cholmod_sdmult-Fehler (rhs)cholmod_solve (CHOLMOD_A) fehlgeschlagen: Status %d, Minor %d von ncol %dcholmod_sort gab einen Fehlerkode zurückcholmod_updown() gab Fehlerkode %d zurückcholmod_write_sparse gab Fehlerkode zurückcls = »%s« endet nicht in »CMatrix«cls = »%s« muss mit »d«, »l« oder »n« beginnenKode für cholmod_dense mit Löchern noch nicht geschriebenKode noch nicht für cls = »lgCMatrix« geschriebenKode für komplexe dünn besetzte Matrizen noch nicht geschriebencs-Matrix nicht kompatibel mit Klasse »%s«cs_lu(A) fehlgeschlagen: near-Singuläres A (oder außerhalb des Speichers)cs_lusol fehlgeschlagencs_qr fehlgeschlagencs_qrsol() innerhalb dgCMatrix_qrsol() fehlgeschlagencs_sqr fehlgeschlagencsp_eye-Argument n muss positiv seinddense_to_symmetric(): Matrix ist nicht quadratisch.dgCMatrix_cholsol benötigt eine »short, wide«-rechteckige MatrixdgCMatrix_lusol benötigt eine quadratische, nicht leere MatrixdgCMatrix_qrsol(., Anordnung) benötigt Anordnung in {0,..,3}dgCMatrix_qrsol(<%d x %d>-Matrix) benötigt eine »lange« rechteckige MatrixdgeMatrix_Schur: Argument x muss eine quadratische Matrix ungleich Null seindgeMatrix_Schur: dgees gab Fehlerkode %d zurückdgeMatrix_Schur: Erster Aufruf von dgees fehlgeschlagendgeMatrix_exp: LAPACK-Routine dgebal gab %d zurückdgeMatrix_exp: dgetrf gab Fehlerkode %d zurückdgeMatrix_exp: dgetrs gab Fehlerkode %d zurückdiag_tC(): »resultKind« ungültigDiagonalelement %d des Choleskyfaktors fehltes ist nicht klar, ob eine dicht besetzte Mustermatrix sinnvoll istdpoMatrix ist nicht positiv definitdtrMatrix in %*% muss quadratisch mit passender Dimension seindtrMatrix muss quadratisch seinFehler [%d] von Lapack-'dgecon()'exakt 1 von »i«, »j« oder »p« muss NULL seinf->xtype von %d nicht erkanntFaktoren-Slot muss eine benannte Liste seinMisserfolg in as_cholmod_factorÖffnen von Datei »%s« zum Schreiben fehlgeschlagenerstes Element von Slot p muss Null seini und j müssen Ganzzahlvektoren mit der gleichen Länge seinin_place cholmod_sort gab einen Fehlerkode zurückfalsches zyklisches Linksverschieben, j (%d) < 0falsches zyklisches Linksverschieben, j (%d) >= k (%d)falsches zyklisches Linksverschieben, k (%d) > ldx (%d)internal_chm_factor: Cholesky-Faktorisierung fehlgeschlagenungültige Klasse »%s« für dup_mMatrix_as_dgeMatrixungültige Klasse »%s« für dup_mMatrix_as_geMatrixungültige Klasse von 'value' in Csparse_subassign()ungültige Klasse von 'x' in Csparse_subassign()ungültige Klasse von »x« in Matrix_as_cs(a, x)ungültige Klasse des Objektes zu %sungültige Klasse des Objektes zu as_cholmod_denseungültige Klasse des Objektes zu as_cholmod_factorungültige Klasse des Objektes zu as_cholmod_sparseungültige Klasse des Objektes zu as_cholmod_tripletungültige class(x) »%s« in R_to_CMatrix(x)ungültige class(x) »%s« in compressed_to_TMatrix(x)ungültiger Spaltenindex an Position %dungültige Objekt an Klasse as_cholmod_sparse übergebenungültiger Zeilenindex an Position %dletztes Element von Slot p muss eine zu den Slots j und x passende Länge habenLänge von x-Slot != prod(Dim)length(p) muss zu nrow(V) passenlength(q) muss null oder ncol(R) seinLängen der Slots »i« und »x« müssen passenLängen der Slots »j« und »x« müssen passenLängen der Slots i und j müssen passenLängen der Slots i und x müssen zusammen passenMatrix ist nicht quadratisch. (schief-symmetrischer Teil)Matrix ist nicht quadratisch. (symmetrischer Teil)Matrix ist nicht symmetrisch [%d,%d]fehlender 'Matrix'-Namensraum: Sollte niemals vorkommennegative Vektorlänge ist nicht erlaubt: np = %d, nnz = %dkeine 'n.CMatrix'keine CsparseMatrixnp = %d, muss Null sein, wenn p NULL istAnzahl der Zeilen in y (%d) passt nicht zur Anzahl der Zeilen in X (%d)nz2Csparse(): ungültiges/nicht implementiertes r_kind = %dObjekt muss ein benannter numerischer Vektor seinp darf nicht abnehmend seinp[0] = %d, sollte Null seinFehler in Csparse_subassign(); sollte niemals vorkommenrcond benötigt eine quadratische, nicht leere MatrixSlot Dim muss die Länge 2 habenSlot j ist nicht *strikt* zunehmend innerhalb einer SpalteSlot j ist nicht zunehmend innerhalb einer SpalteSlot p darf nicht abnehmend seinSlot p muss Länge = nrow(.) + 1 habenstrlen des cls-Arguments = %d, sollte 8 seinSubskript »i« außerhalb des Bereichs in M[ij]Subskript »j« außerhalb des Bereichs in M[ij]Systemargument ist nicht gültigder führende Minor der Ordnung %d ist nicht positiv definittol, als %g gegeben, muss <= 1 seintol, als %g gegeben, darf nicht negativ seinunerwartetes ctype = %d in dup_mMatrix_as_geMatrix»Rkind« unbekanntunbekannter xtypeunbekannter xtype in Objekt cholmod_sparseunbekannter xtype in Objekt cholmod_tripletuplo=»L« darf keine dünn besetzten Einträge unterhalb der Diagonale habenuplo=»U« darf keine dünn besetzten Einträge unterhalb der Diagonale habenx-Slot muss ein numerisch »double« seiny muss eine numerische (doppelte Genauigkeit) Matrix seinMatrix/inst/po/de/LC_MESSAGES/R-Matrix.mo0000644000175100001440000005267112256121033017312 0ustar hornikusers 8863J~9 6,1c/,-* #Ko;#6D.,sK1#Q4u$9( 02$c0:Ix>8&'J?:(/5,T#887,O|.$QDS4%=&1&X=6_:C7(M*v *9 Ded""1BIa8"@&@g56  6 E T u 2 * ' "!19!3k!(!%!:!-)"W"@l"="8"$#2;#9n#,#0#E$HL$=$5$1 %';%c%{%%%%?%&,&&K&r&$&&&/&h'nk'.' (B!(Dd(A(&(G)?Z)%)+)))@*"W*z*;*%**)+!F+9h+>++A+8,3U,,,B,,'-0<-m-#-5-,-7.J.>f.,..Cu0C090871&p1K1#1!2)27D26|222?23&31Z3$33L3$494CO4R4345[65545.5A6'U6I}6-636))73S7A7S78C878)9bH9E9597':@_:6:*::;:=;9x;C;;1<H<#^<c<L<;3=+o=R=9=+(>ET>>9D?K~?J?8@:N@.@ @@-@7%A"]AA6B67B3nBBSBBC(XC#CJCKC:G=G)H>CH>H3H7HK-INyIBI; JCGJ&JJJJK#KH=KK+K5KK)L-@L:nLL-M6MMJNZPNRN,NQ+O@}O8O.O-&PITP"P$PLP+3Q)_Q+Q Q<QARURMmRR9RS'SY?SS2S9S)T)GT1qT/TGT$U@@U7U#{Kh9o+Bc`!A</sqW0[Pe4=GMjTJ 5$EpL.8 -"^Qy 1Ri '):nX S2~Ym%}FCwgUrO,tlNzbH*(3?7kuD x&\]_vfZI|;d>aV6@"dMatrix" object with NAs cannot be coerced to "nMatrix""lMatrix" object with NAs cannot be coerced to "nMatrix"'%s()' is not yet implemented for representation '%s''%s()' is not yet implemented for element type '%s''A' must be a square matrix'NA' indices are not (yet?) supported for sparse Matrices'V' is not a *square* matrix'V' is not a square matrix'by' argument is much too small'diagonals' matrix must have %d columns (= length(k) )'diagonals' must have the same length (%d) as 'k''file' must be a character string or connection'force' must be (coercable to) TRUE or FALSE'lag' and 'differences' must be integers >= 1'lwd' must be NULL or non-negative numeric'ncol' is not a factor of length(x)'ncol' must be >= 0'nrow' and 'ncol' must be the same when 'symmetric' is true'nrow' is not a factor of length(x)'nrow' must be >= 0'nrow', 'ncol', etc, are disregarded for matrix 'data''nrow', 'ncol', etc, are disregarded when 'data' is "Matrix" already'p' must be a non-decreasing vector (0, ...)'times >= 0' is required'update' must be logical or '+' or '-'; 'C' a matrix, and 'L' a "CHMfactor"'x' has invalid data type'x' is not positive definite -- chol() undefined.'x' is not symmetric nor triangular'x' must have length nrow^2 when 'symmetric' is true'x' must inherit from "sparseVector"(un)packing only applies to dense matrices, class(x)='%s'.M.repl.i.2col(): drop 'matrix' case ... --> is not yet implemented[i] is not yet implemented --> is not yet implemented[ ] : .M.sub.i.logical() maybe inefficientCholesky() -> *symbolic* factorization -- not yet implementedCholesky(A) called for 'A' of class "%s"; it is currently defined for sparseMatrix only; consider using chol() insteadCmp.Mat.atomic() should not be called for diagonalMatrixFIXME: NOT YET FINISHED IMPLEMENTATIONInternal bug: nargs()=%d; please reportLU computationally singular: ratio of extreme entries in |diag(U)| = %9.4gLogic.Mat.atomic() should not be called for diagonalMatrixMatrices must have same dimensions in %sMatrices must have same number of columns in %sMatrices must have same number of rows for arithmeticMatrices must have same number of rows in %sMatrix seems negative semi-definiteMatrix-internal error in [i,,d]; please reportMatrix-internal error in [i,,d]; please reportMatrix-internal error in [i,,d]; please reportMust specify 'nrow' when 'symmetric' is trueNA's in (i,j) are not allowedNAs are not allowed in subscripted assignmentsNot a valid formatOnly numeric sparse matrices allowedQuadratic matrix '%s' (=: A) is not formally symmetric. Will be treated as A A'RHS 'value' (class %s) matches 'ANY', but must match matrix class %s[ ] indexing not allowed: forgot a "," ?all() is not yet implementedc(,..) of different kinds, coercing all to 'rleDiff'cannot coerce 'NA's to "nsparseMatrix"cannot coerce 'NA's to "nsparseVector"chol() is undefined for diagonal matrix with negative entriescoercion from list(i1,...,ik, d) to "indMatrix" failed. All entries must be integer valued and the number of columns, d, not smaller than the maximal index i*.complex matrices not yet implemented in Matrix packagediag(.) had 0 or NA entries; non-finite result is doubtfuldiagonalMatrix in .dense2C() -- should never happen, please report!dim [product %d] do not match the length of object [%d]dim(.) value must be numeric of length 2dimensions don't match the number of cellsdimnames [%d] mismatch in %selement type '%s' not recognizedelement type 'complex' not yet implementedexactly one of 'i', 'j', or 'p' must be missing from callfile is not a MatrixMarket filefor symmetric band matrix, only specify upper or lower triangle hence, all k must have the same signhit a cycle (1) -- stop iterationshit a cycle (2) -- stop iterationsi1[1] == 0 ==> C-level verbosity will not happen!incompatible matrix dimensionsindex must be numeric, logical or sparseVector for indexing sparseVectorsinefficient coercion (lost triangularity); please reportinefficient method used for "- e1"intermediate 'r' is of type %sinternal bug in "Compare" method (Cmp.Mat.atomic); please reportinternal bug in "Logic" method (Logic.Mat.atomic); please reportinternal bug: matrix 'i' in replTmat(): please reportinternal bug: missing 'i' in replTmat(): please reportinvalid 'contrasts.arg' argumentinvalid 'data'invalid 'type'invalid (to - from)/by in seq(.)invalid character indexinginvalid or not-yet-implemented 'Matrix' subsettingis not a multiple of shorter object lengthkronecker method must use default 'FUN'length must be non-negative numberlength of 1st arg does not match dimension of 2ndlength of 2nd arg does not match dimension of firstlength(i) is not a multiple of length(x)length(x) must be either 1 or #{cols}logic programming error in printSpMatrix2(), please reportlogical subscript too long (%d, should be %d)longer object lengthlonger object length is not a multiple of shorter object lengthm[ ] <- v: inefficiently treating single elementsm[ ]: inefficiently indexing single elementsmatrix is not diagonalmodel frame and formula mismatch in model.matrix()must either specify 'A' or the functions 'A.x' and 'At.x'must have exactly one non-zero entry per rownargs() = %d should never happen; please report.nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.2col)?nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.logical)?nargs() = %d. Extraneous illegal arguments inside '[ .. ]' ?negative values are not allowed in a matrix subscriptno 'dimnames[[.]]': cannot use character indexingnon-conformable matrix dimensions in %snon-matching dimensionsnon-square matrixnot a positive definite matrixnot a skinny matrixnot a square matrixnot a symmetric matrix; consider forceSymmetric() or symmpart()not a triangular matrixnot converged in %d iterationsnot enough new vecs -- stop iterationsnot yet implementednot yet implemented .. please reportnot-yet-implemented 'Matrix[<-' methodnot-yet-implemented coercion to "TsparseMatrix"not-yet-implemented method for %s(<%s>). ->> Ask the package authors to implement the missing feature.not-yet-implemented method for %s(<%s>, <%s>). ->> Ask the package authors to implement the missing feature.not-yet-implemented method for <%s> %%*%% <%s>nothing to replace withnumber of items to replace is not a multiple of replacement lengthonly 2-dimensional tables can be directly coerced to sparse matricesonly square matrices can be used as incidence matrices for graphsprod() is not yet implementedprogramming error: min() should have dispatched w/ 1st arg much earlierrankMatrix(x, method='qr'): computing t(x) as nrow(x) < ncol(x)rcond(.) via sparse -> dense coercionreadMM(): column values 'j' are not in 1:ncreadMM(): row values 'i' are not in 1:nrreplacing "indMatrix" entries is not allowed, as rarely sensiblerepresentation '%s' not recognizedsome arguments are not matricessuch indexing must be by logical or 2-column numeric matrixsum() is not yet implementedsymmetric matrix must be squaresymmetry form '%s' is not yet implementedsymmetry form '%s' not recognizedsymmetry form 'hermitian' not yet implemented for readingsymmetry form 'skew-symmetric' not yet implemented for readingtemporarily disabledthe %d-th (sub)-diagonal (k = %d) is too short; filling with NA'sthe matrix is not triangularthe number of non-zero entries differs from nrow(.)too many argumentstoo many replacement valuestrimmed mean of 'sparseVector' -- suboptimally using as.numeric(.)type '%s' not recognizedupdate must be TRUE/FALSE or '+' or '-'using "old code" part in Csparse subassignmentusing slow kronecker() methodvariable '%s' converted to a factorvariable '%s' is absent, its contrast will be ignoredvector too long in Matrix - vector operationwhen 'A' is specified, 'A.x' and 'At.x' are disregardedwrong sign in 'by' argumentx[.,.] <- val : x being coerced from Tsparse* to CsparseMatrixyou cannot mix negative and positive indicesProject-Id-Version: R 2.15.2 / matrix 1.0-10 Report-Msgid-Bugs-To: bugs.r-project.org POT-Creation-Date: 2013-12-23 21:27 PO-Revision-Date: 2012-10-01 15:38+0200 Last-Translator: Chris Leick Language-Team: German Language: de MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Plural-Forms: nplurals=2; plural=(n != 1); "dMatrix"-Objekt mit NAs kann nicht in "nMatrix" umgewandelt werden'lMatrix'-Objekt mit NAs kann nicht zu 'nMatrix' umgewandelt werden'%s()' ist noch nicht implementiert für Darstellung '%s''%s()' ist noch nicht für Elementtyp '%s' implementiert'A' muss eine quadratische Matrix sein'NA'-Indizes werden (noch?) nicht für dünn besetzte Matrizen unterstützt'V' ist keine *quadratische* Matrix'V' ist keine quadratische MatrixArgument 'by' ist zu klein'diagonals'-Matrix muss %d Spalten haben (= length(k) )'diagonals' muss die gleiche Länge (%d) wie 'k' haben'file' muss eine Zeichenkette oder Verbindung sein'force' muss (mindestens umwandelbar nach) TRUE oder FALSE sein'lag' und 'differences' müssen Ganzzahlen >=1 sein'lwd' muss NULL oder nicht negativ numerisch sein'ncol' ist kein Faktor der length(x)'ncol' muss >= 0 sein'nrow' und 'ncol' müssen gleich sein, wenn 'symmetric' auf true gesetzt ist'nrow' ist kein Faktor der length(x)'nrow' muss >= 0 sein'nrow', 'ncol', etc werden nicht für Matrix 'data' berücksichtigt'nrow', 'ncol', etc werden nicht berücksichtigt, wenn 'data' bereits 'Matrix' ist'p' muss ein nicht abnehmender Vektor (0, ...) sein'times >= 0' wird benötigt'update' muss entweder boolesch, '+' oder '-' sein; 'C' eine Matrix und 'L' ein "CHMfactor"'x' hat ungültigen Datentyp'x' ist nicht positiv definit -- chol() undefiniert.'x' ist weder symmetrisch noch in Dreiecksform'x' muss die Länge nrow^2, wenn 'symmetric' auf true gesetzt ist'x' muss von "sparseVector" geerbt sein(ent)packen ist nur für dicht besetzte Matrizen anwendbar, class(x)='%s'.M.repl.i.2col(): 'matrix'-Fall weglassen ... --> ist noch nicht implementiert[i] ist noch nicht implementiert --> ist noch nicht implementiert[ ] : .M.sub.i.logical() könnte ineffizient seinCholesky() -> *symbolische* Faktorisierung – noch nicht implementiertCholesky(A) für 'A' der Klasse "%s" aufgerufen; es ist derzeit nur für sparseMatrix definiert; erwägen Sie, chol() zu benutzen Cmp.Mat.atomic() sollte nicht für diagonalMatrix aufgerufen werdenZU ERLEDIGEN: NOCH NICHT ABGESCHLOSSENE IMPLEMENTIERUNGInterner Fehler: nargs()=%d; bitte meldenDie LU Zerlegung ist computational singulär; Quotient der extremen Elemente von |diag(U)| = %9.4gLogic.mat.atomic() sollte für diagonalMatrix nicht aufgerufen werdenMatrizen müssen in %s die gleichen Dimensionen habenMatrizen müssen die gleiche Anzahl Spalten in %s habenMatrizen müssen für Arithmetik die gleiche Anzahl Zeilen habenMatrizen müssen die gleiche Anzahl Zeilen in %s habenMatrix scheint negativ semidefinit zu seinMatrixinterner Fehler in [i,,d]. Bitte berichtenMatrixinterner Fehler in [i,,d]; Bitte berichtenMatrixinterner Fehler in [i,,d]. Bitte berichten'nrow' muss angegeben werden, wenn 'symmetric' auf true gesetzt istNAs sind in (i,j) nicht erlaubtNAs sind in indexierten Anweisungen nicht erlaubtKein gültiges FormatNur dünn besetzte Matrizen erlaubtDie quadratische Matrix '%s' (=: A) ist formal nicht symmetrisch. Wird behandelt wie A A'RHS 'value' (Klasse %s) passt zu 'ANY', muss aber zur Matrixklasse %s passen[ ] Indexierung nicht erlaubt: Ein ',' vergessen?all() ist noch nicht implementiertc(,..) von unterschiedlichen Arten, alle werden in 'rleDiff' umgewandelt'NA's können nicht in "nsparseMatrix" umgewandelt werdenKann NAs nicht in 'nsparseVector' umwandelnchol() ist undefiniert für diagonale Matrix mit negativen EinträgenUmwandlung von list(i1,...,ik, d) zu "indMatrix" gescheitert. Alle Elemente müssen ganzzahlig sein und die Anzahl Spalten, d, nicht kleiner als der maximale Index i*.komplexe Matrizen noch nicht im Matrixpaket implementiertdiag(.) hatte 0 oder NA Einträge. Nicht-endliches Ergebnis ist zweifelhaftdiagonalMatrix in .dense2C() -- sollte niemals vorkommen. Bitte berichten.dim [produkt %d] passt nicht zur Länge des Objekts [%d]dim(.)-Wert muss numerisch sein und von die Länge 2 habenDimensionen passen nicht zur Anzahl der Zellendimnames [%d] passen nicht in %sElementtyp '%s' nicht erkanntElementtyp 'complex' noch nicht implementiertexakt eins von 'i', 'j' oder 'p' muss vom Aufruf fehlenDatei ist keine MatrixMarket-Dateigeben Sie für symmetrische Bandmatrizen nur oberes oder unteres Dreieck an. deshalb müssen alle k dasselbe Vorzeichen haben.auf einen Zyklus getroffen (1) – Iterationen stoppenauf einen Zyklus getroffen (2) – Iterationen stoppeni1[1] == 0 ==> C-Ebene wird nicht detailliert sein!inkompatible MatrixdimensionenIndex muss numerisch, logisch oder sparseVector sein, um sparseVector zu indizierenineffiziente Umwandlung (verlorene Dreieckigkeit). Bitte berichtenineffiziente Methode für '- e1' benutztZwischenergebnis 'r' ist vom Typ %sinterner Fehler in der "Compare"-Methode (Cmp.Mat.atomic). Bitte berichteninterner Fehler in der "Logic"-Methode (.Logic.Mat.atomic). Bitte berichteninterner Fehler: Matrix 'i' in replTmat(): Bitte berichteninterner Fehler: Fehlendes 'i' in replTmat(): Bitte berichtenunzulässiges 'contrasts.arg' Argumentungültiges 'data'ungültiger 'type'unzulässiges (to - from)/by in seq(.)ungültige Zeichenindexierungungültige oder noch nicht implementierte 'Matrix'-Untermengeist kein Vielfaches der kürzeren Objektlängekronecker-Methode muss Standard 'FUN' benutzenLänge muss eine nicht negative Zahl seinLänge des ersten arg passt nicht zur Dimension des zweitenLänge des zweiten Arguments passt nicht zur Dimension des erstenlength(i) ist kein Vielfaches von length(x)length(x) muss 1 oder #{cols} seinlogischer Programmierungsfehler in printSpMatrix2(), bitte berichtenlogisches Subskript zu lang (%d, sollte %d sein)längere Objektlängelängere Objektlänge ist kein Vielfaches der kürzeren Objektlängem[ ] <- v: Einzelne Elemente ineffizient behandeltm[ ]: ineffiziente Indexierung einzelner ElementeMatrix ist nicht diagonalModel-Frame und Formel passen nicht zusammen in model.matrix()muss entweder 'A' angeben oder die Funktionen 'A.x' und 'At.x'muss genau einen Nicht-Null-Eintrag pro Zeile habennargs() = %d sollte niemals vorkommen. Bitte berichten.nargs() = %d. Irrelevante ungültige Argumente innerhalb '[ .. ]' (i.2col)?nargs() = %d. Irrelevante ungültige Argumente innerhalb '[ .. ]' (i.logical)?nargs() = %d. Irrelevante ungültige Argumente innerhalb '[ .. ]'?negative Werte sind in einer Matrix-Subskript nicht erlaubtkeine 'dimnames[[.]]': Zeichenindexierung kann nicht benutzt werdennicht konforme Matrixdimensionen in %snicht passende Dimensionennicht quadratische Matrixkeine positiv definite Matrixkeine lange ("skinny") Matrixkeine quadratische Matrixkeine symmetrische Matrix. Erwägen Sie forceSymmetric() oder symmpart()keine Dreiecksmatrixnicht konvergiert in %d Iterationsschrittennicht genügend neue Vektoren – Iterationen stoppennoch nicht implementiertnoch nicht implementiert ... bitte meldennoch nicht implementierte 'Matrix[<-'-Methodenoch nicht implementierte Typumwandlung zu 'TsparseMatrix'noch nicht implementierte Methode für %s(<%s>). ->> Bitten Sie die Autoren des Pakets, diese fehlende Funktion zu implementieren.noch nicht implementierte Methode für %s(<%s>, <%s>). ->> Bitten Sie die Autoren des Pakets, diese fehlende Funktion zu implementieren.noch nicht implementierte Methode für <%s> %%*%% <%s>nichts zu ersetzen mitAnzahl der zu ersetzenden Elemente ist kein Vielfaches der Austauschlängenur 2-dimensionale Tabellen könne direkt in eine dünn besetzte Matrix umgewandelt werdennur quadratische Matrizen können als Inzidenzmatrizen für Graphen benutzt werdenprod() ist noch nicht implementiertProgrammierfehler: min() ohne erstes Argument hätte eher abgefangen sein müssenrankMatrix(x, method='qr'): t(x) berechnet, da nrow(x) < ncol(x)rcond(.) über Umwandlung dünn besetzt -> dicht besetztreadMM(): Spalte Werte 'j' sind nicht in 1:ncreadMM(): Zeile Werte 'i' sind nicht in 1:nrErsetzen von "indMatrix"-Einträgen ist nicht erlaubt, da selten sinnvollRepräsentation '%s' nicht erkannteinige Argumente sind keine Matrizensolche Indexierung muss von logischer oder 2-spaltig numerischer Matrix seinsum() ist noch nicht implementiertsymmetrische Matrix muss quadratisch seinSymmetrieform '%s' noch nicht implementiertSymmetrieform '%s' nicht erkanntSymmetrieform 'hermitian' noch nicht zum Lesen implementiertSymmetrieform 'skew-symmetric' noch nicht zum Lesen implementiertzeitweise ausgeschaltetdie %d-te (Unter)-Diagonale (k = %d) ist zu kurz und wird mit NA aufgefülltdie Matrix ist nicht dreieckigdie Anzahl der Nicht-Null-Einträge weicht von nrow(.) abzu viele Argumentezu viele Austauschwertegetrimmter Mittelwert von 'sparseVector' – suboptimalerweise wird as.numeric(.) benutztTyp '%s' nicht erkanntupdate muss entweder TRUE/FALSE, '+' oder '-' seinbenutzt wird 'alter Kode'-Teil in Csparse-Unterzuweisunglangsame kronecker()-Methode wird benutztVariable '%s' konvertiert in einen FaktorVariable '%s' fehlt, ihr Kontrast wird irgnoriertVektor zu lang in der Matrix - Vektor Operationwenn 'A' angegeben wurde, werden 'A.x' und 'At.x' nicht berücksichtigtfalsches Vorzeichen im Argument 'by'x[.,.] <- val : x wird von Tsparse* in CsparseMatrix umgewandeltSie können positive und negative Indizes nicht mischenMatrix/inst/test-tools.R0000644000175100001440000000111712021103253014736 0ustar hornikusers#### Will be sourced by several R scripts in ../tests/ ### ------- Part I & -- unrelated to "Matrix" classes --------------- ### ------- Part II -- related to matrices, but *not* "Matrix" ----------- source(system.file("test-tools-1.R", package = "Matrix"), keep.source = FALSE) ### ------- Part III -- "Matrix" (classes) specific ---------------------- source(system.file("test-tools-Matrix.R", package = "Matrix"), keep.source = FALSE) doExtras <- interactive() || nzchar(Sys.getenv("R_MATRIX_CHECK_EXTRA")) || identical("true", unname(Sys.getenv("R_PKG_CHECKING_doExtras"))) Matrix/inst/test-tools-1.R0000644000175100001440000002506512271746775015141 0ustar hornikusers#### Tools for Package Testing --- in Matrix, sourced by ./test-tools.R #### ------------------------- ## to be used as, e.g., ## source(system.file("test-tools-1.R", package="Matrix"), keep.source=FALSE) ### ------- Part I -- unrelated to "Matrix" classes --------------- if(!exists("paste0", .BaseNamespaceEnv)) # have in R >= 2.15.0 paste0 <- function(...) paste(..., sep = '') identical3 <- function(x,y,z) identical(x,y) && identical (y,z) identical4 <- function(a,b,c,d) identical(a,b) && identical3(b,c,d) identical5 <- function(a,b,c,d,e) identical(a,b) && identical4(b,c,d,e) identical6 <- function(a,b,c,d,e,f) identical(a,b) && identical5(b,c,d,e,f) identical7 <- function(a,b,c,d,e,f,g)identical(a,b) && identical6(b,c,d,e,f,g) if( exists("assertCondition", asNamespace("tools")) ) { ## R > 3.0.1 assertError <- function(expr, verbose=getOption("verbose")) tools::assertCondition(expr, "error", verbose=verbose) assertWarning <- function(expr, verbose=getOption("verbose")) tools::assertCondition(expr, "warning", verbose=verbose) assertWarningAtLeast <- function(expr, verbose=getOption("verbose")) tools::assertCondition(expr, "error", "warning", verbose=verbose) } else { ## in R <= 3.0.1 : ##' @title Ensure evaluating 'expr' signals an error ##' @param expr ##' @return the caught error, invisibly ##' @author Martin Maechler assertError <- function(expr, verbose=getOption("verbose")) { d.expr <- deparse(substitute(expr)) t.res <- tryCatch(expr, error = function(e) e) if(!inherits(t.res, "error")) stop(d.expr, "\n\t did not give an error", call. = FALSE) cat("Asserted Error:", conditionMessage(t.res),"\n") invisible(t.res) } ## Note that our previous version of assertWarning() did *not* work correctly: ## x <- 1:3; assertWarning({warning("bla:",x[1]); x[2] <- 99}); x ## had 'x' not changed! ## From ~/R/D/r-devel/R/src/library/tools/R/assertCondition.R : assertCondition <- function(expr, ..., .exprString = .deparseTrim(substitute(expr), cutoff = 30L), verbose = FALSE) { fe <- function(e)e getConds <- function(expr) { conds <- list() tryCatch(withCallingHandlers(expr, warning = function(w) { conds <<- c(conds, list(w)) invokeRestart("muffleWarning") }, condition = function(cond) conds <<- c(conds, list(cond))), error = function(e) conds <<- c(conds, list(e))) conds } conds <- if(nargs() > 1) c(...) # else NULL .Wanted <- if(nargs() > 1) paste(c(...), collapse = " or ") else "any condition" res <- getConds(expr) if(length(res)) { if(is.null(conds)) { if(verbose) message("assertConditon: Successfully caught a condition\n") invisible(res) } else { ii <- sapply(res, function(cond) any(class(cond) %in% conds)) if(any(ii)) { if(verbose) { found <- unique(sapply(res, function(cond) class(cond)[class(cond) %in% conds])) message(sprintf("assertCondition: caught %s", paste(dQuote(found), collapse =", "))) } invisible(res) } else { .got <- paste(unique((sapply(res, function(obj)class(obj)[[1]]))), collapse = ", ") stop(gettextf("Got %s in evaluating %s; wanted %s", .got, .exprString, .Wanted)) } } } else stop(gettextf("Failed to get %s in evaluating %s", .Wanted, .exprString)) } assertWarning <- function(expr, verbose=getOption("verbose")) assertCondition(expr, "warning", verbose=verbose) assertWarningAtLeast <- function(expr, verbose=getOption("verbose")) assertCondition(expr, "error", "warning", verbose=verbose) }# [else: no assertCondition ] ##' [ from R's demo(error.catching) ] ##' We want to catch *and* save both errors and warnings, and in the case of ##' a warning, also keep the computed result. ##' ##' @title tryCatch both warnings and errors ##' @param expr ##' @return a list with 'value' and 'warning', where ##' 'value' may be an error caught. ##' @author Martin Maechler tryCatch.W.E <- function(expr) { W <- NULL w.handler <- function(w){ # warning handler W <<- w invokeRestart("muffleWarning") } list(value = withCallingHandlers(tryCatch(expr, error = function(e) e), warning = w.handler), warning = W) } isValid <- function(x, class) isTRUE(validObject(x, test=TRUE)) && is(x, class) ## Some (sparse) Lin.Alg. algorithms return 0 instead of NA, e.g. ## qr.coef(, y). ## For those cases, need to compare with a version where NA's are replaced by 0 mkNA.0 <- function(x) { x[is.na(x)] <- 0 ; x } is.all.equal3 <- function(x,y,z, tol = .Machine$double.eps^0.5) isTRUE(all.equal(x,y, tolerance=tol)) && isTRUE(all.equal(y,z, tolerance=tol)) is.all.equal4 <- function(x,y,z,u, tol = .Machine$double.eps^0.5) is.all.equal3(x,y,z, tol=tol) && isTRUE(all.equal(z,u, tolerance=tol)) ## A version of all.equal() for the slots all.slot.equal <- function(x,y, ...) { slts <- slotNames(x) for(sl in slts) { aeq <- all.equal(slot(x,sl), slot(y,sl), ...) if(!identical(TRUE, aeq)) return(paste("slot '",sl,"': ", aeq, sep='')) } TRUE } ## all.equal() for list-coercible objects -- apart from *some* components all.equal.X <- function(x,y, except, tol = .Machine$double.eps^0.5, ...) { .trunc <- function(x) { ll <- as.list(x) ll[ - match(except, names(ll), nomatch = 0L)] } all.equal(.trunc(x), .trunc(y), tolerance = tol, ...) } ## e.g. in lme4: ## all.equal.X(env(m1), env(m2), except = c("call", "frame")) ## The relative error typically returned by all.equal: relErr <- function(target, current) { ## make this work for 'Matrix' ## ==> no mean() .. n <- length(current) if(length(target) < n) target <- rep(target, length.out = n) sum(abs(target - current)) / sum(abs(target)) } ##' Compute the signed relative error between target and current vector -- vectorized ##' @title Relative Error (:= 0 when absolute error == 0) ##' @param target ##' @param current {maybe scalar; need length(current) a multiple of length(target)} ##' @return *vector* of the same length as target and current ##' @author Martin Maechler relErrV <- function(target, current) { n <- length(target <- as.vector(target)) ## assert( is multiple of ) : if(length(current) %% n) stop("length(current) must be a multiple of length(target)") RE <- current RE[] <- 0 fr <- current/target neq <- is.na(current) | (current != target) RE[neq] <- 1 - fr[neq] RE } ## is.R22 <- (paste(R.version$major, R.version$minor, sep=".") >= "2.2") pkgRversion <- function(pkgname) sub("^R ([0-9.]+).*", "\\1", packageDescription(pkgname)[["Built"]]) showSys.time <- function(expr) { ## prepend 'Time' for R CMD Rdiff st <- system.time(expr) writeLines(paste("Time", capture.output(print(st)))) invisible(st) } showProc.time <- local({ ## function + 'pct' variable pct <- proc.time() function(final="\n") { ## CPU elapsed __since last called__ ot <- pct ; pct <<- proc.time() ## 'Time ..' *not* to be translated: tools::Rdiff() skips its lines! cat('Time elapsed: ', (pct - ot)[1:3], final) } }) ##' @title turn an S4 object (with slots) into a list with corresponding components ##' @param obj an R object with a formal class (aka "S4") ##' @return a list with named components where \code{obj} had slots ##' @author Martin Maechler S4_2list <- function(obj) { sn <- slotNames(obj) structure(lapply(sn, slot, object = obj), .Names = sn) } assert.EQ <- function(target, current, tol = if(showOnly) 0 else 1e-15, giveRE = FALSE, showOnly = FALSE, ...) { ## Purpose: check equality *and* show non-equality ## ---------------------------------------------------------------------- ## showOnly: if TRUE, return (and hence typically print) all.equal(...) T <- isTRUE(ae <- all.equal(target, current, tolerance = tol, ...)) if(showOnly) return(ae) else if(giveRE && T) { ## don't show if stop() later: ae0 <- if(tol == 0) ae else all.equal(target, current, tolerance = 0, ...) if(!isTRUE(ae0)) cat(ae0,"\n") } if(!T) stop("all.equal() |-> ", paste(ae, collapse=sprintf("%-19s","\n"))) } ##' a version with other "useful" defaults (tol, giveRE, check.attr..) assert.EQ. <- function(target, current, tol = if(showOnly) 0 else .Machine$double.eps^0.5, giveRE = TRUE, showOnly = FALSE, ...) { assert.EQ(target, current, tol=tol, giveRE=giveRE, showOnly=showOnly, check.attributes=FALSE, ...) } ### ------- Part II -- related to matrices, but *not* "Matrix" ----------- add.simpleDimnames <- function(m) { stopifnot(length(d <- dim(m)) == 2) dimnames(m) <- list(if(d[1]) paste0("r", seq_len(d[1])), if(d[2]) paste0("c", seq_len(d[2]))) m } as.mat <- function(m) { ## as(., "matrix") but with no extraneous empty dimnames m <- as(m, "matrix") if(identical(dimnames(m), list(NULL,NULL))) dimnames(m) <- NULL m } assert.EQ.mat <- function(M, m, tol = if(showOnly) 0 else 1e-15, showOnly=FALSE, giveRE = FALSE, ...) { ## Purpose: check equality of 'Matrix' M with 'matrix' m ## ---------------------------------------------------------------------- ## Arguments: M: is(., "Matrix") typically {but just needs working as(., "matrix")} ## m: is(., "matrix") ## showOnly: if TRUE, return (and hence typically print) all.equal(...) validObject(M) MM <- as.mat(M) # as(M, "matrix") if(is.logical(MM) && is.numeric(m)) storage.mode(MM) <- "integer" attr(MM, "dimnames") <- attr(m, "dimnames") <- NULL assert.EQ(MM, m, tol=tol, showOnly=showOnly, giveRE=giveRE) } ## a short cut assert.EQ.Mat <- function(M, M2, tol = if(showOnly) 0 else 1e-15, showOnly=FALSE, giveRE = FALSE, ...) assert.EQ.mat(M, as.mat(M2), tol=tol, showOnly=showOnly, giveRE=giveRE) chk.matrix <- function(M) { ## check object; including coercion to "matrix" : cl <- class(M) cat("class ", dQuote(cl), " [",nrow(M)," x ",ncol(M),"]; slots (", paste(slotNames(M), collapse=","), ")\n", sep='') stopifnot(validObject(M), dim(M) == c(nrow(M), ncol(M)), identical(dim(m <- as(M, "matrix")), dim(M)) ) } isOrthogonal <- function(x, tol = 1e-15) { all.equal(diag(as(zapsmall(crossprod(x)), "diagonalMatrix")), rep(1, ncol(x)), tolerance = tol) } Matrix/inst/test-tools-Matrix.R0000644000175100001440000005342312271746775016244 0ustar hornikusers#### Tools for Package Testing --- in Matrix, sourced by ./test-tools.R #### ------------------------- ### ------- Part III -- "Matrix" (classes) specific ---------------------- lsM <- function(...) { for(n in ls(..., envir=parent.frame())) if(is((. <- get(n)),"Matrix")) cat(sprintf("%5s: '%s' [%d x %d]\n",n,class(.), nrow(.),ncol(.))) } asD <- function(m) { ## as "Dense" if(canCoerce(m, "denseMatrix")) as(m, "denseMatrix") else if(canCoerce(m, (cl <- paste(.M.kind(m), "denseMatrix", sep='')))) as(m, cl) else if(canCoerce(m, "dgeMatrix")) as(m, "dgeMatrix") else stop("cannot coerce to a typical dense Matrix") } ## "normal" sparse Matrix: Csparse, no diag="U" asCsp <- function(x) Matrix:::diagU2N(as(x, "CsparseMatrix")) Qidentical.DN <- function(dx, dy) { ## quasi-identical dimnames stopifnot(is.list(dx) || is.null(dx), is.list(dy) || is.null(dy)) ## "empty" (is.null.DN(dx) && is.null.DN(dy)) || identical(dx, dy) } Qidentical <- function(x,y, strictClass = TRUE) { ## quasi-identical - for 'Matrix' matrices if(class(x) != class(y)) { if(strictClass || !is(x, class(y))) return(FALSE) ## else try further } slts <- slotNames(x) if("Dimnames" %in% slts) { ## always (or we have no 'Matrix') slts <- slts[slts != "Dimnames"] if(!(Qidentical.DN(x@Dimnames, y@Dimnames))) return(FALSE) } if("factors" %in% slts) { ## allow one empty and one non-empty 'factors' slts <- slts[slts != "factors"] ## if both are not empty, they must be the same: if(length(xf <- x@factors) && length(yf <- y@factors)) if(!identical(xf, yf)) return(FALSE) } for(sl in slts) if(!identical(slot(x,sl), slot(y,sl))) return(FALSE) TRUE } Q.C.identical <- function(x,y, sparse = is(x,"sparseMatrix"), checkClass = TRUE, strictClass = TRUE) { if(checkClass && class(x) != class(y)) { if(strictClass || !is(x, class(y))) return(FALSE) ## else try further } if(sparse) Qidentical(as(x,"CsparseMatrix"), as(y,"CsparseMatrix"), strictClass=strictClass) else Qidentical(x,y, strictClass=strictClass) } ##' ##' ##'
##' @title Quasi-equal for 'Matrix' matrices ##' @param x Matrix ##' @param y Matrix ##' @param superclasses x and y must coincide in (not) extending these ##' @param dimnames.check logical indicating if dimnames(.) much match ##' @param tol NA (--> use "==") or numerical tolerance for all.equal() ##' @return logical: Are x and y (quasi) equal ? Q.eq <- function(x, y, superclasses = c("sparseMatrix", "denseMatrix", "dMatrix", "lMatrix", "nMatrix"), dimnames.check = TRUE, tol = NA) { ## quasi-equal - for 'Matrix' matrices if(any(dim(x) != dim(y))) return(FALSE) if(dimnames.check && !identical(dimnames(x), dimnames(y))) return(FALSE) xcl <- getClassDef(class(x)) ycl <- getClassDef(class(y)) for(SC in superclasses) { if( extends(xcl, SC) && !extends(ycl, SC)) return(FALSE) } asC <- ## asCommon if((isDense <- extends(xcl,"denseMatrix"))) function(m) as(m, "matrix") else function(m) as(as(as(m,"CsparseMatrix"), "dMatrix"), "dgCMatrix") if(is.na(tol)) { if(isDense) all(x == y | (is.na(x) & is.na(y))) else ## 'x == y' blows up for large sparse matrices: isTRUE(all.equal(asC(x), asC(y), tolerance = 0., check.attributes = dimnames.check)) } else if(is.numeric(tol) && tol >= 0) { isTRUE(all.equal(asC(x), asC(y), tolerance = tol, check.attributes = dimnames.check)) } else stop("'tol' must be NA or non-negative number") } Q.eq2 <- function(x, y, superclasses = c("sparseMatrix", "denseMatrix"), dimnames.check = FALSE, tol = NA) Q.eq(x,y, superclasses=superclasses, dimnames.check=dimnames.check, tol=tol) ##' ##' ##'
##' @title Quasi-equality of symmpart(m) + skewpart(m) with m ##' @param m Matrix ##' @param tol numerical tolerance for all.equal() ##' @return logical ##' @author Martin Maechler Q.eq.symmpart <- function(m, tol = 8 * .Machine$double.eps) { ss <- symmpart(m) + skewpart(m) if(hasNA <- any(iNA <- is.na(ss))) { ## ss has the NA's symmetrically, but typically m has *not* iiNA <- which(iNA) # <- useful! -- this tests which() methods! ## assign NA's too -- using correct kind of NA: m[iiNA] <- as(NA, Matrix:::.type.kind[Matrix:::.M.kind(m)]) } Q.eq2(m, ss, tol = tol) } ##' sample.int(n, size, replace=FALSE) for really large n: sampleL <- function(n, size) { if(n < .Machine$integer.max) sample.int(n, size) else { i <- unique(round(n * runif(1.8 * size))) while(length(i) < size) { i <- unique(c(i, round(n * runif(size)))) } i[seq_len(size)] } } ## Useful Matrix constructors for testing: ##' @title Random Sparse Matrix ##' @param n ##' @param m number of columns; default (=n) ==> square matrix ##' @param density the desired sparseness density: ##' @param nnz number of non-zero entries; default from \code{density} ##' @param giveCsparse logical specifying if result should be CsparseMatrix ##' @return a [TC]sparseMatrix, n x m ##' @author Martin Maechler, Mar 2008 rspMat <- function(n, m = n, density = 1/4, nnz = round(density * n*m), giveCsparse = TRUE) { stopifnot(length(n) == 1, n == as.integer(n), length(m) == 1, m == as.integer(m), 0 <= density, density <= 1, 0 <= nnz, nnz <= (N <- n*m)) in0 <- sampleL(N, nnz) x <- sparseVector(i = in0, x = as.numeric(1L + seq_along(in0)), length = N) dim(x) <- c(n,m)#-> sparseMatrix if (giveCsparse) as(x, "CsparseMatrix") else x } ## From \examples{..} in ../man/sparseMatrix.Rd : rSparseMatrix <- function(nrow, ncol, nnz, rand.x = function(n) round(rnorm(nnz), 2), ...) { stopifnot((nnz <- as.integer(nnz)) >= 0, nrow >= 0, ncol >= 0, nnz <= nrow * ncol) sparseMatrix(i = sample(nrow, nnz, replace = TRUE), j = sample(ncol, nnz, replace = TRUE), x = rand.x(nnz), dims = c(nrow, ncol), ...) } rUnitTri <- function(n, upper = TRUE, ...) { ## Purpose: random unit-triangular sparse Matrix .. built from rspMat() ## ---------------------------------------------------------------------- ## Arguments: n: matrix dimension ## upper: logical indicating if upper or lower triangular ## ... : further arguments passed to rspMat(), eg. 'density' ## ---------------------------------------------------------------------- ## Author: Martin Maechler, Date: 5 Mar 2008, 11:35 r <- (if(upper) triu else tril)(rspMat(n, ...)) ## make sure the diagonal is empty diag(r) <- 0 r <- drop0(r) r@diag <- "U" r } mkLDL <- function(n, density = 1/3) { ## Purpose: make nice artificial A = L D L' (with exact numbers) decomp ## ---------------------------------------------------------------------- ## Author: Martin Maechler, Date: 15 Mar 2008 stopifnot(n == round(n)) n <- as.integer(n) L <- Matrix(0, n,n) nnz <- round(n*n * density) L[sample(n*n, nnz)] <- seq_len(nnz) L <- tril(L,-1) diag(L) <- 1 d.half <- sample(10*(n:1))# random permutation ; use '10*' to be "different" from L entries D <- Diagonal(x = d.half * d.half) A <- tcrossprod(L * rep(d.half, each=n)) ## = as(L %*% D %*% t(L), "symmetricMatrix") list(A = A, L = L, d.half = d.half, D = D) } eqDeterminant <- function(m1, m2, NA.Inf.ok=FALSE, tol=.Machine$double.eps^0.5, ...) { d1 <- determinant(m1) ## logarithm = TRUE d2 <- determinant(m2) d1m <- as.vector(d1$modulus)# dropping attribute d2m <- as.vector(d2$modulus) if((identical(d1m, -Inf) && identical(d2m, -Inf)) || ## <==> det(m1) == det(m2) == 0, then 'sign' may even differ ! (is.na(d1m) && is.na(d2m))) ## if both are NaN or NA, we "declare" that's fine here return(TRUE) else if(NA.Inf.ok && ## first can be NA, second infinite: ## wanted: base::determinant.matrix() sometimes gives -Inf instead ## of NA,e.g. for matrix(c(0,NA,0,0,NA,NA,0,NA,0,0,1,0,0,NA,0,1), 4,4)) is.na(d1m) && is.infinite(d2m)) return(TRUE) ## else if(is.infinite(d1m)) d1$modulus <- sign(d1m)* .Machine$double.xmax if(is.infinite(d2m)) d2$modulus <- sign(d2m)* .Machine$double.xmax ## now they are finite or *one* of them is NA/NaN, and all.equal() will tell so: all.equal(d1, d2, tolerance=tol, ...) } ##' @param A a non-negative definite sparseMatrix, typically "dsCMatrix" ##' ##' @return a list with components resulting from calling ##' Cholesky(., perm = .P., LDL = .L., super = .S.) ##' ##' for all 2*2*3 combinations of (.P., .L., .S.) allCholesky <- function(A, verbose = FALSE, silentTry = FALSE) { ## Author: Martin Maechler, Date: 16 Jul 2009 ##' @param r list of CHMfactor objects, typically with names() as '. | .' ##' ##' @return an is(perm,LDL,super) matrix with interesting and *named* rownames CHM_to_pLs <- function(r) { is.perm <- function(.) if(inherits(., "try-error")) NA else !all(.@perm == 0:(.@Dim[1]-1)) is.LDL <- function(.)if(inherits(., "try-error")) NA else isLDL(.) r.st <- cbind(perm = sapply(r, is.perm), LDL = sapply(r, is.LDL), super = sapply(r, class) == "dCHMsuper") names(dimnames(r.st)) <- list(" p L s", "") r.st } my.Cholesky <- { if(verbose) function (A, perm = TRUE, LDL = !super, super = FALSE, Imult = 0, ...) { cat(sprintf("Chol..(*, perm= %1d, LDL= %1d, super=%1d):", perm, LDL, super)) r <- Cholesky(A, perm=perm, LDL=LDL, super=super, Imult=Imult, ...) cat(" [Ok]\n") r } else Cholesky } logi <- c(FALSE, TRUE) d12 <- expand.grid(perm = logi, LDL = logi, super = c(logi,NA), KEEP.OUT.ATTRS = FALSE) r1 <- lapply(seq_len(nrow(d12)), function(i) try(do.call(my.Cholesky, c(list(A = A), as.list(d12[i,]))), silent=silentTry)) names(r1) <- apply(d12, 1, function(.) paste(symnum(.), collapse=" ")) dup.r1 <- duplicated(r1) r.all <- CHM_to_pLs(r1) if(!identical(dup.r1, duplicated(r.all))) warning("duplicated( ) differs from duplicated( )", immediate. = TRUE) list(Chol.A = r1, dup.r.all = dup.r1, r.all = r.all, r.uniq = CHM_to_pLs(r1[ ! dup.r1])) } ###----- Checking a "Matrix" ----------------------------------------- ##' Check the compatibility of \pkg{Matrix} package Matrix with a ##' \dQuote{traditional} \R matrix and perform a host of internal consistency ##' checks. ##' ##' @title Check Compatibility of Matrix Package Matrix with Traditional R Matrices ##' ##' @param m a "Matrix" ##' @param m.m as(m, "matrix") {if 'do.matrix' } ##' @param do.matrix logical indicating if as(m, "matrix") should be applied; ##' typically false for large sparse matrices ##' @param do.t logical: is t(m) "feasible" ? ##' @param doNorm ##' @param doOps ##' @param doSummary ##' @param doCoerce ##' @param doCoerce2 ##' @param do.prod ##' @param verbose logical indicating if "progress output" is produced. ##' @param catFUN (when 'verbose' is TRUE): function to be used as generalized cat() ##' @return TRUE (invisibly), unless an error is signalled ##' @author Martin Maechler, since 11 Apr 2008 checkMatrix <- function(m, m.m = if(do.matrix) as(m, "matrix"), do.matrix = !isSparse || prod(dim(m)) < 1e6, do.t = TRUE, doNorm = TRUE, doOps = TRUE, doSummary = TRUE, doCoerce = TRUE, doCoerce2 = doCoerce && !isRsp, doDet = do.matrix, do.prod = do.t && do.matrix && !isRsp, verbose = TRUE, catFUN = cat) { ## is also called from dotestMat() in ../tests/Class+Meth.R stopifnot(is(m, "Matrix")) validObject(m) # or error(....) clNam <- class(m) cld <- getClassDef(clNam) ## extends(cld, FOO) is faster than is(m, FOO) isCor <- extends(cld, "corMatrix") isSym <- extends(cld, "symmetricMatrix") if(isSparse <- extends(cld, "sparseMatrix")) { # also true for these isRsp <- extends(cld, "RsparseMatrix") isDiag <- extends(cld, "diagonalMatrix") isInd <- extends(cld, "indMatrix") isPerm <- extends(cld, "pMatrix") } else isRsp <- isDiag <- isInd <- isPerm <- FALSE isTri <- !isSym && !isDiag && !isInd && extends(cld, "triangularMatrix") is.n <- extends(cld, "nMatrix") nonMatr <- clNam != Matrix:::MatrixClass(clNam, cld) Cat <- function(...) if(verbose) cat(...) CatF <- function(...) if(verbose) catFUN(...) ## warnNow <- function(...) warning(..., call. = FALSE, immediate. = TRUE) DO.m <- function(expr) if(do.matrix) eval(expr) else TRUE vec <- function(x) { dim(x) <- c(length(x), 1L) dimnames(x) <- list(NULL,NULL) x } eps16 <- 16 * .Machine$double.eps ina <- is.na(m) if(do.matrix) { stopifnot(all(ina == is.na(m.m)), all(is.finite(m) == is.finite(m.m)), all(is.infinite(m) == is.infinite(m.m)), all(m == m | ina), ## check all() , "==" [Compare], "|" [Logic] if(ncol(m) > 0) identical3(unname(m[,1]), unname(m.m[,1]), as(m[,1,drop=FALSE], "vector")) else identical(as(m, "vector"), as.vector(m.m))) if(any(m != m & !ina)) stop(" any (m != m) should not be true") } else { if(any(m != m)) stop(" any (m != m) should not be true") if(ncol(m) > 0) stopifnot(identical(unname(m[,1]), as(m[,1,drop=FALSE], "vector"))) else stopifnot(identical(as(m, "vector"), as.vector(as(m, "matrix")))) } if(do.t) { tm <- t(m) if(isSym) ## check that t() swaps 'uplo' L <--> U : stopifnot(c("L","U") == sort(c(m@uplo, tm@uplo))) ttm <- t(tm) ## notInd: "pMatrix" ok, but others inheriting from "indMatrix" are not notInd <- (!isInd || isPerm) if(notInd && (extends(cld, "CsparseMatrix") || extends(cld, "generalMatrix") || isDiag)) stopifnot(Qidentical(m, ttm, strictClass = !nonMatr)) else if(do.matrix) { if(notInd) stopifnot(nonMatr || class(ttm) == clNam) stopifnot(all(m == ttm | ina)) ## else : not testing } ## crossprod() %*% etc if(do.prod) { c.m <- crossprod(m) tcm <- tcrossprod(m) tolQ <- if(isSparse) NA else eps16 stopifnot(dim(c.m) == rep.int(ncol(m), 2), dim(tcm) == rep.int(nrow(m), 2), ## FIXME: %*% drops dimnames Q.eq2(c.m, tm %*% m, tol = tolQ), Q.eq2(tcm, m %*% tm, tol = tolQ)) } } if(!do.matrix) { CatF(" will *not* coerce to 'matrix' since do.matrix is FALSE\n") } else if(doNorm) { CatF(sprintf(" norm(m [%d x %d]) :", nrow(m), ncol(m))) for(typ in c("1","I","F","M")) { Cat('', typ, '') stopifnot(all.equal(norm(m,typ), norm(m.m,typ))) } Cat(" ok\n") } if(do.matrix && doSummary) { summList <- lapply(getGroupMembers("Summary"), get, envir = asNamespace("Matrix")) CatF(" Summary: ") for(f in summList) { ## suppressWarnings(): e.g. any() would warn here: r <- suppressWarnings(if(isCor) all.equal(f(m), f(m.m)) else identical(f(m), f(m.m))) if(!isTRUE(r)) { f.nam <- sub("..$", '', sub("^\\.Primitive..", '', format(f))) ## prod() is delicate: NA or NaN can both happen (if(f.nam == "prod") message else stop)( sprintf("%s(m) [= %g] differs from %s(m.m) [= %g]", f.nam, f(m), f.nam, f(m.m))) } } if(verbose) cat(" ok\n") } ## and test 'dim()' as well: d <- dim(m) isSqr <- d[1] == d[2] if(do.t) stopifnot(identical(diag(m), diag(t(m)))) ## TODO: also === diag(band(m,0,0)) if(prod(d) < .Machine$integer.max && !extends(cld, "modelMatrix")) { vm <- vec(m) stopifnot(is(vm, "Matrix"), validObject(vm), dim(vm) == c(d[1]*d[2], 1)) } if(!isInd) m.d <- local({ m. <- m; diag(m.) <- diag(m); m. }) if(do.matrix) stopifnot(identical(dim(m.m), dim(m)), ## base::diag() keeps names [Matrix FIXME] ## now that "pMatrix" subsetting gives *LOGICAL* ## if(isPerm) { ## identical(as.integer(unname(diag(m))), unname(diag(m.m))) ## } else identical(unname(diag(m)), unname(diag(m.m))),## not for NA: diag(m) == diag(m.m), identical(nnzero(m), sum(m.m != 0)), identical(nnzero(m, na.= FALSE), sum(m.m != 0, na.rm = TRUE)), identical(nnzero(m, na.= TRUE), sum(m.m != 0 | is.na(m.m))) ) if(isSparse) { n0m <- drop0(m) #==> n0m is Csparse has0 <- !Qidentical(n0m, as(m,"CsparseMatrix")) if(!isInd && !isRsp && !(extends(cld, "TsparseMatrix") && Matrix:::is_duplicatedT(m, di = d))) # 'diag<-' is does not change attrib: stopifnot(Qidentical(m, m.d))# e.g., @factors may differ } else if(!identical(m, m.d)) { # dense : 'diag<-' is does not change attrib if(isTri && m@diag == "U" && m.d@diag == "N" && all(m == m.d)) message("unitriangular m: diag(m) <- diag(m) lost \"U\" .. is ok") else stop("diag(m) <- diag(m) has changed 'm' too much") } ## use non-square matrix when "allowed": ## m12: sparse and may have 0s even if this is not: if(isSparse && has0) m12 <- as(as( m, "lMatrix"),"CsparseMatrix") m12 <- drop0(m12) if(do.matrix) { ## "!" should work (via as(*, "l...")) : m11 <- as(as(!!m,"CsparseMatrix"), "lMatrix") if(!Qidentical(m11, m12)) stopifnot(Qidentical(as(m11, "generalMatrix"), as(m12, "generalMatrix"))) } if(isSparse && !is.n) { ## ensure that as(., "nMatrix") gives nz-pattern CatF("as(., \"nMatrix\") giving full nonzero-pattern: ") n1 <- as(m, "nMatrix") ns <- as(m, "nsparseMatrix") stopifnot(identical(n1,ns), isDiag || ((if(isSym) Matrix:::nnzSparse else sum)(n1) == length(if(isInd) m@perm else Matrix:::diagU2N(m)@x))) Cat("ok\n") } if(doOps) { ## makes sense with non-trivial m (!) CatF("2*m =?= m+m: ") if(identical(2*m, m+m)) Cat("identical\n") else if(do.matrix) { eq <- as(2*m,"matrix") == as(m+m, "matrix") # but work for NA's: stopifnot(all(eq | (is.na(m) & is.na(eq)))) Cat("ok\n") } else {# !do.matrix stopifnot(identical(as(2*m, "CsparseMatrix"), as(m+m, "CsparseMatrix"))) Cat("ok\n") } if(do.matrix) { ## m == m etc, now for all, see above CatF("m >= m for all: "); stopifnot(all(m >= m | ina)); Cat("ok\n") } if(prod(d) > 0) { CatF("m < m for none: ") mlm <- m < m if(!any(ina)) stopifnot(!any(mlm)) else if(do.matrix) stopifnot(!any(mlm & !ina)) else { ## !do.matrix & any(ina) : !ina can *not* be used mlm[ina] <- FALSE stopifnot(!any(mlm)) } Cat("ok\n") } if(isSqr) { if(do.matrix) { ## determinant() "fails" for triangular with NA such as ## (m <- matrix(c(1:0,NA,1), 2)) CatF("symmpart(m) + skewpart(m) == m: ") Q.eq.symmpart(m) CatF("ok; determinant(): ") if(!doDet) Cat(" skipped (!doDet): ") else if(any(is.na(m.m)) && extends(cld, "triangularMatrix")) Cat(" skipped: is triang. and has NA: ") else stopifnot(eqDeterminant(m, m.m, NA.Inf.ok=TRUE)) Cat("ok\n") } } else assertError(determinant(m)) }# end{doOps} if(doCoerce && do.matrix && canCoerce("matrix", clNam)) { CatF("as(, ",clNam,"): ", sep='') m3 <- as(m.m, clNam) Cat("valid:", validObject(m3), "\n") ## m3 should ``ideally'' be identical to 'm' } if(doCoerce2 && do.matrix) { ## not for large m: !m will be dense if(is.n) { stopifnot(identical(m, as(as(m, "dMatrix"),"nMatrix")), identical(m, as(as(m, "lMatrix"),"nMatrix")), identical(which(m), which(m.m))) } else if(extends(cld, "lMatrix")) { ## should fulfill even with NA: stopifnot(all(m | !m | ina), !any(!m & m & !ina)) if(extends(cld, "TsparseMatrix")) # allow modify, since at end here m <- Matrix:::uniqTsparse(m, clNam) stopifnot(identical(m, m & TRUE), identical(m, FALSE | m)) ## also check the coercions to [dln]Matrix m. <- if(isSparse && has0) n0m else m m1. <- m. # replace NA by 1 in m1. , carefully not changing class: if(any(ina)) m1.@x[is.na(m1.@x)] <- TRUE stopifnot(identical(m. , as(as(m. , "dMatrix"),"lMatrix")), clNam == "ldiMatrix" || # <- there's no "ndiMatrix" ## coercion to n* and back: only identical when no extra 0s: identical(m1., as(as(m1., "nMatrix"),"lMatrix")), identical(which(m), which(m.m))) } else if(extends(cld, "dMatrix")) { m. <- if(isSparse && has0) n0m else m m1 <- (m. != 0)*1 if(!isSparse && substr(clNam,1,3) == "dpp") ## no "nppMatrix" possible m1 <- unpack(m1) m1. <- m1 # replace NA by 1 in m1. , carefully not changing class: if(any(ina)) m1.@x[is.na(m1.@x)] <- 1 ## coercion to n* (nz-pattern!) and back: only identical when no extra 0s and no NAs: stopifnot(Q.C.identical(m1., as(as(m., "nMatrix"),"dMatrix"), isSparse, checkClass = FALSE), Q.C.identical(m1 , as(as(m., "lMatrix"),"dMatrix"), isSparse, checkClass = FALSE)) } if(extends(cld, "triangularMatrix")) { mm. <- m i0 <- if(m@uplo == "L") upper.tri(mm.) else lower.tri(mm.) n.catchWarn <- if(is.n) suppressWarnings else identity n.catchWarn( mm.[i0] <- 0 ) # ideally, mm. remained triangular, but can be dge* CatF("as(, ",clNam,"): ", sep='') tm <- as(as(mm., "triangularMatrix"), clNam) Cat("valid:", validObject(tm), "\n") if(m@uplo == tm@uplo) ## otherwise, the matrix effectively was *diagonal* ## note that diagU2N() |-> dtC : stopifnot(Qidentical(tm, as(Matrix:::diagU2N(m), clNam))) } else if(isDiag) { ## TODO } else { ## TODO } }# end {doCoerce2 && ..} if(doCoerce && isSparse) { ## coerce to sparseVector and back : v <- as(m, "sparseVector") stopifnot(length(v) == prod(d)) dim(v) <- d stopifnot(Q.eq2(m, v)) } invisible(TRUE) } Matrix/inst/Copyrights0000644000175100001440000000460110500266672014574 0ustar hornikusersThe files src/iohb.[ch] are available at http://math.nist.gov/~KRemington/harwell_io/ and carry the following copyright Fri Aug 15 16:29:47 EDT 1997 Harwell-Boeing File I/O in C V. 1.0 National Institute of Standards and Technology, MD. K.A. Remington ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ NOTICE Permission to use, copy, modify, and distribute this software and its documentation for any purpose and without fee is hereby granted provided that the above copyright notice appear in all copies and that both the copyright notice and this permission notice appear in supporting documentation. Neither the Author nor the Institution (National Institute of Standards and Technology) make any representations about the suitability of this software for any purpose. This software is provided "as is" without expressed or implied warranty. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ The files src/mmio.[ch] are available through http://math.nist.gov/MatrixMarket/mmio-c.html and carry the following copyright Fri Aug 15 16:29:47 EDT 1997 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Matrix Market I/O library for ANSI C Roldan Pozo, NIST (pozo@nist.gov) See http://math.nist.gov/MatrixMarket for details and sample calling programs. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ NOTICE Permission to use, copy, modify, and distribute this software and its documentation for any purpose and without fee is hereby granted provided that the above copyright notice appear in all copies and that both the copyright notice and this permission notice appear in supporting documentation. Neither the Author nor the Institution (National Institute of Standards and Technology) make any representations about the suitability of this software for any purpose. This software is provided "as is" without expressed or implied warranty. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ The function mm_read_banner in mmio.c has been edited to conform with the definitions of constants in mmio.h. (String constants in mmio.h are in lower case and variables containing strings were being converted to upper case before being compared to the constants.) Matrix/inst/doc/0000755000175100001440000000000012271765436013273 5ustar hornikusersMatrix/inst/doc/Announce.txt0000644000175100001440000000732311620523257015575 0ustar hornikusersBasically the text of the R-packages posting on Mar 28, 2008 : https://stat.ethz.ch/pipermail/r-packages/2008/000911.html ------------------------------------------------------------------------ This weekend, a new version of "the Matrix" (well, actually the R package named "Matrix") will become available on the CRAN mirrors. As some of you have noticed, the version numbers (current is version 0.999375-8) are converging to one, and we feel that we have solved enough of the many (mostly small) problems to announce that release 1.0-0 is imminent. In the DESCRIPTION of the package we say -------------------------------------------------------------- Title: A Matrix package for R Author: Douglas Bates <....> and Martin Maechler <....> Maintainer: Doug and Martin Description: Classes and methods for dense and sparse matrices and operations on them using Lapack, CSparse and CHOLMOD -------------------------------------------------------------- The Matrix package provides efficient methods for several formal (i.e. S4) classes of matrices where each of the actual classes are some combination of the following three categories 1) dense or sparse 2) symmmetric, triangular, diagonal or "general" (or "permutation") 3) numeric ("d"ouble), logical (TRUE/FALSE/NA) or "patter[n]" (0/1) matrices Interfaces to many efficient algorithms from Lapack (for "dense") and from CHOLMOD / Csparse (for "sparse") are all implemented via method definitions for the customary linear algebra functions %*%, t(), crossprod(), tcrossprod(), chol(), qr(), solve(), colSums(), rowSums(), kronecker(), determinant(), ... and for various formal groups of generics, such as "Math" (sin,exp,gamma,..) "Arith" (+,-,*,...), "Logic" (>, <=, ..), "Summary" (sum, max, ...) etc; is.na() Furthermore, 'indexing' : "A[...]" and "A[..] <- value" of all(!) kinds of S/R indexing and some new generic functions such as lu() {LU decomposition} Schur(), BunchKaufman(), norm(), rcond() {Matrix norms and condition numbers} expm() {Matrix exponential}, band(), triu(), tril() {extract band-diagonal or triangular sub-matrices} symmpart(), skewpart() { (x + t(x))/2 and (x - t(x)) / 2 } are provided. Further, an extension to the xtabs function xtabs(*, sparse=TRUE) for large sparse, two-way contingency tables and coercion of one *factor* (possibly crossed with one ) to the corresponding (potentially huge) sparse model matrix for sparse least squares and related computations. Further to the above, "Matrix" objects are also constructed by Matrix(), spMatrix(), bdiag() {block-diagonal}, Diagonal() and many as(., "....Matrix") possibilities. The Matrix package also provides a C level API (header files of exported C functions providing low-level functionality) to many of its internal algorithms that other packages can link to. Currently, the 'lme4' package makes heavy use of these exported C functions. --------------------------------------------------------------------------- One of the things we plan to improve considerably is the documentation for the package. Currently there are four vignettes but all but the Comparisons: Comparisons of Least Squares calculation speeds are really not complete in one way or another. --------------------------------------------------------------------------- We would appreciate current users of the Matrix package (and also generally interested useRs) exploring the package's capabilities and giving us feedback about problems that they might encounter or missing features, inefficiencies and maybe even "infelicities" (a.k.a. bugs). Fixing problems before the release of the 1.0-0 version of "The Matrix", rather than after its release, is our preferred approach Matrix/inst/doc/Comparisons.pdf0000644000175100001440000022530412271765427016271 0ustar hornikusers%PDF-1.5 % 1 0 obj << /Type /ObjStm /Length 4717 /Filter /FlateDecode /N 99 /First 829 >> stream x\YsH~_QoӎuR-uX( 8M2 rɬ@ U#ˬ̬,rB IrD!%D1K QKs%R9NKL0e3 k8(o .,_rkM&N*h9>DX/I")^+"rH>{(AoeJS0FC%B5E4B5pq@SMስPR `qx(9qRQ@)r ro8/(ͨ%A)9hBq RtF@  ,GP`  H&0b&,Q#+(h$iY 蘆@LQhzl"BwAm\ z @ZR@`i2m` " 8t&(0j6@@m%f 3#qukefr li'kTcd0l-Ŭ8Qh 'PA͎c'΄Vfa6 di@l]nlSvx!uTjF lMo LNSU[u0b4#-|V ~:JZ%W?\ jb{8Y8PTx,?g9o{Xruef8Y=%VwKs qEjj OÇq*b79x 7pӈ 7|7s¸0ZP' o#,Vp$x8fVɨ"<,,"$Vҥ| '>IFOf<%fwHr18*s[< Gl^~MQW~x#Ab2Or5޿$a=@)h"JDكKz|7@,-[TXݳK}4hWPH&P7n}x3YNߒlHK O~hrGd>ZkXy0X?*ZҗaX[u+:02SQ^x*׬Y EHps<}- Lttw_\P~I,&7I%d<$d<&_Y2Od'mYOBuhsxx0`PwÇɰ#0>F7;;C e4< = H 8gidߧ"ΦuuK6WbX <x_jpwGzI1pVh'65oW;op; ư4j*sdJ}:I CFVq1a }zh[M *Cȁ=QՉqGg:NDgi r\lֆ'=tkV!Q@?QzW@m"ΆZoj*]JF33Z5 f1?fw,F?L=*΍a@Ȩݗ4v}1;grs/)~ھ=lV"*<2L$_F %65gH˕Yi=yJ~ԧuD.<GW6`횰!+z?.LlȤ+7 m{'xOt:qfZF,y[tj0JNم3dv+'1cx'6MoN/wn6ޙ4/oeӐ3ƫKITY(@Ay|18gay@Ϡ=Óm'# vF ˽~&:*9emͫQo< ,誅СۤZ\?]xwV'nm#\F "*Na0SWQe56]a4ssZ.Y0?mQtDvK:#kJ3 H8ZhP+*""'hc]Pe-*?h[uz16J:E!4}QEtZP#8σ0,b?r3+Jgm'#7mFm`3:Oў )]Tlzs ;׵I-K*/ҶAqdu4CkHl*nѮ$uA/XXw8K?+:?:h V&" a4ny()-BtjjmʖӋ(gDxW6/,ml YS* λ:9mRNZKtOoZ-WLkfL4I*h97g, g66vQT>«l"ž|? 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H uS= %$^ ]@# @ Ձ endstream endobj startxref 59744 %%EOF Matrix/inst/doc/SuiteSparse/0000755000175100001440000000000012271765426015541 5ustar hornikusersMatrix/inst/doc/SuiteSparse/UserGuides.txt0000644000175100001440000000133710500056651020347 0ustar hornikusersPDF files of the User's Guides for the CHOLMOD, AMD and CAMD sparse matrix libraries are available from Tim Davis's web site for his sparse matrix packages. The base URL for the web site is http://www.cise.ufl.edu/research/sparse A direct link to "The CHOLMOD User's Guide" is http://www.cise.ufl.edu/research/sparse/cholmod/current/CHOLMOD/Doc/UserGuide.pdf A direct link to "The AMD User's Guide" is http://www.cise.ufl.edu/research/sparse/amd/current/AMD/Doc/AMD_UserGuide.pdf (Apparently Tim has taken Oscar Wilde's observation that "consistency is the last refuge of the unimaginative" to heart.) A direct link to "The CAMD User's Guide" is http://www.cise.ufl.edu/research/sparse/camd/current/CAMD/Doc/AMD_UserGuide.pdf Matrix/inst/doc/SuiteSparse/AMD.txt0000644000175100001440000002130111770402705016667 0ustar hornikusersAMD, Copyright (c) 2009-2012 by Timothy A. Davis (http://www.suitesparse.com), Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved. AMD is available under alternate licences; contact T. Davis for details. AMD: a set of routines for permuting sparse matrices prior to factorization. Includes a version in C, a version in Fortran, and a MATLAB mexFunction. Requires SuiteSparse_config, in the ../SuiteSparse_config directory relative to this directory. Quick start (Unix, or Windows with Cygwin): To compile, test, and install AMD, you may wish to first configure the installation by editting the ../SuiteSparse_config/SuiteSparse_config.mk file. Next, cd to this directory (AMD) and type "make" (or "make lib" if you do not have MATLAB). To compile and run a demo program for the Fortran version, type "make fortran". When done, type "make clean" to remove unused *.o files (keeps the compiled libraries and demo programs). See the User Guide (Doc/AMD_UserGuide.pdf), or ../SuiteSparse_config/SuiteSparse_config.mk for more details. Quick start (for MATLAB users); To compile, test, and install the AMD mexFunction, cd to the AMD/MATLAB directory and type amd_make at the MATLAB prompt. ------------------------------------------------------------------------------- AMD License: Your use or distribution of AMD or any modified version of AMD implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU LGPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. Availability: http://www.suitesparse.com ------------------------------------------------------------------------------- This is the AMD README file. It is a terse overview of AMD. Refer to the User Guide (Doc/AMD_UserGuide.pdf) for how to install and use AMD. Description: AMD is a set of routines for pre-ordering sparse matrices prior to Cholesky or LU factorization, using the approximate minimum degree ordering algorithm. Written in ANSI/ISO C with a MATLAB interface, and in Fortran 77. Authors: Timothy A. Davis (DrTimothyAldenDavis@gmail.com) Patrick R. Amestory, ENSEEIHT, Toulouse, France. Iain S. Duff, Rutherford Appleton Laboratory, UK. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974, DMS-9803599, and CCR-0203270. Portions of this work were done while on sabbatical at Stanford University and Lawrence Berkeley National Laboratory (with funding from the SciDAC program). I would like to thank Gene Golub, Esmond Ng, and Horst Simon for making this sabbatical possible. ------------------------------------------------------------------------------- Files and directories in the AMD distribution: ------------------------------------------------------------------------------- --------------------------------------------------------------------------- Subdirectories of the AMD directory: --------------------------------------------------------------------------- Doc documentation Source primary source code Include include file for use in your code that calls AMD Demo demo programs. also serves as test of the AMD installation. MATLAB AMD mexFunction for MATLAB, and supporting m-files Lib where the compiled C-callable and Fortran-callable AMD libraries placed. --------------------------------------------------------------------------- Files in the AMD directory: --------------------------------------------------------------------------- Makefile top-level Makefile for GNU make or original make. Windows users would require Cygwin to use "make" README.txt this file --------------------------------------------------------------------------- Doc directory: documentation --------------------------------------------------------------------------- ChangeLog change log License the AMD License Makefile for creating the documentation AMD_UserGuide.bib AMD User Guide (references) AMD_UserGuide.tex AMD User Guide (LaTeX) AMD_UserGuide.pdf AMD User Guide (PDF) lesser.txt the GNU LGPL license --------------------------------------------------------------------------- Source directory: --------------------------------------------------------------------------- amd_order.c user-callable, primary AMD ordering routine amd_control.c user-callable, prints the control parameters amd_defaults.c user-callable, sets default control parameters amd_info.c user-callable, prints the statistics from AMD amd_1.c non-user-callable, construct A+A' amd_2.c user-callable, primary ordering kernel (a C version of amd.f and amdbar.f, with post-ordering added) amd_aat.c non-user-callable, computes nnz (A+A') amd_dump.c non-user-callable, debugging routines amd_postorder.c non-user-callable, postorder amd_post_tree.c non-user-callable, postorder just one tree amd_valid.c non-user-callable, verifies a matrix amd_preprocess.c non-user-callable, computes A', removes duplic amd.f user-callable Fortran 77 version amdbar.f user-callable Fortran 77 version --------------------------------------------------------------------------- Include directory: --------------------------------------------------------------------------- amd.h include file for C programs that use AMD amd_internal.h non-user-callable, include file for AMD --------------------------------------------------------------------------- Demo directory: --------------------------------------------------------------------------- Makefile for GNU make or original make amd_demo.c C demo program for AMD amd_demo.out output of amd_demo.c amd_demo2.c C demo program for AMD, jumbled matrix amd_demo2.out output of amd_demo2.c amd_l_demo.c C demo program for AMD (long integer version) amd_l_demo.out output of amd_l_demo.c amd_simple.c simple C demo program for AMD amd_simple.out output of amd_simple.c amd_f77demo.f Fortran 77 demo program for AMD amd_f77demo.out output of amd_f77demo.f amd_f77simple.c simple Fortran 77 demo program for AMD amd_f77simple.out output of amd_f77simple.f amd_f77cross.f Fortran 77 demo, calls the C version of AMD amd_f77cross.out output of amd_f77cross.f amd_f77wrapper.c Fortran-callable wrapper for C version of AMD --------------------------------------------------------------------------- MATLAB directory: --------------------------------------------------------------------------- GNUmakefile a nice Makefile, for GNU make Makefile an ugly Unix Makefile (for older make's) Contents.m for "help amd2" listing of toolbox contents amd2.m MATLAB help file for AMD amd_make.m MATLAB m-file for compiling AMD mexFunction amd_install.m compile and install the AMD mexFunction amd_mex.c AMD mexFunction for MATLAB amd_demo.m MATLAB demo for AMD amd_demo.m.out diary output of amd_demo.m can_24.mat input file for AMD demo --------------------------------------------------------------------------- Lib directory: libamd.a and libamdf77.a libraries placed here --------------------------------------------------------------------------- GNUmakefile a nice Makefile, for GNU make Makefile an ugly Unix Makefile (for older make's) libamd.def AMD definitions for Windows Matrix/inst/doc/SuiteSparse/COLAMD.txt0000644000175100001440000001157311770402705017237 0ustar hornikusersCOLAMD, Copyright 1998-2012, Timothy A. Davis. http://www.suitesparse.com ------------------------------------------------------------------------------- The COLAMD column approximate minimum degree ordering algorithm computes a permutation vector P such that the LU factorization of A (:,P) tends to be sparser than that of A. The Cholesky factorization of (A (:,P))'*(A (:,P)) will also tend to be sparser than that of A'*A. SYMAMD is a symmetric minimum degree ordering method based on COLAMD, available as a MATLAB-callable function. It constructs a matrix M such that M'*M has the same pattern as A, and then uses COLAMD to compute a column ordering of M. Colamd and symamd tend to be faster and generate better orderings than their MATLAB counterparts, colmmd and symmmd. To compile and test the colamd m-files and mexFunctions, just unpack the COLAMD/ directory from the COLAMD.tar.gz file, and run MATLAB from within that directory. Next, type colamd_test to compile and test colamd and symamd. This will work on any computer with MATLAB (Unix, PC, or Mac). Alternatively, type "make" (in Unix) to compile and run a simple example C code, without using MATLAB. To compile and install the colamd m-files and mexFunctions, just cd to COLAMD/MATLAB and type colamd_install in the MATLAB command window. A short demo will run. Optionally, type colamd_test to run an extensive tests. Type "make" in Unix in the COLAMD directory to compile the C-callable library and to run a short demo. Colamd is a built-in routine in MATLAB, available from The Mathworks, Inc. Under most cases, the compiled COLAMD from Versions 2.0 to the current version do not differ. Colamd Versions 2.2 and 2.3 differ only in their mexFunction interaces to MATLAB. v2.4 fixes a bug in the symamd routine in v2.3. The bug (in v2.3 and earlier) has no effect on the MATLAB symamd mexFunction. v2.5 adds additional checks for integer overflow, so that the "int" version can be safely used with 64-bit pointers. Refer to the ChangeLog for more details. To use colamd and symamd within an application written in C, all you need are colamd.c, colamd_global.c, and colamd.h, which are the C-callable colamd/symamd codes. See colamd.c for more information on how to call colamd from a C program. Requires SuiteSparse_config, in the ../SuiteSparse_config directory relative to this directory. See the colamd.c file or http://www.suitesparse.com for the license to COLAMD. Related papers: T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, An approximate column minimum degree ordering algorithm, ACM Transactions on Mathematical Software, vol. 30, no. 3., pp. 353-376, 2004. T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836: COLAMD, an approximate column minimum degree ordering algorithm, ACM Transactions on Mathematical Software, vol. 30, no. 3., pp. 377-380, 2004. "An approximate minimum degree column ordering algorithm", S. I. Larimore, MS Thesis, Dept. of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, 1998. CISE Tech Report TR-98-016. Approximate Deficiency for Ordering the Columns of a Matrix, J. L. Kern, Senior Thesis, Dept. of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, 1999. Authors: Stefan I. Larimore and Timothy A. Davis, in collaboration with John Gilbert, Xerox PARC (now at UC Santa Barbara), and Esmong Ng, Lawrence Berkeley National Laboratory (much of this work he did while at Oak Ridge National Laboratory). COLAMD files: Demo simple demo Doc additional documentation (see colamd.c for more) Include include file Lib compiled C-callable library Makefile primary Unix Makefile MATLAB MATLAB functions README.txt this file Source C source code ./Demo: colamd_example.c simple example colamd_example.out output of colamd_example.c colamd_l_example.c simple example, long integers colamd_l_example.out output of colamd_l_example.c Makefile Makefile for C demos ./Doc: ChangeLog change log lesser.txt license ./Include: colamd.h include file ./Lib: Makefile Makefile for C-callable library ./MATLAB: colamd2.m MATLAB interface for colamd2 colamd_demo.m simple demo colamd_install.m compile and install colamd2 and symamd2 colamd_make.m compile colamd2 and symamd2 colamdmex.ca MATLAB mexFunction for colamd2 colamd_test.m extensive test colamdtestmex.c test function for colamd Contents.m contents of the MATLAB directory luflops.m test code Makefile Makefile for MATLAB functions symamd2.m MATLAB interface for symamd2 symamdmex.c MATLAB mexFunction for symamd2 symamdtestmex.c test function for symamd ./Source: colamd.c primary source code colamd_global.c globally defined function pointers (malloc, free, ...) Matrix/inst/doc/SuiteSparse/CHOLMOD.txt0000644000175100001440000001002111770402705017350 0ustar hornikusersCHOLMOD: a sparse CHOLesky MODification package, Copyright (c) 2005-2012. http://www.suitesparse.com ----------------------------------------------- CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AA', updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx=b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level-3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both C and MATLAB interfaces. This code works on Microsoft Windows and many versions of Unix and Linux. Some Modules of CHOLMOD are copyrighted by the University of Florida (the Core and Partition Modules). The rest are copyrighted by the authors: Timothy A. Davis (all of them), and William W. Hager (the Modify Module). CHOLMOD relies on several other packages: AMD, CAMD, COLAMD, CCOLAMD, SuiteSparse_config, METIS, the BLAS, and LAPACK. All but METIS, the BLAS, and LAPACK are part of SuiteSparse. AMD is authored by T. Davis, Iain Duff, and Patrick Amestoy. COLAMD is authored by T. Davis and Stefan Larimore, with algorithmic design in collaboration with John Gilbert and Esmond Ng. CCOLAMD is authored by T. Davis and Siva Rajamanickam. CAMD is authored by T. Davis and Y. Chen. LAPACK and the BLAS are authored by Jack Dongarra and many others. LAPACK is available at http://www.netlib.org/lapack METIS is authored by George Karypis, Univ. of Minnesota. Its use in CHOLMOD is optional. See http://www-users.cs.umn.edu/~karypis/metis. Place a copy of the metis-4.0 directory in the same directory that contains the CHOLMOD, AMD, COLAMD, and CCOLAMD directories prior to compiling with "make". If you do not wish to use METIS, you must edit SuiteSparse_config and change the line: CHOLMOD_CONFIG = to CHOLMOD_CONFIG = -DNPARTITION The CHOLMOD, AMD, COLAMD, CCOLAMD, and SuiteSparse)config directories must all reside in a common parent directory. To compile all these libraries, edit SuiteSparse)config/SuiteSparse)config.mk to reflect your environment (C compiler, location of the BLAS, and so on) and then type "make" in either the CHOLMOD directory or in the parent directory of CHOLMOD. See each package for more details on how to compile them. For use in MATLAB (on any system, including Windows): start MATLAB, cd to the CHOLMOD/MATLAB directory, and type cholmod_make in the MATLAB Command Window. This is the best way to compile CHOLMOD for MATLAB; it provides a workaround for a METIS design feature, in which METIS terminates your program (and thus MATLAB) if it runs out of memory. Using cholmod_make also ensures your mexFunctions are compiled with -fexceptions, so that exceptions are handled properly (when hitting control-C in the MATLAB command window, for example). On the Pentium, do NOT use the Intel MKL BLAS prior to MKL Version 8.0 with CHOLMOD. Older versions (prior to 8.0) have a bug in dgemm when computing A*B'. The bug generates a NaN result, when the inputs are well-defined. Use the Goto BLAS or the MKL v8.0 BLAS instead. The Goto BLAS is faster and more reliable. See http://www.tacc.utexas.edu/~kgoto/ or http://www.cs.utexas.edu/users/flame/goto/. Sadly, the Intel MKL BLAS 7.x is the default for MATLAB 7.0.4. See http://www.mathworks.com/support/bugreports/details.html?rp=252103 for more details. To workaround this problem on Linux, set environment variable BLAS_VERSION to libmkl_p3.so:libguide.so. On Windows, set environment variable BLAS_VERSION to mkl_p3.dll. Better yet, get MATLAB 7sp3 (MATLAB 7.1) or later. Acknowledgements: this work was supported in part by the National Science Foundation (NFS CCR-0203270 and DMS-9803599), and a grant from Sandia National Laboratories (Dept. of Energy) which supported the development of CHOLMOD's Partition Module. Matrix/inst/doc/SuiteSparse/SPQR.txt0000644000175100001440000000434311072415476017066 0ustar hornikusersSuiteSparseQR version 1.1.0, Sept 20, 2008, Copyright (c) 2008, Timothy A. Davis SuiteSparseQR is a a multithread, multifrontal, rank-revealing sparse QR factorization method. QUICK START FOR MATLAB USERS (on Windows, Linux, Solaris, or the Mac OS): To compile and test the MATLAB mexFunctions, do this in the MATLAB command window: cd SuiteSparse/SPQR/MATLAB spqr_install spqr_demo FOR MORE DETAILS: please see the User Guide in Doc/spqr_user_guide.pdf. FOR LINUX/UNIX/Mac USERS who want to use the C++ callable library: To compile the C++ library and run a short demo, just type "make" in the Unix shell. To compile the SuiteSparseQR C++ library, in the Unix shell, do: cd Lib ; make To compile and test an exhaustive test, edit the Tcov/Makefile to select the LAPACK and BLAS libraries, and then do (in the Unix shell): cd Tcov ; make Compilation options in UFconfig/UFconfig.mk, SPQR/*/Makefile, or SPQR/MATLAB/spqr_make.m: -DNPARTITION to compile without METIS (default is to use METIS) -DNEXPERT to compile without the min 2-norm solution option (default is to include the Expert routines) -DHAVE_TBB to compile with Intel's Threading Building Blocks (default is to not use Intel TBB) -DTIMING to compile with timing and exact flop counts enabled (default is to not compile with timing and flop counts) -------------------------------------------------------------------------------- SuiteSparseQR is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. SuiteSparseQR is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. Matrix/inst/doc/SuiteSparse/SuiteSparse_config.txt0000644000175100001440000000451312215610421022057 0ustar hornikusersSuiteSparse_config, 2013, Timothy A. Davis, http://www.suitesparse.com (formerly the UFconfig package) SuiteSparse_config contains configuration settings for all many of the software packages that I develop or co-author. Note that older versions of some of these packages do not require SuiteSparse_config. Package Description ------- ----------- AMD approximate minimum degree ordering CAMD constrained AMD COLAMD column approximate minimum degree ordering CCOLAMD constrained approximate minimum degree ordering UMFPACK sparse LU factorization, with the BLAS CXSparse int/long/real/complex version of CSparse CHOLMOD sparse Cholesky factorization, update/downdate KLU sparse LU factorization, BLAS-free BTF permutation to block triangular form LDL concise sparse LDL' LPDASA LP Dual Active Set Algorithm RBio read/write files in Rutherford/Boeing format SPQR sparse QR factorization (full name: SuiteSparseQR) SuiteSparse_config is not required by these packages: CSparse a Concise Sparse matrix package MATLAB_Tools toolboxes for use in MATLAB In addition, the xerbla/ directory contains Fortan and C versions of the BLAS/LAPACK xerbla routine, which is called when an invalid input is passed to the BLAS or LAPACK. The xerbla provided here does not print any message, so the entire Fortran I/O library does not need to be linked into a C application. Most versions of the BLAS contain xerbla, but those from K. Goto do not. Use this if you need too. If you edit this directory (SuiteSparse_config.mk in particular) then you must do "make purge ; make" in the parent directory to recompile all of SuiteSparse. Otherwise, the changes will not necessarily be applied. -------------------------------------------------------------------------------- A note on the update to SuiteSparse Version 4.0.0: The SuiteSparse_long macro defines an integer that is 64-bits in size on 64-bit platforms, and 32-bits on 32-bit platforms. It was formerly called UF_long, but UF_long has been removed because of potential name conflicts. UF_long is still available to user codes, but it can now be safely #undef'd in case of name conflicts in user code. Future codes should use SuiteSparse_long in place of UF_long. -------------------------------------------------------------------------------- Matrix/inst/external/0000755000175100001440000000000012271765436014350 5ustar hornikusersMatrix/inst/external/symA.rda0000644000175100001440000000153712215114135015735 0ustar hornikusersmTiHTa}3c˨9-:iP RI%{n)ea4樥6e9DDK4HRAd?ȐH2"Z{{̢䠢 EQ̊bR>,LbqQ1 QS ֢gB|ϜalW_sP Ն ͕s"µo~ >Q9Y۪t˜vEj%f/m_LEH2zp,XM΍3p\΋o <4ǰX Q(lRm.l"a&udVղ<QY9lE݄E;H; tLHԶ$ j'3DTۘ?<|7ID-՟ꞟxY=)+b/ <v>B-n"u YO&?0_}?.7 Բ6HO3𦾢} Ro=50s#ÚMOD?[iǹQ~ ov'źQ?eƼCg-^xL hw;ꎡ18xW:h0`2x*PM~x1zzT_J{u&&huc/WSPp]ѬӄnȀ:z}'r3 G<7o?!0k{r}ں{Nr}G>G{OУ^4uI~[ A:~ù=E>ו L/sp_dfWM꿗@ 8,ko~=j"i77f9Z\βjg~P/Q<vMatrix/inst/external/KNex_slots.rda0000644000175100001440000015620010464427703017127 0ustar hornikusers}XT:TFc/c9b{E#슢+v{=* b8$by;̝k3}ft:% "GLolpN]!G|hѶG{_ө+n3 M5~ E{po4 s\hxxߥ='8^K4+<zk4O^4;4\/g=s-Km5Z~h0( \p/^Eh=%J~ Zrxh*9 \+UB5V D_:Z 4셮6ZFh5jAchњ5go{w]zhߣzn Z3x/o؁5Z[x= '6h:R^ 3ZW~ '.hzx ߫yuG 7Z_c>h 븇c hCц C6m$ڏhSO9 m Xxcc&MD suzړIhS~B6gh3pƢfBs{6h:ƫ'mh<Жu.tжvB[`m=BTFݫ.=ulRY up_m=7;*=0m#&-6SJ}->`z‰/hvAۋC"?0U=*U GuOc4U{' D;vZ Y|z0݋Q0^@>X=a0Qh'NB;>TshhahE}v -cmu:520!/*lL% _C> Ld`GTآJD'& X8% 쩰_~S0e`H^dQ&|͓7tc|*:||=D\` @NTF;ȀaK:qC #D( uyˣwaF!谟:6:؈Cau1lG@ g1D@غ§ ⊀X`L >*| _! 3& vdKC*|" * $  *(79*I/qE@[6- &` PZ+{R`O*bU~]WTSOw~O| } N!{*⺊Ǹ~D/!. 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Matrix/inst/external/lund_a.rsa0000644000175100001440000007024410275502035016312 0ustar hornikusers1SYMMETRIC MATRIX A OF LUND EIGENVALUE PROBLEM, MAY 1974 LUND A 352 10 82 260 0 RSA 147 147 1298 0 (16I5) (16I5) (5E16.8) 1 7 15 23 31 39 47 53 58 68 77 85 97 108 118 130 141 151 163 174 184 196 207 217 228 238 247 254 260 265 275 284 292 304 315 325 337 348 358 370 381 391 403 414 424 435 445 454 461 467 472 482 491 499 510 521 531 543 554 564 576 587 597 609 620 630 641 651 660 667 673 678 688 697 705 717 728 738 750 761 771 783 794 804 815 826 836 847 857 866 873 879 884 894 903 911 923 934 944 956 967 977 989 1000 1010 1022 1033 1043 1053 1063 1072 1079 1085 1090 1099 1107 1114 1124 1133 1141 1151 1160 1168 1178 1187 1195 1205 1214 1222 1231 1239 1246 1251 1255 1258 1262 1265 1269 1272 1276 1279 1283 1286 1290 1293 1296 1298 1299 1 2 8 9 10 11 2 3 9 10 11 12 13 14 3 4 12 13 14 15 16 17 4 5 15 16 17 18 19 20 5 6 18 19 20 21 22 23 6 7 21 22 23 24 25 26 7 24 25 26 27 28 8 9 10 11 29 9 10 11 12 13 14 29 30 31 32 10 11 12 13 14 29 30 31 32 11 12 13 14 29 30 31 32 12 13 14 15 16 17 30 31 32 33 34 35 13 14 15 16 17 30 31 32 33 34 35 14 15 16 17 30 31 32 33 34 35 15 16 17 18 19 20 33 34 35 36 37 38 16 17 18 19 20 33 34 35 36 37 38 17 18 19 20 33 34 35 36 37 38 18 19 20 21 22 23 36 37 38 39 40 41 19 20 21 22 23 36 37 38 39 40 41 20 21 22 23 36 37 38 39 40 41 21 22 23 24 25 26 39 40 41 42 43 44 22 23 24 25 26 39 40 41 42 43 44 23 24 25 26 39 40 41 42 43 44 24 25 26 27 28 42 43 44 45 46 47 25 26 27 28 42 43 44 45 46 47 26 27 28 42 43 44 45 46 47 27 28 45 46 47 48 49 28 45 46 47 48 49 29 30 31 32 50 30 31 32 33 34 35 50 51 52 53 31 32 33 34 35 50 51 52 53 32 33 34 35 50 51 52 53 33 34 35 36 37 38 51 52 53 54 55 56 34 35 36 37 38 51 52 53 54 55 56 35 36 37 38 51 52 53 54 55 56 36 37 38 39 40 41 54 55 56 57 58 59 37 38 39 40 41 54 55 56 57 58 59 38 39 40 41 54 55 56 57 58 59 39 40 41 42 43 44 57 58 59 60 61 62 40 41 42 43 44 57 58 59 60 61 62 41 42 43 44 57 58 59 60 61 62 42 43 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121 122 123 124 125 105 106 107 108 109 110 123 124 125 126 127 128 106 107 108 109 110 123 124 125 126 127 128 107 108 109 110 123 124 125 126 127 128 108 109 110 111 112 127 128 129 130 131 109 110 111 112 126 127 128 129 130 131 110 111 112 126 127 128 129 130 131 111 112 129 130 131 132 133 112 129 130 131 132 133 113 114 115 116 134 114 115 116 117 118 119 134 135 136 115 116 117 118 119 134 135 136 116 117 118 119 134 135 136 117 118 119 120 121 122 135 136 137 138 118 119 120 121 122 135 136 137 138 119 120 121 122 135 136 137 138 120 121 122 123 124 125 137 138 139 140 121 122 123 124 125 137 138 139 140 122 123 124 125 137 138 139 140 123 124 125 126 127 128 139 140 141 142 124 125 126 127 128 139 140 141 142 125 126 127 128 139 140 141 142 126 127 128 129 130 131 141 142 143 144 127 128 129 130 131 141 142 143 144 128 129 130 131 141 142 143 144 129 130 131 132 133 143 144 145 146 130 131 132 133 143 144 145 146 131 132 133 143 144 145 146 132 133 145 146 147 133 145 146 147 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text after a hash (#) is considered a comment and will be ignored. # The format is: # TAG = value [value, ...] # For lists items can also be appended using: # TAG += value [value, ...] # Values that contain spaces should be placed between quotes (" "). #--------------------------------------------------------------------------- # Project related configuration options #--------------------------------------------------------------------------- # This tag specifies the encoding used for all characters in the config file # that follow. The default is UTF-8 which is also the encoding used for all # text before the first occurrence of this tag. Doxygen uses libiconv (or the # iconv built into libc) for the transcoding. See # http://www.gnu.org/software/libiconv for the list of possible encodings. DOXYFILE_ENCODING = UTF-8 # The PROJECT_NAME tag is a single word (or a sequence of words surrounded # by quotes) that should identify the project. PROJECT_NAME = Matrix # The PROJECT_NUMBER tag can be used to enter a project or revision number. # This could be handy for archiving the generated documentation or # if some version control system is used. PROJECT_NUMBER = "$Rev: 2721 $ at $LastChangedDate: 2011-10-06 14:59:16 +0200 (Thu, 06 Oct 2011) $" # Using the PROJECT_BRIEF tag one can provide an optional one line description # for a project that appears at the top of each page and should give viewer # a quick idea about the purpose of the project. Keep the description short. PROJECT_BRIEF = # With the PROJECT_LOGO tag one can specify an logo or icon that is # included in the documentation. The maximum height of the logo should not # exceed 55 pixels and the maximum width should not exceed 200 pixels. # Doxygen will copy the logo to the output directory. PROJECT_LOGO = # The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) # base path where the generated documentation will be put. # If a relative path is entered, it will be relative to the location # where doxygen was started. If left blank the current directory will be used. OUTPUT_DIRECTORY = ../../../www/doxygen # If the CREATE_SUBDIRS tag is set to YES, then doxygen will create # 4096 sub-directories (in 2 levels) under the output directory of each output # format and will distribute the generated files over these directories. # Enabling this option can be useful when feeding doxygen a huge amount of # source files, where putting all generated files in the same directory would # otherwise cause performance problems for the file system. CREATE_SUBDIRS = NO # The OUTPUT_LANGUAGE tag is used to specify the language in which all # documentation generated by doxygen is written. Doxygen will use this # information to generate all constant output in the proper language. # The default language is English, other supported languages are: # Afrikaans, Arabic, Brazilian, Catalan, Chinese, Chinese-Traditional, # Croatian, Czech, Danish, Dutch, Esperanto, Farsi, Finnish, French, German, # Greek, Hungarian, Italian, Japanese, Japanese-en (Japanese with English # messages), Korean, Korean-en, Lithuanian, Norwegian, Macedonian, Persian, # Polish, Portuguese, Romanian, Russian, Serbian, Serbian-Cyrillic, Slovak, # Slovene, Spanish, Swedish, Ukrainian, and Vietnamese. OUTPUT_LANGUAGE = English # If the BRIEF_MEMBER_DESC tag is set to YES (the default) Doxygen will # include brief member descriptions after the members that are listed in # the file and class documentation (similar to JavaDoc). # Set to NO to disable this. BRIEF_MEMBER_DESC = YES # If the REPEAT_BRIEF tag is set to YES (the default) Doxygen will prepend # the brief description of a member or function before the detailed description. # Note: if both HIDE_UNDOC_MEMBERS and BRIEF_MEMBER_DESC are set to NO, the # brief descriptions will be completely suppressed. REPEAT_BRIEF = YES # This tag implements a quasi-intelligent brief description abbreviator # that is used to form the text in various listings. Each string # in this list, if found as the leading text of the brief description, will be # stripped from the text and the result after processing the whole list, is # used as the annotated text. Otherwise, the brief description is used as-is. # If left blank, the following values are used ("$name" is automatically # replaced with the name of the entity): "The $name class" "The $name widget" # "The $name file" "is" "provides" "specifies" "contains" # "represents" "a" "an" "the" ABBREVIATE_BRIEF = # If the ALWAYS_DETAILED_SEC and REPEAT_BRIEF tags are both set to YES then # Doxygen will generate a detailed section even if there is only a brief # description. ALWAYS_DETAILED_SEC = YES # If the INLINE_INHERITED_MEMB tag is set to YES, doxygen will show all # inherited members of a class in the documentation of that class as if those # members were ordinary class members. Constructors, destructors and assignment # operators of the base classes will not be shown. INLINE_INHERITED_MEMB = NO # If the FULL_PATH_NAMES tag is set to YES then Doxygen will prepend the full # path before files name in the file list and in the header files. If set # to NO the shortest path that makes the file name unique will be used. FULL_PATH_NAMES = NO # If the FULL_PATH_NAMES tag is set to YES then the STRIP_FROM_PATH tag # can be used to strip a user-defined part of the path. Stripping is # only done if one of the specified strings matches the left-hand part of # the path. The tag can be used to show relative paths in the file list. # If left blank the directory from which doxygen is run is used as the # path to strip. STRIP_FROM_PATH = # The STRIP_FROM_INC_PATH tag can be used to strip a user-defined part of # the path mentioned in the documentation of a class, which tells # the reader which header file to include in order to use a class. # If left blank only the name of the header file containing the class # definition is used. Otherwise one should specify the include paths that # are normally passed to the compiler using the -I flag. STRIP_FROM_INC_PATH = # If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter # (but less readable) file names. This can be useful if your file system # doesn't support long names like on DOS, Mac, or CD-ROM. SHORT_NAMES = NO # If the JAVADOC_AUTOBRIEF tag is set to YES then Doxygen # will interpret the first line (until the first dot) of a JavaDoc-style # comment as the brief description. If set to NO, the JavaDoc # comments will behave just like regular Qt-style comments # (thus requiring an explicit @brief command for a brief description.) JAVADOC_AUTOBRIEF = YES # If the QT_AUTOBRIEF tag is set to YES then Doxygen will # interpret the first line (until the first dot) of a Qt-style # comment as the brief description. If set to NO, the comments # will behave just like regular Qt-style comments (thus requiring # an explicit \brief command for a brief description.) QT_AUTOBRIEF = NO # The MULTILINE_CPP_IS_BRIEF tag can be set to YES to make Doxygen # treat a multi-line C++ special comment block (i.e. a block of //! or /// # comments) as a brief description. This used to be the default behaviour. # The new default is to treat a multi-line C++ comment block as a detailed # description. Set this tag to YES if you prefer the old behaviour instead. MULTILINE_CPP_IS_BRIEF = NO # If the INHERIT_DOCS tag is set to YES (the default) then an undocumented # member inherits the documentation from any documented member that it # re-implements. INHERIT_DOCS = YES # If the SEPARATE_MEMBER_PAGES tag is set to YES, then doxygen will produce # a new page for each member. If set to NO, the documentation of a member will # be part of the file/class/namespace that contains it. SEPARATE_MEMBER_PAGES = NO # The TAB_SIZE tag can be used to set the number of spaces in a tab. # Doxygen uses this value to replace tabs by spaces in code fragments. TAB_SIZE = 8 # This tag can be used to specify a number of aliases that acts # as commands in the documentation. An alias has the form "name=value". # For example adding "sideeffect=\par Side Effects:\n" will allow you to # put the command \sideeffect (or @sideeffect) in the documentation, which # will result in a user-defined paragraph with heading "Side Effects:". # You can put \n's in the value part of an alias to insert newlines. ALIASES = # Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C # sources only. Doxygen will then generate output that is more tailored for C. # For instance, some of the names that are used will be different. The list # of all members will be omitted, etc. OPTIMIZE_OUTPUT_FOR_C = YES # Set the OPTIMIZE_OUTPUT_JAVA tag to YES if your project consists of Java # sources only. Doxygen will then generate output that is more tailored for # Java. For instance, namespaces will be presented as packages, qualified # scopes will look different, etc. OPTIMIZE_OUTPUT_JAVA = NO # Set the OPTIMIZE_FOR_FORTRAN tag to YES if your project consists of Fortran # sources only. Doxygen will then generate output that is more tailored for # Fortran. OPTIMIZE_FOR_FORTRAN = NO # Set the OPTIMIZE_OUTPUT_VHDL tag to YES if your project consists of VHDL # sources. Doxygen will then generate output that is tailored for # VHDL. OPTIMIZE_OUTPUT_VHDL = NO # Doxygen selects the parser to use depending on the extension of the files it # parses. With this tag you can assign which parser to use for a given extension. # Doxygen has a built-in mapping, but you can override or extend it using this # tag. The format is ext=language, where ext is a file extension, and language # is one of the parsers supported by doxygen: IDL, Java, Javascript, CSharp, C, # C++, D, PHP, Objective-C, Python, Fortran, VHDL, C, C++. For instance to make # doxygen treat .inc files as Fortran files (default is PHP), and .f files as C # (default is Fortran), use: inc=Fortran f=C. Note that for custom extensions # you also need to set FILE_PATTERNS otherwise the files are not read by doxygen. EXTENSION_MAPPING = # If you use STL classes (i.e. std::string, std::vector, etc.) but do not want # to include (a tag file for) the STL sources as input, then you should # set this tag to YES in order to let doxygen match functions declarations and # definitions whose arguments contain STL classes (e.g. func(std::string); v.s. # func(std::string) {}). This also makes the inheritance and collaboration # diagrams that involve STL classes more complete and accurate. BUILTIN_STL_SUPPORT = NO # If you use Microsoft's C++/CLI language, you should set this option to YES to # enable parsing support. CPP_CLI_SUPPORT = NO # Set the SIP_SUPPORT tag to YES if your project consists of sip sources only. # Doxygen will parse them like normal C++ but will assume all classes use public # instead of private inheritance when no explicit protection keyword is present. SIP_SUPPORT = NO # For Microsoft's IDL there are propget and propput attributes to indicate getter # and setter methods for a property. Setting this option to YES (the default) # will make doxygen replace the get and set methods by a property in the # documentation. This will only work if the methods are indeed getting or # setting a simple type. If this is not the case, or you want to show the # methods anyway, you should set this option to NO. IDL_PROPERTY_SUPPORT = YES # If member grouping is used in the documentation and the DISTRIBUTE_GROUP_DOC # tag is set to YES, then doxygen will reuse the documentation of the first # member in the group (if any) for the other members of the group. By default # all members of a group must be documented explicitly. DISTRIBUTE_GROUP_DOC = NO # Set the SUBGROUPING tag to YES (the default) to allow class member groups of # the same type (for instance a group of public functions) to be put as a # subgroup of that type (e.g. under the Public Functions section). Set it to # NO to prevent subgrouping. Alternatively, this can be done per class using # the \nosubgrouping command. SUBGROUPING = YES # When the INLINE_GROUPED_CLASSES tag is set to YES, classes, structs and # unions are shown inside the group in which they are included (e.g. using # @ingroup) instead of on a separate page (for HTML and Man pages) or # section (for LaTeX and RTF). INLINE_GROUPED_CLASSES = NO # When TYPEDEF_HIDES_STRUCT is enabled, a typedef of a struct, union, or enum # is documented as struct, union, or enum with the name of the typedef. So # typedef struct TypeS {} TypeT, will appear in the documentation as a struct # with name TypeT. When disabled the typedef will appear as a member of a file, # namespace, or class. And the struct will be named TypeS. This can typically # be useful for C code in case the coding convention dictates that all compound # types are typedef'ed and only the typedef is referenced, never the tag name. TYPEDEF_HIDES_STRUCT = NO # The SYMBOL_CACHE_SIZE determines the size of the internal cache use to # determine which symbols to keep in memory and which to flush to disk. # When the cache is full, less often used symbols will be written to disk. # For small to medium size projects (<1000 input files) the default value is # probably good enough. For larger projects a too small cache size can cause # doxygen to be busy swapping symbols to and from disk most of the time # causing a significant performance penalty. # If the system has enough physical memory increasing the cache will improve the # performance by keeping more symbols in memory. Note that the value works on # a logarithmic scale so increasing the size by one will roughly double the # memory usage. The cache size is given by this formula: # 2^(16+SYMBOL_CACHE_SIZE). The valid range is 0..9, the default is 0, # corresponding to a cache size of 2^16 = 65536 symbols SYMBOL_CACHE_SIZE = 0 #--------------------------------------------------------------------------- # Build related configuration options #--------------------------------------------------------------------------- # If the EXTRACT_ALL tag is set to YES doxygen will assume all entities in # documentation are documented, even if no documentation was available. # Private class members and static file members will be hidden unless # the EXTRACT_PRIVATE and EXTRACT_STATIC tags are set to YES EXTRACT_ALL = YES # If the EXTRACT_PRIVATE tag is set to YES all private members of a class # will be included in the documentation. EXTRACT_PRIVATE = NO # If the EXTRACT_STATIC tag is set to YES all static members of a file # will be included in the documentation. EXTRACT_STATIC = YES # If the EXTRACT_LOCAL_CLASSES tag is set to YES classes (and structs) # defined locally in source files will be included in the documentation. # If set to NO only classes defined in header files are included. EXTRACT_LOCAL_CLASSES = YES # This flag is only useful for Objective-C code. When set to YES local # methods, which are defined in the implementation section but not in # the interface are included in the documentation. # If set to NO (the default) only methods in the interface are included. EXTRACT_LOCAL_METHODS = NO # If this flag is set to YES, the members of anonymous namespaces will be # extracted and appear in the documentation as a namespace called # 'anonymous_namespace{file}', where file will be replaced with the base # name of the file that contains the anonymous namespace. By default # anonymous namespaces are hidden. EXTRACT_ANON_NSPACES = NO # If the HIDE_UNDOC_MEMBERS tag is set to YES, Doxygen will hide all # undocumented members of documented classes, files or namespaces. # If set to NO (the default) these members will be included in the # various overviews, but no documentation section is generated. # This option has no effect if EXTRACT_ALL is enabled. HIDE_UNDOC_MEMBERS = NO # If the HIDE_UNDOC_CLASSES tag is set to YES, Doxygen will hide all # undocumented classes that are normally visible in the class hierarchy. # If set to NO (the default) these classes will be included in the various # overviews. This option has no effect if EXTRACT_ALL is enabled. HIDE_UNDOC_CLASSES = NO # If the HIDE_FRIEND_COMPOUNDS tag is set to YES, Doxygen will hide all # friend (class|struct|union) declarations. # If set to NO (the default) these declarations will be included in the # documentation. HIDE_FRIEND_COMPOUNDS = NO # If the HIDE_IN_BODY_DOCS tag is set to YES, Doxygen will hide any # documentation blocks found inside the body of a function. # If set to NO (the default) these blocks will be appended to the # function's detailed documentation block. HIDE_IN_BODY_DOCS = NO # The INTERNAL_DOCS tag determines if documentation # that is typed after a \internal command is included. If the tag is set # to NO (the default) then the documentation will be excluded. # Set it to YES to include the internal documentation. INTERNAL_DOCS = NO # If the CASE_SENSE_NAMES tag is set to NO then Doxygen will only generate # file names in lower-case letters. If set to YES upper-case letters are also # allowed. This is useful if you have classes or files whose names only differ # in case and if your file system supports case sensitive file names. Windows # and Mac users are advised to set this option to NO. CASE_SENSE_NAMES = YES # If the HIDE_SCOPE_NAMES tag is set to NO (the default) then Doxygen # will show members with their full class and namespace scopes in the # documentation. If set to YES the scope will be hidden. HIDE_SCOPE_NAMES = NO # If the SHOW_INCLUDE_FILES tag is set to YES (the default) then Doxygen # will put a list of the files that are included by a file in the documentation # of that file. SHOW_INCLUDE_FILES = YES # If the FORCE_LOCAL_INCLUDES tag is set to YES then Doxygen # will list include files with double quotes in the documentation # rather than with sharp brackets. FORCE_LOCAL_INCLUDES = NO # If the INLINE_INFO tag is set to YES (the default) then a tag [inline] # is inserted in the documentation for inline members. INLINE_INFO = YES # If the SORT_MEMBER_DOCS tag is set to YES (the default) then doxygen # will sort the (detailed) documentation of file and class members # alphabetically by member name. If set to NO the members will appear in # declaration order. SORT_MEMBER_DOCS = YES # If the SORT_BRIEF_DOCS tag is set to YES then doxygen will sort the # brief documentation of file, namespace and class members alphabetically # by member name. If set to NO (the default) the members will appear in # declaration order. SORT_BRIEF_DOCS = YES # If the SORT_MEMBERS_CTORS_1ST tag is set to YES then doxygen # will sort the (brief and detailed) documentation of class members so that # constructors and destructors are listed first. If set to NO (the default) # the constructors will appear in the respective orders defined by # SORT_MEMBER_DOCS and SORT_BRIEF_DOCS. # This tag will be ignored for brief docs if SORT_BRIEF_DOCS is set to NO # and ignored for detailed docs if SORT_MEMBER_DOCS is set to NO. SORT_MEMBERS_CTORS_1ST = NO # If the SORT_GROUP_NAMES tag is set to YES then doxygen will sort the # hierarchy of group names into alphabetical order. If set to NO (the default) # the group names will appear in their defined order. SORT_GROUP_NAMES = NO # If the SORT_BY_SCOPE_NAME tag is set to YES, the class list will be # sorted by fully-qualified names, including namespaces. If set to # NO (the default), the class list will be sorted only by class name, # not including the namespace part. # Note: This option is not very useful if HIDE_SCOPE_NAMES is set to YES. # Note: This option applies only to the class list, not to the # alphabetical list. SORT_BY_SCOPE_NAME = NO # If the STRICT_PROTO_MATCHING option is enabled and doxygen fails to # do proper type resolution of all parameters of a function it will reject a # match between the prototype and the implementation of a member function even # if there is only one candidate or it is obvious which candidate to choose # by doing a simple string match. By disabling STRICT_PROTO_MATCHING doxygen # will still accept a match between prototype and implementation in such cases. STRICT_PROTO_MATCHING = NO # The GENERATE_TODOLIST tag can be used to enable (YES) or # disable (NO) the todo list. This list is created by putting \todo # commands in the documentation. GENERATE_TODOLIST = YES # The GENERATE_TESTLIST tag can be used to enable (YES) or # disable (NO) the test list. This list is created by putting \test # commands in the documentation. GENERATE_TESTLIST = YES # The GENERATE_BUGLIST tag can be used to enable (YES) or # disable (NO) the bug list. This list is created by putting \bug # commands in the documentation. GENERATE_BUGLIST = YES # The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or # disable (NO) the deprecated list. This list is created by putting # \deprecated commands in the documentation. GENERATE_DEPRECATEDLIST= YES # The ENABLED_SECTIONS tag can be used to enable conditional # documentation sections, marked by \if sectionname ... \endif. ENABLED_SECTIONS = # The MAX_INITIALIZER_LINES tag determines the maximum number of lines # the initial value of a variable or macro consists of for it to appear in # the documentation. If the initializer consists of more lines than specified # here it will be hidden. Use a value of 0 to hide initializers completely. # The appearance of the initializer of individual variables and macros in the # documentation can be controlled using \showinitializer or \hideinitializer # command in the documentation regardless of this setting. MAX_INITIALIZER_LINES = 30 # Set the SHOW_USED_FILES tag to NO to disable the list of files generated # at the bottom of the documentation of classes and structs. If set to YES the # list will mention the files that were used to generate the documentation. SHOW_USED_FILES = YES # If the sources in your project are distributed over multiple directories # then setting the SHOW_DIRECTORIES tag to YES will show the directory hierarchy # in the documentation. The default is NO. SHOW_DIRECTORIES = NO # Set the SHOW_FILES tag to NO to disable the generation of the Files page. # This will remove the Files entry from the Quick Index and from the # Folder Tree View (if specified). The default is YES. SHOW_FILES = YES # Set the SHOW_NAMESPACES tag to NO to disable the generation of the # Namespaces page. # This will remove the Namespaces entry from the Quick Index # and from the Folder Tree View (if specified). The default is YES. SHOW_NAMESPACES = YES # The FILE_VERSION_FILTER tag can be used to specify a program or script that # doxygen should invoke to get the current version for each file (typically from # the version control system). Doxygen will invoke the program by executing (via # popen()) the command , where is the value of # the FILE_VERSION_FILTER tag, and is the name of an input file # provided by doxygen. Whatever the program writes to standard output # is used as the file version. See the manual for examples. FILE_VERSION_FILTER = # The LAYOUT_FILE tag can be used to specify a layout file which will be parsed # by doxygen. The layout file controls the global structure of the generated # output files in an output format independent way. The create the layout file # that represents doxygen's defaults, run doxygen with the -l option. # You can optionally specify a file name after the option, if omitted # DoxygenLayout.xml will be used as the name of the layout file. LAYOUT_FILE = #--------------------------------------------------------------------------- # configuration options related to warning and progress messages #--------------------------------------------------------------------------- # The QUIET tag can be used to turn on/off the messages that are generated # by doxygen. Possible values are YES and NO. If left blank NO is used. QUIET = NO # The WARNINGS tag can be used to turn on/off the warning messages that are # generated by doxygen. Possible values are YES and NO. If left blank # NO is used. WARNINGS = YES # If WARN_IF_UNDOCUMENTED is set to YES, then doxygen will generate warnings # for undocumented members. If EXTRACT_ALL is set to YES then this flag will # automatically be disabled. WARN_IF_UNDOCUMENTED = YES # If WARN_IF_DOC_ERROR is set to YES, doxygen will generate warnings for # potential errors in the documentation, such as not documenting some # parameters in a documented function, or documenting parameters that # don't exist or using markup commands wrongly. WARN_IF_DOC_ERROR = YES # The WARN_NO_PARAMDOC option can be enabled to get warnings for # functions that are documented, but have no documentation for their parameters # or return value. If set to NO (the default) doxygen will only warn about # wrong or incomplete parameter documentation, but not about the absence of # documentation. WARN_NO_PARAMDOC = NO # The WARN_FORMAT tag determines the format of the warning messages that # doxygen can produce. The string should contain the $file, $line, and $text # tags, which will be replaced by the file and line number from which the # warning originated and the warning text. Optionally the format may contain # $version, which will be replaced by the version of the file (if it could # be obtained via FILE_VERSION_FILTER) WARN_FORMAT = "$file:$line: $text " # The WARN_LOGFILE tag can be used to specify a file to which warning # and error messages should be written. If left blank the output is written # to stderr. WARN_LOGFILE = #--------------------------------------------------------------------------- # configuration options related to the input files #--------------------------------------------------------------------------- # The INPUT tag can be used to specify the files and/or directories that contain # documented source files. You may enter file names like "myfile.cpp" or # directories like "/usr/src/myproject". Separate the files or directories # with spaces. INPUT = ../src # This tag can be used to specify the character encoding of the source files # that doxygen parses. Internally doxygen uses the UTF-8 encoding, which is # also the default input encoding. Doxygen uses libiconv (or the iconv built # into libc) for the transcoding. See http://www.gnu.org/software/libiconv for # the list of possible encodings. INPUT_ENCODING = UTF-8 # If the value of the INPUT tag contains directories, you can use the # FILE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp # and *.h) to filter out the source-files in the directories. If left # blank the following patterns are tested: # *.c *.cc *.cxx *.cpp *.c++ *.d *.java *.ii *.ixx *.ipp *.i++ *.inl *.h *.hh # *.hxx *.hpp *.h++ *.idl *.odl *.cs *.php *.php3 *.inc *.m *.mm *.dox *.py # *.f90 *.f *.for *.vhd *.vhdl FILE_PATTERNS = # The RECURSIVE tag can be used to turn specify whether or not subdirectories # should be searched for input files as well. Possible values are YES and NO. # If left blank NO is used. RECURSIVE = NO # The EXCLUDE tag can be used to specify files and/or directories that should # excluded from the INPUT source files. This way you can easily exclude a # subdirectory from a directory tree whose root is specified with the INPUT tag. EXCLUDE = # The EXCLUDE_SYMLINKS tag can be used select whether or not files or # directories that are symbolic links (a Unix file system feature) are excluded # from the input. EXCLUDE_SYMLINKS = NO # If the value of the INPUT tag contains directories, you can use the # EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude # certain files from those directories. Note that the wildcards are matched # against the file with absolute path, so to exclude all test directories # for example use the pattern */test/* EXCLUDE_PATTERNS = # The EXCLUDE_SYMBOLS tag can be used to specify one or more symbol names # (namespaces, classes, functions, etc.) that should be excluded from the # output. The symbol name can be a fully qualified name, a word, or if the # wildcard * is used, a substring. Examples: ANamespace, AClass, # AClass::ANamespace, ANamespace::*Test EXCLUDE_SYMBOLS = # The EXAMPLE_PATH tag can be used to specify one or more files or # directories that contain example code fragments that are included (see # the \include command). EXAMPLE_PATH = # If the value of the EXAMPLE_PATH tag contains directories, you can use the # EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp # and *.h) to filter out the source-files in the directories. If left # blank all files are included. EXAMPLE_PATTERNS = # If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be # searched for input files to be used with the \include or \dontinclude # commands irrespective of the value of the RECURSIVE tag. # Possible values are YES and NO. If left blank NO is used. EXAMPLE_RECURSIVE = NO # The IMAGE_PATH tag can be used to specify one or more files or # directories that contain image that are included in the documentation (see # the \image command). IMAGE_PATH = # The INPUT_FILTER tag can be used to specify a program that doxygen should # invoke to filter for each input file. Doxygen will invoke the filter program # by executing (via popen()) the command , where # is the value of the INPUT_FILTER tag, and is the name of an # input file. Doxygen will then use the output that the filter program writes # to standard output. # If FILTER_PATTERNS is specified, this tag will be # ignored. INPUT_FILTER = # The FILTER_PATTERNS tag can be used to specify filters on a per file pattern # basis. # Doxygen will compare the file name with each pattern and apply the # filter if there is a match. # The filters are a list of the form: # pattern=filter (like *.cpp=my_cpp_filter). See INPUT_FILTER for further # info on how filters are used. If FILTER_PATTERNS is empty or if # non of the patterns match the file name, INPUT_FILTER is applied. FILTER_PATTERNS = # If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using # INPUT_FILTER) will be used to filter the input files when producing source # files to browse (i.e. when SOURCE_BROWSER is set to YES). FILTER_SOURCE_FILES = NO # The FILTER_SOURCE_PATTERNS tag can be used to specify source filters per file # pattern. A pattern will override the setting for FILTER_PATTERN (if any) # and it is also possible to disable source filtering for a specific pattern # using *.ext= (so without naming a filter). This option only has effect when # FILTER_SOURCE_FILES is enabled. FILTER_SOURCE_PATTERNS = #--------------------------------------------------------------------------- # configuration options related to source browsing #--------------------------------------------------------------------------- # If the SOURCE_BROWSER tag is set to YES then a list of source files will # be generated. Documented entities will be cross-referenced with these sources. # Note: To get rid of all source code in the generated output, make sure also # VERBATIM_HEADERS is set to NO. SOURCE_BROWSER = YES # Setting the INLINE_SOURCES tag to YES will include the body # of functions and classes directly in the documentation. INLINE_SOURCES = NO # Setting the STRIP_CODE_COMMENTS tag to YES (the default) will instruct # doxygen to hide any special comment blocks from generated source code # fragments. Normal C and C++ comments will always remain visible. STRIP_CODE_COMMENTS = YES # If the REFERENCED_BY_RELATION tag is set to YES # then for each documented function all documented # functions referencing it will be listed. REFERENCED_BY_RELATION = YES # If the REFERENCES_RELATION tag is set to YES # then for each documented function all documented entities # called/used by that function will be listed. REFERENCES_RELATION = YES # If the REFERENCES_LINK_SOURCE tag is set to YES (the default) # and SOURCE_BROWSER tag is set to YES, then the hyperlinks from # functions in REFERENCES_RELATION and REFERENCED_BY_RELATION lists will # link to the source code. # Otherwise they will link to the documentation. REFERENCES_LINK_SOURCE = YES # If the USE_HTAGS tag is set to YES then the references to source code # will point to the HTML generated by the htags(1) tool instead of doxygen # built-in source browser. The htags tool is part of GNU's global source # tagging system (see http://www.gnu.org/software/global/global.html). You # will need version 4.8.6 or higher. USE_HTAGS = NO # If the VERBATIM_HEADERS tag is set to YES (the default) then Doxygen # will generate a verbatim copy of the header file for each class for # which an include is specified. Set to NO to disable this. VERBATIM_HEADERS = YES #--------------------------------------------------------------------------- # configuration options related to the alphabetical class index #--------------------------------------------------------------------------- # If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index # of all compounds will be generated. Enable this if the project # contains a lot of classes, structs, unions or interfaces. ALPHABETICAL_INDEX = NO # If the alphabetical index is enabled (see ALPHABETICAL_INDEX) then # the COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns # in which this list will be split (can be a number in the range [1..20]) COLS_IN_ALPHA_INDEX = 5 # In case all classes in a project start with a common prefix, all # classes will be put under the same header in the alphabetical index. # The IGNORE_PREFIX tag can be used to specify one or more prefixes that # should be ignored while generating the index headers. IGNORE_PREFIX = #--------------------------------------------------------------------------- # configuration options related to the HTML output #--------------------------------------------------------------------------- # If the GENERATE_HTML tag is set to YES (the default) Doxygen will # generate HTML output. GENERATE_HTML = YES # The HTML_OUTPUT tag is used to specify where the HTML docs will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `html' will be used as the default path. HTML_OUTPUT = . # The HTML_FILE_EXTENSION tag can be used to specify the file extension for # each generated HTML page (for example: .htm,.php,.asp). If it is left blank # doxygen will generate files with .html extension. HTML_FILE_EXTENSION = .html # The HTML_HEADER tag can be used to specify a personal HTML header for # each generated HTML page. If it is left blank doxygen will generate a # standard header. Note that when using a custom header you are responsible # for the proper inclusion of any scripts and style sheets that doxygen # needs, which is dependent on the configuration options used. # It is adviced to generate a default header using "doxygen -w html # header.html footer.html stylesheet.css YourConfigFile" and then modify # that header. Note that the header is subject to change so you typically # have to redo this when upgrading to a newer version of doxygen or when changing the value of configuration settings such as GENERATE_TREEVIEW! HTML_HEADER = # The HTML_FOOTER tag can be used to specify a personal HTML footer for # each generated HTML page. If it is left blank doxygen will generate a # standard footer. HTML_FOOTER = # If the HTML_TIMESTAMP tag is set to YES then the generated HTML documentation will contain the timesstamp. HTML_TIMESTAMP = NO # The HTML_STYLESHEET tag can be used to specify a user-defined cascading # style sheet that is used by each HTML page. It can be used to # fine-tune the look of the HTML output. If the tag is left blank doxygen # will generate a default style sheet. Note that doxygen will try to copy # the style sheet file to the HTML output directory, so don't put your own # stylesheet in the HTML output directory as well, or it will be erased! HTML_STYLESHEET = # The HTML_EXTRA_FILES tag can be used to specify one or more extra images or # other source files which should be copied to the HTML output directory. Note # that these files will be copied to the base HTML output directory. Use the # $relpath$ marker in the HTML_HEADER and/or HTML_FOOTER files to load these # files. In the HTML_STYLESHEET file, use the file name only. Also note that # the files will be copied as-is; there are no commands or markers available. HTML_EXTRA_FILES = # The HTML_COLORSTYLE_HUE tag controls the color of the HTML output. # Doxygen will adjust the colors in the stylesheet and background images # according to this color. Hue is specified as an angle on a colorwheel, # see http://en.wikipedia.org/wiki/Hue for more information. # For instance the value 0 represents red, 60 is yellow, 120 is green, # 180 is cyan, 240 is blue, 300 purple, and 360 is red again. # The allowed range is 0 to 359. HTML_COLORSTYLE_HUE = 220 # The HTML_COLORSTYLE_SAT tag controls the purity (or saturation) of # the colors in the HTML output. For a value of 0 the output will use # grayscales only. A value of 255 will produce the most vivid colors. HTML_COLORSTYLE_SAT = 100 # The HTML_COLORSTYLE_GAMMA tag controls the gamma correction applied to # the luminance component of the colors in the HTML output. Values below # 100 gradually make the output lighter, whereas values above 100 make # the output darker. The value divided by 100 is the actual gamma applied, # so 80 represents a gamma of 0.8, The value 220 represents a gamma of 2.2, # and 100 does not change the gamma. HTML_COLORSTYLE_GAMMA = 80 # If the HTML_TIMESTAMP tag is set to YES then the footer of each generated HTML # page will contain the date and time when the page was generated. Setting # this to NO can help when comparing the output of multiple runs. HTML_TIMESTAMP = YES # If the HTML_ALIGN_MEMBERS tag is set to YES, the members of classes, # files or namespaces will be aligned in HTML using tables. If set to # NO a bullet list will be used. HTML_ALIGN_MEMBERS = YES # If the HTML_DYNAMIC_SECTIONS tag is set to YES then the generated HTML # documentation will contain sections that can be hidden and shown after the # page has loaded. For this to work a browser that supports # JavaScript and DHTML is required (for instance Mozilla 1.0+, Firefox # Netscape 6.0+, Internet explorer 5.0+, Konqueror, or Safari). HTML_DYNAMIC_SECTIONS = NO # If the GENERATE_DOCSET tag is set to YES, additional index files # will be generated that can be used as input for Apple's Xcode 3 # integrated development environment, introduced with OSX 10.5 (Leopard). # To create a documentation set, doxygen will generate a Makefile in the # HTML output directory. Running make will produce the docset in that # directory and running "make install" will install the docset in # ~/Library/Developer/Shared/Documentation/DocSets so that Xcode will find # it at startup. # See http://developer.apple.com/tools/creatingdocsetswithdoxygen.html # for more information. GENERATE_DOCSET = NO # When GENERATE_DOCSET tag is set to YES, this tag determines the name of the # feed. A documentation feed provides an umbrella under which multiple # documentation sets from a single provider (such as a company or product suite) # can be grouped. DOCSET_FEEDNAME = "Doxygen generated docs" # When GENERATE_DOCSET tag is set to YES, this tag specifies a string that # should uniquely identify the documentation set bundle. This should be a # reverse domain-name style string, e.g. com.mycompany.MyDocSet. Doxygen # will append .docset to the name. DOCSET_BUNDLE_ID = org.doxygen.Project # When GENERATE_PUBLISHER_ID tag specifies a string that should uniquely identify # the documentation publisher. This should be a reverse domain-name style # string, e.g. com.mycompany.MyDocSet.documentation. DOCSET_PUBLISHER_ID = org.doxygen.Publisher # The GENERATE_PUBLISHER_NAME tag identifies the documentation publisher. DOCSET_PUBLISHER_NAME = Publisher # If the GENERATE_HTMLHELP tag is set to YES, additional index files # will be generated that can be used as input for tools like the # Microsoft HTML help workshop to generate a compiled HTML help file (.chm) # of the generated HTML documentation. GENERATE_HTMLHELP = NO # If the GENERATE_HTMLHELP tag is set to YES, the CHM_FILE tag can # be used to specify the file name of the resulting .chm file. You # can add a path in front of the file if the result should not be # written to the html output directory. CHM_FILE = # If the GENERATE_HTMLHELP tag is set to YES, the HHC_LOCATION tag can # be used to specify the location (absolute path including file name) of # the HTML help compiler (hhc.exe). If non-empty doxygen will try to run # the HTML help compiler on the generated index.hhp. HHC_LOCATION = # If the GENERATE_HTMLHELP tag is set to YES, the GENERATE_CHI flag # controls if a separate .chi index file is generated (YES) or that # it should be included in the master .chm file (NO). GENERATE_CHI = NO # If the GENERATE_HTMLHELP tag is set to YES, the CHM_INDEX_ENCODING # is used to encode HtmlHelp index (hhk), content (hhc) and project file # content. CHM_INDEX_ENCODING = # If the GENERATE_HTMLHELP tag is set to YES, the BINARY_TOC flag # controls whether a binary table of contents is generated (YES) or a # normal table of contents (NO) in the .chm file. BINARY_TOC = NO # The TOC_EXPAND flag can be set to YES to add extra items for group members # to the contents of the HTML help documentation and to the tree view. TOC_EXPAND = NO # If the GENERATE_QHP tag is set to YES and both QHP_NAMESPACE and # QHP_VIRTUAL_FOLDER are set, an additional index file will be generated # that can be used as input for Qt's qhelpgenerator to generate a # Qt Compressed Help (.qch) of the generated HTML documentation. GENERATE_QHP = NO # If the QHG_LOCATION tag is specified, the QCH_FILE tag can # be used to specify the file name of the resulting .qch file. # The path specified is relative to the HTML output folder. QCH_FILE = # The QHP_NAMESPACE tag specifies the namespace to use when generating # Qt Help Project output. For more information please see # http://doc.trolltech.com/qthelpproject.html#namespace QHP_NAMESPACE = # The QHP_VIRTUAL_FOLDER tag specifies the namespace to use when generating # Qt Help Project output. For more information please see # http://doc.trolltech.com/qthelpproject.html#virtual-folders QHP_VIRTUAL_FOLDER = doc # If QHP_CUST_FILTER_NAME is set, it specifies the name of a custom filter to # add. For more information please see # http://doc.trolltech.com/qthelpproject.html#custom-filters QHP_CUST_FILTER_NAME = # The QHP_CUST_FILT_ATTRS tag specifies the list of the attributes of the # custom filter to add. For more information please see # # Qt Help Project / Custom Filters. QHP_CUST_FILTER_ATTRS = # The QHP_SECT_FILTER_ATTRS tag specifies the list of the attributes this # project's # filter section matches. # # Qt Help Project / Filter Attributes. QHP_SECT_FILTER_ATTRS = # If the GENERATE_QHP tag is set to YES, the QHG_LOCATION tag can # be used to specify the location of Qt's qhelpgenerator. # If non-empty doxygen will try to run qhelpgenerator on the generated # .qhp file. QHG_LOCATION = # If the GENERATE_ECLIPSEHELP tag is set to YES, additional index files # will be generated, which together with the HTML files, form an Eclipse help # plugin. To install this plugin and make it available under the help contents # menu in Eclipse, the contents of the directory containing the HTML and XML # files needs to be copied into the plugins directory of eclipse. The name of # the directory within the plugins directory should be the same as # the ECLIPSE_DOC_ID value. After copying Eclipse needs to be restarted before # the help appears. GENERATE_ECLIPSEHELP = NO # A unique identifier for the eclipse help plugin. When installing the plugin # the directory name containing the HTML and XML files should also have # this name. ECLIPSE_DOC_ID = org.doxygen.Project # The DISABLE_INDEX tag can be used to turn on/off the condensed index at # top of each HTML page. The value NO (the default) enables the index and # the value YES disables it. DISABLE_INDEX = NO # The ENUM_VALUES_PER_LINE tag can be used to set the number of enum values # (range [0,1..20]) that doxygen will group on one line in the generated HTML # documentation. Note that a value of 0 will completely suppress the enum # values from appearing in the overview section. ENUM_VALUES_PER_LINE = 8 # The GENERATE_TREEVIEW tag is used to specify whether a tree-like index # structure should be generated to display hierarchical information. # If the tag value is set to YES, a side panel will be generated # containing a tree-like index structure (just like the one that # is generated for HTML Help). For this to work a browser that supports # JavaScript, DHTML, CSS and frames is required (i.e. any modern browser). # Windows users are probably better off using the HTML help feature. GENERATE_TREEVIEW = YES # By enabling USE_INLINE_TREES, doxygen will generate the Groups, Directories, # and Class Hierarchy pages using a tree view instead of an ordered list. USE_INLINE_TREES = NO # If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be # used to set the initial width (in pixels) of the frame in which the tree # is shown. TREEVIEW_WIDTH = 250 # When the EXT_LINKS_IN_WINDOW option is set to YES doxygen will open # links to external symbols imported via tag files in a separate window. EXT_LINKS_IN_WINDOW = NO # Use this tag to change the font size of Latex formulas included # as images in the HTML documentation. The default is 10. Note that # when you change the font size after a successful doxygen run you need # to manually remove any form_*.png images from the HTML output directory # to force them to be regenerated. FORMULA_FONTSIZE = 10 # Use the FORMULA_TRANPARENT tag to determine whether or not the images # generated for formulas are transparent PNGs. Transparent PNGs are # not supported properly for IE 6.0, but are supported on all modern browsers. # Note that when changing this option you need to delete any form_*.png files # in the HTML output before the changes have effect. FORMULA_TRANSPARENT = YES # Enable the USE_MATHJAX option to render LaTeX formulas using MathJax # (see http://www.mathjax.org) which uses client side Javascript for the # rendering instead of using prerendered bitmaps. Use this if you do not # have LaTeX installed or if you want to formulas look prettier in the HTML # output. When enabled you also need to install MathJax separately and # configure the path to it using the MATHJAX_RELPATH option. USE_MATHJAX = NO # When MathJax is enabled you need to specify the location relative to the # HTML output directory using the MATHJAX_RELPATH option. The destination # directory should contain the MathJax.js script. For instance, if the mathjax # directory is located at the same level as the HTML output directory, then # MATHJAX_RELPATH should be ../mathjax. The default value points to the # mathjax.org site, so you can quickly see the result without installing # MathJax, but it is strongly recommended to install a local copy of MathJax # before deployment. MATHJAX_RELPATH = http://www.mathjax.org/mathjax # When the SEARCHENGINE tag is enabled doxygen will generate a search box # for the HTML output. The underlying search engine uses javascript # and DHTML and should work on any modern browser. Note that when using # HTML help (GENERATE_HTMLHELP), Qt help (GENERATE_QHP), or docsets # (GENERATE_DOCSET) there is already a search function so this one should # typically be disabled. For large projects the javascript based search engine # can be slow, then enabling SERVER_BASED_SEARCH may provide a better solution. SEARCHENGINE = NO # When the SERVER_BASED_SEARCH tag is enabled the search engine will be # implemented using a PHP enabled web server instead of at the web client # using Javascript. Doxygen will generate the search PHP script and index # file to put on the web server. The advantage of the server # based approach is that it scales better to large projects and allows # full text search. The disadvantages are that it is more difficult to setup # and does not have live searching capabilities. SERVER_BASED_SEARCH = NO #--------------------------------------------------------------------------- # configuration options related to the LaTeX output #--------------------------------------------------------------------------- # If the GENERATE_LATEX tag is set to YES (the default) Doxygen will # generate Latex output. GENERATE_LATEX = NO # The LATEX_OUTPUT tag is used to specify where the LaTeX docs will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `latex' will be used as the default path. LATEX_OUTPUT = latex # The LATEX_CMD_NAME tag can be used to specify the LaTeX command name to be # invoked. If left blank `latex' will be used as the default command name. # Note that when enabling USE_PDFLATEX this option is only used for # generating bitmaps for formulas in the HTML output, but not in the # Makefile that is written to the output directory. LATEX_CMD_NAME = latex # The MAKEINDEX_CMD_NAME tag can be used to specify the command name to # generate index for LaTeX. If left blank `makeindex' will be used as the # default command name. MAKEINDEX_CMD_NAME = makeindex # If the COMPACT_LATEX tag is set to YES Doxygen generates more compact # LaTeX documents. This may be useful for small projects and may help to # save some trees in general. COMPACT_LATEX = NO # The PAPER_TYPE tag can be used to set the paper type that is used # by the printer. Possible values are: a4, letter, legal and # executive. If left blank a4wide will be used. PAPER_TYPE = letter # The EXTRA_PACKAGES tag can be to specify one or more names of LaTeX # packages that should be included in the LaTeX output. EXTRA_PACKAGES = # The LATEX_HEADER tag can be used to specify a personal LaTeX header for # the generated latex document. The header should contain everything until # the first chapter. If it is left blank doxygen will generate a # standard header. Notice: only use this tag if you know what you are doing! LATEX_HEADER = # The LATEX_FOOTER tag can be used to specify a personal LaTeX footer for # the generated latex document. The footer should contain everything after # the last chapter. If it is left blank doxygen will generate a # standard footer. Notice: only use this tag if you know what you are doing! LATEX_FOOTER = # If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated # is prepared for conversion to pdf (using ps2pdf). The pdf file will # contain links (just like the HTML output) instead of page references # This makes the output suitable for online browsing using a pdf viewer. PDF_HYPERLINKS = NO # If the USE_PDFLATEX tag is set to YES, pdflatex will be used instead of # plain latex in the generated Makefile. Set this option to YES to get a # higher quality PDF documentation. USE_PDFLATEX = YES # If the LATEX_BATCHMODE tag is set to YES, doxygen will add the \\batchmode. # command to the generated LaTeX files. This will instruct LaTeX to keep # running if errors occur, instead of asking the user for help. # This option is also used when generating formulas in HTML. LATEX_BATCHMODE = YES # If LATEX_HIDE_INDICES is set to YES then doxygen will not # include the index chapters (such as File Index, Compound Index, etc.) # in the output. LATEX_HIDE_INDICES = NO # If LATEX_SOURCE_CODE is set to YES then doxygen will include # source code with syntax highlighting in the LaTeX output. # Note that which sources are shown also depends on other settings # such as SOURCE_BROWSER. LATEX_SOURCE_CODE = NO #--------------------------------------------------------------------------- # configuration options related to the RTF output #--------------------------------------------------------------------------- # If the GENERATE_RTF tag is set to YES Doxygen will generate RTF output # The RTF output is optimized for Word 97 and may not look very pretty with # other RTF readers or editors. GENERATE_RTF = NO # The RTF_OUTPUT tag is used to specify where the RTF docs will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `rtf' will be used as the default path. RTF_OUTPUT = rtf # If the COMPACT_RTF tag is set to YES Doxygen generates more compact # RTF documents. This may be useful for small projects and may help to # save some trees in general. COMPACT_RTF = NO # If the RTF_HYPERLINKS tag is set to YES, the RTF that is generated # will contain hyperlink fields. The RTF file will # contain links (just like the HTML output) instead of page references. # This makes the output suitable for online browsing using WORD or other # programs which support those fields. # Note: wordpad (write) and others do not support links. RTF_HYPERLINKS = NO # Load stylesheet definitions from file. Syntax is similar to doxygen's # config file, i.e. a series of assignments. You only have to provide # replacements, missing definitions are set to their default value. RTF_STYLESHEET_FILE = # Set optional variables used in the generation of an rtf document. # Syntax is similar to doxygen's config file. RTF_EXTENSIONS_FILE = #--------------------------------------------------------------------------- # configuration options related to the man page output #--------------------------------------------------------------------------- # If the GENERATE_MAN tag is set to YES (the default) Doxygen will # generate man pages GENERATE_MAN = NO # The MAN_OUTPUT tag is used to specify where the man pages will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `man' will be used as the default path. MAN_OUTPUT = man # The MAN_EXTENSION tag determines the extension that is added to # the generated man pages (default is the subroutine's section .3) MAN_EXTENSION = .3 # If the MAN_LINKS tag is set to YES and Doxygen generates man output, # then it will generate one additional man file for each entity # documented in the real man page(s). These additional files # only source the real man page, but without them the man command # would be unable to find the correct page. The default is NO. MAN_LINKS = NO #--------------------------------------------------------------------------- # configuration options related to the XML output #--------------------------------------------------------------------------- # If the GENERATE_XML tag is set to YES Doxygen will # generate an XML file that captures the structure of # the code including all documentation. GENERATE_XML = NO # The XML_OUTPUT tag is used to specify where the XML pages will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `xml' will be used as the default path. XML_OUTPUT = xml # The XML_SCHEMA tag can be used to specify an XML schema, # which can be used by a validating XML parser to check the # syntax of the XML files. XML_SCHEMA = # The XML_DTD tag can be used to specify an XML DTD, # which can be used by a validating XML parser to check the # syntax of the XML files. XML_DTD = # If the XML_PROGRAMLISTING tag is set to YES Doxygen will # dump the program listings (including syntax highlighting # and cross-referencing information) to the XML output. Note that # enabling this will significantly increase the size of the XML output. XML_PROGRAMLISTING = YES #--------------------------------------------------------------------------- # configuration options for the AutoGen Definitions output #--------------------------------------------------------------------------- # If the GENERATE_AUTOGEN_DEF tag is set to YES Doxygen will # generate an AutoGen Definitions (see autogen.sf.net) file # that captures the structure of the code including all # documentation. Note that this feature is still experimental # and incomplete at the moment. GENERATE_AUTOGEN_DEF = NO #--------------------------------------------------------------------------- # configuration options related to the Perl module output #--------------------------------------------------------------------------- # If the GENERATE_PERLMOD tag is set to YES Doxygen will # generate a Perl module file that captures the structure of # the code including all documentation. Note that this # feature is still experimental and incomplete at the # moment. GENERATE_PERLMOD = NO # If the PERLMOD_LATEX tag is set to YES Doxygen will generate # the necessary Makefile rules, Perl scripts and LaTeX code to be able # to generate PDF and DVI output from the Perl module output. PERLMOD_LATEX = NO # If the PERLMOD_PRETTY tag is set to YES the Perl module output will be # nicely formatted so it can be parsed by a human reader. # This is useful # if you want to understand what is going on. # On the other hand, if this # tag is set to NO the size of the Perl module output will be much smaller # and Perl will parse it just the same. PERLMOD_PRETTY = YES # The names of the make variables in the generated doxyrules.make file # are prefixed with the string contained in PERLMOD_MAKEVAR_PREFIX. # This is useful so different doxyrules.make files included by the same # Makefile don't overwrite each other's variables. PERLMOD_MAKEVAR_PREFIX = #--------------------------------------------------------------------------- # Configuration options related to the preprocessor #--------------------------------------------------------------------------- # If the ENABLE_PREPROCESSING tag is set to YES (the default) Doxygen will # evaluate all C-preprocessor directives found in the sources and include # files. ENABLE_PREPROCESSING = YES # If the MACRO_EXPANSION tag is set to YES Doxygen will expand all macro # names in the source code. If set to NO (the default) only conditional # compilation will be performed. Macro expansion can be done in a controlled # way by setting EXPAND_ONLY_PREDEF to YES. MACRO_EXPANSION = NO # If the EXPAND_ONLY_PREDEF and MACRO_EXPANSION tags are both set to YES # then the macro expansion is limited to the macros specified with the # PREDEFINED and EXPAND_AS_DEFINED tags. EXPAND_ONLY_PREDEF = NO # If the SEARCH_INCLUDES tag is set to YES (the default) the includes files # pointed to by INCLUDE_PATH will be searched when a #include is found. SEARCH_INCLUDES = YES # The INCLUDE_PATH tag can be used to specify one or more directories that # contain include files that are not input files but should be processed by # the preprocessor. INCLUDE_PATH = # You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard # patterns (like *.h and *.hpp) to filter out the header-files in the # directories. If left blank, the patterns specified with FILE_PATTERNS will # be used. INCLUDE_FILE_PATTERNS = # The PREDEFINED tag can be used to specify one or more macro names that # are defined before the preprocessor is started (similar to the -D option of # gcc). The argument of the tag is a list of macros of the form: name # or name=definition (no spaces). If the definition and the = are # omitted =1 is assumed. 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DOT_CLEANUP = YES Matrix/inst/include/0000755000175100001440000000000012271765426014150 5ustar hornikusersMatrix/inst/include/cholmod.h0000644000175100001440000013577012221625374015753 0ustar hornikusers#ifndef MATRIX_CHOLMOD_H #define MATRIX_CHOLMOD_H #include #include #ifdef __cplusplus extern "C" { #endif // from ../../src/UFconfig/UFconfig.h - line 51 : #ifndef UF_long #ifdef _WIN64 #define UF_long __int64 #define UF_long_max _I64_MAX #define UF_long_idd "I64d" #else #define UF_long long #define UF_long_max LONG_MAX #define UF_long_idd "ld" #endif #define UF_long_id "%" UF_long_idd #endif #define CHOLMOD_HAS_VERSION_FUNCTION #define CHOLMOD_DATE "April 25, 2013" #define CHOLMOD_VER_CODE(main,sub) ((main) * 1000 + (sub)) #define CHOLMOD_MAIN_VERSION 2 #define CHOLMOD_SUB_VERSION 1 #define CHOLMOD_SUBSUB_VERSION 2 #define CHOLMOD_VERSION \ CHOLMOD_VER_CODE(CHOLMOD_MAIN_VERSION,CHOLMOD_SUB_VERSION) // from ../../src/CHOLMOD/Include/cholmod_core.h - line 275 : /* Each CHOLMOD object has its own type code. */ #define CHOLMOD_COMMON 0 #define CHOLMOD_SPARSE 1 #define CHOLMOD_FACTOR 2 #define CHOLMOD_DENSE 3 #define CHOLMOD_TRIPLET 4 /* ========================================================================== */ /* === CHOLMOD Common ======================================================= */ /* ========================================================================== */ /* itype defines the types of integer used: */ #define CHOLMOD_INT 0 /* all integer arrays are int */ #define CHOLMOD_INTLONG 1 /* most are int, some are SuiteSparse_long */ #define CHOLMOD_LONG 2 /* all integer arrays are SuiteSparse_long */ /* The itype of all parameters for all CHOLMOD routines must match. * FUTURE WORK: CHOLMOD_INTLONG is not yet supported. */ /* dtype defines what the numerical type is (double or float): */ #define CHOLMOD_DOUBLE 0 /* all numerical values are double */ #define CHOLMOD_SINGLE 1 /* all numerical values are float */ /* The dtype of all parameters for all CHOLMOD routines must match. * * Scalar floating-point values are always passed as double arrays of size 2 * (for the real and imaginary parts). They are typecast to float as needed. * FUTURE WORK: the float case is not supported yet. */ /* xtype defines the kind of numerical values used: */ #define CHOLMOD_PATTERN 0 /* pattern only, no numerical values */ #define CHOLMOD_REAL 1 /* a real matrix */ #define CHOLMOD_COMPLEX 2 /* a complex matrix (ANSI C99 compatible) */ #define CHOLMOD_ZOMPLEX 3 /* a complex matrix (MATLAB compatible) */ /* Definitions for cholmod_common: */ #define CHOLMOD_MAXMETHODS 9 /* maximum number of different methods that */ /* cholmod_analyze can try. Must be >= 9. */ /* Common->status values. zero means success, negative means a fatal error, * positive is a warning. */ #define CHOLMOD_OK 0 /* success */ #define CHOLMOD_NOT_INSTALLED (-1) /* failure: method not installed */ #define CHOLMOD_OUT_OF_MEMORY (-2) /* failure: out of memory */ #define CHOLMOD_TOO_LARGE (-3) /* failure: integer overflow occured */ #define CHOLMOD_INVALID (-4) /* failure: invalid input */ #define CHOLMOD_GPU_PROBLEM (-5) /* failure: GPU fatal error */ #define CHOLMOD_NOT_POSDEF (1) /* warning: matrix not pos. def. */ #define CHOLMOD_DSMALL (2) /* warning: D for LDL' or diag(L) or */ /* LL' has tiny absolute value */ /* ordering method (also used for L->ordering) */ #define CHOLMOD_NATURAL 0 /* use natural ordering */ #define CHOLMOD_GIVEN 1 /* use given permutation */ #define CHOLMOD_AMD 2 /* use minimum degree (AMD) */ #define CHOLMOD_METIS 3 /* use METIS' nested dissection */ #define CHOLMOD_NESDIS 4 /* use CHOLMOD's version of nested dissection:*/ /* node bisector applied recursively, followed * by constrained minimum degree (CSYMAMD or * CCOLAMD) */ #define CHOLMOD_COLAMD 5 /* use AMD for A, COLAMD for A*A' */ /* POSTORDERED is not a method, but a result of natural ordering followed by a * weighted postorder. It is used for L->ordering, not method [ ].ordering. */ #define CHOLMOD_POSTORDERED 6 /* natural ordering, postordered. */ /* supernodal strategy (for Common->supernodal) */ #define CHOLMOD_SIMPLICIAL 0 /* always do simplicial */ #define CHOLMOD_AUTO 1 /* select simpl/super depending on matrix */ #define CHOLMOD_SUPERNODAL 2 /* always do supernodal */ typedef struct cholmod_common_struct { /* ---------------------------------------------------------------------- */ /* parameters for symbolic/numeric factorization and update/downdate */ /* ---------------------------------------------------------------------- */ double dbound ; /* Smallest absolute value of diagonal entries of D * for LDL' factorization and update/downdate/rowadd/ * rowdel, or the diagonal of L for an LL' factorization. * Entries in the range 0 to dbound are replaced with dbound. * Entries in the range -dbound to 0 are replaced with -dbound. No * changes are made to the diagonal if dbound <= 0. Default: zero */ double grow0 ; /* For a simplicial factorization, L->i and L->x can * grow if necessary. grow0 is the factor by which * it grows. For the initial space, L is of size MAX (1,grow0) times * the required space. If L runs out of space, the new size of L is * MAX(1.2,grow0) times the new required space. If you do not plan on * modifying the LDL' factorization in the Modify module, set grow0 to * zero (or set grow2 to 0, see below). Default: 1.2 */ double grow1 ; size_t grow2 ; /* For a simplicial factorization, each column j of L * is initialized with space equal to * grow1*L->ColCount[j] + grow2. If grow0 < 1, grow1 < 1, or grow2 == 0, * then the space allocated is exactly equal to L->ColCount[j]. If the * column j runs out of space, it increases to grow1*need + grow2 in * size, where need is the total # of nonzeros in that column. If you do * not plan on modifying the factorization in the Modify module, set * grow2 to zero. Default: grow1 = 1.2, grow2 = 5. */ size_t maxrank ; /* rank of maximum update/downdate. Valid values: * 2, 4, or 8. A value < 2 is set to 2, and a * value > 8 is set to 8. It is then rounded up to the next highest * power of 2, if not already a power of 2. Workspace (Xwork, below) of * size nrow-by-maxrank double's is allocated for the update/downdate. * If an update/downdate of rank-k is requested, with k > maxrank, * it is done in steps of maxrank. Default: 8, which is fastest. * Memory usage can be reduced by setting maxrank to 2 or 4. */ double supernodal_switch ; /* supernodal vs simplicial factorization */ int supernodal ; /* If Common->supernodal <= CHOLMOD_SIMPLICIAL * (0) then cholmod_analyze performs a * simplicial analysis. If >= CHOLMOD_SUPERNODAL (2), then a supernodal * analysis is performed. If == CHOLMOD_AUTO (1) and * flop/nnz(L) < Common->supernodal_switch, then a simplicial analysis * is done. A supernodal analysis done otherwise. * Default: CHOLMOD_AUTO. Default supernodal_switch = 40 */ int final_asis ; /* If TRUE, then ignore the other final_* parameters * (except for final_pack). * The factor is left as-is when done. Default: TRUE.*/ int final_super ; /* If TRUE, leave a factor in supernodal form when * supernodal factorization is finished. If FALSE, * then convert to a simplicial factor when done. * Default: TRUE */ int final_ll ; /* If TRUE, leave factor in LL' form when done. * Otherwise, leave in LDL' form. Default: FALSE */ int final_pack ; /* If TRUE, pack the columns when done. If TRUE, and * cholmod_factorize is called with a symbolic L, L is * allocated with exactly the space required, using L->ColCount. If you * plan on modifying the factorization, set Common->final_pack to FALSE, * and each column will be given a little extra slack space for future * growth in fill-in due to updates. Default: TRUE */ int final_monotonic ; /* If TRUE, ensure columns are monotonic when done. * Default: TRUE */ int final_resymbol ;/* if cholmod_factorize performed a supernodal * factorization, final_resymbol is true, and * final_super is FALSE (convert a simplicial numeric factorization), * then numerically zero entries that resulted from relaxed supernodal * amalgamation are removed. This does not remove entries that are zero * due to exact numeric cancellation, since doing so would break the * update/downdate rowadd/rowdel routines. Default: FALSE. */ /* supernodal relaxed amalgamation parameters: */ double zrelax [3] ; size_t nrelax [3] ; /* Let ns be the total number of columns in two adjacent supernodes. * Let z be the fraction of zero entries in the two supernodes if they * are merged (z includes zero entries from prior amalgamations). The * two supernodes are merged if: * (ns <= nrelax [0]) || (no new zero entries added) || * (ns <= nrelax [1] && z < zrelax [0]) || * (ns <= nrelax [2] && z < zrelax [1]) || (z < zrelax [2]) * * Default parameters result in the following rule: * (ns <= 4) || (no new zero entries added) || * (ns <= 16 && z < 0.8) || (ns <= 48 && z < 0.1) || (z < 0.05) */ int prefer_zomplex ; /* X = cholmod_solve (sys, L, B, Common) computes * x=A\b or solves a related system. If L and B are * both real, then X is real. Otherwise, X is returned as * CHOLMOD_COMPLEX if Common->prefer_zomplex is FALSE, or * CHOLMOD_ZOMPLEX if Common->prefer_zomplex is TRUE. This parameter * is needed because there is no supernodal zomplex L. Suppose the * caller wants all complex matrices to be stored in zomplex form * (MATLAB, for example). A supernodal L is returned in complex form * if A is zomplex. B can be real, and thus X = cholmod_solve (L,B) * should return X as zomplex. This cannot be inferred from the input * arguments L and B. Default: FALSE, since all data types are * supported in CHOLMOD_COMPLEX form and since this is the native type * of LAPACK and the BLAS. Note that the MATLAB/cholmod.c mexFunction * sets this parameter to TRUE, since MATLAB matrices are in * CHOLMOD_ZOMPLEX form. */ int prefer_upper ; /* cholmod_analyze and cholmod_factorize work * fastest when a symmetric matrix is stored in * upper triangular form when a fill-reducing ordering is used. In * MATLAB, this corresponds to how x=A\b works. When the matrix is * ordered as-is, they work fastest when a symmetric matrix is in lower * triangular form. In MATLAB, R=chol(A) does the opposite. This * parameter affects only how cholmod_read returns a symmetric matrix. * If TRUE (the default case), a symmetric matrix is always returned in * upper-triangular form (A->stype = 1). */ int quick_return_if_not_posdef ; /* if TRUE, the supernodal numeric * factorization will return quickly if * the matrix is not positive definite. Default: FALSE. */ /* ---------------------------------------------------------------------- */ /* printing and error handling options */ /* ---------------------------------------------------------------------- */ int print ; /* print level. Default: 3 */ int precise ; /* if TRUE, print 16 digits. Otherwise print 5 */ int (*print_function) (const char *, ...) ; /* pointer to printf */ int try_catch ; /* if TRUE, then ignore errors; CHOLMOD is in the middle * of a try/catch block. No error message is printed * and the Common->error_handler function is not called. */ void (*error_handler) (int status, const char *file, int line, const char *message) ; /* Common->error_handler is the user's error handling routine. If not * NULL, this routine is called if an error occurs in CHOLMOD. status * can be CHOLMOD_OK (0), negative for a fatal error, and positive for * a warning. file is a string containing the name of the source code * file where the error occured, and line is the line number in that * file. message is a string describing the error in more detail. */ /* ---------------------------------------------------------------------- */ /* ordering options */ /* ---------------------------------------------------------------------- */ /* The cholmod_analyze routine can try many different orderings and select * the best one. It can also try one ordering method multiple times, with * different parameter settings. The default is to use three orderings, * the user's permutation (if provided), AMD which is the fastest ordering * and generally gives good fill-in, and METIS. CHOLMOD's nested dissection * (METIS with a constrained AMD) usually gives a better ordering than METIS * alone (by about 5% to 10%) but it takes more time. * * If you know the method that is best for your matrix, set Common->nmethods * to 1 and set Common->method [0] to the set of parameters for that method. * If you set it to 1 and do not provide a permutation, then only AMD will * be called. * * If METIS is not available, the default # of methods tried is 2 (the user * permutation, if any, and AMD). * * To try other methods, set Common->nmethods to the number of methods you * want to try. The suite of default methods and their parameters is * described in the cholmod_defaults routine, and summarized here: * * Common->method [i]: * i = 0: user-provided ordering (cholmod_analyze_p only) * i = 1: AMD (for both A and A*A') * i = 2: METIS * i = 3: CHOLMOD's nested dissection (NESDIS), default parameters * i = 4: natural * i = 5: NESDIS with nd_small = 20000 * i = 6: NESDIS with nd_small = 4, no constrained minimum degree * i = 7: NESDIS with no dense node removal * i = 8: AMD for A, COLAMD for A*A' * * You can modify the suite of methods you wish to try by modifying * Common.method [...] after calling cholmod_start or cholmod_defaults. * * For example, to use AMD, followed by a weighted postordering: * * Common->nmethods = 1 ; * Common->method [0].ordering = CHOLMOD_AMD ; * Common->postorder = TRUE ; * * To use the natural ordering (with no postordering): * * Common->nmethods = 1 ; * Common->method [0].ordering = CHOLMOD_NATURAL ; * Common->postorder = FALSE ; * * If you are going to factorize hundreds or more matrices with the same * nonzero pattern, you may wish to spend a great deal of time finding a * good permutation. In this case, try setting Common->nmethods to 9. * The time spent in cholmod_analysis will be very high, but you need to * call it only once. * * cholmod_analyze sets Common->current to a value between 0 and nmethods-1. * Each ordering method uses the set of options defined by this parameter. */ int nmethods ; /* The number of ordering methods to try. Default: 0. * nmethods = 0 is a special case. cholmod_analyze * will try the user-provided ordering (if given) and AMD. Let fl and * lnz be the flop count and nonzeros in L from AMD's ordering. Let * anz be the number of nonzeros in the upper or lower triangular part * of the symmetric matrix A. If fl/lnz < 500 or lnz/anz < 5, then this * is a good ordering, and METIS is not attempted. Otherwise, METIS is * tried. The best ordering found is used. If nmethods > 0, the * methods used are given in the method[ ] array, below. The first * three methods in the default suite of orderings is (1) use the given * permutation (if provided), (2) use AMD, and (3) use METIS. Maximum * allowed value is CHOLMOD_MAXMETHODS. */ int current ; /* The current method being tried. Default: 0. Valid * range is 0 to nmethods-1. */ int selected ; /* The best method found. */ /* The suite of ordering methods and parameters: */ struct cholmod_method_struct { /* statistics for this method */ double lnz ; /* nnz(L) excl. zeros from supernodal amalgamation, * for a "pure" L */ double fl ; /* flop count for a "pure", real simplicial LL' * factorization, with no extra work due to * amalgamation. Subtract n to get the LDL' flop count. Multiply * by about 4 if the matrix is complex or zomplex. */ /* ordering method parameters */ double prune_dense ;/* dense row/col control for AMD, SYMAMD, CSYMAMD, * and NESDIS (cholmod_nested_dissection). For a * symmetric n-by-n matrix, rows/columns with more than * MAX (16, prune_dense * sqrt (n)) entries are removed prior to * ordering. They appear at the end of the re-ordered matrix. * * If prune_dense < 0, only completely dense rows/cols are removed. * * This paramater is also the dense column control for COLAMD and * CCOLAMD. For an m-by-n matrix, columns with more than * MAX (16, prune_dense * sqrt (MIN (m,n))) entries are removed prior * to ordering. They appear at the end of the re-ordered matrix. * CHOLMOD factorizes A*A', so it calls COLAMD and CCOLAMD with A', * not A. Thus, this parameter affects the dense *row* control for * CHOLMOD's matrix, and the dense *column* control for COLAMD and * CCOLAMD. * * Removing dense rows and columns improves the run-time of the * ordering methods. It has some impact on ordering quality * (usually minimal, sometimes good, sometimes bad). * * Default: 10. */ double prune_dense2 ;/* dense row control for COLAMD and CCOLAMD. * Rows with more than MAX (16, dense2 * sqrt (n)) * for an m-by-n matrix are removed prior to ordering. CHOLMOD's * matrix is transposed before ordering it with COLAMD or CCOLAMD, * so this controls the dense *columns* of CHOLMOD's matrix, and * the dense *rows* of COLAMD's or CCOLAMD's matrix. * * If prune_dense2 < 0, only completely dense rows/cols are removed. * * Default: -1. Note that this is not the default for COLAMD and * CCOLAMD. -1 is best for Cholesky. 10 is best for LU. */ double nd_oksep ; /* in NESDIS, when a node separator is computed, it * discarded if nsep >= nd_oksep*n, where nsep is * the number of nodes in the separator, and n is the size of the * graph being cut. Valid range is 0 to 1. If 1 or greater, the * separator is discarded if it consists of the entire graph. * Default: 1 */ double other1 [4] ; /* future expansion */ size_t nd_small ; /* do not partition graphs with fewer nodes than * nd_small, in NESDIS. Default: 200 (same as * METIS) */ size_t other2 [4] ; /* future expansion */ int aggressive ; /* Aggresive absorption in AMD, COLAMD, SYMAMD, * CCOLAMD, and CSYMAMD. Default: TRUE */ int order_for_lu ; /* CCOLAMD can be optimized to produce an ordering * for LU or Cholesky factorization. CHOLMOD only * performs a Cholesky factorization. However, you may wish to use * CHOLMOD as an interface for CCOLAMD but use it for your own LU * factorization. In this case, order_for_lu should be set to FALSE. * When factorizing in CHOLMOD itself, you should *** NEVER *** set * this parameter FALSE. Default: TRUE. */ int nd_compress ; /* If TRUE, compress the graph and subgraphs before * partitioning them in NESDIS. Default: TRUE */ int nd_camd ; /* If 1, follow the nested dissection ordering * with a constrained minimum degree ordering that * respects the partitioning just found (using CAMD). If 2, use * CSYMAMD instead. If you set nd_small very small, you may not need * this ordering, and can save time by setting it to zero (no * constrained minimum degree ordering). Default: 1. */ int nd_components ; /* The nested dissection ordering finds a node * separator that splits the graph into two parts, * which may be unconnected. If nd_components is TRUE, each of * these connected components is split independently. If FALSE, * each part is split as a whole, even if it consists of more than * one connected component. Default: FALSE */ /* fill-reducing ordering to use */ int ordering ; size_t other3 [4] ; /* future expansion */ } method [CHOLMOD_MAXMETHODS + 1] ; int postorder ; /* If TRUE, cholmod_analyze follows the ordering with a * weighted postorder of the elimination tree. Improves * supernode amalgamation. Does not affect fundamental nnz(L) and * flop count. Default: TRUE. */ /* ---------------------------------------------------------------------- */ /* memory management routines */ /* ---------------------------------------------------------------------- */ void *(*malloc_memory) (size_t) ; /* pointer to malloc */ void *(*realloc_memory) (void *, size_t) ; /* pointer to realloc */ void (*free_memory) (void *) ; /* pointer to free */ void *(*calloc_memory) (size_t, size_t) ; /* pointer to calloc */ /* ---------------------------------------------------------------------- */ /* routines for complex arithmetic */ /* ---------------------------------------------------------------------- */ int (*complex_divide) (double ax, double az, double bx, double bz, double *cx, double *cz) ; /* flag = complex_divide (ax, az, bx, bz, &cx, &cz) computes the complex * division c = a/b, where ax and az hold the real and imaginary part * of a, and b and c are stored similarly. flag is returned as 1 if * a divide-by-zero occurs, or 0 otherwise. By default, the function * pointer Common->complex_divide is set equal to cholmod_divcomplex. */ double (*hypotenuse) (double x, double y) ; /* s = hypotenuse (x,y) computes s = sqrt (x*x + y*y), but does so more * accurately. By default, the function pointer Common->hypotenuse is * set equal to cholmod_hypot. See also the hypot function in the C99 * standard, which has an identical syntax and function. If you have * a C99-compliant compiler, you can set Common->hypotenuse = hypot. */ /* ---------------------------------------------------------------------- */ /* METIS workarounds */ /* ---------------------------------------------------------------------- */ double metis_memory ; /* This is a parameter for CHOLMOD's interface to * METIS, not a parameter to METIS itself. METIS * uses an amount of memory that is difficult to estimate precisely * beforehand. If it runs out of memory, it terminates your program. * All routines in CHOLMOD except for CHOLMOD's interface to METIS * return an error status and safely return to your program if they run * out of memory. To mitigate this problem, the CHOLMOD interface * can allocate a single block of memory equal in size to an empirical * upper bound of METIS's memory usage times the Common->metis_memory * parameter, and then immediately free it. It then calls METIS. If * this pre-allocation fails, it is possible that METIS will fail as * well, and so CHOLMOD returns with an out-of-memory condition without * calling METIS. * * METIS_NodeND (used in the CHOLMOD_METIS ordering option) with its * default parameter settings typically uses about (4*nz+40n+4096) * times sizeof(int) memory, where nz is equal to the number of entries * in A for the symmetric case or AA' if an unsymmetric matrix is * being ordered (where nz includes both the upper and lower parts * of A or AA'). The observed "upper bound" (with 2 exceptions), * measured in an instrumented copy of METIS 4.0.1 on thousands of * matrices, is (10*nz+50*n+4096) * sizeof(int). Two large matrices * exceeded this bound, one by almost a factor of 2 (Gupta/gupta2). * * If your program is terminated by METIS, try setting metis_memory to * 2.0, or even higher if needed. By default, CHOLMOD assumes that METIS * does not have this problem (so that CHOLMOD will work correctly when * this issue is fixed in METIS). Thus, the default value is zero. * This work-around is not guaranteed anyway. * * If a matrix exceeds this predicted memory usage, AMD is attempted * instead. It, too, may run out of memory, but if it does so it will * not terminate your program. */ double metis_dswitch ; /* METIS_NodeND in METIS 4.0.1 gives a seg */ size_t metis_nswitch ; /* fault with one matrix of order n = 3005 and * nz = 6,036,025. This is a very dense graph. * The workaround is to use AMD instead of METIS for matrices of dimension * greater than Common->metis_nswitch (default 3000) or more and with * density of Common->metis_dswitch (default 0.66) or more. * cholmod_nested_dissection has no problems with the same matrix, even * though it uses METIS_NodeComputeSeparator on this matrix. If this * seg fault does not affect you, set metis_nswitch to zero or less, * and CHOLMOD will not switch to AMD based just on the density of the * matrix (it will still switch to AMD if the metis_memory parameter * causes the switch). */ /* ---------------------------------------------------------------------- */ /* workspace */ /* ---------------------------------------------------------------------- */ /* CHOLMOD has several routines that take less time than the size of * workspace they require. Allocating and initializing the workspace would * dominate the run time, unless workspace is allocated and initialized * just once. CHOLMOD allocates this space when needed, and holds it here * between calls to CHOLMOD. cholmod_start sets these pointers to NULL * (which is why it must be the first routine called in CHOLMOD). * cholmod_finish frees the workspace (which is why it must be the last * call to CHOLMOD). */ size_t nrow ; /* size of Flag and Head */ UF_long mark ; /* mark value for Flag array */ size_t iworksize ; /* size of Iwork. Upper bound: 6*nrow+ncol */ size_t xworksize ; /* size of Xwork, in bytes. * maxrank*nrow*sizeof(double) for update/downdate. * 2*nrow*sizeof(double) otherwise */ /* initialized workspace: contents needed between calls to CHOLMOD */ void *Flag ; /* size nrow, an integer array. Kept cleared between * calls to cholmod rouines (Flag [i] < mark) */ void *Head ; /* size nrow+1, an integer array. Kept cleared between * calls to cholmod routines (Head [i] = EMPTY) */ void *Xwork ; /* a double array. Its size varies. It is nrow for * most routines (cholmod_rowfac, cholmod_add, * cholmod_aat, cholmod_norm, cholmod_ssmult) for the real case, twice * that when the input matrices are complex or zomplex. It is of size * 2*nrow for cholmod_rowadd and cholmod_rowdel. For cholmod_updown, * its size is maxrank*nrow where maxrank is 2, 4, or 8. Kept cleared * between calls to cholmod (set to zero). */ /* uninitialized workspace, contents not needed between calls to CHOLMOD */ void *Iwork ; /* size iworksize, 2*nrow+ncol for most routines, * up to 6*nrow+ncol for cholmod_analyze. */ int itype ; /* If CHOLMOD_LONG, Flag, Head, and Iwork are UF_long. * Otherwise all three arrays are int. */ int dtype ; /* double or float */ /* Common->itype and Common->dtype are used to define the types of all * sparse matrices, triplet matrices, dense matrices, and factors * created using this Common struct. The itypes and dtypes of all * parameters to all CHOLMOD routines must match. */ int no_workspace_reallocate ; /* this is an internal flag, used as a * precaution by cholmod_analyze. It is normally false. If true, * cholmod_allocate_work is not allowed to reallocate any workspace; * they must use the existing workspace in Common (Iwork, Flag, Head, * and Xwork). Added for CHOLMOD v1.1 */ /* ---------------------------------------------------------------------- */ /* statistics */ /* ---------------------------------------------------------------------- */ /* fl and lnz are set only in cholmod_analyze and cholmod_rowcolcounts, * in the Cholesky modudle. modfl is set only in the Modify module. */ int status ; /* error code */ double fl ; /* LL' flop count from most recent analysis */ double lnz ; /* fundamental nz in L */ double anz ; /* nonzeros in tril(A) if A is symmetric/lower, * triu(A) if symmetric/upper, or tril(A*A') if * unsymmetric, in last call to cholmod_analyze. */ double modfl ; /* flop count from most recent update/downdate/ * rowadd/rowdel (excluding flops to modify the * solution to Lx=b, if computed) */ size_t malloc_count ; /* # of objects malloc'ed minus the # free'd*/ size_t memory_usage ; /* peak memory usage in bytes */ size_t memory_inuse ; /* current memory usage in bytes */ double nrealloc_col ; /* # of column reallocations */ double nrealloc_factor ;/* # of factor reallocations due to col. reallocs */ double ndbounds_hit ; /* # of times diagonal modified by dbound */ double rowfacfl ; /* # of flops in last call to cholmod_rowfac */ double aatfl ; /* # of flops to compute A(:,f)*A(:,f)' */ /* ---------------------------------------------------------------------- */ /* future expansion */ /* ---------------------------------------------------------------------- */ /* To allow CHOLMOD to be updated without recompiling the user application, * additional space is set aside here for future statistics, parameters, * and workspace. Note: additional entries were added in v1.1 to the * method array, above, and thus v1.0 and v1.1 are not binary compatible. * * v1.1 to the current version are binary compatible. */ /* ---------------------------------------------------------------------- */ double other1 [10] ; double SPQR_xstat [4] ; /* for SuiteSparseQR statistics */ /* SuiteSparseQR control parameters: */ double SPQR_grain ; /* task size is >= max (total flops / grain) */ double SPQR_small ; /* task size is >= small */ /* ---------------------------------------------------------------------- */ UF_long SPQR_istat [10] ; /* for SuiteSparseQR statistics */ UF_long other2 [6] ; /* reduced from size 16 in v1.6 */ /* ---------------------------------------------------------------------- */ int other3 [10] ; /* reduced from size 16 in v1.1. */ int prefer_binary ; /* cholmod_read_triplet converts a symmetric * pattern-only matrix into a real matrix. If * prefer_binary is FALSE, the diagonal entries are set to 1 + the degree * of the row/column, and off-diagonal entries are set to -1 (resulting * in a positive definite matrix if the diagonal is zero-free). Most * symmetric patterns are the pattern a positive definite matrix. If * this parameter is TRUE, then the matrix is returned with a 1 in each * entry, instead. Default: FALSE. Added in v1.3. */ /* control parameter (added for v1.2): */ int default_nesdis ; /* Default: FALSE. If FALSE, then the default * ordering strategy (when Common->nmethods == 0) * is to try the given ordering (if present), AMD, and then METIS if AMD * reports high fill-in. If Common->default_nesdis is TRUE then NESDIS * is used instead in the default strategy. */ /* statistic (added for v1.2): */ int called_nd ; /* TRUE if the last call to * cholmod_analyze called NESDIS or METIS. */ int blas_ok ; /* FALSE if BLAS int overflow; TRUE otherwise */ /* SuiteSparseQR control parameters: */ int SPQR_shrink ; /* controls stack realloc method */ int SPQR_nthreads ; /* number of TBB threads, 0 = auto */ /* ---------------------------------------------------------------------- */ size_t other4 [16] ; /* ---------------------------------------------------------------------- */ void *other5 [16] ; } cholmod_common ; // in ../../src/CHOLMOD/Include/cholmod_core.h skip forward to - line 1114 : /* A sparse matrix stored in compressed-column form. */ typedef struct cholmod_sparse_struct { size_t nrow ; /* the matrix is nrow-by-ncol */ size_t ncol ; size_t nzmax ; /* maximum number of entries in the matrix */ /* pointers to int or UF_long: */ void *p ; /* p [0..ncol], the column pointers */ void *i ; /* i [0..nzmax-1], the row indices */ /* for unpacked matrices only: */ void *nz ; /* nz [0..ncol-1], the # of nonzeros in each col. In * packed form, the nonzero pattern of column j is in * A->i [A->p [j] ... A->p [j+1]-1]. In unpacked form, column j is in * A->i [A->p [j] ... A->p [j]+A->nz[j]-1] instead. In both cases, the * numerical values (if present) are in the corresponding locations in * the array x (or z if A->xtype is CHOLMOD_ZOMPLEX). */ /* pointers to double or float: */ void *x ; /* size nzmax or 2*nzmax, if present */ void *z ; /* size nzmax, if present */ int stype ; /* Describes what parts of the matrix are considered: * * 0: matrix is "unsymmetric": use both upper and lower triangular parts * (the matrix may actually be symmetric in pattern and value, but * both parts are explicitly stored and used). May be square or * rectangular. * >0: matrix is square and symmetric, use upper triangular part. * Entries in the lower triangular part are ignored. * <0: matrix is square and symmetric, use lower triangular part. * Entries in the upper triangular part are ignored. * * Note that stype>0 and stype<0 are different for cholmod_sparse and * cholmod_triplet. See the cholmod_triplet data structure for more * details. */ int itype ; /* CHOLMOD_INT: p, i, and nz are int. * CHOLMOD_INTLONG: p is UF_long, i and nz are int. * CHOLMOD_LONG: p, i, and nz are UF_long. */ int xtype ; /* pattern, real, complex, or zomplex */ int dtype ; /* x and z are double or float */ int sorted ; /* TRUE if columns are sorted, FALSE otherwise */ int packed ; /* TRUE if packed (nz ignored), FALSE if unpacked * (nz is required) */ } cholmod_sparse ; // in ../../src/CHOLMOD/Include/cholmod_core.h skip forward to - line 1554 : /* A symbolic and numeric factorization, either simplicial or supernodal. * In all cases, the row indices in the columns of L are kept sorted. */ typedef struct cholmod_factor_struct { /* ---------------------------------------------------------------------- */ /* for both simplicial and supernodal factorizations */ /* ---------------------------------------------------------------------- */ size_t n ; /* L is n-by-n */ size_t minor ; /* If the factorization failed, L->minor is the column * at which it failed (in the range 0 to n-1). A value * of n means the factorization was successful or * the matrix has not yet been factorized. */ /* ---------------------------------------------------------------------- */ /* symbolic ordering and analysis */ /* ---------------------------------------------------------------------- */ void *Perm ; /* size n, permutation used */ void *ColCount ; /* size n, column counts for simplicial L */ void *IPerm ; /* size n, inverse permutation. Only created by * cholmod_solve2 if Bset is used. */ /* ---------------------------------------------------------------------- */ /* simplicial factorization */ /* ---------------------------------------------------------------------- */ size_t nzmax ; /* size of i and x */ void *p ; /* p [0..ncol], the column pointers */ void *i ; /* i [0..nzmax-1], the row indices */ void *x ; /* x [0..nzmax-1], the numerical values */ void *z ; void *nz ; /* nz [0..ncol-1], the # of nonzeros in each column. * i [p [j] ... p [j]+nz[j]-1] contains the row indices, * and the numerical values are in the same locatins * in x. The value of i [p [k]] is always k. */ void *next ; /* size ncol+2. next [j] is the next column in i/x */ void *prev ; /* size ncol+2. prev [j] is the prior column in i/x. * head of the list is ncol+1, and the tail is ncol. */ /* ---------------------------------------------------------------------- */ /* supernodal factorization */ /* ---------------------------------------------------------------------- */ /* Note that L->x is shared with the simplicial data structure. L->x has * size L->nzmax for a simplicial factor, and size L->xsize for a supernodal * factor. */ size_t nsuper ; /* number of supernodes */ size_t ssize ; /* size of s, integer part of supernodes */ size_t xsize ; /* size of x, real part of supernodes */ size_t maxcsize ; /* size of largest update matrix */ size_t maxesize ; /* max # of rows in supernodes, excl. triangular part */ void *super ; /* size nsuper+1, first col in each supernode */ void *pi ; /* size nsuper+1, pointers to integer patterns */ void *px ; /* size nsuper+1, pointers to real parts */ void *s ; /* size ssize, integer part of supernodes */ /* ---------------------------------------------------------------------- */ /* factorization type */ /* ---------------------------------------------------------------------- */ int ordering ; /* ordering method used */ int is_ll ; /* TRUE if LL', FALSE if LDL' */ int is_super ; /* TRUE if supernodal, FALSE if simplicial */ int is_monotonic ; /* TRUE if columns of L appear in order 0..n-1. * Only applicable to simplicial numeric types. */ /* There are 8 types of factor objects that cholmod_factor can represent * (only 6 are used): * * Numeric types (xtype is not CHOLMOD_PATTERN) * -------------------------------------------- * * simplicial LDL': (is_ll FALSE, is_super FALSE). Stored in compressed * column form, using the simplicial components above (nzmax, p, i, * x, z, nz, next, and prev). The unit diagonal of L is not stored, * and D is stored in its place. There are no supernodes. * * simplicial LL': (is_ll TRUE, is_super FALSE). Uses the same storage * scheme as the simplicial LDL', except that D does not appear. * The first entry of each column of L is the diagonal entry of * that column of L. * * supernodal LDL': (is_ll FALSE, is_super TRUE). Not used. * FUTURE WORK: add support for supernodal LDL' * * supernodal LL': (is_ll TRUE, is_super TRUE). A supernodal factor, * using the supernodal components described above (nsuper, ssize, * xsize, maxcsize, maxesize, super, pi, px, s, x, and z). * * * Symbolic types (xtype is CHOLMOD_PATTERN) * ----------------------------------------- * * simplicial LDL': (is_ll FALSE, is_super FALSE). Nothing is present * except Perm and ColCount. * * simplicial LL': (is_ll TRUE, is_super FALSE). Identical to the * simplicial LDL', except for the is_ll flag. * * supernodal LDL': (is_ll FALSE, is_super TRUE). Not used. * FUTURE WORK: add support for supernodal LDL' * * supernodal LL': (is_ll TRUE, is_super TRUE). A supernodal symbolic * factorization. The simplicial symbolic information is present * (Perm and ColCount), as is all of the supernodal factorization * except for the numerical values (x and z). */ int itype ; /* The integer arrays are Perm, ColCount, p, i, nz, * next, prev, super, pi, px, and s. If itype is * CHOLMOD_INT, all of these are int arrays. * CHOLMOD_INTLONG: p, pi, px are SuiteSparse_long, others int. * CHOLMOD_LONG: all integer arrays are SuiteSparse_long. */ int xtype ; /* pattern, real, complex, or zomplex */ int dtype ; /* x and z double or float */ } cholmod_factor ; // in ../../src/CHOLMOD/Include/cholmod_core.h skip forward to - line 1836 : /* A dense matrix in column-oriented form. It has no itype since it contains * no integers. Entry in row i and column j is located in x [i+j*d]. */ typedef struct cholmod_dense_struct { size_t nrow ; /* the matrix is nrow-by-ncol */ size_t ncol ; size_t nzmax ; /* maximum number of entries in the matrix */ size_t d ; /* leading dimension (d >= nrow must hold) */ void *x ; /* size nzmax or 2*nzmax, if present */ void *z ; /* size nzmax, if present */ int xtype ; /* pattern, real, complex, or zomplex */ int dtype ; /* x and z double or float */ } cholmod_dense ; // in ../../src/CHOLMOD/Include/cholmod_core.h skip forward to - line 2033 : /* A sparse matrix stored in triplet form. */ typedef struct cholmod_triplet_struct { size_t nrow ; /* the matrix is nrow-by-ncol */ size_t ncol ; size_t nzmax ; /* maximum number of entries in the matrix */ size_t nnz ; /* number of nonzeros in the matrix */ void *i ; /* i [0..nzmax-1], the row indices */ void *j ; /* j [0..nzmax-1], the column indices */ void *x ; /* size nzmax or 2*nzmax, if present */ void *z ; /* size nzmax, if present */ int stype ; /* Describes what parts of the matrix are considered: * * 0: matrix is "unsymmetric": use both upper and lower triangular parts * (the matrix may actually be symmetric in pattern and value, but * both parts are explicitly stored and used). May be square or * rectangular. * >0: matrix is square and symmetric. Entries in the lower triangular * part are transposed and added to the upper triangular part when * the matrix is converted to cholmod_sparse form. * <0: matrix is square and symmetric. Entries in the upper triangular * part are transposed and added to the lower triangular part when * the matrix is converted to cholmod_sparse form. * * Note that stype>0 and stype<0 are different for cholmod_sparse and * cholmod_triplet. The reason is simple. You can permute a symmetric * triplet matrix by simply replacing a row and column index with their * new row and column indices, via an inverse permutation. Suppose * P = L->Perm is your permutation, and Pinv is an array of size n. * Suppose a symmetric matrix A is represent by a triplet matrix T, with * entries only in the upper triangular part. Then the following code: * * Ti = T->i ; * Tj = T->j ; * for (k = 0 ; k < n ; k++) Pinv [P [k]] = k ; * for (k = 0 ; k < nz ; k++) Ti [k] = Pinv [Ti [k]] ; * for (k = 0 ; k < nz ; k++) Tj [k] = Pinv [Tj [k]] ; * * creates the triplet form of C=P*A*P'. However, if T initially * contains just the upper triangular entries (T->stype = 1), after * permutation it has entries in both the upper and lower triangular * parts. These entries should be transposed when constructing the * cholmod_sparse form of A, which is what cholmod_triplet_to_sparse * does. Thus: * * C = cholmod_triplet_to_sparse (T, 0, &Common) ; * * will return the matrix C = P*A*P'. * * Since the triplet matrix T is so simple to generate, it's quite easy * to remove entries that you do not want, prior to converting T to the * cholmod_sparse form. So if you include these entries in T, CHOLMOD * assumes that there must be a reason (such as the one above). Thus, * no entry in a triplet matrix is ever ignored. */ int itype ; /* CHOLMOD_LONG: i and j are SuiteSparse_long. Otherwise int */ int xtype ; /* pattern, real, complex, or zomplex */ int dtype ; /* x and z are double or float */ } cholmod_triplet ; // -------- our (Matrix) short and const_ forms of of the pointers : typedef cholmod_common* CHM_CM; typedef cholmod_dense* CHM_DN; typedef const cholmod_dense* const_CHM_DN; typedef cholmod_factor* CHM_FR; typedef const cholmod_factor* const_CHM_FR; typedef cholmod_sparse* CHM_SP; typedef const cholmod_sparse* const_CHM_SP; typedef cholmod_triplet* CHM_TR; typedef const cholmod_triplet* const_CHM_TR; // --------- Matrix ("M_") R ("R_") pkg routines "re-exported": --------------- int M_R_cholmod_start(CHM_CM); void M_R_cholmod_error(int status, const char *file, int line, const char *message); int M_cholmod_finish(CHM_CM); CHM_SP M_cholmod_allocate_sparse(size_t nrow, size_t ncol, size_t nzmax, int sorted, int packed, int stype, int xtype, CHM_CM); int M_cholmod_free_factor(CHM_FR *L, CHM_CM); int M_cholmod_free_dense(CHM_DN *A, CHM_CM); int M_cholmod_free_sparse(CHM_SP *A, CHM_CM); int M_cholmod_free_triplet(CHM_TR *T, CHM_CM); long M_cholmod_nnz(const_CHM_SP, CHM_CM); CHM_SP M_cholmod_speye(size_t nrow, size_t ncol, int xtype, CHM_CM); CHM_SP M_cholmod_transpose(const_CHM_SP, int values, CHM_CM); int M_cholmod_sort(CHM_SP A, CHM_CM); CHM_SP M_cholmod_vertcat(const_CHM_SP, const_CHM_SP, int values, CHM_CM); CHM_SP M_cholmod_copy(const_CHM_SP, int stype, int mode, CHM_CM); CHM_SP M_cholmod_add(const_CHM_SP, const_CHM_SP, double alpha [2], double beta [2], int values, int sorted, CHM_CM); // from ../../src/CHOLMOD/Include/cholmod_cholesky.h - line 178 : #define CHOLMOD_A 0 /* solve Ax=b */ #define CHOLMOD_LDLt 1 /* solve LDL'x=b */ #define CHOLMOD_LD 2 /* solve LDx=b */ #define CHOLMOD_DLt 3 /* solve DL'x=b */ #define CHOLMOD_L 4 /* solve Lx=b */ #define CHOLMOD_Lt 5 /* solve L'x=b */ #define CHOLMOD_D 6 /* solve Dx=b */ #define CHOLMOD_P 7 /* permute x=Px */ #define CHOLMOD_Pt 8 /* permute x=P'x */ CHM_DN M_cholmod_solve(int, const_CHM_FR, const_CHM_DN, CHM_CM); CHM_SP M_cholmod_spsolve(int, const_CHM_FR, const_CHM_SP, CHM_CM); int M_cholmod_sdmult(const_CHM_SP, int, const double*, const double*, const_CHM_DN, CHM_DN Y, CHM_CM); CHM_SP M_cholmod_ssmult(const_CHM_SP, const_CHM_SP, int, int, int, CHM_CM); int M_cholmod_factorize(const_CHM_SP, CHM_FR L, CHM_CM); int M_cholmod_factorize_p(const_CHM_SP, double *beta, int *fset, size_t fsize, CHM_FR L, CHM_CM); CHM_SP M_cholmod_copy_sparse(const_CHM_SP, CHM_CM); CHM_DN M_cholmod_copy_dense(const_CHM_DN, CHM_CM); CHM_SP M_cholmod_aat(const_CHM_SP, int *fset, size_t fsize, int mode, CHM_CM); int M_cholmod_band_inplace(CHM_SP A, int k1, int k2, int mode, CHM_CM); CHM_SP M_cholmod_add(const_CHM_SP, const_CHM_SP, double alpha[2], double beta[2], int values, int sorted, CHM_CM); CHM_DN M_cholmod_allocate_dense(size_t nrow, size_t ncol, size_t d, int xtype, CHM_CM); CHM_FR M_cholmod_analyze(const_CHM_SP, CHM_CM); CHM_FR M_cholmod_analyze_p(const_CHM_SP, int *Perm, int *fset, size_t fsize, CHM_CM); int M_cholmod_change_factor(int to_xtype, int to_ll, int to_super, int to_packed, int to_monotonic, CHM_FR L, CHM_CM); CHM_FR M_cholmod_copy_factor(const_CHM_FR, CHM_CM); CHM_SP M_cholmod_factor_to_sparse(const_CHM_FR, CHM_CM); CHM_SP M_cholmod_dense_to_sparse(const_CHM_DN, int values, CHM_CM); int M_cholmod_defaults (CHM_CM); CHM_SP M_cholmod_triplet_to_sparse(const cholmod_triplet*, int nzmax, CHM_CM); CHM_SP M_cholmod_submatrix(const_CHM_SP, int *rset, int rsize, int *cset, int csize, int values, int sorted, CHM_CM); CHM_TR M_cholmod_sparse_to_triplet(const_CHM_SP, CHM_CM); CHM_DN M_cholmod_sparse_to_dense(const_CHM_SP, CHM_CM); CHM_TR M_cholmod_allocate_triplet (size_t nrow, size_t ncol, size_t nzmax, int stype, int xtype, CHM_CM); // from ../../src/CHOLMOD/Include/cholmod_matrixops.h - line 107 : /* scaling modes, selected by the scale input parameter: */ #define CHOLMOD_SCALAR 0 /* A = s*A */ #define CHOLMOD_ROW 1 /* A = diag(s)*A */ #define CHOLMOD_COL 2 /* A = A*diag(s) */ #define CHOLMOD_SYM 3 /* A = diag(s)*A*diag(s) */ int M_cholmod_scale(const_CHM_DN, int scale, CHM_SP, CHM_CM); #ifdef __cplusplus } #endif #endif /* MATRIX_CHOLMOD_H */ Matrix/inst/include/Matrix.h0000644000175100001440000000621611641045200015547 0ustar hornikusers#ifndef MATRIX_H #define MATRIX_H #include #include #include "cholmod.h" //---> M_cholmod_*() declarations #ifdef __cplusplus extern "C" { // and bool is defined #else # define bool Rboolean #endif #ifdef HAVE_VISIBILITY_ATTRIBUTE # define attribute_hidden __attribute__ ((visibility ("hidden"))) #else # define attribute_hidden #endif // Copied from ../../src/Mutils.h ---------------------------------------- #define MATRIX_VALID_dense \ "dmatrix", "dgeMatrix", \ "lmatrix", "lgeMatrix", \ "nmatrix", "ngeMatrix", \ "zmatrix", "zgeMatrix" #define MATRIX_VALID_Csparse \ "dgCMatrix", "dsCMatrix", "dtCMatrix", \ "lgCMatrix", "lsCMatrix", "ltCMatrix", \ "ngCMatrix", "nsCMatrix", "ntCMatrix", \ "zgCMatrix", "zsCMatrix", "ztCMatrix" #define MATRIX_VALID_Tsparse \ "dgTMatrix", "dsTMatrix", "dtTMatrix", \ "lgTMatrix", "lsTMatrix", "ltTMatrix", \ "ngTMatrix", "nsTMatrix", "ntTMatrix", \ "zgTMatrix", "zsTMatrix", "ztTMatrix" #define MATRIX_VALID_Rsparse \ "dgRMatrix", "dsRMatrix", "dtRMatrix", \ "lgRMatrix", "lsRMatrix", "ltRMatrix", \ "ngRMatrix", "nsRMatrix", "ntRMatrix", \ "zgRMatrix", "zsRMatrix", "ztRMatrix" #define MATRIX_VALID_CHMfactor "dCHMsuper", "dCHMsimpl", "nCHMsuper", "nCHMsimpl" CHM_SP M_as_cholmod_sparse (CHM_SP ans, SEXP x, Rboolean check_Udiag, Rboolean sort_in_place); CHM_TR M_as_cholmod_triplet(CHM_TR ans, SEXP x, Rboolean check_Udiag); CHM_DN M_as_cholmod_dense(CHM_DN ans, SEXP x); CHM_DN M_numeric_as_chm_dense(CHM_DN ans, double *v, int nr, int nc); CHM_FR M_as_cholmod_factor(CHM_FR ans, SEXP x); double M_chm_factor_ldetL2(const_CHM_FR f); CHM_FR M_chm_factor_update(CHM_FR f, const_CHM_SP A, double mult); #define AS_CHM_DN(x) M_as_cholmod_dense((CHM_DN)alloca(sizeof(cholmod_dense)), x ) #define AS_CHM_FR(x) M_as_cholmod_factor((CHM_FR)alloca(sizeof(cholmod_factor)), x ) #define AS_CHM_SP(x) M_as_cholmod_sparse ((CHM_SP)alloca(sizeof(cholmod_sparse)), x, (Rboolean)TRUE, (Rboolean)FALSE) #define AS_CHM_TR(x) M_as_cholmod_triplet((CHM_TR)alloca(sizeof(cholmod_triplet)),x, (Rboolean)TRUE) /* the non-diagU2N-checking versions : */ #define AS_CHM_SP__(x) M_as_cholmod_sparse ((CHM_SP)alloca(sizeof(cholmod_sparse)), x, (Rboolean)FALSE, (Rboolean)FALSE) #define AS_CHM_TR__(x) M_as_cholmod_triplet((CHM_TR)alloca(sizeof(cholmod_triplet)), x, (Rboolean)FALSE) #define N_AS_CHM_DN(x,nr,nc) M_numeric_as_chm_dense((CHM_DN)alloca(sizeof(cholmod_dense)), x , nr, nc ) SEXP M_Csparse_diagU2N(SEXP x); SEXP M_chm_factor_to_SEXP(const_CHM_FR f, int dofree); SEXP M_chm_sparse_to_SEXP(const_CHM_SP a, int dofree, int uploT, int Rkind, const char *diag, SEXP dn); SEXP M_chm_triplet_to_SEXP(const CHM_TR a, int dofree, int uploT, int Rkind, const char* diag, SEXP dn); SEXP M_dpoMatrix_chol(SEXP x); int M_Matrix_check_class_etc(SEXP x, const char **valid); // ./Matrix_stubs.c "illustrative example code" (of the above): bool Matrix_isclass_Csparse(SEXP x); bool Matrix_isclass_triplet(SEXP x); bool Matrix_isclass_dense(SEXP x); bool Matrix_isclass_CHMfactor(SEXP x); /* TODO: Utilities for C level of model_matrix(*, sparse) */ #ifdef __cplusplus } #endif #endif /* MATRIX_H */ Matrix/inst/include/Matrix_stubs.c0000644000175100001440000004477111743530637017012 0ustar hornikusers#include #include #include #include #include "cholmod.h" #include "Matrix.h" #ifdef __cplusplus extern "C" { // and bool is defined #else # define bool Rboolean #endif #ifdef HAVE_VISIBILITY_ATTRIBUTE # define attribute_hidden __attribute__ ((visibility ("hidden"))) #else # define attribute_hidden #endif CHM_DN attribute_hidden M_as_cholmod_dense(CHM_DN ans, SEXP x) { static CHM_DN(*fun)(CHM_DN,SEXP) = NULL; if(fun == NULL) fun = (CHM_DN(*)(CHM_DN,SEXP)) R_GetCCallable("Matrix", "as_cholmod_dense"); return fun(ans, x); } CHM_FR attribute_hidden M_as_cholmod_factor(CHM_FR ans, SEXP x) { static CHM_FR(*fun)(CHM_FR,SEXP) = NULL; if(fun == NULL) fun = (CHM_FR(*)(CHM_FR,SEXP)) R_GetCCallable("Matrix", "as_cholmod_factor"); return fun(ans, x); } CHM_SP attribute_hidden M_as_cholmod_sparse(CHM_SP ans, SEXP x, Rboolean check_Udiag, Rboolean sort_in_place) { static CHM_SP(*fun)(CHM_SP,SEXP,Rboolean,Rboolean)= NULL; if(fun == NULL) fun = (CHM_SP(*)(CHM_SP,SEXP,Rboolean,Rboolean)) R_GetCCallable("Matrix", "as_cholmod_sparse"); return fun(ans, x, check_Udiag, sort_in_place); } CHM_TR attribute_hidden M_as_cholmod_triplet(CHM_TR ans, SEXP x, Rboolean check_Udiag) { static CHM_TR(*fun)(CHM_TR,SEXP,Rboolean)= NULL; if(fun == NULL) fun = (CHM_TR(*)(CHM_TR,SEXP,Rboolean)) R_GetCCallable("Matrix", "as_cholmod_triplet"); return fun(ans, x, check_Udiag); } SEXP attribute_hidden M_Csparse_diagU2N(SEXP x) { static SEXP(*fun)(SEXP) = NULL; if(fun == NULL) fun = (SEXP(*)(SEXP)) R_GetCCallable("Matrix", "Csparse_diagU2N"); return fun(x); } SEXP attribute_hidden M_chm_factor_to_SEXP(const_CHM_FR f, int dofree) { static SEXP(*fun)(const_CHM_FR,int) = NULL; if(fun == NULL) fun = (SEXP(*)(const_CHM_FR,int)) R_GetCCallable("Matrix", "chm_factor_to_SEXP"); return fun(f, dofree); } double attribute_hidden M_chm_factor_ldetL2(const_CHM_FR f) { static double(*fun)(const_CHM_FR) = NULL; if(fun == NULL) fun = (double(*)(const_CHM_FR)) R_GetCCallable("Matrix", "chm_factor_ldetL2"); return fun(f); } CHM_FR attribute_hidden M_chm_factor_update(CHM_FR f, const_CHM_SP A, double mult) { static CHM_FR(*fun)(CHM_FR,const_CHM_SP,double) = NULL; if(fun == NULL) fun = (CHM_FR(*)(CHM_FR,const_CHM_SP,double)) R_GetCCallable("Matrix", "chm_factor_update"); return fun(f, A, mult); } SEXP attribute_hidden M_chm_sparse_to_SEXP(const_CHM_SP a, int dofree, int uploT, int Rkind, const char *diag, SEXP dn) { static SEXP(*fun)(const_CHM_SP,int,int,int,const char*,SEXP) = NULL; if(fun == NULL) fun = (SEXP(*)(const_CHM_SP,int,int,int,const char*,SEXP)) R_GetCCallable("Matrix", "chm_sparse_to_SEXP"); return fun(a, dofree, uploT, Rkind, diag, dn); } SEXP attribute_hidden M_chm_triplet_to_SEXP(const CHM_TR a, int dofree, int uploT, int Rkind, const char *diag, SEXP dn) { static SEXP(*fun)(const CHM_TR,int,int,int,const char*,SEXP) = NULL; if(fun == NULL) fun = (SEXP(*)(const CHM_TR,int,int,int,const char*,SEXP)) R_GetCCallable("Matrix", "chm_triplet_to_SEXP"); return fun(a, dofree, uploT, Rkind, diag, dn); } CHM_SP attribute_hidden M_cholmod_aat(const_CHM_SP A, int *fset, size_t fsize, int mode, CHM_CM Common) { static CHM_SP(*fun)(const_CHM_SP,int*,size_t, int,CHM_CM) = NULL; if(fun == NULL) fun = (CHM_SP(*)(const_CHM_SP,int*,size_t, int,CHM_CM)) R_GetCCallable("Matrix", "cholmod_aat"); return fun(A, fset, fsize, mode, Common); } int attribute_hidden M_cholmod_band_inplace(CHM_SP A, int k1, int k2, int mode, CHM_CM Common) { static int(*fun)(CHM_SP,int,int,int,CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(CHM_SP,int,int,int,CHM_CM)) R_GetCCallable("Matrix", "cholmod_band_inplace"); return fun(A, k1, k2, mode, Common); } CHM_SP attribute_hidden M_cholmod_add(const_CHM_SP A, const_CHM_SP B, double alpha[2], double beta[2], int values, int sorted, CHM_CM Common) { static CHM_SP(*fun)(const_CHM_SP,const_CHM_SP, double*,double*,int,int, CHM_CM) = NULL; if (fun == NULL) fun = (CHM_SP(*)(const_CHM_SP,const_CHM_SP, double*,double*,int,int, CHM_CM)) R_GetCCallable("Matrix", "cholmod_add"); return fun(A, B, alpha, beta, values, sorted, Common); } CHM_DN attribute_hidden M_cholmod_allocate_dense(size_t nrow, size_t ncol, size_t d, int xtype, CHM_CM Common) { static CHM_DN(*fun)(size_t,size_t,size_t, int,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_DN(*)(size_t,size_t,size_t, int,CHM_CM)) R_GetCCallable("Matrix", "cholmod_allocate_dense"); return fun(nrow, ncol, d, xtype, Common); } CHM_SP attribute_hidden M_cholmod_allocate_sparse(size_t nrow, size_t ncol, size_t nzmax, int sorted, int packed, int stype, int xtype, CHM_CM Common) { static CHM_SP(*fun)(size_t,size_t,size_t,int,int, int,int,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_SP(*) (size_t,size_t,size_t,int,int,int,int,CHM_CM)) R_GetCCallable("Matrix", "cholmod_allocate_sparse"); return fun(nrow,ncol,nzmax,sorted,packed,stype,xtype,Common); } CHM_TR attribute_hidden M_cholmod_allocate_triplet(size_t nrow, size_t ncol, size_t nzmax, int stype, int xtype, CHM_CM Common) { static CHM_TR(*fun)(size_t,size_t,size_t, int,int,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_TR(*)(size_t,size_t,size_t,int,int,CHM_CM)) R_GetCCallable("Matrix", "cholmod_allocate_triplet"); return fun(nrow,ncol,nzmax,stype,xtype,Common); } CHM_SP attribute_hidden M_cholmod_triplet_to_sparse(const cholmod_triplet* T, int nzmax, CHM_CM Common) { static CHM_SP(*fun)(const cholmod_triplet*,int,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_SP(*)(const cholmod_triplet*,int,CHM_CM)) R_GetCCallable("Matrix", "cholmod_triplet_to_sparse"); return fun(T, nzmax, Common); } CHM_TR attribute_hidden M_cholmod_sparse_to_triplet(const_CHM_SP A, CHM_CM Common) { static CHM_TR(*fun)(const_CHM_SP,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_TR(*)(const_CHM_SP,CHM_CM)) R_GetCCallable("Matrix", "cholmod_sparse_to_triplet"); return fun(A, Common); } CHM_DN attribute_hidden M_cholmod_sparse_to_dense(const_CHM_SP A, CHM_CM Common) { static CHM_DN(*fun)(const_CHM_SP,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_DN(*)(const_CHM_SP,CHM_CM)) R_GetCCallable("Matrix", "cholmod_sparse_to_dense"); return fun(A, Common); } CHM_FR attribute_hidden M_cholmod_analyze(const_CHM_SP A, CHM_CM Common) { static CHM_FR(*fun)(const_CHM_SP,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_FR(*)(const_CHM_SP,CHM_CM)) R_GetCCallable("Matrix", "cholmod_analyze"); return fun(A, Common); } CHM_FR attribute_hidden M_cholmod_analyze_p(const_CHM_SP A, int *Perm, int *fset, size_t fsize, CHM_CM Common) { static CHM_FR(*fun)(const_CHM_SP,int*,int*,size_t, CHM_CM) = NULL; if (fun == NULL) fun = (CHM_FR(*)(const_CHM_SP,int*,int*, size_t,CHM_CM)) R_GetCCallable("Matrix", "cholmod_analyze_p"); return fun(A, Perm, fset, fsize, Common); } CHM_SP attribute_hidden M_cholmod_copy(const_CHM_SP A, int stype, int mode, CHM_CM Common) { static CHM_SP(*fun)(const_CHM_SP,int,int,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_SP(*)(const_CHM_SP,int,int,CHM_CM)) R_GetCCallable("Matrix", "cholmod_copy"); return fun(A, stype, mode, Common); } CHM_DN attribute_hidden M_cholmod_copy_dense(const_CHM_DN A, CHM_CM Common) { static CHM_DN(*fun)(const_CHM_DN,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_DN(*)(const_CHM_DN,CHM_CM)) R_GetCCallable("Matrix", "cholmod_copy_dense"); return fun(A, Common); } CHM_FR attribute_hidden M_cholmod_copy_factor(const_CHM_FR L, CHM_CM Common) { static CHM_FR(*fun)(const_CHM_FR,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_FR(*)(const_CHM_FR,CHM_CM)) R_GetCCallable("Matrix", "cholmod_copy_factor"); return fun(L, Common); } int attribute_hidden M_cholmod_change_factor(int to_xtype, int to_ll, int to_super, int to_packed, int to_monotonic, CHM_FR L, CHM_CM Common) { static int(*fun)(int,int,int,int,int,CHM_FR,CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(int,int,int,int,int,CHM_FR,CHM_CM)) R_GetCCallable("Matrix", "cholmod_change_factor"); return fun(to_xtype, to_ll, to_super, to_packed, to_monotonic, L, Common); } CHM_SP attribute_hidden M_cholmod_copy_sparse(const_CHM_SP A, CHM_CM Common) { static CHM_SP(*fun)(const_CHM_SP,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_SP(*)(const_CHM_SP,CHM_CM)) R_GetCCallable("Matrix", "cholmod_copy_sparse"); return fun(A, Common); } CHM_SP attribute_hidden M_cholmod_factor_to_sparse(const_CHM_FR L, CHM_CM Common) { static CHM_SP(*fun)(const_CHM_FR,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_SP(*)(const_CHM_FR,CHM_CM)) R_GetCCallable("Matrix", "cholmod_factor_to_sparse"); return fun(L, Common); } CHM_SP attribute_hidden M_cholmod_submatrix(const_CHM_SP A, int *rset, int rsize, int *cset, int csize, int values, int sorted, CHM_CM Common) { static CHM_SP(*fun)(const_CHM_SP,int*,int,int*,int, int,int,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_SP(*)(const_CHM_SP,int*,int,int*, int,int,int,CHM_CM)) R_GetCCallable("Matrix", "cholmod_submatrix"); return fun(A, rset, rsize, cset, csize, values, sorted, Common); } CHM_SP attribute_hidden M_cholmod_dense_to_sparse(const_CHM_DN X, int values, CHM_CM Common) { static CHM_SP(*fun)(const_CHM_DN,int,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_SP(*)(const_CHM_DN,int,CHM_CM)) R_GetCCallable("Matrix", "cholmod_dense_to_sparse"); return fun(X, values, Common); } int attribute_hidden M_cholmod_factorize(const_CHM_SP A, CHM_FR L, CHM_CM Common) { static int(*fun)(const_CHM_SP,CHM_FR,CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(const_CHM_SP,CHM_FR,CHM_CM)) R_GetCCallable("Matrix", "cholmod_factorize"); return fun(A, L, Common); } int attribute_hidden M_cholmod_factorize_p(const_CHM_SP A, double *beta, int *fset, size_t fsize, CHM_FR L, CHM_CM Common) { static int(*fun)(const_CHM_SP,double*,int*,size_t, CHM_FR,CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(const_CHM_SP,double*,int*,size_t, CHM_FR,CHM_CM)) R_GetCCallable("Matrix", "cholmod_factorize_p"); return fun(A, beta, fset, fsize, L, Common); } int attribute_hidden M_cholmod_finish(CHM_CM Common) { static int(*fun)(CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(CHM_CM)) R_GetCCallable("Matrix", "cholmod_finish"); return fun(Common); } int attribute_hidden M_cholmod_sort(CHM_SP A, CHM_CM Common) { static int(*fun)(CHM_SP,CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(CHM_SP,CHM_CM)) R_GetCCallable("Matrix", "cholmod_sort"); return fun(A, Common); } int attribute_hidden M_cholmod_free_dense(CHM_DN *A, CHM_CM Common) { static int(*fun)(CHM_DN*,CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(CHM_DN*,CHM_CM)) R_GetCCallable("Matrix", "cholmod_free_dense"); return fun(A, Common); } int attribute_hidden M_cholmod_free_factor(CHM_FR *L, CHM_CM Common) { static int(*fun)(CHM_FR*,CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(CHM_FR*,CHM_CM)) R_GetCCallable("Matrix", "cholmod_free_factor"); return fun(L, Common); } int attribute_hidden M_cholmod_free_sparse(CHM_SP *A, CHM_CM Common) { static int(*fun)(CHM_SP*,CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(CHM_SP*,CHM_CM)) R_GetCCallable("Matrix", "cholmod_free_sparse"); return fun(A, Common); } int attribute_hidden M_cholmod_free_triplet(cholmod_triplet **T, CHM_CM Common) { static int(*fun)(cholmod_triplet**,CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(cholmod_triplet**,CHM_CM)) R_GetCCallable("Matrix", "cholmod_free_triplet"); return fun(T, Common); } long attribute_hidden M_cholmod_nnz(const_CHM_SP A, CHM_CM Common) { static long(*fun)(const_CHM_SP,CHM_CM) = NULL; if (fun == NULL) fun = (long(*)(const_CHM_SP,CHM_CM)) R_GetCCallable("Matrix", "cholmod_nnz"); return fun(A, Common); } int attribute_hidden M_cholmod_sdmult(const_CHM_SP A, int transpose, const double *alpha, const double *beta, const_CHM_DN X, CHM_DN Y, CHM_CM Common) { static int(*fun)(const_CHM_SP,int,const double*, const double*,const_CHM_DN, CHM_DN,CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(const_CHM_SP,int,const double*, const double*, const_CHM_DN, CHM_DN,CHM_CM)) R_GetCCallable("Matrix", "cholmod_sdmult"); return fun(A, transpose, alpha, beta, X, Y, Common); } CHM_SP attribute_hidden M_cholmod_ssmult(const_CHM_SP A, const_CHM_SP B, int stype, int values, int sorted, CHM_CM Common) { static CHM_SP(*fun)(const_CHM_SP,const_CHM_SP, int,int,int,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_SP(*)(const_CHM_SP,const_CHM_SP, int,int,int,CHM_CM)) R_GetCCallable("Matrix", "cholmod_ssmult"); return fun(A, B, stype, values, sorted, Common); } CHM_DN attribute_hidden M_cholmod_solve(int sys, const_CHM_FR L, const_CHM_DN B, CHM_CM Common) { static CHM_DN(*fun)(int,const_CHM_FR,const_CHM_DN, CHM_CM) = NULL; if (fun == NULL) fun = (CHM_DN(*)(int,const_CHM_FR,const_CHM_DN, CHM_CM)) R_GetCCallable("Matrix", "cholmod_solve"); return fun(sys, L, B, Common); } CHM_SP attribute_hidden M_cholmod_speye(size_t nrow, size_t ncol, int xtype, CHM_CM Common) { static CHM_SP(*fun)(size_t,size_t,int,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_SP(*)(size_t,size_t,int,CHM_CM)) R_GetCCallable("Matrix", "cholmod_speye"); return fun(nrow, ncol, xtype, Common); } CHM_SP attribute_hidden M_cholmod_spsolve(int sys, const_CHM_FR L, const_CHM_SP B, CHM_CM Common) { static CHM_SP(*fun)(int,const_CHM_FR, const_CHM_SP, CHM_CM) = NULL; if (fun == NULL) fun = (CHM_SP(*)(int,const_CHM_FR, const_CHM_SP, CHM_CM)) R_GetCCallable("Matrix", "cholmod_spsolve"); return fun(sys, L, B, Common); } int attribute_hidden M_cholmod_defaults (CHM_CM Common) { static int(*fun)(CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(CHM_CM)) R_GetCCallable("Matrix", "cholmod_defaults"); return fun(Common); } int attribute_hidden M_cholmod_updown(int update, const_CHM_SP C, const_CHM_FR L, CHM_CM Common) { static int(*fun)(int,const_CHM_SP,const_CHM_FR, CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(int,const_CHM_SP,const_CHM_FR, CHM_CM)) R_GetCCallable("Matrix", "cholmod_updown"); return fun(update, C, L, Common); } /* extern cholmod_common c; */ void attribute_hidden M_R_cholmod_error(int status, const char *file, int line, const char *message) { /* NB: keep in sync with R_cholmod_error(), ../../src/chm_common.c */ if(status < 0) { /* Note: Matrix itself uses CHM_set_common_env, CHM_store_common * and CHM_restore_common to preserve settings through error calls. * Consider defining your own error handler, *and* possibly restoring * *your* version of the cholmod_common that *you* use. */ error("Cholmod error '%s' at file '%s', line %d", message, file, line); } else warning("Cholmod warning '%s' at file '%s', line %d", message, file, line); } #if 0 /* no longer used */ /* just to get 'int' instead of 'void' as required by CHOLMOD's print_function */ static int R_cholmod_printf(const char* fmt, ...) { va_list(ap); va_start(ap, fmt); Rprintf((char *)fmt, ap); va_end(ap); return 0; } #endif int attribute_hidden M_R_cholmod_start(CHM_CM Common) { int val; static int(*fun)(CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(CHM_CM)) R_GetCCallable("Matrix", "cholmod_start"); val = fun(Common); /*-- NB: keep in sync with R_cholmod_start() --> ../../src/chm_common.c */ /* do not allow CHOLMOD printing - currently */ Common->print_function = NULL;/* was R_cholmod_printf; /.* Rprintf gives warning */ /* Consider using your own error handler: */ Common->error_handler = M_R_cholmod_error; return val; } CHM_SP attribute_hidden M_cholmod_transpose(const_CHM_SP A, int values, CHM_CM Common) { static CHM_SP(*fun)(const_CHM_SP,int,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_SP(*)(const_CHM_SP,int,CHM_CM)) R_GetCCallable("Matrix", "cholmod_transpose"); return fun(A, values, Common); } CHM_SP attribute_hidden M_cholmod_vertcat(const_CHM_SP A, const_CHM_SP B, int values, CHM_CM Common) { static CHM_SP(*fun)(const_CHM_SP,const_CHM_SP,int,CHM_CM) = NULL; if (fun == NULL) fun = (CHM_SP(*)(const_CHM_SP,const_CHM_SP, int, CHM_CM)) R_GetCCallable("Matrix", "cholmod_vertcat"); return fun(A, B, values, Common); } SEXP attribute_hidden M_dpoMatrix_chol(SEXP x) { static SEXP(*fun)(SEXP) = NULL; if (fun == NULL) fun = (SEXP(*)(SEXP)) R_GetCCallable("Matrix", "dpoMatrix_chol"); return fun(x); } CHM_DN attribute_hidden M_numeric_as_chm_dense(CHM_DN ans, double *v, int nr, int nc) { static CHM_DN(*fun)(CHM_DN,double*,int,int) = NULL; if (fun == NULL) fun = (CHM_DN(*)(CHM_DN,double*,int,int)) R_GetCCallable("Matrix", "numeric_as_chm_dense"); return fun(ans, v, nr, nc); } int attribute_hidden M_cholmod_scale(const_CHM_DN S, int scale, CHM_SP A, CHM_CM Common) { static int(*fun)(const_CHM_DN,int,CHM_SP, CHM_CM) = NULL; if (fun == NULL) fun = (int(*)(const_CHM_DN,int,CHM_SP, CHM_CM)) R_GetCCallable("Matrix", "cholmod_scale"); return fun(S, scale, A, Common); } // for now still *export* M_Matrix_check_class_etc() -- deprecate it later__FIXME__ int M_Matrix_check_class_etc(SEXP x, const char **valid) { #if R_VERSION < R_Version(2, 15, 0) // || R_SVN_REVISION < 57849 static int(*fun)(SEXP, const char**) = NULL; if (fun == NULL) fun = (int(*)(SEXP, const char**)) R_GetCCallable("Matrix", "Matrix_check_class_etc"); return fun(x, valid); #else return R_check_class_etc(x, valid); #endif } const char *Matrix_valid_Csparse[] = { MATRIX_VALID_Csparse, ""}; const char *Matrix_valid_dense[] = { MATRIX_VALID_dense, ""}; const char *Matrix_valid_triplet[] = { MATRIX_VALID_Tsparse, ""}; const char *Matrix_valid_CHMfactor[]={ MATRIX_VALID_CHMfactor, ""}; bool Matrix_isclass_Csparse(SEXP x) { return M_Matrix_check_class_etc(x, Matrix_valid_Csparse) >= 0; } bool Matrix_isclass_triplet(SEXP x) { return M_Matrix_check_class_etc(x, Matrix_valid_triplet) >= 0; } bool Matrix_isclass_dense(SEXP x) { return M_Matrix_check_class_etc(x, Matrix_valid_dense) >= 0; } bool Matrix_isclass_CHMfactor(SEXP x) { return M_Matrix_check_class_etc(x, Matrix_valid_CHMfactor) >= 0; } #ifdef __cplusplus } #endif Matrix/tests/0000755000175100001440000000000012271765426012712 5ustar hornikusersMatrix/tests/matprod.R0000644000175100001440000004721312271746775014520 0ustar hornikuserslibrary(Matrix) ### Matrix Products including cross products source(system.file("test-tools.R", package = "Matrix")) ### dimnames -- notably for matrix products ## from ../R/Auxiliaries.R : .M.DN <- function(x) if(!is.null(dn <- dimnames(x))) dn else list(NULL,NULL) dnIdentical <- function(x,y) identical(.M.DN(x), .M.DN(y)) chkDnProd <- function(m, M = Matrix(m), browse=FALSE) { ## TODO: ## if(browse) stopifnot <- f.unction(...) such that it enters browser().. stopifnot(is.matrix(m), is(M, "Matrix")) ## m is n x d (say) p1 <- (tm <- t(m)) %*% m ## d x d p1. <- crossprod(m) stopifnot(dnIdentical(p1, p1.)) t1 <- m %*% tm ## n x n t1. <- tcrossprod(m) stopifnot(dnIdentical(t1, t1.)) ## Now the "Matrix" ones -- should match the "matrix" above M0 <- M cat("sparse: ") for(sparse in c(TRUE, FALSE)) { cat(sparse, "; ") M <- as(M0, if(sparse)"sparseMatrix" else "denseMatrix") P1 <- (tM <- t(M)) %*% M P1. <- crossprod(M) stopifnot(dnIdentical(P1, P1.), dnIdentical(P1, p1), dnIdentical(P1., crossprod(M,M)), dnIdentical(P1., crossprod(M,m)), dnIdentical(P1., crossprod(m,M))) ## P1. is "symmetricMatrix" -- semantically "must have" symm.dimnames PP1 <- P1. %*% P1. ## still d x d R <- triu(PP1);r <- as(R,"matrix") # upper - triangular L <- tril(PP1);l <- as(L,"matrix") # lower - triangular stopifnot(isSymmetric(P1.), isSymmetric(PP1), is(L,"triangularMatrix"), is(R,"triangularMatrix"), dnIdentical(PP1, (pp1 <- p1 %*% p1)), dnIdentical(PP1, R), dnIdentical(L, R)) T1 <- M %*% tM T1. <- tcrossprod(M) stopifnot(dnIdentical(T1, T1.), dnIdentical(T1, t1), dnIdentical(T1., tcrossprod(M,M)), dnIdentical(T1., tcrossprod(M,m)), dnIdentical(T1., tcrossprod(m,M)), dnIdentical(tcrossprod(T1., tM), tcrossprod(t1., tm)), dnIdentical(crossprod(T1., M), crossprod(t1., m))) ## Now, *mixing* Matrix x matrix: stopifnot(dnIdentical(tM %*% m, tm %*% M)) ## Symmetric and Triangular stopifnot(dnIdentical(PP1 %*% tM, pp1 %*% tm), dnIdentical(R %*% tM, r %*% tm), dnIdentical(L %*% tM, L %*% tm)) } cat("\n") invisible(TRUE) } ## All these are ok {now, (2012-06-11) also for dense (m <- matrix(c(0, 0, 2:0), 3, 5)) m00 <- m # *no* dimnames dimnames(m) <- list(LETTERS[1:3], letters[1:5]) (m.. <- m) # has *both* dimnames m0. <- m.0 <- m.. dimnames(m0.)[1] <- list(NULL); m0. dimnames(m.0)[2] <- list(NULL); m.0 ## chkDnProd(m..) chkDnProd(m0.) chkDnProd(m.0) chkDnProd(m00) m5 <- 1 + as(diag(-1:4)[-5,], "dgeMatrix") ## named dimnames: dimnames(m5) <- list(Rows= LETTERS[1:5], paste("C", 1:6, sep="")) tr5 <- tril(m5[,-6]) m. <- as(m5, "matrix") m5.2 <- local({t5 <- as.matrix(tr5); t5 %*% t5}) stopifnot(isValid(tr5, "dtrMatrix"), dim(m5) == 5:6, class(cm5 <- crossprod(m5)) == "dpoMatrix") assert.EQ.mat(t(m5) %*% m5, as(cm5, "matrix")) assert.EQ.mat(tr5.2 <- tr5 %*% tr5, m5.2) stopifnot(isValid(tr5.2, "dtrMatrix"), as.vector(rep(1,6) %*% cm5) == colSums(cm5), as.vector(cm5 %*% rep(1,6)) == rowSums(cm5)) ## uni-diagonal dtrMatrix with "wrong" entries in diagonal ## {the diagonal can be anything: because of diag = "U" it should never be used}: tru <- Diagonal(3, x=3); tru[i.lt <- lower.tri(tru, diag=FALSE)] <- c(2,-3,4) tru@diag <- "U" ; stopifnot(diag(trm <- as.matrix(tru)) == 1) ## TODO: Also add *upper-triangular* *packed* case !! stopifnot((tru %*% tru)[i.lt] == (trm %*% trm)[i.lt]) ## crossprod() with numeric vector RHS and LHS assert.EQ.mat( crossprod(rep(1,5), m5), rbind( colSums(m5))) assert.EQ.mat( crossprod(rep(1,5), m.), rbind( colSums(m5))) assert.EQ.mat( crossprod(m5, rep(1,5)), cbind( colSums(m5))) assert.EQ.mat( crossprod(m., rep(1,5)), cbind( colSums(m5))) ## tcrossprod() with numeric vector RHS and LHS : m51 <- m5[, 1, drop=FALSE] # [6 x 1] m.1 <- m.[, 1, drop=FALSE] ; assert.EQ.mat(m51, m.1) ## The only (M . v) case assert.EQ.mat(tcrossprod(m51, 5:1), tcrossprod(m.1, 5:1)) ## The two (v . M) cases: assert.EQ.mat(tcrossprod(rep(1,6), m.), rbind( rowSums(m5)))# |v| = ncol(m) assert.EQ.mat(tcrossprod(rep(1,3), m51), tcrossprod(rep(1,3), m.1))# ncol(m) = 1 ## classes differ tc.m5 <- m5 %*% t(m5) # "dge*", no dimnames (FIXME) (tcm5 <- tcrossprod(m5)) # "dpo*" w/ dimnames assert.EQ.mat(tc.m5, mm5 <- as(tcm5, "matrix")) ## tcrossprod(x,y) : assert.EQ.mat(tcrossprod(m5, m5), mm5) assert.EQ.mat(tcrossprod(m5, m.), mm5) assert.EQ.mat(tcrossprod(m., m5), mm5) M50 <- m5[,FALSE, drop=FALSE] M05 <- t(M50) s05 <- as(M05, "sparseMatrix") s50 <- t(s05) assert.EQ.mat(M05, matrix(1, 0,5)) assert.EQ.mat(M50, matrix(1, 5,0)) assert.EQ.mat(tcrossprod(M50), tcrossprod(as(M50, "matrix"))) assert.EQ.mat(tcrossprod(s50), tcrossprod(as(s50, "matrix"))) assert.EQ.mat( crossprod(s50), crossprod(as(s50, "matrix"))) stopifnot(identical( crossprod(s50), tcrossprod(s05)), identical( crossprod(s05), tcrossprod(s50))) (M00 <- crossprod(M50))## used to fail -> .Call(dgeMatrix_crossprod, x, FALSE) stopifnot(identical(M00, tcrossprod(M05)), all(M00 == t(M50) %*% M50), dim(M00) == 0) ## simple cases with 'scalars' treated as 1x1 matrices: d <- Matrix(1:5) d %*% 2 10 %*% t(d) assertError(3 %*% d) # must give an error , similar to assertError(5 %*% as.matrix(d)) # -> error ## right and left "numeric" and "matrix" multiplication: (p1 <- m5 %*% c(10, 2:6)) (p2 <- c(10, 2:5) %*% m5) (pd1 <- m5 %*% diag(1:6)) (pd. <- m5 %*% Diagonal(x = 1:6)) (pd2 <- diag (10:6) %*% m5) (pd..<- Diagonal(x = 10:6) %*% m5) stopifnot(dim(crossprod(t(m5))) == c(5,5), c(class(p1),class(p2),class(pd1),class(pd2), class(pd.),class(pd..)) == "dgeMatrix") assert.EQ.mat(p1, cbind(c(20,30,33,38,54))) assert.EQ.mat(pd1, m. %*% diag(1:6)) assert.EQ.mat(pd2, diag(10:6) %*% m.) assert.EQ.mat(pd., as(pd1,"matrix")) assert.EQ.mat(pd..,as(pd2,"matrix")) ## check that 'solve' and '%*%' are inverses set.seed(1) A <- Matrix(rnorm(25), nc = 5) y <- rnorm(5) all.equal((A %*% solve(A, y))@x, y) Atr <- new("dtrMatrix", Dim = A@Dim, x = A@x, uplo = "U") all.equal((Atr %*% solve(Atr, y))@x, y) ### ------ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ### Sparse Matrix products ### ------ ## solve() for dtC* mc <- round(chol(crossprod(A)), 2) B <- A[1:3,] # non-square on purpose stopifnot(all.equal(sum(rowSums(B %*% mc)), 5.82424475145)) assert.EQ.mat(tcrossprod(B, mc), as.matrix(t(tcrossprod(mc, B)))) m <- kronecker(Diagonal(2), mc) stopifnot(is(mc, "Cholesky"), is(m, "sparseMatrix")) im <- solve(m) round(im, 3) itm <- solve(t(m)) iim <- solve(im) # should be ~= 'm' of course iitm <- solve(itm) I <- Diagonal(nrow(m)) (del <- c(mean(abs(as.numeric(im %*% m - I))), mean(abs(as.numeric(m %*% im - I))), mean(abs(as.numeric(im - t(itm)))), mean(abs(as.numeric( m - iim))), mean(abs(as.numeric(t(m)- iitm))))) stopifnot(is(m, "triangularMatrix"), is(m, "sparseMatrix"), is(im, "dtCMatrix"), is(itm, "dtCMatrix"), is(iitm, "dtCMatrix"), del < 1e-15) ## crossprod(.,.) & tcrossprod(), mixing dense & sparse v <- c(0,0,2:0) mv <- as.matrix(v) ## == cbind(v) (V <- Matrix(v, 5,1, sparse=TRUE)) sv <- as(v, "sparseVector") a <- as.matrix(A) cav <- crossprod(a,v) tva <- tcrossprod(v,a) assert.EQ.mat(crossprod(A, V), cav) # gave infinite recursion assert.EQ.mat(crossprod(A,sv), cav) assert.EQ.mat(tcrossprod( sv, A), tva) assert.EQ.mat(tcrossprod(t(V),A), tva) ## [t]crossprod() for . incl. one arg.: stopifnot(isValid(s.s <- crossprod(sv,sv), "Matrix"), identical(s.s, crossprod(sv)), isValid(ss. <- tcrossprod(sv,sv), "sparseMatrix"), identical(ss., tcrossprod(sv))) assert.EQ.mat(s.s, crossprod(v,v)) assert.EQ.mat(ss., tcrossprod(v,v)) dm <- Matrix(v, sparse=FALSE) sm <- Matrix(v, sparse=TRUE) stopifnot( identical4(tcrossprod(v, v), tcrossprod(mv, v), tcrossprod(v,mv), tcrossprod(mv,mv))## (base R) , validObject(d.vvt <- as(as(vvt <- tcrossprod(v, v), "denseMatrix"), "dgeMatrix")) , identical4(d.vvt, tcrossprod(dm, v), tcrossprod(v,dm), tcrossprod(dm,dm)) ## (v, dm) failed , validObject(s.vvt <- as(as(vvt, "sparseMatrix"), "dgCMatrix")) , identical(s.vvt, tcrossprod(sm,sm)) , identical3(d.vvt, tcrossprod(sm, v), tcrossprod(v,sm)) ## both (sm,v) and (v,sm) failed ) assert.EQ.mat(d.vvt, vvt) assert.EQ.mat(s.vvt, vvt) M <- Matrix(0:5, 2,3) ; sM <- as(M, "sparseMatrix"); m <- as(M, "matrix") v <- 1:3; v2 <- 2:1 sv <- as( v, "sparseVector") sv2 <- as(v2, "sparseVector") tvm <- tcrossprod(v, m) assert.EQ.mat(tcrossprod( v, M), tvm) assert.EQ.mat(tcrossprod( v,sM), tvm) assert.EQ.mat(tcrossprod(sv,sM), tvm) assert.EQ.mat(tcrossprod(sv, M), tvm) assert.EQ.mat(crossprod(M, sv2), crossprod(m, v2)) stopifnot(identical(tcrossprod(v, M), v %*% t(M)), identical(tcrossprod(v,sM), v %*% t(sM)), identical(tcrossprod(v, M), crossprod(v, t(M))), identical(tcrossprod(sv,sM), sv %*% t(sM)), identical(crossprod(sM, sv2), t(sM) %*% sv2), identical(crossprod(M, v2), t(M) %*% v2)) ## *unit* triangular : t1 <- new("dtTMatrix", x= c(3,7), i= 0:1, j=3:2, Dim= as.integer(c(4,4))) ## from 0-diagonal to unit-diagonal {low-level step}: tu <- t1 ; tu@diag <- "U" cu <- as(tu, "dtCMatrix") cl <- t(cu) # unit lower-triangular cl10 <- cl %*% Diagonal(4, x=10) assert.EQ.mat(cl10, as(cl, "matrix") %*% diag(4, x=10)) stopifnot(is(cl,"dtCMatrix"), cl@diag == "U") (cu2 <- cu %*% cu) cl2 <- cl %*% cl validObject(cl2) cu3 <- tu[-1,-1] assert.EQ.mat(crossprod(tru, cu3), crossprod(trm, as.matrix(cu3))) ## "FIXME" should return triangular ... cl2 cu2. <- Diagonal(4) + Matrix(c(rep(0,9),14,0,0,6,0,0,0), 4,4) D4 <- Diagonal(4, x=10:7) stopifnot(all(cu2 == cu2.),# was wrong for ver. <= 0.999375-4 is(cu2, "dtCMatrix"), is(cl2, "dtCMatrix"), # triangularity preserved cu2@diag == "U", cl2@diag == "U",# UNIT-triangularity preserved all.equal(D4 %*% cu, D4 %*% as.matrix(cu)), all.equal(cu %*% D4, as.matrix(cu) %*% D4), isValid(su <- crossprod(cu), "dsCMatrix"), all(D4 %*% su == D4 %*% as.mat(su)), all(su %*% D4 == as.mat(su) %*% D4), identical(t(cl2), cu2), # !! identical( crossprod(cu), Matrix( crossprod(as.matrix(cu)),sparse=TRUE)), identical(tcrossprod(cu), Matrix(tcrossprod(as.matrix(cu)),sparse=TRUE))) tr8 <- kronecker(rbind(c(2,0),c(1,4)), cl2) T8 <- tr8 %*% (tr8/2) # triangularity preserved? T8.2 <- (T8 %*% T8) / 4 stopifnot(is(T8, "triangularMatrix"), T8@uplo == "L", is(T8.2, "dtCMatrix")) mr8 <- as(tr8,"matrix") m8. <- (mr8 %*% mr8 %*% mr8 %*% mr8)/16 assert.EQ.mat(T8.2, m8.) data(KNex); mm <- KNex$mm M <- mm[1:500, 1:200] MT <- as(M, "TsparseMatrix") cpr <- t(mm) %*% mm cpr. <- crossprod(mm) cpr.. <- crossprod(mm, mm) stopifnot(is(cpr., "symmetricMatrix"), identical3(cpr, as(cpr., class(cpr)), cpr..)) ## with dimnames: m <- Matrix(c(0, 0, 2:0), 3, 5) dimnames(m) <- list(LETTERS[1:3], letters[1:5]) m p1 <- t(m) %*% m (p1. <- crossprod(m)) t1 <- m %*% t(m) (t1. <- tcrossprod(m)) stopifnot(isSymmetric(p1.), isSymmetric(t1.), identical(p1, as(p1., class(p1))), identical(t1, as(t1., class(t1))), identical(dimnames(p1), dimnames(p1.)), identical(dimnames(p1), list(colnames(m), colnames(m))), identical(dimnames(t1), dimnames(t1.)) ) showMethods("%*%", class=class(M)) v1 <- rep(1, ncol(M)) str(r <- M %*% Matrix(v1)) str(rT <- MT %*% Matrix(v1)) stopifnot(identical(r, rT)) str(r. <- M %*% as.matrix(v1)) stopifnot(identical4(r, r., rT, M %*% as(v1, "matrix"))) v2 <- rep(1,nrow(M)) r2 <- t(Matrix(v2)) %*% M r2T <- v2 %*% MT str(r2. <- v2 %*% M) stopifnot(identical3(r2, r2., t(as(v2, "matrix")) %*% M)) ###------------------------------------------------------------------ ### Close to singular matrix W ### (from micEconAids/tests/aids.R ... priceIndex = "S" ) (load(system.file("external", "symW.rda", package="Matrix"))) # "symW" stopifnot(is(symW, "symmetricMatrix")) n <- nrow(symW) I <- .sparseDiagonal(n, shape="g") S <- as(symW, "matrix") sis <- solve(S, S) ## solve(, ) when Cholmod fails was buggy for *long*: SIS <- solve(symW, symW) iw <- solve(symW) iss <- iw %*% symW ## nb-mm3 assert.EQ.(I, drop0(sis), tol = 1e-9)# 2.6e-10 assert.EQ.(I, SIS, tol = 1e-7)# 8.2e-9 assert.EQ.(I, iss, tol = 4e-4)# 3.3e-5 ## solve(, ) : I <- diag(nr=n) SIS <- solve(symW, as(symW,"denseMatrix")) iw <- solve(symW, I) iss <- iw %*% symW assert.EQ.mat(SIS, I, tol = 1e-7, giveRE=TRUE) assert.EQ.mat(iss, I, tol = 4e-4, giveRE=TRUE) rm(SIS,iss) WW <- as(symW, "generalMatrix") # the one that gave problems IW <- solve(WW) class(I1 <- IW %*% WW)# "dge" or "dgC" (!) class(I2 <- WW %*% IW) ## these two were wrong for for M.._1.0-13: assert.EQ.(as(I1,"matrix"), I, tol = 1e-4) assert.EQ.(as(I2,"matrix"), I, tol = 7e-7) ## now slightly perturb WW (and hence break exact symmetry set.seed(131); ii <- sample(length(WW), size= 100) WW[ii] <- WW[ii] * (1 + 1e-7*runif(100)) SW. <- symmpart(WW) SW2 <- Matrix:::forceSymmetric(WW) stopifnot(all.equal(as(SW.,"matrix"), as(SW2,"matrix"), tol = 1e-7)) (ch <- all.equal(WW, as(SW.,"dgCMatrix"), tolerance =0)) stopifnot(is.character(ch), length(ch) == 1)## had length(.) 2 previously IW <- solve(WW) class(I1 <- IW %*% WW)# "dge" or "dgC" (!) class(I2 <- WW %*% IW) I <- diag(nr=nrow(WW)) stopifnot(all.equal(as(I1,"matrix"), I, check.attributes=FALSE, tolerance = 1e-4), ## "Mean relative difference: 3.296549e-05" (or "1.999949" for Matrix_1.0-13 !!!) all.equal(as(I2,"matrix"), I, check.attributes=FALSE)) #default tol gives "1" for M.._1.0-13 if(doExtras) { print(kappa(WW)) ## [1] 5.129463e+12 print(rcond(WW)) ## [1] 6.216103e-14 ## Warning message: rcond(.) via sparse -> dense coercion } class(Iw. <- solve(SW.))# FIXME? should be "symmetric" but is not class(Iw2 <- solve(SW2))# FIXME? should be "symmetric" but is not class(IW. <- as(Iw., "denseMatrix")) class(IW2 <- as(Iw2, "denseMatrix")) ### The next two were wrong for very long, too assert.EQ.(I, as.matrix(IW. %*% SW.), tol= 4e-4) assert.EQ.(I, as.matrix(IW2 %*% SW2), tol= 4e-4) dIW <- as(IW, "denseMatrix") assert.EQ.(dIW, IW., tol= 4e-4) assert.EQ.(dIW, IW2, tol= 8e-4) ##------------------------------------------------------------------ ## Sparse Cov.matrices from Harri Kiiveri @ CSIRO a <- matrix(0,5,5) a[1,2] <- a[2,3] <- a[3,4] <- a[4,5] <- 1 a <- a + t(a) + 2*diag(5) b <- as(a, "dsCMatrix") ## ok, but we recommend to use Matrix() ``almost always'' : (b. <- Matrix(a, sparse = TRUE)) stopifnot(identical(b, b.)) ## calculate conditional variance matrix ( vars 3 4 5 given 1 2 ) (B2 <- b[1:2, 1:2]) bb <- b[1:2, 3:5] stopifnot(is(B2, "dsCMatrix"), # symmetric indexing keeps symmetry identical(as.mat(bb), rbind(0, c(1,0,0))), ## TODO: use fully-sparse cholmod_spsolve() based solution : is(z.s <- solve(B2, bb), "sparseMatrix")) assert.EQ.mat(B2 %*% z.s, as(bb, "matrix")) ## -> dense RHS and dense result z. <- solve(as(B2, "dgCMatrix"), bb)# now *sparse* z <- solve( B2, as(bb,"dgeMatrix")) stopifnot(is(z., "sparseMatrix"), all.equal(z, as(z.,"denseMatrix"))) ## finish calculating conditional variance matrix v <- b[3:5,3:5] - crossprod(bb,z) stopifnot(all.equal(as.mat(v), matrix(c(4/3, 1:0, 1,2,1, 0:2), 3), tol = 1e-14)) ###--- "logical" Matrices : --------------------- ##__ FIXME __ now works for lsparse* and nsparse* but not yet for lge* and nge* ! ## Robert's Example, a bit more readable fromTo <- rbind(c(2,10), c(3, 9)) N <- 10 nrFT <- nrow(fromTo) rowi <- rep.int(1:nrFT, fromTo[,2]-fromTo[,1] + 1) - 1:1 coli <- unlist(lapply(1:nrFT, function(x) fromTo[x,1]:fromTo[x,2])) - 1:1 ## "n" --- nonzero pattern Matrices sM <- new("ngTMatrix", i = rowi, j=coli, Dim=as.integer(c(N,N))) sM # nice sm <- as(sM, "matrix") sM %*% sM assert.EQ.mat(sM %*% sM, sm %*% sm) assert.EQ.mat(t(sM) %*% sM, (t(sm) %*% sm) > 0, tol=0) crossprod(sM) tcrossprod(sM) stopifnot(identical(as( crossprod(sM), "ngCMatrix"), t(sM) %*% sM), identical(as(tcrossprod(sM), "ngCMatrix"), sM %*% t(sM))) assert.EQ.mat( crossprod(sM), crossprod(sm) > 0) assert.EQ.mat(tcrossprod(sM), as(tcrossprod(sm),"matrix") > 0) ## "l" --- logical Matrices -- use usual 0/1 arithmetic nsM <- sM sM <- as(sM, "lMatrix") sm <- as(sM, "matrix") stopifnot(identical(sm, as.matrix(nsM))) sM %*% sM assert.EQ.mat(sM %*% sM, sm %*% sm) assert.EQ.mat(t(sM) %*% sM, t(sm) %*% sm, tol=0) crossprod(sM) tcrossprod(sM) stopifnot(identical( crossprod(sM), as(t(sM) %*% sM, "symmetricMatrix")), identical(tcrossprod(sM), forceSymmetric(sM %*% t(sM)))) assert.EQ.mat( crossprod(sM), crossprod(sm)) assert.EQ.mat(tcrossprod(sM), as(tcrossprod(sm),"matrix")) dm <- as(sm, "denseMatrix") ## the following 6 products (dm o sM) all failed up to 2013-09-03 isValid(dm %*% sM, "CsparseMatrix")## failed {missing coercion} isValid(crossprod (dm , sM),"CsparseMatrix") isValid(tcrossprod(dm , sM),"CsparseMatrix") dm[2,1] <- TRUE # no longer triangular isValid( dm %*% sM, "CsparseMatrix") isValid(crossprod (dm , sM),"CsparseMatrix") isValid(tcrossprod(dm , sM),"CsparseMatrix") ## A sparse example - with *integer* matrix: M <- Matrix(cbind(c(1,0,-2,0,0,0,0,0,2.2,0), c(2,0,0,1,0), 0, 0, c(0,0,8,0,0),0)) t(M) (-4:5) %*% M stopifnot(as.vector(print(t(M %*% 1:6))) == c(as(M,"matrix") %*% 1:6)) (M.M <- crossprod(M)) MM. <- tcrossprod(M) stopifnot(class(MM.) == "dsCMatrix", class(M.M) == "dsCMatrix") M3 <- Matrix(c(rep(c(2,0),4),3), 3,3, sparse=TRUE) I3 <- as(Diagonal(3), "CsparseMatrix") m3 <- as.matrix(M3) iM3 <- solve(m3) stopifnot(all.equal(unname(iM3), matrix(c(3/2,0,-1,0,1/2,0,-1,0,1), 3))) assert.EQ.mat(solve(as(M3, "sparseMatrix")), iM3) assert.EQ.mat(solve(I3,I3), diag(3)) assert.EQ.mat(solve(M3, I3), iM3)# was wrong because I3 is unit-diagonal assert.EQ.mat(solve(m3, I3), iM3)# gave infinite recursion in (<=) 0.999375-10 isValid(tru %*% I3, "triangularMatrix") isValid(crossprod(tru, I3), "triangularMatrix") isValid(crossprod(I3, tru), "triangularMatrix") isValid(tcrossprod(I3, tru), "triangularMatrix") ## even simpler m <- matrix(0, 4,7); m[c(1, 3, 6, 9, 11, 22, 27)] <- 1 (mm <- Matrix(m)) (cm <- Matrix(crossprod(m))) stopifnot(identical(crossprod(mm), cm)) (tm1 <- Matrix(tcrossprod(m))) #-> had bug in 'Matrix()' ! (tm2 <- tcrossprod(mm)) Im2 <- solve(tm2[-4,-4]) P <- as(as.integer(c(4,1,3,2)),"pMatrix") p <- as(P, "matrix") P %*% mm assertError(mm %*% P) # dimension mismatch assertError(m %*% P) # ditto assertError(crossprod(t(mm), P)) # ditto stopifnot(isValid(tm1, "dsCMatrix"), all.equal(tm1, tm2, tolerance =1e-15), identical(drop0(Im2 %*% tm2[1:3,]), Matrix(cbind(diag(3),0))), identical(p, as.matrix(P)), identical(P %*% m, as.matrix(P) %*% m), all(P %*% mm == P %*% m), all(P %*% mm - P %*% m == 0), all(t(mm) %*% P == t(m) %*% P), identical(crossprod(m, P), crossprod(mm, P)), TRUE) d <- function(m) as(m,"dsparseMatrix") IM1 <- as(c(3,1,2), "indMatrix") IM2 <- as(c(1,2,1), "indMatrix") assert.EQ.Mat(crossprod( IM1, IM2), crossprod(d(IM1),d(IM2)), tol=0)# failed at first set.seed(123) for(n in 1:250) { n1 <- 2 + rpois(1, 10) n2 <- 2 + rpois(1, 10) N <- rpois(1, 25) ii <- seq_len(N + min(n1,n2)) IM1 <- as(c(sample(n1), sample(n1, N, replace=TRUE))[ii], "indMatrix") IM2 <- as(c(sample(n2), sample(n2, N, replace=TRUE))[ii], "indMatrix") ## stopifnot(identical(crossprod( IM1, IM2), ## crossprod(d(IM1), d(IM2)))) if(!identical(C1 <- crossprod( IM1, IM2 ), CC <- crossprod(d(IM1), d(IM2))) && !all(C1 == CC)) { cat("The two crossprod()s differ: C1 - CC =\n") print(C1 - CC) stop("The two crossprod()s differ!") } else if(n %% 25 == 0) cat(n, " ") }; cat("\n") cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons'' Matrix/tests/Class+Meth.R0000644000175100001440000003224312257616323014772 0ustar hornikuserslibrary(Matrix) source(system.file("test-tools.R", package = "Matrix"))# identical3(), # further checkMatrix(), etc if(interactive()) options(error = recover) cat("doExtras:",doExtras,"\n") no.Mcl <- function(cl) ## TRUE if MatrixClass() returns empty, i identical(Matrix:::MatrixClass(cl), character(0)) setClass("myDGC", contains = "dgCMatrix") M <- new("myDGC", as(Matrix(c(-2:4, rep(0,9)), 4), "CsparseMatrix")) M stopifnot(M[-4,2] == 2:4, Matrix:::MatrixClass("myDGC" ) == "dgCMatrix", Matrix:::MatrixClass("Cholesky" ) == "dtrMatrix", Matrix:::MatrixClass("pCholesky") == "dtpMatrix", Matrix:::MatrixClass("corMatrix") == "dpoMatrix", no.Mcl("pMatrix"), no.Mcl("indMatrix")) setClass("posDef", contains = "dspMatrix") N <- as(as(crossprod(M) + Diagonal(4), "denseMatrix"),"dspMatrix") (N <- new("posDef", N)) stopifnot(is(N[1:2, 1:2], "symmetricMatrix")) #### Automatically display the class inheritance structure #### possibly augmented with methods allCl <- getClasses("package:Matrix") cat("actual and virtual classes:\n") tt <- table( isVirt <- sapply(allCl, isVirtualClass) ) names(tt) <- c('"actual"', "virtual") tt ## The "actual" Matrix classes: aCl <- allCl[!isVirt] (aMcl <- aCl[grep("Matrix$", aCl)]) # length 48 aMc2 <- aCl[sapply(aCl, extends, class2 = "Matrix")] stopifnot(all( aMcl %in% aMc2 )) aMc2[!(aMc2 %in% aMcl)] ## only 4 : p?Cholesky & p?BunchKaufman ## Really nice would be to construct an inheritance graph and display ## it. Following things are computational variations on the theme.. ## We use a version of canCoerce() that works with two *classes* instead of ## canCoerce <- function (object, Class) classCanCoerce <- function (class1, class2) { extends(class1, class2) || !is.null(selectMethod("coerce", optional = TRUE, signature = c(from = class1, to = class2), useInherited = c(from = TRUE, to = FALSE))) } .dq <- function(ch) paste0('"', ch, '"') .subclasses <- function(cnam) { cd <- getClass(cnam) unique(c(cd@className, unlist(lapply(names(cd@subclasses), .subclasses)))) } for(n in allCl) { if(isVirtualClass(n)) cat("Virtual class", .dq(n),"\n") else { cat("\"Actual\" class", .dq(n),":\n") x <- new(n) if(doExtras) for(m in allCl) if(classCanCoerce(n,m)) { ext <- extends(n, m) if(ext) { cat(sprintf(" extends %20s %20s \n", "", .dq(m))) } else { cat(sprintf(" can coerce: %20s -> %20s: ", .dq(n), .dq(m))) tt <- try(as(x, m), silent = TRUE) if(inherits(tt, "try-error")) { cat("\t *ERROR* !!\n") } else { cat("as() ok; validObject: ") vo <- validObject(tt, test = TRUE) cat(if(isTRUE(vo)) "ok" else paste("OOOOOOPS:", vo), "\n") } } } cat("---\n") } } cat('Time elapsed: ', proc.time(),'\n') # for the above "part I" if(doExtras && !interactive()) { # don't want to see on source() cat("All classes in the 'Matrix' package:\n") for(cln in allCl) { cat("\n-----\n\nClass", dQuote(cln),":\n ", paste(rep("~",nchar(cln)),collapse=''),"\n") ## A smarter version would use getClass() instead of showClass(), ## build the "graph" and only then display. ## showClass(cln) } cat("\n \n") ## One could extend the `display' by using (something smarter than) ## are the "coerce" methods showing more than the 'Extends' output above? cat("All (S4) methods in the 'Matrix' package:\n") showMethods(where="package:Matrix") } # end{non-interactive} ## 1-indexing instead of 0-indexing for direct "dgT" should give error: ii <- as.integer(c(1,2,2)) jj <- as.integer(c(1,1,3)) assertError(new("dgTMatrix", i=ii, j=jj, x= 10*(1:3), Dim=2:3)) assertError(new("dgTMatrix", i=ii, j=jj - 1:1, x= 10*(1:3), Dim=2:3)) assertError(new("dgTMatrix", i=ii - 1:1, j=jj, x= 10*(1:3), Dim=2:3)) (mm <- new("dgTMatrix", i=ii - 1:1, j=jj - 1:1, x= 10*(1:3), Dim=2:3)) validObject(mm) ### Sparse Logical: m <- Matrix(c(0,0,2:0), 3,5) mT <- as(mC <- as(m, "CsparseMatrix"), "TsparseMatrix") stopifnot(identical(as(mT,"CsparseMatrix"), mC)) (mC. <- as(mT[1:2, 2:3], "CsparseMatrix")) (mlC <- as(mC. , "lMatrix")) as(mlC,"ltCMatrix") if(!doExtras && !interactive()) q("no") ## (saving testing time) ### Test all classes: validObject(new( * )) should be fulfilled ----------- ## need stoplist for now: Rcl.struc <- c("gR", "sR", "tR") (dR.classes <- paste0(paste0("d", Rcl.struc[Rcl.struc != "gR"]), "Matrix")) (.R.classes <- paste0(sort(outer(c("l", "n"), Rcl.struc, paste0)), "Matrix")) # have only stub implementation Mat.MatFact <- c("Cholesky", "pCholesky", "BunchKaufman", "pBunchKaufman")##, "LDL" ##FIXME maybe move to ../../MatrixModels/tests/ : ## (modmat.classes <- .subclasses("modelMatrix")) no.t.etc <- c(.R.classes, dR.classes, Mat.MatFact)#, modmat.classes) no.t.classes <- c(no.t.etc) # no t() available no.norm.classes <- no.t.classes not.Ops <- NULL # "Ops", e.g. "+" fails not.coerce1 <- no.t.etc # not coercable from "dgeMatrix" not.coerce2 <- no.t.etc # not coercable from "matrix" tstMatrixClass <- function(cl, mM = Matrix(c(2,1,1,2) + 0, 2,2, dimnames=rep( list(c("A","B")), 2)), # dimnames: *symmetric* mm = as(mM, "matrix"), recursive = TRUE, offset = 0) { ## Purpose: Test 'Matrix' class {and do this for all of them} ## ---------------------------------------------------------------------- ## Arguments: cl: class object of a class that extends "Matrix" ## mM: a "Matrix"-matrix which will be coerced to class 'cl' ## mm: a S3-matrix which will be coerced to class 'cl' ## ---------------------------------------------------------------------- ## Author: Martin Maechler ## from pkg sfsmisc : bl.string <- function(no) sprintf("%*s", no, "") ## Compute a few things only once : mM <- as(mM, "dgeMatrix") trm <- mm; trm[lower.tri(mm)] <- 0 ## not yet used: ## summList <- lapply(getGroupMembers("Summary"), get, ## envir = asNamespace("Matrix")) if(recursive) cList <- character(0) extraValid <- function(m, cl = class(m)) { sN <- slotNames(cl) sN <- sN[sN != "factors"] for(nm in sN) if(!is.null(a <- attributes(slot(m, nm)))) stop(sprintf("slot '%s' with %d attributes, named: ", nm, length(a)), paste(names(a), collapse=", ")) invisible(TRUE) } ## This is the recursive function dotestMat <- function(cl, offset) { cat. <- function(...) cat(bl.string(offset), ...) clNam <- cl@subClass cat("\n") cat.(clNam) ##--------- clD <- getClassDef(clNam) if(isVirtualClass(clD)) { cat(" - is virtual\n") if(recursive) { cat.("----- begin{class :", clNam, "}----new subclasses----\n") for(ccl in clD@subclasses) { cclN <- ccl@subClass if(cclN %in% cList) cat.(cclN,": see above\n") else { cList <<- c(cList, cclN) dotestMat(ccl, offset = offset + 3) } } cat.("----- end{class :", clNam, "}---------------------\n") } } else { ## --- actual class --- genC <- extends(clD, "generalMatrix") symC <- extends(clD, "symmetricMatrix") triC <- extends(clD, "triangularMatrix") diaC <- extends(clD, "diagonalMatrix") if(!(genC || symC || triC || diaC)) stop("does not extend one of 'general', 'symmetric', 'triangular', or 'diagonal'") sparseC <- extends(clD, "sparseMatrix") denseC <- extends(clD, "denseMatrix") if(!(sparseC || denseC)) stop("does not extend either 'sparse' or 'dense'") cat("; new(..): ") m <- new(clNam) ; cat("ok; ") m0 <- matrix(,0,0) if(canCoerce(m0, clNam)) { cat("; as(matrix(,0,0), <.>): ") stopifnot(Qidentical(m, as(m0, clNam))); cat("ok; ") } is_p <- extends(clD, "indMatrix") is_cor <- extends(clD, "corMatrix") # has diagonal divided out if(canCoerce(mm, clNam)) { ## replace 'm' by `non-empty' version cat("canCoerce() ") m0 <- { if(triC) trm else if(is_p) mm == 1 # logical *and* "true" permutation else mm } if(extends(clD, "lMatrix") || extends(clD, "nMatrix")) storage.mode(m0) <- "logical" else if(extends(clD, "zMatrix")) storage.mode(m0) <- "complex" validObject(m) ## validity of trivial 'm' before replacing m <- as(m0, clNam) if(is_cor) m0 <- cov2cor(m0) } else { m0 <- vector(Matrix:::.type.kind[Matrix:::.M.kindC(clNam)]) dim(m0) <- c(0L,0L) } ## m0 is the 'matrix' version of our 'Matrix' m m. <- m0 ##m. <- if(is_p) as.integer(m0) else m0 EQ <- if(is_cor) all.equal else identical stopifnot(EQ(m0[FALSE], m[FALSE]) , EQ(m.[TRUE], m[TRUE]) , if(length(m) >= 2) EQ(m.[2:1], m[2:1]) else TRUE) if(all(dim(m) > 0)) { ## matrix(0,0,0)[FALSE,] is invalid too m00 <- m[FALSE,FALSE] m.. <- m[TRUE , TRUE] stopifnot(dim(m00) == c(0L,0L), dim(m..) == dim(m)) ## not yet , class(m00) == clNam , identical(m.. , m) } cat("valid: ", validObject(m), extraValid(m, clNam),"\n") ## This can only work as long as 'm' has no NAs : ## not yet -- have version in not.Ops below ## once we have is.na(): ## stopifnot(all(m == m | is.na(m))) ## check all() and "==" [Compare] ## if(any(m != m && !is.na(m))) show(m) ## coerce to 'matrix' m.m <- as(m, "matrix") ##=========## checkMatrix(m, m.m, ##=========## do.t= !(clNam %in% no.t.classes), doNorm= !(clNam %in% no.norm.classes), doOps = all(clNam != not.Ops), doCoerce = all(clNam != not.coerce1), catFUN = cat.) ### FIXME: organize differently : ### 1) produce 'mM' and 'mm' for the other cases, ### 2) use identical code for all cases if(is(m, "dMatrix") && is(m, "compMatrix")) { if(any(clNam == not.coerce1)) cat.("not coercable_1\n") else if(canCoerce(mM, clNam)) { m2 <- as(mM, clNam) cat("valid:", validObject(m2), "\n") if(!is_cor) ## as.vector() stopifnot(as.vector(m2) == as.vector(mM)) cat.("[cr]bind2():"); mm2 <- cbind2(m2,m2) stopifnot(dim(rbind2(m2,m2)) == 2:1 * dim(mM)); cat(" ok") if(genC && class(mm2) == clNam) ## non-square matrix when "allowed" m2 <- mm2 dd <- diag(m2) cat("; `diag<-` ") diag(m2) <- 10*dd stopifnot(is_cor || identical(dd, diag(mM)), identical(10*dd, diag(m2))); cat("ok ") } ## if(all(clNam != not.coerce2)) { if(canCoerce("matrix", clNam)) { cat.("as(matrix, ): ") m3 <- as(mm, clNam) cat("valid:", validObject(m3), "\n") } else cat.(" not coerceable from \"matrix\"\n") ## } } ## else { ... no happens in tstMatrix() above .. } ## if(is(m, "denseMatrix")) { ## ## ......... ## cat.("as dsparse* ") ## msp <- as(m, "dsparseMatrix") ## cat.("; valid coercion: ", validObject(msp), "\n") ## } else if(is(m, "sparseMatrix")) { ## } else cat.("-- not dense nor sparse -- should not happen(!?)\n") if(is(m, "dsparseMatrix")) { if(any(clNam == not.coerce1)) cat.("not coercable_1\n") else { ## make sure we can coerce to dgT* -- needed, e.g. for "image" ## change: use Tsparse instead of dgT, unless it *is* Tsparse: isT <- is(m, "TsparseMatrix") prefix <- if(isT) "dgT" else "Tsparse" Tcl <- paste(prefix, "Matrix", sep='') cat.(sprintf("as %s* ", prefix)) mgT <- as(m, Tcl) cat(sprintf("; valid %s* coercion: %s\n", prefix, validObject(mgT))) } } } } # end{dotestMat} for(scl in getClass(cl)@subclasses) dotestMat(scl, offset + 1) } ## in case we want to make progress: ## codetools::checkUsage(tstMatrixClass, all=TRUE) tstMatrixClass("Matrix") if(FALSE)## or just a sub class tstMatrixClass("triangularMatrix") cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons'' if(!interactive()) warnings() Matrix/tests/matr-exp.R0000644000175100001440000000460612271746775014606 0ustar hornikuserslibrary(Matrix) ## Matrix Exponential source(system.file("test-tools.R", package = "Matrix")) ## e ^ 0 = 1 - for matrices: assert.EQ.mat(expm(Matrix(0, 3,3)), diag(3), tol = 0)# exactly ## e ^ diag(.) = diag(e ^ .): assert.EQ.mat(expm(as(diag(-1:4), "dgeMatrix")), diag(exp(-1:4))) set.seed(1) rE <- replicate(100, { x <- rlnorm(12) relErr(as(expm(as(diag(x), "dgeMatrix")), "matrix"), diag(exp(x))) }) stopifnot(mean(rE) < 1e-15, max(rE) < 1e-14) summary(rE) ## Some small matrices m1 <- Matrix(c(1,0,1,1), nc = 2) e1 <- expm(m1) assert.EQ.mat(e1, cbind(c(exp(1),0), exp(1))) m2 <- Matrix(c(-49, -64, 24, 31), nc = 2) e2 <- expm(m2) ## The true matrix exponential is 'te2': e_1 <- exp(-1) e_17 <- exp(-17) te2 <- rbind(c(3*e_17 - 2*e_1, -3/2*e_17 + 3/2*e_1), c(4*e_17 - 4*e_1, -2 *e_17 + 3 *e_1)) assert.EQ.mat(e2, te2, tol = 1e-13) ## See the (average relative) difference: all.equal(as(e2,"matrix"), te2, tolerance = 0) # 1.48e-14 on "lynne" ## The ``surprising identity'' det(exp(A)) == exp( tr(A) ) ## or log det(exp(A)) == tr(A) : stopifnot(all.equal(c(determinant(e2)$modulus), sum(diag(m2)))) ## a very simple nilpotent one: (m3 <- Matrix(cbind(0,rbind(6*diag(3),0))))# sparse stopifnot(all(m3 %*% m3 %*% m3 %*% m3 == 0))# <-- m3 "^" 4 == 0 e3 <- expm(m3) E3 <- expm(Matrix(m3, sparse=FALSE)) s3 <- symmpart(m3) # dsCMatrix es3 <- expm(s3) e3. <- rbind(c(1,6,18,36), c(0,1, 6,18), c(0,0, 1, 6), c(0,0, 0, 1)) stopifnot(is(e3, "triangularMatrix"), is(es3, "symmetricMatrix"), identical(e3, E3), identical(as.mat(e3), e3.), all.equal(as(es3,"generalMatrix"), expm(as(s3,"generalMatrix"))) ) ## This used to be wrong {bug in octave-origin code}: M6 <- Matrix(c(0, -2, 0, 0, 0, 0, 10, 0, 0, 0,10,-2, 0, 0, 0, 0,-2, 0, 0, 10,-2,-2,-2,10, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0), 6, 6) exp.M6 <- expm(M6) as(exp.M6, "sparseMatrix")# prints a bit more nicely stopifnot(all.equal(t(exp.M6), expm(t(M6)), tol = 1e-12), all.equal(exp.M6[,3], c(0,0,1,0,-2,0), tolerance = 1e-12), all.equal(exp.M6[,5], c(0,0,0,0, 1,0), tolerance = 1e-12), all(exp.M6[3:4, c(1:2,5:6)] == 0) ) cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons'' Matrix/tests/dpo-test.R0000644000175100001440000001403212271746775014602 0ustar hornikusers### Testing positive definite matrices library(Matrix) source(system.file("test-tools.R", package = "Matrix"))# identical3() etc h9 <- Hilbert(9) stopifnot(c(0,0) == dim(Hilbert(0)), c(9,9) == dim(h9), identical(h9@factors, list())) str(h9)# no 'factors' all.equal(c(determinant(h9)$modulus), -96.7369456, tolerance = 2e-8) ## determinant() now working via chol(): ==> h9 now has factorization stopifnot(names(h9@factors) == "Cholesky", identical(ch9 <- chol(h9), h9@factors$Cholesky)) round(ch9, 3) ## round() preserves 'triangular' ! str(f9 <- as(ch9, "dtrMatrix")) stopifnot(all.equal(rcond(h9), 9.0938e-13), all.equal(rcond(f9), 9.1272e-7, tolerance = 1e-6))# more precision fails options(digits=4) (cf9 <- crossprod(f9))# looks the same as h9 : assert.EQ.mat(h9, as.matrix(cf9), tol=1e-15) h9. <- round(h9, 2)# actually loses pos.def. "slightly" # ==> the above may be invalid in the future h9p <- as(h9, "dppMatrix") h9.p <- as(h9., "dppMatrix") ch9p <- chol(h9p) stopifnot(identical(ch9p, h9p@factors$pCholesky), identical(names(h9p@factors), c("Cholesky", "pCholesky"))) h4 <- h9.[1:4, 1:4] # this and the next h9.[1,1] <- 10 # had failed in 0.995-14 h9p[1,1] <- 10 stopifnot(isValid(h9., "symmetricMatrix"), isValid(h9p, "symmetricMatrix"), isValid(h4, "symmetricMatrix")) h9p[1,2] <- 99 stopifnot(class(h9p) == "dgeMatrix", h9p[1,1:2] == c(10,99)) str(h9p <- as(h9, "dppMatrix"))# {again} h6 <- h9[1:6,1:6] stopifnot(all(h6 == Hilbert(6)), length(h6@factors) == 0, is(th9p <- t(h9p), "dppMatrix"), is(h9p@factors$Cholesky,"Cholesky")) H6 <- as(h6, "dspMatrix") pp6 <- as(H6, "dppMatrix") po6 <- as(pp6,"dpoMatrix") hs <- as(h9p, "dspMatrix") stopifnot(names(H6@factors) == "pCholesky", names(pp6@factors) == "pCholesky", names(hs@factors) == "Cholesky") # for now chol(hs) # and that is cached in 'hs' too : stopifnot(names(hs@factors) %in% c("Cholesky","pCholesky"), all.equal(h9, crossprod(hs@factors$pCholesky), tolerance =1e-13), all.equal(h9, crossprod(hs@factors$ Cholesky), tolerance =1e-13)) hs@x <- 1/h9p@x # is not pos.def. anymore validObject(hs) # "but" this does not check stopifnot(diag(hs) == seq(1, by = 2, length = 9)) s9 <- solve(h9p, seq(nrow(h9p))) signif(t(s9)/10000, 4)# only rounded numbers are platform-independent (I9 <- h9p %*% s9) m9 <- matrix(1:9, dimnames = list(NULL,NULL)) stopifnot(all.equal(m9, as.matrix(I9), tolerance = 2e-9)) ### Testing nearPD() --- this is partly in ../man/nearPD.Rd : pr <- Matrix(c(1, 0.477, 0.644, 0.478, 0.651, 0.826, 0.477, 1, 0.516, 0.233, 0.682, 0.75, 0.644, 0.516, 1, 0.599, 0.581, 0.742, 0.478, 0.233, 0.599, 1, 0.741, 0.8, 0.651, 0.682, 0.581, 0.741, 1, 0.798, 0.826, 0.75, 0.742, 0.8, 0.798, 1), nrow = 6, ncol = 6) nL <- list(r = nearPD(pr, conv.tol = 1e-7), # default r.1 = nearPD(pr, conv.tol = 1e-7, corr = TRUE), rs = nearPD(pr, conv.tol = 1e-7, doDyk=FALSE), rs1 = nearPD(pr, conv.tol = 1e-7, doDyk=FALSE, corr = TRUE), rH = nearPD(pr, conv.tol = 1e-15), rH.1= nearPD(pr, conv.tol = 1e-15, corr = TRUE)) sapply(nL, `[`, c("iterations", "normF")) allnorms <- function(d) sapply(c("1","I","F","M"), function(typ) norm(d, typ)) ## "F" and "M" distances are larger for the (corr=TRUE) constrained: 100 * sapply(nL, function(rr) allnorms((pr - rr $ mat))) ## But indeed, the 'corr = TRUE' constraint yield a better solution, ## if you need the constraint : cov2cor() does not just fix it up : 100 * (nn <- sapply(nL, function(rr) allnorms((pr - cov2cor(rr $ mat))))) stopifnot( all.equal(nn["1",], c(r =0.0999444286984696, r.1= 0.0880468666522317, rs=0.0999444286984702, rs1= 0.0874614179943388, rH=0.0999444286984696, rH.1=0.0880468927726625), tolerance=1e-9)) nr <- nL $rH.1 $mat stopifnot( all.equal(nr[lower.tri(nr)], c(0.4877861230299, 0.6429309061748, 0.4904554299278, 0.6447150779852, 0.8082100656035, 0.514511537243, 0.2503412693503, 0.673249718642, 0.7252316891977, 0.5972811755863, 0.5818673040157, 0.7444549621769, 0.7308954865819, 0.7713984381710, 0.8124321235679), tolerance = 1e-9)) showProc.time() set.seed(27) m9 <- h9 + rnorm(9^2)/1000 ; m9 <- (m9 + t(m9))/2 nm9 <- nearPD(m9) showProc.time() nRep <- if(doExtras) 50 else 4 CPU <- 0 for(M in c(5, 12)) for(i in 1:nRep) { m <- matrix(round(rnorm(M^2),2), M, M) m <- m + t(m) diag(m) <- pmax(0, diag(m)) + 1 m <- cov2cor(m) CPU <- CPU + system.time(n.m <- nearPD(m))[1] X <- as(n.m$mat, "matrix") stopifnot(all.equal(X, (X + t(X))/2, tolerance = 8*.Machine$double.eps), all.equal(eigen(n.m$mat, only.values=TRUE)$values, n.m$eigenvalues, tolerance = 4e-8)) } cat('Time elapsed for ',nRep, 'nearPD(): ', CPU,'\n') showProc.time() ## cov2cor() m <- diag(6:1) %*% as(pr,"matrix") %*% diag(6:1) # so we can "vector-index" m[upper.tri(m)] <- 0 ltm <- which(lower.tri(m)) ne <- length(ltm) set.seed(17) m[ltm[sample(ne, 3/4*ne)]] <- 0 m <- (m + t(m))/2 # now is a covariance matrix with many 0 entries (spr <- Matrix(m)) cspr <- cov2cor(spr) ev <- eigen(cspr, only.v = TRUE)$values stopifnot(is(spr, "dsCMatrix"), is(cspr,"dsCMatrix"), all.equal(ev, c(1.5901626099, 1.1902658504, 1, 1, 0.80973414959, 0.40983739006), tolerance=1e-10)) x <- c(2,1,1,2) mM <- Matrix(x, 2,2, dimnames=rep( list(c("A","B")), 2))# dsy mM stopifnot(length(mM@factors)== 0) (po <- as(mM, "dpoMatrix")) # still has dimnames mm <- as(mM, "matrix") msy <- as(mm, "dsyMatrix") stopifnot(Qidentical(mM, msy), length(mM @factors)== 1, length(msy@factors)== 0) c1 <- as(mm, "corMatrix") c2 <- as(mM, "corMatrix") c3 <- as(po, "corMatrix") (co.x <- matrix(x/2, 2,2)) checkMatrix(c1) assert.EQ.mat(c1, co.x) assert.EQ.mat(c2, co.x) # failed in Matrix 0.999375-9, because of ## the wrong automatic "dsyMatrix" -> "corMatrix" coerce method stopifnot(identical(dimnames(c1), dimnames(mM)), all.equal(c1, c3, tolerance =1e-15)) showProc.time() Matrix/tests/spModel.matrix.R0000644000175100001440000001673112271746775015761 0ustar hornikuserslibrary(Matrix) ## This is example(sp....) -- much extended mEQ <- function(x,y, ...) { ## first drop columns from y which are all 0 : if(any(i0 <- colSums(abs(x)) == 0)) { message(gettextf("x had %d zero-columns", sum(i0))) x <- x[, !i0, drop=FALSE] } if(any(i0 <- colSums(abs(y)) == 0)) { message(gettextf("y had %d zero-columns", sum(i0))) y <- y[, !i0, drop=FALSE] } isTRUE(all.equal(x,y, tolerance =0, ...)) } ##' Is sparse.model.matrix() giving the "same" as dense model.matrix() ? ##' ##' @return logical ##' @param frml formula ##' @param dat data frame ##' @param showFactors ##' @param ... isEQsparseDense <- function(frml, dat, showFactors = isTRUE(getOption("verboseSparse")), ...) { ## Author: Martin Maechler, Date: 21 Jul 2009 stopifnot(inherits(frml, "formula"), is.data.frame(dat)) if(showFactors) print(attr(terms(frml, data=dat), "factors")) smm <- sparse.model.matrix(frml, dat, ...) mm <- model.matrix(frml, dat, ...) sc <- smm@contrasts mEQ(as(smm, "generalMatrix"), Matrix(mm, sparse=TRUE)) & identical(smm@assign, attr(mm, "assign")) & (if(is.null(mc <- attr(mm, "contrasts"))) length(sc) == 0 else identical(sc, mc)) } ### ------------ all the "datasets" we construct for use ------------- dd <- data.frame(a = gl(3,4), b = gl(4,1,12))# balanced 2-way (dd3 <- cbind(dd, c = gl(2,6), d = gl(3,8))) dd. <- dd3[- c(1, 13:15, 17), ] set.seed(17) dd4 <- cbind(dd, c = gl(2,6), d = gl(8,3)) dd4 <- cbind(dd4, x = round(rnorm(nrow(dd4)), 1)) dd4 <- dd4[- c(1, 13:15, 17), ] ##-> 'd' has unused levels dM <- dd4 dM$X <- outer(10*rpois(nrow(dM), 2), 1:3) dM$Y <- cbind(pmax(0, dM$x - .3), floor(4*rnorm(nrow(dM)))) str(dM)# contains *matrices* options("contrasts") # the default: "contr.treatment" op <- options(sparse.colnames = TRUE) # for convenience stopifnot(identical(## non-sensical, but "should work" (with a warning each): sparse.model.matrix(a~ 1, dd), sparse.model.matrix( ~ 1, dd))) sparse.model.matrix(~ a + b, dd, contrasts = list(a="contr.sum")) sparse.model.matrix(~ a + b, dd, contrasts = list(b="contr.SAS")) xm <- sparse.model.matrix(~ x, dM) # {no warning anymore ...} dxm <- Matrix(model.matrix(~ x, dM), sparse=TRUE) stopifnot(is(xm, "sparseMatrix"), mEQ(as(xm,"generalMatrix"), dxm)) ## Sparse method is equivalent to the traditional one : stopifnot(isEQsparseDense(~ a + b, dd), suppressWarnings(isEQsparseDense(~ x, dM)), isEQsparseDense(~ 0 + a + b, dd), identical(sparse.model.matrix(~ 0 + a + b, dd), sparse.model.matrix(~ -1 + a + b, dd)), isEQsparseDense(~ a + b, dd, contrasts = list(a="contr.sum")), isEQsparseDense(~ a + b, dd, contrasts = list(a="contr.SAS")), ## contrasts as *functions* or contrast *matrices* : isEQsparseDense(~ a + b, dd, contrasts = list(a=contr.sum, b=contr.treatment(4))), isEQsparseDense(~ a + b, dd, contrasts = list(a=contr.SAS(3),# << ok after 'contrasts<-' update b = function(n, contr=TRUE, sparse=FALSE) contr.sum(n=n, contr=contr, sparse=sparse)))) sm <- sparse.model.matrix(~a * b, dd, contrasts = list(a= contr.SAS(3, sparse = TRUE))) sm ## FIXME: Move part of this to ../../MatrixModels/tests/ ##stopifnot(all(sm == model.Matrix( ~a * b, dd, contrasts= list(a= contr.SAS(3))))) ## stopifnot(isEQsparseDense(~ a + b + c + d, dd.)) stopifnot(isEQsparseDense(~ a + b:c + c + d, dd.)) ## no intercept -- works too stopifnot(isEQsparseDense(~ -1+ a + b + c + d, dd.)) stopifnot(isEQsparseDense(~ 0 + a + b:c + c + d, dd.)) Sparse.model.matrix <- function(...) { s <- sparse.model.matrix(...) as(s, "generalMatrix")# dropping 'assign',.. slots } ## dim(mm <- Matrix(model.matrix(~ a + b + c + d, dd4), sparse=TRUE)) dim(sm <- Sparse.model.matrix(~ a + b + c + d, dd4)) ## was (19 13), when 'drop.unused.levels' was implicitly TRUE dim(sm. <- Sparse.model.matrix(~ a + b + c + d, dd4, drop.unused.levels=TRUE)) stopifnot(mEQ(sm , mm), ## (both have a zero column) mEQ(sm., mm)) ## << that's ok, since mm has all-0 column ! ## look at this : all(mm[,"d5"] == 0) ## !!!! --- correct: a column of all 0 <--> dropped level! stopifnot(all.equal(sm., mm[, - which("d5" == colnames(mm))])) ## indeed ! ## i.e., sm has just dropped an all zero column --- which it should! stopifnot(isEQsparseDense(~ 1 + sin(x) + b*c + a:x, dd4, show=TRUE)) stopifnot(isEQsparseDense(~ I(a) + b*c + a:x, dd4, show=TRUE)) ## no intercept -- works too stopifnot(isEQsparseDense(~ 0+ I(a) + b*c + a:x, dd4, show=TRUE)) f <- ~ 1 + a + b*c + a*x attr(terms(f, data=dd4), "factors") dim(mm <- Matrix(model.matrix(f, data=dd4), sparse=TRUE)) dim(sm <- Sparse.model.matrix(f, data=dd4)) # == stopifnot(mEQ(sm, mm)) f <- ~ a*X + X*Y + a*c attr(terms(f, data=dM), "factors") dim(mm <- Matrix(model.matrix(f, data=dM), sparse=TRUE)) dim(sm <- Sparse.model.matrix(f, data=dM, verbose=TRUE)) stopifnot(mEQ(sm, mm)) ## high order f <- ~ a:b:X:c:Y mm <- Matrix(model.matrix(f, data=dM), sparse=TRUE) sm <- Sparse.model.matrix(f, data=dM, verbose=2) stopifnot(mEQ(sm, mm)) f <- ~ 1 + a + b*c + a*x + b*d*x + b:c:d attr(terms(f, data=dd4), "factors") dim(mm <- Matrix(model.matrix(f, data=dd4), sparse=TRUE)) ## 19 100 dim(sm <- Sparse.model.matrix(f, data=dd4)) ## (ditto) dim(sm. <- Sparse.model.matrix(f, data=dd4, drop.unused.levels=TRUE)) # 19 88 stopifnot(mEQ(sm, mm), mEQ(sm., mm))# {32, 32; 20 and 32 zero-columns ..} ## now get a bit courageous: ## ## stopifnot(isEQsparseDense(~ 1 + c + a:b:d, dat=dd4)) dim(mm <- Matrix(model.matrix(~ 1 + a + b*c + a:b:c:d, data=dd4), sparse=TRUE)) ## 19 202 dim(sm <- Sparse.model.matrix(~ 1 + a + b*c + a:b:c:d, data=dd4)) dim(sm. <- Sparse.model.matrix(~ 1 + a + b*c + a:b:c:d, data=dd4, drop.unused.levels=TRUE)) stopifnot(mEQ(sm, mm), mEQ(sm., mm))# {173, 173, 149 and 173 zero-columns !} ## stopifnot(isEQsparseDense(~ 1 + a + b*c + a:b:c:d, dat=dd4)) dim(mm <- Matrix(model.matrix(~ 1 + a + b:c + a:b:d, data=dd4), sparse=TRUE)) ## 19 107 dim(sm <- Sparse.model.matrix(~ 1 + a + b:c + a:b:d, data=dd4)) dim(sm. <- Sparse.model.matrix(~ 1 + a + b:c + a:b:d, data=dd4, drop.unused.levels=TRUE)) stopifnot(mEQ(sm, mm), mEQ(sm., mm)) dim(mm <- Matrix(model.matrix(~ a*b*c +c*d, dd4), sparse=TRUE)) ## 19 38 dim(sm <- Sparse.model.matrix(~ a*b*c +c*d, dd4))# (ditto) dim(sm. <- Sparse.model.matrix(~ a*b*c +c*d, dd4, drop.unused.levels=TRUE)) stopifnot(mEQ(sm, mm), mEQ(sm., mm)) f1 <- ~ (a+b+c+d)^2 + (a+b):c:d + a:b:c:d f2 <- ~ (a+b+c+d)^4 - a:b:c - a:b:d mm1 <- Matrix(model.matrix(f1, dd4), sparse=TRUE) dim(mm2 <- Matrix(model.matrix(f2, dd4), sparse=TRUE)) sm1 <- sparse.model.matrix(f1, dd4) dim(sm2 <- sparse.model.matrix(f2, dd4)) s.1 <- sparse.model.matrix(f1, dd4, drop.unused.levels=TRUE) dim(s.2 <- sparse.model.matrix(f2, dd4, drop.unused.levels=TRUE)) stopifnot(identical(mm1,mm2), identical(sm1,sm2), identical(s.1,s.2), mEQ(sm1,mm1), mEQ(s.1,mm1)) str(dd <- data.frame(d = gl(10,6), a = ordered(gl(3,20)))) X. <- sparse.model.matrix(~ a + d, data = dd) ## failed because of contr.poly default in Matrix 0.999375-33 stopifnot(dim(X.) == c(60, 12), nnzero(X.) == 234, isEQsparseDense(~ 0 + d + I(as.numeric(d)^2), dd)) ## I(.) failed (upto 2010-05-07) cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons'' if(!interactive()) warnings() Matrix/tests/indexing.Rout.save0000644000175100001440000020336312271755360016332 0ustar hornikusers R Under development (unstable) (2014-01-26 r64897) -- "Unsuffered Consequences" Copyright (C) 2014 The R Foundation for Statistical Computing Platform: x86_64-unknown-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. 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Type 'q()' to quit R. > #### For both 'Extract' ("[") and 'Replace' ("[<-") Method testing > #### aka subsetting and subassignment > > #### suppressPackageStartupMessages(...) as we have an *.Rout.save to Rdiff against > stopifnot(suppressPackageStartupMessages(require(Matrix))) > > source(system.file("test-tools.R", package = "Matrix"), keep.source = FALSE) > ##-> identical3() etc > cat("doExtras:",doExtras,"\n") doExtras: FALSE > > if(interactive()) { + options(error = recover, warn = 1) + } else if(FALSE) { ## MM @ testing *manually* only + options(error = recover, Matrix.verbose = TRUE, warn = 1) + } else { + options(Matrix.verbose = TRUE, warn = 1) + } > > > ### Dense Matrices > > m <- Matrix(1:28 +0, nrow = 7) > validObject(m) [1] TRUE > stopifnot(identical(m, m[]), + identical(m[2, 3], 16), # simple number + identical(m[2, 3:4], c(16,23)), # simple numeric of length 2 + identical(m[NA,NA], as(Matrix(NA, 7,4), "dMatrix"))) > > m[2, 3:4, drop=FALSE] # sub matrix of class 'dgeMatrix' 1 x 2 Matrix of class "dgeMatrix" [,1] [,2] [1,] 16 23 > m[-(4:7), 3:4] # ditto; the upper right corner of 'm' 3 x 2 Matrix of class "dgeMatrix" [,1] [,2] [1,] 15 22 [2,] 16 23 [3,] 17 24 > > ## rows or columns only: > m[1,] # first row, as simple numeric vector [1] 1 8 15 22 > m[,2] # 2nd column [1] 8 9 10 11 12 13 14 > m[,1:2] # sub matrix of first two columns 7 x 2 Matrix of class "dgeMatrix" [,1] [,2] [1,] 1 8 [2,] 2 9 [3,] 3 10 [4,] 4 11 [5,] 5 12 [6,] 6 13 [7,] 7 14 > m[-(1:6),, drop=FALSE] # not the first 6 rows, i.e. only the 7th 1 x 4 Matrix of class "dgeMatrix" [,1] [,2] [,3] [,4] [1,] 7 14 21 28 > m[integer(0),] #-> 0 x 4 Matrix 0 x 4 Matrix of class "dgeMatrix" [,1] [,2] [,3] [,4] > m[2:4, numeric(0)] #-> 3 x 0 Matrix 3 x 0 Matrix of class "dgeMatrix" [1,] [2,] [3,] > > ## logical indexing > stopifnot(identical(m[2,3], m[(1:nrow(m)) == 2, (1:ncol(m)) == 3]), + identical(m[2,], m[(1:nrow(m)) == 2, ]), + identical(m[,3:4], m[, (1:4) >= 3])) > > ## dimnames indexing: > mn <- m > dimnames(mn) <- list(paste("r",letters[1:nrow(mn)],sep=""), + LETTERS[1:ncol(mn)]) > checkMatrix(mn) norm(m [7 x 4]) : 1 I F M ok Summary: ok 2*m =?= m+m: identical m >= m for all: ok m < m for none: ok > mn["rd", "D"] [1] 25 > msr <- ms <- as(mn,"sparseMatrix") > mnr <- mn > v <- rev(as(ms, "vector")) > mnr[] <- v > msr[] <- v # [<- "sparse" -- not very sensical; did fail w/o a message diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) > z <- msr; z[] <- 0 > zz <- as(array(0, dim(z)), "sparseMatrix") > a.m <- as(mnr,"matrix") > stopifnot(identical(mn["rc", "D"], mn[3,4]), mn[3,4] == 24, + identical(mn[, "A"], mn[,1]), mn[,1] == 1:7, + identical(mn[c("re", "rb"), "B"], mn[c(5,2), 2]), + identical(ms["rc", "D"], ms[3,4]), ms[3,4] == 24, + identical(ms[, "A"], ms[,1]), ms[,1] == 1:7, + identical(ms[ci <- c("re", "rb"), "B"], ms[c(5,2), 2]), + identical(rownames(mn[ci, ]), ci), + identical(rownames(ms[ci, ]), ci), + identical(colnames(mn[,cj <- c("B","D")]), cj), + identical(colnames(ms[,cj]), cj), + identical(a.m, as(msr,"matrix")), + identical(unname(z), zz), + identical(a.m, array(v, dim=dim(mn), dimnames=dimnames(mn))) + ) > showProc.time() Time elapsed: 0.232 0.002 0.237 > > ## Printing sparse colnames: > ms[sample(28, 20)] <- 0 diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) > ms <- t(rbind2(ms, 3*ms)) > cnam1 <- capture.output(show(ms))[2] ; op <- options("sparse.colnames" = "abb3") [[ suppressing 14 column names 'ra', 'rb', 'rc' ... ]] > cnam2 <- capture.output(show(ms))[2] ; options(op) # revert > stopifnot(## sparse printing + grep("^ +$", cnam1) == 1, # cnam1 is empty + identical(cnam2, + paste(" ", paste(rep(rownames(mn), 2), collapse=" ")))) > > mo <- m > m[2,3] <- 100 > m[1:2, 4] <- 200 > m[, 1] <- -1 > m[1:3,] 3 x 4 Matrix of class "dgeMatrix" [,1] [,2] [,3] [,4] [1,] -1 8 15 200 [2,] -1 9 100 200 [3,] -1 10 17 24 > > m. <- as.matrix(m) > > ## m[ cbind(i,j) ] indexing: > iN <- ij <- cbind(1:6, 2:3) > iN[2:3,] <- iN[5,2] <- NA > stopifnot(identical(m[ij], m.[ij]), + identical(m[iN], m.[iN])) > > ## testing operations on logical Matrices rather more than indexing: > g10 <- m [ m > 10 ] > stopifnot(18 == length(g10)) > stopifnot(10 == length(m[ m <= 10 ])) > sel <- (20 < m) & (m < 150) > sel.<- (20 < m.)& (m.< 150) > nsel <-(20 >= m) | (m >= 150) > (ssel <- as(sel, "sparseMatrix")) 7 x 4 sparse Matrix of class "lgCMatrix" [1,] . . . . [2,] . . | . [3,] . . . | [4,] . . . | [5,] . . . | [6,] . . . | [7,] . . | | > stopifnot(is(sel, "lMatrix"), is(ssel, "lsparseMatrix"), + identical3(as.mat(sel.), as.mat(sel), as.mat(ssel)), + identical3(!sel, !ssel, nsel), # ! is typically dense + identical3(m[ sel], m[ ssel], as.matrix(m)[as.matrix( ssel)]), + identical3(m[!sel], m[!ssel], as.matrix(m)[as.matrix(!ssel)]) + ) > showProc.time() Time elapsed: 0.122 0.001 0.123 > > ## more sparse Matrices -------------------------------------- > > ##' @title Check sparseMatrix sub-assignment m[i,j] <- v > ##' @param ms sparse Matrix > ##' @param mm its [traditional matrix]-equivalent > ##' @param k (approximate) length of index vectors (i,j) > ##' @param n.uniq (approximate) number of unique values in i,j > ##' @param vRNG function(n) for random 'v' generation > ##' @param show logical; if TRUE, it will not stop on error > ##' @return > ##' @author Martin Maechler > chkAssign <- function(ms, mm = as(ms, "matrix"), + k = min(20,dim(mm)), n.uniq = k %/% 3, + vRNG = { if(is.numeric(mm) || is.complex(mm)) + function(n) rpois(n,lambda= 0.75)# <- about 47% zeros + else ## logical + function(n) runif(n) > 0.8 }, ## 80% zeros + showOnly=FALSE) + { + stopifnot(is(ms,"sparseMatrix")) + d <- dim(ms) + s1 <- function(n) sample(n, pmin(n, pmax(1, rpois(1, n.uniq)))) + i <- sample(s1(d[1]), k/2+ rpois(1, k/2), replace = TRUE) + j <- sample(s1(d[2]), k/2+ rpois(1, k/2), replace = TRUE) + assert.EQ.mat(ms[i,j], mm[i,j]) + ms2 <- ms. <- ms; mm. <- mm # save + ## now sub*assign* to these repeated indices, and then compare ----- + v <- vRNG(length(i) * length(j)) + mm[i,j] <- v + ms[i,j] <- v + ## useful to see (ii,ij), but confusing R/ESS when additionally debugging: + ## if(!showOnly && interactive()) { op <- options(error = recover); on.exit(options(op)) } + assert.EQ.mat(ms, mm, show=showOnly) + ## vector indexing m[cbind(i,j)] == m[i + N(j-1)] , N = nrow(.) + ii <- seq_len(min(length(i), length(j))) + i <- i[ii] + j <- j[ii] + ij <- cbind(i, j) + ii <- i + nrow(ms)*(j - 1) + ord.i <- order(ii) + iio <- ii[ord.i] + ui <- unique(iio) # compare these with : + neg.ii <- - setdiff(seq_len(prod(d)), ii) + stopifnot(identical(mm[ii], mm[ij]), + identical(ms.[ui], ms.[neg.ii]), + ms.[ij] == mm.[ii], ## M[ cbind(i,j) ] was partly broken; now checking + ms.[ii] == mm.[ii]) + v <- v[seq_len(length(i))] + if(is(ms,"nMatrix")) v <- as.logical(v) # ! + mm.[ij] <- v + ms.[ii] <- v + nodup <- (length(ui) == length(ii)) ## <==> ! anyDuplicated(iio) + if(nodup) { cat("[-]") # rare, unfortunately + ms2[neg.ii] <- v[ord.i] + stopifnot(identical(ms2, ms.)) + } + assert.EQ.mat(ms., mm., show=showOnly) + } ##{chkAssign} > > ## Get duplicated index {because these are "hard" (and rare) > getDuplIndex <- function(n, k) { + repeat { + i <- sample(n, k, replace=TRUE) # 3 4 6 9 2 9 : 9 is twice + if(anyDuplicated(i)) break + } + i + } > > ## From package 'sfsmisc': > repChar <- function (char, no) paste(rep.int(char, no), collapse = "") > > m <- 1:800 > set.seed(101) ; m[sample(800, 600)] <- 0 > m0 <- Matrix(m, nrow = 40) > m1 <- add.simpleDimnames(m0) > for(kind in c("n", "l", "d")) { + for(m in list(m0,m1)) { ## -- with and without dimnames ------------------------- + kClass <-paste0(kind, "Matrix" ) + Ckind <- paste0(kind, "gCMatrix") + Tkind <- paste0(kind, "gTMatrix") + str(mC <- as(m, Ckind)) + str(mT <- as(as(as(m, kClass), "TsparseMatrix"), Tkind)) + mm <- as(mC, "matrix") # also logical or double + IDENT <- if(kind == "n") function(x,y) Q.eq2(x,y, tol=0) else identical + stopifnot(identical(mT, as(as(mC, "TsparseMatrix"), Tkind)), + identical(mC, as(mT, Ckind)), + Qidentical(mC[0,0], new(Ckind)), + Qidentical(mT[0,0], new(Tkind)), + identical(unname(mT[0,]), new(Tkind, Dim = c(0L,ncol(m)))), + identical(unname(mT[,0]), new(Tkind, Dim = c(nrow(m),0L))), + IDENT(mC[0,], as(mT[FALSE,], Ckind)), + IDENT(mC[,0], as(mT[,FALSE], Ckind)), + sapply(pmin(min(dim(mC)), c(0:2, 5:10)), + function(k) {i <- seq_len(k); all(mC[i,i] == mT[i,i])}), + TRUE) + cat("ok\n") + show(mC[,1]) + show(mC[1:2,]) + show(mC[7, drop = FALSE]) + assert.EQ.mat(mC[1:2,], mm[1:2,]) + assert.EQ.mat(mC[0,], mm[0,]) + assert.EQ.mat(mC[,FALSE], mm[,FALSE]) + ## + ## *repeated* (aka 'duplicated') indices - did not work at all ... + i <- pmin(nrow(mC), rep(8:10,2)) + j <- c(2:4, 4:3) + assert.EQ.mat(mC[i,], mm[i,]) + assert.EQ.mat(mC[,j], mm[,j]) + ## FIXME? assert.EQ.mat(mC[,NA], mm[,NA]) -- mC[,NA] is all 0 "instead" of all NA + ## MM currently thinks we should NOT allow [ ] + assert.EQ.mat(mC[i, 2:1], mm[i, 2:1]) + assert.EQ.mat(mC[c(4,1,2:1), j], mm[c(4,1,2:1), j]) + assert.EQ.mat(mC[i,j], mm[i,j]) + ## + ## set.seed(7) + op <- options(Matrix.verbose = FALSE) + cat(" for(): ") + for(n in 1:(if(doExtras) 50 else 5)) { + chkAssign(mC, mm) + chkAssign(mC[-3,-2], mm[-3,-2]) + cat(".") + } + options(op) + cat(sprintf("\n[Ok]%s\n\n", repChar("-", 64))) + } + cat(sprintf("\nok( %s )\n== ###%s\n\n", kind, repChar("=", 70))) + }## end{for}--------------------------------------------------------------- Formal class 'ngCMatrix' [package "Matrix"] with 5 slots ..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 ... ..@ p : int [1:21] 0 8 22 28 37 41 50 63 71 81 ... ..@ Dim : int [1:2] 40 20 ..@ Dimnames:List of 2 .. ..$ : NULL .. ..$ : NULL ..@ factors : list() Formal class 'ngTMatrix' [package "Matrix"] with 5 slots ..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 ... ..@ j : int [1:200] 0 0 0 0 0 0 0 0 1 1 ... ..@ Dim : int [1:2] 40 20 ..@ Dimnames:List of 2 .. ..$ : NULL .. ..$ : NULL ..@ factors : list() Note: method with signature 'nsparseMatrix#sparseMatrix' chosen for function '==', target signature 'ngCMatrix#ngTMatrix'. "nMatrix#nMatrix", "sparseMatrix#nsparseMatrix" would also be valid ok [1] FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE [25] TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE [37] FALSE TRUE TRUE FALSE 2 x 20 sparse Matrix of class "ngCMatrix" [1,] . . . | . . | . . . . | . . | . | . . . [2,] . | . . . | . . . . . . | | . . . . | . [1] TRUE for(): ..... [Ok]---------------------------------------------------------------- Formal class 'ngCMatrix' [package "Matrix"] with 5 slots ..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 ... ..@ p : int [1:21] 0 8 22 28 37 41 50 63 71 81 ... ..@ Dim : int [1:2] 40 20 ..@ Dimnames:List of 2 .. ..$ : chr [1:40] "r1" "r2" "r3" "r4" ... .. ..$ : chr [1:20] "c1" "c2" "c3" "c4" ... ..@ factors : list() Formal class 'ngTMatrix' [package "Matrix"] with 5 slots ..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 ... ..@ j : int [1:200] 0 0 0 0 0 0 0 0 1 1 ... ..@ Dim : int [1:2] 40 20 ..@ Dimnames:List of 2 .. ..$ : chr [1:40] "r1" "r2" "r3" "r4" ... .. ..$ : chr [1:20] "c1" "c2" "c3" "c4" ... ..@ factors : list() ok r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE r27 r28 r29 r30 r31 r32 r33 r34 r35 r36 r37 r38 r39 FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE r40 FALSE 2 x 20 sparse Matrix of class "ngCMatrix" [[ suppressing 20 column names 'c1', 'c2', 'c3' ... ]] r1 . . . | . . | . . . . | . . | . | . . . r2 . | . . . | . . . . . . | | . . . . | . [1] TRUE for(): ..... [Ok]---------------------------------------------------------------- ok( n ) == ###====================================================================== Formal class 'lgCMatrix' [package "Matrix"] with 6 slots ..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 ... ..@ p : int [1:21] 0 8 22 28 37 41 50 63 71 81 ... ..@ Dim : int [1:2] 40 20 ..@ Dimnames:List of 2 .. ..$ : NULL .. ..$ : NULL ..@ x : logi [1:200] TRUE TRUE TRUE TRUE TRUE TRUE ... ..@ factors : list() Formal class 'lgTMatrix' [package "Matrix"] with 6 slots ..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 ... ..@ j : int [1:200] 0 0 0 0 0 0 0 0 1 1 ... ..@ Dim : int [1:2] 40 20 ..@ Dimnames:List of 2 .. ..$ : NULL .. ..$ : NULL ..@ x : logi [1:200] TRUE TRUE TRUE TRUE TRUE TRUE ... ..@ factors : list() ok [1] FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE [25] TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE [37] FALSE TRUE TRUE FALSE 2 x 20 sparse Matrix of class "lgCMatrix" [1,] . . . | . . | . . . . | . . | . | . . . [2,] . | . . . | . . . . . . | | . . . . | . [1] TRUE for(): ..... [Ok]---------------------------------------------------------------- Formal class 'lgCMatrix' [package "Matrix"] with 6 slots ..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 ... ..@ p : int [1:21] 0 8 22 28 37 41 50 63 71 81 ... ..@ Dim : int [1:2] 40 20 ..@ Dimnames:List of 2 .. ..$ : chr [1:40] "r1" "r2" "r3" "r4" ... .. ..$ : chr [1:20] "c1" "c2" "c3" "c4" ... ..@ x : logi [1:200] TRUE TRUE TRUE TRUE TRUE TRUE ... ..@ factors : list() Formal class 'lgTMatrix' [package "Matrix"] with 6 slots ..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 ... ..@ j : int [1:200] 0 0 0 0 0 0 0 0 1 1 ... ..@ Dim : int [1:2] 40 20 ..@ Dimnames:List of 2 .. ..$ : chr [1:40] "r1" "r2" "r3" "r4" ... .. ..$ : chr [1:20] "c1" "c2" "c3" "c4" ... ..@ x : logi [1:200] TRUE TRUE TRUE TRUE TRUE TRUE ... ..@ factors : list() ok r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE r27 r28 r29 r30 r31 r32 r33 r34 r35 r36 r37 r38 r39 FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE r40 FALSE 2 x 20 sparse Matrix of class "lgCMatrix" [[ suppressing 20 column names 'c1', 'c2', 'c3' ... ]] r1 . . . | . . | . . . . | . . | . | . . . r2 . | . . . | . . . . . . | | . . . . | . [1] TRUE for(): ..... [Ok]---------------------------------------------------------------- ok( l ) == ###====================================================================== Formal class 'dgCMatrix' [package "Matrix"] with 6 slots ..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 ... ..@ p : int [1:21] 0 8 22 28 37 41 50 63 71 81 ... ..@ Dim : int [1:2] 40 20 ..@ Dimnames:List of 2 .. ..$ : NULL .. ..$ : NULL ..@ x : num [1:200] 3 7 12 22 25 30 38 39 42 45 ... ..@ factors : list() Formal class 'dgTMatrix' [package "Matrix"] with 6 slots ..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 ... ..@ j : int [1:200] 0 0 0 0 0 0 0 0 1 1 ... ..@ Dim : int [1:2] 40 20 ..@ Dimnames:List of 2 .. ..$ : NULL .. ..$ : NULL ..@ x : num [1:200] 3 7 12 22 25 30 38 39 42 45 ... ..@ factors : list() ok [1] 0 0 3 0 0 0 7 0 0 0 0 12 0 0 0 0 0 0 0 0 0 22 0 0 25 [26] 0 0 0 0 30 0 0 0 0 0 0 0 38 39 0 2 x 20 sparse Matrix of class "dgCMatrix" [1,] . . . 121 . . 241 . . . . 441 . . 561 . 641 . . . [2,] . 42 . . . 202 . . . . . . 482 522 . . . . 722 . [1] 7 for(): ..... [Ok]---------------------------------------------------------------- Formal class 'dgCMatrix' [package "Matrix"] with 6 slots ..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 ... ..@ p : int [1:21] 0 8 22 28 37 41 50 63 71 81 ... ..@ Dim : int [1:2] 40 20 ..@ Dimnames:List of 2 .. ..$ : chr [1:40] "r1" "r2" "r3" "r4" ... .. ..$ : chr [1:20] "c1" "c2" "c3" "c4" ... ..@ x : num [1:200] 3 7 12 22 25 30 38 39 42 45 ... ..@ factors : list() Formal class 'dgTMatrix' [package "Matrix"] with 6 slots ..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 ... ..@ j : int [1:200] 0 0 0 0 0 0 0 0 1 1 ... ..@ Dim : int [1:2] 40 20 ..@ Dimnames:List of 2 .. ..$ : chr [1:40] "r1" "r2" "r3" "r4" ... .. ..$ : chr [1:20] "c1" "c2" "c3" "c4" ... ..@ x : num [1:200] 3 7 12 22 25 30 38 39 42 45 ... ..@ factors : list() ok r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 0 0 3 0 0 0 7 0 0 0 0 12 0 0 0 0 0 0 0 0 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35 r36 r37 r38 r39 r40 0 22 0 0 25 0 0 0 0 30 0 0 0 0 0 0 0 38 39 0 2 x 20 sparse Matrix of class "dgCMatrix" [[ suppressing 20 column names 'c1', 'c2', 'c3' ... ]] r1 . . . 121 . . 241 . . . . 441 . . 561 . 641 . . . r2 . 42 . . . 202 . . . . . . 482 522 . . . . 722 . [1] 7 for(): ..... [Ok]---------------------------------------------------------------- ok( d ) == ###====================================================================== > showProc.time() Time elapsed: 0.842 0.001 0.846 > > if(doExtras) {### {was ./AAA_index.R, MM-only} + ## an nsparse-example + A <- Matrix(c(rep(c(1,0,0),2), rep(c(2,0),7), c(0,0,2), rep(0,4)), 3,9) + i <- c(3,1:2) + j <- c(3, 5, 9, 5, 9) + vv <- logical(length(i)*length(j)); vv[6:9] <- TRUE + + print(An <- as(A,"nMatrix")); an <- as(An, "matrix") + assert.EQ.mat(An, an) + An[i, j] <- vv + an[i, j] <- vv + assert.EQ.mat(An, an)## error + if(!all(An == an)) show(drop0(An - an)) + ## all are +1 + + options("Matrix.subassign.verbose" = TRUE)# output from C + An <- as(A,"nMatrix"); An[i, j] <- vv + ## and compare with this: + Al <- as(A,"lMatrix"); Al[i, j] <- vv + options("Matrix.subassign.verbose" = FALSE) + + ##--- An interesting not small not large example for M[i,j] <- v ------------ + ## + M <- Matrix(c(1, rep(0,7), 1:4), 3,4) + N0 <- kronecker(M,M) + mkN1 <- function(M) { + stopifnot(length(d <- dim(M)) == 2) + isC <- is(M,"CsparseMatrix") + M[,d[2]] <- c(0,2,0) + N <- kronecker(diag(x=1:2), M)## remains sparse if 'M' is + if(isC) N <- as(N, "CsparseMatrix") + diag(N[-1,]) <- -2 + N[9,] <- 1:4 # is recycled + N[,12] <- -7:-9 # ditto + N + } + + show(N1 <- t(N <- mkN1(N0))) # transpose {for display reasons} + C1 <- t(C <- mkN1(as(N0,"CsparseMatrix"))) + stopifnot(all(C == N)) + assert.EQ.mat(C, mkN1(as.matrix(N0))) + + C. <- C1 + show(N <- N1) ; n <- as.matrix(N); str(N) + sort(i <- c(6,8,19,11,21,20,10,7,12,9,5,18,17,22,13))## == c(5:13, 17:22)) + sort(j <- c(3,8,6,15,10,4,14,13,16,2,11,17,7,5))## == c(2:8, 10:11, 13:17) + val <- v.l <- 5*c(0,6,0,7,0,0,8:9, 0,0) + show(spv <- as(val, "sparseVector")); str(spv) + + n [i,j] <- v.l + N [i,j] <- val# is recycled, too + C.[i,j] <- val + assert.EQ.mat(N,n) ; stopifnot(all(C. == N)) + ## and the same *again*: + n [i,j] <- v.l + N [i,j] <- val + C.[i,j] <- val + assert.EQ.mat(N,n) + stopifnot(all(C. == N)) + + print(load(system.file("external", "symA.rda", package="Matrix"))) # "As" + stopifnot(isValid(As, "dsCMatrix"), identical(As@factors, list())) + R. <- drop0(chol(As)) + stopifnot(1:32 == sort(diag(R.)), ## ! + R.@x == as.integer(R.@x),## so it is an integer-valued chol-decomp ! + ## shows that (1) As is *not* singular (2) the matrix is not random + all.equal(crossprod(R.), As, tolerance =1e-15)) + print(summary(evA <- eigen(As, only.values=TRUE)$val)) + print(tail(evA)) ## largest three ~= 10^7, smallest two *negative* + print(rcond(As)) # 1.722 e-21 == very bad ! + ##-> this *is* a border line case, i.e. very close to singular ! + ## and also determinant(.) is rather random here! + cc0 <- Cholesky(As)# no problem + try({ + cc <- Cholesky(As, super=TRUE) + ## gives --on 32-bit only-- + ## Cholmod error 'matrix not positive definite' at file:../Supernodal/t_cholmod_super_numeric.c, line 613 + ecc <- expand(cc) + L.P <- with(ecc, crossprod(L,P)) ## == L'P + ## crossprod(L.P) == (L'P)' L'P == P'LL'P + stopifnot( all.equal(crossprod(L.P), As) ) + }) + ##---- end{ eigen( As ) ----------- + + } ## only if(doExtras) > > > ##---- Symmetric indexing of symmetric Matrix ---------- > m. <- mC > m.[, c(2, 7:12)] <- 0 > isValid(S <- crossprod(add.simpleDimnames(m.) %% 100), "dsCMatrix") [1] TRUE > ss <- as(S, "matrix") > ds <- as(S, "denseMatrix") > ## NA-indexing of *dense* Matrices: should work as traditionally > assert.EQ.mat(ds[NA,NA], ss[NA,NA]) > assert.EQ.mat(ds[NA, ], ss[NA,]) > assert.EQ.mat(ds[ ,NA], ss[,NA]) > T <- as(S, "TsparseMatrix") > stopifnot(identical(ds[2 ,NA], ss[2,NA]), + identical(ds[NA, 1], ss[NA, 1]), + identical(S, as(T, "CsparseMatrix")) ) > > ## non-repeated indices: > i <- c(7:5, 2:4);assert.EQ.mat(T[i,i], ss[i,i]) > ## NA in indices -- check that we get a helpful error message: > i[2] <- NA > er <- tryCatch(T[i,i], error = function(e)e) > stopifnot(as.logical(grep("indices.*sparse Matrices", er$message))) > > N <- nrow(T) > set.seed(11) > for(n in 1:(if(doExtras) 50 else 3)) { + i <- sample(N, max(2, sample(N,1)), replace = FALSE) + validObject(Tii <- T[i,i]) ; tTi <- t(T)[i,i] + stopifnot(is(Tii, "dsTMatrix"), # remained symmetric Tsparse + is(tTi, "dsTMatrix"), # may not be identical when *sorted* differently + identical(as(t(Tii),"CsparseMatrix"), as(tTi,"CsparseMatrix"))) + assert.EQ.mat(Tii, ss[i,i]) + } > > b <- diag(1:2)[,c(1,1,2,2)] > cb <- crossprod(b) > cB <- crossprod(Matrix(b, sparse=TRUE)) > a <- matrix(0, 6, 6) > a[1:4, 1:4] <- cb > A1 <- A2 <- Matrix(0, 6, 6)#-> sparse > A1[1:4, 1:4] <- cb > A2[1:4, 1:4] <- cB > assert.EQ.mat(A1, a)# indeed > stopifnot(identical(A1, A2), is(A1, "dsCMatrix")) > > ## repeated ones ``the challenge'' (to do smartly): > j <- c(4, 4, 9, 12, 9, 4, 17, 3, 18, 4, 12, 18, 4, 9) > assert.EQ.mat(T[j,j], ss[j,j]) > ## and another two sets (a, A) & (a., A.) : > a <- matrix(0, 6,6) > a[upper.tri(a)] <- (utr <- c(2, 0,-1, 0,0,5, 7,0,0,0, 0,0,-2,0,8)) > ta <- t(a); ta[upper.tri(a)] <- utr; a <- t(ta) > diag(a) <- c(0,3,0,4,6,0) > A <- as(Matrix(a), "TsparseMatrix") > A. <- A > diag(A.) <- 10 * (1:6) > a. <- as(A., "matrix") > ## More testing {this was not working for a long time..} > set.seed(1) > for(n in 1:(if(doExtras) 100 else 6)) { + i <- sample(1:nrow(A), 3+2*rpois(1, lam=3), replace=TRUE) + Aii <- A[i,i] + A.ii <- A.[i,i] + stopifnot(class(Aii) == class(A), + class(A.ii) == class(A.)) + assert.EQ.mat(Aii , a [i,i]) + assert.EQ.mat(A.ii, a.[i,i]) + assert.EQ.mat(T[i,i], ss[i,i]) + } > showProc.time() Time elapsed: 0.265 0 0.265 > > stopifnot(all.equal(mC[,3], mm[,3]), + identical(mC[ij], mC[ij + 0.4]), + identical(mC[ij], mm[ij]), + identical(mC[iN], mm[iN])) > ## out of bound indexing must be detected: > assertError(mC[cbind(ij[,1] - 5, ij[,2])]) > assertError(mC[cbind(ij[,1], ij[,2] + ncol(mC))]) > > assert.EQ.mat(mC[7, , drop=FALSE], mm[7, , drop=FALSE]) > identical (mC[7, drop=FALSE], mm[7, drop=FALSE]) # *vector* indexing [1] TRUE > > stopifnot(dim(mC[numeric(0), ]) == c(0,20), # used to give warnings + dim(mC[, integer(0)]) == c(40,0), + identical(mC[, integer(0)], mC[, FALSE])) > validObject(print(mT[,c(2,4)])) 40 x 2 sparse Matrix of class "dgTMatrix" c2 c4 r1 . 121 r2 42 . r3 . . r4 . . r5 45 . r6 . . r7 . . r8 . 128 r9 . 129 r10 50 . r11 . . r12 52 132 r13 . 133 r14 . . r15 55 . r16 . . r17 . . r18 . 138 r19 . . r20 . . r21 . 141 r22 . 142 r23 63 . r24 . . r25 65 . r26 . . r27 67 . r28 68 . r29 . . r30 . . r31 71 . r32 72 . r33 . . r34 74 . r35 . . r36 76 . r37 . . r38 . . r39 . 159 r40 80 . [1] TRUE > stopifnot(all.equal(mT[2,], mm[2,]), + ## row or column indexing in combination with t() : + Q.C.identical(mT[2,], t(mT)[,2]), + Q.C.identical(mT[-2,], t(t(mT)[,-2])), + Q.C.identical(mT[c(2,5),], t(t(mT)[,c(2,5)])) ) > assert.EQ.mat(mT[4,, drop = FALSE], mm[4,, drop = FALSE]) > stopifnot(identical3(mm[,1], mC[,1], mT[,1]), + identical3(mm[3,], mC[3,], mT[3,]), + identical3(mT[2,3], mC[2,3], 0), + identical(mT[], mT), + identical4( mm[c(3,7), 2:4], as.mat( m[c(3,7), 2:4]), + as.mat(mT[c(3,7), 2:4]), as.mat(mC[c(3,7), 2:4])) + ) > > x.x <- crossprod(mC) > stopifnot(class(x.x) == "dsCMatrix", + class(x.x. <- round(x.x / 10000)) == "dsCMatrix", + identical(x.x[cbind(2:6, 2:6)], + diag(x.x [2:6, 2:6]))) > head(x.x.) # Note the *non*-structural 0's printed as "0" 6 x 20 sparse Matrix of class "dgCMatrix" [[ suppressing 20 column names 'c1', 'c2', 'c3' ... ]] c1 1 0 . 1 . 1 1 3 . 3 2 1 6 1 . 2 4 6 5 1 c2 0 6 2 1 3 5 7 5 12 14 14 9 11 16 12 13 17 19 19 10 c3 . 2 6 . 4 2 5 3 8 12 5 16 9 11 23 . . 6 7 7 c4 1 1 . 17 . 8 10 13 8 6 18 18 29 35 14 8 25 10 19 21 c5 . 3 4 . 14 4 10 . . 29 8 9 19 11 11 . . 26 26 16 c6 1 5 2 8 4 42 5 19 14 9 8 10 42 56 50 27 29 32 64 16 > tail(x.x., -3) # all but the first three lines 17 x 20 sparse Matrix of class "dgCMatrix" [[ suppressing 20 column names 'c1', 'c2', 'c3' ... ]] c4 1 1 . 17 . 8 10 13 8 6 18 18 29 35 14 8 25 10 19 21 c5 . 3 4 . 14 4 10 . . 29 8 9 19 11 11 . . 26 26 16 c6 1 5 2 8 4 42 5 19 14 9 8 10 42 56 50 27 29 32 64 16 c7 1 7 5 10 10 5 87 14 9 31 77 47 79 43 28 17 67 110 36 121 c8 3 5 3 13 . 19 14 70 10 24 37 13 59 62 34 19 58 21 64 44 c9 . 12 8 8 . 14 9 10 116 41 58 33 33 72 78 43 69 72 75 25 c10 3 14 12 6 29 9 31 24 41 167 69 56 99 44 70 24 105 82 85 32 c11 2 14 5 18 8 8 77 37 58 69 267 80 86 139 49 105 194 119 122 129 c12 1 9 16 18 9 10 47 13 33 56 80 194 70 77 81 . 90 32 . 106 c13 6 11 9 29 19 42 79 59 33 99 86 70 324 157 55 . 69 142 144 155 c14 1 16 11 35 11 56 43 62 72 44 139 77 157 375 123 102 145 39 196 81 c15 . 12 23 14 11 50 28 34 78 70 49 81 55 123 368 71 112 41 41 86 c16 2 13 . 8 . 27 17 19 43 24 105 . . 102 71 233 124 44 139 . c17 4 17 . 25 . 29 67 58 69 105 194 90 69 145 112 124 523 141 245 100 c18 6 19 6 10 26 32 110 21 72 82 119 32 142 39 41 44 141 497 104 111 c19 5 19 7 19 26 64 36 64 75 85 122 . 144 196 41 139 245 104 542 55 c20 1 10 7 21 16 16 121 44 25 32 129 106 155 81 86 . 100 111 55 541 > > lx.x <- as(x.x, "lsCMatrix") # FALSE only for "structural" 0 > (l10 <- lx.x[1:10, 1:10])# "lsC" 10 x 10 sparse Matrix of class "lsCMatrix" [[ suppressing 10 column names 'c1', 'c2', 'c3' ... ]] c1 | | . | . | | | . | c2 | | | | | | | | | | c3 . | | . | | | | | | c4 | | . | . | | | | | c5 . | | . | | | . . | c6 | | | | | | | | | | c7 | | | | | | | | | | c8 | | | | . | | | | | c9 . | | | . | | | | | c10 | | | | | | | | | | > (l3 <- lx.x[1:3, ]) 3 x 20 sparse Matrix of class "lgCMatrix" [[ suppressing 20 column names 'c1', 'c2', 'c3' ... ]] c1 | | . | . | | | . | | | | | . | | | | | c2 | | | | | | | | | | | | | | | | | | | | c3 . | | . | | | | | | | | | | | . . | | | > m.x <- as.mat(x.x) # as.mat() *drops* (NULL,NULL) dimnames > stopifnot(class(l10) == "lsCMatrix", # symmetric indexing -> symmetric ! + identical(as.mat(lx.x), m.x != 0), + identical(as.logical(lx.x), as.logical(m.x)), + identical(as.mat(l10), m.x[1:10, 1:10] != 0), + identical(as.mat(l3 ), m.x[1:3, ] != 0) + ) > > ##-- Sub*assignment* with repeated / duplicated index: > A <- Matrix(0,4,3) ; A[c(1,2,1), 2] <- 1 ; A 4 x 3 sparse Matrix of class "dgCMatrix" [1,] . 1 . [2,] . 1 . [3,] . . . [4,] . . . > B <- A; B[c(1,2,1), 2] <- 1:3; B; B. <- B 4 x 3 sparse Matrix of class "dgCMatrix" [1,] . 3 . [2,] . 2 . [3,] . . . [4,] . . . > B.[3,] <- rbind(4:2) > ## change the diagonal and the upper and lower subdiagonal : > diag(B.) <- 10 * diag(B.) > diag(B.[,-1]) <- 5* diag(B.[,-1]) > diag(B.[-1,]) <- 4* diag(B.[-1,]) ; B. 4 x 3 sparse Matrix of class "dgCMatrix" [1,] . 15 . [2,] . 20 . [3,] 4 12 20 [4,] . . . > C <- B.; C[,2] <- C[,2]; C[1,] <- C[1,]; C[2:3,2:1] <- C[2:3,2:1] > stopifnot(identical(unname(as.matrix(A)), + local({a <- matrix(0,4,3); a[c(1,2,1), 2] <- 1 ; a})), + identical(unname(as.matrix(B)), + local({a <- matrix(0,4,3); a[c(1,2,1), 2] <- 1:3; a})), + identical(C, drop0(B.))) > ## [] <- v failed in the past > T <- as(C,"TsparseMatrix"); C. <- C > T[T>0] <- 21 Note: method with signature 'TsparseMatrix#Matrix#missing#replValue' chosen for function '[<-', target signature 'dgTMatrix#lgTMatrix#missing#numeric'. "Matrix#lsparseMatrix#missing#replValue" would also be valid diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) > C[C>0] <- 21 Note: method with signature 'CsparseMatrix#Matrix#missing#replValue' chosen for function '[<-', target signature 'dgCMatrix#lgCMatrix#missing#numeric'. "Matrix#lsparseMatrix#missing#replValue" would also be valid diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) > a. <- local({a <- as.matrix(C.); a[a>0] <- 21; a}) > assert.EQ.mat(C, a.) > stopifnot(identical(C, as(T, "CsparseMatrix"))) > > ## used to fail > n <- 5 ## or much larger > sm <- new("dsTMatrix", i=1L, j=1L, Dim=as.integer(c(n,n)), x = 1) > (cm <- as(sm, "CsparseMatrix")) 5 x 5 sparse Matrix of class "dsCMatrix" [1,] . . . . . [2,] . 1 . . . [3,] . . . . . [4,] . . . . . [5,] . . . . . > sm[2,] [1] 0 1 0 0 0 > stopifnot(sm[2,] == c(0:1, rep.int(0,ncol(sm)-2)), + sm[2,] == cm[2,], + sm[,3] == sm[3,], + all(sm[,-(1:3)] == t(sm[-(1:3),])), # all() + all(sm[,-(1:3)] == 0) + ) > showProc.time() Time elapsed: 0.149 0.001 0.151 > > ##--- "nsparse*" sub-assignment :---------- > M <- Matrix(c(1, rep(0,7), 1:4), 3,4) > N0 <- kronecker(M,M) > Nn <- as(N0, "nMatrix"); nn <- as(Nn,"matrix") > (Nn00 <- Nn0 <- Nn); nn00 <- nn0 <- nn 9 x 16 sparse Matrix of class "ngTMatrix" [1,] | . . | . . . . . . . . | . . | [2,] . . . | . . . . . . . . . . . | [3,] . . | | . . . . . . . . . . | | [4,] . . . . . . . . . . . . | . . | [5,] . . . . . . . . . . . . . . . | [6,] . . . . . . . . . . . . . . | | [7,] . . . . . . . . | . . | | . . | [8,] . . . . . . . . . . . | . . . | [9,] . . . . . . . . . . | | . . | | > > set.seed(1) > Nn0 <- Nn00; nn0 <- nn00 > for(i in 1:(if(doExtras) 200 else 25)) { + Nn <- Nn0 + nn <- nn0 + i. <- getDuplIndex(nrow(N0), 6) + j. <- getDuplIndex(ncol(N0), 4) + vv <- sample(c(FALSE,TRUE), + length(i.)*length(j.), replace=TRUE) + cat(",") + Nn[i., j.] <- vv + nn[i., j.] <- vv + assert.EQ.mat(Nn, nn) + if(!all(Nn == nn)) { + cat("i=",i,":\n i. <- "); dput(i.) + cat("j. <- "); dput(j.) + cat("which(vv): "); dput(which(vv)) + cat("Difference matrix:\n") + show(drop0(Nn - nn)) + } + cat("k") + ## sub-assign double precision to logical sparseMatrices: now *with* warning: + ## {earlier: gave *no* warning}: + assertWarning(Nn[1:2,] <- -pi) + assertWarning(Nn[, 5] <- -pi) + assertWarning(Nn[2:4, 5:8] <- -pi) + stopifnot(isValid(Nn,"nsparseMatrix")) + ## + cat(".") + if(i %% 10 == 0) cat("\n") + if(i == 100) { + Nn0 <- as(Nn0, "CsparseMatrix") + cat("Now: class", class(Nn0)," :\n~~~~~~~~~~~~~~~~~\n") + } + } ,k.,k.,k.,k.,k.,k.,k.,k.,k.,k. ,k.,k.,k.,k.,k.,k.,k.,k.,k.,k. ,k.,k.,k.,k.,k.> showProc.time() Time elapsed: 0.198 0 0.199 > Nn <- Nn0 > ## Check that NA is interpreted as TRUE (with a warning), for "nsparseMatrix": > assertWarning(Nn[ii <- 3 ] <- NA); stopifnot(isValid(Nn,"nsparseMatrix"), Nn[ii]) diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) > assertWarning(Nn[ii <- 22:24] <- NA); stopifnot(isValid(Nn,"nsparseMatrix"), Nn[ii]) diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) > assertWarning(Nn[ii <- -(1:99)] <- NA); stopifnot(isValid(Nn,"nsparseMatrix"), Nn[ii]) diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) > assertWarning(Nn[ii <- 3:4 ] <- c(0,NA)) diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) > stopifnot(isValid(Nn,"nsparseMatrix"), Nn[ii] == 0:1) > assertWarning(Nn[ii <- 25:27] <- c(0,1,NA)) diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) > stopifnot(isValid(Nn,"nsparseMatrix"), Nn[ii] == c(FALSE,TRUE,TRUE)) > > m0 <- Diagonal(5) > stopifnot(identical(m0[2,], m0[,2]), + identical(m0[,1], c(1,0,0,0,0))) > ### Diagonal -- Sparse: > (m1 <- as(m0, "TsparseMatrix")) # dtTMatrix unitriangular 5 x 5 sparse Matrix of class "dtTMatrix" (unitriangular) [1,] 1 . . . . [2,] . 1 . . . [3,] . . 1 . . [4,] . . . 1 . [5,] . . . . 1 > (m2 <- as(m0, "CsparseMatrix")) # dtCMatrix unitriangular 5 x 5 sparse Matrix of class "dtCMatrix" (unitriangular) [1,] 1 . . . . [2,] . 1 . . . [3,] . . 1 . . [4,] . . . 1 . [5,] . . . . 1 > m1g <- as(m1, "generalMatrix") > stopifnot(is(m1g, "dgTMatrix")) > assert.EQ.mat(m2[1:3,], diag(5)[1:3,]) > assert.EQ.mat(m2[,c(4,1)], diag(5)[,c(4,1)]) > stopifnot(identical(m2[1:3,], as(m1[1:3,], "CsparseMatrix")), + identical(Matrix:::uniqTsparse(m1[, c(4,2)]), + Matrix:::uniqTsparse(as(m2[, c(4,2)], "TsparseMatrix"))) + )## failed in 0.9975-11 > > (uTr <- new("dtTMatrix", Dim = c(3L,3L), diag="U")) 3 x 3 sparse Matrix of class "dtTMatrix" (unitriangular) [1,] 1 . . [2,] . 1 . [3,] . . 1 > uTr[1,] <- 0 > assert.EQ.mat(uTr, cbind(0, rbind(0,diag(2)))) > > M <- m0; M[1,] <- 0 > Z <- m0; Z[] <- 0; z <- array(0, dim(M)) > stopifnot(identical(M, Diagonal(x=c(0, rep(1,4)))), + all(Z == 0), Qidentical(as(Z, "matrix"), z)) > M <- m0; M[,3] <- 3 ; M ; stopifnot(is(M, "sparseMatrix"), M[,3] == 3) 5 x 5 sparse Matrix of class "dgCMatrix" [1,] 1 . 3 . . [2,] . 1 3 . . [3,] . . 3 . . [4,] . . 3 1 . [5,] . . 3 . 1 > checkMatrix(M) Note: method with signature 'sparseMatrix#ldiMatrix' chosen for function '==', target signature 'nsCMatrix#ldiMatrix'. "nsparseMatrix#sparseMatrix", "nMatrix#lMatrix" would also be valid norm(m [5 x 5]) : 1 I F M ok Summary: ok as(., "nMatrix") giving full nonzero-pattern: ok 2*m =?= m+m: identical m >= m for all: ok m < m for none: ok symmpart(m) + skewpart(m) == m: ok; determinant(): ok > M <- m0; M[1:3, 3] <- 0 ;M 5 x 5 diagonal matrix of class "ddiMatrix" [,1] [,2] [,3] [,4] [,5] [1,] 1 . . . . [2,] . 1 . . . [3,] . . 0 . . [4,] . . . 1 . [5,] . . . . 1 > T <- m0; T[1:3, 3] <- 10 > stopifnot(identical(M, Diagonal(x=c(1,1, 0, 1,1))), + isValid(T, "triangularMatrix"), identical(T[,3], c(10,10,10,0,0))) > > M <- m1; M[1,] <- 0 ; M ; assert.EQ.mat(M, diag(c(0,rep(1,4))), tol=0) 5 x 5 sparse Matrix of class "dtTMatrix" [1,] . . . . . [2,] . 1 . . . [3,] . . 1 . . [4,] . . . 1 . [5,] . . . . 1 > M <- m1; M[,3] <- 3 ; stopifnot(is(M,"sparseMatrix"), M[,3] == 3) M[i,j] <- v : coercing symmetric M[] into non-symmetric > Z <- m1; Z[] <- 0 > checkMatrix(M) norm(m [5 x 5]) : 1 I F M ok Summary: ok as(., "nMatrix") giving full nonzero-pattern: ok 2*m =?= m+m: Note: method with signature 'sparseMatrix#ldiMatrix' chosen for function '&', target signature 'nsCMatrix#ldiMatrix'. "nsparseMatrix#sparseMatrix", "nMatrix#lMatrix" would also be valid ok m >= m for all: ok m < m for none: ok symmpart(m) + skewpart(m) == m: ok; determinant(): ok > M <- m1; M[1:3, 3] <- 0 ;M 5 x 5 sparse Matrix of class "dtTMatrix" [1,] 1 . . . . [2,] . 1 . . . [3,] . . . . . [4,] . . . 1 . [5,] . . . . 1 > assert.EQ.mat(M, diag(c(1,1, 0, 1,1)), tol=0) > T <- m1; T[1:3, 3] <- 10; checkMatrix(T) norm(m [5 x 5]) : 1 I F M ok Summary: ok as(., "nMatrix") giving full nonzero-pattern: ok 2*m =?= m+m: identical m >= m for all: ok m < m for none: ok symmpart(m) + skewpart(m) == m: ok; determinant(): ok diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix as(, dtTMatrix): valid: TRUE > stopifnot(is(T, "triangularMatrix"), identical(T[,3], c(10,10,10,0,0)), + Qidentical(as(Z, "matrix"), z)) > > M <- m2; M[1,] <- 0 ; M ; assert.EQ.mat(M, diag(c(0,rep(1,4))), tol=0) 5 x 5 sparse Matrix of class "dtCMatrix" [1,] . . . . . [2,] . 1 . . . [3,] . . 1 . . [4,] . . . 1 . [5,] . . . . 1 > M <- m2; M[,3] <- 3 ; stopifnot(is(M,"sparseMatrix"), M[,3] == 3) > checkMatrix(M) norm(m [5 x 5]) : 1 I F M ok Summary: ok as(., "nMatrix") giving full nonzero-pattern: ok 2*m =?= m+m: identical m >= m for all: ok m < m for none: ok symmpart(m) + skewpart(m) == m: ok; determinant(): ok > Z <- m2; Z[] <- 0 > M <- m2; M[1:3, 3] <- 0 ;M 5 x 5 sparse Matrix of class "dtCMatrix" [1,] 1 . . . . [2,] . 1 . . . [3,] . . . . . [4,] . . . 1 . [5,] . . . . 1 > assert.EQ.mat(M, diag(c(1,1, 0, 1,1)), tol=0) > T <- m2; T[1:3, 3] <- 10; checkMatrix(T) norm(m [5 x 5]) : 1 I F M ok Summary: ok as(., "nMatrix") giving full nonzero-pattern: ok 2*m =?= m+m: identical m >= m for all: ok m < m for none: ok symmpart(m) + skewpart(m) == m: ok; determinant(): ok diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix as(, dtCMatrix): valid: TRUE > stopifnot(is(T, "dtCMatrix"), identical(T[,3], c(10,10,10,0,0)), + Qidentical(as(Z, "matrix"), z)) > showProc.time() Time elapsed: 0.75 0.002 0.756 > > > ## "Vector indices" ------------------- > asLogical <- function(x) { + stopifnot(is.atomic(x)) + storage.mode(x) <- "logical" + x + } > .iniDiag.example <- expression({ + D <- Diagonal(6) + M <- as(D,"dgeMatrix") + m <- as(D,"matrix") + s <- as(D,"TsparseMatrix"); N <- as(s,"nMatrix") + S <- as(s,"CsparseMatrix"); C <- as(S,"nMatrix") + }) > eval(.iniDiag.example) > i <- c(3,1,6); v <- c(10,15,20) > ## (logical,value) which both are recycled: > L <- c(TRUE, rep(FALSE,8)) ; z <- c(50,99) > > ## vector subassignment, both with integer & logical > ## these now work correctly {though not very efficiently; hence warnings} > m[i] <- v # the role model: only first column is affected > M[i] <- v; assert.EQ.mat(M,m) # dge > D[i] <- v; assert.EQ.mat(D,m) # ddi -> dtT -> dgT diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix > s[i] <- v; assert.EQ.mat(s,m) # dtT -> dgT diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix > S[i] <- v; assert.EQ.mat(S,m); S # dtC -> dtT -> dgT -> dgC diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix 6 x 6 sparse Matrix of class "dgCMatrix" [1,] 15 . . . . . [2,] . 1 . . . . [3,] 10 . 1 . . . [4,] . . . 1 . . [5,] . . . . 1 . [6,] 20 . . . . 1 > m.L <- asLogical(m) > C[i] <- v; assert.EQ.mat(C,m.L); validObject(C) diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class ntTMatrix to ngTMatrix Warning in `[<-`(`*tmp*`, i, value = c(10, 15, 20)) : x[.] <- val: x is "ngTMatrix", val not in {TRUE, FALSE} is coerced. [1] TRUE > N[i] <- v; assert.EQ.mat(N,m.L); validObject(N) diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class ntTMatrix to ngTMatrix Warning in `[<-`(`*tmp*`, i, value = c(10, 15, 20)) : x[.] <- val: x is "ngTMatrix", val not in {TRUE, FALSE} is coerced. [1] TRUE > stopifnot(Q.C.identical(D,s, checkClass=FALSE)) > ## logical *vector* indexing > eval(.iniDiag.example) > m[L] <- z; m.L <- asLogical(m) > M[L] <- z; assert.EQ.mat(M,m) > D[L] <- z; assert.EQ.mat(D,m) diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix > s[L] <- z; assert.EQ.mat(s,m) diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix > S[L] <- z; assert.EQ.mat(S,m) ; S diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix 6 x 6 sparse Matrix of class "dgCMatrix" [1,] 50 . . 50 . . [2,] . 1 . . . . [3,] . . 1 . . . [4,] . 99 . 1 99 . [5,] . . . . 1 . [6,] . . . . . 1 > C[L] <- z; assert.EQ.mat(C,m.L) diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class ntTMatrix to ngTMatrix Warning in `[<-`(`*tmp*`, i, value = c(50, 99)) : x[.] <- val: x is "ngTMatrix", val not in {TRUE, FALSE} is coerced. > N[L] <- z; assert.EQ.mat(N,m.L) diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class ntTMatrix to ngTMatrix Warning in `[<-`(`*tmp*`, L, value = c(50, 99)) : x[.] <- val: x is "ngTMatrix", val not in {TRUE, FALSE} is coerced. > > > ## indexing [i] vs [i,] --- now ok > eval(.iniDiag.example) > stopifnot(identical5(m[i], M[i], D[i], s[i], S[i]), identical3(as.logical(m[i]), C[i], N[i]), + identical5(m[L], M[L], D[L], s[L], S[L]), identical3(as.logical(m[L]), C[L], N[L])) [ ] : .M.sub.i.logical() maybe inefficient [ ] : .M.sub.i.logical() maybe inefficient [ ] : .M.sub.i.logical() maybe inefficient [ ] : .M.sub.i.logical() maybe inefficient [ ] : .M.sub.i.logical() maybe inefficient > ## bordercase ' drop = .' *vector* indexing {failed till 2009-04-..) > stopifnot(identical5(m[i,drop=FALSE], M[i,drop=FALSE], D[i,drop=FALSE], + s[i,drop=FALSE], S[i,drop=FALSE]), + identical3(as.logical(m[i,drop=FALSE]), + C[i,drop=FALSE], N[i,drop=FALSE])) > stopifnot(identical5(m[L,drop=FALSE], M[L,drop=FALSE], D[L,drop=FALSE], + s[L,drop=FALSE], S[L,drop=FALSE]), + identical3(as.logical(m[L,drop=FALSE]), + C[L,drop=FALSE], N[L,drop=FALSE])) > ## using L for row-indexing should give an error > assertError(m[L,]); assertError(m[L,, drop=FALSE]) > ## these did not signal an error, upto (including) 0.999375-30: > assertError(s[L,]); assertError(s[L,, drop=FALSE]) > assertError(S[L,]); assertError(S[L,, drop=FALSE]) > assertError(N[L,]); assertError(N[L,, drop=FALSE]) > > ## row indexing: > assert.EQ.mat(D[i,], m[i,]) > assert.EQ.mat(M[i,], m[i,]) > assert.EQ.mat(s[i,], m[i,]) > assert.EQ.mat(S[i,], m[i,]) > assert.EQ.mat(C[i,], asLogical(m[i,])) > assert.EQ.mat(N[i,], asLogical(m[i,])) > ## column indexing: > assert.EQ.mat(D[,i], m[,i]) > assert.EQ.mat(M[,i], m[,i]) > assert.EQ.mat(s[,i], m[,i]) > assert.EQ.mat(S[,i], m[,i]) > assert.EQ.mat(C[,i], asLogical(m[,i])) > assert.EQ.mat(N[,i], asLogical(m[,i])) > > > ### --- negative indices ---------- > > ## 1) negative *vector* indexing > eval(.iniDiag.example) > i <- -(2:30) > stopifnot(identical5(m[i], M[i], D[i], s[i], S[i]), + identical3(as.logical(m[i]), C[i], N[i])) > ## negative vector subassignment : > v <- seq_along(m[i]) > m[i] <- v; m.L <- asLogical(m) > M[i] <- v; assert.EQ.mat(M,m) # dge > D[i] <- v; assert.EQ.mat(D,m) # ddi -> dtT -> dgT diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix > s[i] <- v; assert.EQ.mat(s,m) # dtT -> dgT diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix > S[i] <- v; assert.EQ.mat(S,m); S # dtC -> dtT -> dgT -> dgC diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix 6 x 6 sparse Matrix of class "dgCMatrix" [1,] 1 . . . . 2 [2,] . 1 . . . 3 [3,] . . 1 . . 4 [4,] . . . 1 . 5 [5,] . . . . 1 6 [6,] . . . . . 7 > N[i] <- v; assert.EQ.mat(N,m.L); N # diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class ntTMatrix to ngTMatrix Warning in `[<-`(`*tmp*`, i, value = 1:7) : x[.] <- val: x is "ngTMatrix", val not in {TRUE, FALSE} is coerced. 6 x 6 sparse Matrix of class "ngTMatrix" [1,] | . . . . | [2,] . | . . . | [3,] . . | . . | [4,] . . . | . | [5,] . . . . | | [6,] . . . . . | > C[i] <- v; assert.EQ.mat(C,m.L); C # diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class ntTMatrix to ngTMatrix Warning in `[<-`(`*tmp*`, i, value = 1:7) : x[.] <- val: x is "ngTMatrix", val not in {TRUE, FALSE} is coerced. 6 x 6 sparse Matrix of class "ngCMatrix" [1,] | . . . . | [2,] . | . . . | [3,] . . | . . | [4,] . . . | . | [5,] . . . . | | [6,] . . . . . | > > > ## 2) negative [i,j] indices > mc <- mC[1:5, 1:7] > mt <- mT[1:5, 1:7] > ## sub matrix > assert.EQ.mat(mC[1:2, 0:3], mm[1:2, 0:3]) # test 0-index > stopifnot(identical(mc[-(3:5), 0:2], mC[1:2, 0:2]), + identical(mt[-(3:5), 0:2], mT[1:2, 0:2]), + identical(mC[2:3, 4], mm[2:3, 4])) > assert.EQ.mat(mC[1:2,], mm[1:2,]) > ## sub vector > stopifnot(identical4(mc[-(1:4), ], mC[5, 1:7], + mt[-(1:4), ], mT[5, 1:7])) > stopifnot(identical4(mc[-(1:4), -(2:4)], mC[5, c(1,5:7)], + mt[-(1:4), -(2:4)], mT[5, c(1,5:7)])) > > ## mixing of negative and positive must give error > assertError(mT[-1:1,]) > showProc.time() Time elapsed: 0.183 0 0.184 > > ## Sub *Assignment* ---- now works (partially): > mt0 <- mt > nt <- as(mt, "nMatrix") > mt[1, 4] <- -99 > mt[2:3, 1:6] <- 0 > mt 5 x 7 sparse Matrix of class "dgTMatrix" c1 c2 c3 c4 c5 c6 c7 r1 . . . -99 . . 241 r2 . . . . . . . r3 . . . . . . 243 r4 . . . . . . . r5 . 45 . . . . . > m2 <- mt+mt > m2[1,4] <- -200 > m2[c(1,3), c(5:6,2)] <- 1:6 > stopifnot(m2[1,4] == -200, + as.vector(m2[c(1,3), c(5:6,2)]) == 1:6) > mt[,3] <- 30 > mt[2:3,] <- 250 > mt[1:5 %% 2 == 1, 3] <- 0 > mt[3:1, 1:7 > 5] <- 0 > mt 5 x 7 sparse Matrix of class "dgTMatrix" c1 c2 c3 c4 c5 c6 c7 r1 . . . -99 . . . r2 250 250 250 250 250 . . r3 250 250 . 250 250 . . r4 . . 30 . . . . r5 . 45 . . . . . > > tt <- as(mt,"matrix") > ii <- c(0,2,5) > jj <- c(2:3,5) > tt[ii, jj] <- 1:6 # 0 is just "dropped" > mt[ii, jj] <- 1:6 > assert.EQ.mat(mt, tt) > > mt[1:5, 2:6] 5 x 5 sparse Matrix of class "dgTMatrix" c2 c3 c4 c5 c6 r1 . . -99 . . r2 1 3 250 5 . r3 250 . 250 250 . r4 . 30 . . . r5 2 4 . 6 . > as((mt0 - mt)[1:5,], "dsparseMatrix")# [1,5] and lines 2:3 5 x 7 sparse Matrix of class "dgCMatrix" c1 c2 c3 c4 c5 c6 c7 r1 . . . 220 . . 241 r2 -250 41 -3 -250 -5 202 . r3 -247 -250 . -250 -250 . 243 r4 . . -30 . . . . r5 . 43 -4 . -6 . . > > mt[c(2,4), ] <- 0; stopifnot(as(mt[c(2,4), ],"matrix") == 0) > mt[2:3, 4:7] <- 33 > checkMatrix(mt) norm(m [5 x 7]) : 1 I F M ok Summary: ok as(., "nMatrix") giving full nonzero-pattern: ok 2*m =?= m+m: ok m >= m for all: ok m < m for none: ok > mt 5 x 7 sparse Matrix of class "dgTMatrix" c1 c2 c3 c4 c5 c6 c7 r1 . . . -99 . . . r2 . . . 33 33 33 33 r3 250 250 . 33 33 33 33 r4 . . . . . . . r5 . 2 4 . 6 . . > > mc[1,4] <- -99 ; stopifnot(mc[1,4] == -99) > mc[1,4] <- 00 ; stopifnot(mc[1,4] == 00) > mc[1,4] <- -99 ; stopifnot(mc[1,4] == -99) > mc[1:2,4:3] <- 4:1; stopifnot(as.matrix(mc[1:2,4:3]) == 4:1) > > mc[-1, 3] <- -2:1 # 0 should not be entered; 'value' recycled > mt[-1, 3] <- -2:1 > stopifnot(mc@x != 0, mt@x != 0, + mc[-1,3] == -2:1, mt[-1,3] == -2:1) ## failed earlier > > mc0 <- mc > mt0 <- as(mc0, "TsparseMatrix") > m0 <- as(mc0, "matrix") > set.seed(1); options(Matrix.verbose = FALSE) > for(i in 1:(if(doExtras) 50 else 4)) { + mc <- mc0; mt <- mt0 ; m <- m0 + ev <- 1:5 %% 2 == round(runif(1))# 0 or 1 + j <- sample(ncol(mc), 1 + round(runif(1))) + nv <- rpois(sum(ev) * length(j), lambda = 1) + mc[ev, j] <- nv + m[ev, j] <- nv + mt[ev, j] <- nv + if(i %% 10 == 1) print(mc[ev,j, drop = FALSE]) + stopifnot(as.vector(mc[ev, j]) == nv, ## failed earlier... + as.vector(mt[ev, j]) == nv) + validObject(mc) ; assert.EQ.mat(mc, m) + validObject(mt) ; assert.EQ.mat(mt, m) + } 2 x 1 sparse Matrix of class "dgCMatrix" c5 r2 2 r4 . > showProc.time() Time elapsed: 0.157 0.001 0.158 > options(Matrix.verbose = TRUE) > > mc # no longer has non-structural zeros 5 x 7 sparse Matrix of class "dgCMatrix" c1 c2 c3 c4 c5 c6 c7 r1 . . 2 4 . . 241 r2 . 42 . 3 . 202 . r3 3 . -1 . . . 243 r4 . . 1 . . . . r5 . 45 1 . . . . > mc[ii, jj] <- 1:6 > mc[c(2,5), c(3,5)] <- 3.2 > checkMatrix(mc) norm(m [5 x 7]) : 1 I F M ok Summary: ok as(., "nMatrix") giving full nonzero-pattern: ok 2*m =?= m+m: identical m >= m for all: ok m < m for none: ok > m. <- mc > mc[4,] <- 0 > mc 5 x 7 sparse Matrix of class "dgCMatrix" c1 c2 c3 c4 c5 c6 c7 r1 . . 2.0 4 . . 241 r2 . 1 3.2 3 3.2 202 . r3 3 . -1.0 . . . 243 r4 . . . . . . . r5 . 2 3.2 . 3.2 . . > > S <- as(Diagonal(5),"TsparseMatrix") > H <- Hilbert(9) > Hc <- as(round(H, 3), "dsCMatrix")# a sparse matrix with no 0 ... > (trH <- tril(Hc[1:5, 1:5])) 5 x 5 sparse Matrix of class "dtCMatrix" [1,] 1.000 . . . . [2,] 0.500 0.333 . . . [3,] 0.333 0.250 0.200 . . [4,] 0.250 0.200 0.167 0.143 . [5,] 0.200 0.167 0.143 0.125 0.111 > stopifnot(is(trH, "triangularMatrix"), trH@uplo == "L", + is(S, "triangularMatrix")) > > ## triangular assignment > ## the slick (but inefficient in case of sparse!) way to assign sub-diagonals: > ## equivalent to tmp <- `diag<-`(S[,-1], -2:1); S[,-1] <- tmp > ## which dispatches to (x="TsparseMatrix", i="missing",j="index", value="replValue") > diag(S[,-1]) <- -2:1 # used to give a wrong warning M[i,j] <- v : coercing symmetric M[] into non-symmetric > S <- as(S,"triangularMatrix") > assert.EQ.mat(S, local({s <- diag(5); diag(s[,-1]) <- -2:1; s})) > > trH[c(1:2,4), c(2:3,5)] <- 0 # gave an *error* upto Jan.2008 > trH[ lower.tri(trH) ] <- 0 # ditto, because of callNextMethod() diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) 'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix > > m <- Matrix(0+1:28, nrow = 4) > m[-3,c(2,4:5,7)] <- m[ 3, 1:4] <- m[1:3, 6] <- 0 > mT <- as(m, "dgTMatrix") > stopifnot(identical(mT[lower.tri(mT)], + m [lower.tri(m) ])) [ ] : .M.sub.i.logical() maybe inefficient > lM <- upper.tri(mT, diag=TRUE) > mT[lM] <- 0 diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) > m[lM] <- 0 > assert.EQ.mat(mT, as(m,"matrix")) > mT[lM] <- -1:0 diagnosing replTmat(x,i,j,v): nargs()= 3; missing (i,j) = (0,1) > m[lM] <- -1:0 > assert.EQ.mat(mT, as(m,"matrix")) > (mT <- drop0(mT)) 4 x 7 sparse Matrix of class "dgCMatrix" [1,] -1 . . -1 -1 -1 -1 [2,] 2 -1 -1 . . . . [3,] . . . -1 -1 -1 -1 [4,] 4 . 12 . . . . > > i <- c(1:2, 4, 6:7); j <- c(2:4,6) > H[i,j] <- 0 > (H. <- round(as(H, "sparseMatrix"), 3)[ , 2:7]) 9 x 6 sparse Matrix of class "dgCMatrix" [1,] . . . 0.200 . 0.143 [2,] . . . 0.167 . 0.125 [3,] 0.250 0.200 0.167 0.143 0.125 0.111 [4,] . . . 0.125 . 0.100 [5,] 0.167 0.143 0.125 0.111 0.100 0.091 [6,] . . . 0.100 . 0.083 [7,] . . . 0.091 . 0.077 [8,] 0.111 0.100 0.091 0.083 0.077 0.071 [9,] 0.100 0.091 0.083 0.077 0.071 0.067 > Hc. <- Hc > Hc.[i,j] <- 0 ## now "works", but setting "non-structural" 0s > stopifnot(as.matrix(Hc.[i,j]) == 0) > Hc.[, 1:6] 9 x 6 sparse Matrix of class "dgCMatrix" [1,] 1.000 . . . 0.200 . [2,] 0.500 . . . 0.167 . [3,] 0.333 0.250 0.200 0.167 0.143 0.125 [4,] 0.250 . . . 0.125 . [5,] 0.200 0.167 0.143 0.125 0.111 0.100 [6,] 0.167 . . . 0.100 . [7,] 0.143 . . . 0.091 . [8,] 0.125 0.111 0.100 0.091 0.083 0.077 [9,] 0.111 0.100 0.091 0.083 0.077 0.071 > > ## an example that failed for a long time > sy3 <- new("dsyMatrix", Dim = as.integer(c(2, 2)), x = c(14, -1, 2, -7)) > checkMatrix(dm <- kronecker(Diagonal(2), sy3))# now sparse with new kronecker Note: method with signature 'sparseMatrix#ANY' chosen for function 'kronecker', target signature 'dtTMatrix#dsyMatrix'. "ANY#Matrix" would also be valid norm(m [4 x 4]) : 1 I F M ok Summary: ok as(., "nMatrix") giving full nonzero-pattern: ok 2*m =?= m+m: ok m >= m for all: ok m < m for none: ok symmpart(m) + skewpart(m) == m: ok; determinant(): ok > dm <- Matrix(as.matrix(dm))# -> "dsyMatrix" > (s2 <- as(dm, "sparseMatrix")) 4 x 4 sparse Matrix of class "dsCMatrix" [1,] 14 2 . . [2,] 2 -7 . . [3,] . . 14 2 [4,] . . 2 -7 > checkMatrix(st <- as(s2, "TsparseMatrix")) norm(m [4 x 4]) : 1 I F M ok Summary: ok as(., "nMatrix") giving full nonzero-pattern: ok 2*m =?= m+m: suboptimal 'Arith' implementation of 'dsC* o dsC*' identical m >= m for all: ok m < m for none: ok symmpart(m) + skewpart(m) == m: suboptimal 'Arith' implementation of 'dsC* o dsC*' ok; determinant(): ok > stopifnot(is(s2, "symmetricMatrix"), + is(st, "symmetricMatrix")) > checkMatrix(s.32 <- st[1:3,1:2]) ## 3 x 2 - and *not* dsTMatrix norm(m [3 x 2]) : 1 I F M ok Summary: ok as(., "nMatrix") giving full nonzero-pattern: ok 2*m =?= m+m: ok m >= m for all: ok m < m for none: ok > checkMatrix(s2.32 <- s2[1:3,1:2]) norm(m [3 x 2]) : 1 I F M ok Summary: ok as(., "nMatrix") giving full nonzero-pattern: ok 2*m =?= m+m: identical m >= m for all: ok m < m for none: ok > I <- c(1,4:3) > stopifnot(is(s2.32, "generalMatrix"), + is(s.32, "generalMatrix"), + identical(as.mat(s.32), as.mat(s2.32)), + identical3(dm[1:3,-1], asD(s2[1:3,-1]), asD(st[1:3,-1])), + identical4(2, dm[4,3], s2[4,3], st[4,3]), + identical3(diag(dm), diag(s2), diag(st)), + is((cI <- s2[I,I]), "dsCMatrix"), + is((tI <- st[I,I]), "dsTMatrix"), + identical4(as.mat(dm)[I,I], as.mat(dm[I,I]), as.mat(tI), as.mat(cI)) + ) > > ## now sub-assign and check for consistency > ## symmetric subassign should keep symmetry > st[I,I] <- 0; checkMatrix(st); stopifnot(is(st,"symmetricMatrix")) norm(m [4 x 4]) : 1 I F M ok Summary: ok as(., "nMatrix") giving full nonzero-pattern: ok 2*m =?= m+m: suboptimal 'Arith' implementation of 'dsC* o dsC*' identical m >= m for all: ok m < m for none: ok symmpart(m) + skewpart(m) == m: suboptimal 'Arith' implementation of 'dsC* o dsC*' ok; determinant(): ok > s2[I,I] <- 0; checkMatrix(s2); stopifnot(is(s2,"symmetricMatrix")) norm(m [4 x 4]) : 1 I F M ok Summary: ok as(., "nMatrix") giving full nonzero-pattern: ok 2*m =?= m+m: suboptimal 'Arith' implementation of 'dsC* o dsC*' identical m >= m for all: ok m < m for none: ok symmpart(m) + skewpart(m) == m: suboptimal 'Arith' implementation of 'dsC* o dsC*' ok; determinant(): ok > ## > m <- as.mat(st) > m[2:1,2:1] <- 4:1 > st[2:1,2:1] <- 4:1 M[i,j] <- v : coercing symmetric M[] into non-symmetric > s2[2:1,2:1] <- 4:1 > stopifnot(identical(m, as.mat(st)), + 1:4 == as.vector(s2[1:2,1:2]), + identical(m, as.mat(s2))) > > ## now a slightly different situation for 's2' (had bug) > s2 <- as(dm, "sparseMatrix") > s2[I,I] <- 0; diag(s2)[2:3] <- -(1:2) > stopifnot(is(s2,"symmetricMatrix"), diag(s2) == c(0:-2,0)) > t2 <- as(s2, "TsparseMatrix") > m <- as.mat(s2) > s2[2:1,2:1] <- 4:1 > t2[2:1,2:1] <- 4:1 M[i,j] <- v : coercing symmetric M[] into non-symmetric > m[2:1,2:1] <- 4:1 > assert.EQ.mat(t2, m) > assert.EQ.mat(s2, m) > ## and the same (for a different s2 !) > s2[2:1,2:1] <- 4:1 > t2[2:1,2:1] <- 4:1 > assert.EQ.mat(t2, m)# ok > assert.EQ.mat(s2, m)# failed in 0.9975-8 > showProc.time() Time elapsed: 0.709 0.001 0.713 > > > ## m[cbind(i,j)] <- value: (2-column matrix subassignment): > m.[ cbind(3:5, 1:3) ] <- 1:3 > stopifnot(m.[3,1] == 1, m.[4,2] == 2) > nt. <- nt ; nt[rbind(2:3, 3:4, c(3,3))] <- FALSE > s. <- m. ; m.[cbind(3,4:6)] <- 0 ## assigning 0 where there *is* 0 .. > stopifnot(identical(nt.,nt), ## should not have changed + identical(s., m.)) > x.x[ cbind(2:6, 2:6)] <- 12:16 > stopifnot(isValid(x.x, "dsCMatrix"), + 12:16 == as.mat(x.x)[cbind(2:6, 2:6)]) > (ne1 <- (mc - m.) != 0) 5 x 7 sparse Matrix of class "lgCMatrix" c1 c2 c3 c4 c5 c6 c7 r1 . . : : . . : r2 . : : : : : . r3 | . : . . . : r4 . | | . . . . r5 . : | . : . . > stopifnot(identical(ne1, 0 != abs(mc - m.))) > (ge <- m. >= mc) # contains "=" -> result is dense 5 x 7 Matrix of class "lgeMatrix" c1 c2 c3 c4 c5 c6 c7 r1 TRUE TRUE TRUE TRUE TRUE TRUE TRUE r2 TRUE TRUE TRUE TRUE TRUE TRUE TRUE r3 FALSE TRUE TRUE TRUE TRUE TRUE TRUE r4 TRUE TRUE TRUE TRUE TRUE TRUE TRUE r5 TRUE TRUE FALSE TRUE TRUE TRUE TRUE > ne. <- mc != m. # was wrong (+ warning) > stopifnot(identical(!(m. < mc), m. >= mc), + identical(m. < mc, as(!ge, "sparseMatrix")), + identical(ne., drop0(ne1))) > > d6 <- Diagonal(6) > ii <- c(1:2, 4:5) > d6[cbind(ii,ii)] <- 7*ii > stopifnot(is(d6, "ddiMatrix"), identical(d6, Diagonal(x=c(7*1:2,1,7*4:5,1)))) > > for(j in 3:6) { ## even and odd j used to behave differently + M <- Matrix(0, j,j); m <- matrix(0, j,j) + T <- as(M, "TsparseMatrix") + TG <- as(T, "generalMatrix") + G <- as(M, "generalMatrix") + id <- cbind(1:j,1:j) + i2 <- cbind(1:j,j:1) + m[id] <- 1:j + M[id] <- 1:j ; stopifnot(is(M,"symmetricMatrix")) + T[id] <- 1:j ; stopifnot(is(T,"symmetricMatrix")) + G[id] <- 1:j + TG[id]<- 1:j + m[i2] <- 10 + M[i2] <- 10 ; stopifnot(is(M,"symmetricMatrix")) + T[i2] <- 10 ; stopifnot(is(T,"symmetricMatrix")) + G[i2] <- 10 + TG[i2]<- 10 + ## + assert.EQ.mat(M, m) + assert.EQ.mat(T, m) + assert.EQ.mat(G, m) + assert.EQ.mat(TG,m) + } > > > ## drop, triangular, ... > (M3 <- Matrix(upper.tri(matrix(, 3, 3)))) # ltC; indexing used to fail 3 x 3 sparse Matrix of class "ltCMatrix" [1,] . | | [2,] . . | [3,] . . . > T3 <- as(M3, "TsparseMatrix") > stopifnot(identical(drop(M3), M3), + identical4(drop(M3[,2, drop = FALSE]), M3[,2, drop = TRUE], + drop(T3[,2, drop = FALSE]), T3[,2, drop = TRUE]), + is(T3, "triangularMatrix"), + !is(T3[,2, drop=FALSE], "triangularMatrix") + ) > > (T6 <- as(as(kronecker(Matrix(c(0,0,1,0),2,2), t(T3)), "lMatrix"), + "triangularMatrix")) 6 x 6 sparse Matrix of class "ltTMatrix" [1,] . . . . . . [2,] . . . | . . [3,] . . . | | . [4,] . . . . . . [5,] . . . . . . [6,] . . . . . . > T6[1:4, -(1:3)] # failed (trying to coerce back to ltTMatrix) 4 x 3 sparse Matrix of class "lgTMatrix" [1,] . . . [2,] | . . [3,] | | . [4,] . . . > stopifnot(identical(T6[1:4, -(1:3)][2:3, -3], + spMatrix(2,2, i=c(1,2,2), j=c(1,1,2), x=rep(TRUE,3)))) > > M <- Diagonal(4); M[1,2] <- 2 > M. <- as(M, "CsparseMatrix") > (R <- as(M., "RsparseMatrix")) 4 x 4 sparse Matrix of class "dtRMatrix" (unitriangular) [1,] 1 2 . . [2,] . 1 . . [3,] . . 1 . [4,] . . . 1 > (Ms <- symmpart(M.)) 4 x 4 sparse Matrix of class "dsCMatrix" [1,] 1 1 . . [2,] 1 1 . . [3,] . . 1 . [4,] . . . 1 > Rs <- as(Ms, "RsparseMatrix") > stopifnot(isValid(M, "triangularMatrix"), + isValid(M.,"triangularMatrix"), + isValid(Ms, "dsCMatrix"), + isValid(R, "dtRMatrix"), + isValid(Rs, "dsRMatrix") ) > stopifnot(dim(M[2:3, FALSE]) == c(2,0), + dim(R[2:3, FALSE]) == c(2,0), + identical(M [2:3,TRUE], M [2:3,]), + identical(M.[2:3,TRUE], M.[2:3,]), + identical(R [2:3,TRUE], R [2:3,]), + dim(R[FALSE, FALSE]) == c(0,0)) > > n <- 50000L > Lrg <- new("dgTMatrix", Dim = c(n,n)) > diag(Lrg) <- 1:n > dLrg <- as(Lrg, "diagonalMatrix") > stopifnot(identical(Diagonal(x = 1:n), dLrg)) > diag(dLrg) <- 1 + diag(dLrg) > Clrg <- as(Lrg,"CsparseMatrix") > Ctrg <- as(Clrg, "triangularMatrix") > diag(Ctrg) <- 1 + diag(Ctrg) > stopifnot(identical(Diagonal(x = 1+ 1:n), dLrg), + identical(Ctrg, as(dLrg,"CsparseMatrix"))) > > cc <- capture.output(show(dLrg))# show() used to error for large n > showProc.time() Time elapsed: 0.687 0.003 0.692 > > ## Large Matrix indexing / subassignment > ## ------------------------------------- (from ex. by Imran Rashid) > n <- 7000000 > m <- 100000 > nnz <- 20000 > > set.seed(12) > f <- sparseMatrix(i = sample(n, size=nnz, replace=TRUE), + j = sample(m, size=nnz, replace=TRUE)) > str(f) Formal class 'ngCMatrix' [package "Matrix"] with 5 slots ..@ i : int [1:20000] 6692226 4657233 4490801 3688935 344371 6380246 2797160 3584813 6553304 2327896 ... ..@ p : int [1:99993] 0 1 1 1 1 1 1 1 1 1 ... ..@ Dim : int [1:2] 6999863 99992 ..@ Dimnames:List of 2 .. ..$ : NULL .. ..$ : NULL ..@ factors : list() > dim(f) # 6999863 x 99992 [1] 6999863 99992 > prod(dim(f)) # 699930301096 == 699'930'301'096 (~ 700'000 millions) [1] 699930301096 > str(thisCol <- f[,5000])# logi [~ 7 mio....] logi [1:6999863] FALSE FALSE FALSE FALSE FALSE FALSE ... > sv <- as(thisCol, "sparseVector") > str(sv) ## "empty" ! Formal class 'lsparseVector' [package "Matrix"] with 3 slots ..@ x : logi(0) ..@ length: int 6999863 ..@ i : int(0) > validObject(spCol <- f[,5000, drop=FALSE]) [1] TRUE > ## > ## *not* identical(): as(spCol, "sparseVector")@length is "double"prec: > stopifnot(all.equal(as(spCol, "sparseVector"), + as(sv, "nsparseVector"), tolerance=0)) > if(doExtras) {#----------------------------------------------------------------- + f[,5762] <- thisCol # now "fine" <<<<<<<<<< FIXME uses LARGE objects -- slow -- + ## is using replCmat() in ../R/Csparse.R, then + ## replTmat() in ../R/Tsparse.R + + fx <- sparseMatrix(i = sample(n, size=nnz, replace=TRUE), + j = sample(m, size=nnz, replace=TRUE), + x = round(10*rnorm(nnz))) + class(fx)## dgCMatrix + fx[,6000] <- (tC <- rep(thisCol, length=nrow(fx)))# slow (as above) + thCol <- fx[,2000] + fx[,5762] <- thCol# slow + stopifnot(is(f, "ngCMatrix"), is(fx, "dgCMatrix"), + identical(thisCol, f[,5762]),# perfect + identical(as.logical(fx[,6000]), tC), + identical(thCol, fx[,5762])) + + showProc.time() + ## + cat("checkMatrix() of all: \n---------\n") + Sys.setlocale("LC_COLLATE", "C")# to keep ls() reproducible + for(nm in ls()) if(is(.m <- get(nm), "Matrix")) { + cat(nm, "\n") + checkMatrix(.m, verbose = FALSE + , doDet = nm != "As" ## <- "As" almost singular <=> det() "ill posed" + ) + } + showProc.time() + }#--------------end if(doExtras) ----------------------------------------------- > > if(!interactive()) warnings() NULL > > proc.time() user system elapsed 6.942 0.118 7.167 Matrix/tests/dtpMatrix.R0000644000175100001440000000414312271746775015021 0ustar hornikusers### triangular packed library(Matrix) source(system.file("test-tools.R", package = "Matrix"))# identical3() etc cp6 <- chol(H6 <- Hilbert(6)) tp6 <- as(cp6,"dtpMatrix") round(tp6, 3)## round() is "Math2" group method 1/tp6 ## "Arith" group : gives 'dgeMatrix' str(tp6) ## arithmetic with a mix of dimnames / no dimnames tp <- tp6; dimnames(tp) <- list(LETTERS[1:6], letters[11:16]) ## as.matrix() --> "logical" matrix stopifnot(as.matrix(tp - tp6 == tp6 - tp), as.matrix(0 == tp - tp6), identical(as(tp6,"CsparseMatrix"), as(cp6,"CsparseMatrix"))) stopifnot(validObject(tp6), all.equal(tp6 %*% diag(6), as(tp6, "dgeMatrix")), validObject(tp6. <- diag(6) %*% tp6), class((tt6 <- t(tp6))) == "dtpMatrix", identical(t(tt6), tp6), tp6@uplo == "U" && tt6@uplo == "L") all.equal(as(tp6.,"matrix"), as(tp6, "matrix"), tolerance= 1e-15) (tr6 <- as(tp6, "dtrMatrix")) dH6 <- determinant(H6) D. <- determinant(tp6) rc <- rcond(tp6) stopifnot(all.equal(dH6$modulus, determinant(as.matrix(H6))$modulus), is.all.equal3(c(D.$modulus), c(dH6$modulus) / 2, -19.883103353), all.equal(rc, 1.791511257e-4), all.equal(norm(tp6, "I") , 2.45), all.equal(norm(tp6, "1") , 1), all.equal(norm(tp6, "F") , 1.37047826623) ) object.size(tp6) object.size(as(tp6, "dtrMatrix")) object.size(as(tp6, "matrix")) D6 <- as(diag(6), "dgeMatrix") ge6 <- as(tp6, "dgeMatrix") stopifnot(all.equal(D6 %*% tp6, ge6), all.equal(tp6 %*% D6, ge6)) ## larger case set.seed(123) rl <- new("dtpMatrix", uplo="L", diag="N", Dim = rep.int(1000:1000,2), x = rnorm(500*1001)) validObject(rl) str(rl) sapply(c("I", "1", "F"), function(type) norm(rl, type=type)) rcond(rl)# 0 ! stopifnot(all.equal(as(rl %*% diag(1000),"matrix"), as(rl, "matrix"))) object.size(rl) ## 4 MB object.size(as(rl, "dtrMatrix"))# 8 MB object.size(as(rl, "matrix"))# ditto print(drl <- determinant(rl), digits = 12) stopifnot(all.equal(c(drl$modulus), -638.257312422)) cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons'' Matrix/tests/indexing.R0000644000175100001440000010472112271746775014655 0ustar hornikusers#### For both 'Extract' ("[") and 'Replace' ("[<-") Method testing #### aka subsetting and subassignment #### suppressPackageStartupMessages(...) as we have an *.Rout.save to Rdiff against stopifnot(suppressPackageStartupMessages(require(Matrix))) source(system.file("test-tools.R", package = "Matrix"), keep.source = FALSE) ##-> identical3() etc cat("doExtras:",doExtras,"\n") if(interactive()) { options(error = recover, warn = 1) } else if(FALSE) { ## MM @ testing *manually* only options(error = recover, Matrix.verbose = TRUE, warn = 1) } else { options(Matrix.verbose = TRUE, warn = 1) } ### Dense Matrices m <- Matrix(1:28 +0, nrow = 7) validObject(m) stopifnot(identical(m, m[]), identical(m[2, 3], 16), # simple number identical(m[2, 3:4], c(16,23)), # simple numeric of length 2 identical(m[NA,NA], as(Matrix(NA, 7,4), "dMatrix"))) m[2, 3:4, drop=FALSE] # sub matrix of class 'dgeMatrix' m[-(4:7), 3:4] # ditto; the upper right corner of 'm' ## rows or columns only: m[1,] # first row, as simple numeric vector m[,2] # 2nd column m[,1:2] # sub matrix of first two columns m[-(1:6),, drop=FALSE] # not the first 6 rows, i.e. only the 7th m[integer(0),] #-> 0 x 4 Matrix m[2:4, numeric(0)] #-> 3 x 0 Matrix ## logical indexing stopifnot(identical(m[2,3], m[(1:nrow(m)) == 2, (1:ncol(m)) == 3]), identical(m[2,], m[(1:nrow(m)) == 2, ]), identical(m[,3:4], m[, (1:4) >= 3])) ## dimnames indexing: mn <- m dimnames(mn) <- list(paste("r",letters[1:nrow(mn)],sep=""), LETTERS[1:ncol(mn)]) checkMatrix(mn) mn["rd", "D"] msr <- ms <- as(mn,"sparseMatrix") mnr <- mn v <- rev(as(ms, "vector")) mnr[] <- v msr[] <- v # [<- "sparse" -- not very sensical; did fail w/o a message z <- msr; z[] <- 0 zz <- as(array(0, dim(z)), "sparseMatrix") a.m <- as(mnr,"matrix") stopifnot(identical(mn["rc", "D"], mn[3,4]), mn[3,4] == 24, identical(mn[, "A"], mn[,1]), mn[,1] == 1:7, identical(mn[c("re", "rb"), "B"], mn[c(5,2), 2]), identical(ms["rc", "D"], ms[3,4]), ms[3,4] == 24, identical(ms[, "A"], ms[,1]), ms[,1] == 1:7, identical(ms[ci <- c("re", "rb"), "B"], ms[c(5,2), 2]), identical(rownames(mn[ci, ]), ci), identical(rownames(ms[ci, ]), ci), identical(colnames(mn[,cj <- c("B","D")]), cj), identical(colnames(ms[,cj]), cj), identical(a.m, as(msr,"matrix")), identical(unname(z), zz), identical(a.m, array(v, dim=dim(mn), dimnames=dimnames(mn))) ) showProc.time() ## Printing sparse colnames: ms[sample(28, 20)] <- 0 ms <- t(rbind2(ms, 3*ms)) cnam1 <- capture.output(show(ms))[2] ; op <- options("sparse.colnames" = "abb3") cnam2 <- capture.output(show(ms))[2] ; options(op) # revert stopifnot(## sparse printing grep("^ +$", cnam1) == 1, # cnam1 is empty identical(cnam2, paste(" ", paste(rep(rownames(mn), 2), collapse=" ")))) mo <- m m[2,3] <- 100 m[1:2, 4] <- 200 m[, 1] <- -1 m[1:3,] m. <- as.matrix(m) ## m[ cbind(i,j) ] indexing: iN <- ij <- cbind(1:6, 2:3) iN[2:3,] <- iN[5,2] <- NA stopifnot(identical(m[ij], m.[ij]), identical(m[iN], m.[iN])) ## testing operations on logical Matrices rather more than indexing: g10 <- m [ m > 10 ] stopifnot(18 == length(g10)) stopifnot(10 == length(m[ m <= 10 ])) sel <- (20 < m) & (m < 150) sel.<- (20 < m.)& (m.< 150) nsel <-(20 >= m) | (m >= 150) (ssel <- as(sel, "sparseMatrix")) stopifnot(is(sel, "lMatrix"), is(ssel, "lsparseMatrix"), identical3(as.mat(sel.), as.mat(sel), as.mat(ssel)), identical3(!sel, !ssel, nsel), # ! is typically dense identical3(m[ sel], m[ ssel], as.matrix(m)[as.matrix( ssel)]), identical3(m[!sel], m[!ssel], as.matrix(m)[as.matrix(!ssel)]) ) showProc.time() ## more sparse Matrices -------------------------------------- ##' @title Check sparseMatrix sub-assignment m[i,j] <- v ##' @param ms sparse Matrix ##' @param mm its [traditional matrix]-equivalent ##' @param k (approximate) length of index vectors (i,j) ##' @param n.uniq (approximate) number of unique values in i,j ##' @param vRNG function(n) for random 'v' generation ##' @param show logical; if TRUE, it will not stop on error ##' @return ##' @author Martin Maechler chkAssign <- function(ms, mm = as(ms, "matrix"), k = min(20,dim(mm)), n.uniq = k %/% 3, vRNG = { if(is.numeric(mm) || is.complex(mm)) function(n) rpois(n,lambda= 0.75)# <- about 47% zeros else ## logical function(n) runif(n) > 0.8 }, ## 80% zeros showOnly=FALSE) { stopifnot(is(ms,"sparseMatrix")) d <- dim(ms) s1 <- function(n) sample(n, pmin(n, pmax(1, rpois(1, n.uniq)))) i <- sample(s1(d[1]), k/2+ rpois(1, k/2), replace = TRUE) j <- sample(s1(d[2]), k/2+ rpois(1, k/2), replace = TRUE) assert.EQ.mat(ms[i,j], mm[i,j]) ms2 <- ms. <- ms; mm. <- mm # save ## now sub*assign* to these repeated indices, and then compare ----- v <- vRNG(length(i) * length(j)) mm[i,j] <- v ms[i,j] <- v ## useful to see (ii,ij), but confusing R/ESS when additionally debugging: ## if(!showOnly && interactive()) { op <- options(error = recover); on.exit(options(op)) } assert.EQ.mat(ms, mm, show=showOnly) ## vector indexing m[cbind(i,j)] == m[i + N(j-1)] , N = nrow(.) ii <- seq_len(min(length(i), length(j))) i <- i[ii] j <- j[ii] ij <- cbind(i, j) ii <- i + nrow(ms)*(j - 1) ord.i <- order(ii) iio <- ii[ord.i] ui <- unique(iio) # compare these with : neg.ii <- - setdiff(seq_len(prod(d)), ii) stopifnot(identical(mm[ii], mm[ij]), identical(ms.[ui], ms.[neg.ii]), ms.[ij] == mm.[ii], ## M[ cbind(i,j) ] was partly broken; now checking ms.[ii] == mm.[ii]) v <- v[seq_len(length(i))] if(is(ms,"nMatrix")) v <- as.logical(v) # ! mm.[ij] <- v ms.[ii] <- v nodup <- (length(ui) == length(ii)) ## <==> ! anyDuplicated(iio) if(nodup) { cat("[-]") # rare, unfortunately ms2[neg.ii] <- v[ord.i] stopifnot(identical(ms2, ms.)) } assert.EQ.mat(ms., mm., show=showOnly) } ##{chkAssign} ## Get duplicated index {because these are "hard" (and rare) getDuplIndex <- function(n, k) { repeat { i <- sample(n, k, replace=TRUE) # 3 4 6 9 2 9 : 9 is twice if(anyDuplicated(i)) break } i } ## From package 'sfsmisc': repChar <- function (char, no) paste(rep.int(char, no), collapse = "") m <- 1:800 set.seed(101) ; m[sample(800, 600)] <- 0 m0 <- Matrix(m, nrow = 40) m1 <- add.simpleDimnames(m0) for(kind in c("n", "l", "d")) { for(m in list(m0,m1)) { ## -- with and without dimnames ------------------------- kClass <-paste0(kind, "Matrix" ) Ckind <- paste0(kind, "gCMatrix") Tkind <- paste0(kind, "gTMatrix") str(mC <- as(m, Ckind)) str(mT <- as(as(as(m, kClass), "TsparseMatrix"), Tkind)) mm <- as(mC, "matrix") # also logical or double IDENT <- if(kind == "n") function(x,y) Q.eq2(x,y, tol=0) else identical stopifnot(identical(mT, as(as(mC, "TsparseMatrix"), Tkind)), identical(mC, as(mT, Ckind)), Qidentical(mC[0,0], new(Ckind)), Qidentical(mT[0,0], new(Tkind)), identical(unname(mT[0,]), new(Tkind, Dim = c(0L,ncol(m)))), identical(unname(mT[,0]), new(Tkind, Dim = c(nrow(m),0L))), IDENT(mC[0,], as(mT[FALSE,], Ckind)), IDENT(mC[,0], as(mT[,FALSE], Ckind)), sapply(pmin(min(dim(mC)), c(0:2, 5:10)), function(k) {i <- seq_len(k); all(mC[i,i] == mT[i,i])}), TRUE) cat("ok\n") show(mC[,1]) show(mC[1:2,]) show(mC[7, drop = FALSE]) assert.EQ.mat(mC[1:2,], mm[1:2,]) assert.EQ.mat(mC[0,], mm[0,]) assert.EQ.mat(mC[,FALSE], mm[,FALSE]) ## ## *repeated* (aka 'duplicated') indices - did not work at all ... i <- pmin(nrow(mC), rep(8:10,2)) j <- c(2:4, 4:3) assert.EQ.mat(mC[i,], mm[i,]) assert.EQ.mat(mC[,j], mm[,j]) ## FIXME? assert.EQ.mat(mC[,NA], mm[,NA]) -- mC[,NA] is all 0 "instead" of all NA ## MM currently thinks we should NOT allow [ ] assert.EQ.mat(mC[i, 2:1], mm[i, 2:1]) assert.EQ.mat(mC[c(4,1,2:1), j], mm[c(4,1,2:1), j]) assert.EQ.mat(mC[i,j], mm[i,j]) ## ## set.seed(7) op <- options(Matrix.verbose = FALSE) cat(" for(): ") for(n in 1:(if(doExtras) 50 else 5)) { chkAssign(mC, mm) chkAssign(mC[-3,-2], mm[-3,-2]) cat(".") } options(op) cat(sprintf("\n[Ok]%s\n\n", repChar("-", 64))) } cat(sprintf("\nok( %s )\n== ###%s\n\n", kind, repChar("=", 70))) }## end{for}--------------------------------------------------------------- showProc.time() if(doExtras) {### {was ./AAA_index.R, MM-only} ## an nsparse-example A <- Matrix(c(rep(c(1,0,0),2), rep(c(2,0),7), c(0,0,2), rep(0,4)), 3,9) i <- c(3,1:2) j <- c(3, 5, 9, 5, 9) vv <- logical(length(i)*length(j)); vv[6:9] <- TRUE print(An <- as(A,"nMatrix")); an <- as(An, "matrix") assert.EQ.mat(An, an) An[i, j] <- vv an[i, j] <- vv assert.EQ.mat(An, an)## error if(!all(An == an)) show(drop0(An - an)) ## all are +1 options("Matrix.subassign.verbose" = TRUE)# output from C An <- as(A,"nMatrix"); An[i, j] <- vv ## and compare with this: Al <- as(A,"lMatrix"); Al[i, j] <- vv options("Matrix.subassign.verbose" = FALSE) ##--- An interesting not small not large example for M[i,j] <- v ------------ ## M <- Matrix(c(1, rep(0,7), 1:4), 3,4) N0 <- kronecker(M,M) mkN1 <- function(M) { stopifnot(length(d <- dim(M)) == 2) isC <- is(M,"CsparseMatrix") M[,d[2]] <- c(0,2,0) N <- kronecker(diag(x=1:2), M)## remains sparse if 'M' is if(isC) N <- as(N, "CsparseMatrix") diag(N[-1,]) <- -2 N[9,] <- 1:4 # is recycled N[,12] <- -7:-9 # ditto N } show(N1 <- t(N <- mkN1(N0))) # transpose {for display reasons} C1 <- t(C <- mkN1(as(N0,"CsparseMatrix"))) stopifnot(all(C == N)) assert.EQ.mat(C, mkN1(as.matrix(N0))) C. <- C1 show(N <- N1) ; n <- as.matrix(N); str(N) sort(i <- c(6,8,19,11,21,20,10,7,12,9,5,18,17,22,13))## == c(5:13, 17:22)) sort(j <- c(3,8,6,15,10,4,14,13,16,2,11,17,7,5))## == c(2:8, 10:11, 13:17) val <- v.l <- 5*c(0,6,0,7,0,0,8:9, 0,0) show(spv <- as(val, "sparseVector")); str(spv) n [i,j] <- v.l N [i,j] <- val# is recycled, too C.[i,j] <- val assert.EQ.mat(N,n) ; stopifnot(all(C. == N)) ## and the same *again*: n [i,j] <- v.l N [i,j] <- val C.[i,j] <- val assert.EQ.mat(N,n) stopifnot(all(C. == N)) print(load(system.file("external", "symA.rda", package="Matrix"))) # "As" stopifnot(isValid(As, "dsCMatrix"), identical(As@factors, list())) R. <- drop0(chol(As)) stopifnot(1:32 == sort(diag(R.)), ## ! R.@x == as.integer(R.@x),## so it is an integer-valued chol-decomp ! ## shows that (1) As is *not* singular (2) the matrix is not random all.equal(crossprod(R.), As, tolerance =1e-15)) print(summary(evA <- eigen(As, only.values=TRUE)$val)) print(tail(evA)) ## largest three ~= 10^7, smallest two *negative* print(rcond(As)) # 1.722 e-21 == very bad ! ##-> this *is* a border line case, i.e. very close to singular ! ## and also determinant(.) is rather random here! cc0 <- Cholesky(As)# no problem try({ cc <- Cholesky(As, super=TRUE) ## gives --on 32-bit only-- ## Cholmod error 'matrix not positive definite' at file:../Supernodal/t_cholmod_super_numeric.c, line 613 ecc <- expand(cc) L.P <- with(ecc, crossprod(L,P)) ## == L'P ## crossprod(L.P) == (L'P)' L'P == P'LL'P stopifnot( all.equal(crossprod(L.P), As) ) }) ##---- end{ eigen( As ) ----------- } ## only if(doExtras) ##---- Symmetric indexing of symmetric Matrix ---------- m. <- mC m.[, c(2, 7:12)] <- 0 isValid(S <- crossprod(add.simpleDimnames(m.) %% 100), "dsCMatrix") ss <- as(S, "matrix") ds <- as(S, "denseMatrix") ## NA-indexing of *dense* Matrices: should work as traditionally assert.EQ.mat(ds[NA,NA], ss[NA,NA]) assert.EQ.mat(ds[NA, ], ss[NA,]) assert.EQ.mat(ds[ ,NA], ss[,NA]) T <- as(S, "TsparseMatrix") stopifnot(identical(ds[2 ,NA], ss[2,NA]), identical(ds[NA, 1], ss[NA, 1]), identical(S, as(T, "CsparseMatrix")) ) ## non-repeated indices: i <- c(7:5, 2:4);assert.EQ.mat(T[i,i], ss[i,i]) ## NA in indices -- check that we get a helpful error message: i[2] <- NA er <- tryCatch(T[i,i], error = function(e)e) stopifnot(as.logical(grep("indices.*sparse Matrices", er$message))) N <- nrow(T) set.seed(11) for(n in 1:(if(doExtras) 50 else 3)) { i <- sample(N, max(2, sample(N,1)), replace = FALSE) validObject(Tii <- T[i,i]) ; tTi <- t(T)[i,i] stopifnot(is(Tii, "dsTMatrix"), # remained symmetric Tsparse is(tTi, "dsTMatrix"), # may not be identical when *sorted* differently identical(as(t(Tii),"CsparseMatrix"), as(tTi,"CsparseMatrix"))) assert.EQ.mat(Tii, ss[i,i]) } b <- diag(1:2)[,c(1,1,2,2)] cb <- crossprod(b) cB <- crossprod(Matrix(b, sparse=TRUE)) a <- matrix(0, 6, 6) a[1:4, 1:4] <- cb A1 <- A2 <- Matrix(0, 6, 6)#-> sparse A1[1:4, 1:4] <- cb A2[1:4, 1:4] <- cB assert.EQ.mat(A1, a)# indeed stopifnot(identical(A1, A2), is(A1, "dsCMatrix")) ## repeated ones ``the challenge'' (to do smartly): j <- c(4, 4, 9, 12, 9, 4, 17, 3, 18, 4, 12, 18, 4, 9) assert.EQ.mat(T[j,j], ss[j,j]) ## and another two sets (a, A) & (a., A.) : a <- matrix(0, 6,6) a[upper.tri(a)] <- (utr <- c(2, 0,-1, 0,0,5, 7,0,0,0, 0,0,-2,0,8)) ta <- t(a); ta[upper.tri(a)] <- utr; a <- t(ta) diag(a) <- c(0,3,0,4,6,0) A <- as(Matrix(a), "TsparseMatrix") A. <- A diag(A.) <- 10 * (1:6) a. <- as(A., "matrix") ## More testing {this was not working for a long time..} set.seed(1) for(n in 1:(if(doExtras) 100 else 6)) { i <- sample(1:nrow(A), 3+2*rpois(1, lam=3), replace=TRUE) Aii <- A[i,i] A.ii <- A.[i,i] stopifnot(class(Aii) == class(A), class(A.ii) == class(A.)) assert.EQ.mat(Aii , a [i,i]) assert.EQ.mat(A.ii, a.[i,i]) assert.EQ.mat(T[i,i], ss[i,i]) } showProc.time() stopifnot(all.equal(mC[,3], mm[,3]), identical(mC[ij], mC[ij + 0.4]), identical(mC[ij], mm[ij]), identical(mC[iN], mm[iN])) ## out of bound indexing must be detected: assertError(mC[cbind(ij[,1] - 5, ij[,2])]) assertError(mC[cbind(ij[,1], ij[,2] + ncol(mC))]) assert.EQ.mat(mC[7, , drop=FALSE], mm[7, , drop=FALSE]) identical (mC[7, drop=FALSE], mm[7, drop=FALSE]) # *vector* indexing stopifnot(dim(mC[numeric(0), ]) == c(0,20), # used to give warnings dim(mC[, integer(0)]) == c(40,0), identical(mC[, integer(0)], mC[, FALSE])) validObject(print(mT[,c(2,4)])) stopifnot(all.equal(mT[2,], mm[2,]), ## row or column indexing in combination with t() : Q.C.identical(mT[2,], t(mT)[,2]), Q.C.identical(mT[-2,], t(t(mT)[,-2])), Q.C.identical(mT[c(2,5),], t(t(mT)[,c(2,5)])) ) assert.EQ.mat(mT[4,, drop = FALSE], mm[4,, drop = FALSE]) stopifnot(identical3(mm[,1], mC[,1], mT[,1]), identical3(mm[3,], mC[3,], mT[3,]), identical3(mT[2,3], mC[2,3], 0), identical(mT[], mT), identical4( mm[c(3,7), 2:4], as.mat( m[c(3,7), 2:4]), as.mat(mT[c(3,7), 2:4]), as.mat(mC[c(3,7), 2:4])) ) x.x <- crossprod(mC) stopifnot(class(x.x) == "dsCMatrix", class(x.x. <- round(x.x / 10000)) == "dsCMatrix", identical(x.x[cbind(2:6, 2:6)], diag(x.x [2:6, 2:6]))) head(x.x.) # Note the *non*-structural 0's printed as "0" tail(x.x., -3) # all but the first three lines lx.x <- as(x.x, "lsCMatrix") # FALSE only for "structural" 0 (l10 <- lx.x[1:10, 1:10])# "lsC" (l3 <- lx.x[1:3, ]) m.x <- as.mat(x.x) # as.mat() *drops* (NULL,NULL) dimnames stopifnot(class(l10) == "lsCMatrix", # symmetric indexing -> symmetric ! identical(as.mat(lx.x), m.x != 0), identical(as.logical(lx.x), as.logical(m.x)), identical(as.mat(l10), m.x[1:10, 1:10] != 0), identical(as.mat(l3 ), m.x[1:3, ] != 0) ) ##-- Sub*assignment* with repeated / duplicated index: A <- Matrix(0,4,3) ; A[c(1,2,1), 2] <- 1 ; A B <- A; B[c(1,2,1), 2] <- 1:3; B; B. <- B B.[3,] <- rbind(4:2) ## change the diagonal and the upper and lower subdiagonal : diag(B.) <- 10 * diag(B.) diag(B.[,-1]) <- 5* diag(B.[,-1]) diag(B.[-1,]) <- 4* diag(B.[-1,]) ; B. C <- B.; C[,2] <- C[,2]; C[1,] <- C[1,]; C[2:3,2:1] <- C[2:3,2:1] stopifnot(identical(unname(as.matrix(A)), local({a <- matrix(0,4,3); a[c(1,2,1), 2] <- 1 ; a})), identical(unname(as.matrix(B)), local({a <- matrix(0,4,3); a[c(1,2,1), 2] <- 1:3; a})), identical(C, drop0(B.))) ## [] <- v failed in the past T <- as(C,"TsparseMatrix"); C. <- C T[T>0] <- 21 C[C>0] <- 21 a. <- local({a <- as.matrix(C.); a[a>0] <- 21; a}) assert.EQ.mat(C, a.) stopifnot(identical(C, as(T, "CsparseMatrix"))) ## used to fail n <- 5 ## or much larger sm <- new("dsTMatrix", i=1L, j=1L, Dim=as.integer(c(n,n)), x = 1) (cm <- as(sm, "CsparseMatrix")) sm[2,] stopifnot(sm[2,] == c(0:1, rep.int(0,ncol(sm)-2)), sm[2,] == cm[2,], sm[,3] == sm[3,], all(sm[,-(1:3)] == t(sm[-(1:3),])), # all() all(sm[,-(1:3)] == 0) ) showProc.time() ##--- "nsparse*" sub-assignment :---------- M <- Matrix(c(1, rep(0,7), 1:4), 3,4) N0 <- kronecker(M,M) Nn <- as(N0, "nMatrix"); nn <- as(Nn,"matrix") (Nn00 <- Nn0 <- Nn); nn00 <- nn0 <- nn set.seed(1) Nn0 <- Nn00; nn0 <- nn00 for(i in 1:(if(doExtras) 200 else 25)) { Nn <- Nn0 nn <- nn0 i. <- getDuplIndex(nrow(N0), 6) j. <- getDuplIndex(ncol(N0), 4) vv <- sample(c(FALSE,TRUE), length(i.)*length(j.), replace=TRUE) cat(",") Nn[i., j.] <- vv nn[i., j.] <- vv assert.EQ.mat(Nn, nn) if(!all(Nn == nn)) { cat("i=",i,":\n i. <- "); dput(i.) cat("j. <- "); dput(j.) cat("which(vv): "); dput(which(vv)) cat("Difference matrix:\n") show(drop0(Nn - nn)) } cat("k") ## sub-assign double precision to logical sparseMatrices: now *with* warning: ## {earlier: gave *no* warning}: assertWarning(Nn[1:2,] <- -pi) assertWarning(Nn[, 5] <- -pi) assertWarning(Nn[2:4, 5:8] <- -pi) stopifnot(isValid(Nn,"nsparseMatrix")) ## cat(".") if(i %% 10 == 0) cat("\n") if(i == 100) { Nn0 <- as(Nn0, "CsparseMatrix") cat("Now: class", class(Nn0)," :\n~~~~~~~~~~~~~~~~~\n") } } showProc.time() Nn <- Nn0 ## Check that NA is interpreted as TRUE (with a warning), for "nsparseMatrix": assertWarning(Nn[ii <- 3 ] <- NA); stopifnot(isValid(Nn,"nsparseMatrix"), Nn[ii]) assertWarning(Nn[ii <- 22:24] <- NA); stopifnot(isValid(Nn,"nsparseMatrix"), Nn[ii]) assertWarning(Nn[ii <- -(1:99)] <- NA); stopifnot(isValid(Nn,"nsparseMatrix"), Nn[ii]) assertWarning(Nn[ii <- 3:4 ] <- c(0,NA)) stopifnot(isValid(Nn,"nsparseMatrix"), Nn[ii] == 0:1) assertWarning(Nn[ii <- 25:27] <- c(0,1,NA)) stopifnot(isValid(Nn,"nsparseMatrix"), Nn[ii] == c(FALSE,TRUE,TRUE)) m0 <- Diagonal(5) stopifnot(identical(m0[2,], m0[,2]), identical(m0[,1], c(1,0,0,0,0))) ### Diagonal -- Sparse: (m1 <- as(m0, "TsparseMatrix")) # dtTMatrix unitriangular (m2 <- as(m0, "CsparseMatrix")) # dtCMatrix unitriangular m1g <- as(m1, "generalMatrix") stopifnot(is(m1g, "dgTMatrix")) assert.EQ.mat(m2[1:3,], diag(5)[1:3,]) assert.EQ.mat(m2[,c(4,1)], diag(5)[,c(4,1)]) stopifnot(identical(m2[1:3,], as(m1[1:3,], "CsparseMatrix")), identical(Matrix:::uniqTsparse(m1[, c(4,2)]), Matrix:::uniqTsparse(as(m2[, c(4,2)], "TsparseMatrix"))) )## failed in 0.9975-11 (uTr <- new("dtTMatrix", Dim = c(3L,3L), diag="U")) uTr[1,] <- 0 assert.EQ.mat(uTr, cbind(0, rbind(0,diag(2)))) M <- m0; M[1,] <- 0 Z <- m0; Z[] <- 0; z <- array(0, dim(M)) stopifnot(identical(M, Diagonal(x=c(0, rep(1,4)))), all(Z == 0), Qidentical(as(Z, "matrix"), z)) M <- m0; M[,3] <- 3 ; M ; stopifnot(is(M, "sparseMatrix"), M[,3] == 3) checkMatrix(M) M <- m0; M[1:3, 3] <- 0 ;M T <- m0; T[1:3, 3] <- 10 stopifnot(identical(M, Diagonal(x=c(1,1, 0, 1,1))), isValid(T, "triangularMatrix"), identical(T[,3], c(10,10,10,0,0))) M <- m1; M[1,] <- 0 ; M ; assert.EQ.mat(M, diag(c(0,rep(1,4))), tol=0) M <- m1; M[,3] <- 3 ; stopifnot(is(M,"sparseMatrix"), M[,3] == 3) Z <- m1; Z[] <- 0 checkMatrix(M) M <- m1; M[1:3, 3] <- 0 ;M assert.EQ.mat(M, diag(c(1,1, 0, 1,1)), tol=0) T <- m1; T[1:3, 3] <- 10; checkMatrix(T) stopifnot(is(T, "triangularMatrix"), identical(T[,3], c(10,10,10,0,0)), Qidentical(as(Z, "matrix"), z)) M <- m2; M[1,] <- 0 ; M ; assert.EQ.mat(M, diag(c(0,rep(1,4))), tol=0) M <- m2; M[,3] <- 3 ; stopifnot(is(M,"sparseMatrix"), M[,3] == 3) checkMatrix(M) Z <- m2; Z[] <- 0 M <- m2; M[1:3, 3] <- 0 ;M assert.EQ.mat(M, diag(c(1,1, 0, 1,1)), tol=0) T <- m2; T[1:3, 3] <- 10; checkMatrix(T) stopifnot(is(T, "dtCMatrix"), identical(T[,3], c(10,10,10,0,0)), Qidentical(as(Z, "matrix"), z)) showProc.time() ## "Vector indices" ------------------- asLogical <- function(x) { stopifnot(is.atomic(x)) storage.mode(x) <- "logical" x } .iniDiag.example <- expression({ D <- Diagonal(6) M <- as(D,"dgeMatrix") m <- as(D,"matrix") s <- as(D,"TsparseMatrix"); N <- as(s,"nMatrix") S <- as(s,"CsparseMatrix"); C <- as(S,"nMatrix") }) eval(.iniDiag.example) i <- c(3,1,6); v <- c(10,15,20) ## (logical,value) which both are recycled: L <- c(TRUE, rep(FALSE,8)) ; z <- c(50,99) ## vector subassignment, both with integer & logical ## these now work correctly {though not very efficiently; hence warnings} m[i] <- v # the role model: only first column is affected M[i] <- v; assert.EQ.mat(M,m) # dge D[i] <- v; assert.EQ.mat(D,m) # ddi -> dtT -> dgT s[i] <- v; assert.EQ.mat(s,m) # dtT -> dgT S[i] <- v; assert.EQ.mat(S,m); S # dtC -> dtT -> dgT -> dgC m.L <- asLogical(m) C[i] <- v; assert.EQ.mat(C,m.L); validObject(C) N[i] <- v; assert.EQ.mat(N,m.L); validObject(N) stopifnot(Q.C.identical(D,s, checkClass=FALSE)) ## logical *vector* indexing eval(.iniDiag.example) m[L] <- z; m.L <- asLogical(m) M[L] <- z; assert.EQ.mat(M,m) D[L] <- z; assert.EQ.mat(D,m) s[L] <- z; assert.EQ.mat(s,m) S[L] <- z; assert.EQ.mat(S,m) ; S C[L] <- z; assert.EQ.mat(C,m.L) N[L] <- z; assert.EQ.mat(N,m.L) ## indexing [i] vs [i,] --- now ok eval(.iniDiag.example) stopifnot(identical5(m[i], M[i], D[i], s[i], S[i]), identical3(as.logical(m[i]), C[i], N[i]), identical5(m[L], M[L], D[L], s[L], S[L]), identical3(as.logical(m[L]), C[L], N[L])) ## bordercase ' drop = .' *vector* indexing {failed till 2009-04-..) stopifnot(identical5(m[i,drop=FALSE], M[i,drop=FALSE], D[i,drop=FALSE], s[i,drop=FALSE], S[i,drop=FALSE]), identical3(as.logical(m[i,drop=FALSE]), C[i,drop=FALSE], N[i,drop=FALSE])) stopifnot(identical5(m[L,drop=FALSE], M[L,drop=FALSE], D[L,drop=FALSE], s[L,drop=FALSE], S[L,drop=FALSE]), identical3(as.logical(m[L,drop=FALSE]), C[L,drop=FALSE], N[L,drop=FALSE])) ## using L for row-indexing should give an error assertError(m[L,]); assertError(m[L,, drop=FALSE]) ## these did not signal an error, upto (including) 0.999375-30: assertError(s[L,]); assertError(s[L,, drop=FALSE]) assertError(S[L,]); assertError(S[L,, drop=FALSE]) assertError(N[L,]); assertError(N[L,, drop=FALSE]) ## row indexing: assert.EQ.mat(D[i,], m[i,]) assert.EQ.mat(M[i,], m[i,]) assert.EQ.mat(s[i,], m[i,]) assert.EQ.mat(S[i,], m[i,]) assert.EQ.mat(C[i,], asLogical(m[i,])) assert.EQ.mat(N[i,], asLogical(m[i,])) ## column indexing: assert.EQ.mat(D[,i], m[,i]) assert.EQ.mat(M[,i], m[,i]) assert.EQ.mat(s[,i], m[,i]) assert.EQ.mat(S[,i], m[,i]) assert.EQ.mat(C[,i], asLogical(m[,i])) assert.EQ.mat(N[,i], asLogical(m[,i])) ### --- negative indices ---------- ## 1) negative *vector* indexing eval(.iniDiag.example) i <- -(2:30) stopifnot(identical5(m[i], M[i], D[i], s[i], S[i]), identical3(as.logical(m[i]), C[i], N[i])) ## negative vector subassignment : v <- seq_along(m[i]) m[i] <- v; m.L <- asLogical(m) M[i] <- v; assert.EQ.mat(M,m) # dge D[i] <- v; assert.EQ.mat(D,m) # ddi -> dtT -> dgT s[i] <- v; assert.EQ.mat(s,m) # dtT -> dgT S[i] <- v; assert.EQ.mat(S,m); S # dtC -> dtT -> dgT -> dgC N[i] <- v; assert.EQ.mat(N,m.L); N # C[i] <- v; assert.EQ.mat(C,m.L); C # ## 2) negative [i,j] indices mc <- mC[1:5, 1:7] mt <- mT[1:5, 1:7] ## sub matrix assert.EQ.mat(mC[1:2, 0:3], mm[1:2, 0:3]) # test 0-index stopifnot(identical(mc[-(3:5), 0:2], mC[1:2, 0:2]), identical(mt[-(3:5), 0:2], mT[1:2, 0:2]), identical(mC[2:3, 4], mm[2:3, 4])) assert.EQ.mat(mC[1:2,], mm[1:2,]) ## sub vector stopifnot(identical4(mc[-(1:4), ], mC[5, 1:7], mt[-(1:4), ], mT[5, 1:7])) stopifnot(identical4(mc[-(1:4), -(2:4)], mC[5, c(1,5:7)], mt[-(1:4), -(2:4)], mT[5, c(1,5:7)])) ## mixing of negative and positive must give error assertError(mT[-1:1,]) showProc.time() ## Sub *Assignment* ---- now works (partially): mt0 <- mt nt <- as(mt, "nMatrix") mt[1, 4] <- -99 mt[2:3, 1:6] <- 0 mt m2 <- mt+mt m2[1,4] <- -200 m2[c(1,3), c(5:6,2)] <- 1:6 stopifnot(m2[1,4] == -200, as.vector(m2[c(1,3), c(5:6,2)]) == 1:6) mt[,3] <- 30 mt[2:3,] <- 250 mt[1:5 %% 2 == 1, 3] <- 0 mt[3:1, 1:7 > 5] <- 0 mt tt <- as(mt,"matrix") ii <- c(0,2,5) jj <- c(2:3,5) tt[ii, jj] <- 1:6 # 0 is just "dropped" mt[ii, jj] <- 1:6 assert.EQ.mat(mt, tt) mt[1:5, 2:6] as((mt0 - mt)[1:5,], "dsparseMatrix")# [1,5] and lines 2:3 mt[c(2,4), ] <- 0; stopifnot(as(mt[c(2,4), ],"matrix") == 0) mt[2:3, 4:7] <- 33 checkMatrix(mt) mt mc[1,4] <- -99 ; stopifnot(mc[1,4] == -99) mc[1,4] <- 00 ; stopifnot(mc[1,4] == 00) mc[1,4] <- -99 ; stopifnot(mc[1,4] == -99) mc[1:2,4:3] <- 4:1; stopifnot(as.matrix(mc[1:2,4:3]) == 4:1) mc[-1, 3] <- -2:1 # 0 should not be entered; 'value' recycled mt[-1, 3] <- -2:1 stopifnot(mc@x != 0, mt@x != 0, mc[-1,3] == -2:1, mt[-1,3] == -2:1) ## failed earlier mc0 <- mc mt0 <- as(mc0, "TsparseMatrix") m0 <- as(mc0, "matrix") set.seed(1); options(Matrix.verbose = FALSE) for(i in 1:(if(doExtras) 50 else 4)) { mc <- mc0; mt <- mt0 ; m <- m0 ev <- 1:5 %% 2 == round(runif(1))# 0 or 1 j <- sample(ncol(mc), 1 + round(runif(1))) nv <- rpois(sum(ev) * length(j), lambda = 1) mc[ev, j] <- nv m[ev, j] <- nv mt[ev, j] <- nv if(i %% 10 == 1) print(mc[ev,j, drop = FALSE]) stopifnot(as.vector(mc[ev, j]) == nv, ## failed earlier... as.vector(mt[ev, j]) == nv) validObject(mc) ; assert.EQ.mat(mc, m) validObject(mt) ; assert.EQ.mat(mt, m) } showProc.time() options(Matrix.verbose = TRUE) mc # no longer has non-structural zeros mc[ii, jj] <- 1:6 mc[c(2,5), c(3,5)] <- 3.2 checkMatrix(mc) m. <- mc mc[4,] <- 0 mc S <- as(Diagonal(5),"TsparseMatrix") H <- Hilbert(9) Hc <- as(round(H, 3), "dsCMatrix")# a sparse matrix with no 0 ... (trH <- tril(Hc[1:5, 1:5])) stopifnot(is(trH, "triangularMatrix"), trH@uplo == "L", is(S, "triangularMatrix")) ## triangular assignment ## the slick (but inefficient in case of sparse!) way to assign sub-diagonals: ## equivalent to tmp <- `diag<-`(S[,-1], -2:1); S[,-1] <- tmp ## which dispatches to (x="TsparseMatrix", i="missing",j="index", value="replValue") diag(S[,-1]) <- -2:1 # used to give a wrong warning S <- as(S,"triangularMatrix") assert.EQ.mat(S, local({s <- diag(5); diag(s[,-1]) <- -2:1; s})) trH[c(1:2,4), c(2:3,5)] <- 0 # gave an *error* upto Jan.2008 trH[ lower.tri(trH) ] <- 0 # ditto, because of callNextMethod() m <- Matrix(0+1:28, nrow = 4) m[-3,c(2,4:5,7)] <- m[ 3, 1:4] <- m[1:3, 6] <- 0 mT <- as(m, "dgTMatrix") stopifnot(identical(mT[lower.tri(mT)], m [lower.tri(m) ])) lM <- upper.tri(mT, diag=TRUE) mT[lM] <- 0 m[lM] <- 0 assert.EQ.mat(mT, as(m,"matrix")) mT[lM] <- -1:0 m[lM] <- -1:0 assert.EQ.mat(mT, as(m,"matrix")) (mT <- drop0(mT)) i <- c(1:2, 4, 6:7); j <- c(2:4,6) H[i,j] <- 0 (H. <- round(as(H, "sparseMatrix"), 3)[ , 2:7]) Hc. <- Hc Hc.[i,j] <- 0 ## now "works", but setting "non-structural" 0s stopifnot(as.matrix(Hc.[i,j]) == 0) Hc.[, 1:6] ## an example that failed for a long time sy3 <- new("dsyMatrix", Dim = as.integer(c(2, 2)), x = c(14, -1, 2, -7)) checkMatrix(dm <- kronecker(Diagonal(2), sy3))# now sparse with new kronecker dm <- Matrix(as.matrix(dm))# -> "dsyMatrix" (s2 <- as(dm, "sparseMatrix")) checkMatrix(st <- as(s2, "TsparseMatrix")) stopifnot(is(s2, "symmetricMatrix"), is(st, "symmetricMatrix")) checkMatrix(s.32 <- st[1:3,1:2]) ## 3 x 2 - and *not* dsTMatrix checkMatrix(s2.32 <- s2[1:3,1:2]) I <- c(1,4:3) stopifnot(is(s2.32, "generalMatrix"), is(s.32, "generalMatrix"), identical(as.mat(s.32), as.mat(s2.32)), identical3(dm[1:3,-1], asD(s2[1:3,-1]), asD(st[1:3,-1])), identical4(2, dm[4,3], s2[4,3], st[4,3]), identical3(diag(dm), diag(s2), diag(st)), is((cI <- s2[I,I]), "dsCMatrix"), is((tI <- st[I,I]), "dsTMatrix"), identical4(as.mat(dm)[I,I], as.mat(dm[I,I]), as.mat(tI), as.mat(cI)) ) ## now sub-assign and check for consistency ## symmetric subassign should keep symmetry st[I,I] <- 0; checkMatrix(st); stopifnot(is(st,"symmetricMatrix")) s2[I,I] <- 0; checkMatrix(s2); stopifnot(is(s2,"symmetricMatrix")) ## m <- as.mat(st) m[2:1,2:1] <- 4:1 st[2:1,2:1] <- 4:1 s2[2:1,2:1] <- 4:1 stopifnot(identical(m, as.mat(st)), 1:4 == as.vector(s2[1:2,1:2]), identical(m, as.mat(s2))) ## now a slightly different situation for 's2' (had bug) s2 <- as(dm, "sparseMatrix") s2[I,I] <- 0; diag(s2)[2:3] <- -(1:2) stopifnot(is(s2,"symmetricMatrix"), diag(s2) == c(0:-2,0)) t2 <- as(s2, "TsparseMatrix") m <- as.mat(s2) s2[2:1,2:1] <- 4:1 t2[2:1,2:1] <- 4:1 m[2:1,2:1] <- 4:1 assert.EQ.mat(t2, m) assert.EQ.mat(s2, m) ## and the same (for a different s2 !) s2[2:1,2:1] <- 4:1 t2[2:1,2:1] <- 4:1 assert.EQ.mat(t2, m)# ok assert.EQ.mat(s2, m)# failed in 0.9975-8 showProc.time() ## m[cbind(i,j)] <- value: (2-column matrix subassignment): m.[ cbind(3:5, 1:3) ] <- 1:3 stopifnot(m.[3,1] == 1, m.[4,2] == 2) nt. <- nt ; nt[rbind(2:3, 3:4, c(3,3))] <- FALSE s. <- m. ; m.[cbind(3,4:6)] <- 0 ## assigning 0 where there *is* 0 .. stopifnot(identical(nt.,nt), ## should not have changed identical(s., m.)) x.x[ cbind(2:6, 2:6)] <- 12:16 stopifnot(isValid(x.x, "dsCMatrix"), 12:16 == as.mat(x.x)[cbind(2:6, 2:6)]) (ne1 <- (mc - m.) != 0) stopifnot(identical(ne1, 0 != abs(mc - m.))) (ge <- m. >= mc) # contains "=" -> result is dense ne. <- mc != m. # was wrong (+ warning) stopifnot(identical(!(m. < mc), m. >= mc), identical(m. < mc, as(!ge, "sparseMatrix")), identical(ne., drop0(ne1))) d6 <- Diagonal(6) ii <- c(1:2, 4:5) d6[cbind(ii,ii)] <- 7*ii stopifnot(is(d6, "ddiMatrix"), identical(d6, Diagonal(x=c(7*1:2,1,7*4:5,1)))) for(j in 3:6) { ## even and odd j used to behave differently M <- Matrix(0, j,j); m <- matrix(0, j,j) T <- as(M, "TsparseMatrix") TG <- as(T, "generalMatrix") G <- as(M, "generalMatrix") id <- cbind(1:j,1:j) i2 <- cbind(1:j,j:1) m[id] <- 1:j M[id] <- 1:j ; stopifnot(is(M,"symmetricMatrix")) T[id] <- 1:j ; stopifnot(is(T,"symmetricMatrix")) G[id] <- 1:j TG[id]<- 1:j m[i2] <- 10 M[i2] <- 10 ; stopifnot(is(M,"symmetricMatrix")) T[i2] <- 10 ; stopifnot(is(T,"symmetricMatrix")) G[i2] <- 10 TG[i2]<- 10 ## assert.EQ.mat(M, m) assert.EQ.mat(T, m) assert.EQ.mat(G, m) assert.EQ.mat(TG,m) } ## drop, triangular, ... (M3 <- Matrix(upper.tri(matrix(, 3, 3)))) # ltC; indexing used to fail T3 <- as(M3, "TsparseMatrix") stopifnot(identical(drop(M3), M3), identical4(drop(M3[,2, drop = FALSE]), M3[,2, drop = TRUE], drop(T3[,2, drop = FALSE]), T3[,2, drop = TRUE]), is(T3, "triangularMatrix"), !is(T3[,2, drop=FALSE], "triangularMatrix") ) (T6 <- as(as(kronecker(Matrix(c(0,0,1,0),2,2), t(T3)), "lMatrix"), "triangularMatrix")) T6[1:4, -(1:3)] # failed (trying to coerce back to ltTMatrix) stopifnot(identical(T6[1:4, -(1:3)][2:3, -3], spMatrix(2,2, i=c(1,2,2), j=c(1,1,2), x=rep(TRUE,3)))) M <- Diagonal(4); M[1,2] <- 2 M. <- as(M, "CsparseMatrix") (R <- as(M., "RsparseMatrix")) (Ms <- symmpart(M.)) Rs <- as(Ms, "RsparseMatrix") stopifnot(isValid(M, "triangularMatrix"), isValid(M.,"triangularMatrix"), isValid(Ms, "dsCMatrix"), isValid(R, "dtRMatrix"), isValid(Rs, "dsRMatrix") ) stopifnot(dim(M[2:3, FALSE]) == c(2,0), dim(R[2:3, FALSE]) == c(2,0), identical(M [2:3,TRUE], M [2:3,]), identical(M.[2:3,TRUE], M.[2:3,]), identical(R [2:3,TRUE], R [2:3,]), dim(R[FALSE, FALSE]) == c(0,0)) n <- 50000L Lrg <- new("dgTMatrix", Dim = c(n,n)) diag(Lrg) <- 1:n dLrg <- as(Lrg, "diagonalMatrix") stopifnot(identical(Diagonal(x = 1:n), dLrg)) diag(dLrg) <- 1 + diag(dLrg) Clrg <- as(Lrg,"CsparseMatrix") Ctrg <- as(Clrg, "triangularMatrix") diag(Ctrg) <- 1 + diag(Ctrg) stopifnot(identical(Diagonal(x = 1+ 1:n), dLrg), identical(Ctrg, as(dLrg,"CsparseMatrix"))) cc <- capture.output(show(dLrg))# show() used to error for large n showProc.time() ## Large Matrix indexing / subassignment ## ------------------------------------- (from ex. by Imran Rashid) n <- 7000000 m <- 100000 nnz <- 20000 set.seed(12) f <- sparseMatrix(i = sample(n, size=nnz, replace=TRUE), j = sample(m, size=nnz, replace=TRUE)) str(f) dim(f) # 6999863 x 99992 prod(dim(f)) # 699930301096 == 699'930'301'096 (~ 700'000 millions) str(thisCol <- f[,5000])# logi [~ 7 mio....] sv <- as(thisCol, "sparseVector") str(sv) ## "empty" ! validObject(spCol <- f[,5000, drop=FALSE]) ## ## *not* identical(): as(spCol, "sparseVector")@length is "double"prec: stopifnot(all.equal(as(spCol, "sparseVector"), as(sv, "nsparseVector"), tolerance=0)) if(doExtras) {#----------------------------------------------------------------- f[,5762] <- thisCol # now "fine" <<<<<<<<<< FIXME uses LARGE objects -- slow -- ## is using replCmat() in ../R/Csparse.R, then ## replTmat() in ../R/Tsparse.R fx <- sparseMatrix(i = sample(n, size=nnz, replace=TRUE), j = sample(m, size=nnz, replace=TRUE), x = round(10*rnorm(nnz))) class(fx)## dgCMatrix fx[,6000] <- (tC <- rep(thisCol, length=nrow(fx)))# slow (as above) thCol <- fx[,2000] fx[,5762] <- thCol# slow stopifnot(is(f, "ngCMatrix"), is(fx, "dgCMatrix"), identical(thisCol, f[,5762]),# perfect identical(as.logical(fx[,6000]), tC), identical(thCol, fx[,5762])) showProc.time() ## cat("checkMatrix() of all: \n---------\n") Sys.setlocale("LC_COLLATE", "C")# to keep ls() reproducible for(nm in ls()) if(is(.m <- get(nm), "Matrix")) { cat(nm, "\n") checkMatrix(.m, verbose = FALSE , doDet = nm != "As" ## <- "As" almost singular <=> det() "ill posed" ) } showProc.time() }#--------------end if(doExtras) ----------------------------------------------- if(!interactive()) warnings() Matrix/tests/base-matrix-fun.R0000644000175100001440000000302511601431575016026 0ustar hornikusers#### Thanks to the manipulation in base namespace, see ../R/zzz.R , #### all the functions (in 'base' or namespaces that import it) #### starting with something like #### " x <- as.matrix(x) " or " X <- as.array(X) " #### will work for 'Matrix'-matrices library(Matrix) data(KNex); mm <- KNex$mm str(m1 <- mm[1:500, 1:200]) m11 <- m1[1:100, 1:20] ## These now work thanks to using our as.matrix(): str(D1 <- dist(m11)) str(rs <- apply(m1, 1, sum)) stopifnot(identical(kappa(Matrix(2:5, 2)), kappa(matrix(2:5, 2)))) ## used to seg.fault, PR#7984, ## because qr() was calling the wrong as.matrix() ## also matplot() or pairs(). ## a regression test for as.matrix.dist(.) still working stopifnot(c(43, 43) == dim(as.matrix(d <- dist(USJudgeRatings)))) m <- Matrix(0:5, 3, 2) (m2 <- Matrix(diag(c(3,1)))) (m3 <- crossprod(t(m))) # <- that's an S4 method; nothing "base" str( svd(m) ) str( lapply(eigen(m3), zapsmall)) ### outer() used to work thanks to as.array() -- up to R 2.2.1 ## no longer, because the definition of outer has changed -- FIXME? ## Whould work by providing an as.vector(.) method ## *and* is.array(.) \-> TRUE which may be too strong ##--> For %o%: "need" to make outer(.,.) an S3 generic ## *and* provide Matrix S3 methods ## stopifnot(identical(outer(m, m2), ## outer(as(m,"matrix"), as(m2,"matrix"))), ## identical(outer(m3, m2), ## outer(as(m3,"matrix"), as(m2,"matrix")))) cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons'' Matrix/tests/Simple.R0000644000175100001440000010006612271746775014277 0ustar hornikusers#### Currently a collection of simple tests ## (since 'Matrix' takes long to load, rather have fewer source files!) ##-------- *BEFORE* attaching Matrix: -------------------------------- str(Matrix::Matrix)# -> load the namespace T <- new("ngTMatrix", i=0L, j=2L, Dim = c(2L,6L)) T as(T, "CsparseMatrix") ## gave Error in asMethod(object) : could not find function ".M.classEnv" ## from 0.999375-23 to *-25 ## another even shorter version of this: n <- new("dgCMatrix") n ## this: m <- Matrix::Matrix(cbind(1,0,diag(x=2:4))) m ##-------------------------------------------------------------------- library(Matrix) source(system.file("test-tools.R", package = "Matrix"))# identical3() etc if(interactive()) { options(error = recover) } else options(Matrix.verbose = TRUE)# to show Matrix.msg()s ### Matrix() ''smartness'' (d4 <- Matrix(diag(4))) (z4 <- Matrix(0*diag(4))) (o4 <- Matrix(1+diag(4))) (tr <- Matrix(cbind(1,0:1))) (M4 <- Matrix(m4 <- cbind(0,rbind(6*diag(3),0)))) dM4 <- Matrix(M4, sparse = FALSE) class(mN <- Matrix(NA, 3,4)) # NA *is* logical validObject(Matrix(NA)) bd4 <- bdiag(M4,dM4,M4) stopifnot(isValid(o4, "dsyMatrix"), isValid(M4, "dtCMatrix"), validObject(dM4), validObject(mN), identical(bdiag(M4), bdiag(dM4)), identical(bd4@p, c(0L,0:3,3:6,6:9)), identical(bd4@i, c(0:2, 4:6, 8:10)), bd4@x == 6 ) assert.EQ.mat(dM4, m4) assert.EQ.mat(M4^M4, m4^m4) assert.EQ.mat(mN, matrix(NA, 3,4)) assert.EQ.mat(bdiag(diag(4)), diag(4)) sL <- Matrix(, 3,4, sparse=TRUE)# -> "lgC" trS <- Matrix(tr, sparse=TRUE)# failed in 0.9975-11 stopifnot(isValid(d4, "diagonalMatrix"), isValid(z4, "diagonalMatrix"), isValid(tr, "triangularMatrix"), isValid(trS, "triangularMatrix"), all(is.na(sL@x)), ## not yet: all(is.na(sL)), !any(sL, na.rm=TRUE), all(!sL, na.rm=TRUE), validObject(Matrix(c(NA,0), 4, 3, byrow = TRUE)), validObject(Matrix(c(NA,0), 4, 4)), isValid(Matrix(c(NA,0,0,0), 4, 4), "sparseMatrix")) I <- i1 <- I1 <- Diagonal(1) I1[1,1] <- i1[1, ] <- I [ ,1] <- NA stopifnot(identical3(I,i1,I1)) image(d4) # gave infinite recursion assertError( Matrix(factor(letters)) ) mlp <- matrix(.leap.seconds)## 24 x 1 numeric matrix Mlp <- Matrix(.leap.seconds) assert.EQ.mat(Mlp, mlp) if(FALSE) { ## TODO -- once R itself does better ... .Leap.seconds <- as.POSIXlt(.leap.seconds) mLp <- matrix(.Leap.seconds)## 24 x 1 list each of length 24 -- yuck!!! MLp <- Matrix(.Leap.seconds)## --> error (for now) } E <- rep(c(TRUE,NA,TRUE), length=8) F <- new("nsparseVector", length = 8L, i = c(2L, 5L, 8L)) e <- as(E, "sparseVector"); f <- as(F,"lsparseVector") stopifnot(E | as.vector(F), identical(E | F, F | E), all(e | f), all(E | F)) # <- failed Ops.spv.spv dT <- new("dgTMatrix", i = c(1:2,1:2), j=rep(1:2, each=2), Dim = c(4L, 4L), x = c(1, 1, NA, 2)) dt <- new("dtTMatrix", i = 0:3, j = 0:3, Dim = c(4L, 4L), x = c(1,0,0,0), uplo = "U", diag = "N") c1 <- as(dT, "CsparseMatrix") c2 <- as(dt, "CsparseMatrix") isValid(lc <- c1 > c2,"lgCMatrix") isValid(lt <- dT > dt,"lgCMatrix") stopifnot(identical(lc,lt)) M <- Diagonal(4); M[1,2] <- 2 ; M cM <- crossprod(M) # >> as_cholmod_l_triplet(): could not reallocate for internal diagU2N() stopifnot(identical(cM, tcrossprod(t(M)))) if(doExtras) { ## formerly in MM-only's ./AAA_latest.R ## 2010-11-29 --- prompted by BDR: mlp <- matrix(.leap.seconds)## 24 x 1 numeric matrix Mlp <- Matrix(.leap.seconds) assert.EQ.mat(Mlp, mlp) S.na <- spMatrix(3, 4, c(1,2,3), c(2,3,3), c(NA,1,0)) show(S.na <- S.na - 2 * S.na) show(L <- S.na != 0) M0 <- Matrix(0, 3, 4) show(Ln0 <- S.na != rep(0, prod(dim(L)))) stopifnot(Q.eq(L, Ln0), identical(Ln0, M0 != S.na)) }## (doExtras) only ### Unit-diagonal and unitriangular {methods need diagU2N() or similar} I <- Diagonal(3) (T <- as(I,"TsparseMatrix")) # unitriangular (C <- as(I,"CsparseMatrix")) # (ditto) lT <- as(T,"lMatrix") lC <- as(C,"lMatrix") stopifnot( identical((n0 <- I != 0), Diagonal(3, TRUE)), I@diag == "U", identical(n0, I & TRUE), identical(n0, I | FALSE), identical(n0, TRUE & I), identical(n0, FALSE | I), all(n0 == !(I == 0)), all(I == n0), identical(n0 == I, I == n0) , identical4(lT, as(Diagonal(3, x=TRUE),"TsparseMatrix"), T & TRUE, TRUE & T), identical4(lC, as(Diagonal(3, x=TRUE),"CsparseMatrix"), C & TRUE, TRUE & C), identical3(lT, T | FALSE, FALSE | T), identical3(lC, C | FALSE, FALSE | C), TRUE) I[,1] <- NA; I[2,2] <- NA ; I[3,] <- NaN stopifnot(isValid(I, "sparseMatrix")) I # gave error in printSpMatrix() - because of R bug in format.info() L <- spMatrix(9, 30, i = rep(1:9, 3), 1:27, (1:27) %% 4 != 1) M <- drop0(crossprod(L)) diag(M) <- diag(M) + 5 # to make it pos.def. M. <- M[1:12,1:12] # small ex N3 <- as(Matrix(upper.tri(diag(3))), "nMatrix") isValid(bdN <- bdiag(N3, N3),"nsparseMatrix") stopifnot(identical(L, L == TRUE), ## used to give infinite recursion all(drop0((0 - L) != 0) == drop0(L))) L[sample(length(L), 10)] <- NA ll <- as(L,"logical") stopifnot(all.equal(mean(L, na.rm=TRUE), mean(ll, na.rm=TRUE), tol= 1e-14), all.equal(mean(L, na.rm=TRUE, trim=1/4),# <- with a warning mean(ll, na.rm=TRUE, trim=1/4), tol= 1e-14)) ## Examples where is.na(.) was wrong: validObject(sc <- new("dsCMatrix", i=as.integer(c(0,0:1,1:2,0:1,3)), Dim=c(4L,4L), p = c(0L,1L,3L,5L,8L), x = c(0,NA,NA,0:1,0,NA,1))) validObject(gc <- as(sc, "generalMatrix")) stopifnot(isSymmetric(M), isSymmetric(M.), is(bdiag(M., M.),"symmetricMatrix"), is(bdN, "triangularMatrix"), all(sc == gc | (is.na(sc) & is.na(gc))), all.equal(N3,N3), tail(all.equal(N3, t(N3)), 1) == all.equal(1,-1),# ~= "Mean relative difference: 2" all((bdN != t(bdN)) == (bdN + t(bdN))), # != failed to work... !any((0+bdN) > bdN), # o !any(bdN != (0+bdN)), # o length(grep("Length", all.equal(M., (vM <- as.vector(M.))))) > 0, identical(M., (M2 <- Matrix(vM, 12,12))), all.equal(M., M2, tolerance =0) ) ## large sparse ones: these now directly "go sparse": str(m0 <- Matrix(0, nrow=100, ncol = 1000)) str(l0 <- Matrix(FALSE, nrow=100, ncol = 200)) stopifnot(all(!l0), identical(FALSE, any(l0))) if(!interactive()) warnings() ## really large {length() is beyond R's limits}: op <- options(warn = 2) # warnings (e.g. integer overflow!) become errors: n <- 50000L stopifnot(n^2 > .Machine$integer.max) ## had integer overflow in index constructions: x <- 1:n D <- Diagonal(n, x=x[n:1]) summary(D)# special method summary(D != 0) stopifnot(identical(x*D, (Dx <- D*x)), identical(D != 0, as(D, "lMatrix")), identical(Dx, local({d <- D; d@x <- d@x * x; d}))) Lrg <- new("dgTMatrix", Dim = c(n,n)) diag(Lrg[2:9,1:8]) <- 1:8 ## ==: Lrg[2:9,1:8] <- `diag<-`(Lrg[2:9,1:8], 1:8) e1 <- try(Lrg == Lrg) # error message almost ok e2 <- try(!Lrg) # error message was "bad", now perfect ina <- is.na(Lrg)# "all FALSE" stopifnot(grep("too large", e1) == 1, grep("too large", e2) == 1, !any(ina))# <- gave warning previously stopifnot(suppressWarnings(any(Lrg)))# (double -> logical warning) ## with dimnames: v <- c(a=1, b=2:3) m <- as.matrix(v) M <- as(v, "dgeMatrix") stopifnot(identical(dimnames(m), list(c("a", "b1", "b2"), NULL)), identical(M, as(m, "dgeMatrix")), identical(dimnames(M), dimnames(m))) m. <- matrix(c(0, 0, 2:0), 3, 5) dimnames(m.) <- list(LETTERS[1:3], letters[1:5]) (m0 <- m <- Matrix(m.)) m@Dimnames[[2]] <- m@Dimnames[[1]] ## not valid anymore: (val <- validObject(m, test=TRUE)); stopifnot(is.character(val)) dm <- as(m0, "denseMatrix") stopifnot(all.equal(rcond(dm), rcond(m.), tolerance = 1e-14), ##^^^^^^^ dm and m. are both dense, interestingly small differences ## show in at least one case of optimized BLAS all.equal(rcond(dm), 0.4899474520656), ## show() had revealed a bug in C: identical(capture.output(show(as(m0, "RsparseMatrix")))[-(1:2)], gsub("0", ".", capture.output(show(m.))[-1]))) rm(m) ###-- Sparse Triangular : g5 <- new("dgCMatrix", Dim = c(5L, 5L), x = c(10, 1, 3, 10, 1, 10, 1, 10, 10), i = c(0L,2L,4L, 1L, 3L,2L,4L, 3L, 4L), p = c(0L, 3L, 5L, 7:9)) t5 <- as(g5, "triangularMatrix") # fine stopifnot(class(t5) == "dtCMatrix", identical(t5, tril(g5))) ## This is really a regression test for 'methods::selectMethod()' ## Maybe move to R once 'Matrix' is recommended sm <- selectMethod(coerce, c("dgCMatrix", "triangularMatrix"), verbose=TRUE) stopifnot(identical(sm(g5), t5)) (t1 <- new("dtTMatrix", x= c(3,7), i= 0:1, j=3:2, Dim= as.integer(c(4,4)))) ## Diagonal o Sparse I4 <- Diagonal(4) D4 <- Diagonal(4, x=1:4) validObject(t2 <- t1 + I4) validObject(tt2 <- t(t1) + I4) validObject(t1c <- as(t1, "CsparseMatrix")) validObject(t2c <- as(t2, "CsparseMatrix")) stopifnot(validObject(t1), isValid(2 * I4, "diagonalMatrix"), isValid(D4 * 3, "diagonalMatrix"), isValid(I4 / 5, "diagonalMatrix"), isValid(D4 / 2, "diagonalMatrix"), identical(t1, t(t(t1))), identical(t1c, t(t(t1c))), isValid(t1c + I4,"triangularMatrix"), isValid(t2c + I4,"triangularMatrix"), c(class(t2), class(t1c), class(t2c), class(tt2)) == "dtCMatrix", identical(t(tt2), t2)) assert.EQ.mat(t1, as(t1c, "matrix")) D4. <- D4 * (A4 <- Matrix(1:4, 4,4)) D4p <- A4 + D4 Lg1 <- D4 > 0 & D4 > 1 nLg <- !Lg1 nnLg <- !nLg D4m <- D4 * 4:1 assert.EQ.mat(D4., diag(x= (1:4)^2)) assert.EQ.mat(D4p, diag(x= (1:4)) + (1:4)) assert.EQ.mat(D4m, diag(x=c(4,6,6,4))) assert.EQ.mat(Lg1, diag(x= c(FALSE, rep(TRUE,3)))) stopifnot(is(Lg1, "diagonalMatrix"), is(D4m, "diagonalMatrix"), is(D4., "diagonalMatrix"), is(nLg, "symmetricMatrix"), is(nnLg, "symmetricMatrix"), identical3(Lg1, Matrix(nnLg), as(nnLg, "diagonalMatrix")), all(Lg1 != (!Lg1))) ## as(, ) : str(cls <- names(getClass("Matrix")@subclasses))# all Matrix classes for(cl in cls) if(canCoerce(I4, cl)) { cat(cl,":") M <- as(I4, cl) M. <- as(D4, cl) stopifnot(diag(4) == as(M,"matrix"), if(is(cl,"dMatrix")) diag(x=1:4) == as(M.,"matrix") else TRUE) cat(" [Ok]\n") } s4 <- as(D4,"sparseMatrix") v <- c(11,2,2,12); s4[2:3,2:3] <- v; validObject(s4) s4. <- D4; s4.[2:3,2:3] <- v; validObject(s4.) stopifnot(all(s4 == s4.)) ## now assign symmetrically to symmetricMatrix s4 <- as(as(D4,"sparseMatrix"),"symmetricMatrix") s4[2:3,2:3] <- v validObject(s4) stopifnot(is(s4,"symmetricMatrix")) assert.EQ.mat(s4, as(s4.,"matrix"),tol=0) ## lower-triangular unit-diagonal L <- new("dtCMatrix", i = 1L, p = c(0:1, 1L), Dim = c(2L, 2L), x = 0.5, uplo = "L", diag = "U") stopifnot(range(L) == 0:1, all.equal(mean(L), 5/8)) ## from 0-diagonal to unit-diagonal triangular {low-level step}: tu <- t1 ; tu@diag <- "U" tu validObject(cu <- as(tu, "dtCMatrix")) validObject(cnu <- diagU2N(cu))# <- testing diagU2N validObject(tu. <- as(cu, "dtTMatrix")) validObject(tt <- as(cu, "TsparseMatrix")) stopifnot(## NOT: identical(tu, tu.), # since T* is not unique! identical(cu, as(tu., "dtCMatrix")), length(cnu@i) == length(cu@i) + nrow(cu), identical(cu, diagN2U(cnu)),# <- testing diagN2U all(cu >= 0, na.rm = TRUE), all(cu >= 0), any(cu >= 7)) validObject(tcu <- t(cu)) validObject(ttu <- t(tu)) validObject(ltu <- as(ttu, "lMatrix")) validObject(ldtu <- as(ltu, "denseMatrix")) validObject(Cltu <- as(ltu, "CsparseMatrix")) stopifnot(identical(asCsp(ttu > 0), asCsp(ltu)), all(ltu == as(ttu > 0,"denseMatrix"))) ltu - (ttu > 0) # failed assert.EQ.mat(cu, as(tu,"matrix"), tol=0) assert.EQ.mat(cnu, as(tu,"matrix"), tol=0) C <- suppressWarnings(Matrix(c(0,1,0,0), 5,5)) + Diagonal(5) (tU <- diagN2U(tril(C))) # dtC Unitriangular ntU <- as(tU, "nMatrix") nT <- as(ntU, "TsparseMatrix") R <- as(tU, "RsparseMatrix") Tt <- diagU2N(R) # used to accidentally drop the diag. stopifnot(R@x == c(1,1,1), diag(Tt) == 1) lcu <- new("ltCMatrix", Dim = c(4L, 4L), i = c(0:1, 0L), p = c(0L, 0:3), x = c(TRUE, FALSE, FALSE), uplo = "U", diag = "U") (lTu <- as(lcu,"TsparseMatrix"))# prints wrongly (in Matrix 0.999375-31) stopifnot(identical3(rowSums(lcu), rowSums(lTu), rowSums(drop0(lcu)))) (ncu <- as(lcu, "nMatrix"))# -- gives the "pattern" of lcu, i.e. FALSE are *there* ncn <- diagU2N(ncu) (cncn <- crossprod(ncn))# works -> "nsCMatrix" stopifnot(identical(ncu, as(lcu,"nsparseMatrix")), identical(rowSums(ncu), c(3:1, 1L)), Q.eq(ncn, ncu), Q.eq(crossprod(drop0(lcu)), crossprod(lcu)),# crossprod works -> "dsCMatrix" identical(crossprod(ncu), cncn), Q.eq(cncn, t(ncu) %*% ncu)) #used to seg.fault U <- new("dtCMatrix", Dim = c(6L, 6L), i = c(0:1, 0L, 2:3, 1L, 4L), p = c(0L,0L,0L, 2:3, 5L, 7L), x = rep.int(-0.5, 7), diag = "U") validObject(U) U. <- solve(iU <- solve(U))#-> gave segmentation fault stopifnot(validObject(U), ## had a case where solve(U) modified U ! validObject(iU), validObject(U.), ## no rounding error, since have iU@x * 8 is integer : identical(U, diagN2U(drop0(U.)))) ## o (of length > 1): stopifnot(isValid(tm <- tu * 1:8, "sparseMatrix"), identical4(tm, cu * 1:8, 1:8 * cu, 1:8 * tu)) cu[1,2] <- tu[1,2] <- NA mu <- as(tu,"matrix") stopifnot(isValid(cu, "CsparseMatrix"), isValid(cu, "triangularMatrix"), isValid(tu, "TsparseMatrix"), isValid(tu, "triangularMatrix"), identical(cu * 1:8, tu * 1:8), # but are no longer triangular identical(cu > .1, as(tu > .1, "CsparseMatrix")), all(cu >= 0, na.rm=TRUE), !all(cu >= 1), is.na(all(tu >= 0)), ## Csparse_drop: preserves triangularity incl diag="U" identical(cu, .Call(Matrix:::Csparse_drop, cu, 0.)) ) assert.EQ.mat(cu * 1:8, mu * 1:8) ina <- is.na(as(cu,"matrix")) ## These 3 were each different (2008-03) !! stopifnot(all(ina == is.na(cu)), all(ina == is.na(as(cu,"generalMatrix"))), all(ina == as(is.na(as(cu,"matrix")),"nMatrix"))) set.seed(7) xx <- rpois(10, 50) Samp <- function(n,size) sample(n, size, replace=TRUE) Tn <- sparseMatrix(i=Samp(8, 50), j=Samp(9,50), x=xx, giveCsparse=FALSE) Tn stopifnot(xx == Tn@x, max(xx) < max(Tn), 0 == min(Tn), (sT <- sum(Tn)) == sum(colSums(Tn)), sT == sum(Tn@x), range(Tn) == range(as(Tn, "CsparseMatrix"))) ## tu. is diag "U", but tu2 not: tu2 <- as(as(tu., "generalMatrix"), "triangularMatrix") assert.EQ.mat(cu, mu, tol=0) stopifnot(identical3(cu[cu > 1], tu [tu > 1], mu [mu > 1]), identical3(cu <= 1, tu <= 1, as(mu <= 1, "lMatrix")),# all lgeMatrix identical3(cu[cu <= 1], tu[tu <= 1], mu[mu <= 1]), identical3(cu , triu(cu ), t(t(cu))), identical3(tu , triu(tu ), t(t(tu))), identical3(tu., triu(tu.), t(t(tu.))), identical(tu2, triu(tu2)), identical(tcu , tril(tcu)), identical(ttu , tril(ttu)), identical(t(tu), tril(t(tu))) ) assert.EQ.mat(triu(cu), as.matrix(triu(as.matrix(cu)))) for(k in -1:1) assert.EQ.mat(tril(cu,k), as.matrix(tril(as.matrix(cu),k))) (dtr <- Matrix(local({m <- diag(2); m[1,2] <- 3;m}))) identical(dtr, triu(dtr)) assert.EQ.mat(tril(dtr), diag(2)) (t4 <- new("dgTMatrix", i = 3:0, j = 0:3, x = rep(1,4), Dim = as.integer(c(4,4)))) c4 <- as(t4, "CsparseMatrix") ## the same but "dsT" (symmetric) suppressWarnings(M <- Matrix(c(0, rep(c(0,0:1),4)), 4,4))# warning:.. length [13] is not ..multiple tt <- as(M, "TsparseMatrix") stopifnot(all.equal(triu(t4) + tril(t4), c4), all.equal(triu(tt) + tril(tt), c4)) ###-- Numeric Dense: Crossprod & Solve set.seed(123) mm. <- mm <- Matrix(rnorm(500 * 150), nc = 150) stopifnot(validObject(mm)) xpx <- crossprod(mm) stopifnot(identical(mm, mm.),# once upon a time, mm was altered by crossprod() isValid(xpx, "dpoMatrix")) str(mm) # 'dge*" str(xpx)# 'dpo*" xpy <- crossprod(mm, rnorm(500)) res <- solve(xpx, xpy) str(xpx)# now with Cholesky factor stopifnot(validObject(xpx), validObject(xpy), validObject(res)) stopifnot(all.equal(xpx %*% res, xpy, tolerance = 1e-12)) lp <- xpx >= 1 slp <- as(lp, "sparseMatrix") ltlp <- lp[ lower.tri(lp) ] sltlp <- slp[ lower.tri(slp) ] dim(ij <- which(lower.tri(lp), arr.ind = TRUE)) ss <- slp[ij] # now fast (!) stopifnot(identical4(lp[ij], ltlp, sltlp, as(lp, "matrix")[ij]), identical(ss, sltlp), isValid(lp, "lsyMatrix"), lp@uplo == "U") ###-- more solve() methods {was ./solve.R } ## first for "dgeMatrix" and all kinds of RHS : (m6 <- 1 + as(diag(0:5), "dgeMatrix")) rcond(m6) I6 <- as(diag(6), "dgeMatrix") stopifnot(all.equal(I6, m6 %*% solve(m6)), all.equal(I6, solve(m6) %*% m6) ) (i6 <- solve(m6, Matrix(1:6))) stopifnot(identical(i6, as(cbind(c(-4, rep(1,5))), "dgeMatrix")), identical(i6, solve(m6, 1:6)), identical(i6, solve(m6, matrix(1:6))), identical(i6, solve(m6, matrix(c(1,2,3,4,5,6)))) ) ## solve() (m <- t1+ t(t1) + Diagonal(4)) i.m <- solve(as.mat(m)) I1 <- m %*% i.m o4 <- diag(I1) im <- solve(m)# is now sparse {not yet} (I2 <- m %*% im) (ms <- as(m, "symmetricMatrix")) ## solve(, ): s.mm <- solve(m,m) s.mms <- solve(m, ms) ## these now work "fully-sparse" s.ms2 <- solve(ms, ms) s.msm <- solve(ms, m) I4c <- as(Matrix(diag(4),sparse=TRUE), "generalMatrix") stopifnot(isValid(im, "Matrix"), isValid(I2, "Matrix"), class(I4c) == "dgCMatrix", all.equal(I1, as(I2,"dgeMatrix"), tolerance = 1e-14), all.equal(diag(4), as.mat(I2), tolerance = 1e-12), all.equal(s.mm, I2, tolerance = 1e-14), all.equal(s.mms, I2, tolerance = 1e-14), all.equal(s.ms2, s.msm, tolerance = 4e-15), all.equal(s.ms2, I4c , tolerance = 4e-15), abs(o4 - 1) < 1e-14) image(T125 <- kronecker(kronecker(t5,t5),t5), main = paste("T125:",class(T125))) dim(T3k <- kronecker(t5,kronecker(T125, t5))) system.time(IT3 <- solve(T3k))# incredibly fast I. <- drop0(zapsmall(IT3 %*% T3k)) I.. <- diagN2U(I.) I <- Diagonal(5^5) stopifnot(isValid(IT3, "dtCMatrix"), ## something like the equivalent of all(I. == Diagonal(3125)) : identical(as(I., "diagonalMatrix"), I), identical(as(I..,"diagonalMatrix"), I) ) ###-- row- and column operations {was ./rowcolOps.R } set.seed(321) (m1 <- round(Matrix(rnorm(25), 5), 2)) m1k <- Matrix(round(rnorm(1000), 2), 50, 20) m.m <- as(m1k, "matrix") stopifnot(all.equal(colMeans(m1k), colMeans(m.m)), all.equal(colSums (m1k), colSums (m.m)), all.equal(rowMeans(m1k), rowMeans(m.m)), all.equal(rowSums (m1k), rowSums (m.m))) ###-- kronecker for nonsparse uses Matrix(.): stopifnot(isValid(kr <- kronecker(m1, m6), "Matrix")) assert.EQ.mat(kr, kronecker(as(m1, "matrix"), as(m6, "matrix")), tol = 0) ## sparse: (kt1 <- kronecker(t1, tu)) kt2 <- kronecker(t1c, cu) stopifnot(identical(Matrix:::uniq(kt1), Matrix:::uniq(kt2))) ## but kt1 and kt2, both "dgT" are different since entries are not ordered! ktf <- kronecker(as.matrix(t1), as.matrix(tu)) if(FALSE) # FIXME? our kronecker treats "0 * NA" as "0" for structural-0 assert.EQ.mat(kt2, ktf, tol= 0) (cs1 <- colSums(kt1)) NA.or.True <- function(x) is.na(x) | x eq <- (cs1 == colSums(as(kt1, "matrix"))) stopifnot(NA.or.True(eq), identical(is.na(eq), is.na(cs1))) nt1 <- as(kt1, "nMatrix") # no NA's anymore (ng1 <- as(as(nt1, "generalMatrix"),"CsparseMatrix")) # ngC dg1 <- as(ng1, "dMatrix")# dgC lt1 <- kt1 > 5 nt1 <- as(lt1, "nMatrix") (colSums(nt1, sparseResult = TRUE)) (colSums(kt1, sparseResult = TRUE)) # dsparse, with NA (colSums(lt1, sparseResult = TRUE)) # isparse, with NA (colSums(lt1, sparseResult = TRUE, na.rm = TRUE)) (colSums(nt1, sparseResult = TRUE)) # isparse, no NA ## check correct sparseness of both: for(M in list(kt1, nt1, ng1, dg1, lt1, nt1)) { m <- as(M, "matrix") for(na.rm in c(FALSE,TRUE)) { cs <- colSums(M, na.rm = na.rm) cs. <- colSums(M, na.rm = na.rm, sparseResult = TRUE) rs <- rowSums(M, na.rm = na.rm) rs. <- rowSums(M, na.rm = na.rm, sparseResult = TRUE) stopifnot(isValid(cs., "sparseVector"), identical(cs, as(cs., "vector")), isValid(rs., "sparseVector"), identical(rs, as(rs., "vector")), {eq <- cs == colSums(m, na.rm = na.rm) ; ineq <- is.na(eq) all(ineq | eq) && identical(ineq, is.na(cs)) }, {eq <- rs == rowSums(m, na.rm = na.rm) ; ineq <- is.na(eq) all(ineq | eq) && identical(ineq, is.na(rs)) } ) } } i1 <- cs. == 1 cs2 <- cs. cs2[i1] <- 0 # failed in *-31 !! ## now *index* with a NA-sparseVector : i2 <- i1 ; i2[3] <- NA ; li2 <- as.logical(i2) cs3 <- cs. ; cs3 [i2] <- 0 v3 <- as(cs.,"vector"); v3[li2] <- 0 cs4 <- cs. ; cs4[li2] <- 0 stopifnot(length(i1@x) == 2, identical(li2, as(i2,"vector")), identical(cs3, cs4), cs3 == v3, all(as(v3, "sparseVector") == cs3) ## indexing simple "numeric" with sparseVector: ## see 'R_FIXME' in ../R/sparseVector.R ## , identical(v3[i2], v3[li2]) ## TODO: ## sub-assigning into simple "numeric" with sparseVector index: ) M <- Matrix(c(2:0,1),2); M. <- as(M, "sparseMatrix") (N <- as(crossprod(kronecker(diag(2), M)) > 0, "nMatrix")) (L. <- as(N,"lMatrix")) stopifnot(identical(N, as(L.,"nMatrix")), identical(kronecker( c(1,0), M), kronecker(cbind(1:0), M))) assert.EQ.mat(kronecker(M, c(1,0,0)), kronecker(as.matrix(M), c(1,0,0))) ## coercion from "dpo" or "dsy" xx <- as(xpx, "dsyMatrix") stopifnot(isSymmetric(xxS <- as(xx, "sparseMatrix")), isSymmetric(xpxS <- as(xpx, "sparseMatrix"))) tm <- matrix(0, 8,8) tm[cbind(c(1,1,2,7,8), c(3,6,4,8,8))] <- c(2,-30,15,20,80) (tM <- Matrix(tm)) ## dtC (mM <- Matrix(m <- (tm + t(tm)))) ## dsC mT <- as(mM, "dsTMatrix") gC <- as(as(mT, "dgTMatrix"), "dgCMatrix") lT <- as(Matrix(TRUE, 2,2),"TsparseMatrix") ## Check that mT, lT, and gC print properly : pr.mT <- capture.output(mT) pr.lT <- capture.output(lT)[-(1:2)] nn <- unlist(strsplit(gsub(" +\\.", "", sub("^....", "", pr.mT[-(1:2)])), " ")) stopifnot(as.numeric(nn[nn != ""]) == m[m != 0], identical(1:2, grep("|", pr.lT, fixed=TRUE)), identical(pr.lT, capture.output(as(lT, "nMatrix"))[-(1:2)]), capture.output(gC)[-1] == pr.mT[-1]) assert.EQ.mat(tM, tm, tol=0) assert.EQ.mat(gC, m, tol=0) assert.EQ.mat(mT, m, tol=0) stopifnot(isValid(mM, "dsCMatrix"), isValid(tM, "dtCMatrix") , identical(mT, as(mM, "TsparseMatrix")) , identical(gC, as(mM, "generalMatrix")) ## coercions general <-> symmetric , identical(as(as(mM, "generalMatrix"), "symmetricMatrix"), mM) , identical(as(as(mM, "dgTMatrix"), "symmetricMatrix"), mT) , identical(as(as(tM, "generalMatrix"),"triangularMatrix"), tM) , identical(tM + Diagonal(8), tMD <- Diagonal(8) + tM) , isValid(tMD, "dtCMatrix") ) eM <- eigen(mM) # works thanks to base::as.matrix hack in ../R/zzz.R stopifnot(all.equal(eM$values, { v <- c(162.462112512353, 30.0665927567458) c(v, 15, 0, 0, 160-v[1], -15, -v[2])}, tol=1e-14)) ##--- symmetric -> pos.def. needs valid test: m5 <- Matrix(diag(5) - 1) assertError(as(m5, "dpoMatrix"))# not pos.definite! pm5 <- as(m5, "dspMatrix") # packed assertError(as(pm5, "dppMatrix"))# not pos.definite! sm <- as(Matrix(diag(5) + 1),"dspMatrix") pm <- as(sm,"dpoMatrix")## gave infinite recursion (for a day or so) pp <- as(pm,"dppMatrix") x <- round(100 * crossprod(Matrix(runif(25),5))) D <- Diagonal(5, round(1000*runif(5))) px <- pack(x) stopifnot(is(x, "dpoMatrix"), is(px,"dppMatrix"), is(D, "ddiMatrix")) class(x+D)#--> now "dsyMatrix" stopifnot(is(x+D, "symmetricMatrix"), is(D+px, "dspMatrix"), identical(x+D, D+x), identical(px+D, D+px), identical(pack(x-D), px-D)) tx <- tril(x) ptx <- pack(tx) stopifnot(is(tx, "dtrMatrix"), is(ptx, "dtpMatrix"), is(t(tx), "dtrMatrix"), is(t(ptx), "dtpMatrix"), is(D + tx, "dtrMatrix"), is(tx + D, "dtrMatrix"), is(ptx + D, "dtpMatrix"), is(D + ptx, "dtpMatrix")) ###-- dense nonzero pattern: class(m <- Matrix(TRUE,2,2)) # lsy isValid(n <- as(m, "nMatrix"), "nsyMatrix") ## 1) as(n,"CsparseMatrix") # used to give CHOLMOD error: invalid xtype... ls2 <- as(m, "CsparseMatrix") # works fine ## and really 'm' and 'n' are interally slot identical (!!!) as(n,"sparseMatrix") as(m,"sparseMatrix") ### -- now when starting with nsparse : nT <- new("ngTMatrix", i = as.integer(c(0, 1, 0)), j = as.integer(c(0, 0, 1)), Dim = as.integer(c(2,2))) (nC <- as(nT, "ngCMatrix")) str(nC)# of course, no 'x' slot tt <- as(nT,"denseMatrix") # nge (was lge "wrongly") stopifnot(is(tt,"ngeMatrix"), identical(as(tt, "lMatrix"), as(as(nT, "lMatrix"), "denseMatrix"))) tt as(nC,"denseMatrix") ###-- sparse nonzero pattern : ---------- (nkt <- as(as(as(kt1, "generalMatrix"), "CsparseMatrix"), "ngCMatrix"))# ok dkt <- as(nkt, "denseMatrix") (clt <- crossprod(nkt)) stopifnot(isValid(nkt, "ngCMatrix"), isValid(clt, "nsCMatrix")) suppressWarnings(crossprod(clt)) ## warning "crossprod() of symmetric ..." ## a Csparse with *repeated* entry is not valid! assertError(new("ngCMatrix", p = c(0L,2L), i = c(0L,0L), Dim = 2:1)) ### "d" <-> "l" for (symmetric) sparse : --------------------------------------- suppressWarnings( data(KNex) ) ## may warn, as 'Matrix' is recommended ## and exist more than once at check-time mm <- KNex$mm xpx <- crossprod(mm) ## extract nonzero pattern nxpx <- as(xpx, "nsCMatrix") show(nxpx) ## now ok, since subsetting works r <- nxpx[1:2,] lmm <- as(mm, "lgCMatrix") nmm <- as(lmm, "nMatrix") xlx <- crossprod(lmm) x.x <- crossprod(nmm) ## now A = lxpx and B = xlx should be close, but not quite the same ## since = 0 is well possible when x!=0 and y!=0 . ## However, A[i,j] != 0 ==> B[i,j] != 0: A <- as(as(nxpx, "lMatrix"), "TsparseMatrix") B <- as(as(xlx, "lMatrix"), "TsparseMatrix") ij <- function(a) a@i + ncol(a) * a@j stopifnot(all(ij(A) %in% ij(B))) l3 <- upper.tri(matrix(,3,3)) stopifnot(isValid(c3 <- as(l3, "CsparseMatrix"), "CsparseMatrix"),# lgC is(c3, "lMatrix")) (M <- Matrix(l3)) stopifnot(isValid(M, "ltCMatrix"), isValid(M2 <- M %x% M, "triangularMatrix"), # is "dtT" (why not "dtC" ?) dim(M2) == c(9,9), identical(M2, kronecker(M,M))) M3 <- M %x% M2 #ok (cM3 <- colSums(M3, sparse=TRUE)) identical(as.vector(cM3), as(rev(rowSums(M3, sparse=TRUE)), "vector")) M. <- M2 %x% M # gave infinite recursion ## diagonal, sparse & interactions stopifnot(isValid(as(Diagonal(3), "TsparseMatrix"), "TsparseMatrix"), isValid(X <- Diagonal(7) + 1.5 * tM[1:7,1:7], "sparseMatrix"), isValid(X, "triangularMatrix"), isValid(XX <- X - chol(crossprod(X)), "triangularMatrix")) X XX XX <- as(drop0(XX), "dsCMatrix") stopifnot(identical(XX, Matrix(0, nrow(X), ncol(X)))) M <- Matrix(m., sparse = FALSE) (sM <- Matrix(m.)) class(dlM <- M >= 1) stopifnot(identical(dlM, !(M < 1)), isValid(sM, "sparseMatrix"), isValid(dlM, "denseMatrix")) (lM <- as(dlM, "sparseMatrix")) lM2 <- as(dlM, "CsparseMatrix") #-> now ok lM0 <- Matrix:::as_Csparse(dlM) stopifnot(identical3(lM, lM2, lM0)) selectMethod("coerce", c("lgeMatrix", "CsparseMatrix"), useInherited = c(from = TRUE, to = FALSE)) ms0 <- Matrix(c(0,1,1,0), 2,2) ms <- as(ms0, "TsparseMatrix") cs <- as(ms, "CsparseMatrix") ll <- as(ms, "lMatrix") lt <- as(ll, "lgTMatrix") nn <- as(cs, "nsparseMatrix") l2 <- as(cs, "lsparseMatrix") nt <- triu(nn) n3 <- as(nt, "lsparseMatrix") da <- nt + t(nt) dm <- nt * t(nt) + da ## mnt <- as(nt, "matrix") m <- rbind(v <- 2:3) assert.EQ.mat(nt %*% v, mnt %*% v) assert.EQ.mat(v %*% nt, v %*% mnt) assert.EQ.mat( crossprod(nt, v), crossprod(mnt,v)) assert.EQ.mat( crossprod(v, nt), crossprod(v,mnt)) assert.EQ.mat(tcrossprod(v, nt), tcrossprod(v,mnt)) assert.EQ.mat(tcrossprod(nt, m), tcrossprod(mnt, m)) ## stopifnot(isValid(ms, "dsTMatrix"), as(ms0,"matrix") == as(ll, "matrix"), # coercing num |-> log as(lt, "matrix") == as(ll, "matrix"), identical(ms, as(ll, "dMatrix")), identical4(as(ll, "CsparseMatrix"), as(cs, "lMatrix"),# lsC* as(nn, "lsparseMatrix"), l2), identical3(da, dm, as(cs, "generalMatrix")), # dgC* identical(as(da, "lMatrix"), as(lt, "CsparseMatrix")) # lgC* ) ## Dense *packed* ones: s4 <- as(D4, "symmetricMatrix") sp <- as(as(as(D4, "symmetricMatrix"),"denseMatrix"),"dspMatrix") tp <- as(triu(sp),"dtpMatrix") tpL <- as(tril(sp),"dtpMatrix") (spL <- t(sp)) stopifnot(sp @uplo=="U", tp @uplo=="U", spL@uplo=="L", tpL@uplo=="L") ## band(): n <- 4 ; m <- 6 r1 <- Matrix(1:24, n,m) validObject(M1 <- band(r1, 0,0)) (M1 <- as(M1, "sparseMatrix")) r2 <- Matrix(1:18, 3, 6) stopifnot(identical(M1, bandSparse(n,m, k=0, diag = list(diag(r1)))), identical(band(r2, 0,4), band(r2, 0,3) + band(r2, 4,4))) s1 <- as(r1, "sparseMatrix") # such that band(s1) is sparse, too for(k1 in (-n):m) for(k2 in k1:m) { isValid(br1 <- band(r1, k1,k2), "ddenseMatrix") isValid(bs1 <- band(s1, k1,k2), "CsparseMatrix") stopifnot(all(r1 == s1)) } D. <- Diagonal(x= c(-2,3:4)); D.[lower.tri(D.)] <- 1:3 ; D. D0 <- Diagonal(x= 0:3); D0[upper.tri(D0)] <- 1:6 ; D0 stopifnot(all.equal(list(modulus = structure(24, logarithm = FALSE), sign = -1L), unclass(determinant(D.,FALSE)), tol=1e-15), det(Matrix(0,1)) == 0, all.equal(list(modulus = structure(0, logarithm = FALSE), sign = 1L), unclass(determinant(D0,FALSE)), tol=0) ) ### More sparseVector checks: ------------------------------- validObject(new("isparseVector")) R <- sv <- as(D4, "sparseVector") ## dim() <- (n1,n2) --> sparse Matrix : dim(R) <- dim(D4) stopifnot(isValid(sv,"sparseVector"), isValid(R, "sparseMatrix"), identical(D4, as(R, "diagonalMatrix"))) iv <- c(rep(0, 5), 3, 0,0,7,0,0,0) sv <- as(iv, "sparseVector") sv. <- as(as.integer(iv), "sparseVector") ## Note: Method with signature "numeric#sparseVector" chosen ... (sv2 <- as(sv, "isparseVector")) ## gave error as(sv, "zsparseVector") stopifnot(identical(sv., sv2), identical( Matrix(sv, 3,4, byrow=TRUE), t(Matrix(sv, 4,3)))) options(warn = 0)# no longer error ## "Large" sparse: n <- 100000 m <- 50000 ; nnz <- 47 M <- spMatrix(n, m, i = sample(n, nnz, replace = TRUE), j = sample(m, nnz, replace = TRUE), x = round(rnorm(nnz),1)) validObject(Mv <- as(M, "sparseVector")) validObject(Dv <- as(Diagonal(60000), "sparseVector")) validObject(LD <- Diagonal(60000, TRUE)) validObject(Lv <- as(LD, "sparseVector")) Dm <- Dv; dim(Dm) <- c(180000L, 20000L) stopifnot(!doExtras || isValid(Md <- M * rowSums(M, sparseResult=TRUE), "sparseMatrix"), LD@diag == "U", isValid(Dm, "sparseMatrix"), identical(Dv, as(Dm, "sparseVector"))) p. <- new("dtCMatrix", i = c(2:3, 2L), p = c(0L, 2:3, 3L, 3L), Dim = c(4L, 4L), x = rep(-0.5, 3), uplo = "L", diag = "U") assert.EQ.mat(solve(solve(p.)), as(p., "matrix")) dimnames(p.)[[1]] <- paste(1:4) ii <- is.na(p.) stopifnot(all(!ii), !any(as(ii, "denseMatrix")))# used to fail lst <- ls() table(istri <- sapply(lst, function(.) is(get(.),"triangularMatrix"))) table(triC <- sapply(lst[istri], function(.) class(get(.)))) table(uniC <- sapply(lst[istri], function(.) get(.)@diag == "U")) lsUtr <- lst[istri][uniC] (di <- sapply(lsUtr, function(.) dim(get(.)))) ## TODO: use %*%, crossprod(), .. on all those 4 x 4 -- and check "triangular rules" cat('Time elapsed: ', (.pt <- proc.time()),'\n') # "stats" ## cat("doExtras:",doExtras,"\n") if(doExtras) { cat("checkMatrix() of all: \n---------\n") Sys.setlocale("LC_COLLATE", "C") # to keep ls() reproducible for(nm in ls()) if(is(.m <- get(nm), "Matrix")) { cat("\n", rep("-",nchar(nm)),"\n",nm, ":\n", sep='') checkMatrix(.m) } cat('Time elapsed: ', proc.time() - .pt,'\n') # "stats" } if(!interactive()) warnings() ## Platform - and other such info -- so we find it in old saved outputs .libPaths() SysI <- Sys.info() structure(Sys.info()[c(4,5,1:3)], class="simple.list") sessionInfo() c(Matrix = packageDescription("Matrix")$Built) if(SysI[["sysname"]] == "Linux" && require("sfsmisc")) local({ nn <- names(.Sc <- sfsmisc::Sys.cpuinfo()) nn <- names(.Sc <- .Sc[nn != "flags"]) print(.Sc[grep("\\.[0-9]$", nn, invert=TRUE)]) }) Matrix/tests/bind.Rout.save0000644000175100001440000002656011723000662015430 0ustar hornikusers R Under development (unstable) (2012-02-27 r58508) Copyright (C) 2012 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: x86_64-unknown-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. 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Type 'q()' to quit R. > #### Testing cBind() & rBind() > > library(Matrix) Loading required package: lattice > > source(system.file("test-tools.R", package = "Matrix"))# identical3() etc > > ### --- Dense Matrices --- > > m1 <- m2 <- m <- Matrix(1:12, 3,4) > dimnames(m2) <- list(LETTERS[1:3], + letters[1:4]) > dimnames(m1) <- list(NULL,letters[1:4]) > > stopifnot(identical(cBind ( m, 10*m) -> R, + cbind2( m, 10*m))); R 3 x 8 Matrix of class "dgeMatrix" [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 1 4 7 10 10 40 70 100 [2,] 2 5 8 11 20 50 80 110 [3,] 3 6 9 12 30 60 90 120 > stopifnot(identical(cBind (m1,100+m1) -> R, + cbind2(m1,100+m1))); R 3 x 8 Matrix of class "dgeMatrix" a b c d a b c d [1,] 1 4 7 10 101 104 107 110 [2,] 2 5 8 11 102 105 108 111 [3,] 3 6 9 12 103 106 109 112 > stopifnot(identical(cBind (m1, 10*m2) -> R, + cbind2(m1, 10*m2))); R 3 x 8 Matrix of class "dgeMatrix" a b c d a b c d A 1 4 7 10 10 40 70 100 B 2 5 8 11 20 50 80 110 C 3 6 9 12 30 60 90 120 > stopifnot(identical(cBind (m2, m1+m2) -> R, + cbind2(m2, m1+m2))); R 3 x 8 Matrix of class "dgeMatrix" a b c d a b c d A 1 4 7 10 2 8 14 20 B 2 5 8 11 4 10 16 22 C 3 6 9 12 6 12 18 24 > > cBind(m1, MM = -1) 3 x 5 Matrix of class "dgeMatrix" a b c d MM [1,] 1 4 7 10 -1 [2,] 2 5 8 11 -1 [3,] 3 6 9 12 -1 > rBind(R1 = 10:11, m1) 4 x 4 Matrix of class "dgeMatrix" a b c d R1 10 11 10 11 1 4 7 10 2 5 8 11 3 6 9 12 > cBind(0, Matrix(0+0:1, 1,2), 3:2)# FIXME? should warn - as with matrix() 1 x 4 Matrix of class "dgeMatrix" [,1] [,2] [,3] [,4] [1,] 0 0 1 3 > > as(rBind(0, Matrix(0+0:1, 1,2), 3:2), + "sparseMatrix") 3 x 2 sparse Matrix of class "dgCMatrix" [1,] . . [2,] . 1 [3,] 3 2 > cBind(m2, 10*m2[nrow(m2):1 ,])# keeps the rownames from the first 3 x 8 Matrix of class "dgeMatrix" a b c d a b c d A 1 4 7 10 30 60 90 120 B 2 5 8 11 20 50 80 110 C 3 6 9 12 10 40 70 100 > > (im <- cBind(I = 100, m)) 3 x 5 Matrix of class "dgeMatrix" I [1,] 100 1 4 7 10 [2,] 100 2 5 8 11 [3,] 100 3 6 9 12 > str(im) Formal class 'dgeMatrix' [package "Matrix"] with 4 slots ..@ x : num [1:15] 100 100 100 1 2 3 4 5 6 7 ... ..@ Dim : int [1:2] 3 5 ..@ Dimnames:List of 2 .. ..$ : NULL .. ..$ : chr [1:5] "I" "" "" "" ... ..@ factors : list() > (mi <- cBind(m2, I = 1000)) 3 x 5 Matrix of class "dgeMatrix" a b c d I A 1 4 7 10 1000 B 2 5 8 11 1000 C 3 6 9 12 1000 > str(mi) Formal class 'dgeMatrix' [package "Matrix"] with 4 slots ..@ x : num [1:15] 1 2 3 4 5 6 7 8 9 10 ... ..@ Dim : int [1:2] 3 5 ..@ Dimnames:List of 2 .. ..$ : chr [1:3] "A" "B" "C" .. ..$ : chr [1:5] "a" "b" "c" "d" ... ..@ factors : list() > (m1m <- cBind(m,I=100,m2)) 3 x 9 Matrix of class "dgeMatrix" I a b c d A 1 4 7 10 100 1 4 7 10 B 2 5 8 11 100 2 5 8 11 C 3 6 9 12 100 3 6 9 12 > showProc.time() Time elapsed: 0.176 0.012 0.189 > > ### --- Diagonal / Sparse - had bugs > > D4 <- Diagonal(4) > (D4T <- as(D4, "TsparseMatrix")) 4 x 4 sparse Matrix of class "dtTMatrix" (unitriangular) [1,] 1 . . . [2,] . 1 . . [3,] . . 1 . [4,] . . . 1 > D4C <- as(D4T, "CsparseMatrix") > c1 <- Matrix(0+0:3, 4, sparse=TRUE) ; r1 <- t(c1); r1 1 x 4 sparse Matrix of class "dgCMatrix" [1,] . 1 2 3 > > d4 <- rBind(Diagonal(4), 0:3) > m4 <- cBind(Diagonal(x=-1:2), 0:3) > c4. <- cBind(Diagonal(4), c1) > c.4 <- cBind(c1, Diagonal(4)) > r4. <- rBind(Diagonal(4), r1) > r.4 <- rBind(r1, Diagonal(4)) > assert.EQ.mat(d4, rBind(diag(4), 0:3)) > assert.EQ.mat(m4, cBind(diag(-1:2), 0:3)) > stopifnot(identical(Matrix(cbind(diag(3),0)), cbind2(Diagonal(3),0)), + is(d4, "sparseMatrix"), is(m4, "sparseMatrix"), + identical(t(d4), cBind(Diagonal(4), 0:3)), + identical(t(m4), rBind(Diagonal(x=-1:2), 0:3))) > showProc.time() Time elapsed: 0.076 0 0.076 > > ### --- Sparse Matrices --- > > identical4(cBind(diag(4), diag(4)), + cBind(D4C, D4C), + cBind(D4T, D4C), + cBind(D4C, D4T)) [1] FALSE > nr <- 4 > m. <- matrix(c(0, 2:-1), nr ,6) Warning message: In matrix(c(0, 2:-1), nr, 6) : data length [5] is not a sub-multiple or multiple of the number of rows [4] > M <- Matrix(m.) > (mC <- as(M, "dgCMatrix")) 4 x 6 sparse Matrix of class "dgCMatrix" [1,] . -1 . 1 2 . [2,] 2 . -1 . 1 2 [3,] 1 2 . -1 . 1 [4,] . 1 2 . -1 . > (mT <- as(M, "dgTMatrix")) 4 x 6 sparse Matrix of class "dgTMatrix" [1,] . -1 . 1 2 . [2,] 2 . -1 . 1 2 [3,] 1 2 . -1 . 1 [4,] . 1 2 . -1 . > stopifnot(identical(mT, as(mC, "dgTMatrix")), + identical(mC, as(mT, "dgCMatrix"))) > > for(v in list(0, 2, 1:0)) + for(fnam in c("cBind", "rBind")) { + cat(fnam,"(m, v=", deparse(v),"), class(m) :") + FUN <- get(fnam) + for(m in list(M, mC, mT)) { + cat("", class(m),"") + assert.EQ.mat(FUN(v, m), FUN(v, m.)) ; cat(",") + assert.EQ.mat(FUN(m, v), FUN(m., v)) ; cat(".") + } + cat("\n") + } cBind (m, v= 0 ), class(m) : dgeMatrix ,. dgCMatrix ,. dgTMatrix ,. rBind (m, v= 0 ), class(m) : dgeMatrix ,. dgCMatrix ,. dgTMatrix ,. cBind (m, v= 2 ), class(m) : dgeMatrix ,. dgCMatrix ,. dgTMatrix ,. rBind (m, v= 2 ), class(m) : dgeMatrix ,. dgCMatrix ,. dgTMatrix ,. cBind (m, v= c(1L, 0L) ), class(m) : dgeMatrix ,. dgCMatrix ,. dgTMatrix ,. rBind (m, v= c(1L, 0L) ), class(m) : dgeMatrix ,. dgCMatrix ,. dgTMatrix ,. > showProc.time() Time elapsed: 0.248 0 0.249 > > cBind(0, mC); cBind(mC, 0) 4 x 7 sparse Matrix of class "dgCMatrix" [1,] . . -1 . 1 2 . [2,] . 2 . -1 . 1 2 [3,] . 1 2 . -1 . 1 [4,] . . 1 2 . -1 . 4 x 7 sparse Matrix of class "dgCMatrix" [1,] . -1 . 1 2 . . [2,] 2 . -1 . 1 2 . [3,] 1 2 . -1 . 1 . [4,] . 1 2 . -1 . . > cBind(0, mT); cBind(mT, 2) 4 x 7 sparse Matrix of class "dgCMatrix" [1,] . . -1 . 1 2 . [2,] . 2 . -1 . 1 2 [3,] . 1 2 . -1 . 1 [4,] . . 1 2 . -1 . 4 x 7 sparse Matrix of class "dgCMatrix" [1,] . -1 . 1 2 . 2 [2,] 2 . -1 . 1 2 2 [3,] 1 2 . -1 . 1 2 [4,] . 1 2 . -1 . 2 > cBind(diag(nr), mT) 4 x 10 sparse Matrix of class "dgCMatrix" [1,] 1 . . . . -1 . 1 2 . [2,] . 1 . . 2 . -1 . 1 2 [3,] . . 1 . 1 2 . -1 . 1 [4,] . . . 1 . 1 2 . -1 . > stopifnot(identical(t(cBind(diag(nr), mT)), + rBind(diag(nr), t(mT)))) > (cc <- cBind(mC, 0,7,0, diag(nr), 0)) 4 x 14 sparse Matrix of class "dgCMatrix" [1,] . -1 . 1 2 . . 7 . 1 . . . . [2,] 2 . -1 . 1 2 . 7 . . 1 . . . [3,] 1 2 . -1 . 1 . 7 . . . 1 . . [4,] . 1 2 . -1 . . 7 . . . . 1 . > stopifnot(identical3(cc, cBind(mT, 0,7,0, diag(nr), 0), + as( cBind( M, 0,7,0, diag(nr), 0), "dgCMatrix"))) > > cBind(mC, 1, 100*mC, 0, 0:2) 4 x 15 sparse Matrix of class "dgCMatrix" [1,] . -1 . 1 2 . 1 . -100 . 100 200 . . . [2,] 2 . -1 . 1 2 1 200 . -100 . 100 200 . 1 [3,] 1 2 . -1 . 1 1 100 200 . -100 . 100 . 2 [4,] . 1 2 . -1 . 1 . 100 200 . -100 . . . > cBind(mT, 1, 0, mT+10*mT, 0, 0:2) 4 x 16 sparse Matrix of class "dgCMatrix" [1,] . -1 . 1 2 . 1 . . -11 . 11 22 . . . [2,] 2 . -1 . 1 2 1 . 22 . -11 . 11 22 . 1 [3,] 1 2 . -1 . 1 1 . 11 22 . -11 . 11 . 2 [4,] . 1 2 . -1 . 1 . . 11 22 . -11 . . . > > ## logical (sparse) - should remain logical : > L5 <- Diagonal(n = 5, x = TRUE); v5 <- rep(x = c(FALSE,TRUE), length = ncol(L5)) > stopifnot(is(show(rBind(L5,v5)), "lsparseMatrix"), + is(show(cBind(v5,L5)), "lsparseMatrix"), + is(rBind(L5, 2* v5), "dsparseMatrix"), + is(cBind(2* v5, L5), "dsparseMatrix")) 6 x 5 sparse Matrix of class "lgCMatrix" | . . . . . | . . . . . | . . . . . | . . . . . | v5 . | . | . 5 x 6 sparse Matrix of class "lgCMatrix" v5 [1,] . | . . . . [2,] | . | . . . [3,] . . . | . . [4,] | . . . | . [5,] . . . . . | > > ## print() / show() of non-structural zeros: > (m <- Matrix(c(0, 0, 2:0), 3, 5)) 3 x 5 sparse Matrix of class "dgCMatrix" [1,] . 1 . . 2 [2,] . . 2 . 1 [3,] 2 . 1 . . > (m2 <- cBind(m,m)) 3 x 10 sparse Matrix of class "dgCMatrix" [1,] . 1 . . 2 . 1 . . 2 [2,] . . 2 . 1 . . 2 . 1 [3,] 2 . 1 . . 2 . 1 . . > (m4 <- rBind(m2,m2)) 6 x 10 sparse Matrix of class "dgCMatrix" [1,] . 1 . . 2 . 1 . . 2 [2,] . . 2 . 1 . . 2 . 1 [3,] 2 . 1 . . 2 . 1 . . [4,] . 1 . . 2 . 1 . . 2 [5,] . . 2 . 1 . . 2 . 1 [6,] 2 . 1 . . 2 . 1 . . > diag(m4) [1] 0 0 1 0 1 2 > for(i in 1:6) { + m4[i, i ] <- i + m4[i,i+1] <- 0 + } > m4 ## now show some non-structural zeros: 6 x 10 sparse Matrix of class "dgCMatrix" [1,] 1 . . . 2 . 1 . . 2 [2,] . 2 . . 1 . . 2 . 1 [3,] 2 . 3 . . 2 . 1 . . [4,] . 1 . 4 . . 1 . . 2 [5,] . . 2 . 5 . . 2 . 1 [6,] 2 . 1 . . 6 . 1 . . > > ## Mixture of dense and sparse/diagonal -- used to fail, even in 1.0-0 > D5 <- Diagonal(x = 10*(1:5)) > (D5.1 <- cbind2(D5, 1)) 5 x 6 sparse Matrix of class "dgCMatrix" [1,] 10 . . . . 1 [2,] . 20 . . . 1 [3,] . . 30 . . 1 [4,] . . . 40 . 1 [5,] . . . . 50 1 > ## "FIXME" in newer versions of R, do not need Matrix() here: > s42 <- Matrix(z42 <- cbind2(rep(0:1,4), rep(1:0,4)), + sparse=TRUE) > (C86 <- rBind(1, 0, D5.1, 0)) 8 x 6 sparse Matrix of class "dgCMatrix" [1,] 1 1 1 1 1 1 [2,] . . . . . . [3,] 10 . . . . 1 [4,] . 20 . . . 1 [5,] . . 30 . . 1 [6,] . . . 40 . 1 [7,] . . . . 50 1 [8,] . . . . . . > stopifnot(TRUE + ,isValid(D5.1, "dgCMatrix") + ,isValid(print(rbind2(Matrix(1:10, 2,5), D5)), "dgCMatrix") + ,isValid(print(cbind2(Matrix(10:1, 5,2), D5.1)), "dgeMatrix") + ,isValid(zz <- cbind2(z42, C86), "dgCMatrix") + ,identical(zz, cbind2(s42, C86)) + ) 7 x 5 sparse Matrix of class "dgCMatrix" [1,] 1 3 5 7 9 [2,] 2 4 6 8 10 [3,] 10 . . . . [4,] . 20 . . . [5,] . . 30 . . [6,] . . . 40 . [7,] . . . . 50 5 x 8 Matrix of class "dgeMatrix" [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 10 5 10 0 0 0 0 1 [2,] 9 4 0 20 0 0 0 1 [3,] 8 3 0 0 30 0 0 1 [4,] 7 2 0 0 0 40 0 1 [5,] 6 1 0 0 0 0 50 1 > > showProc.time() Time elapsed: 0.208 0.004 0.213 > > proc.time() user system elapsed 2.716 0.060 2.779 Matrix/tests/abIndex-tsts.R0000644000175100001440000001036612271746775015416 0ustar hornikusers#### Testing consistency of "abIndex" == "abstract-indexing vectors" class : library(Matrix) source(system.file("test-tools.R", package = "Matrix"))# identical3() etc validObject(ab <- new("abIndex")) str(ab) set.seed(1) ex. <- list(2:1000, 0:10, sample(100), c(-3:40, 20:70), c(1:100,77L, 50:40, 10L), c(17L, 3L*(12:3))) ## we know which kinds will come out: "compressed" for all but random: rD <- "rleDiff"; kinds <- c(rD,rD,"int32", rD, rD, rD) isCmpr <- kinds == rD ab. <- lapply(ex., as, Class = "abIndex") nu. <- lapply(ab., as, Class = "numeric") in. <- lapply(ab., as, Class = "integer") rles <- lapply(ab.[isCmpr], function(u) u@rleD@rle) r.x <- lapply(ex.[isCmpr], function(.) rle(diff(.))) stopifnot(sapply(ab., validObject), identical(ex., nu.), identical(ex., in.), ## Check that the relevant cases really *are* "compressed": sapply(ab., slot, "kind") == kinds, ## Using rle(diff(.)) is equivalent to using our C code: identical(rles, r.x), ## Checking Group Methods - "Summary" : sapply(ab., range) == sapply(ex., range), sapply(ab., any) == sapply(ex., any), TRUE) ## testing c() method, i.e. currently c.abIndex(): tst.c.abI <- function(lii) { stopifnot(is.list(lii), all(unlist(lapply(lii, mode)) == "numeric")) aii <- lapply(lii, as, "abIndex") v.i <- do.call(c, lii) a.i <- do.call(c, aii) avi <- as(v.i, "abIndex") ## identical() is too hard, as values & lengths can be double/integer stopifnot(all.equal(a.i, avi, tolerance = 0)) } tst.c.abI(list(2:6, 70:50, 5:-2)) ## now an example where *all* are uncompressed: tst.c.abI(list(c(5, 3, 2, 4, 7, 1, 6), 3:4, 1:-1)) ## and one with parts that are already non-trivial: exc <- ex.[isCmpr] tst.c.abI(exc) set.seed(101) N <- length(exc) # 5 for(i in 1:10) { tst.c.abI(exc[sample(N, replace=TRUE)]) tst.c.abI(exc[sample(N, N-1)]) tst.c.abI(exc[sample(N, N-2)]) } for(n in 1:120) { cat(".") k <- 1 + 4*rpois(1, 5) # >= 1 ## "random" rle -- NB: consecutive values *must* differ (for uniqueness) v <- as.integer(1+ 10*rnorm(k)) while(any(dv <- duplicated(v))) v[dv] <- v[dv] + 1L rl <- structure(list(lengths = as.integer(1 + rpois(k, 10)), values = v), class = "rle") ai <- new("abIndex", kind = "rleDiff", rleD = new("rleDiff", first = rpois(1, 20), rle = rl)) validObject(ai) ii <- as(ai, "numeric") iN <- ii; iN[180] <- NA; aiN <- as(iN,"abIndex") iN <- as(aiN, "numeric") ## NA from 180 on stopifnot(is.numeric(ii), ii == round(ii), identical(ai, as(ii, "abIndex")), identical(is.na(ai), is.na(ii)), identical(is.na(aiN), is.na(iN)), identical(is.finite (aiN), is.finite(iN)), identical(is.infinite(aiN), is.infinite(iN)) ) if(n %% 40 == 0) cat(n,"\n") } ## we have : identical(lapply(ex., as, "abIndex"), ab.) mkStr <- function(ch, n) paste(rep.int(ch, n), collapse="") ##O for(grMeth in getGroupMembers("Ops")) { ##O cat(sprintf("\n%s :\n%s\n", grMeth, mkStr("=", nchar(grMeth)))) grMeth <- "Arith" for(ng in getGroupMembers(grMeth)) { cat(ng, ": ") G <- get(ng) t.tol <- if(ng == "/") 1e-12 else 0 ## "/" with no long double (e.g. on Sparc Solaris): 1.125e-14 AEq <- function(a,b, ...) assert.EQ(a, b, tol=t.tol, giveRE=TRUE) for(v in ex.) { va <- as(v, "abIndex") for(s in list(-1, 17L, TRUE, FALSE)) # numeric *and* logical if(!((identical(s, FALSE) && ng == "/"))) { ## division by 0 may "fail" AEq(as(G(v, s), "abIndex"), G(va, s)) AEq(as(G(s, v), "abIndex"), G(s, va)) } cat(".") } cat(" [Ok]\n") } ##O } ## check the abIndex versions of indDiag() and indTri() : for(n in 1:7) stopifnot(isValid(ii <- Matrix:::abIindDiag(n), "abIndex"), ii@kind == "rleDiff", Matrix:::indDiag(n) == as(ii, "numeric")) for(n in 0:7) for(diag in c(TRUE,FALSE)) for(upper in c(TRUE,FALSE)) stopifnot(isValid(ii <- Matrix:::abIindTri(n, diag=diag,upper=upper), "abIndex"), Matrix:::indTri(n, diag=diag,upper=upper) == as(ii, "numeric")) cat('Time elapsed: ', (.pt <- proc.time()),'\n') # "stats" Matrix/tests/bind.R0000644000175100001440000000754311644127607013756 0ustar hornikusers#### Testing cBind() & rBind() library(Matrix) source(system.file("test-tools.R", package = "Matrix"))# identical3() etc ### --- Dense Matrices --- m1 <- m2 <- m <- Matrix(1:12, 3,4) dimnames(m2) <- list(LETTERS[1:3], letters[1:4]) dimnames(m1) <- list(NULL,letters[1:4]) stopifnot(identical(cBind ( m, 10*m) -> R, cbind2( m, 10*m))); R stopifnot(identical(cBind (m1,100+m1) -> R, cbind2(m1,100+m1))); R stopifnot(identical(cBind (m1, 10*m2) -> R, cbind2(m1, 10*m2))); R stopifnot(identical(cBind (m2, m1+m2) -> R, cbind2(m2, m1+m2))); R cBind(m1, MM = -1) rBind(R1 = 10:11, m1) cBind(0, Matrix(0+0:1, 1,2), 3:2)# FIXME? should warn - as with matrix() as(rBind(0, Matrix(0+0:1, 1,2), 3:2), "sparseMatrix") cBind(m2, 10*m2[nrow(m2):1 ,])# keeps the rownames from the first (im <- cBind(I = 100, m)) str(im) (mi <- cBind(m2, I = 1000)) str(mi) (m1m <- cBind(m,I=100,m2)) showProc.time() ### --- Diagonal / Sparse - had bugs D4 <- Diagonal(4) (D4T <- as(D4, "TsparseMatrix")) D4C <- as(D4T, "CsparseMatrix") c1 <- Matrix(0+0:3, 4, sparse=TRUE) ; r1 <- t(c1); r1 d4 <- rBind(Diagonal(4), 0:3) m4 <- cBind(Diagonal(x=-1:2), 0:3) c4. <- cBind(Diagonal(4), c1) c.4 <- cBind(c1, Diagonal(4)) r4. <- rBind(Diagonal(4), r1) r.4 <- rBind(r1, Diagonal(4)) assert.EQ.mat(d4, rBind(diag(4), 0:3)) assert.EQ.mat(m4, cBind(diag(-1:2), 0:3)) stopifnot(identical(Matrix(cbind(diag(3),0)), cbind2(Diagonal(3),0)), is(d4, "sparseMatrix"), is(m4, "sparseMatrix"), identical(t(d4), cBind(Diagonal(4), 0:3)), identical(t(m4), rBind(Diagonal(x=-1:2), 0:3))) showProc.time() ### --- Sparse Matrices --- identical4(cBind(diag(4), diag(4)), cBind(D4C, D4C), cBind(D4T, D4C), cBind(D4C, D4T)) nr <- 4 m. <- matrix(c(0, 2:-1), nr ,6) M <- Matrix(m.) (mC <- as(M, "dgCMatrix")) (mT <- as(M, "dgTMatrix")) stopifnot(identical(mT, as(mC, "dgTMatrix")), identical(mC, as(mT, "dgCMatrix"))) for(v in list(0, 2, 1:0)) for(fnam in c("cBind", "rBind")) { cat(fnam,"(m, v=", deparse(v),"), class(m) :") FUN <- get(fnam) for(m in list(M, mC, mT)) { cat("", class(m),"") assert.EQ.mat(FUN(v, m), FUN(v, m.)) ; cat(",") assert.EQ.mat(FUN(m, v), FUN(m., v)) ; cat(".") } cat("\n") } showProc.time() cBind(0, mC); cBind(mC, 0) cBind(0, mT); cBind(mT, 2) cBind(diag(nr), mT) stopifnot(identical(t(cBind(diag(nr), mT)), rBind(diag(nr), t(mT)))) (cc <- cBind(mC, 0,7,0, diag(nr), 0)) stopifnot(identical3(cc, cBind(mT, 0,7,0, diag(nr), 0), as( cBind( M, 0,7,0, diag(nr), 0), "dgCMatrix"))) cBind(mC, 1, 100*mC, 0, 0:2) cBind(mT, 1, 0, mT+10*mT, 0, 0:2) ## logical (sparse) - should remain logical : L5 <- Diagonal(n = 5, x = TRUE); v5 <- rep(x = c(FALSE,TRUE), length = ncol(L5)) stopifnot(is(show(rBind(L5,v5)), "lsparseMatrix"), is(show(cBind(v5,L5)), "lsparseMatrix"), is(rBind(L5, 2* v5), "dsparseMatrix"), is(cBind(2* v5, L5), "dsparseMatrix")) ## print() / show() of non-structural zeros: (m <- Matrix(c(0, 0, 2:0), 3, 5)) (m2 <- cBind(m,m)) (m4 <- rBind(m2,m2)) diag(m4) for(i in 1:6) { m4[i, i ] <- i m4[i,i+1] <- 0 } m4 ## now show some non-structural zeros: ## Mixture of dense and sparse/diagonal -- used to fail, even in 1.0-0 D5 <- Diagonal(x = 10*(1:5)) (D5.1 <- cbind2(D5, 1)) ## "FIXME" in newer versions of R, do not need Matrix() here: s42 <- Matrix(z42 <- cbind2(rep(0:1,4), rep(1:0,4)), sparse=TRUE) (C86 <- rBind(1, 0, D5.1, 0)) stopifnot(TRUE ,isValid(D5.1, "dgCMatrix") ,isValid(print(rbind2(Matrix(1:10, 2,5), D5)), "dgCMatrix") ,isValid(print(cbind2(Matrix(10:1, 5,2), D5.1)), "dgeMatrix") ,isValid(zz <- cbind2(z42, C86), "dgCMatrix") ,identical(zz, cbind2(s42, C86)) ) showProc.time() Matrix/tests/validObj.R0000644000175100001440000001515012211567675014571 0ustar hornikuserslibrary(Matrix) ### Do all kinds of object creation and coercion source(system.file("test-tools.R", package = "Matrix")) ## the empty ones: checkMatrix(new("dgeMatrix")) checkMatrix(Matrix(,0,0)) ## "dge" assertError( new("dgeMatrix", Dim = c(2,2), x= 1:4) )# double 'Dim' assertError( new("dgeMatrix", Dim = as.integer(c(2,2)), x= 1:4) )# int 'x' assertError( new("dgeMatrix", Dim = 2:2, x=as.double(1:4)) )# length(Dim) !=2 assertError( new("dgeMatrix", Dim = as.integer(c(2,2)), x= as.double(1:5))) checkMatrix(m1 <- Matrix(1:6, ncol=2)) checkMatrix(m2 <- Matrix(1:7 +0, ncol=3)) # a (desired) warning stopifnot(all(match(is(m1), c("dgeMatrix", "ddenseMatrix", "generalMatrix", "dMatrix", "denseMatrix", "compMatrix", "Matrix", "xMatrix", "mMatrix"), 0) > 0), dim(t(m1)) == 2:3, identical(m1, t(t(m1)))) c.nam <- paste("C",1:2, sep='') dimnames(m1) <- list(NULL, c.nam) checkMatrix(m1) # failed in 0.999375-10 checkMatrix(tm1 <- t(m1)) stopifnot(colnames(m1) == c.nam, identical(dimnames(tm1), list(c.nam, NULL)), identical(m1, t(tm1))) ## an example of *named* dimnames (t34N <- as(unclass(table(x = gl(3,4), y=gl(4,3))), "dgeMatrix")) stopifnot(identical(dimnames(t34N), dimnames(as(t34N, "matrix"))), identical(t34N, t(t(t34N)))) ## "dpo" checkMatrix(cm <- crossprod(m1)) checkMatrix(cp <- as(cm, "dppMatrix"))# 'dpp' + factors checkMatrix(cs <- as(cm, "dsyMatrix"))# 'dsy' + factors checkMatrix(dcm <- as(cm, "dgeMatrix"))#'dge' checkMatrix(mcm <- as(cm, "dMatrix")) # 'dsy' + factors -- buglet? rather == cm? checkMatrix(mc. <- as(cm, "Matrix")) # dpo --> dsy -- (as above) FIXME? ?? stopifnot(identical(mc., mcm), identical(cm, (2*cm)/2),# remains dpo identical(cm + cp, cp + cs),# dge identical(mc., mcm), all(2*cm == mcm * 2)) checkMatrix(eq <- cm == cs) stopifnot(all(eq@x), identical3(pack(eq), cs == cp, cm == cp), as.logical(!(cs < cp)), identical4(!(cs < cp), !(cp > cs), cp <= cs, cs >= cp)) ## Coercion to 'dpo' should give an error if result would be invalid M <- Matrix(diag(4) - 1) assertError(as(M, "dpoMatrix")) M. <- as(M, "dgeMatrix") M.[1,2] <- 10 # -> not even symmetric anymore assertError(as(M., "dpoMatrix")) ## Cholesky checkMatrix(ch <- chol(cm)) checkMatrix(ch2 <- chol(as(cm, "dsyMatrix"))) checkMatrix(ch3 <- chol(as(cm, "dgeMatrix"))) stopifnot(is.all.equal3(as(ch, "matrix"), as(ch2, "matrix"), as(ch3, "matrix"))) ### Very basic triangular matrix stuff assertError( new("dtrMatrix", Dim = c(2,2), x= 1:4) )# double 'Dim' assertError( new("dtrMatrix", Dim = as.integer(c(2,2)), x= 1:4) )# int 'x' ## This caused a segfault (before revision r1172 in ../src/dtrMatrix.c): assertError( new("dtrMatrix", Dim = 2:2, x=as.double(1:4)) )# length(Dim) !=2 assertError( new("dtrMatrix", Dim = as.integer(c(2,2)), x= as.double(1:5))) tr22 <- new("dtrMatrix", Dim = as.integer(c(2,2)), x=as.double(1:4)) tt22 <- t(tr22) (tPt <- tr22 + tt22) stopifnot(identical(10 * tPt, tPt * 10), as.vector(t.22 <- (tr22 / .5)* .5) == c(1,0,3,4), TRUE) ## not yet: class(t.22) == "dtrMatrix") ## non-square triagonal Matrices --- are forbidden --- assertError(new("dtrMatrix", Dim = 2:3, x=as.double(1:6), uplo="L", diag="U")) n <- 3:3 assertError(new("dtCMatrix", Dim = c(n,n), diag = "U")) stopifnot(validObject(T <- new("dtTMatrix", Dim = c(n,n), diag = "U")), identical(as.mat(T), diag(n)), validObject(M <- new("dtCMatrix", Dim = c(n,n), diag = "U", p = rep.int(0:0, n+1))) ) set.seed(3) ; (p9 <- as(sample(9), "pMatrix")) ## Check that the correct error message is triggered ind.try <- try(p9[1,1] <- 1, silent = TRUE) stopifnot(grep("replacing.*sensible", ind.try[1]) == 1, is.logical(p9[1,]), is(p9[2,, drop=FALSE], "indMatrix"), is(p9[9:1,], "indMatrix"), isTRUE(p9[-c(1:6, 8:9), 1]), identical(t(p9), solve(p9)), ## identical(p9[TRUE,], as(p9, "ngTMatrix")), identical(as(diag(9), "pMatrix"), as(1:9, "pMatrix")) ) assert.EQ.mat(p9[TRUE,], as.matrix(as(p9, "ngTMatrix"))) ## validObject --> Cparse_validate(.) mm <- new("dgCMatrix", Dim = c(3L, 5L), i = c(2L, 0L, 1L, 2L, 0L, 1L), x = c( 2, 1, 1, 2, 1, 2), p = c(0:2, 4L, 4L, 6L)) ## Previously unsorted columns were sorted - now are flagged as invalid m. <- mm ip <- c(1:2, 4:3, 6:5) # permute the 'i' and 'x' slot just "inside column": m.@i <- m.i <- mm@i[ip] m.@x <- m.x <- mm@x[ip] stopifnot(grep("row indices are not", validObject(m., test=TRUE)) == 1) Matrix:::.sortCsparse(m.) # don't use this at home, boys! m. # now is fixed ## Make sure that validObject() objects... ## 1) to wrong 'p' m. <- mm; m.@p[1] <- 1L stopifnot(grep("first element of slot p", validObject(m., test=TRUE)) == 1) m.@p <- mm@p[c(1,3:2,4:6)] stopifnot(grep("^slot p.* non-decreasing", validObject(m., test=TRUE)) == 1) ## 2) to non-strictly increasing i's: m. <- mm ; ix <- c(1:3,3,5:6) m.@i <- mm@i[ix] m.@x <- mm@x[ix] stopifnot(identical(grep("slot i is not.* increasing .*column$", validObject(m., test=TRUE)), 1L)) ## ix <- c(1:3, 3:6) # now the the (i,x) slots are too large (and decreasing at end) ## m.@i <- mm@i[ix] ## m.@x <- mm@x[ix] ## stopifnot(identical(grep("^slot i is not.* increasing .*sort", ## (msg <- validObject(m., test=TRUE))),# seg.fault in the past ## 1L)) ## over-allocation of the i- and x- slot should be allowed: ## (though it does not really help in M[.,.] <- * yet) m. <- mm m.@i <- c(mm@i, NA, NA, NA) m.@x <- c(mm@x, 10:12) stopifnot(validObject(m.)) m. # show() now works stopifnot(all(m. == mm), # in spite of length(m.@i) > length(mm@i), identical(t(t(m.)), mm), identical3(m. * m., m. * mm, mm * mm)) m.[1,4] <- 99 ## FIXME: warning and cuts (!) the over-allocated slots ## Low-level construction of invalid object: ## Ensure that it does *NOT* segfault foo <- new("ngCMatrix", i = as.integer(c(12204, 16799, 16799, 33517, 1128, 11930, 1128, 11930, 32183)), p = rep(0:9, c(2,4,1,11,10,0,1,0,9,12)), Dim = c(36952L, 49L)) validObject(foo)# TRUE foo@i[5] <- foo@i[5] + 50000L msg <- validObject(foo, test=TRUE)# is -- correctly -- *not* valid anymore stopifnot(is.character(msg)) ## Error in validObject(foo) : ## invalid class "ngCMatrix" object: all row indices must be between 0 and nrow-1 getLastMsg <- function(tryRes) { ## Extract "final" message from erronous try result sub("\n$", "", sub(".*: ", "", as.character(tryRes))) } t <- try(show(foo)) ## error t2 <- try(head(foo)) stopifnot(identical(msg, getLastMsg(t)), identical(1L, grep("as_cholmod_sparse", getLastMsg(t2)))) cat('Time elapsed: ', proc.time(),'\n') # "stats" if(!interactive()) warnings() Matrix/tests/dg_Matrix.R0000644000175100001440000000656112271746775014771 0ustar hornikuserslibrary(Matrix) source(system.file("test-tools.R", package = "Matrix")) data(KNex) ; mm <- KNex$mm stopifnot(##is(mm) == c("dgCMatrix", "dMatrix", "Matrix"), dim(mm) == (dm <- c(1850, 712)), identical(dimnames(mm), list(NULL,NULL))) str(mm) tmm <- t(mm) str(tmm) str(mTm <- crossprod(mm)) mmT <- crossprod(tmm) mmT. <- tcrossprod(mm) stopifnot(all.equal(mmT, mmT.)) ## Previously these were not the same ## Should be the same but not quite: even length( * @ x ) differs! ##str(mmT, max=2)# much larger than mTm (i.e less sparse) ##str(mmT., max=2)# x slot is currently slightly larger --> improve tcrossprod()? ##system.time(ae <- all.equal(as(mmT.,"matrix"), as(mmT,"matrix"), tolerance = 1e-14)) ## 4-5 seconds on a 850 MHz, P III ##stopifnot(ae) stopifnot(validObject(tmm), dim(tmm) == dm[2:1], validObject(mTm), dim(mTm) == dm[c(2,2)], validObject(mmT), dim(mmT) == dm[c(1,1)], identical(as(tmm, "matrix"), t(as(mm, "matrix")))) ## from a bug report by Guissepe Ragusa set.seed(101) for(i in 1:10) { A <- matrix(rnorm(400), nrow = 100, ncol = 4) A[A < +1] <- 0 ; Am <- A Acsc <- as(Am, "dgCMatrix") A <- as(Am, "dgeMatrix") b <- matrix(rnorm(400), nrow = 4, ncol = 100) B <- as(b, "dgeMatrix") assert.EQ.mat(A %*% B, Am %*% b, tol=0) assert.EQ.mat(B %*% A, b %*% Am, tol=0) stopifnot(identical(A, as(Acsc, "dgeMatrix")), identical(Acsc, as(A, "dgCMatrix")), is.all.equal4(A %*% B, Acsc %*% B, A %*% b, Acsc %*% b), is.all.equal4(b %*% A, b %*% Acsc, B %*% A, B %*% Acsc)) } ###--- dgTMatrix {was ./dgTMatrix.R } ------- ### Use ``non-unique'' versions of dgTMatrix objects N <- 200 set.seed(1) i <- as.integer(round(runif (N, 0, 100))) j <- as.integer(3* rpois (N, lam=15)) x <- round(rnorm(N), 2) which(duplicated(cbind(i,j))) # 8 index pairs are duplicated m1 <- new("dgTMatrix", Dim = c(max(i)+1:1, max(j)+1:1), i = i, j = j, x = x) mc <- as(m1, "dgCMatrix") m2 <- as(mc, "dgTMatrix")## the same as 'm1' but without duplicates stopifnot(!isTRUE(all.equal.default(m1, m2)), all.equal(as(m1,"matrix"), as(m2,"matrix"), tolerance =1e-15), all.equal(crossprod(m1), crossprod(m2), tolerance =1e-15), identical(mc, as(m2, "dgCMatrix"))) ### -> uniq* functions now in ../R/Auxiliaries.R (t2 <- system.time(um2 <- Matrix:::uniq(m1))) stopifnot(identical(m2,um2)) ### -> error/warning condition for solve() of a singular matrix (Barry Rowlingson) (M <- Matrix(0+ 1:16, nc = 4)) assertError(solve(M), verbose=TRUE)## ".. computationally singular" + warning + caches LU assertError(solve(t(M))) options(warn=2) # no more warnings allowed from here lum <- lu(M, warnSing=FALSE) stopifnot(is(fLU <- M@factors $ LU, "MatrixFactorization"), identical(lum, fLU)) (e.lu <- expand(fLU)) M2 <- with(e.lu, P %*% L %*% U) assert.EQ.mat(M2, as(M, "matrix")) ## now the sparse LU : M. <- as(M,"sparseMatrix") tt <- try(solve(M.)) # less nice: factor is *not* cached ## use a non-singular one: M1 <- M. + 0.5*Diagonal(nrow(M.)) luM1 <- lu(M1) d1 <- determinant(as(M1,"denseMatrix")) stopifnot(identical(luM1, M1@factors$LU), diag(luM1@L) == 1,# L is *unit*-triangular all.equal(log(-prod(diag(luM1@U))), c(d1$modulus))) cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons'' Matrix/tests/factorizing.R0000644000175100001440000005301612271746775015367 0ustar hornikusers#### Matrix Factorizations --- of all kinds library(Matrix) source(system.file("test-tools.R", package = "Matrix"))# identical3() etc doExtras ### "sparseQR" : Check consistency of methods ## -------- data(KNex); mm <- KNex$mm; y <- KNex$y stopifnot(is((Y <- Matrix(y)), "dgeMatrix")) md <- as(mm, "matrix") # dense (cS <- system.time(Sq <- qr(mm))) (cD <- system.time(Dq <- qr(md))) # 1.1 sec. (lynne, 2011) cD[1] / cS[1] # dense is much ( ~ 100--170 times) slower chkQR <- function(a, y = seq_len(nrow(a)),## RHS: made to contain no 0 a.qr = qr(a), tol = 1e-13, # 1e-13 failing very rarely (interesting) ##---------- Qinv.chk = !sp.rank.def, QtQ.chk = !sp.rank.def, verbose=getOption("verbose")) { d <- dim(a) stopifnot((n <- d[1]) >= (p <- d[2]), is.numeric(y)) kind <- if(is.qr(a.qr)) "qr" else if(is(a.qr, "sparseQR")) "spQR" else stop("unknown qr() class: ", class(a.qr)) ## rank.def <- switch(kind, ## "qr" = a.qr$rank < length(a.qr$pivot), ## "spQR" = a.qr@V@Dim[1] > a.qr@Dim[1]) sp.rank.def <- (kind == "spQR") && (a.qr@V@Dim[1] > a.qr@Dim[1]) if(sp.rank.def && (missing(Qinv.chk) || missing(QtQ.chk))) message("is sparse *structurally* rank deficient: Qinv.chk=", Qinv.chk,", QtQ.chk=",QtQ.chk) if(is.na(QtQ.chk )) QtQ.chk <- !sp.rank.def if(is.na(Qinv.chk)) Qinv.chk <- !sp.rank.def if(Qinv.chk) ## qr.qy and qr.qty should be inverses, Q'Q y = y = QQ' y : ## FIXME: Fails for structurally rank deficient sparse a's, but never for classical stopifnot(all.equal(drop(qr.qy (a.qr, qr.qty(a.qr, y))), y), all.equal(drop(qr.qty(a.qr, qr.qy (a.qr, y))), y)) piv <- switch(kind, "qr" = a.qr$pivot, "spQR" = 1L + a.qr@q)# 'q', not 'p' !! invP <- sort.list(piv) .ckQR <- function(cmpl) { ## local function, using parent's variables if(verbose) cat("complete = ",cmpl,":\n", sep="") Q <- qr.Q(a.qr, complete=cmpl) R <- qr.R(a.qr, complete=cmpl) rr <- if(cmpl) n else p stopifnot(dim(Q) == c(n,rr), dim(R) == c(rr,p)) assert.EQ.Mat(a, Q %*% R[, invP], tol = tol) ## = =============== if(QtQ.chk) assert.EQ.mat(crossprod(Q), diag(rr), tol = tol) ## =========== ==== } .ckQR(FALSE) .ckQR(TRUE) invisible(a.qr) }## end{chkQR} ##' Check QR-consistency of dense and sparse chk.qr.D.S <- function(d., s., y, Y = Matrix(y), force = FALSE) { stopifnot(is.qr(d.), is(s., "sparseQR")) cc <- qr.coef(d.,y) rank.def <- any(is.na(cc)) && d.$rank < length(d.$pivot) if(rank.def && force) cc <- mkNA.0(cc) ## set NA's to 0 .. ok, in some case ## when system is rank deficient, have differing cases, not always just NA <-> 0 coef ## FIXME though: resid & fitted should be well determined if(force || !rank.def) stopifnot( is.all.equal3( cc , drop(qr.coef (s.,y)), drop(qr.coef (s.,Y))) , is.all.equal3(qr.resid (d.,y), drop(qr.resid (s.,y)), drop(qr.resid (s.,Y))) , is.all.equal3(qr.fitted(d.,y), drop(qr.fitted(s.,y)), drop(qr.fitted(s.,Y))) ) } ##' "Combi" calling chkQR() on both "(sparse)Matrix" and 'traditional' version ##' ------ and combine the two qr decomp.s using chk.qr.D.S() ##' ##' @title check QR-decomposition, and compare sparse and dense one ##' @param A a 'Matrix' , typically 'sparseMatrix' ##' @param Qinv.chk ##' @param QtQ.chk ##' @param quiet ##' @return list with 'qA' (sparse QR) and 'qa' (traditional (dense) QR) ##' @author Martin Maechler checkQR.DS.both <- function(A, Qinv.chk, QtQ.chk=NA, quiet=FALSE, tol = 1e-13) { stopifnot(is(A,"Matrix")) if(!quiet) cat("classical: ") qa <- chkQR(as.matrix(A), Qinv.chk=TRUE, QtQ.chk=TRUE, tol=tol)# works always if(!quiet) cat("[Ok] --- sparse: ") qA <- chkQR(A, Qinv.chk=Qinv.chk, QtQ.chk=QtQ.chk, tol=tol) validObject(qA) if(!quiet) cat("[Ok]\n") chk.qr.D.S(qa, qA, y = 10 + 1:nrow(A))# ok [not done in rank deficient case!] invisible(list(qA=qA, qa=qa)) } if(doExtras) system.time({ ## ~ 20 sec {"large" example} + 2x qr.R() warnings cat("chkQR( ) .. takes time .. ") chkQR(mm, y=y, a.qr = Sq) chkQR(md, y=y, a.qr = Dq) cat(" done: [Ok]\n") }) ## consistency of results dense and sparse chk.qr.D.S(Dq, Sq, y, Y) ## rank deficient QR cases: --------------- ## From Simon (15 Jul 2009): set.seed(10) a <- matrix(round(10 * runif(90)), 10,9); a[a < 7.5] <- 0 (A <- Matrix(a))# first column = all zeros qD <- chkQR(a) ## using base qr qS <- chkQR(A) ## using Matrix "sparse qr" -- "structurally rank deficient! validObject(qS)# with the validity now (2012-11-18) -- ok, also for "bad" case chk.qr.D.S(qD, qS, y = 10 + 1:nrow(A), force=TRUE) try( ## NOTE: *Both* checks currently fail here: chkQR(A, Qinv.chk=TRUE, QtQ.chk=TRUE) ) ## Larger Scale random testing oo <- options(Matrix.quiet.qr.R = TRUE, Matrix.verbose = TRUE) set.seed(101) for(N in 1:(if(doExtras) 1008 else 24)) { A <- rSparseMatrix(8,5, nnz = rpois(1, lambda=16)) cat(sprintf("%4d -", N)) checkQR.DS.both(A, Qinv.chk= NA, QtQ.chk=NA) ## --- => FALSE if struct. rank deficient } ## Look at single "hard" cases: -------------------------------------- ## This is *REALLY* nice and small : A0 <- new("dgCMatrix", Dim = 4:3, i = c(0:3, 3L), p = c(0L, 3:5), x = rep(1,5)) A0 checkQR.DS.both(A0, Qinv.chk = FALSE, QtQ.chk=FALSE) ## ----- *both* still needed : try( checkQR.DS.both(A0, TRUE, FALSE) ) try( checkQR.DS.both(A0, FALSE, TRUE) ) ## and the same when dropping the first row { --> 3 x 3 }: A1 <- A0[-1 ,] checkQR.DS.both(A1, Qinv.chk = FALSE, QtQ.chk=FALSE) ## ----- *both* still needed : try( checkQR.DS.both(A1, TRUE, FALSE) ) try( checkQR.DS.both(A1, FALSE, TRUE) ) qa <- qr(as.matrix(A0)) qA <- qr(A0) drop0(crossprod( Qd <- qr.Q(qa) ), 1e-15) # perfect = diag( 3 ) drop0(crossprod( Qs <- qr.Q(qA) ), 1e-15) # R[3,3] == 0 -- OOPS! ## OTOH, qr.R() is fine, as checked in the checkQR.DS.both(A0, *) above ## zero-row *and* zero-column : (A2 <- new("dgCMatrix", i = c(0L, 1L, 4L, 7L, 5L, 2L, 4L) , p = c(0L, 3L, 4L, 4L, 5L, 7L) , Dim = c(8L, 5L) , x = c(0.92, 1.06, -1.74, 0.74, 0.19, -0.63, 0.68))) checkQR.DS.both(A2, Qinv.chk = FALSE, QtQ.chk=FALSE) ## ----- *both* still needed : try( checkQR.DS.both(A2, TRUE, FALSE) ) try( checkQR.DS.both(A2, FALSE, TRUE) ) ## Case of *NO* zero-row or zero-column: (A3 <- new("dgCMatrix", Dim = 6:5 , i = c(0L, 2L, 4L, 0L, 1L, 5L, 1L, 3L, 0L) , p = c(0L, 1L, 3L, 6L, 8L, 9L) , x = c(40, -54, -157, -28, 75, 166, 134, 3, -152))) checkQR.DS.both(A3, Qinv.chk = FALSE, QtQ.chk=FALSE) ## ----- *both* still needed : try( checkQR.DS.both(A3, TRUE, FALSE) ) try( checkQR.DS.both(A3, FALSE, TRUE) ) (A4 <- new("dgCMatrix", Dim = c(7L, 5L) , i = c(1:2, 4L, 6L, 1L, 5L, 0:3, 0L, 2:4) , p = c(0L, 4L, 6L, 10L, 10L, 14L) , x = c(9, -8, 1, -9, 1, 10, -1, -2, 6, 14, 10, 2, 12, -9))) checkQR.DS.both(A4, Qinv.chk = FALSE, QtQ.chk=FALSE) ## ----- *both* still needed : try( checkQR.DS.both(A4, TRUE, FALSE) ) try( checkQR.DS.both(A4, FALSE, TRUE) ) (A5 <- new("dgCMatrix", Dim = c(4L, 4L) , i = c(2L, 2L, 0:1, 0L, 2:3), p = c(0:2, 4L, 7L) , x = c(48, 242, 88, 18, -167, -179, 18))) checkQR.DS.both(A5, Qinv.chk = FALSE, QtQ.chk=FALSE) ## ----- *both* still needed : try( checkQR.DS.both(A5, TRUE, FALSE) ) try( checkQR.DS.both(A5, FALSE, TRUE) ) for(N in 1:(if(doExtras) 2^12 else 128)) { A <- round(100*rSparseMatrix(5,3, nnz = min(15,rpois(1, lambda=10)))) if(any(apply(A, 2, function(x) all(x == 0)))) ## "column of all 0" next cat(sprintf("%4d -", N)) checkQR.DS.both(A, Qinv.chk=NA, tol = 1e-12) ## --- => FALSE if struct. rank deficient } 1 options(oo) ### "denseLU" ## Testing expansions of factorizations {was ./expand.R, then in simple.R } ## new: [m x n] where m and n may differ x. <- c(2^(0:5),9:1,-3:8, round(sqrt(0:16))) set.seed(1) for(nnn in 1:100) { y <- sample(x., replace=TRUE) m <- sample(2:6, 1) n <- sample(2:7, 1) x <- suppressWarnings(matrix(y, m,n)) lux <- lu(x)# occasionally a warning about exact singularity xx <- with(expand(lux), (P %*% L %*% U)) print(dim(xx)) assert.EQ.mat(xx, x, tol = 16*.Machine$double.eps) } ### "sparseLU" por1 <- readMM(system.file("external/pores_1.mtx", package = "Matrix")) lu1 <- lu(por1) pm <- as(por1, "CsparseMatrix") (pmLU <- lu(pm)) # -> show() xp <- expand(pmLU) ## permute rows and columns of original matrix ppm <- pm[pmLU@p + 1:1, pmLU@q + 1:1] Ppm <- pmLU@L %*% pmLU@U ## identical only as long as we don't keep the original class info: stopifnot(identical3(lu1, pmLU, pm@factors$LU),# TODO === por1@factors$LU identical(ppm, with(xp, P %*% pm %*% t(Q))), sapply(xp, is, class="Matrix")) Ipm <- solve(pm, sparse=FALSE) Spm <- solve(pm, sparse=TRUE) # is not sparse at all, here assert.EQ.Mat(Ipm, Spm, giveRE=TRUE, tol = 1e-13)# seen 7.36e-15 only on 32-bit stopifnot(abs(as.vector(solve(Diagonal(30, x=10) %*% pm) / Ipm) - 1/10) < 1e-7, abs(as.vector(solve(rep.int(4, 30) * pm) / Ipm) - 1/ 4) < 1e-7) ## these two should be the same, and `are' in some ways: assert.EQ.mat(ppm, as(Ppm, "matrix"), tol = 1e-14, giveRE=TRUE) ## *however* length(ppm@x)# 180 length(Ppm@x)# 317 ! table(Ppm@x == 0)# (194, 123) - has 123 "zero" and 14 ``almost zero" entries ##-- determinant() and det() --- working via LU --- m <- matrix(c(0, NA, 0, NA, NA, 0, 0, 0, 1), 3,3) m0 <- rbind(0,cbind(0,m)) M <- as(m,"Matrix"); M ## "dsCMatrix" ... M0 <- rBind(0, cBind(0, M)) dM <- as(M, "denseMatrix") dM0 <- as(M0,"denseMatrix") try( lum <- lu(M) )# Err: "near-singular A" (lum <- lu(M, errSing=FALSE))# NA --- *BUT* it is not stored in @factors (lum0 <- lu(M0, errSing=FALSE))# NA --- and it is stored in M0@factors[["LU"]] ## "FIXME" - TODO: Consider replNA <- function(x, value) { x[is.na(x)] <- value ; x } (EL.1 <- expand(lu.1 <- lu(M.1 <- replNA(M, -10)))) ## so it's quite clear how lu() of the *singular* matrix M should work ## but it's not supported by the C code in ../src/cs.c which errors out stopifnot(all.equal(M.1, with(EL.1, P %*% L %*% U %*% Q)), is.na(det(M)), is.na(det(dM)), is.na(det(M0)), is.na(det(dM0)) ) ###________ Cholesky() ________ ##-------- LDL' ---- small exact examples set.seed(1) for(n in c(5:12)) { cat("\nn = ",n,"\n-------\n") rr <- mkLDL(n) ## -------- from 'test-tools.R' stopifnot(all(with(rr, A == as(L %*% D %*% t(L), "symmetricMatrix"))), all(with(rr, A == tcrossprod(L %*% sqrt(D))))) d <- rr$d.half A <- rr$A R <- chol(A) assert.EQ.Mat(R, chol(as(A, "TsparseMatrix"))) # gave infinite recursion print(d. <- diag(R)) D. <- Diagonal(x= d.^2) L. <- t(R) %*% Diagonal(x = 1/d.) stopifnot(all.equal(as.matrix(D.), as.matrix(rr$ D)), all.equal(as.matrix(L.), as.matrix(rr$ L))) ## CAp <- Cholesky(A)# perm=TRUE --> Permutation: p <- CAp@perm + 1L P <- as(p, "pMatrix") ## the inverse permutation: invP <- solve(P)@perm lDet <- sum(2* log(d))# the "true" value ldet <- Matrix:::.diag.dsC(Chx = CAp, res.kind = "sumLog") ## CA <- Cholesky(A,perm=FALSE) ldet2 <- Matrix:::.diag.dsC(Chx = CA, res.kind = "sumLog") ## not printing CAp : ends up non-integer for n >= 11 mCAp <- as(CAp,"sparseMatrix") print(mCA <- drop0(as(CA, "sparseMatrix"))) stopifnot(identical(A[p,p], as(P %*% A %*% t(P), "symmetricMatrix")), all.equal(lDet, sum(log(Matrix:::.diag.dsC(Chx= CAp,res.kind="diag")))), relErr(d.^2, Matrix:::.diag.dsC(Chx= CA, res.kind="diag")) < 1e-14, all.equal(lDet, ldet), all.equal(lDet, ldet2), relErr(A[p,p], tcrossprod(mCAp)) < 1e-14) }## for() set.seed(17) (rr <- mkLDL(4)) (CA <- Cholesky(rr$A)) stopifnot(all.equal(determinant(rr$A) -> detA, determinant(as(rr$A, "matrix"))), is.all.equal3(c(detA$modulus), log(det(rr$D)), sum(log(rr$D@x)))) A12 <- mkLDL(12, 1/10) (r12 <- allCholesky(A12$A))[-1] aCh.hash <- r12$r.all %*% (2^(2:0)) if(FALSE)## if(require("sfsmisc")) split(rownames(r12$r.all), Duplicated(aCh.hash)) ## TODO: find cases for both choices when we leave it to CHOLMOD to choose for(n in 1:50) { ## used to seg.fault at n = 10 ! mkA <- mkLDL(1+rpois(1, 30), 1/10) cat(sprintf("n = %3d, LDL-dim = %d x %d ", n, nrow(mkA$A), ncol(mkA$A))) r <- allCholesky(mkA$A, silentTry=TRUE) ## Compare .. apart from the NAs that happen from (perm=FALSE, super=TRUE) iNA <- apply(is.na(r$r.all), 1, any) cat(sprintf(" -> %3s NAs\n", if(any(iNA)) format(sum(iNA)) else "no")) stopifnot(aCh.hash[!iNA] == r$r.all[!iNA,] %*% (2^(2:0))) ## cat("--------\n") } ## This is a relatively small "critical example" : A. <- new("dsCMatrix", Dim = c(25L, 25L), uplo = "U" , i = as.integer( c(0, 1, 2, 3, 4, 2, 5, 6, 0, 8, 8, 9, 3, 4, 10, 11, 6, 12, 13, 4, 10, 14, 15, 1, 2, 5, 16, 17, 0, 7, 8, 18, 9, 19, 10, 11, 16, 20, 0, 6, 7, 16, 17, 18, 20, 21, 6, 9, 12, 14, 19, 21, 22, 9, 11, 19, 20, 22, 23, 1, 16, 24)) ## , p = c(0:6, 8:10, 12L, 15:16, 18:19, 22:23, 27:28, 32L, 34L, 38L, 46L, 53L, 59L, 62L) ## , x = c(1, 1, 1, 1, 2, 100, 2, 40, 1, 2, 100, 6700, 100, 100, 13200, 1, 50, 4100, 1, 5, 400, 20, 1, 40, 100, 5600, 9100, 5000, 5, 100, 100, 5900, 100, 6200, 30, 20, 9, 2800, 1, 100, 8, 10, 8000, 100, 600, 23900, 30, 100, 2800, 50, 5000, 3100, 15100, 100, 10, 5600, 800, 4500, 5500, 7, 600, 18200)) validObject(A.) ## A1: the same pattern as A. just simply filled with '1's : A1 <- A.; A1@x[] <- 1; A1@factors <- list() A1.8 <- A1; diag(A1.8) <- 8 ## nT. <- as(AT <- as(A., "TsparseMatrix"),"nMatrix") stopifnot(all(nT.@i <= nT.@j), identical(qr(A1.8), qr(as(A1.8, "dgCMatrix")))) CA <- Cholesky(A.) stopifnot(isValid(CAinv <- solve(CA), "dsCMatrix")) MA <- as(CA, "Matrix") # with a confusing warning -- FIXME! isValid(MAinv <- solve(MA), "dtCMatrix") ## comparing MAinv with some solve(CA, system="...") .. *not* trivial? - TODO ## CAinv2 <- solve(CA, Diagonal(nrow(A.))) CAinv2 <- as(CAinv2, "symmetricMatrix") stopifnot(identical(CAinv, CAinv2)) ## FINALLY fix this "TODO": try( tc <- Cholesky(nT.) ) for(p in c(FALSE,TRUE)) for(L in c(FALSE,TRUE)) for(s in c(FALSE,TRUE, NA)) { cat(sprintf("p,L,S = (%2d,%2d,%2d): ", p,L,s)) r <- tryCatch(Cholesky(A., perm=p, LDL=L, super=s), error = function(e)e) cat(if(inherits(r, "error")) " *** E ***" else sprintf("%3d", r@type),"\n", sep="") } str(A., max=3) ## look at the 'factors' facs <- A.@factors names(facs) <- sub("Cholesky$", "", names(facs)) facs <- facs[order(names(facs))] sapply(facs, class) str(lapply(facs, slot, "type")) ## super = TRUE currently always entails LDL=FALSE : ## hence isLDL is TRUE for ("D" and not "S"): sapply(facs, isLDL) chkCholesky <- function(chmf, A) { stopifnot(is(chmf, "CHMfactor"), is(A, "Matrix"), isSymmetric(A)) if(!is(A, "dsCMatrix")) A <- as(A, "dsCMatrix") L <- drop0(zapsmall(L. <- as(chmf, "Matrix"))) cat("no. nonzeros in L {before / after drop0(zapsmall(.))}: ", c(nnzero(L.), nnzero(L)), "\n") ## 112, 95 ecc <- expand(chmf) A... <- with(ecc, crossprod(crossprod(L,P))) stopifnot(all.equal(L., ecc$L, tolerance = 1e-14), all.equal(A, A..., tolerance = 1e-14, factorsCheck = FALSE)) invisible(ecc) } c1.8 <- try(Cholesky(A1.8, super = TRUE))# works "always", interestingly ... chkCholesky(c1.8, A1.8) ## --- now a "large" (712 x 712) real data example --------------------------- data(KNex) mtm <- with(KNex, crossprod(mm)) ld.3 <- .Call("dsCMatrix_LDL_D", mtm, perm=TRUE, "sumLog") stopifnot(names(mtm@factors) == "sPDCholesky") ld.4 <- .Call("dsCMatrix_LDL_D", mtm, perm=FALSE, "sumLog")# clearly slower stopifnot(names(mtm@factors) == paste(c("sPD", "spD"),"Cholesky", sep='')) c2 <- Cholesky(mtm, super = TRUE) stopifnot(names(mtm@factors) == paste(c("sPD", "spD", "SPd"), "Cholesky", sep='')) r <- allCholesky(mtm) r[-1] ## is now taken from cache c1 <- Cholesky(mtm) bv <- 1:nrow(mtm) # even integer b <- matrix(bv) ## solve(c2, b) by default solves Ax = b, where A = c2'c2 ! x <- solve(c2,b) stopifnot(identical3(x, solve(c2, bv), solve(c2, b, system = "A")), all.equal(x, solve(mtm, b))) for(sys in c("A", "LDLt", "LD", "DLt", "L", "Lt", "D", "P", "Pt")) { x <- solve(c2, b, system = sys) cat(sys,":\n"); print(head(x)) stopifnot(dim(x) == c(712, 1), identical(x, solve(c2, bv, system = sys))) } ## log(|LL'|) - check if super = TRUE and simplicial give same determinant ld1 <- .Call("CHMfactor_ldetL2", c1) ld2 <- .Call("CHMfactor_ldetL2", c2) (ld1. <- determinant(mtm)) ## experimental ld3 <- .Call("dsCMatrix_LDL_D", mtm, TRUE, "sumLog") ld4 <- .Call("dsCMatrix_LDL_D", mtm, FALSE, "sumLog") stopifnot(all.equal(ld1, ld2), is.all.equal3(ld2, ld3, ld4), all.equal(ld.3, ld3, tolerance = 1e-14), all.equal(ld.4, ld4, tolerance = 1e-14), all.equal(ld1, as.vector(ld1.$modulus), tolerance = 1e-14)) ## Some timing measurements mtm <- with(KNex, crossprod(mm)) I <- .symDiagonal(n=nrow(mtm)) set.seed(101); r <- runif(100) system.time(D1 <- sapply(r, function(rho) Matrix:::ldet1.dsC(mtm + (1/rho) * I))) ## 0.842 on fast cmath-5 system.time(D2 <- sapply(r, function(rho) Matrix:::ldet2.dsC(mtm + (1/rho) * I))) ## 0.819 system.time(D3 <- sapply(r, function(rho) Matrix:::ldet3.dsC(mtm + (1/rho) * I))) ## 0.810 stopifnot(is.all.equal3(D1,D2,D3, tol = 1e-13)) ## Updating LL' should remain LL' and not become LDL' : cholCheck <- function(Ut, tol = 1e-12, super = FALSE, LDL = !super) { L <- Cholesky(UtU <- tcrossprod(Ut), super=super, LDL=LDL, Imult = 1) L1 <- update(L, UtU, mult = 1) L2 <- update(L, Ut, mult = 1) stopifnot(is.all.equal3(L, L1, L2, tol = tol), all.equal(update(L, UtU, mult = pi), update(L, Ut, mult = pi), tolerance = tol) ) } ## Inspired by ## data(Dyestuff, package = "lme4") ## Zt <- as(Dyestuff$Batch, "sparseMatrix") Zt <- new("dgCMatrix", Dim = c(6L, 30L), x = 2*1:30, i = rep(0:5, each=5), p = 0:30, Dimnames = list(LETTERS[1:6], NULL)) cholCheck(0.78 * Zt, tol=1e-14) for(i in 1:120) { set.seed(i); cat(sprintf("%3d: ", i)) M <- rspMat(n=rpois(1,50), m=rpois(1,20), density = 1/(4*rpois(1, 4))) for(super in c(FALSE,TRUE)) { cat("super=",super," M: ") cholCheck( M , super=super); cat(" M': ") cholCheck(t(M), super=super) } cat(" [Ok]\n") } .updateCHMfactor ## TODO: (--> ../TODO "Cholesky"): ## ---- ## allow Cholesky(A,..) when A is not symmetric *AND* ## we really want to factorize AA' ( + beta * I) ## Schur() ---------------------- checkSchur <- function(A, SchurA = Schur(A), tol = 1e-14) { stopifnot(is(SchurA, "Schur"), isOrthogonal(Q <- SchurA@Q), all.equal(as.mat(A), as.mat(Q %*% SchurA@T %*% t(Q)), tolerance = tol)) } SH <- Schur(H5 <- Hilbert(5)) checkSchur(H5, SH) checkSchur(Diagonal(x = 9:3)) p <- 4L uTp <- new("dtpMatrix", x=c(2, 3, -1, 4:6, -2:1), Dim = c(p,p)) (uT <- as(uTp, "dtrMatrix")) ## Schur ( ) <--> Schur( ) Su <- Schur(uT) ; checkSchur(uT, Su) gT <- as(uT,"generalMatrix") Sg <- Schur(gT) ; checkSchur(gT, Sg) Stg <- Schur(t(gT));checkSchur(t(gT), Stg) Stu <- Schur(t(uT));checkSchur(t(uT), Stu) stopifnot(identical3(Sg@T, uT, Su@T), identical(Sg@Q, as(diag(p), "dgeMatrix")), identical(Stg@T, as(t(gT[,p:1])[,p:1], "triangularMatrix")), identical(Stg@Q, as(diag(p)[,p:1], "dgeMatrix")), identical(Stu@T, Stg@T)) assert.EQ.mat(Stu@Q, as(Stg@Q,"matrix"), tol=0) ## the pedigreemm example where solve(.) failed: p <- new("dtCMatrix", i = c(2L, 3L, 2L, 5L, 4L, 4:5), p = c(0L, 2L, 4:7, 7L), Dim = c(6L, 6L), Dimnames = list(as.character(1:6), NULL), x = rep.int(-0.5, 7), uplo = "L", diag = "U") Sp <- Schur(p) Sp. <- Schur(as(p,"generalMatrix")) Sp.p <- Schur(crossprod(p)) ## the last two failed ip <- solve(p) assert.EQ.mat(solve(ip), as(p,"matrix")) ## chol2inv() for a traditional matrix assert.EQ.mat( crossprod(chol2inv(chol(Diagonal(x = 5:1)))), C <- crossprod(chol2inv(chol( diag(x = 5:1))))) stopifnot(all.equal(C, diag((5:1)^-2))) ## failed in some versions because of a "wrong" implicit generic ## From [Bug 14834] New: chol2inv *** caught segfault *** n <- 1e6 # was 595362 A <- chol( D <- Diagonal(n) ) stopifnot(identical(A,D)) # A remains (unit)diagonal is(tA <- as(A,"triangularMatrix")) isValid(tA, "dsparseMatrix")# currently is dtTMatrix CA <- as(tA, "CsparseMatrix") selectMethod(solve, c("dtCMatrix","missing")) ##--> .Call(dtCMatrix_sparse_solve, a, .trDiagonal(n)) in ../src/dtCMatrix.c sA <- solve(CA)## -- R_CheckStack() segfault in Matrix <= 1.0-4 nca <- diagU2N(CA) stopifnot(identical(sA, nca)) ## same check with non-unit-diagonal D : A <- chol(D <- Diagonal(n, x = 0.5)) ia <- chol2inv(A) stopifnot(is(ia, "diagonalMatrix"), all.equal(ia@x, rep(2,n), tolerance = 1e-15)) cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons'' if(!interactive()) warnings() Matrix/tests/other-pkgs.R0000644000175100001440000001162312247126702015112 0ustar hornikusers####--------- Test interfaces to other non-standard Packages --------------- library(Matrix) source(system.file("test-tools.R", package = "Matrix"))# identical3() etc MatrixRversion <- pkgRversion("Matrix") ###-- 1) 'graph' (from Bioconductor) --------------------------- ###-- == ======= --------------------------- ## do not run the test "usually" for now [Solaris problem after detach() ..]: if((Sys.getenv("USER")=="maechler" || nzchar(Sys.getenv("R_MATRIX_CHECK_EXTRA"))) && isTRUE(try(require(graph)))) { # may be there and fail (with R-devel) if(packageDescription("graph")$Version <= "1.10.2") { ## graph 1.10.x for x <= 2 had too many problems as(, "matrix") cat("Version of 'graph' is too old --- no tests done here!\n") } else if(pkgRversion("graph") != MatrixRversion) { cat(sprintf("The R version (%s) of 'graph' installation differs from the Matrix one (%s)\n", pkgRversion("graph"), MatrixRversion)) } else { ## do things pdf("other-pkg-graph.pdf") ## 0) Simplest non-trivial graph: has no weights: g0 <- graphNEL(paste(1:2), edgeL=list("1"="2"), "directed") m0 <- as(g0, "Matrix") stopifnot(is(m0,"ngCMatrix"), dim(m0) == c(2,2), which(m0) == 3) g. <- as(m0, "graph") ## failed in Matrix <= 1.1-0 m. <- as(g., "Matrix") stopifnot( identical(m., m0) ) ## but (g0, g.) differ: the latter has '1' weights ## 1) undirected V <- LETTERS[1:4] edL <- vector("list", length=4) names(edL) <- V ## 1a) unweighted for(i in 1:4) edL[[i]] <- list(edges = 5-i) gR <- new("graphNEL", nodes=V, edgeL=edL) str(edges(gR)) sm.g <- as(gR, "sparseMatrix") str(sm.g) ## dgC: TODO: want 'ds.' (symmetric) validObject(sm.g) show( sm.g )## (incl colnames !) ## 1b) weighted set.seed(123) for(i in 1:4) edL[[i]] <- list(edges = 5-i, weights=runif(1)) gRw <- new("graphNEL", nodes=V, edgeL=edL) str(edgeWeights(gRw)) sm.gw <- as(gRw, "sparseMatrix") str(sm.gw) ## *numeric* dgCMatrix validObject(sm.gw) show( sm.gw )## U[0,1] numbers in anti-diagonal ## 2) directed gU <- gR; edgemode(gU) <- "directed" sgU <- as(gU, "sparseMatrix") str(sgU) ## 'dgC' validObject(sgU) show( sgU ) ## Reverse : sparseMatrix -> graph sm.g[1,2] <- 1 gmg <- as(sm.g, "graph") validObject(gmg2 <- as(sm.g, "graphNEL")) gmgw <- as(sm.gw, "graph") validObject(gmgw2 <- as(sm.gw, "graphNEL")) gmgU <- as(sgU, "graph") validObject(gmgU2 <- as(sgU, "graphNEL")) stopifnot(identical(gmg, gmg2), identical(gmgw, gmgw2), identical(gmgU, gmgU2)) data(CAex) cc <- crossprod(CAex) ## work around bug in 'graph': diagonal must be empty: diag(cc) <- 0; cc <- drop0(cc) image(cc) gg <- as(cc, "graph") .r <- require# cheat checks - do *not* want it in DESCRIPTION: if(.r("Rgraphviz")) { plot(gg, "circo") detach("package:Rgraphviz", unload = TRUE) } stopifnot(all.equal(edgeMatrix(gg), rbind(from = c(rep(1:24, each=2), 25:48), to = c(rbind(25:48,49:72), 49:72)))) detach("package:graph", unload = TRUE) dev.off() } # {else} } ## end{graph} ###-- 2) 'SparseM' --------------------------------------------- ###-- == ======== --------------------------------------------- if(isTRUE(try(require(SparseM)))) { # may be there and fail if(pkgRversion("SparseM") != MatrixRversion) { cat(sprintf("The R version (%s) of 'SparseM' installation differs from the Matrix one (%s)\n", pkgRversion("SparseM"), MatrixRversion)) } else { ## do things set.seed(1) a <- round(rnorm(5*4), 2) a[abs(a) < 0.7] <- 0 A <- matrix(a,5,4) print(M <- Matrix(A)) stopifnot( validObject(A.csr <- as.matrix.csr(A)), validObject(At.csr <- as.matrix.csr(t(A))), validObject(A.csc <- as.matrix.csc(A)), identical(At.csr, t(A.csr)), identical(A, as.matrix(A.csr)), identical(A.csr, as(M, "matrix.csr")), identical(A.csc, as(M, "matrix.csc")), identical3(M, as(A.csr, "CsparseMatrix"), as(A.csr, "dgCMatrix")), identical(t(M), as(At.csr, "CsparseMatrix")) ) ## More tests, notably for triplets A.coo <- as.matrix.coo(A) str(T <- as(M, "TsparseMatrix")) # has 'j' sorted str(T. <- as(A.coo, "TsparseMatrix")) # has 'i' sorted T3 <- as(as(T, "matrix.coo"), "Matrix") # dgT M3 <- as(A.csr, "Matrix") # dgC M4 <- as(A.csc, "Matrix") # dgC M5 <- as(as(M, "matrix.coo"), "Matrix") # dgT uniqT <- Matrix:::uniqTsparse stopifnot(identical4(uniqT(T), uniqT(T.), uniqT(T3), uniqT(M5)), identical3(M, M3, M4)) if(FALSE) # detaching the package gives error ".GenericTable" not found detach("package:SparseM") } }## end{SparseM} Matrix/tests/group-methods.R0000644000175100001440000002200712257616323015626 0ustar hornikusers### Testing the group methods --- some also happens in ./Class+Meth.R library(Matrix) source(system.file("test-tools.R", package = "Matrix"))# identical3() etc cat("doExtras:",doExtras,"\n") set.seed(2001) mm <- Matrix(rnorm(50 * 7), nc = 7) xpx <- crossprod(mm)# -> "factors" in mm ! round(xpx, 3) # works via "Math2" y <- rnorm(nrow(mm)) xpy <- crossprod(mm, y) res <- solve(xpx, xpy) signif(res, 4) # 7 x 1 Matrix stopifnot(all(signif(res) == signif(res, 6)), all(round (xpx) == round (xpx, 0))) ## exp(): component wise signif(dd <- (expm(xpx) - exp(xpx)) / 1e34, 3)# 7 x 7 stopifnot(validObject(xpx), validObject(xpy), validObject(dd)) ## "Math" also, for log() and [l]gamma() which need special treatment stopifnot(identical(exp(res)@x, exp(res@x)), identical(log(abs(res))@x, log(abs((res@x)))), identical(lgamma(res)@x, lgamma(res@x))) ###--- sparse matrices --------- m <- Matrix(c(0,0,2:0), 3,5) (mC <- as(m, "dgCMatrix")) sm <- sin(mC) stopifnot(class(sm) == class(mC), class(mC) == class(mC^2), dim(sm) == dim(mC), class(0 + 100*mC) == class(mC), all.equal(0.1 * ((0 + 100*mC)/10), mC), all.equal(sqrt(mC ^ 2), mC), all.equal(m^m, mC^mC), identical(mC^2, mC * mC), identical(mC*2, mC + mC) ) x <- Matrix(rbind(0,cbind(0, 0:3,0,0,-1:2,0),0)) x # sparse (x2 <- x + 10*t(x)) stopifnot(is(x2, "sparseMatrix"), identical(x2, t(x*10 + t(x))), identical(x, as((x + 10) - 10, class(x)))) (px <- Matrix(x^x - 1))#-> sparse again stopifnot(px@i == c(3,4,1,4), px@x == c(3,26,-2,3)) ## From: "Florent D." .. Thu, 23 Feb 2012 -- bug report ##---> MM: Make a regression test: tst <- function(n, i = 1) { stopifnot(i >= 1, n >= i) D <- .sparseDiagonal(n) ee <- numeric(n) ; ee[i] <- 1 stopifnot(all(D - ee == diag(n) - ee), all(D * ee == diag(n) * ee), all(ee - D == ee - diag(n)), {C <- (ee / D == ee / diag(n)); all(is.na(C) | C)}, TRUE) } nn <- if(doExtras) 27 else 7 tmp <- sapply(1:nn, tst) # failed in Matrix 1.0-4 i <- sapply(1:nn, function(i) sample(i,1)) tmp <- mapply(tst, n= 1:nn, i= i)# failed too showProc.time() set.seed(111) local({ for(i in 1:(if(doExtras) 20 else 5)) { M <- rspMat(n=1000, 200, density = 1/20) v <- rnorm(ncol(M)) m <- as(M,"matrix") stopifnot(all(t(M)/v == t(m)/v)) cat(".") }});cat("\n") ## Now just once, with a large such matrix: local({ n <- 100000; m <- 30000 AA <- rspMat(n, m, density = 1/20000) v <- rnorm(m) st <- system.time({ BB <- t(AA)/v # should happen *fast* stopifnot(dim(BB) == c(m,n), is(BB, "sparseMatrix")) }) str(BB) print(st) if(Sys.info()[["sysname"]] == "Linux") { mips <- as.numeric(sub(".*: *", '', grep("bogomips", readLines("/proc/cpuinfo"), value=TRUE)[[1]])) stopifnot(st[1] < 1000/mips)# ensure there was no gross inefficiency } }) ###----- Compare methods ---> logical Matrices ------------ l3 <- upper.tri(matrix(, 3, 3)) (ll3 <- Matrix(l3)) dt3 <- (99* Diagonal(3) + (10 * ll3 + Diagonal(3)))/10 (dsc <- crossprod(ll3)) stopifnot(validObject(ll3), validObject(dsc), identical(ll3, t(t(ll3))), identical(dsc, t(t(dsc))), isValid(dsc + 3 * Diagonal(nrow(dsc)), "dsCMatrix"), isValid(dt3, "triangularMatrix"), # remained triangular isValid(dt3 > 0, "triangularMatrix")# ditto ) (lm1 <- dsc >= 1) # now ok (lm2 <- dsc == 1) # now ok nm1 <- as(lm1, "nMatrix") (nm2 <- as(lm2, "nMatrix")) stopifnot(validObject(lm1), validObject(lm2), validObject(nm1), validObject(nm2), identical(dsc, as(dsc * as(lm1, "dMatrix"), "dsCMatrix"))) crossprod(lm1) # lm1: "lsC*" cnm1 <- crossprod(nm1) stopifnot(is(cnm1, "symmetricMatrix"), ## whereas the %*% is not: Q.eq(cnm1, nm1 %*% nm1)) dn1 <- as(nm1, "denseMatrix") stopifnot(all(dn1 == nm1)) dsc[2,3] <- NA ## now has an NA (and no longer is symmetric) ## ----- and "everything" is different ## also add "non-structural 0": dsc@x[1] <- 0 dsc dsc/ 5 dsc + dsc dsc - dsc dsc + 1 # -> no longer sparse Tsc <- as(dsc, "TsparseMatrix") dsc. <- drop0(dsc) stopifnot(identical(dsc., Matrix((dsc + 1) -1)), identical(as(-Tsc,"CsparseMatrix"), (-1) * Tsc), identical(-dsc., (-1) * dsc.), identical3(-Diagonal(3), Diagonal(3, -1), (-1) * Diagonal(3)), identical(dsc., Matrix((Tsc + 1) -1)), # ok (exact arithmetic) Q.eq(0 != dsc, dsc != Matrix(0, 3, 3)), Q.eq(0 != dsc, dsc != c(0,0)) # with a warning ("not multiple ..") ) str(lm1 <- dsc >= 1) # now ok (NA in proper place, however: lm1 ## NA used to print as ' ' , now 'N' (lm2 <- dsc == 1)# ditto ddsc <- kronecker(Diagonal(7), dsc) isValid(ddv <- rowSums(ddsc, sparse=TRUE), "sparseVector") sv <- colSums(kC <- kronecker(mC,kronecker(mC,mC)), sparse=TRUE) EQ <- ddv == rowSums(ddsc) na.ddv <- is.na(ddv) sM <- Matrix(pmax(0, round(rnorm(50*15, -1.5), 2)), 50,15) stopifnot(sv == colSums(kC), is.na(as.vector(ddv)) == na.ddv, isValid(sM/(-7:7), "CsparseMatrix"), all(EQ | na.ddv)) ## Just for print "show": z <- round(rnorm(77), 2) z[sample(77,10)] <- NA (D <- Matrix(z, 7)) # dense z[sample(77,15)] <- 0 (D <- Matrix(z, 7)) # sparse abs(D) >= 0.5 # logical sparse stopifnot(identical(crossprod(lm1),# "lgC": here works! crossprod(as(lm1, "dMatrix")) )) ## For the checks below, remove some and add a few more objects: rm(list= ls(pat="^.[mMC]?$")) D3 <- Diagonal(x=4:2); L7 <- Diagonal(7) > 0 T3 <- Diagonal(3) > 0; stopifnot(T3@diag == "U") # "uni-diagonal" validObject(xpp <- pack(round(xpx,2))) validObject(dtp <- pack(as(dt3, "denseMatrix"))) lsp <- xpp > 0 isValid(lsC <- as(lsp, "sparseMatrix"), "lsCMatrix") showProc.time() if(!doExtras && !interactive()) q("no") ## (saving testing time) ### Systematically look at all "Ops" group generics for "all" Matrix classes ### -------------- Main issue: Detect infinite recursion problems cl <- sapply(ls(), function(.) class(get(.))) Mcl <- c(grep("Matrix$", cl, value=TRUE), grep("sparseVector", cl, value=TRUE)) table(Mcl) ## choose *one* of each class: ## M.objs <- names(Mcl[!duplicated(Mcl)]) ## choose all M.objs <- names(Mcl) Mat.objs <- M.objs[vapply(M.objs, function(nm) is(get(nm), "Matrix"), NA)] MatDims <- t(vapply(Mat.objs, function(nm) dim(get(nm)), 0:1)) noquote(cbind(Mcl[Mat.objs], format(MatDims))) mDims <- MatDims %*% (d.sig <- c(1, 1000)) # "dim-signature" to match against m2num <- function(m) { if(is.integer(m)) storage.mode(m) <- "double" ; m } M.knd <- Matrix:::.M.kind cat("Checking all group generics for a set of arguments:\n", "---------------------------------------------------\n", sep='') options(warn = 2)#, error=recover) for(gr in getGroupMembers("Ops")) { cat(gr,"\n",paste(rep.int("=",nchar(gr)),collapse=""),"\n", sep='') for(f in getGroupMembers(gr)) { cat(sprintf("%9s :\n%9s\n", paste0('"',f,'"'), "--")) for(nm in M.objs) { if(doExtras) cat(" '",nm,"' ", sep="") M <- get(nm, inherits=FALSE) n.m <- NROW(M) cat("o") for(x in list(TRUE, -3.2, 0L, seq_len(n.m))) { cat(".") validObject(r1 <- do.call(f, list(M,x))) validObject(r2 <- do.call(f, list(x,M))) stopifnot(dim(r1) == dim(M), dim(r2) == dim(M)) } ## M o x <- numeric(n.m) x[c(1,length(x))] <- 1:2 sv <- as(x, "sparseVector") cat("s.") validObject(r3 <- do.call(f, list(M, sv))) stopifnot(dim(r3) == dim(M)) if(doExtras && is(M, "Matrix")) { ## M o d <- dim(M) ds <- sum(d * d.sig) # signature .. match with all other sigs match. <- ds == mDims # (matches at least itself) cat("\nM o M:") for(oM in Mat.objs[match.]) { M2 <- get(oM) ## R4 := M f M2 validObject(R4 <- do.call(f, list(M, M2))) cat(".") for(M. in list(as.mat(M), M)) { ## two cases .. r4 <- m2num(as.mat(do.call(f, list(M., as.mat(M2))))) cat(",") if(!identical(r4, as.mat(R4))) { cat(sprintf("\n %s %s %s not identical: r4 \\ R4:\n", nm, f, oM)) print(r4); print(R4) C1 <- (eq <- R4 == r4) | ((nr4 <- is.na(r4)) & !is.finite(R4)) if(isTRUE(all(C1)) && (k1 <- M.knd(M)) != "d" && (k2 <- M.knd(M2)) != "d") cat(" --> ",k1,"",f,"", k2, " (ok): only difference is NA (matrix) and NaN/Inf (Matrix)\n") else if(isTRUE(all(eq | (nr4 & Matrix:::is0(R4))))) cat(" --> 'ok': only difference is 'NA' (matrix) and 0 (Matrix)\n") else stop("differing \"too much\"") } } cat("i") } } } cat("\n") } } stopifnot(identical(lm2, lm1 & lm2), identical(lm1, lm1 | lm2)) cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons'' Matrix/tests/write-read.R0000644000175100001440000000334611200260001015050 0ustar hornikuserslibrary(Matrix) #### Read / Write (sparse) Matrix objects ---------------------- ### Rebuild the 'mm' example matrix, now in KNex data ### This is no longer really important, as we now use ### ../data/KNex.R which creates the S4 object *every time* data(KNex) ## recreate 'mm' from list : sNms <- c("Dim", "i","p","x") L <- lapply(sNms, function(SN) slot(KNex$mm, SN)); names(L) <- sNms mm2 <- new(class(KNex$mm)) for (n in sNms) slot(mm2, n) <- L[[n]] stopifnot(validObject(mm2), identical(mm2, KNex$mm)) L$y <- KNex$y ## save(L, file = "/u/maechler/R/Pkgs/Matrix/inst/external/KNex_slots.rda") ## recreate 'mm' from ASCI file : mmT <- as(KNex$mm, "dgTMatrix") str(mmT) mm3 <- cbind(i = mmT@i, j = mmT@j, x = mmT@x) write.table(mm3, file = "mm-Matrix.tab", row.names=FALSE)# -> ASCII version str(mmr <- read.table("mm-Matrix.tab", header = TRUE)) mmr$i <- as.integer(mmr$i) mmr$j <- as.integer(mmr$j) mmN <- with(mmr, new("dgTMatrix", Dim = c(max(i)+1:1,max(j)+1:1), i = i, j = j, x = x)) stopifnot(identical(mmT, mmN)) # !! ## weaker (and hence TRUE too): stopifnot(all.equal(as(mmN, "matrix"), as(mmT, "matrix"), tol=0)) mm <- as(mmN, "dgCMatrix") stopifnot(all.equal(mm, KNex$mm)) ## save(mm, file = "....../Matrix/data/mm.rda", compress = TRUE) A <- Matrix(c(1,0,3,0,0,5), 10, 10, sparse = TRUE) # warning about [6] vs [10] (fname <- file.path(tempdir(), "kk.mm")) writeMM(A, fname) (B <- readMM(fname)) validObject(B) Bc <- as(B, "CsparseMatrix") stopifnot(identical(A, Bc)) fname <- system.file("external", "wrong.mtx", package = "Matrix") r <- try(readMM(fname)) stopifnot(inherits(r, "try-error"), length(grep("readMM.*row.*1:nr", r)) == 1) ## gave a much less intelligible error message Matrix/src/0000755000175100001440000000000012271765426012337 5ustar hornikusersMatrix/src/Mutils.c0000644000175100001440000007776312271765436014005 0ustar hornikusers#include #include "Mutils.h" #include // La_norm_type() & La_rcond_type() have been in R_ext/Lapack.h // but have still not been available to package writers ... char La_norm_type(const char *typstr) { char typup; if (strlen(typstr) != 1) error( _("argument type[1]='%s' must be a one-letter character string"), typstr); typup = toupper(*typstr); if (typup == '1') typup = 'O'; /* alias */ else if (typup == 'E') typup = 'F'; else if (typup != 'M' && typup != 'O' && typup != 'I' && typup != 'F') error(_("argument type[1]='%s' must be one of 'M','1','O','I','F' or 'E'"), typstr); return typup; } char La_rcond_type(const char *typstr) { char typup; if (strlen(typstr) != 1) error( _("argument type[1]='%s' must be a one-letter character string"), typstr); typup = toupper(*typstr); if (typup == '1') typup = 'O'; /* alias */ else if (typup != 'O' && typup != 'I') error(_("argument type[1]='%s' must be one of '1','O', or 'I'"), typstr); return typup; } double get_double_by_name(SEXP obj, char *nm) { SEXP nms = getAttrib(obj, R_NamesSymbol); int i, len = length(obj); if ((!isReal(obj)) || (length(obj) > 0 && nms == R_NilValue)) error(_("object must be a named, numeric vector")); for (i = 0; i < len; i++) { if (!strcmp(nm, CHAR(STRING_ELT(nms, i)))) { return REAL(obj)[i]; } } return R_NaReal; } SEXP set_double_by_name(SEXP obj, double val, char *nm) { SEXP nms = getAttrib(obj, R_NamesSymbol); int i, len = length(obj); if ((!isReal(obj)) || (length(obj) > 0 && nms == R_NilValue)) error(_("object must be a named, numeric vector")); for (i = 0; i < len; i++) { if (!strcmp(nm, CHAR(STRING_ELT(nms, i)))) { REAL(obj)[i] = val; return obj; } } { SEXP nx = PROTECT(allocVector(REALSXP, len + 1)), nnms = allocVector(STRSXP, len + 1); setAttrib(nx, R_NamesSymbol, nnms); for (i = 0; i < len; i++) { REAL(nx)[i] = REAL(obj)[i]; SET_STRING_ELT(nnms, i, duplicate(STRING_ELT(nms, i))); } REAL(nx)[len] = val; SET_STRING_ELT(nnms, len, mkChar(nm)); UNPROTECT(1); return nx; } } SEXP as_det_obj(double val, int log, int sign) { SEXP det = PROTECT(allocVector(VECSXP, 2)), nms = PROTECT(allocVector(STRSXP, 2)), vv = PROTECT(ScalarReal(val)); setAttrib(det, R_NamesSymbol, nms); SET_STRING_ELT(nms, 0, mkChar("modulus")); SET_STRING_ELT(nms, 1, mkChar("sign")); setAttrib(vv, install("logarithm"), ScalarLogical(log)); SET_VECTOR_ELT(det, 0, vv); SET_VECTOR_ELT(det, 1, ScalarInteger(sign)); setAttrib(det, R_ClassSymbol, mkString("det")); UNPROTECT(3); return det; } SEXP get_factors(SEXP obj, char *nm) { SEXP fac = GET_SLOT(obj, Matrix_factorSym), nms = getAttrib(fac, R_NamesSymbol); int i, len = length(fac); if ((!isNewList(fac)) || (length(fac) > 0 && nms == R_NilValue)) error(_("'factors' slot must be a named list")); for (i = 0; i < len; i++) { if (!strcmp(nm, CHAR(STRING_ELT(nms, i)))) { return VECTOR_ELT(fac, i); } } return R_NilValue; } /** * Caches 'val' in the 'factors' slot of obj, i.e. modifies obj, and * returns val. * In the past this function installed a duplicate of * factors slot for obj then returned the (typically unprotected) * val. This is now changed to return the duplicate, which will be * protected if obj is protected. */ SEXP set_factors(SEXP obj, SEXP val, char *nm) { SEXP fac = GET_SLOT(obj, Matrix_factorSym), nms = getAttrib(fac, R_NamesSymbol); int i, len = length(fac); if ((!isNewList(fac)) || (length(fac) > 0 && nms == R_NilValue)) error(_("'factors' slot must be a named list")); PROTECT(val); /* set_factors(..) may be called as "finalizer" after UNPROTECT()*/ // if there's already a 'nm' factor, we replace it and return: for (i = 0; i < len; i++) { if (!strcmp(nm, CHAR(STRING_ELT(nms, i)))) { SET_VECTOR_ELT(fac, i, duplicate(val)); UNPROTECT(1); return val; } } // Otherwise: create a new 'nm' entry in the 'factors' list: // create a list of length (len + 1), SEXP nfac = PROTECT(allocVector(VECSXP, len + 1)), nnms = PROTECT(allocVector(STRSXP, len + 1)); setAttrib(nfac, R_NamesSymbol, nnms); // copy all the previous entries, for (i = 0; i < len; i++) { SET_VECTOR_ELT(nfac, i, VECTOR_ELT(fac, i)); SET_STRING_ELT(nnms, i, duplicate(STRING_ELT(nms, i))); } // and add the new entry at the end. SET_VECTOR_ELT(nfac, len, duplicate(val)); SET_STRING_ELT(nnms, len, mkChar(nm)); SET_SLOT(obj, Matrix_factorSym, nfac); UNPROTECT(3); return VECTOR_ELT(nfac, len); } // R interface [for updating the '@ factors' slot of a function *argument* [CARE!] SEXP R_set_factors(SEXP obj, SEXP val, SEXP name) { return set_factors(obj, val, (char *)CHAR(asChar(name))); } #if 0 /* unused */ /* useful for all the ..CMatrix classes (and ..R by [0] <-> [1]); but unused */ SEXP CMatrix_set_Dim(SEXP x, int nrow) { int *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)); dims[0] = nrow; dims[1] = length(GET_SLOT(x, Matrix_pSym)) - 1; return x; } #endif /* unused */ /* Fill in the "trivial remainder" in n*m array ; * typically the 'x' slot of a "dtrMatrix" : * But should be usable for double/logical/int/complex : */ #define MAKE_TRIANGULAR_BODY(_TO_, _FROM_, _ZERO_, _ONE_) \ { \ int i, j, *dims = INTEGER(GET_SLOT(_FROM_, Matrix_DimSym)); \ int n = dims[0], m = dims[1]; \ \ if (*uplo_P(_FROM_) == 'U') { \ for (j = 0; j < n; j++) \ for (i = j+1; i < m; i++) \ _TO_[i + j*m] = _ZERO_; \ } else { \ for (j = 1; j < n; j++) \ for (i = 0; i < j && i < m; i++) \ _TO_[i + j*m] = _ZERO_; \ } \ if (*diag_P(_FROM_) == 'U') { \ j = (n < m) ? n : m; \ for (i = 0; i < j; i++) \ _TO_[i * (m + 1)] = _ONE_; \ } \ } void make_d_matrix_triangular(double *to, SEXP from) MAKE_TRIANGULAR_BODY(to, from, 0., 1.) void make_i_matrix_triangular(int *to, SEXP from) MAKE_TRIANGULAR_BODY(to, from, 0, 1) /* Should work for double/logical/int/complex : */ #define MAKE_SYMMETRIC_BODY(_TO_, _FROM_) \ { \ int i, j, n = INTEGER(GET_SLOT(_FROM_, Matrix_DimSym))[0]; \ \ if (*uplo_P(_FROM_) == 'U') { \ for (j = 0; j < n; j++) \ for (i = j+1; i < n; i++) \ _TO_[i + j*n] = _TO_[j + i*n]; \ } else { \ for (j = 1; j < n; j++) \ for (i = 0; i < j && i < n; i++) \ _TO_[i + j*n] = _TO_[j + i*n]; \ } \ } void make_d_matrix_symmetric(double *to, SEXP from) MAKE_SYMMETRIC_BODY(to, from) void make_i_matrix_symmetric(int *to, SEXP from) MAKE_SYMMETRIC_BODY(to, from) #define Matrix_Error_Bufsiz 4096 /** * Check validity of 1-letter string from a set of possible values * (typically used in S4 validity method) * * @param sP * @param vals a string containing the possible valid letters * @param nm the name of the slot being checked * * @return a SEXP, either NULL (= success) or an error message */ SEXP check_scalar_string(SEXP sP, char *vals, char *nm) { SEXP val = ScalarLogical(1); char *buf; /* only allocate when needed: in good case, none is needed */ #define SPRINTF buf = Alloca(Matrix_Error_Bufsiz, char); R_CheckStack(); sprintf if (length(sP) != 1) { SPRINTF(buf, _("'%s' slot must have length 1"), nm); } else { const char *str = CHAR(STRING_ELT(sP, 0)); if (strlen(str) != 1) { SPRINTF(buf, _("'%s' must have string length 1"), nm); } else { int i, len; for (i = 0, len = strlen(vals); i < len; i++) { if (str[0] == vals[i]) return R_NilValue; } SPRINTF(buf, _("'%s' must be in '%s'"), nm, vals); } } /* 'error' returns : */ val = mkString(buf); return val; #undef SPRINTF } /* FIXME? Something like this should be part of the R API ? * But then, R has the more general compute_identical() * in src/main/identical.c: Rboolean compute_identical(SEXP x, SEXP y); */ Rboolean equal_string_vectors(SEXP s1, SEXP s2) { Rboolean n1 = isNull(s1), n2 = isNull(s2); if (n1 || n2) return (n1 == n2) ? TRUE : FALSE; else if (TYPEOF(s1) != STRSXP || TYPEOF(s2) != STRSXP) { error(_("'s1' and 's2' must be \"character\" vectors")); return FALSE; /* -Wall */ } else { int n = LENGTH(s1), i; if (n != LENGTH(s2)) return FALSE; for(i = 0; i < n; i++) { /* note that compute_identical() code for STRSXP is careful about NA's which we don't need */ if(strcmp(CHAR(STRING_ELT(s1, i)), CHAR(STRING_ELT(s2, i)))) return FALSE; } return TRUE; /* they *are* equal */ } } SEXP dense_nonpacked_validate(SEXP obj) { int *dims = INTEGER(GET_SLOT(obj, Matrix_DimSym)); if ((dims[0] * dims[1]) != length(GET_SLOT(obj, Matrix_xSym))) return mkString(_("length of x slot != prod(Dim)")); return ScalarLogical(1); } #define PACKED_TO_FULL(TYPE) \ TYPE *packed_to_full_ ## TYPE(TYPE *dest, const TYPE *src, \ int n, enum CBLAS_UPLO uplo) \ { \ int i, j, pos = 0; \ \ AZERO(dest, n*n); \ for (j = 0; j < n; j++) { \ switch(uplo) { \ case UPP: \ for (i = 0; i <= j; i++) dest[i + j * n] = src[pos++]; \ break; \ case LOW: \ for (i = j; i < n; i++) dest[i + j * n] = src[pos++]; \ break; \ default: \ error(_("'uplo' must be UPP or LOW")); \ } \ } \ return dest; \ } PACKED_TO_FULL(double) PACKED_TO_FULL(int) #define FULL_TO_PACKED(TYPE) \ TYPE *full_to_packed_ ## TYPE(TYPE *dest, const TYPE *src, int n, \ enum CBLAS_UPLO uplo, enum CBLAS_DIAG diag) \ { \ int i, j, pos = 0; \ \ for (j = 0; j < n; j++) { \ switch(uplo) { \ case UPP: \ for (i = 0; i <= j; i++) \ dest[pos++] = (i == j && diag== UNT) ? 1 : src[i + j*n]; \ break; \ case LOW: \ for (i = j; i < n; i++) \ dest[pos++] = (i == j && diag== UNT) ? 1 : src[i + j*n]; \ break; \ default: \ error(_("'uplo' must be UPP or LOW")); \ } \ } \ return dest; \ } FULL_TO_PACKED(double) FULL_TO_PACKED(int) /** * Copy the diagonal elements of the packed denseMatrix x to dest * * @param dest vector of length ncol(x) * @param x (pointer to) a "d?pMatrix" object * @param n number of columns in the matrix represented by x * * @return dest */ void d_packed_getDiag(double *dest, SEXP x, int n) { double *xx = REAL(GET_SLOT(x, Matrix_xSym)); #define END_packed_getDiag \ int j, pos = 0; \ \ if (*uplo_P(x) == 'U') { \ for(pos= 0, j=0; j < n; pos += 1+(++j)) dest[j] = xx[pos]; \ } else { \ for(pos= 0, j=0; j < n; pos += (n - j), j++) dest[j] = xx[pos]; \ } \ return END_packed_getDiag; } void l_packed_getDiag(int *dest, SEXP x, int n) { int *xx = LOGICAL(GET_SLOT(x, Matrix_xSym)); END_packed_getDiag; } #undef END_packed_getDiag //---------------------------------------------------------------------- SEXP d_packed_setDiag(double *diag, int l_d, SEXP x, int n) { #define SET_packed_setDiag \ SEXP ret = PROTECT(duplicate(x)), \ r_x = GET_SLOT(ret, Matrix_xSym); \ Rboolean d_full = (l_d == n); \ if (!d_full && l_d != 1) \ error("replacement diagonal has wrong length") #define END_packed_setDiag \ int j, pos = 0; \ \ if (*uplo_P(x) == 'U') { \ if(d_full) \ for(pos= 0, j=0; j < n; pos += 1+(++j)) xx[pos] = diag[j]; \ else /* l_d == 1 */ \ for(pos= 0, j=0; j < n; pos += 1+(++j)) xx[pos] = *diag; \ } else { \ if(d_full) \ for(pos= 0, j=0; j < n; pos += (n - j), j++) xx[pos] = diag[j]; \ else /* l_d == 1 */ \ for(pos= 0, j=0; j < n; pos += (n - j), j++) xx[pos] = *diag; \ } \ UNPROTECT(1); \ return ret SET_packed_setDiag; double *xx = REAL(r_x); END_packed_setDiag; } SEXP l_packed_setDiag(int *diag, int l_d, SEXP x, int n) { SET_packed_setDiag; int *xx = LOGICAL(r_x); END_packed_setDiag; } #define tr_END_packed_setDiag \ if (*diag_P(x) == 'U') { /* uni-triangular */ \ /* after setting, typically is not uni-triangular anymore: */ \ SET_STRING_ELT(GET_SLOT(ret, Matrix_diagSym), 0, mkChar("N")); \ } \ END_packed_setDiag SEXP tr_d_packed_setDiag(double *diag, int l_d, SEXP x, int n) { SET_packed_setDiag; double *xx = REAL(r_x); tr_END_packed_setDiag; } SEXP tr_l_packed_setDiag(int *diag, int l_d, SEXP x, int n) { SET_packed_setDiag; int *xx = LOGICAL(r_x); tr_END_packed_setDiag; } #undef SET_packed_setDiag #undef END_packed_setDiag #undef tr_END_packed_setDiag //---------------------------------------------------------------------- SEXP d_packed_addDiag(double *diag, int l_d, SEXP x, int n) { SEXP ret = PROTECT(duplicate(x)), r_x = GET_SLOT(ret, Matrix_xSym); double *xx = REAL(r_x); int j, pos = 0; if (*uplo_P(x) == 'U') { for(pos= 0, j=0; j < n; pos += 1+(++j)) xx[pos] += diag[j]; } else { for(pos= 0, j=0; j < n; pos += (n - j), j++) xx[pos] += diag[j]; } UNPROTECT(1); return ret; } SEXP tr_d_packed_addDiag(double *diag, int l_d, SEXP x, int n) { SEXP ret = PROTECT(d_packed_addDiag(diag, l_d, x, n)); if (*diag_P(x) == 'U') /* uni-triangular */ SET_STRING_ELT(GET_SLOT(ret, Matrix_diagSym), 0, mkChar("N")); UNPROTECT(1); return ret; } //---------------------------------------------------------------------- void tr_d_packed_getDiag(double *dest, SEXP x, int n) { if (*diag_P(x) == 'U') { for (int j = 0; j < n; j++) dest[j] = 1.; } else { d_packed_getDiag(dest, x, n); } return; } void tr_l_packed_getDiag( int *dest, SEXP x, int n) { if (*diag_P(x) == 'U') for (int j = 0; j < n; j++) dest[j] = 1; else l_packed_getDiag(dest, x, n); return; } SEXP Matrix_expand_pointers(SEXP pP) { int n = length(pP) - 1; int *p = INTEGER(pP); SEXP ans = PROTECT(allocVector(INTSXP, p[n])); expand_cmprPt(n, p, INTEGER(ans)); UNPROTECT(1); return ans; } /** * Return the element of a given name from a named list * * @param list * @param nm name of desired element * * @return element of list with name nm */ SEXP Matrix_getElement(SEXP list, char *nm) { SEXP names = getAttrib(list, R_NamesSymbol); int i; for (i = 0; i < LENGTH(names); i++) if (!strcmp(CHAR(STRING_ELT(names, i)), nm)) return(VECTOR_ELT(list, i)); return R_NilValue; } /** * Zero a square matrix of size nc then copy a vector to the diagonal * * @param dest destination array of length nc * nc * @param A pointer to a square Matrix object * * @return dest */ static double * install_diagonal(double *dest, SEXP A) { int nc = INTEGER(GET_SLOT(A, Matrix_DimSym))[0]; int i, ncp1 = nc + 1, unit = *diag_P(A) == 'U'; double *ax = REAL(GET_SLOT(A, Matrix_xSym)); AZERO(dest, nc * nc); for (i = 0; i < nc; i++) dest[i * ncp1] = (unit) ? 1. : ax[i]; return dest; } static int * install_diagonal_int(int *dest, SEXP A) { int nc = INTEGER(GET_SLOT(A, Matrix_DimSym))[0]; int i, ncp1 = nc + 1, unit = *diag_P(A) == 'U'; int *ax = INTEGER(GET_SLOT(A, Matrix_xSym)); AZERO(dest, nc * nc); for (i = 0; i < nc; i++) dest[i * ncp1] = (unit) ? 1 : ax[i]; return dest; } /** Duplicate a [dln]denseMatrix _or_ a numeric matrix or even vector as * a [dln]geMatrix. * This is for the many "*_matrix_{prod,crossprod,tcrossprod, etc.}" * functions that work with both classed and unclassed matrices. * * @param A either a denseMatrix object or a matrix object */ /* NOTA BENE: If you enlarge this list, do change '14' and '6' below ! * --------- ddiMatrix & ldiMatrix are no longer ddense or ldense on the R level, * --- --- but are still dealt with here. */ #define ddense_CLASSES \ "dgeMatrix", "dtrMatrix", \ "dsyMatrix", "dpoMatrix", "ddiMatrix", \ "dtpMatrix", "dspMatrix", "dppMatrix", \ /* sub classes of those above:*/ \ /* dtr */ "Cholesky", "LDL", "BunchKaufman", \ /* dtp */ "pCholesky", "pBunchKaufman", \ /* dpo */ "corMatrix" #define ldense_CLASSES \ "lgeMatrix", "ltrMatrix", \ "lsyMatrix", "ldiMatrix", \ "ltpMatrix", "lspMatrix" #define ndense_CLASSES \ "ngeMatrix", "ntrMatrix", \ "nsyMatrix", \ "ntpMatrix", "nspMatrix" /* Generalized -- "geMatrix" -- dispatch where needed : */ SEXP dup_mMatrix_as_geMatrix(SEXP A) { SEXP ans, ad = R_NilValue, an = R_NilValue; /* -Wall */ static const char *valid[] = { "_NOT_A_CLASS_",/* *_CLASSES defined in ./Mutils.h */ ddense_CLASSES, /* 14 */ ldense_CLASSES, /* 6 */ ndense_CLASSES, /* 5 */ ""}; int sz, ctype = Matrix_check_class_etc(A, valid), nprot = 1; enum dense_enum { ddense, ldense, ndense } M_type = ddense /* -Wall */; if (ctype > 0) { /* a [nld]denseMatrix object */ ad = GET_SLOT(A, Matrix_DimSym); an = GET_SLOT(A, Matrix_DimNamesSym); M_type = (ctype <= 14) ? ddense : ((ctype <= 14+6) ? ldense : ndense); } else if (ctype < 0) { /* not a (recognized) classed matrix */ if (isReal(A)) M_type = ddense; else if (isInteger(A)) { A = PROTECT(coerceVector(A, REALSXP)); nprot++; M_type = ddense; } else if (isLogical(A)) M_type = ldense; else error(_("invalid class '%s' to dup_mMatrix_as_geMatrix"), class_P(A)); #define DUP_MMATRIX_NON_CLASS \ if (isMatrix(A)) { /* "matrix" */ \ ad = getAttrib(A, R_DimSymbol); \ an = getAttrib(A, R_DimNamesSymbol); \ } else {/* maybe "numeric" (incl integer,logical) --> (n x 1) */ \ int* dd = INTEGER(ad = PROTECT(allocVector(INTSXP, 2))); \ nprot++; \ dd[0] = LENGTH(A); \ dd[1] = 1; \ SEXP nms = getAttrib(A, R_NamesSymbol); \ if(nms != R_NilValue) { \ an = PROTECT(allocVector(VECSXP, 2)); \ nprot++; \ SET_VECTOR_ELT(an, 0, nms); \ /* not needed: SET_VECTOR_ELT(an, 1, R_NilValue); */ \ } /* else nms = NULL ==> an remains NULL */ \ } \ ctype = 0 DUP_MMATRIX_NON_CLASS; } ans = PROTECT(NEW_OBJECT(MAKE_CLASS(M_type == ddense ? "dgeMatrix" : (M_type == ldense ? "lgeMatrix" : "ngeMatrix")))); #define DUP_MMATRIX_SET_1 \ SET_SLOT(ans, Matrix_DimSym, duplicate(ad)); \ SET_SLOT(ans, Matrix_DimNamesSym, (LENGTH(an) == 2) ? \ duplicate(an): allocVector(VECSXP, 2)); \ sz = INTEGER(ad)[0] * INTEGER(ad)[1] DUP_MMATRIX_SET_1; if(M_type == ddense) { /* ddense -> dge */ double *ansx; #define DUP_MMATRIX_ddense_CASES \ ansx = REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, sz)); \ switch(ctype) { \ case 0: /* unclassed real matrix */ \ Memcpy(ansx, REAL(A), sz); \ break; \ case 1: /* dgeMatrix */ \ Memcpy(ansx, REAL(GET_SLOT(A, Matrix_xSym)), sz); \ break; \ case 2: /* dtrMatrix and subclasses */ \ case 9: case 10: case 11: /* --- Cholesky, LDL, BunchKaufman */ \ Memcpy(ansx, REAL(GET_SLOT(A, Matrix_xSym)), sz); \ make_d_matrix_triangular(ansx, A); \ break; \ case 3: /* dsyMatrix */ \ case 4: /* dpoMatrix + subclass */ \ case 14: /* --- corMatrix */ \ Memcpy(ansx, REAL(GET_SLOT(A, Matrix_xSym)), sz); \ make_d_matrix_symmetric(ansx, A); \ break; \ case 5: /* ddiMatrix */ \ install_diagonal(ansx, A); \ break; \ case 6: /* dtpMatrix + subclasses */ \ case 12: case 13: /* --- pCholesky, pBunchKaufman */ \ packed_to_full_double(ansx, REAL(GET_SLOT(A, Matrix_xSym)), \ INTEGER(ad)[0], \ *uplo_P(A) == 'U' ? UPP : LOW); \ make_d_matrix_triangular(ansx, A); \ break; \ case 7: /* dspMatrix */ \ case 8: /* dppMatrix */ \ packed_to_full_double(ansx, REAL(GET_SLOT(A, Matrix_xSym)), \ INTEGER(ad)[0], \ *uplo_P(A) == 'U' ? UPP : LOW); \ make_d_matrix_symmetric(ansx, A); \ break; \ } /* switch(ctype) */ DUP_MMATRIX_ddense_CASES } else { /* M_type == ldense || M_type = ndense */ /* ldense -> lge */ /* ndense -> nge */ int *ansx = LOGICAL(ALLOC_SLOT(ans, Matrix_xSym, LGLSXP, sz)); switch(ctype) { case 0: /* unclassed logical matrix */ Memcpy(ansx, LOGICAL(A), sz); break; case 1+14: /* lgeMatrix */ case 1+14+6: /* ngeMatrix */ Memcpy(ansx, LOGICAL(GET_SLOT(A, Matrix_xSym)), sz); break; case 2+14: /* ltrMatrix */ case 2+14+6: /* ntrMatrix */ Memcpy(ansx, LOGICAL(GET_SLOT(A, Matrix_xSym)), sz); make_i_matrix_triangular(ansx, A); break; case 3+14: /* lsyMatrix */ case 3+14+6: /* nsyMatrix */ Memcpy(ansx, LOGICAL(GET_SLOT(A, Matrix_xSym)), sz); make_i_matrix_symmetric(ansx, A); break; case 4+14: /* ldiMatrix */ case 4+14+6: /* ndiMatrix */ install_diagonal_int(ansx, A); break; case 5+14: /* ltpMatrix */ case 5+14+6: /* ntpMatrix */ packed_to_full_int(ansx, LOGICAL(GET_SLOT(A, Matrix_xSym)), INTEGER(ad)[0], *uplo_P(A) == 'U' ? UPP : LOW); make_i_matrix_triangular(ansx, A); break; case 6+14: /* lspMatrix */ case 6+14+6: /* nspMatrix */ packed_to_full_int(ansx, LOGICAL(GET_SLOT(A, Matrix_xSym)), INTEGER(ad)[0], *uplo_P(A) == 'U' ? UPP : LOW); make_i_matrix_symmetric(ansx, A); break; default: error(_("unexpected ctype = %d in dup_mMatrix_as_geMatrix"), ctype); } /* switch(ctype) */ } /* if(M_type == .) */ UNPROTECT(nprot); return ans; } SEXP dup_mMatrix_as_dgeMatrix(SEXP A) { SEXP ans = PROTECT(NEW_OBJECT(MAKE_CLASS("dgeMatrix"))), ad = R_NilValue , an = R_NilValue; /* -Wall */ static const char *valid[] = {"_NOT_A_CLASS_", ddense_CLASSES, ""}; int ctype = Matrix_check_class_etc(A, valid), nprot = 1, sz; double *ansx; if (ctype > 0) { /* a ddenseMatrix object */ ad = GET_SLOT(A, Matrix_DimSym); an = GET_SLOT(A, Matrix_DimNamesSym); } else if (ctype < 0) { /* not a (recognized) classed matrix */ DUP_MMATRIX_NON_CLASS; if (isInteger(A) || isLogical(A)) { A = PROTECT(coerceVector(A, REALSXP)); nprot++; } if (!isReal(A)) error(_("invalid class '%s' to dup_mMatrix_as_dgeMatrix"), class_P(A)); } DUP_MMATRIX_SET_1; DUP_MMATRIX_ddense_CASES UNPROTECT(nprot); return ans; } SEXP new_dgeMatrix(int nrow, int ncol) { SEXP ans = PROTECT(NEW_OBJECT(MAKE_CLASS("dgeMatrix"))), ad = PROTECT(allocVector(INTSXP, 2)); INTEGER(ad)[0] = nrow; INTEGER(ad)[1] = ncol; SET_SLOT(ans, Matrix_DimSym, ad); SET_SLOT(ans, Matrix_DimNamesSym, allocVector(VECSXP, 2)); ALLOC_SLOT(ans, Matrix_xSym, REALSXP, nrow * ncol); UNPROTECT(2); return ans; } /** * Encode Matrix index (i,j) |--> i + j * nrow {i,j : 0-origin} * * @param ij: 2-column integer matrix * @param di: dim(.), i.e. length 2 integer vector * @param chk_bnds: logical indicating 0 <= ij[,k] < di[k] need to be checked. * * @return encoded index; integer if prod(dim) is small; double otherwise */ SEXP m_encodeInd(SEXP ij, SEXP di, SEXP chk_bnds) { SEXP ans; int *ij_di = NULL, n, *Di = INTEGER(di), *IJ, *j_; Rboolean check_bounds = asLogical(chk_bnds); ij = PROTECT(coerceVector(ij, INTSXP)); if(!isMatrix(ij) || (ij_di = INTEGER(getAttrib(ij, R_DimSymbol)))[1] != 2) error(_("Argument ij must be 2-column integer matrix")); n = ij_di[0]; IJ = INTEGER(ij); j_ = IJ+n;/* pointer offset! */ if((Di[0] * (double) Di[1]) >= 1 + (double)INT_MAX) { /* need double */ ans = PROTECT(allocVector(REALSXP, n)); double *ii = REAL(ans), nr = (double) Di[0]; #define do_ii_FILL(_i_, _j_) \ int i; \ if(check_bounds) { \ for(i=0; i < n; i++) { \ if(_i_[i] == NA_INTEGER || _j_[i] == NA_INTEGER) \ ii[i] = NA_INTEGER; \ else { \ if(_i_[i] < 0 || _i_[i] >= Di[0]) \ error(_("subscript 'i' out of bounds in M[ij]")); \ if(_j_[i] < 0 || _j_[i] >= Di[1]) \ error(_("subscript 'j' out of bounds in M[ij]")); \ ii[i] = _i_[i] + _j_[i] * nr; \ } \ } \ } else { \ for(i=0; i < n; i++) \ ii[i] = (_i_[i] == NA_INTEGER || _j_[i] == NA_INTEGER) \ ? NA_INTEGER : _i_[i] + _j_[i] * nr; \ } do_ii_FILL(IJ, j_); } else { ans = PROTECT(allocVector(INTSXP, n)); int *ii = INTEGER(ans), nr = Di[0]; do_ii_FILL(IJ, j_); } UNPROTECT(2); return ans; } /** * Encode Matrix index (i,j) |--> i + j * nrow {i,j : 0-origin} * * @param i: integer vector * @param j: integer vector of same length as 'i' * @param di: dim(.), i.e. length 2 integer vector * @param chk_bnds: logical indicating 0 <= ij[,k] < di[k] need to be checked. * * @return encoded index; integer if prod(dim) is small; double otherwise */ SEXP m_encodeInd2(SEXP i, SEXP j, SEXP di, SEXP chk_bnds) { SEXP ans; int n = LENGTH(i); int *Di = INTEGER(di), *i_, *j_; Rboolean check_bounds = asLogical(chk_bnds); if(LENGTH(j) != n || !isInteger(i) || !isInteger(j)) error(_("i and j must be integer vectors of the same length")); i_ = INTEGER(i); j_ = INTEGER(j); if((Di[0] * (double) Di[1]) >= 1 + (double)INT_MAX) { /* need double */ ans = PROTECT(allocVector(REALSXP, n)); double *ii = REAL(ans), nr = (double) Di[0]; do_ii_FILL(i_, j_); } else { ans = PROTECT(allocVector(INTSXP, n)); int *ii = INTEGER(ans), nr = Di[0]; do_ii_FILL(i_, j_); } UNPROTECT(1); return ans; } #undef do_ii_FILL // fails, as R_SVN_REVISION is a string #if R_SVN_REVISION < 60943 //__ no "if" so it *runs* in older R even if installed in R >= 2.15.2: //__ #if R_VERSION < R_Version(2, 15, 2) // it is *hidden* in earlier versions of R void copyListMatrix(SEXP s, SEXP t, Rboolean byrow) { SEXP pt, tmp; int i, j, nr, nc; R_xlen_t ns; nr = nrows(s); nc = ncols(s); ns = ((R_xlen_t) nr) * nc; pt = t; if(byrow) { R_xlen_t NR = nr; PROTECT(tmp = allocVector(STRSXP, ns)); for (i = 0; i < nr; i++) for (j = 0; j < nc; j++) { SET_STRING_ELT(tmp, i + j * NR, duplicate(CAR(pt))); pt = CDR(pt); if(pt == R_NilValue) pt = t; } for (i = 0; i < ns; i++) { SETCAR(s, STRING_ELT(tmp, i++)); s = CDR(s); } UNPROTECT(1); } else { for (i = 0; i < ns; i++) { SETCAR(s, duplicate(CAR(pt))); s = CDR(s); pt = CDR(pt); if(pt == R_NilValue) pt = t; } } } //__ #endif // Almost "Cut n Paste" from ...R../src/main/array.c do_matrix() : // used in ../R/Matrix.R as // // .External(Mmatrix, // data, nrow, ncol, byrow, dimnames, // missing(nrow), missing(ncol)) SEXP Mmatrix(SEXP args) { SEXP vals, ans, snr, snc, dimnames; int nr = 1, nc = 1, byrow, miss_nr, miss_nc; R_xlen_t lendat; args = CDR(args); /* skip 'name' */ vals = CAR(args); args = CDR(args); /* Supposedly as.vector() gave a vector type, but we check */ switch(TYPEOF(vals)) { case LGLSXP: case INTSXP: case REALSXP: case CPLXSXP: case STRSXP: case RAWSXP: case EXPRSXP: case VECSXP: break; default: error(_("'data' must be of a vector type")); } lendat = XLENGTH(vals); snr = CAR(args); args = CDR(args); snc = CAR(args); args = CDR(args); byrow = asLogical(CAR(args)); args = CDR(args); if (byrow == NA_INTEGER) error(_("invalid '%s' argument"), "byrow"); dimnames = CAR(args); args = CDR(args); miss_nr = asLogical(CAR(args)); args = CDR(args); miss_nc = asLogical(CAR(args)); if (!miss_nr) { if (!isNumeric(snr)) error(_("non-numeric matrix extent")); nr = asInteger(snr); if (nr == NA_INTEGER) error(_("invalid 'nrow' value (too large or NA)")); if (nr < 0) error(_("invalid 'nrow' value (< 0)")); } if (!miss_nc) { if (!isNumeric(snc)) error(_("non-numeric matrix extent")); nc = asInteger(snc); if (nc == NA_INTEGER) error(_("invalid 'ncol' value (too large or NA)")); if (nc < 0) error(_("invalid 'ncol' value (< 0)")); } if (miss_nr && miss_nc) { if (lendat > INT_MAX) error("data is too long"); nr = (int) lendat; } else if (miss_nr) { if (lendat > (double) nc * INT_MAX) error("data is too long"); nr = (int) ceil((double) lendat / (double) nc); } else if (miss_nc) { if (lendat > (double) nr * INT_MAX) error("data is too long"); nc = (int) ceil((double) lendat / (double) nr); } if(lendat > 0) { R_xlen_t nrc = (R_xlen_t) nr * nc; if (lendat > 1 && nrc % lendat != 0) { if (((lendat > nr) && (lendat / nr) * nr != lendat) || ((lendat < nr) && (nr / lendat) * lendat != nr)) warning(_("data length [%d] is not a sub-multiple or multiple of the number of rows [%d]"), lendat, nr); else if (((lendat > nc) && (lendat / nc) * nc != lendat) || ((lendat < nc) && (nc / lendat) * lendat != nc)) warning(_("data length [%d] is not a sub-multiple or multiple of the number of columns [%d]"), lendat, nc); } else if ((lendat > 1) && (nrc == 0)){ warning(_("data length exceeds size of matrix")); } } #ifndef LONG_VECTOR_SUPPORT if ((double)nr * (double)nc > INT_MAX) error(_("too many elements specified")); #endif PROTECT(ans = allocMatrix(TYPEOF(vals), nr, nc)); if(lendat) { if (isVector(vals)) copyMatrix(ans, vals, byrow); else copyListMatrix(ans, vals, byrow); } else if (isVector(vals)) { /* fill with NAs */ R_xlen_t N = (R_xlen_t) nr * nc, i; switch(TYPEOF(vals)) { case STRSXP: for (i = 0; i < N; i++) SET_STRING_ELT(ans, i, NA_STRING); break; case LGLSXP: for (i = 0; i < N; i++) LOGICAL(ans)[i] = NA_LOGICAL; break; case INTSXP: for (i = 0; i < N; i++) INTEGER(ans)[i] = NA_INTEGER; break; case REALSXP: for (i = 0; i < N; i++) REAL(ans)[i] = NA_REAL; break; case CPLXSXP: { Rcomplex na_cmplx; na_cmplx.r = NA_REAL; na_cmplx.i = 0; for (i = 0; i < N; i++) COMPLEX(ans)[i] = na_cmplx; } break; case RAWSXP: memset(RAW(ans), 0, N); break; default: /* don't fill with anything */ ; } } if(!isNull(dimnames)&& length(dimnames) > 0) ans = dimnamesgets(ans, dimnames); UNPROTECT(1); return ans; } #define TRUE_ ScalarLogical(1) #define FALSE_ ScalarLogical(0) // Fast implementation of [ originally in ../R/Auxiliaries.R ] // all0 <- function(x) !any(is.na(x)) && all(!x) ## ~= allFalse // allFalse <- function(x) !any(x) && !any(is.na(x)) ## ~= all0 SEXP R_all0(SEXP x) { R_xlen_t i, n = XLENGTH(x); if(n == 0) return TRUE_; switch(TYPEOF(x)) { case LGLSXP: { int *xx = LOGICAL(x); for(i=0; i < n; i++) if(xx[i] == NA_LOGICAL || xx[i] != 0) return FALSE_; return TRUE_; } case INTSXP: { int *xx = INTEGER(x); for(i=0; i < n; i++) if(xx[i] == NA_INTEGER || xx[i] != 0) return FALSE_; return TRUE_; } case REALSXP: { double *xx = REAL(x); for(i=0; i < n; i++) if(ISNAN(xx[i]) || xx[i] != 0.) return FALSE_; return TRUE_; } case RAWSXP: { unsigned char *xx = RAW(x); for(i=0; i < n; i++) if(xx[i] != 0) return FALSE_; return TRUE_; } } error(_("Argument must be numeric-like atomic vector")); return R_NilValue; // -Wall } // Fast implementation of [ originally in ../R/Auxiliaries.R ] // any0 <- function(x) isTRUE(any(x == 0)) ## ~= anyFalse // anyFalse <- function(x) isTRUE(any(!x)) ## ~= any0 SEXP R_any0(SEXP x) { R_xlen_t i, n = XLENGTH(x); if(n == 0) return FALSE_; switch(TYPEOF(x)) { case LGLSXP: { int *xx = LOGICAL(x); for(i=0; i < n; i++) if(xx[i] == 0) return TRUE_; return FALSE_; } case INTSXP: { int *xx = INTEGER(x); for(i=0; i < n; i++) if(xx[i] == 0) return TRUE_; return FALSE_; } case REALSXP: { double *xx = REAL(x); for(i=0; i < n; i++) if(xx[i] == 0.) return TRUE_; return FALSE_; } case RAWSXP: { unsigned char *xx = RAW(x); for(i=0; i < n; i++) if(xx[i] == 0) return TRUE_; return FALSE_; } } error(_("Argument must be numeric-like atomic vector")); return R_NilValue; // -Wall } #undef TRUE_ #undef FALSE_ Matrix/src/ldense.h0000644000175100001440000000060212271765436013761 0ustar hornikusers#ifndef MATRIX_LDENSE_H #define MATRIX_LDENSE_H #include "Mutils.h" SEXP lspMatrix_as_lsyMatrix(SEXP from, SEXP kind); SEXP lsyMatrix_as_lspMatrix(SEXP from, SEXP kind); SEXP lsyMatrix_as_lgeMatrix(SEXP from, SEXP kind); SEXP ltpMatrix_as_ltrMatrix(SEXP from, SEXP kind); SEXP ltrMatrix_as_ltpMatrix(SEXP from, SEXP kind); SEXP ltrMatrix_as_lgeMatrix(SEXP from, SEXP kind); #endif Matrix/src/dense.h0000644000175100001440000000062512271765436013612 0ustar hornikusers#ifndef MATRIX_DENSE_H #define MATRIX_DENSE_H #include "Rdefines.h" #include "R_ext/Lapack.h" SEXP lsq_dense_Chol(SEXP X, SEXP y); SEXP lsq_dense_QR(SEXP X, SEXP y); SEXP lapack_qr(SEXP Xin, SEXP tl); SEXP dense_to_Csparse(SEXP x); SEXP dense_band(SEXP x, SEXP k1, SEXP k2); SEXP dense_to_symmetric(SEXP x, SEXP uplo, SEXP symm_test); SEXP ddense_symmpart(SEXP x); SEXP ddense_skewpart(SEXP x); #endif Matrix/src/Makevars0000644000175100001440000000204412102041354014007 0ustar hornikusers# -*- Makefile -*- PKG_CPPFLAGS = -DNTIMER -I./SuiteSparse_config ## we use the BLAS and the LAPACK library: PKG_LIBS = $(SUBLIBS) $(LAPACK_LIBS) $(BLAS_LIBS) $(FLIBS) MkInclude = $(R_HOME)/etc${R_ARCH}/Makeconf include scripts/SOURCES_C.mkf OBJECTS = $(SOURCES_C:.c=.o) SUBDIRS = CHOLMOD COLAMD AMD SuiteSparse_config SUBLIBS = $(SUBDIRS:=.a) all: $(SHLIB) ## making src/*.o and in sublibs can be done simultaneously # for development: #$(SHLIB): $(OBJECTS) sublibraries # for real: $(SHLIB): $(OBJECTS) sublibs ## We have to clean here, to clean up between architectures: ## INSTALL only cleans src/*.o src/*$(SHLIB_EXT) for each arch sublibs: subclean sublibraries sublibraries: subclean @for d in $(SUBDIRS); do \ (cd $${d} && CFLAGS="$(CFLAGS)" CXXFLAGS="$(CXXFLAGS)" MkInclude="$(MkInclude)" $(MAKE) library) || exit 1; \ done clean: subclean @-rm -rf .libs _libs @-rm -f *.o $(SHLIB) subclean: @-rm -f *.a @for d in $(SUBDIRS); do \ (cd $${d} && MkInclude="$(MkInclude)" $(MAKE) clean) || exit 1; \ done include scripts/DEPS.mkf Matrix/src/Csparse.c0000644000175100001440000007023012271765436014106 0ustar hornikusers /* Sparse matrices in compressed column-oriented form */ #include "Csparse.h" #include "Tsparse.h" #include "chm_common.h" /** "Cheap" C version of Csparse_validate() - *not* sorting : */ Rboolean isValid_Csparse(SEXP x) { /* NB: we do *NOT* check a potential 'x' slot here, at all */ SEXP pslot = GET_SLOT(x, Matrix_pSym), islot = GET_SLOT(x, Matrix_iSym); int *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)), j, nrow = dims[0], ncol = dims[1], *xp = INTEGER(pslot), *xi = INTEGER(islot); if (length(pslot) != dims[1] + 1) return FALSE; if (xp[0] != 0) return FALSE; if (length(islot) < xp[ncol]) /* allow larger slots from over-allocation!*/ return FALSE; for (j = 0; j < xp[ncol]; j++) { if (xi[j] < 0 || xi[j] >= nrow) return FALSE; } for (j = 0; j < ncol; j++) { if (xp[j] > xp[j + 1]) return FALSE; } return TRUE; } SEXP Csparse_validate(SEXP x) { return Csparse_validate_(x, FALSE); } #define _t_Csparse_validate #include "t_Csparse_validate.c" #define _t_Csparse_sort #include "t_Csparse_validate.c" // R: .validateCsparse(x, sort.if.needed = FALSE) : SEXP Csparse_validate2(SEXP x, SEXP maybe_modify) { return Csparse_validate_(x, asLogical(maybe_modify)); } // R: Matrix:::.sortCsparse(x) : SEXP Csparse_sort (SEXP x) { int ok = Csparse_sort_2(x, TRUE); // modifying x directly if(!ok) warning(_("Csparse_sort(x): x is not a valid (apart from sorting) CsparseMatrix")); return x; } SEXP Rsparse_validate(SEXP x) { /* NB: we do *NOT* check a potential 'x' slot here, at all */ SEXP pslot = GET_SLOT(x, Matrix_pSym), jslot = GET_SLOT(x, Matrix_jSym); Rboolean sorted, strictly; int i, k, *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)), nrow = dims[0], ncol = dims[1], *xp = INTEGER(pslot), *xj = INTEGER(jslot); if (length(pslot) != dims[0] + 1) return mkString(_("slot p must have length = nrow(.) + 1")); if (xp[0] != 0) return mkString(_("first element of slot p must be zero")); if (length(jslot) < xp[nrow]) /* allow larger slots from over-allocation!*/ return mkString(_("last element of slot p must match length of slots j and x")); for (i = 0; i < length(jslot); i++) { if (xj[i] < 0 || xj[i] >= ncol) return mkString(_("all column indices must be between 0 and ncol-1")); } sorted = TRUE; strictly = TRUE; for (i = 0; i < nrow; i++) { if (xp[i] > xp[i+1]) return mkString(_("slot p must be non-decreasing")); if(sorted) for (k = xp[i] + 1; k < xp[i + 1]; k++) { if (xj[k] < xj[k - 1]) sorted = FALSE; else if (xj[k] == xj[k - 1]) strictly = FALSE; } } if (!sorted) /* cannot easily use cholmod_sort(.) ... -> "error out" :*/ return mkString(_("slot j is not increasing inside a column")); else if(!strictly) /* sorted, but not strictly */ return mkString(_("slot j is not *strictly* increasing inside a column")); return ScalarLogical(1); } /* Called from ../R/Csparse.R : */ /* Can only return [dln]geMatrix (no symm/triang); * FIXME: replace by non-CHOLMOD code ! */ SEXP Csparse_to_dense(SEXP x) { CHM_SP chxs = AS_CHM_SP__(x); /* This loses the symmetry property, since cholmod_dense has none, * BUT, much worse (FIXME!), it also transforms CHOLMOD_PATTERN ("n") matrices * to numeric (CHOLMOD_REAL) ones : */ CHM_DN chxd = cholmod_sparse_to_dense(chxs, &c); int Rkind = (chxs->xtype == CHOLMOD_PATTERN)? -1 : Real_kind(x); R_CheckStack(); return chm_dense_to_SEXP(chxd, 1, Rkind, GET_SLOT(x, Matrix_DimNamesSym)); } // FIXME: do not go via CHM (should not be too hard, to just *drop* the x-slot, right? SEXP Csparse_to_nz_pattern(SEXP x, SEXP tri) { CHM_SP chxs = AS_CHM_SP__(x); CHM_SP chxcp = cholmod_copy(chxs, chxs->stype, CHOLMOD_PATTERN, &c); int tr = asLogical(tri); R_CheckStack(); return chm_sparse_to_SEXP(chxcp, 1/*do_free*/, tr ? ((*uplo_P(x) == 'U') ? 1 : -1) : 0, 0, tr ? diag_P(x) : "", GET_SLOT(x, Matrix_DimNamesSym)); } // n.CMatrix --> [dli].CMatrix (not going through CHM!) SEXP nz_pattern_to_Csparse(SEXP x, SEXP res_kind) { return nz2Csparse(x, asInteger(res_kind)); } // n.CMatrix --> [dli].CMatrix (not going through CHM!) SEXP nz2Csparse(SEXP x, enum x_slot_kind r_kind) { const char *cl_x = class_P(x); if(cl_x[0] != 'n') error(_("not a 'n.CMatrix'")); if(cl_x[2] != 'C') error(_("not a CsparseMatrix")); int nnz = LENGTH(GET_SLOT(x, Matrix_iSym)); SEXP ans; char *ncl = alloca(strlen(cl_x) + 1); /* not much memory required */ strcpy(ncl, cl_x); double *dx_x; int *ix_x; ncl[0] = (r_kind == x_double ? 'd' : (r_kind == x_logical ? 'l' : /* else (for now): r_kind == x_integer : */ 'i')); PROTECT(ans = NEW_OBJECT(MAKE_CLASS(ncl))); // create a correct 'x' slot: switch(r_kind) { int i; case x_double: // 'd' dx_x = REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, nnz)); for (i=0; i < nnz; i++) dx_x[i] = 1.; break; case x_logical: // 'l' ix_x = LOGICAL(ALLOC_SLOT(ans, Matrix_xSym, LGLSXP, nnz)); for (i=0; i < nnz; i++) ix_x[i] = TRUE; break; case x_integer: // 'i' ix_x = INTEGER(ALLOC_SLOT(ans, Matrix_xSym, INTSXP, nnz)); for (i=0; i < nnz; i++) ix_x[i] = 1; break; default: error(_("nz2Csparse(): invalid/non-implemented r_kind = %d"), r_kind); } // now copy all other slots : slot_dup(ans, x, Matrix_iSym); slot_dup(ans, x, Matrix_pSym); slot_dup(ans, x, Matrix_DimSym); slot_dup(ans, x, Matrix_DimNamesSym); if(ncl[1] != 'g') { // symmetric or triangular ... slot_dup_if_has(ans, x, Matrix_uploSym); slot_dup_if_has(ans, x, Matrix_diagSym); } UNPROTECT(1); return ans; } SEXP Csparse_to_matrix(SEXP x, SEXP chk) { return chm_dense_to_matrix(cholmod_sparse_to_dense(AS_CHM_SP2(x, asLogical(chk)), &c), 1 /*do_free*/, GET_SLOT(x, Matrix_DimNamesSym)); } SEXP Csparse_to_vector(SEXP x) { return chm_dense_to_vector(cholmod_sparse_to_dense(AS_CHM_SP__(x), &c), 1); } SEXP Csparse_to_Tsparse(SEXP x, SEXP tri) { CHM_SP chxs = AS_CHM_SP__(x); CHM_TR chxt = cholmod_sparse_to_triplet(chxs, &c); int tr = asLogical(tri); int Rkind = (chxs->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0; R_CheckStack(); return chm_triplet_to_SEXP(chxt, 1, tr ? ((*uplo_P(x) == 'U') ? 1 : -1) : 0, Rkind, tr ? diag_P(x) : "", GET_SLOT(x, Matrix_DimNamesSym)); } /* this used to be called sCMatrix_to_gCMatrix(..) [in ./dsCMatrix.c ]: */ SEXP Csparse_symmetric_to_general(SEXP x) { CHM_SP chx = AS_CHM_SP__(x), chgx; int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0; R_CheckStack(); if (!(chx->stype)) error(_("Nonsymmetric matrix in Csparse_symmetric_to_general")); chgx = cholmod_copy(chx, /* stype: */ 0, chx->xtype, &c); /* xtype: pattern, "real", complex or .. */ return chm_sparse_to_SEXP(chgx, 1, 0, Rkind, "", GET_SLOT(x, Matrix_DimNamesSym)); } SEXP Csparse_general_to_symmetric(SEXP x, SEXP uplo) { int *adims = INTEGER(GET_SLOT(x, Matrix_DimSym)), n = adims[0]; if(n != adims[1]) { error(_("Csparse_general_to_symmetric(): matrix is not square!")); return R_NilValue; /* -Wall */ } CHM_SP chx = AS_CHM_SP__(x), chgx; int uploT = (*CHAR(STRING_ELT(uplo,0)) == 'U') ? 1 : -1; int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0; R_CheckStack(); chgx = cholmod_copy(chx, /* stype: */ uploT, chx->xtype, &c); /* xtype: pattern, "real", complex or .. */ return chm_sparse_to_SEXP(chgx, 1, 0, Rkind, "", GET_SLOT(x, Matrix_DimNamesSym)); } SEXP Csparse_transpose(SEXP x, SEXP tri) { /* TODO: lgCMatrix & igC* currently go via double prec. cholmod - * since cholmod (& cs) lacks sparse 'int' matrices */ CHM_SP chx = AS_CHM_SP__(x); int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0; CHM_SP chxt = cholmod_transpose(chx, chx->xtype, &c); SEXP dn = PROTECT(duplicate(GET_SLOT(x, Matrix_DimNamesSym))), tmp; int tr = asLogical(tri); R_CheckStack(); tmp = VECTOR_ELT(dn, 0); /* swap the dimnames */ SET_VECTOR_ELT(dn, 0, VECTOR_ELT(dn, 1)); SET_VECTOR_ELT(dn, 1, tmp); UNPROTECT(1); return chm_sparse_to_SEXP(chxt, 1, /* SWAP 'uplo' for triangular */ tr ? ((*uplo_P(x) == 'U') ? -1 : 1) : 0, Rkind, tr ? diag_P(x) : "", dn); } SEXP Csparse_Csparse_prod(SEXP a, SEXP b) { CHM_SP cha = AS_CHM_SP(a), chb = AS_CHM_SP(b), chc = cholmod_ssmult(cha, chb, /*out_stype:*/ 0, /* values:= is_numeric (T/F) */ cha->xtype > 0, /*out sorted:*/ 1, &c); const char *cl_a = class_P(a), *cl_b = class_P(b); char diag[] = {'\0', '\0'}; int uploT = 0; SEXP dn = PROTECT(allocVector(VECSXP, 2)); R_CheckStack(); #ifdef DEBUG_Matrix_verbose Rprintf("DBG Csparse_C*_prod(%s, %s)\n", cl_a, cl_b); #endif /* Preserve triangularity and even unit-triangularity if appropriate. * Note that in that case, the multiplication itself should happen * faster. But there's no support for that in CHOLMOD */ /* UGLY hack -- rather should have (fast!) C-level version of * is(a, "triangularMatrix") etc */ if (cl_a[1] == 't' && cl_b[1] == 't') /* FIXME: fails for "Cholesky","BunchKaufmann"..*/ if(*uplo_P(a) == *uplo_P(b)) { /* both upper, or both lower tri. */ uploT = (*uplo_P(a) == 'U') ? 1 : -1; if(*diag_P(a) == 'U' && *diag_P(b) == 'U') { /* return UNIT-triag. */ /* "remove the diagonal entries": */ chm_diagN2U(chc, uploT, /* do_realloc */ FALSE); diag[0]= 'U'; } else diag[0]= 'N'; } SET_VECTOR_ELT(dn, 0, /* establish dimnames */ duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), 0))); SET_VECTOR_ELT(dn, 1, duplicate(VECTOR_ELT(GET_SLOT(b, Matrix_DimNamesSym), 1))); UNPROTECT(1); return chm_sparse_to_SEXP(chc, 1, uploT, /*Rkind*/0, diag, dn); } SEXP Csparse_Csparse_crossprod(SEXP a, SEXP b, SEXP trans) { int tr = asLogical(trans); CHM_SP cha = AS_CHM_SP(a), chb = AS_CHM_SP(b), chTr, chc; const char *cl_a = class_P(a), *cl_b = class_P(b); char diag[] = {'\0', '\0'}; int uploT = 0; SEXP dn = PROTECT(allocVector(VECSXP, 2)); R_CheckStack(); chTr = cholmod_transpose((tr) ? chb : cha, chb->xtype, &c); chc = cholmod_ssmult((tr) ? cha : chTr, (tr) ? chTr : chb, /*out_stype:*/ 0, cha->xtype, /*out sorted:*/ 1, &c); cholmod_free_sparse(&chTr, &c); /* Preserve triangularity and unit-triangularity if appropriate; * see Csparse_Csparse_prod() for comments */ if (cl_a[1] == 't' && cl_b[1] == 't') if(*uplo_P(a) != *uplo_P(b)) { /* one 'U', the other 'L' */ uploT = (*uplo_P(b) == 'U') ? 1 : -1; if(*diag_P(a) == 'U' && *diag_P(b) == 'U') { /* return UNIT-triag. */ chm_diagN2U(chc, uploT, /* do_realloc */ FALSE); diag[0]= 'U'; } else diag[0]= 'N'; } SET_VECTOR_ELT(dn, 0, /* establish dimnames */ duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), (tr) ? 0 : 1))); SET_VECTOR_ELT(dn, 1, duplicate(VECTOR_ELT(GET_SLOT(b, Matrix_DimNamesSym), (tr) ? 0 : 1))); UNPROTECT(1); return chm_sparse_to_SEXP(chc, 1, uploT, /*Rkind*/0, diag, dn); } SEXP Csparse_dense_prod(SEXP a, SEXP b) { CHM_SP cha = AS_CHM_SP(a); SEXP b_M = PROTECT(mMatrix_as_dgeMatrix(b)); CHM_DN chb = AS_CHM_DN(b_M); CHM_DN chc = cholmod_allocate_dense(cha->nrow, chb->ncol, cha->nrow, chb->xtype, &c); SEXP dn = PROTECT(allocVector(VECSXP, 2)); double one[] = {1,0}, zero[] = {0,0}; int nprot = 2; R_CheckStack(); /* Tim Davis, please FIXME: currently (2010-11) *fails* when a is a pattern matrix:*/ if(cha->xtype == CHOLMOD_PATTERN) { /* warning(_("Csparse_dense_prod(): cholmod_sdmult() not yet implemented for pattern./ ngCMatrix" */ /* " --> slightly inefficient coercion")); */ // This *fails* to produce a CHOLMOD_REAL .. // CHM_SP chd = cholmod_l_copy(cha, cha->stype, CHOLMOD_REAL, &c); // --> use our Matrix-classes SEXP da = PROTECT(nz2Csparse(a, x_double)); nprot++; cha = AS_CHM_SP(da); } cholmod_sdmult(cha, 0, one, zero, chb, chc, &c); SET_VECTOR_ELT(dn, 0, /* establish dimnames */ duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), 0))); SET_VECTOR_ELT(dn, 1, duplicate(VECTOR_ELT(GET_SLOT(b_M, Matrix_DimNamesSym), 1))); UNPROTECT(nprot); return chm_dense_to_SEXP(chc, 1, 0, dn); } SEXP Csparse_dense_crossprod(SEXP a, SEXP b) { CHM_SP cha = AS_CHM_SP(a); SEXP b_M = PROTECT(mMatrix_as_dgeMatrix(b)); CHM_DN chb = AS_CHM_DN(b_M); CHM_DN chc = cholmod_allocate_dense(cha->ncol, chb->ncol, cha->ncol, chb->xtype, &c); SEXP dn = PROTECT(allocVector(VECSXP, 2)); int nprot = 2; double one[] = {1,0}, zero[] = {0,0}; R_CheckStack(); // -- see Csparse_dense_prod() above : if(cha->xtype == CHOLMOD_PATTERN) { SEXP da = PROTECT(nz2Csparse(a, x_double)); nprot++; cha = AS_CHM_SP(da); } cholmod_sdmult(cha, 1, one, zero, chb, chc, &c); SET_VECTOR_ELT(dn, 0, /* establish dimnames */ duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), 1))); SET_VECTOR_ELT(dn, 1, duplicate(VECTOR_ELT(GET_SLOT(b_M, Matrix_DimNamesSym), 1))); UNPROTECT(nprot); return chm_dense_to_SEXP(chc, 1, 0, dn); } /* Computes x'x or x x' -- *also* for Tsparse (triplet = TRUE) see Csparse_Csparse_crossprod above for x'y and x y' */ SEXP Csparse_crossprod(SEXP x, SEXP trans, SEXP triplet) { int trip = asLogical(triplet), tr = asLogical(trans); /* gets reversed because _aat is tcrossprod */ #ifdef AS_CHM_DIAGU2N_FIXED_FINALLY CHM_TR cht = trip ? AS_CHM_TR(x) : (CHM_TR) NULL; #else /* workaround needed:*/ SEXP xx = PROTECT(Tsparse_diagU2N(x)); CHM_TR cht = trip ? AS_CHM_TR__(xx) : (CHM_TR) NULL; #endif CHM_SP chcp, chxt, chx = (trip ? cholmod_triplet_to_sparse(cht, cht->nnz, &c) : AS_CHM_SP(x)); SEXP dn = PROTECT(allocVector(VECSXP, 2)); R_CheckStack(); if (!tr) chxt = cholmod_transpose(chx, chx->xtype, &c); chcp = cholmod_aat((!tr) ? chxt : chx, (int *) NULL, 0, chx->xtype, &c); if(!chcp) { UNPROTECT(1); error(_("Csparse_crossprod(): error return from cholmod_aat()")); } cholmod_band_inplace(0, chcp->ncol, chcp->xtype, chcp, &c); chcp->stype = 1; if (trip) cholmod_free_sparse(&chx, &c); if (!tr) cholmod_free_sparse(&chxt, &c); SET_VECTOR_ELT(dn, 0, /* establish dimnames */ duplicate(VECTOR_ELT(GET_SLOT(x, Matrix_DimNamesSym), (tr) ? 0 : 1))); SET_VECTOR_ELT(dn, 1, duplicate(VECTOR_ELT(dn, 0))); #ifdef AS_CHM_DIAGU2N_FIXED_FINALLY UNPROTECT(1); #else UNPROTECT(2); #endif return chm_sparse_to_SEXP(chcp, 1, 0, 0, "", dn); } /* Csparse_drop(x, tol): drop entries with absolute value < tol, i.e, * at least all "explicit" zeros */ SEXP Csparse_drop(SEXP x, SEXP tol) { const char *cl = class_P(x); /* dtCMatrix, etc; [1] = the second character =?= 't' for triangular */ int tr = (cl[1] == 't'); CHM_SP chx = AS_CHM_SP__(x); CHM_SP ans = cholmod_copy(chx, chx->stype, chx->xtype, &c); double dtol = asReal(tol); int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0; R_CheckStack(); if(!cholmod_drop(dtol, ans, &c)) error(_("cholmod_drop() failed")); return chm_sparse_to_SEXP(ans, 1, tr ? ((*uplo_P(x) == 'U') ? 1 : -1) : 0, Rkind, tr ? diag_P(x) : "", GET_SLOT(x, Matrix_DimNamesSym)); } SEXP Csparse_horzcat(SEXP x, SEXP y) { CHM_SP chx = AS_CHM_SP__(x), chy = AS_CHM_SP__(y); int Rk_x = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0, Rk_y = (chy->xtype != CHOLMOD_PATTERN) ? Real_kind(y) : 0, Rkind = /* logical if both x and y are */ (Rk_x == 1 && Rk_y == 1) ? 1 : 0; R_CheckStack(); /* TODO: currently drops dimnames - and we fix at R level */ return chm_sparse_to_SEXP(cholmod_horzcat(chx, chy, 1, &c), 1, 0, Rkind, "", R_NilValue); } SEXP Csparse_vertcat(SEXP x, SEXP y) { CHM_SP chx = AS_CHM_SP__(x), chy = AS_CHM_SP__(y); int Rk_x = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0, Rk_y = (chy->xtype != CHOLMOD_PATTERN) ? Real_kind(y) : 0, Rkind = /* logical if both x and y are */ (Rk_x == 1 && Rk_y == 1) ? 1 : 0; R_CheckStack(); /* TODO: currently drops dimnames - and we fix at R level */ return chm_sparse_to_SEXP(cholmod_vertcat(chx, chy, 1, &c), 1, 0, Rkind, "", R_NilValue); } SEXP Csparse_band(SEXP x, SEXP k1, SEXP k2) { CHM_SP chx = AS_CHM_SP__(x); int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0; CHM_SP ans = cholmod_band(chx, asInteger(k1), asInteger(k2), chx->xtype, &c); R_CheckStack(); return chm_sparse_to_SEXP(ans, 1, 0, Rkind, "", GET_SLOT(x, Matrix_DimNamesSym)); } SEXP Csparse_diagU2N(SEXP x) { const char *cl = class_P(x); /* dtCMatrix, etc; [1] = the second character =?= 't' for triangular */ if (cl[1] != 't' || *diag_P(x) != 'U') { /* "trivially fast" when not triangular (<==> no 'diag' slot), or not *unit* triangular */ return (x); } else { /* unit triangular (diag='U'): "fill the diagonal" & diag:= "N" */ CHM_SP chx = AS_CHM_SP__(x); CHM_SP eye = cholmod_speye(chx->nrow, chx->ncol, chx->xtype, &c); double one[] = {1, 0}; CHM_SP ans = cholmod_add(chx, eye, one, one, TRUE, TRUE, &c); int uploT = (*uplo_P(x) == 'U') ? 1 : -1; int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0; R_CheckStack(); cholmod_free_sparse(&eye, &c); return chm_sparse_to_SEXP(ans, 1, uploT, Rkind, "N", GET_SLOT(x, Matrix_DimNamesSym)); } } SEXP Csparse_diagN2U(SEXP x) { const char *cl = class_P(x); /* dtCMatrix, etc; [1] = the second character =?= 't' for triangular */ if (cl[1] != 't' || *diag_P(x) != 'N') { /* "trivially fast" when not triangular (<==> no 'diag' slot), or already *unit* triangular */ return (x); } else { /* triangular with diag='N'): now drop the diagonal */ /* duplicate, since chx will be modified: */ SEXP xx = PROTECT(duplicate(x)); CHM_SP chx = AS_CHM_SP__(xx); int uploT = (*uplo_P(x) == 'U') ? 1 : -1, Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0; R_CheckStack(); chm_diagN2U(chx, uploT, /* do_realloc */ FALSE); SEXP ans = chm_sparse_to_SEXP(chx, /*dofree*/ 0/* or 1 ?? */, uploT, Rkind, "U", GET_SLOT(x, Matrix_DimNamesSym)); UNPROTECT(1);// only now ! return ans; } } /** * "Indexing" aka subsetting : Compute x[i,j], also for vectors i and j * Working via CHOLMOD_submatrix, see ./CHOLMOD/MatrixOps/cholmod_submatrix.c * @param x CsparseMatrix * @param i row indices (0-origin), or NULL (R's) * @param j columns indices (0-origin), or NULL * * @return x[i,j] still CsparseMatrix --- currently, this loses dimnames */ SEXP Csparse_submatrix(SEXP x, SEXP i, SEXP j) { CHM_SP chx = AS_CHM_SP(x); /* << does diagU2N() when needed */ int rsize = (isNull(i)) ? -1 : LENGTH(i), csize = (isNull(j)) ? -1 : LENGTH(j); int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0; R_CheckStack(); if (rsize >= 0 && !isInteger(i)) error(_("Index i must be NULL or integer")); if (csize >= 0 && !isInteger(j)) error(_("Index j must be NULL or integer")); if (!chx->stype) {/* non-symmetric Matrix */ return chm_sparse_to_SEXP(cholmod_submatrix(chx, (rsize < 0) ? NULL : INTEGER(i), rsize, (csize < 0) ? NULL : INTEGER(j), csize, TRUE, TRUE, &c), 1, 0, Rkind, "", /* FIXME: drops dimnames */ R_NilValue); } /* for now, cholmod_submatrix() only accepts "generalMatrix" */ CHM_SP tmp = cholmod_copy(chx, /* stype: */ 0, chx->xtype, &c); CHM_SP ans = cholmod_submatrix(tmp, (rsize < 0) ? NULL : INTEGER(i), rsize, (csize < 0) ? NULL : INTEGER(j), csize, TRUE, TRUE, &c); cholmod_free_sparse(&tmp, &c); return chm_sparse_to_SEXP(ans, 1, 0, Rkind, "", R_NilValue); } #define _d_Csp_ #include "t_Csparse_subassign.c" #define _l_Csp_ #include "t_Csparse_subassign.c" #define _i_Csp_ #include "t_Csparse_subassign.c" #define _n_Csp_ #include "t_Csparse_subassign.c" #define _z_Csp_ #include "t_Csparse_subassign.c" SEXP Csparse_MatrixMarket(SEXP x, SEXP fname) { FILE *f = fopen(CHAR(asChar(fname)), "w"); if (!f) error(_("failure to open file \"%s\" for writing"), CHAR(asChar(fname))); if (!cholmod_write_sparse(f, AS_CHM_SP(x), (CHM_SP)NULL, (char*) NULL, &c)) error(_("cholmod_write_sparse returned error code")); fclose(f); return R_NilValue; } /** * Extract the diagonal entries from *triangular* Csparse matrix __or__ a * cholmod_sparse factor (LDL = TRUE). * * @param n dimension of the matrix. * @param x_p 'p' (column pointer) slot contents * @param x_x 'x' (non-zero entries) slot contents * @param perm 'perm' (= permutation vector) slot contents; only used for "diagBack" * @param resultKind a (SEXP) string indicating which kind of result is desired. * * @return a SEXP, either a (double) number or a length n-vector of diagonal entries */ SEXP diag_tC_ptr(int n, int *x_p, double *x_x, int *perm, SEXP resultKind) /* ^^^^^^ FIXME[Generalize] to int / ... */ { const char* res_ch = CHAR(STRING_ELT(resultKind,0)); enum diag_kind { diag, diag_backpermuted, trace, prod, sum_log } res_kind = ((!strcmp(res_ch, "trace")) ? trace : ((!strcmp(res_ch, "sumLog")) ? sum_log : ((!strcmp(res_ch, "prod")) ? prod : ((!strcmp(res_ch, "diag")) ? diag : ((!strcmp(res_ch, "diagBack")) ? diag_backpermuted : -1))))); int i, n_x, i_from = 0; SEXP ans = PROTECT(allocVector(REALSXP, /* ^^^^ FIXME[Generalize] */ (res_kind == diag || res_kind == diag_backpermuted) ? n : 1)); double *v = REAL(ans); /* ^^^^^^ ^^^^ FIXME[Generalize] */ #define for_DIAG(v_ASSIGN) \ for(i = 0; i < n; i++, i_from += n_x) { \ /* looking at i-th column */ \ n_x = x_p[i+1] - x_p[i];/* #{entries} in this column */ \ v_ASSIGN; \ } /* NOTA BENE: we assume -- uplo = "L" i.e. lower triangular matrix * for uplo = "U" (makes sense with a "dtCMatrix" !), * should use x_x[i_from + (nx - 1)] instead of x_x[i_from], * where nx = (x_p[i+1] - x_p[i]) */ switch(res_kind) { case trace: v[0] = 0.; for_DIAG(v[0] += x_x[i_from]); break; case sum_log: v[0] = 0.; for_DIAG(v[0] += log(x_x[i_from])); break; case prod: v[0] = 1.; for_DIAG(v[0] *= x_x[i_from]); break; case diag: for_DIAG(v[i] = x_x[i_from]); break; case diag_backpermuted: for_DIAG(v[i] = x_x[i_from]); warning(_("%s = '%s' (back-permuted) is experimental"), "resultKind", "diagBack"); /* now back_permute : */ for(i = 0; i < n; i++) { double tmp = v[i]; v[i] = v[perm[i]]; v[perm[i]] = tmp; /*^^^^ FIXME[Generalize] */ } break; default: /* -1 from above */ error(_("diag_tC(): invalid 'resultKind'")); /* Wall: */ ans = R_NilValue; v = REAL(ans); } UNPROTECT(1); return ans; } /** * Extract the diagonal entries from *triangular* Csparse matrix __or__ a * cholmod_sparse factor (LDL = TRUE). * * @param pslot 'p' (column pointer) slot of Csparse matrix/factor * @param xslot 'x' (non-zero entries) slot of Csparse matrix/factor * @param perm_slot 'perm' (= permutation vector) slot of corresponding CHMfactor; * only used for "diagBack" * @param resultKind a (SEXP) string indicating which kind of result is desired. * * @return a SEXP, either a (double) number or a length n-vector of diagonal entries */ SEXP diag_tC(SEXP pslot, SEXP xslot, SEXP perm_slot, SEXP resultKind) { int n = length(pslot) - 1, /* n = ncol(.) = nrow(.) */ *x_p = INTEGER(pslot), *perm = INTEGER(perm_slot); double *x_x = REAL(xslot); /* ^^^^^^ ^^^^ FIXME[Generalize] to INTEGER(.) / LOGICAL(.) / ... xslot !*/ return diag_tC_ptr(n, x_p, x_x, perm, resultKind); } /** * Create a Csparse matrix object from indices and/or pointers. * * @param cls name of actual class of object to create * @param i optional integer vector of length nnz of row indices * @param j optional integer vector of length nnz of column indices * @param p optional integer vector of length np of row or column pointers * @param np length of integer vector p. Must be zero if p == (int*)NULL * @param x optional vector of values * @param nnz length of vectors i, j and/or x, whichever is to be used * @param dims optional integer vector of length 2 to be used as * dimensions. If dims == (int*)NULL then the maximum row and column * index are used as the dimensions. * @param dimnames optional list of length 2 to be used as dimnames * @param index1 indicator of 1-based indices * * @return an SEXP of class cls inheriting from CsparseMatrix. */ SEXP create_Csparse(char* cls, int* i, int* j, int* p, int np, void* x, int nnz, int* dims, SEXP dimnames, int index1) { SEXP ans; int *ij = (int*)NULL, *tri, *trj, mi, mj, mp, nrow = -1, ncol = -1; int xtype = -1; /* -Wall */ CHM_TR T; CHM_SP A; if (np < 0 || nnz < 0) error(_("negative vector lengths not allowed: np = %d, nnz = %d"), np, nnz); if (1 != ((mi = (i == (int*)NULL)) + (mj = (j == (int*)NULL)) + (mp = (p == (int*)NULL)))) error(_("exactly 1 of 'i', 'j' or 'p' must be NULL")); if (mp) { if (np) error(_("np = %d, must be zero when p is NULL"), np); } else { if (np) { /* Expand p to form i or j */ if (!(p[0])) error(_("p[0] = %d, should be zero"), p[0]); for (int ii = 0; ii < np; ii++) if (p[ii] > p[ii + 1]) error(_("p must be non-decreasing")); if (p[np] != nnz) error("p[np] = %d != nnz = %d", p[np], nnz); ij = Calloc(nnz, int); if (mi) { i = ij; nrow = np; } else { j = ij; ncol = np; } /* Expand p to 0-based indices */ for (int ii = 0; ii < np; ii++) for (int jj = p[ii]; jj < p[ii + 1]; jj++) ij[jj] = ii; } else { if (nnz) error(_("Inconsistent dimensions: np = 0 and nnz = %d"), nnz); } } /* calculate nrow and ncol */ if (nrow < 0) { for (int ii = 0; ii < nnz; ii++) { int i1 = i[ii] + (index1 ? 0 : 1); /* 1-based index */ if (i1 < 1) error(_("invalid row index at position %d"), ii); if (i1 > nrow) nrow = i1; } } if (ncol < 0) { for (int jj = 0; jj < nnz; jj++) { int j1 = j[jj] + (index1 ? 0 : 1); if (j1 < 1) error(_("invalid column index at position %d"), jj); if (j1 > ncol) ncol = j1; } } if (dims != (int*)NULL) { if (dims[0] > nrow) nrow = dims[0]; if (dims[1] > ncol) ncol = dims[1]; } /* check the class name */ if (strlen(cls) != 8) error(_("strlen of cls argument = %d, should be 8"), strlen(cls)); if (!strcmp(cls + 2, "CMatrix")) error(_("cls = \"%s\" does not end in \"CMatrix\""), cls); switch(cls[0]) { case 'd': case 'l': xtype = CHOLMOD_REAL; break; case 'n': xtype = CHOLMOD_PATTERN; break; default: error(_("cls = \"%s\" must begin with 'd', 'l' or 'n'"), cls); } if (cls[1] != 'g') error(_("Only 'g'eneral sparse matrix types allowed")); /* allocate and populate the triplet */ T = cholmod_allocate_triplet((size_t)nrow, (size_t)ncol, (size_t)nnz, 0, xtype, &c); T->x = x; tri = (int*)T->i; trj = (int*)T->j; for (int ii = 0; ii < nnz; ii++) { tri[ii] = i[ii] - ((!mi && index1) ? 1 : 0); trj[ii] = j[ii] - ((!mj && index1) ? 1 : 0); } /* create the cholmod_sparse structure */ A = cholmod_triplet_to_sparse(T, nnz, &c); cholmod_free_triplet(&T, &c); /* copy the information to the SEXP */ ans = PROTECT(NEW_OBJECT(MAKE_CLASS(cls))); /* FIXME: This has been copied from chm_sparse_to_SEXP in chm_common.c */ /* allocate and copy common slots */ nnz = cholmod_nnz(A, &c); dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2)); dims[0] = A->nrow; dims[1] = A->ncol; Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_pSym, INTSXP, A->ncol + 1)), (int*)A->p, A->ncol + 1); Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_iSym, INTSXP, nnz)), (int*)A->i, nnz); switch(cls[1]) { case 'd': Memcpy(REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, nnz)), (double*)A->x, nnz); break; case 'l': error(_("code not yet written for cls = \"lgCMatrix\"")); } /* FIXME: dimnames are *NOT* put there yet (if non-NULL) */ cholmod_free_sparse(&A, &c); UNPROTECT(1); return ans; } Matrix/src/dtpMatrix.h0000644000175100001440000000122712271765436014467 0ustar hornikusers #ifndef MATRIX_TPMATRIX_H #define MATRIX_TPMATRIX_H #include #include "Mutils.h" SEXP dtpMatrix_validate(SEXP obj); SEXP dtpMatrix_norm(SEXP obj, SEXP type); SEXP dtpMatrix_rcond(SEXP obj, SEXP type); SEXP dtpMatrix_addDiag(SEXP x, SEXP d); SEXP dtpMatrix_getDiag(SEXP x); SEXP ltpMatrix_getDiag(SEXP x); SEXP dtpMatrix_setDiag(SEXP x, SEXP d); SEXP ltpMatrix_setDiag(SEXP x, SEXP d); SEXP dtpMatrix_solve(SEXP a); SEXP dtpMatrix_matrix_solve(SEXP a, SEXP b); SEXP dtpMatrix_as_dtrMatrix(SEXP from); SEXP dgeMatrix_dtpMatrix_mm(SEXP x, SEXP y); SEXP dtpMatrix_matrix_mm(SEXP x, SEXP y, SEXP right, SEXP trans); #endif /* MATRIX_TPMATRIX_H */ Matrix/src/dgTMatrix.h0000644000175100001440000000054312271765436014416 0ustar hornikusers#ifndef MATRIX_TRIPLET_H #define MATRIX_TRIPLET_H #include "Mutils.h" SEXP xTMatrix_validate(SEXP x); SEXP dgTMatrix_to_dgeMatrix(SEXP x); SEXP lgTMatrix_to_lgeMatrix(SEXP x); SEXP dgTMatrix_to_matrix(SEXP x); SEXP lgTMatrix_to_matrix(SEXP x); #ifdef _valid_only_for_old_graph_package SEXP graphNEL_as_dgTMatrix(SEXP x, SEXP symmetric); #endif #endif Matrix/src/Tsparse.c0000644000175100001440000001044312271765436014127 0ustar hornikusers /* Sparse matrices in triplet form */ #include "Tsparse.h" #include "chm_common.h" SEXP Tsparse_validate(SEXP x) { /* NB: we do *NOT* check a potential 'x' slot here, at all */ SEXP islot = GET_SLOT(x, Matrix_iSym), jslot = GET_SLOT(x, Matrix_jSym), dimslot = GET_SLOT(x, Matrix_DimSym); int j, nrow = INTEGER(dimslot)[0], ncol = INTEGER(dimslot)[1], nnz = length(islot), *xj = INTEGER(jslot), *xi = INTEGER(islot); if (length(jslot) != nnz) return mkString(_("lengths of slots i and j must match")); /* FIXME: this is checked in super class -- no need to do here: */ if (length(dimslot) != 2) return mkString(_("slot Dim must have length 2")); for (j = 0; j < nnz; j++) { if (xi[j] < 0 || xi[j] >= nrow) return mkString(_("all row indices (slot 'i') must be between 0 and nrow-1 in a TsparseMatrix")); if (xj[j] < 0 || xj[j] >= ncol) return mkString(_("all column indices (slot 'j') must be between 0 and ncol-1 in a TsparseMatrix")); } return ScalarLogical(1); } SEXP Tsparse_to_Csparse(SEXP x, SEXP tri) { CHM_TR chxt = AS_CHM_TR__(x); /* << should *preserve* diag = "U" ! */ CHM_SP chxs = cholmod_triplet_to_sparse(chxt, chxt->nnz, &c); int tr = asLogical(tri); int Rkind = (chxt->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0; R_CheckStack(); return chm_sparse_to_SEXP(chxs, 1, tr ? ((*uplo_P(x) == 'U') ? 1 : -1) : 0, Rkind, tr ? diag_P(x) : "", GET_SLOT(x, Matrix_DimNamesSym)); } /* speedup utility, needed e.g. after subsetting: */ SEXP Tsparse_to_tCsparse(SEXP x, SEXP uplo, SEXP diag) { CHM_TR chxt = AS_CHM_TR__(x); CHM_SP chxs = cholmod_triplet_to_sparse(chxt, chxt->nnz, &c); int Rkind = (chxt->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0; R_CheckStack(); return chm_sparse_to_SEXP(chxs, 1, /* uploT = */ (*CHAR(asChar(uplo)) == 'U')? 1: -1, Rkind, /* diag = */ CHAR(STRING_ELT(diag, 0)), GET_SLOT(x, Matrix_DimNamesSym)); } SEXP Tsparse_diagU2N(SEXP x) { static const char *valid[] = { "dtTMatrix", /* 0 */ "ltTMatrix", /* 1 */ "ntTMatrix", /* 2 : no x slot */ "ztTMatrix", /* 3 */ ""}; /* #define xSXP(iTyp) ((iTyp == 0) ? REALSXP : ((iTyp == 1) ? LGLSXP : /\* else *\/ CPLXSXP)); */ /* #define xTYPE(iTyp) ((iTyp == 0) ? double : ((iTyp == 1) ? int : /\* else *\/ Rcomplex)); */ int ctype = Matrix_check_class_etc(x, valid); if (ctype < 0 || *diag_P(x) != 'U') { /* "trivially fast" when not triangular (<==> no 'diag' slot), or not *unit* triangular */ return (x); } else { /* instead of going to Csparse -> Cholmod -> Csparse -> Tsparse, work directly: */ int i, n = INTEGER(GET_SLOT(x, Matrix_DimSym))[0], nnz = length(GET_SLOT(x, Matrix_iSym)), new_n = nnz + n; SEXP ans = PROTECT(NEW_OBJECT(MAKE_CLASS(class_P(x)))); int *islot = INTEGER(ALLOC_SLOT(ans, Matrix_iSym, INTSXP, new_n)), *jslot = INTEGER(ALLOC_SLOT(ans, Matrix_jSym, INTSXP, new_n)); slot_dup(ans, x, Matrix_DimSym); SET_DimNames(ans, x); slot_dup(ans, x, Matrix_uploSym); SET_SLOT(ans, Matrix_diagSym, mkString("N")); /* Build the new i- and j- slots : first copy the current : */ Memcpy(islot, INTEGER(GET_SLOT(x, Matrix_iSym)), nnz); Memcpy(jslot, INTEGER(GET_SLOT(x, Matrix_jSym)), nnz); /* then, add the new (i,j) slot entries: */ for(i = 0; i < n; i++) { islot[i + nnz] = i; jslot[i + nnz] = i; } /* build the new x-slot : */ switch(ctype) { case 0: { /* "d" */ double *x_new = REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, new_n)); Memcpy(x_new, REAL(GET_SLOT(x, Matrix_xSym)), nnz); for(i = 0; i < n; i++) /* add x[i,i] = 1. */ x_new[i + nnz] = 1.; break; } case 1: { /* "l" */ int *x_new = LOGICAL(ALLOC_SLOT(ans, Matrix_xSym, LGLSXP, new_n)); Memcpy(x_new, LOGICAL(GET_SLOT(x, Matrix_xSym)), nnz); for(i = 0; i < n; i++) /* add x[i,i] = 1 (= TRUE) */ x_new[i + nnz] = 1; break; } case 2: /* "n" */ /* nothing to do here */ break; case 3: { /* "z" */ Rcomplex *x_new = COMPLEX(ALLOC_SLOT(ans, Matrix_xSym, CPLXSXP, new_n)); Memcpy(x_new, COMPLEX(GET_SLOT(x, Matrix_xSym)), nnz); for(i = 0; i < n; i++) /* add x[i,i] = 1 (= TRUE) */ x_new[i + nnz] = (Rcomplex) {1., 0.}; break; } }/* switch() */ UNPROTECT(1); return ans; } } Matrix/src/dgeMatrix.h0000644000175100001440000000325212271765436014437 0ustar hornikusers#ifndef MATRIX_GEMATRIX_H #define MATRIX_GEMATRIX_H #include #include #include "Mutils.h" SEXP dMatrix_validate(SEXP obj); SEXP dgeMatrix_validate(SEXP obj); SEXP dgeMatrix_norm(SEXP obj, SEXP norm); SEXP dgeMatrix_rcond(SEXP obj, SEXP type); /* for crossprod() and tcrossprod() : */ SEXP dgeMatrix_crossprod(SEXP x, SEXP trans); SEXP dgeMatrix_dgeMatrix_crossprod(SEXP x, SEXP y, SEXP trans); SEXP dgeMatrix_matrix_crossprod(SEXP x, SEXP y, SEXP trans); SEXP dgeMatrix_addDiag(SEXP x, SEXP d); SEXP dgeMatrix_getDiag(SEXP x); SEXP lgeMatrix_getDiag(SEXP x); SEXP dgeMatrix_setDiag(SEXP x, SEXP d); SEXP lgeMatrix_setDiag(SEXP x, SEXP d); SEXP dgeMatrix_LU (SEXP x, SEXP warn_singularity); SEXP dgeMatrix_LU_(SEXP x, Rboolean warn_sing); SEXP dgeMatrix_determinant(SEXP x, SEXP logarithm); SEXP dgeMatrix_Schur(SEXP x, SEXP vectors, SEXP isDGE); SEXP dgeMatrix_solve(SEXP a); SEXP dgeMatrix_matrix_solve(SEXP a, SEXP b); SEXP dgeMatrix_matrix_mm(SEXP a, SEXP b, SEXP right); SEXP dgeMatrix_svd(SEXP x, SEXP nu, SEXP nv); SEXP dgeMatrix_exp(SEXP x); SEXP dgeMatrix_colsums(SEXP x, SEXP naRmP, SEXP cols, SEXP mean); /* DGESDD - compute the singular value decomposition (SVD); of a */ /* real M-by-N matrix A, optionally computing the left and/or */ /* right singular vectors. If singular vectors are desired, it uses a */ /* divide-and-conquer algorithm. */ void F77_NAME(dgesdd)(const char *jobz, const int *m, const int *n, double *a, const int *lda, double *s, double *u, const int *ldu, double *vt, const int *ldvt, double *work, const int *lwork, int *iwork, int *info); #endif Matrix/src/CHMfactor.h0000644000175100001440000000113212271765436014314 0ustar hornikusers#ifndef MATRIX_CHMFACTOR_H #define MATRIX_CHMFACTOR_H #include "Mutils.h" #include "chm_common.h" SEXP CHMfactor_ldetL2(SEXP x); SEXP CHMfactor_to_sparse(SEXP x); SEXP CHMfactor_solve(SEXP a, SEXP b, SEXP type); SEXP CHMfactor_spsolve(SEXP a, SEXP b, SEXP type); SEXP CHMfactor_update(SEXP object, SEXP parent, SEXP mult); SEXP destructive_CHM_update(SEXP object, SEXP parent, SEXP mult); SEXP CHMfactor_ldetL2up(SEXP x, SEXP parent, SEXP mult); double chm_factor_ldetL2(CHM_FR f); CHM_FR chm_factor_update(CHM_FR f, CHM_SP A, double fac); SEXP CHMfactor_updown(SEXP update, SEXP C, SEXP L); #endif Matrix/src/dppMatrix.c0000644000175100001440000000545712271765436014467 0ustar hornikusers#include "dppMatrix.h" SEXP dppMatrix_validate(SEXP obj) { /* int i, n = INTEGER(GET_SLOT(obj, Matrix_DimSym))[0]; */ /* double *x = REAL(GET_SLOT(obj, Matrix_xSym)); */ /* quick but nondefinitive check on positive definiteness */ /* for (i = 0; i < n; i++) */ /* if (x[i * np1] < 0) */ /* return mkString(_("dppMatrix is not positive definite")); */ return dspMatrix_validate(obj); } SEXP dppMatrix_chol(SEXP x) { SEXP val = get_factors(x, "pCholesky"), dimP = GET_SLOT(x, Matrix_DimSym), uploP = GET_SLOT(x, Matrix_uploSym); const char *uplo = CHAR(STRING_ELT(uploP, 0)); int *dims = INTEGER(dimP), info; if (val != R_NilValue) return val; dims = INTEGER(dimP); val = PROTECT(NEW_OBJECT(MAKE_CLASS("pCholesky"))); SET_SLOT(val, Matrix_uploSym, duplicate(uploP)); SET_SLOT(val, Matrix_diagSym, mkString("N")); SET_SLOT(val, Matrix_DimSym, duplicate(dimP)); slot_dup(val, x, Matrix_xSym); F77_CALL(dpptrf)(uplo, dims, REAL(GET_SLOT(val, Matrix_xSym)), &info); if (info) { if(info > 0) /* e.g. x singular */ error(_("the leading minor of order %d is not positive definite"), info); else /* should never happen! */ error(_("Lapack routine %s returned error code %d"), "dpptrf", info); } UNPROTECT(1); return set_factors(x, val, "pCholesky"); } SEXP dppMatrix_rcond(SEXP obj, SEXP type) { SEXP Chol = dppMatrix_chol(obj); char typnm[] = {'O', '\0'}; /* always use the one norm */ int *dims = INTEGER(GET_SLOT(Chol, Matrix_DimSym)), info; double anorm = get_norm_sp(obj, typnm), rcond; F77_CALL(dppcon)(uplo_P(Chol), dims, REAL(GET_SLOT(Chol, Matrix_xSym)), &anorm, &rcond, (double *) R_alloc(3*dims[0], sizeof(double)), (int *) R_alloc(dims[0], sizeof(int)), &info); return ScalarReal(rcond); } SEXP dppMatrix_solve(SEXP x) { SEXP Chol = dppMatrix_chol(x); SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dppMatrix"))); int *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)), info; slot_dup(val, Chol, Matrix_uploSym); slot_dup(val, Chol, Matrix_xSym); slot_dup(val, Chol, Matrix_DimSym); F77_CALL(dpptri)(uplo_P(val), dims, REAL(GET_SLOT(val, Matrix_xSym)), &info); UNPROTECT(1); return val; } SEXP dppMatrix_matrix_solve(SEXP a, SEXP b) { SEXP val = PROTECT(dup_mMatrix_as_dgeMatrix(b)); SEXP Chol = dppMatrix_chol(a); int *adims = INTEGER(GET_SLOT(a, Matrix_DimSym)), *bdims = INTEGER(GET_SLOT(val, Matrix_DimSym)); int n = bdims[0], nrhs = bdims[1], info; if (*adims != *bdims || bdims[1] < 1 || *adims < 1) error(_("Dimensions of system to be solved are inconsistent")); F77_CALL(dpptrs)(uplo_P(Chol), &n, &nrhs, REAL(GET_SLOT(Chol, Matrix_xSym)), REAL(GET_SLOT(val, Matrix_xSym)), &n, &info); UNPROTECT(1); return val; } Matrix/src/CHMfactor.c0000644000175100001440000001211712271765436014314 0ustar hornikusers /* CHOLMOD factors */ #include "CHMfactor.h" SEXP CHMfactor_to_sparse(SEXP x) { CHM_FR L = AS_CHM_FR(x), Lcp; CHM_SP Lm; R_CheckStack(); /* cholmod_factor_to_sparse changes its first argument. Make a copy */ Lcp = cholmod_copy_factor(L, &c); if (!(Lcp->is_ll)) if (!cholmod_change_factor(Lcp->xtype, 1, 0, 1, 1, Lcp, &c)) error(_("cholmod_change_factor failed with status %d"), c.status); Lm = cholmod_factor_to_sparse(Lcp, &c); cholmod_free_factor(&Lcp, &c); return chm_sparse_to_SEXP(Lm, 1/*do_free*/, -1/*uploT*/, 0/*Rkind*/, "N"/*non_unit*/, R_NilValue/*dimNames*/); } SEXP CHMfactor_solve(SEXP a, SEXP b, SEXP system) { CHM_FR L = AS_CHM_FR(a); SEXP bb = PROTECT(dup_mMatrix_as_dgeMatrix(b)); CHM_DN B = AS_CHM_DN(bb), X; int sys = asInteger(system); R_CheckStack(); if (!(sys--)) /* align with CHOLMOD defs: R's {1:9} --> {0:8}, see ./CHOLMOD/Cholesky/cholmod_solve.c */ error(_("system argument is not valid")); X = cholmod_solve(sys, L, B, &c); UNPROTECT(1); return chm_dense_to_SEXP(X, 1/*do_free*/, 0/*Rkind*/, GET_SLOT(bb, Matrix_DimNamesSym)); } SEXP CHMfactor_updown(SEXP upd, SEXP C_, SEXP L_) { CHM_FR L = AS_CHM_FR(L_), Lcp; CHM_SP C = AS_CHM_SP__(C_); int update = asInteger(upd); R_CheckStack(); Lcp = cholmod_copy_factor(L, &c); int r = cholmod_updown(update, C, Lcp, &c); if(!r) error(_("cholmod_updown() returned %d"), r); return chm_factor_to_SEXP(Lcp, 1); } SEXP CHMfactor_spsolve(SEXP a, SEXP b, SEXP system) { CHM_FR L = AS_CHM_FR(a); CHM_SP B = AS_CHM_SP__(b); int sys = asInteger(system); R_CheckStack(); if (!(sys--)) /* align with CHOLMOD defs: R's {1:9} --> {0:8}, see ./CHOLMOD/Cholesky/cholmod_solve.c */ error(_("system argument is not valid")); return chm_sparse_to_SEXP(cholmod_spsolve(sys, L, B, &c), 1/*do_free*/, 0/*uploT*/, 0/*Rkind*/, "", GET_SLOT(b, Matrix_DimNamesSym)); } /** * Evaluate the logarithm of the square of the determinant of L * * @param f pointer to a CHMfactor object * * @return log(det(L)^2) * */ double chm_factor_ldetL2(CHM_FR f) { int i, j, p; double ans = 0; if (f->is_super) { int *lpi = (int*)(f->pi), *lsup = (int*)(f->super); for (i = 0; i < f->nsuper; i++) { /* supernodal block i */ int nrp1 = 1 + lpi[i + 1] - lpi[i], nc = lsup[i + 1] - lsup[i]; double *x = (double*)(f->x) + ((int*)(f->px))[i]; for (j = 0; j < nc; j++) { ans += 2 * log(fabs(x[j * nrp1])); } } } else { int *li = (int*)(f->i), *lp = (int*)(f->p); double *lx = (double *)(f->x); for (j = 0; j < f->n; j++) { for (p = lp[j]; li[p] != j && p < lp[j + 1]; p++) {}; if (li[p] != j) { error(_("diagonal element %d of Cholesky factor is missing"), j); break; /* -Wall */ } ans += log(lx[p] * ((f->is_ll) ? lx[p] : 1.)); } } return ans; } SEXP CHMfactor_ldetL2(SEXP x) { CHM_FR L = AS_CHM_FR(x); R_CheckStack(); return ScalarReal(chm_factor_ldetL2(L)); } /** * Update the numerical values in the factor f as A + mult * I, if A is * symmetric, otherwise AA' + mult * I * * @param f pointer to a CHM_FR object. f is updated upon return. * @param A pointer to a CHM_SP object, possibly symmetric * @param mult multiple of the identity to be added to A or AA' before * decomposing. * * \note: A and f must be compatible. There is no check on this * here. Incompatibility of A and f will cause the CHOLMOD functions * to take an error exit. * */ CHM_FR chm_factor_update(CHM_FR f, CHM_SP A, double mult) { int ll = f->is_ll; double mm[2] = {0, 0}; mm[0] = mult; // NB: Result depends if A is "dsC" or "dgC"; the latter case assumes we mean AA' !!! if (!cholmod_factorize_p(A, mm, (int*)NULL, 0 /*fsize*/, f, &c)) /* -> ./CHOLMOD/Cholesky/cholmod_factorize.c */ error(_("cholmod_factorize_p failed: status %d, minor %d of ncol %d"), c.status, f->minor, f->n); if (f->is_ll != ll) if(!cholmod_change_factor(f->xtype, ll, f->is_super, 1 /*to_packed*/, 1 /*to_monotonic*/, f, &c)) error(_("cholmod_change_factor failed")); return f; } SEXP CHMfactor_update(SEXP object, SEXP parent, SEXP mult) { CHM_FR L = AS_CHM_FR(object), Lcp; CHM_SP A = AS_CHM_SP__(parent); R_CheckStack(); Lcp = cholmod_copy_factor(L, &c); return chm_factor_to_SEXP(chm_factor_update(Lcp, A, asReal(mult)), 1); } SEXP destructive_CHM_update(SEXP object, SEXP parent, SEXP mult) { CHM_FR L = AS_CHM_FR(object); CHM_SP A = AS_CHM_SP__(parent); R_CheckStack(); return chm_factor_to_SEXP(chm_factor_update(L, A, asReal(mult)), 0); } SEXP CHMfactor_ldetL2up(SEXP x, SEXP parent, SEXP mult) { SEXP ans = PROTECT(duplicate(mult)); int i, nmult = LENGTH(mult); double *aa = REAL(ans), *mm = REAL(mult); CHM_FR L = AS_CHM_FR(x), Lcp; CHM_SP A = AS_CHM_SP__(parent); R_CheckStack(); Lcp = cholmod_copy_factor(L, &c); for (i = 0; i < nmult; i++) aa[i] = chm_factor_ldetL2(chm_factor_update(Lcp, A, mm[i])); cholmod_free_factor(&Lcp, &c); UNPROTECT(1); return ans; } Matrix/src/dtCMatrix.c0000644000175100001440000001052212271765436014403 0ustar hornikusers /* Sparse triangular numeric matrices */ #include "dtCMatrix.h" #include "cs_utils.h" #define RETURN(_CH_) UNPROTECT(1); return (_CH_); /* This is used for *BOTH* triangular and symmetric Csparse: */ SEXP tCMatrix_validate(SEXP x) { SEXP val = xCMatrix_validate(x);/* checks x slot */ if(isString(val)) return(val); else { SEXP islot = GET_SLOT(x, Matrix_iSym), pslot = GET_SLOT(x, Matrix_pSym); int uploT = (*uplo_P(x) == 'U'), k, nnz = length(islot), *xi = INTEGER(islot), *xj = INTEGER(PROTECT(allocVector(INTSXP, nnz))); expand_cmprPt(length(pslot) - 1, INTEGER(pslot), xj); /* Maybe FIXME: ">" should be ">=" for diag = 'U' (uplo = 'U') */ if(uploT) { for (k = 0; k < nnz; k++) if(xi[k] > xj[k]) { RETURN(mkString(_("uplo='U' must not have sparse entries below the diagonal"))); } } else { for (k = 0; k < nnz; k++) if(xi[k] < xj[k]) { RETURN(mkString(_("uplo='L' must not have sparse entries above the diagonal"))); } } RETURN(ScalarLogical(1)); } } /* This is used for *BOTH* triangular and symmetric Rsparse: */ SEXP tRMatrix_validate(SEXP x) { SEXP val = xRMatrix_validate(x);/* checks x slot */ if(isString(val)) return(val); else { SEXP jslot = GET_SLOT(x, Matrix_jSym), pslot = GET_SLOT(x, Matrix_pSym); int uploT = (*uplo_P(x) == 'U'), k, nnz = length(jslot), *xj = INTEGER(jslot), *xi = INTEGER(PROTECT(allocVector(INTSXP, nnz))); expand_cmprPt(length(pslot) - 1, INTEGER(pslot), xi); /* Maybe FIXME: ">" should be ">=" for diag = 'U' (uplo = 'U') */ if(uploT) { for (k = 0; k < nnz; k++) if(xi[k] > xj[k]) { RETURN(mkString(_("uplo='U' must not have sparse entries below the diagonal"))); } } else { for (k = 0; k < nnz; k++) if(xi[k] < xj[k]) { RETURN(mkString(_("uplo='L' must not have sparse entries above the diagonal"))); } } RETURN(ScalarLogical(1)); } } SEXP dtCMatrix_matrix_solve(SEXP a, SEXP b, SEXP classed) { int cl = asLogical(classed); SEXP ans = PROTECT(NEW_OBJECT(MAKE_CLASS("dgeMatrix"))); CSP A = AS_CSP(a); int *adims = INTEGER(GET_SLOT(a, Matrix_DimSym)), *bdims = INTEGER(cl ? GET_SLOT(b, Matrix_DimSym) : getAttrib(b, R_DimSymbol)); int j, n = bdims[0], nrhs = bdims[1], lo = (*uplo_P(a) == 'L'); double *bx; R_CheckStack(); if (*adims != n || nrhs < 1 || *adims < 1 || *adims != adims[1]) error(_("Dimensions of system to be solved are inconsistent")); Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2)), bdims, 2); /* FIXME: copy dimnames or Dimnames as well */ bx = Memcpy(REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, n * nrhs)), REAL(cl ? GET_SLOT(b, Matrix_xSym):b), n * nrhs); for (j = 0; j < nrhs; j++) lo ? cs_lsolve(A, bx + n * j) : cs_usolve(A, bx + n * j); RETURN(ans); } SEXP dtCMatrix_sparse_solve(SEXP a, SEXP b) { SEXP ans = PROTECT(NEW_OBJECT(MAKE_CLASS("dgCMatrix"))); CSP A = AS_CSP(a), B = AS_CSP(b); R_CheckStack(); if (A->m != A->n || B->n < 1 || A->n < 1 || A->n != B->m) error(_("Dimensions of system to be solved are inconsistent")); // *before* Calloc()ing below [memory leak]! int *xp = INTEGER(ALLOC_SLOT(ans, Matrix_pSym, INTSXP, (B->n) + 1)), xnz = 10 * B->p[B->n]; /* initial estimate of nnz in x */ int k, lo = uplo_P(a)[0] == 'L', pos = 0; int *ti = Calloc(xnz, int), *xi = Calloc(2*A->n, int); /* for cs_reach */ double *tx = Calloc(xnz, double), *wrk = Calloc( A->n, double); slot_dup(ans, b, Matrix_DimSym); SET_DimNames(ans, b); xp[0] = 0; for (k = 0; k < B->n; k++) { int top = cs_spsolve (A, B, k, xi, wrk, (int *)NULL, lo); int nz = A->n - top; xp[k + 1] = nz + xp[k]; if (xp[k + 1] > xnz) { while (xp[k + 1] > xnz) xnz *= 2; ti = Realloc(ti, xnz, int); tx = Realloc(tx, xnz, double); } if (lo) /* increasing row order */ for(int p = top; p < A->n; p++, pos++) { ti[pos] = xi[p]; tx[pos] = wrk[xi[p]]; } else /* decreasing order, reverse copy */ for(int p = A->n - 1; p >= top; p--, pos++) { ti[pos] = xi[p]; tx[pos] = wrk[xi[p]]; } } xnz = xp[B->n]; Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_iSym, INTSXP, xnz)), ti, xnz); Memcpy( REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, xnz)), tx, xnz); Free(ti); Free(tx); Free(wrk); Free(xi); RETURN(ans); } #undef RETURN Matrix/src/dpoMatrix.h0000644000175100001440000000060412271765436014460 0ustar hornikusers#ifndef MATRIX_POMATRIX_H #define MATRIX_POMATRIX_H #include #include "Mutils.h" SEXP dpoMatrix_rcond(SEXP obj, SEXP type); SEXP dpoMatrix_validate(SEXP obj); SEXP dpoMatrix_solve(SEXP a); SEXP dpoMatrix_matrix_solve(SEXP a, SEXP b); SEXP dpoMatrix_dgeMatrix_solve(SEXP a, SEXP b); SEXP dpoMatrix_chol(SEXP x); double get_norm_sy(SEXP obj, const char *typstr); #endif Matrix/src/ldense.c0000644000175100001440000001107712271765436013764 0ustar hornikusers#include "ldense.h" /* dense logical Matrices "ldenseMatrix" classes --- almost identical to * dense nonzero-pattern: "ndenseMatrix" ones */ /* this is very close to dspMatrix_as_dsy* () in ./dspMatrix.c : */ SEXP lspMatrix_as_lsyMatrix(SEXP from, SEXP kind) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS((asInteger(kind) == 1) ? "nsyMatrix" : "lsyMatrix"))), uplo = GET_SLOT(from, Matrix_uploSym), dimP = GET_SLOT(from, Matrix_DimSym), dmnP = GET_SLOT(from, Matrix_DimNamesSym); int n = *INTEGER(dimP); SET_SLOT(val, Matrix_DimSym, duplicate(dimP)); SET_SLOT(val, Matrix_DimNamesSym, duplicate(dmnP)); SET_SLOT(val, Matrix_uploSym, duplicate(uplo)); packed_to_full_int(LOGICAL(ALLOC_SLOT(val, Matrix_xSym, LGLSXP, n*n)), LOGICAL( GET_SLOT(from, Matrix_xSym)), n, *CHAR(STRING_ELT(uplo, 0)) == 'U' ? UPP : LOW); UNPROTECT(1); return val; } // this is very close to dsyMatrix_as_lsp*() in ./dsyMatrix.c -- keep synced ! SEXP lsyMatrix_as_lspMatrix(SEXP from, SEXP kind) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS((asInteger(kind) == 1) ? "nspMatrix" : "lspMatrix"))), uplo = GET_SLOT(from, Matrix_uploSym), dimP = GET_SLOT(from, Matrix_DimSym); int n = *INTEGER(dimP); SET_SLOT(val, Matrix_DimSym, duplicate(dimP)); SET_SLOT(val, Matrix_uploSym, duplicate(uplo)); full_to_packed_int( LOGICAL(ALLOC_SLOT(val, Matrix_xSym, LGLSXP, (n*(n+1))/2)), LOGICAL( GET_SLOT(from, Matrix_xSym)), n, *CHAR(STRING_ELT(uplo, 0)) == 'U' ? UPP : LOW, NUN); SET_SLOT(val, Matrix_DimNamesSym, duplicate(GET_SLOT(from, Matrix_DimNamesSym))); SET_SLOT(val, Matrix_factorSym, duplicate(GET_SLOT(from, Matrix_factorSym))); UNPROTECT(1); return val; } // this is very close to dtpMatrix_as_dtr*() in ./dtpMatrix.c -- keep synced! SEXP ltpMatrix_as_ltrMatrix(SEXP from, SEXP kind) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS((asInteger(kind) == 1) ? "ntrMatrix" : "ltrMatrix"))), uplo = GET_SLOT(from, Matrix_uploSym), diag = GET_SLOT(from, Matrix_diagSym), dimP = GET_SLOT(from, Matrix_DimSym), dmnP = GET_SLOT(from, Matrix_DimNamesSym); int n = *INTEGER(dimP); SET_SLOT(val, Matrix_DimSym, duplicate(dimP)); SET_SLOT(val, Matrix_DimNamesSym, duplicate(dmnP)); SET_SLOT(val, Matrix_diagSym, duplicate(diag)); SET_SLOT(val, Matrix_uploSym, duplicate(uplo)); packed_to_full_int(LOGICAL(ALLOC_SLOT(val, Matrix_xSym, LGLSXP, n*n)), LOGICAL(GET_SLOT(from, Matrix_xSym)), n, *CHAR(STRING_ELT(uplo, 0)) == 'U' ? UPP : LOW); SET_SLOT(val, Matrix_DimNamesSym, duplicate(GET_SLOT(from, Matrix_DimNamesSym))); UNPROTECT(1); return val; } /* this is very close to dtrMatrix_as_dtp* () in ./dtrMatrix.c : */ SEXP ltrMatrix_as_ltpMatrix(SEXP from, SEXP kind) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS((asInteger(kind) == 1) ? "ntpMatrix" : "ltpMatrix"))), uplo = GET_SLOT(from, Matrix_uploSym), diag = GET_SLOT(from, Matrix_diagSym), dimP = GET_SLOT(from, Matrix_DimSym); int n = *INTEGER(dimP); SET_SLOT(val, Matrix_DimSym, duplicate(dimP)); SET_SLOT(val, Matrix_diagSym, duplicate(diag)); SET_SLOT(val, Matrix_uploSym, duplicate(uplo)); full_to_packed_int( LOGICAL(ALLOC_SLOT(val, Matrix_xSym, LGLSXP, (n*(n+1))/2)), LOGICAL(GET_SLOT(from, Matrix_xSym)), n, *CHAR(STRING_ELT(uplo, 0)) == 'U' ? UPP : LOW, *CHAR(STRING_ELT(diag, 0)) == 'U' ? UNT : NUN); SET_SLOT(val, Matrix_DimNamesSym, duplicate(GET_SLOT(from, Matrix_DimNamesSym))); UNPROTECT(1); return val; } /* this is very close to dtrMatrix_as_dge*() :*/ SEXP ltrMatrix_as_lgeMatrix(SEXP from, SEXP kind) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS((asInteger(kind) == 1) ? "ngeMatrix" : "lgeMatrix"))); slot_dup(val, from, Matrix_xSym); slot_dup(val, from, Matrix_DimSym); slot_dup(val, from, Matrix_DimNamesSym); SET_SLOT(val, Matrix_factorSym, allocVector(VECSXP, 0)); make_i_matrix_triangular(LOGICAL(GET_SLOT(val, Matrix_xSym)), from); UNPROTECT(1); return val; } /* this is very close to dsyMatrix_as_dge*() :*/ SEXP lsyMatrix_as_lgeMatrix(SEXP from, SEXP kind) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS((asInteger(kind) == 1) ? "ngeMatrix" : "lgeMatrix"))); slot_dup(val, from, Matrix_xSym); slot_dup(val, from, Matrix_DimSym); slot_dup(val, from, Matrix_DimNamesSym); SET_SLOT(val, Matrix_factorSym, allocVector(VECSXP, 0)); make_i_matrix_symmetric(LOGICAL(GET_SLOT(val, Matrix_xSym)), from); UNPROTECT(1); return val; } Matrix/src/Tsparse.h0000644000175100001440000000036012271765436014131 0ustar hornikusers#ifndef MATRIX_TSPARSE_H #define MATRIX_TSPARSE_H #include "Mutils.h" SEXP Tsparse_validate(SEXP x); SEXP Tsparse_diagU2N(SEXP x); SEXP Tsparse_to_Csparse(SEXP x, SEXP tri); SEXP Tsparse_to_tCsparse(SEXP x, SEXP uplo, SEXP diag); #endif Matrix/src/abIndex.c0000644000175100001440000000077412271765436014066 0ustar hornikusers/* C-level Methods for the ``abstract Index'' class * * Note: this heavily builds on ideas and code from Jens Oehlschlaegel, * ---- as implemented (in the GPL'ed part of) package 'ff'. */ #include "abIndex.h" /** * RLE (Run Length Encoding) -- only when it's worth * * @param x R vector which can be coerced to "integer" * * @return NULL or a valid R object of class "rle" */ #define _rle_d_ #include "t_Matrix_rle.c" #undef _rle_d_ #define _rle_i_ #include "t_Matrix_rle.c" #undef _rle_i_ Matrix/src/dgCMatrix.c0000644000175100001440000004663512271765436014404 0ustar hornikusers#include "dgCMatrix.h" /* for Csparse_transpose() : */ #include "Csparse.h" #include "chm_common.h" /* -> Mutils.h / SPQR ... */ /* FIXME -- we "forget" about dimnames almost everywhere : */ /* for dgCMatrix _and_ lgCMatrix and others (but *not* ngC...) : */ SEXP xCMatrix_validate(SEXP x) { /* Almost everything now in Csparse_validate ( ./Csparse.c ) * *but* the checking of the 'x' slot : */ if (length(GET_SLOT(x, Matrix_iSym)) != length(GET_SLOT(x, Matrix_xSym))) return mkString(_("lengths of slots 'i' and 'x' must match")); return ScalarLogical(1); } /* for dgRMatrix _and_ lgRMatrix and others (but *not* ngC...) : */ SEXP xRMatrix_validate(SEXP x) { /* Almost everything now in Rsparse_validate ( ./Csparse.c ) * *but* the checking of the 'x' slot : */ if (length(GET_SLOT(x, Matrix_jSym)) != length(GET_SLOT(x, Matrix_xSym))) return mkString(_("lengths of slots 'j' and 'x' must match")); return ScalarLogical(1); } /* This and the following R_to_CMatrix() lead to memory-not-mapped seg.faults * only with {32bit + R-devel + enable-R-shlib} -- no idea why */ SEXP compressed_to_TMatrix(SEXP x, SEXP colP) { int col = asLogical(colP); /* 1 if "C"olumn compressed; 0 if "R"ow */ /* however, for Csparse, we now effectively use the cholmod-based * Csparse_to_Tsparse() in ./Csparse.c ; maybe should simply write * an as_cholmod_Rsparse() function and then do "as there" ...*/ SEXP indSym = col ? Matrix_iSym : Matrix_jSym, ans, indP = GET_SLOT(x, indSym), pP = GET_SLOT(x, Matrix_pSym); int npt = length(pP) - 1; char *ncl = strdup(class_P(x)); static const char *valid[] = { MATRIX_VALID_Csparse, MATRIX_VALID_Rsparse, ""}; int ctype = Matrix_check_class_etc(x, valid); if (ctype < 0) error(_("invalid class(x) '%s' in compressed_to_TMatrix(x)"), ncl); /* replace 'C' or 'R' with 'T' :*/ ncl[2] = 'T'; ans = PROTECT(NEW_OBJECT(MAKE_CLASS(ncl))); slot_dup(ans, x, Matrix_DimSym); if((ctype / 3) % 4 != 2) /* not n..Matrix */ slot_dup(ans, x, Matrix_xSym); if(ctype % 3) { /* s(ymmetric) or t(riangular) : */ slot_dup(ans, x, Matrix_uploSym); if(ctype % 3 == 2) /* t(riangular) : */ slot_dup(ans, x, Matrix_diagSym); } SET_DimNames(ans, x); SET_SLOT(ans, indSym, duplicate(indP)); expand_cmprPt(npt, INTEGER(pP), INTEGER(ALLOC_SLOT(ans, col ? Matrix_jSym : Matrix_iSym, INTSXP, length(indP)))); free(ncl); UNPROTECT(1); return ans; } SEXP R_to_CMatrix(SEXP x) { SEXP ans, tri = PROTECT(allocVector(LGLSXP, 1)); char *ncl = strdup(class_P(x)); static const char *valid[] = { MATRIX_VALID_Rsparse, ""}; int ctype = Matrix_check_class_etc(x, valid); int *x_dims = INTEGER(GET_SLOT(x, Matrix_DimSym)), *a_dims; PROTECT_INDEX ipx; if (ctype < 0) error(_("invalid class(x) '%s' in R_to_CMatrix(x)"), ncl); /* replace 'R' with 'C' : */ ncl[2] = 'C'; PROTECT_WITH_INDEX(ans = NEW_OBJECT(MAKE_CLASS(ncl)), &ipx); a_dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2)); /* reversed dim() since we will transpose: */ a_dims[0] = x_dims[1]; a_dims[1] = x_dims[0]; /* triangular: */ LOGICAL(tri)[0] = 0; if((ctype / 3) != 2) /* not n..Matrix */ slot_dup(ans, x, Matrix_xSym); if(ctype % 3) { /* s(ymmetric) or t(riangular) : */ SET_SLOT(ans, Matrix_uploSym, mkString((*uplo_P(x) == 'U') ? "L" : "U")); if(ctype % 3 == 2) { /* t(riangular) : */ LOGICAL(tri)[0] = 1; slot_dup(ans, x, Matrix_diagSym); } } SET_SLOT(ans, Matrix_iSym, duplicate(GET_SLOT(x, Matrix_jSym))); slot_dup(ans, x, Matrix_pSym); REPROTECT(ans = Csparse_transpose(ans, tri), ipx); SET_DimNames(ans, x); free(ncl); UNPROTECT(2); return ans; } /** Return a 2 column matrix '' cbind(i, j) '' of 0-origin index vectors (i,j) * which entirely correspond to the (i,j) slots of * as(x, "TsparseMatrix") : */ SEXP compressed_non_0_ij(SEXP x, SEXP colP) { int col = asLogical(colP); /* 1 if "C"olumn compressed; 0 if "R"ow */ SEXP ans, indSym = col ? Matrix_iSym : Matrix_jSym; SEXP indP = GET_SLOT(x, indSym), pP = GET_SLOT(x, Matrix_pSym); int i, *ij; int nouter = INTEGER(GET_SLOT(x, Matrix_DimSym))[col ? 1 : 0], n_el = INTEGER(pP)[nouter]; /* is only == length(indP), if the inner slot is not over-allocated */ ij = INTEGER(ans = PROTECT(allocMatrix(INTSXP, n_el, 2))); /* expand the compressed margin to 'i' or 'j' : */ expand_cmprPt(nouter, INTEGER(pP), &ij[col ? n_el : 0]); /* and copy the other one: */ if (col) for(i = 0; i < n_el; i++) ij[i] = INTEGER(indP)[i]; else /* row compressed */ for(i = 0; i < n_el; i++) ij[i + n_el] = INTEGER(indP)[i]; UNPROTECT(1); return ans; } #if 0 /* unused */ SEXP dgCMatrix_lusol(SEXP x, SEXP y) { SEXP ycp = PROTECT((TYPEOF(y) == REALSXP) ? duplicate(y) : coerceVector(y, REALSXP)); CSP xc = AS_CSP__(x); R_CheckStack(); if (xc->m != xc->n || xc->m <= 0) error(_("dgCMatrix_lusol requires a square, non-empty matrix")); if (LENGTH(ycp) != xc->m) error(_("Dimensions of system to be solved are inconsistent")); if (!cs_lusol(/*order*/ 1, xc, REAL(ycp), /*tol*/ 1e-7)) error(_("cs_lusol failed")); UNPROTECT(1); return ycp; } #endif SEXP dgCMatrix_qrsol(SEXP x, SEXP y, SEXP ord) { /* FIXME: extend this to work in multivariate case, i.e. y a matrix with > 1 column ! */ SEXP ycp = PROTECT((TYPEOF(y) == REALSXP) ? duplicate(y) : coerceVector(y, REALSXP)); CSP xc = AS_CSP(x); /* <--> x may be dgC* or dtC* */ int order = INTEGER(ord)[0]; #ifdef _not_yet_do_FIXME__ const char *nms[] = {"L", "coef", "Xty", "resid", ""}; SEXP ans = PROTECT(Rf_mkNamed(VECSXP, nms)); #endif R_CheckStack(); if (order < 0 || order > 3) error(_("dgCMatrix_qrsol(., order) needs order in {0,..,3}")); /* --> cs_amd() --- order 0: natural, 1: Chol, 2: LU, 3: QR */ if (LENGTH(ycp) != xc->m) error(_("Dimensions of system to be solved are inconsistent")); /* FIXME? Note that qr_sol() would allow *under-determined systems; * In general, we'd need LENGTH(ycp) = max(n,m) * FIXME also: multivariate y (see above) */ if (xc->m < xc->n || xc->n <= 0) error(_("dgCMatrix_qrsol(<%d x %d>-matrix) requires a 'tall' rectangular matrix"), xc->m, xc->n); /* cs_qrsol(): Tim Davis (2006) .. "8.2 Using a QR factorization", p.136f , calling * ------- cs_sqr(order, ..), see p.76 */ /* MM: FIXME: write our *OWN* version of - the first case (m >= n) - of cs_qrsol() * --------- which will (1) work with a *multivariate* y * (2) compute coefficients properly, not overwriting RHS */ if (!cs_qrsol(order, xc, REAL(ycp))) /* return value really is 0 or 1 - no more info there */ error(_("cs_qrsol() failed inside dgCMatrix_qrsol()")); /* Solution is only in the first part of ycp -- cut its length back to n : */ ycp = lengthgets(ycp, (R_len_t) xc->n); UNPROTECT(1); return ycp; } // Modified version of Tim Davis's cs_qr_mex.c file for MATLAB (in CSparse) // Usage: [V,beta,p,R,q] = cs_qr(A) ; SEXP dgCMatrix_QR(SEXP Ap, SEXP order) { CSP A = AS_CSP__(Ap), D; int io = INTEGER(order)[0]; Rboolean verbose = (io < 0);// verbose=TRUE, encoded with negative 'order' int m = A->m, n = A->n, ord = asLogical(order) ? 3 : 0, *p; R_CheckStack(); if (m < n) error(_("A must have #{rows} >= #{columns}")) ; SEXP ans = PROTECT(NEW_OBJECT(MAKE_CLASS("sparseQR"))); int *dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2)); dims[0] = m; dims[1] = n; css *S = cs_sqr(ord, A, 1); /* symbolic QR ordering & analysis*/ if (!S) error(_("cs_sqr failed")); if(verbose && S->m2 > m) // in ./cs.h , m2 := # of rows for QR, after adding fictitious rows Rprintf("Symbolic QR(): Matrix structurally rank deficient (m2-m = %d)\n", S->m2 - m); csn *N = cs_qr(A, S); /* numeric QR factorization */ if (!N) error(_("cs_qr failed")) ; cs_dropzeros(N->L); /* drop zeros from V and sort */ D = cs_transpose(N->L, 1); cs_spfree(N->L); N->L = cs_transpose(D, 1); cs_spfree(D); cs_dropzeros(N->U); /* drop zeros from R and sort */ D = cs_transpose(N->U, 1); cs_spfree(N->U) ; N->U = cs_transpose(D, 1); cs_spfree(D); m = N->L->m; /* m may be larger now */ // MM: m := S->m2 also counting the ficticious rows (Tim Davis, p.72, 74f) p = cs_pinv(S->pinv, m); /* p = pinv' */ SET_SLOT(ans, install("V"), Matrix_cs_to_SEXP(N->L, "dgCMatrix", 0)); Memcpy(REAL(ALLOC_SLOT(ans, install("beta"), REALSXP, n)), N->B, n); Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_pSym, INTSXP, m)), p, m); SET_SLOT(ans, install("R"), Matrix_cs_to_SEXP(N->U, "dgCMatrix", 0)); if (ord) Memcpy(INTEGER(ALLOC_SLOT(ans, install("q"), INTSXP, n)), S->q, n); else ALLOC_SLOT(ans, install("q"), INTSXP, 0); cs_nfree(N); cs_sfree(S); cs_free(p); UNPROTECT(1); return ans; } #ifdef Matrix_with_SPQR /** * Return a SuiteSparse QR factorization of the sparse matrix A * * @param Ap (pointer to) a [m x n] dgCMatrix * @param ordering integer SEXP specifying the ordering strategy to be used * see SPQR/Include/SuiteSparseQR_definitions.h * @param econ integer SEXP ("economy"): number of rows of R and columns of Q * to return. The default is m. Using n gives the standard economy form. * A value less than the estimated rank r is set to r, so econ=0 gives the * "rank-sized" factorization, where nrow(R)==nnz(diag(R))==r. * @param tol double SEXP: if tol <= -2 use SPQR's default, * if -2 < tol < 0, then no tol is used; otherwise, * tol > 0, use as tolerance: columns with 2-norm <= tol treated as 0 * * * @return SEXP "SPQR" object with slots (Q, R, p, rank, Dim): * Q: dgCMatrix; R: dgCMatrix [subject to change to dtCMatrix FIXME ?] * p: integer: 0-based permutation (or length 0 <=> identity); * rank: integer, the "revealed" rank Dim: integer, original matrix dim. */ SEXP dgCMatrix_SPQR(SEXP Ap, SEXP ordering, SEXP econ, SEXP tol) { /* SEXP ans = PROTECT(allocVector(VECSXP, 4)); */ SEXP ans = PROTECT(NEW_OBJECT(MAKE_CLASS("SPQR"))); CHM_SP A = AS_CHM_SP(Ap), Q, R; UF_long *E, rank;/* not always = int FIXME (Windows_64 ?) */ if ((rank = SuiteSparseQR_C_QR(asInteger(ordering), asReal(tol),/* originally had SPQR_DEFAULT_TOL */ (UF_long)asInteger(econ),/* originally had 0 */ A, &Q, &R, &E, &cl)) == -1) error(_("SuiteSparseQR_C_QR returned an error code")); SET_SLOT(ans, Matrix_DimSym, duplicate(GET_SLOT(Ap, Matrix_DimSym))); /* SET_VECTOR_ELT(ans, 0, */ /* chm_sparse_to_SEXP(Q, 0, 0, 0, "", R_NilValue)); */ SET_SLOT(ans, install("Q"), chm_sparse_to_SEXP(Q, 0, 0, 0, "", R_NilValue)); /* Also gives a dgCMatrix (not a dtC* *triangular*) : * may make sense if to be used in the "spqr_solve" routines .. ?? */ /* SET_VECTOR_ELT(ans, 1, */ /* chm_sparse_to_SEXP(R, 0, 0, 0, "", R_NilValue)); */ SET_SLOT(ans, install("R"), chm_sparse_to_SEXP(R, 0, 0, 0, "", R_NilValue)); cholmod_free_sparse(&Al, &cl); cholmod_free_sparse(&R, &cl); cholmod_free_sparse(&Q, &cl); if (E) { int *Er; SET_VECTOR_ELT(ans, 2, allocVector(INTSXP, A->ncol)); Er = INTEGER(VECTOR_ELT(ans, 2)); for (int i = 0; i < A->ncol; i++) Er[i] = (int) E[i]; Free(E); } else SET_VECTOR_ELT(ans, 2, allocVector(INTSXP, 0)); SET_VECTOR_ELT(ans, 3, ScalarInteger((int)rank)); UNPROTECT(1); return ans; } #endif /* Matrix_with_SPQR */ /* Modified version of Tim Davis's cs_lu_mex.c file for MATLAB */ void install_lu(SEXP Ap, int order, double tol, Rboolean err_sing) { // (order, tol) == (1, 1) by default, when called from R. SEXP ans; css *S; csn *N; int n, *p, *dims; CSP A = AS_CSP__(Ap), D; R_CheckStack(); n = A->n; if (A->m != n) error(_("LU decomposition applies only to square matrices")); if (order) { /* not using natural order */ order = (tol == 1) ? 2 /* amd(S'*S) w/dense rows or I */ : 1; /* amd (A+A'), or natural */ } S = cs_sqr(order, A, /*qr = */ 0); /* symbolic ordering */ N = cs_lu(A, S, tol); /* numeric factorization */ if (!N) { if(err_sing) error(_("cs_lu(A) failed: near-singular A (or out of memory)")); else { /* No warning: The useR should be careful : * Put NA into "LU" factor */ set_factors(Ap, ScalarLogical(NA_LOGICAL), "LU"); return; } } cs_dropzeros(N->L); /* drop zeros from L and sort it */ D = cs_transpose(N->L, 1); cs_spfree(N->L); N->L = cs_transpose(D, 1); cs_spfree(D); cs_dropzeros(N->U); /* drop zeros from U and sort it */ D = cs_transpose(N->U, 1); cs_spfree(N->U); N->U = cs_transpose(D, 1); cs_spfree(D); p = cs_pinv(N->pinv, n); /* p=pinv' */ ans = PROTECT(NEW_OBJECT(MAKE_CLASS("sparseLU"))); dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2)); dims[0] = n; dims[1] = n; SET_SLOT(ans, install("L"), Matrix_cs_to_SEXP(N->L, "dtCMatrix", 0)); SET_SLOT(ans, install("U"), Matrix_cs_to_SEXP(N->U, "dtCMatrix", 0)); Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_pSym, /* "p" */ INTSXP, n)), p, n); if (order) Memcpy(INTEGER(ALLOC_SLOT(ans, install("q"), INTSXP, n)), S->q, n); cs_nfree(N); cs_sfree(S); cs_free(p); UNPROTECT(1); set_factors(Ap, ans, "LU"); } SEXP dgCMatrix_LU(SEXP Ap, SEXP orderp, SEXP tolp, SEXP error_on_sing) { SEXP ans; Rboolean err_sing = asLogical(error_on_sing); /* FIXME: dgCMatrix_LU should check ans for consistency in * permutation type with the requested value - Should have two * classes or two different names in the factors list for LU with * permuted columns or not. * OTOH, currently (order, tol) === (1, 1) always. * It is true that length(LU@q) does flag the order argument. */ if (!isNull(ans = get_factors(Ap, "LU"))) return ans; install_lu(Ap, asInteger(orderp), asReal(tolp), err_sing); return get_factors(Ap, "LU"); } SEXP dgCMatrix_matrix_solve(SEXP Ap, SEXP b, SEXP give_sparse) { Rboolean sparse = asLogical(give_sparse); if(sparse) { // FIXME: implement this error(_("dgCMatrix_matrix_solve(.., sparse=TRUE) not yet implemented")); /* Idea: in the for(j = 0; j < nrhs ..) loop below, build the *sparse* result matrix * ----- *column* wise -- which is perfect for dgCMatrix * --> build (i,p,x) slots "increasingly" [well, allocate in batches ..] * * --> maybe first a protoype in R */ } SEXP ans = PROTECT(dup_mMatrix_as_dgeMatrix(b)), lu, qslot; CSP L, U; int *bdims = INTEGER(GET_SLOT(ans, Matrix_DimSym)), *p, *q; int j, n = bdims[0], nrhs = bdims[1]; double *ax = REAL(GET_SLOT(ans, Matrix_xSym)), *x = Alloca(n, double); R_CheckStack(); if (isNull(lu = get_factors(Ap, "LU"))) { install_lu(Ap, /* order = */ 1, /* tol = */ 1.0, /* err_sing = */ TRUE); lu = get_factors(Ap, "LU"); } qslot = GET_SLOT(lu, install("q")); L = AS_CSP__(GET_SLOT(lu, install("L"))); U = AS_CSP__(GET_SLOT(lu, install("U"))); R_CheckStack(); p = INTEGER(GET_SLOT(lu, Matrix_pSym)); q = LENGTH(qslot) ? INTEGER(qslot) : (int *) NULL; if (U->n != n || nrhs < 1 || n < 1) error(_("Dimensions of system to be solved are inconsistent")); for (j = 0; j < nrhs; j++) { cs_pvec(p, ax + j * n, x, n); /* x = b(p) */ cs_lsolve(L, x); /* x = L\x */ cs_usolve(U, x); /* x = U\x */ if (q) /* r(q) = x , hence r = Q' U{^-1} L{^-1} P b = A^{-1} b */ cs_ipvec(q, x, ax + j * n, n); else Memcpy(ax + j * n, x, n); } UNPROTECT(1); return ans; } SEXP dgCMatrix_cholsol(SEXP x, SEXP y) { /* Solve Sparse Least Squares X %*% beta ~= y with dense RHS y, * where X = t(x) i.e. we pass x = t(X) as argument, * via "Cholesky(X'X)" .. well not really: * cholmod_factorize("x", ..) finds L in X'X = L'L directly */ CHM_SP cx = AS_CHM_SP(x); /* FIXME: extend this to work in multivariate case, i.e. y a matrix with > 1 column ! */ CHM_DN cy = AS_CHM_DN(coerceVector(y, REALSXP)), rhs, cAns, resid; CHM_FR L; int n = cx->ncol;/* #{obs.} {x = t(X) !} */ double one[] = {1,0}, zero[] = {0,0}, neg1[] = {-1,0}; const char *nms[] = {"L", "coef", "Xty", "resid", ""}; SEXP ans = PROTECT(Rf_mkNamed(VECSXP, nms)); R_CheckStack(); if (n < cx->nrow || n <= 0) error(_("dgCMatrix_cholsol requires a 'short, wide' rectangular matrix")); if (cy->nrow != n) error(_("Dimensions of system to be solved are inconsistent")); rhs = cholmod_allocate_dense(cx->nrow, 1, cx->nrow, CHOLMOD_REAL, &c); /* cholmod_sdmult(A, transp, alpha, beta, X, Y, &c): * Y := alpha*(A*X) + beta*Y or alpha*(A'*X) + beta*Y ; * here: rhs := 1 * x %*% y + 0 = x %*% y = X'y */ if (!(cholmod_sdmult(cx, 0 /* trans */, one, zero, cy, rhs, &c))) error(_("cholmod_sdmult error (rhs)")); L = cholmod_analyze(cx, &c); if (!cholmod_factorize(cx, L, &c)) error(_("cholmod_factorize failed: status %d, minor %d from ncol %d"), c.status, L->minor, L->n); /* FIXME: Do this in stages so an "effects" vector can be calculated */ if (!(cAns = cholmod_solve(CHOLMOD_A, L, rhs, &c))) error(_("cholmod_solve (CHOLMOD_A) failed: status %d, minor %d from ncol %d"), c.status, L->minor, L->n); /* L : */ SET_VECTOR_ELT(ans, 0, chm_factor_to_SEXP(L, 0)); /* coef : */ SET_VECTOR_ELT(ans, 1, allocVector(REALSXP, cx->nrow)); Memcpy(REAL(VECTOR_ELT(ans, 1)), (double*)(cAns->x), cx->nrow); /* X'y : */ /* FIXME: Change this when the "effects" vector is available */ SET_VECTOR_ELT(ans, 2, allocVector(REALSXP, cx->nrow)); Memcpy(REAL(VECTOR_ELT(ans, 2)), (double*)(rhs->x), cx->nrow); /* resid := y */ resid = cholmod_copy_dense(cy, &c); /* cholmod_sdmult(A, transp, alp, bet, X, Y, &c): * Y := alp*(A*X) + bet*Y or alp*(A'*X) + beta*Y ; * here: resid := -1 * x' %*% coef + 1 * y = y - X %*% coef */ if (!(cholmod_sdmult(cx, 1/* trans */, neg1, one, cAns, resid, &c))) error(_("cholmod_sdmult error (resid)")); /* FIXME: for multivariate case, i.e. resid *matrix* with > 1 column ! */ SET_VECTOR_ELT(ans, 3, allocVector(REALSXP, n)); Memcpy(REAL(VECTOR_ELT(ans, 3)), (double*)(resid->x), n); cholmod_free_factor(&L, &c); cholmod_free_dense(&rhs, &c); cholmod_free_dense(&cAns, &c); UNPROTECT(1); return ans; } /* Define all of * dgCMatrix_colSums(....) * igCMatrix_colSums(....) * lgCMatrix_colSums_d(....) * lgCMatrix_colSums_i(....) * ngCMatrix_colSums_d(....) * ngCMatrix_colSums_i(....) */ #define _dgC_ #include "t_gCMatrix_colSums.c" #define _igC_ #include "t_gCMatrix_colSums.c" #define _lgC_ #include "t_gCMatrix_colSums.c" #define _ngC_ #include "t_gCMatrix_colSums.c" #define _lgC_mn #include "t_gCMatrix_colSums.c" #define _ngC_mn #include "t_gCMatrix_colSums.c" SEXP lgCMatrix_colSums(SEXP x, SEXP NArm, SEXP spRes, SEXP trans, SEXP means) { if(asLogical(means)) /* ==> result will be "double" / "dsparseVector" */ return lgCMatrix_colSums_d(x, NArm, spRes, trans, means); else return lgCMatrix_colSums_i(x, NArm, spRes, trans, means); } SEXP ngCMatrix_colSums(SEXP x, SEXP NArm, SEXP spRes, SEXP trans, SEXP means) { if(asLogical(means)) /* ==> result will be "double" / "dsparseVector" */ return ngCMatrix_colSums_d(x, NArm, spRes, trans, means); else return ngCMatrix_colSums_i(x, NArm, spRes, trans, means); } Matrix/src/t_gCMatrix_colSums.c0000644000175100001440000001177212271765436016262 0ustar hornikusers/*------ Definition of a template for [diln]gCMatrix_colsums(...) : * * -------- ~~~~~~~~~~~~~~~~~~~~~~ * i.e., included several times from ./dgCMatrix.c * ~~~~~~~~~~~~~ */ /* for all cases with an 'x' slot -- i.e. almost all cases ; * just redefine this in the other cases: */ #ifdef _dgC_ # define gCMatrix_colSums dgCMatrix_colSums # define _DOUBLE_ans # define _has_x_slot_ /*Future? # define _has_x_d_slot_ */ # undef _dgC_ #elif defined (_igC_) # define gCMatrix_colSums igCMatrix_colSums # define _DOUBLE_ans # define _has_x_slot_ /*Future? # define _has_x_d_slot_ */ # undef _igC_ #elif defined (_lgC_) # define gCMatrix_colSums lgCMatrix_colSums_i # define _INT_ans # define _has_x_slot_ /*Future? # define _has_x_l_slot_ */ # undef _lgC_ #elif defined (_lgC_mn) # define gCMatrix_colSums lgCMatrix_colSums_d # define _DOUBLE_ans # define _has_x_slot_ /*Future? # define _has_x_l_slot_ */ # undef _lgC_mn #elif defined (_ngC_) # define gCMatrix_colSums ngCMatrix_colSums_i # define _INT_ans /* withOUT 'x' slot */ # undef _ngC_ #elif defined (_ngC_mn) # define gCMatrix_colSums ngCMatrix_colSums_d # define _DOUBLE_ans /* withOUT 'x' slot */ # undef _ngC_mn #elif defined (_zgC_) # error "zgC* not yet implemented" #else # error "no valid _[dilnz]gC_ option" #endif /* - - - - - - - - - - - - - - - - - - - - */ /* Most of this is maybe for the future, * when cholmod has integer 'x' slot :*/ #ifdef _has_x_d_slot_ # define Type_x_ double # define STYP_x_ REAL # define _has_x_slot_ # undef _has_x_d_slot_ #elif defined (_has_x_i_slot_) # define Type_x_ int # define STYP_x_ INTEGER # define _has_x_slot_ # undef _has_x_i_slot_ #elif defined (_has_x_l_slot_) # define Type_x_ int # define STYP_x_ LOGICAL # define _has_x_slot_ # undef _has_x_l_slot_ #endif /* - - - - - - - - - - - - - - - - - - - - */ #ifdef _DOUBLE_ans # define SparseResult_class "dsparseVector" # define Type_ans double # define STYP_ans REAL # define NA_ans NA_REAL # define SXP_ans REALSXP # define COERCED(x) (x) #undef _DOUBLE_ans #elif defined (_INT_ans) # define SparseResult_class "isparseVector" # define Type_ans int # define STYP_ans INTEGER # define NA_ans NA_INTEGER # define SXP_ans INTSXP # define COERCED(x) (Type_ans)(x != 0) #undef _INT_ans #else # error "invalid macro logic" #endif /* - - - - - - - - - - - - - - - - - - - - */ #ifdef _has_x_slot_ /* currently have x slot always double (cholmod restriction): */ # define is_NA_x_(u) ISNAN(u) # define ColSUM_column(_i1_,_i2_,_SUM_) \ if(mn) dnm = cx->nrow; /* denominator for means */ \ for(i = _i1_, _SUM_ = 0; i < _i2_; i++) { \ if (is_NA_x_(xx[i])) { \ if(!na_rm) { \ _SUM_ = NA_ans; \ break; \ } \ /* else: na_rm : skip NAs , */ \ if(mn) /* but decrement denominator */ \ dnm--; \ } else _SUM_ += COERCED(xx[i]); \ } \ if(mn) _SUM_ = (dnm > 0) ? _SUM_/dnm : NA_ans #else /* no 'x' slot -> no NAs ... */ # define ColSUM_column(_i1_,_i2_,_SUM_) \ _SUM_ = _i2_ - _i1_; \ if(mn) _SUM_ /= cx->nrow #endif /* Now the template which depends on the above macros : */ SEXP gCMatrix_colSums(SEXP x, SEXP NArm, SEXP spRes, SEXP trans, SEXP means) { int mn = asLogical(means), sp = asLogical(spRes), tr = asLogical(trans); /* cholmod_sparse: drawback of coercing lgC to double: */ CHM_SP cx = AS_CHM_SP__(x); R_CheckStack(); if (tr) { cholmod_sparse *cxt = cholmod_transpose(cx, (int)cx->xtype, &c); cx = cxt; } /* everything else *after* the above potential transpose : */ /* Don't declarations here require the C99 standard? Can we assume C99? */ int j, nc = cx->ncol; int *xp = (int *)(cx -> p); #ifdef _has_x_slot_ int na_rm = asLogical(NArm), i, dnm = 0/*Wall*/; double *xx = (double *)(cx -> x); #endif SEXP ans = PROTECT(sp ? NEW_OBJECT(MAKE_CLASS(SparseResult_class)) : allocVector(SXP_ans, nc)); if (sp) { // sparseResult, i.e. *sparseVector (never allocating length-nc) int nza, i1, i2, p, *ai; Type_ans *ax; for (j = 0, nza = 0; j < nc; j++) if(xp[j] < xp[j + 1]) nza++; ai = INTEGER(ALLOC_SLOT(ans, Matrix_iSym, INTSXP, nza)); ax = STYP_ans(ALLOC_SLOT(ans, Matrix_xSym, SXP_ans, nza)); SET_SLOT(ans, Matrix_lengthSym, ScalarInteger(nc)); i2 = xp[0]; for (j = 1, p = 0; j <= nc; j++) { /* j' =j+1, since 'i' slot will be 1-based */ i1 = i2; i2 = xp[j]; if(i1 < i2) { Type_ans sum; ColSUM_column(i1,i2, sum); ai[p] = j; ax[p++] = sum; } } } else { /* "numeric" (non sparse) result */ Type_ans *a = STYP_ans(ans); for (j = 0; j < nc; j++) { ColSUM_column(xp[j], xp[j + 1], a[j]); } } if (tr) cholmod_free_sparse(&cx, &c); UNPROTECT(1); return ans; } #undef ColSUM_column #undef NA_ans #undef STYP_ans #undef SXP_ans #undef SparseResult_class #undef Type_ans #undef COERCED #ifdef _has_x_slot_ # undef NA_x_ # undef Type_x_ # undef STYP_x_ # undef _has_x_slot_ #endif #undef gCMatrix_colSums Matrix/src/dsyMatrix.c0000644000175100001440000001364512271765436014501 0ustar hornikusers#include "dsyMatrix.h" SEXP symmetricMatrix_validate(SEXP obj) { SEXP val = GET_SLOT(obj, Matrix_DimSym); if (LENGTH(val) < 2) return mkString(_("'Dim' slot has length less than two")); if (INTEGER(val)[0] != INTEGER(val)[1]) return mkString(_("Matrix is not square")); if (isString(val = check_scalar_string(GET_SLOT(obj, Matrix_uploSym), "LU", "uplo"))) return val; return ScalarLogical(1); } SEXP dsyMatrix_validate(SEXP obj) { /* since "dsy" inherits from "symmetric", and "dMatrix", only need this:*/ return dense_nonpacked_validate(obj); } double get_norm_sy(SEXP obj, const char *typstr) { char typnm[] = {'\0', '\0'}; int *dims = INTEGER(GET_SLOT(obj, Matrix_DimSym)); double *work = (double *) NULL; typnm[0] = La_norm_type(typstr); if (*typnm == 'I' || *typnm == 'O') { work = (double *) R_alloc(dims[0], sizeof(double)); } return F77_CALL(dlansy)(typnm, uplo_P(obj), dims, REAL(GET_SLOT(obj, Matrix_xSym)), dims, work); } SEXP dsyMatrix_norm(SEXP obj, SEXP type) { return ScalarReal(get_norm_sy(obj, CHAR(asChar(type)))); } SEXP dsyMatrix_rcond(SEXP obj, SEXP type) { SEXP trf = dsyMatrix_trf(obj); int *dims = INTEGER(GET_SLOT(obj, Matrix_DimSym)), info; double anorm = get_norm_sy(obj, "O"); double rcond; F77_CALL(dsycon)(uplo_P(trf), dims, REAL (GET_SLOT(trf, Matrix_xSym)), dims, INTEGER(GET_SLOT(trf, Matrix_permSym)), &anorm, &rcond, (double *) R_alloc(2*dims[0], sizeof(double)), (int *) R_alloc(dims[0], sizeof(int)), &info); return ScalarReal(rcond); } SEXP dsyMatrix_solve(SEXP a) { SEXP trf = dsyMatrix_trf(a); SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dsyMatrix"))); int *dims = INTEGER(GET_SLOT(trf, Matrix_DimSym)), info; slot_dup(val, trf, Matrix_uploSym); slot_dup(val, trf, Matrix_xSym); slot_dup(val, trf, Matrix_DimSym); F77_CALL(dsytri)(uplo_P(val), dims, REAL(GET_SLOT(val, Matrix_xSym)), dims, INTEGER(GET_SLOT(trf, Matrix_permSym)), (double *) R_alloc((long) dims[0], sizeof(double)), &info); UNPROTECT(1); return val; } SEXP dsyMatrix_matrix_solve(SEXP a, SEXP b) { SEXP trf = dsyMatrix_trf(a), val = PROTECT(dup_mMatrix_as_dgeMatrix(b)); int *adims = INTEGER(GET_SLOT(a, Matrix_DimSym)), *bdims = INTEGER(GET_SLOT(val, Matrix_DimSym)), info; if (*adims != *bdims || bdims[1] < 1 || *adims < 1) error(_("Dimensions of system to be solved are inconsistent")); F77_CALL(dsytrs)(uplo_P(trf), adims, bdims + 1, REAL(GET_SLOT(trf, Matrix_xSym)), adims, INTEGER(GET_SLOT(trf, Matrix_permSym)), REAL(GET_SLOT(val, Matrix_xSym)), bdims, &info); UNPROTECT(1); return val; } SEXP dsyMatrix_as_matrix(SEXP from, SEXP keep_dimnames) { int n = INTEGER(GET_SLOT(from, Matrix_DimSym))[0]; SEXP val = PROTECT(allocMatrix(REALSXP, n, n)); make_d_matrix_symmetric(Memcpy(REAL(val), REAL(GET_SLOT(from, Matrix_xSym)), n * n), from); if(asLogical(keep_dimnames)) setAttrib(val, R_DimNamesSymbol, GET_SLOT(from, Matrix_DimNamesSym)); UNPROTECT(1); return val; } SEXP dsyMatrix_matrix_mm(SEXP a, SEXP b, SEXP rtP) { SEXP val = PROTECT(dup_mMatrix_as_dgeMatrix(b));// incl. its dimnames int rt = asLogical(rtP); /* if(rt), compute b %*% a, else a %*% b */ int *adims = INTEGER(GET_SLOT(a, Matrix_DimSym)), *bdims = INTEGER(GET_SLOT(val, Matrix_DimSym)), m = bdims[0], n = bdims[1]; double one = 1., zero = 0.; double *vx = REAL(GET_SLOT(val, Matrix_xSym)); double *bcp = Memcpy(Alloca(m * n, double), vx, m * n); R_CheckStack(); if ((rt && n != adims[0]) || (!rt && m != adims[0])) error(_("Matrices are not conformable for multiplication")); if (m < 1 || n < 1) { /* error(_("Matrices with zero extents cannot be multiplied")); */ } else F77_CALL(dsymm)(rt ? "R" :"L", uplo_P(a), &m, &n, &one, REAL(GET_SLOT(a, Matrix_xSym)), adims, bcp, &m, &zero, vx, &m); UNPROTECT(1); return val; } SEXP dsyMatrix_trf(SEXP x) { SEXP val = get_factors(x, "BunchKaufman"), dimP = GET_SLOT(x, Matrix_DimSym), uploP = GET_SLOT(x, Matrix_uploSym); int *dims = INTEGER(dimP), *perm, info; int lwork = -1, n = dims[0]; const char *uplo = CHAR(STRING_ELT(uploP, 0)); double tmp, *vx, *work; if (val != R_NilValue) return val; dims = INTEGER(dimP); val = PROTECT(NEW_OBJECT(MAKE_CLASS("BunchKaufman"))); SET_SLOT(val, Matrix_uploSym, duplicate(uploP)); SET_SLOT(val, Matrix_diagSym, mkString("N")); SET_SLOT(val, Matrix_DimSym, duplicate(dimP)); vx = REAL(ALLOC_SLOT(val, Matrix_xSym, REALSXP, n * n)); AZERO(vx, n * n); F77_CALL(dlacpy)(uplo, &n, &n, REAL(GET_SLOT(x, Matrix_xSym)), &n, vx, &n); perm = INTEGER(ALLOC_SLOT(val, Matrix_permSym, INTSXP, n)); F77_CALL(dsytrf)(uplo, &n, vx, &n, perm, &tmp, &lwork, &info); lwork = (int) tmp; work = Alloca(lwork, double); R_CheckStack(); F77_CALL(dsytrf)(uplo, &n, vx, &n, perm, work, &lwork, &info); if (info) error(_("Lapack routine dsytrf returned error code %d"), info); UNPROTECT(1); return set_factors(x, val, "BunchKaufman"); } // this is very close to lsyMatrix_as_lsp*() in ./ldense.c -- keep synced ! SEXP dsyMatrix_as_dspMatrix(SEXP from) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dspMatrix"))), uplo = GET_SLOT(from, Matrix_uploSym), dimP = GET_SLOT(from, Matrix_DimSym); int n = *INTEGER(dimP); SET_SLOT(val, Matrix_DimSym, duplicate(dimP)); SET_SLOT(val, Matrix_uploSym, duplicate(uplo)); full_to_packed_double( REAL(ALLOC_SLOT(val, Matrix_xSym, REALSXP, (n*(n+1))/2)), REAL( GET_SLOT(from, Matrix_xSym)), n, *CHAR(STRING_ELT(uplo, 0)) == 'U' ? UPP : LOW, NUN); SET_SLOT(val, Matrix_DimNamesSym, duplicate(GET_SLOT(from, Matrix_DimNamesSym))); SET_SLOT(val, Matrix_factorSym, duplicate(GET_SLOT(from, Matrix_factorSym))); UNPROTECT(1); return val; } Matrix/src/scripts/0000755000175100001440000000000012271765436014027 5ustar hornikusersMatrix/src/scripts/0get-SuiteSparse.sh0000755000175100001440000001277212222300242017453 0ustar hornikusers#!/bin/sh ## This *REPLACES* former ./UFsparse_download.sh ## Update Libraries from Tim Davis (University of Florida (UF))' "SuiteSparse": # if [ ! -d ../src -o ! -d ./scripts ] then echo 'Must run in Matrix/src/ !' ; exit 1 fi getSPQR=no ## --- since late summer 2010, we no longer get SPQR ufl_URL=http://www.cise.ufl.edu/research/sparse/SuiteSparse/current/ TGZ=SuiteSparse.tar.gz # if [ -f $TGZ ] # then echo 'Tarfile present; not downloading (remove it to change this!)' ; ls -l $TGZ # else wget -nc $ufl_URL/$TGZ # fi SS=SuiteSparse SSdocDir=../inst/doc/SuiteSparse ## 1) SuiteSparse_config --------------------------------------------- ## NOTA BENE: SuiteSparse_config/ is what UFconfig/ used to be Sdir=$SS/SuiteSparse_config ## install SuiteSparse_config.h file (now needed by some SuiteSparse libraries) tar zxf $TGZ $Sdir/SuiteSparse_config.h $Sdir/SuiteSparse_config.c $Sdir/Makefile $Sdir/README.txt ## Move the SuiteSparse_config/README.txt file to docs: mv $Sdir/README.txt $SSdocDir/SuiteSparse_config.txt mv $Sdir/Makefile $Sdir/Makefile_orig ## touch the file $Sdir/SuiteSparse_config.mk. We use other configuration ## environment variables but this name is embedded in some Makefiles touch $Sdir/SuiteSparse_config.mk ## Need to add the Matrix-specific changes to SuiteSparse_config/SuiteSparse_config.h : ## 2012-06: *no longer* patch -p0 < scripts/SuiteSparse_config.patch ## move directory *up* dd=`basename $Sdir`; mv $Sdir/* $dd/ ## 2) COLAMD ----------------------------------------------- Sdir=$SS/COLAMD ## install COLAMD/Source and COLAMD/Include directories tar zxf $TGZ $Sdir/Source/ $Sdir/Include/ $Sdir/Doc/ $Sdir/README.txt f=$Sdir/Source/Makefile if [ -f $f ] then Rscript --vanilla -e 'source("scripts/fixup-fn.R")' -e 'fixup("'$f'")' fi ## install documentation for COLAMD mv $Sdir/README.txt $SSdocDir/COLAMD.txt mv $Sdir/Doc/ChangeLog $SSdocDir/COLAMD-ChangeLog.txt rm -rf $Sdir/Doc patch -p0 < scripts/COLAMD.patch ## --------------------- ## move directory *up* dd=`basename $Sdir`; rsync -auv $Sdir/ $dd/ ## 3) AMD -------------------------------------------------- Sdir=$SS/AMD ## install AMD/Source, AMD/Include and AMD/Lib directories tar zxf $TGZ $Sdir/Source $Sdir/Include $Sdir/Lib $Sdir/README.txt ## install AMD documentation mv $Sdir/README.txt $SSdocDir/AMD.txt ## remove Fortran source files and GNUMakefile rm $Sdir/Source/*.f $Sdir/Lib/GNUmakefile #(for f in $Sdir/Include/amd_internal.h $Sdir/Source/amd_global.c; do diff -ubBw ${f}.~1~ $f ; done ) | tee scripts/AMD-noprint.patch patch -p0 < scripts/AMD-noprint.patch ## --------------------- ## move directory *up* dd=`basename $Sdir`; rsync -auv $Sdir/ $dd/ ## 4) CHOLMOD ---------------------------------------------- Sdir=$SS/CHOLMOD ## install CHOLMOD source files for d in Check Cholesky Core Include Lib MatrixOps Modify Partition Supernodal README.txt do tar zxf $TGZ $Sdir/$d done ## install CHOLMOD documentation mv $Sdir/README.txt $SSdocDir/CHOLMOD.txt cp -p $Sdir/Lib/Makefile $Sdir/Lib/Makefile_CHOLMOD Rscript --vanilla -e 'source("scripts/fixup-fn.R")' -e 'fixup("'$Sdir'/Lib/Makefile")' ## but typically, this is not good enough, so we need manual work: mv $Sdir/Lib/Makefile $Sdir/Lib/Makefile_pre ## move directory *up* dd=`basename $Sdir`; rsync -auv $Sdir/ $dd/ echo 'If there changes in the following you ** MUST ** manually update / inst/include/cholmod.h --- to export what we have. Also, RcppEigen headers may also need to be updated -- ask Doug Bates. This can be VERY IMPORTANT, not the least for lme4 ' svn diff --diff-cmd /usr/bin/diff -x "-bBw" $dd/Include/cholmod_core.h echo 'Did the above show any non trivial diffs? --> do update inst/include/cholmod.h !! ' svn revert $dd/Lib/Makefile ls -l $dd/Lib/Makefile_pre echo "now diff $dd/Lib/Makefile $dd/Lib/Makefile_pre " echo ' make changes as necessary, and then (later)' echo " rm $dd"'/Lib/Makefile_*' ; echo ## 5) CCparse ------------------------------------------------- Sdir=$SS/CSparse ## install CSparse/Source & CSparse/Include tar zxf $TGZ $Sdir/Source $Sdir/Include $Sdir/README.txt ## Include: echo -n "Moving from $Sdir/Include .. " f=$Sdir/Include/cs.h chmod a+r $f && mv $f . ## Source: MatrixDir=`pwd` cd $Sdir/Source cat cs_*.c | sed -e '1 p' -e '/^#include/d' -e 's/\bprintf/Rprintf/g' > $MatrixDir/cs.c cd $MatrixDir patch -p0 < scripts/cs.patch echo '[Ok]' echo -n "removing $Sdir .." rm -rf $Sdir echo '[Ok]' ## 6) SPQR ------------------------------------------------- if [ $getSPQR = yes ] then ## install SPQR source files for d in Source Include Lib do tar zxf ./SPQR.tar.gz SPQR/$d done ## install CHOLMOD documentation in ../inst/doc/UFsparse tar zxf ./SPQR.tar.gz SPQR/README.txt mv SPQR/README.txt $SSdocDir/SPQR.txt ## patch for Matrix: patch -p0 < scripts/SPQR.patch cp -p SPQR/Lib/Makefile SPQR/Lib/Makefile_SPQR Rscript --vanilla -e 'source("scripts/fixup-fn.R")' -e 'fixup("SPQR/Lib/Makefile")' mv SPQR/Lib/Makefile SPQR/Lib/Makefile_pre svn revert SPQR/Lib/Makefile ## ls -l SPQR/Lib/Makefile_pre echo 'now diff SPQR/Lib/Makefile with SPQR/Lib/Makefile_pre' echo ' make changes as necessary, and then (later)' echo ' rm SPQR/Lib/Makefile_*' ; echo fi ## ----- remove the downloaded tar file ------------------- echo 'You could (eventually) do rm '"$TGZ"' but keeping it will not download it anew, if not changed. Further, consider updating the doxygen docu on the R-forge web site via /u/maechler/R/Pkgs/Matrix-doxygen-update ' Matrix/src/scripts/DEPS.mkf0000644000175100001440000001346012201004116015233 0ustar hornikusersCHMfactor.o: CHMfactor.c CHMfactor.h Mutils.h Syms.h \ chm_common.h SuiteSparse_config/SuiteSparse_config.h CHOLMOD/Include/cholmod.h \ CHOLMOD/Include/cholmod_io64.h CHOLMOD/Include/cholmod_config.h \ CHOLMOD/Include/cholmod_core.h CHOLMOD/Include/cholmod_check.h \ CHOLMOD/Include/cholmod_cholesky.h CHOLMOD/Include/cholmod_partition.h \ CHOLMOD/Include/cholmod_supernodal.h \ CHOLMOD/Include/cholmod_matrixops.h CHOLMOD/Include/cholmod_modify.h Csparse.o: Csparse.c Csparse.h Tsparse.h Mutils.h Syms.h t_Csparse_subassign.c t_Csparse_validate.c \ chm_common.h SuiteSparse_config/SuiteSparse_config.h CHOLMOD/Include/cholmod.h \ CHOLMOD/Include/cholmod_io64.h CHOLMOD/Include/cholmod_config.h \ CHOLMOD/Include/cholmod_core.h CHOLMOD/Include/cholmod_check.h \ CHOLMOD/Include/cholmod_cholesky.h CHOLMOD/Include/cholmod_partition.h \ CHOLMOD/Include/cholmod_supernodal.h \ CHOLMOD/Include/cholmod_matrixops.h CHOLMOD/Include/cholmod_modify.h Mutils.o: Mutils.c Mutils.h Syms.h TMatrix_as.o: TMatrix_as.c TMatrix_as.h Mutils.h Syms.h Tsparse.o: Tsparse.c Tsparse.h Mutils.h Syms.h \ chm_common.h SuiteSparse_config/SuiteSparse_config.h CHOLMOD/Include/cholmod.h \ CHOLMOD/Include/cholmod_io64.h CHOLMOD/Include/cholmod_config.h \ CHOLMOD/Include/cholmod_core.h CHOLMOD/Include/cholmod_check.h \ CHOLMOD/Include/cholmod_cholesky.h CHOLMOD/Include/cholmod_partition.h \ CHOLMOD/Include/cholmod_supernodal.h \ CHOLMOD/Include/cholmod_matrixops.h CHOLMOD/Include/cholmod_modify.h chm_common.o: chm_common.c chm_common.h Mutils.h Syms.h \ SuiteSparse_config/SuiteSparse_config.h \ CHOLMOD/Include/cholmod.h CHOLMOD/Include/cholmod_io64.h \ CHOLMOD/Include/cholmod_config.h CHOLMOD/Include/cholmod_core.h \ CHOLMOD/Include/cholmod_check.h CHOLMOD/Include/cholmod_cholesky.h \ CHOLMOD/Include/cholmod_partition.h \ CHOLMOD/Include/cholmod_supernodal.h \ CHOLMOD/Include/cholmod_matrixops.h CHOLMOD/Include/cholmod_modify.h cs.o: cs.c cs.h cs_utils.o: cs_utils.c cs_utils.h cs.h Mutils.h Syms.h dense.o: dense.c dense.h Mutils.h Syms.h \ chm_common.h SuiteSparse_config/SuiteSparse_config.h CHOLMOD/Include/cholmod.h \ CHOLMOD/Include/cholmod_io64.h CHOLMOD/Include/cholmod_config.h \ CHOLMOD/Include/cholmod_core.h CHOLMOD/Include/cholmod_check.h \ CHOLMOD/Include/cholmod_cholesky.h CHOLMOD/Include/cholmod_partition.h \ CHOLMOD/Include/cholmod_supernodal.h \ CHOLMOD/Include/cholmod_matrixops.h CHOLMOD/Include/cholmod_modify.h dgCMatrix.o: dgCMatrix.c dgCMatrix.h t_gCMatrix_colSums.c \ Csparse.h Mutils.h Syms.h \ cs_utils.h cs.h chm_common.h SuiteSparse_config/SuiteSparse_config.h \ CHOLMOD/Include/cholmod.h CHOLMOD/Include/cholmod_io64.h \ CHOLMOD/Include/cholmod_config.h CHOLMOD/Include/cholmod_core.h \ CHOLMOD/Include/cholmod_check.h CHOLMOD/Include/cholmod_cholesky.h \ CHOLMOD/Include/cholmod_partition.h \ CHOLMOD/Include/cholmod_supernodal.h \ CHOLMOD/Include/cholmod_matrixops.h CHOLMOD/Include/cholmod_modify.h dgTMatrix.o: dgTMatrix.c dgTMatrix.h Mutils.h Syms.h Tsparse.h \ chm_common.h SuiteSparse_config/SuiteSparse_config.h CHOLMOD/Include/cholmod.h \ CHOLMOD/Include/cholmod_io64.h CHOLMOD/Include/cholmod_config.h \ CHOLMOD/Include/cholmod_core.h CHOLMOD/Include/cholmod_check.h \ CHOLMOD/Include/cholmod_cholesky.h CHOLMOD/Include/cholmod_partition.h \ CHOLMOD/Include/cholmod_supernodal.h \ CHOLMOD/Include/cholmod_matrixops.h CHOLMOD/Include/cholmod_modify.h dgeMatrix.o: dgeMatrix.c dgeMatrix.h Mutils.h Syms.h dpoMatrix.o: dpoMatrix.c dpoMatrix.h Mutils.h Syms.h dppMatrix.o: dppMatrix.c dppMatrix.h Mutils.h Syms.h dspMatrix.h dgeMatrix.h dsCMatrix.o: dsCMatrix.c dsCMatrix.h Mutils.h Syms.h \ chm_common.h SuiteSparse_config/SuiteSparse_config.h CHOLMOD/Include/cholmod.h \ CHOLMOD/Include/cholmod_io64.h CHOLMOD/Include/cholmod_config.h \ CHOLMOD/Include/cholmod_core.h CHOLMOD/Include/cholmod_check.h \ CHOLMOD/Include/cholmod_cholesky.h CHOLMOD/Include/cholmod_partition.h \ CHOLMOD/Include/cholmod_supernodal.h \ CHOLMOD/Include/cholmod_matrixops.h CHOLMOD/Include/cholmod_modify.h dspMatrix.o: dspMatrix.c dspMatrix.h dgeMatrix.h Mutils.h Syms.h dsyMatrix.o: dsyMatrix.c dsyMatrix.h Mutils.h Syms.h dtCMatrix.o: dtCMatrix.c dtCMatrix.h Mutils.h Syms.h dgCMatrix.h cs_utils.h cs.h dtTMatrix.o: dtTMatrix.c dtTMatrix.h dgTMatrix.h Mutils.h Syms.h \ chm_common.h SuiteSparse_config/SuiteSparse_config.h CHOLMOD/Include/cholmod.h \ CHOLMOD/Include/cholmod_io64.h CHOLMOD/Include/cholmod_config.h \ CHOLMOD/Include/cholmod_core.h CHOLMOD/Include/cholmod_check.h \ CHOLMOD/Include/cholmod_cholesky.h CHOLMOD/Include/cholmod_partition.h \ CHOLMOD/Include/cholmod_supernodal.h \ CHOLMOD/Include/cholmod_matrixops.h CHOLMOD/Include/cholmod_modify.h dtpMatrix.o: dtpMatrix.c dtpMatrix.h Mutils.h Syms.h dtrMatrix.o: dtrMatrix.c dtrMatrix.h Mutils.h Syms.h factorizations.o: factorizations.c factorizations.h Mutils.h Syms.h init.o: init.c Mutils.h Syms.h \ chm_common.h SuiteSparse_config/SuiteSparse_config.h CHOLMOD/Include/cholmod.h \ CHOLMOD/Include/cholmod_io64.h CHOLMOD/Include/cholmod_config.h \ CHOLMOD/Include/cholmod_core.h CHOLMOD/Include/cholmod_check.h \ CHOLMOD/Include/cholmod_cholesky.h CHOLMOD/Include/cholmod_partition.h \ CHOLMOD/Include/cholmod_supernodal.h \ CHOLMOD/Include/cholmod_matrixops.h CHOLMOD/Include/cholmod_modify.h \ CHMfactor.h Csparse.h Tsparse.h dense.h dgCMatrix.h \ cs_utils.h cs.h dgTMatrix.h dgeMatrix.h dpoMatrix.h \ dppMatrix.h dspMatrix.h dsCMatrix.h TMatrix_as.h dsyMatrix.h \ dtCMatrix.h dtTMatrix.h dtrMatrix.h dtpMatrix.h factorizations.h \ ldense.h lgCMatrix.h sparseQR.h ldense.o: ldense.c ldense.h Mutils.h Syms.h lgCMatrix.o: lgCMatrix.c lgCMatrix.h Mutils.h Syms.h dgCMatrix.h \ cs_utils.h cs.h sparseQR.o: sparseQR.c sparseQR.h Mutils.h Syms.h cs_utils.h cs.h sparseVector.o: sparseVector.c Mutils.h t_sparseVector.c Matrix/src/scripts/SOURCES_C.mkf0000644000175100001440000000114711601432164016077 0ustar hornikusersSOURCES_C = \ CHMfactor.c \ Csparse.c \ TMatrix_as.c \ Tsparse.c \ init.c \ Mutils.c \ chm_common.c \ cs.c \ cs_utils.c \ dense.c \ dgCMatrix.c \ dgTMatrix.c \ dgeMatrix.c \ dpoMatrix.c \ dppMatrix.c \ dsCMatrix.c \ dsyMatrix.c \ dspMatrix.c \ dtCMatrix.c \ dtTMatrix.c \ dtrMatrix.c \ dtpMatrix.c \ factorizations.c \ ldense.c \ lgCMatrix.c \ sparseQR.c \ abIndex.c Matrix/src/scripts/fixup-fn.R0000644000175100001440000000277611076041562015707 0ustar hornikusers## From: Prof Brian Ripley ## To: Martin Maechler ## cc: Kurt.Hornik@wu-wien.ac.at, Matrix-authors@r-project.org, ## simon.urbanek@r-project.org ## Subject: Re: Matrix 0.999375-16 uploaded to CRAN ## Date: Thu, 16 Oct 2008 16:26:57 +0100 (BST) ## ................ ## A) The good news is that I have a set of Makefiles that work on Sun make ## and I believe are POSIX-compliant. The following R script ## was applied to src/CHOLMOD/Lib/Makefile ## and src/SPQR/Lib/Makefile ## to 'POSIXify' them, fixup <- function(file="Makefile") { file.copy(file, paste(file, "orig", sep=".")) orig <- readLines(file) current <- "" for(i in seq_along(orig)) { if (length(grep(".o: ", orig[i], fixed = TRUE))) { print(orig[i]) # "verbose info" current <- sub("[^ ]* (.*)", "\\1", orig[i]) current <- strsplit(current, " ")[[1]][1] } else if (length(grep("$<", orig[i], fixed = TRUE))) { ## use last line's current : orig[i] <- sub("$<", current, orig[i], fixed = TRUE) } else if (length(grep("^PKG_CFLAGS *= *-I", orig[i]))) { orig[i] <- sub("^PKG_CFLAGS", "PKG_CPPFLAGS", orig[i]) } } writeLines(orig, file) } ## and I hand edited ../AMD/Source/Makefile and ## ../CHOLMOD/Lib/Makefile. If I did it right those changes are attached as ## Matrix.patch2. Hopefully such a script makes future maintenance easy. ## MM: Try to apply it to all 4 Makefiles and only use a patch file for ## "the rest" Matrix/src/scripts/DEPS.mkf_make.sh0000755000175100001440000000135111770366335016670 0ustar hornikusers#!/bin/sh # R=${R:-R-patched} if [ x$R_HOME = x ] ; then R_HOME=`$R RHOME`; fi RINC=${R_HOME}/include # MatrixDir=`dirname $0`/..; cd $MatrixDir; MatrixDir=`pwd` if [ ! -d $MatrixDir ] then echo "no directory '$MatrixDir' .. exiting"; exit 3 fi cd $MatrixDir ## CHOLMOD has one include for which gcc -MM fails below: FIX=CHOLMOD/Include/cholmod.h if [ -f $FIX ] then sed '/^#include "SuiteSparse_config/s/\(.*\)/\/* \1 *\//' $FIX > ${FIX}_fixed mv $FIX ${FIX}_orig mv ${FIX}_fixed $FIX fi ## __end fix__ out=scripts/DEPS.mkf_automade gcc -I$RINC -MM *.c | perl -pe "s{$RINC/[^.]*.h( \\\\\\n)?}{}g" > $out # ^^^ ~~~ if [ -f ${FIX}_orig ] ; then mv ${FIX}_orig $FIX ; fi echo ''; echo "$0 done. Resulting file is $MatrixDir/$out" Matrix/src/cs_utils.h0000644000175100001440000000110412271765436014332 0ustar hornikusers#ifndef CS_UTILS_H #define CS_UTILS_H #include "cs.h" #include "Mutils.h" typedef cs *CSP ; CSP Matrix_as_cs(CSP ans, SEXP x, Rboolean check_Udiag); SEXP Matrix_cs_to_SEXP(CSP A, char *cl, int dofree); #define AS_CSP(x) Matrix_as_cs((CSP)alloca(sizeof(cs)), x, TRUE) #define AS_CSP__(x) Matrix_as_cs((CSP)alloca(sizeof(cs)), x, FALSE) #if 0 /* unused */ css *Matrix_as_css(css *ans, SEXP x); csn *Matrix_as_csn(csn *ans, SEXP x); SEXP Matrix_css_to_SEXP(css *S, char *cl, int dofree, int m, int n); SEXP Matrix_csn_to_SEXP(csn *N, char *cl, int dofree); #endif #endif Matrix/src/Mutils.h0000644000175100001440000002676312271765436014004 0ustar hornikusers#ifndef MATRIX_MUTILS_H #define MATRIX_MUTILS_H #undef Matrix_with_SPQR #ifdef __cplusplus extern "C" { #endif #include // C99 for int64_t #include #include /* includes Rconfig.h */ #include #include /* Rinternals.h + GET_SLOT etc */ #ifdef ENABLE_NLS #include #define _(String) dgettext ("Matrix", String) #else #define _(String) (String) /* Note that this is not yet supported (for Windows, e.g.) in R 2.9.0 : */ #define dngettext(pkg, String, StringP, N) (N > 1 ? StringP : String) #endif #ifdef __GNUC__ # undef alloca # define alloca(x) __builtin_alloca((x)) #elif defined(__sun) || defined(_AIX) /* this is necessary (and sufficient) for Solaris 10 and AIX 6: */ # include #endif #ifndef LONG_VECTOR_SUPPORT // notably for R <= 2.15.x : # define XLENGTH(x) LENGTH(x) # if R_VERSION < R_Version(2,16,0) typedef int R_xlen_t; # endif #endif #define Alloca(n, t) (t *) alloca( (size_t) ( (n) * sizeof(t) ) ) SEXP triangularMatrix_validate(SEXP obj); SEXP symmetricMatrix_validate(SEXP obj); SEXP dense_nonpacked_validate(SEXP obj); // La_norm_type() & La_rcond_type() have been in R_ext/Lapack.h // but have still not been available to package writers ... char La_norm_type (const char *typstr); char La_rcond_type(const char *typstr); /* enum constants from cblas.h and some short forms */ enum CBLAS_ORDER {CblasRowMajor=101, CblasColMajor=102}; enum CBLAS_TRANSPOSE {CblasNoTrans=111, CblasTrans=112, CblasConjTrans=113}; enum CBLAS_UPLO {CblasUpper=121, CblasLower=122}; enum CBLAS_DIAG {CblasNonUnit=131, CblasUnit=132}; enum CBLAS_SIDE {CblasLeft=141, CblasRight=142}; #define RMJ CblasRowMajor #define CMJ CblasColMajor #define NTR CblasNoTrans #define TRN CblasTrans #define CTR CblasConjTrans #define UPP CblasUpper #define LOW CblasLower #define NUN CblasNonUnit #define UNT CblasUnit #define LFT CblasLeft #define RGT CblasRight double get_double_by_name(SEXP obj, char *nm); SEXP set_double_by_name(SEXP obj, double val, char *nm); SEXP as_det_obj(double val, int log, int sign); SEXP get_factors(SEXP obj, char *nm); SEXP set_factors(SEXP obj, SEXP val, char *nm); SEXP R_set_factors(SEXP obj, SEXP val, SEXP name); #if 0 SEXP dgCMatrix_set_Dim(SEXP x, int nrow); #endif /* unused */ /* int csc_unsorted_columns(int ncol, const int p[], const int i[]); */ /* void csc_sort_columns(int ncol, const int p[], int i[], double x[]); */ /* SEXP csc_check_column_sorting(SEXP A); */ SEXP check_scalar_string(SEXP sP, char *vals, char *nm); Rboolean equal_string_vectors(SEXP s1, SEXP s2); void d_packed_getDiag(double *dest, SEXP x, int n); void l_packed_getDiag( int *dest, SEXP x, int n); SEXP d_packed_setDiag(double *diag, int l_d, SEXP x, int n); SEXP l_packed_setDiag( int *diag, int l_d, SEXP x, int n); SEXP d_packed_addDiag(double *diag, int l_d, SEXP x, int n); void tr_d_packed_getDiag(double *dest, SEXP x, int n); void tr_l_packed_getDiag( int *dest, SEXP x, int n); SEXP tr_d_packed_setDiag(double *diag, int l_d, SEXP x, int n); SEXP tr_l_packed_setDiag( int *diag, int l_d, SEXP x, int n); SEXP tr_d_packed_addDiag(double *diag, int l_d, SEXP x, int n); SEXP Matrix_getElement(SEXP list, char *nm); #define PACKED_TO_FULL(TYPE) \ TYPE *packed_to_full_ ## TYPE(TYPE *dest, const TYPE *src, \ int n, enum CBLAS_UPLO uplo) PACKED_TO_FULL(double); PACKED_TO_FULL(int); #undef PACKED_TO_FULL #define FULL_TO_PACKED(TYPE) \ TYPE *full_to_packed_ ## TYPE(TYPE *dest, const TYPE *src, int n, \ enum CBLAS_UPLO uplo, enum CBLAS_DIAG diag) FULL_TO_PACKED(double); FULL_TO_PACKED(int); #undef FULL_TO_PACKED extern /* stored pointers to symbols initialized in R_init_Matrix */ #include "Syms.h" /* zero an array */ #define AZERO(x, n) {int _I_, _SZ_ = (n); for(_I_ = 0; _I_ < _SZ_; _I_++) (x)[_I_] = 0;} /* number of elements in one triangle of a square matrix of order n */ #define PACKED_LENGTH(n) ((n) * ((n) + 1))/2 /* duplicate the slot with name given by sym from src to dest */ #define slot_dup(dest, src, sym) SET_SLOT(dest, sym, duplicate(GET_SLOT(src, sym))) /* is not yet used: */ #define slot_nonNull_dup(dest, src, sym) \ if(GET_SLOT(src, sym) != R_NilValue) \ SET_SLOT(dest, sym, duplicate(GET_SLOT(src, sym))) #define slot_dup_if_has(dest, src, sym) \ if(R_has_slot(src, sym)) \ SET_SLOT(dest, sym, duplicate(GET_SLOT(src, sym))) /* TODO: Make this faster for the case where dimnames = list(NULL,NULL) * and hence don't have to be set ! */ #define SET_DimNames(dest, src) slot_dup(dest, src, Matrix_DimNamesSym) #define uplo_P(_x_) CHAR(STRING_ELT(GET_SLOT(_x_, Matrix_uploSym), 0)) #define diag_P(_x_) CHAR(STRING_ELT(GET_SLOT(_x_, Matrix_diagSym), 0)) #define Diag_P(_x_) (R_has_slot(x, Matrix_diagSym) ? \ CHAR(STRING_ELT(GET_SLOT(_x_, Matrix_diagSym), 0)) : " ") #define class_P(_x_) CHAR(asChar(getAttrib(_x_, R_ClassSymbol))) // Define this "Cholmod compatible" to some degree enum x_slot_kind {x_pattern=-1, x_double=0, x_logical=1, x_integer=2, x_complex=3}; // n d l i z /* should also work for "matrix" matrices: */ #define Real_KIND(_x_) (IS_S4_OBJECT(_x_) ? Real_kind(_x_) : \ (isReal(_x_) ? x_double : (isLogical(_x_) ? x_logical : -1))) /* This one gives '0' also for integer "matrix" :*/ #define Real_KIND2(_x_) (IS_S4_OBJECT(_x_) ? Real_kind(_x_) : \ (isLogical(_x_) ? x_logical : 0)) /* requires 'x' slot: */ #define Real_kind(_x_) (isReal(GET_SLOT(_x_, Matrix_xSym)) ? 0 : \ (isLogical(GET_SLOT(_x_, Matrix_xSym)) ? 1 : -1)) #define DECLARE_AND_GET_X_SLOT(__C_TYPE, __SEXP) \ __C_TYPE *xx = __SEXP(GET_SLOT(x, Matrix_xSym)) /** * Check for valid length of a packed triangular array and return the * corresponding number of columns * * @param len length of a packed triangular array * * @return number of columns */ static R_INLINE int packed_ncol(int len) { int disc = 8 * len + 1; /* discriminant */ int sqrtd = (int) sqrt((double) disc); if (len < 0 || disc != sqrtd * sqrtd) error(_("invalid 'len' = %d in packed_ncol")); return (sqrtd - 1)/2; } /** * Allocate an SEXP of given type and length, assign it as slot nm in * the object, and return the SEXP. The validity of this function * depends on SET_SLOT not duplicating val when NAMED(val) == 0. If * this behavior changes then ALLOC_SLOT must use SET_SLOT followed by * GET_SLOT to ensure that the value returned is indeed the SEXP in * the slot. * NOTE: GET_SLOT(x, what) :== R_do_slot (x, what) * ---- SET_SLOT(x, what, value) :== R_do_slot_assign(x, what, value) * and the R_do_slot* are in src/main/attrib.c * * @param obj object in which to assign the slot * @param nm name of the slot, as an R name object * @param type type of SEXP to allocate * @param length length of SEXP to allocate * * @return SEXP of given type and length assigned as slot nm in obj */ static R_INLINE SEXP ALLOC_SLOT(SEXP obj, SEXP nm, SEXPTYPE type, int length) { SEXP val = allocVector(type, length); SET_SLOT(obj, nm, val); return val; } /** * Expand compressed pointers in the array mp into a full set of indices * in the array mj. * * @param ncol number of columns (or rows) * @param mp column pointer vector of length ncol + 1 * @param mj vector of length mp[ncol] to hold the result * * @return mj */ static R_INLINE int* expand_cmprPt(int ncol, const int mp[], int mj[]) { int j; for (j = 0; j < ncol; j++) { int j2 = mp[j+1], jj; for (jj = mp[j]; jj < j2; jj++) mj[jj] = j; } return mj; } /** * Check if slot(obj, "x") contains any NA (or NaN). * * @param obj a 'Matrix' object with a (double precision) 'x' slot. * * @return Rboolean :== any(is.na(slot(obj, "x") ) */ static R_INLINE Rboolean any_NA_in_x(SEXP obj) { double *x = REAL(GET_SLOT(obj, Matrix_xSym)); int i, n = LENGTH(GET_SLOT(obj, Matrix_xSym)); for(i=0; i < n; i++) if(ISNAN(x[i])) return TRUE; /* else */ return FALSE; } /** Inverse Permutation * C version of .inv.perm.R <- function(p) { p[p] <- seq_along(p) ; p } */ static R_INLINE SEXP inv_permutation(SEXP p_, SEXP zero_p, SEXP zero_res) { int *p = INTEGER(p_), n = LENGTH(p_); SEXP val = allocVector(INTSXP, n); int *v = INTEGER(val), p_0 = asLogical(zero_p), r_0 = asLogical(zero_res); if(!p_0) v--; // ==> use 1-based indices // shorter (but not 100% sure if ok: is LHS always eval'ed *before* RHS ?) : // for(int i=0; i < n; ) v[p[i]] = ++i; for(int i=0; i < n; ) { int j = p[i]; v[j] = (r_0) ? i++ : ++i; } return val; } SEXP Mmatrix(SEXP args); void make_d_matrix_triangular(double *x, SEXP from); void make_i_matrix_triangular( int *x, SEXP from); void make_d_matrix_symmetric(double *to, SEXP from); void make_i_matrix_symmetric( int *to, SEXP from); SEXP Matrix_expand_pointers(SEXP pP); SEXP dup_mMatrix_as_dgeMatrix(SEXP A); SEXP dup_mMatrix_as_geMatrix (SEXP A); SEXP new_dgeMatrix(int nrow, int ncol); SEXP m_encodeInd (SEXP ij, SEXP di, SEXP chk_bnds); SEXP m_encodeInd2(SEXP i, SEXP j, SEXP di, SEXP chk_bnds); SEXP R_all0(SEXP x); SEXP R_any0(SEXP x); static R_INLINE SEXP mMatrix_as_dgeMatrix(SEXP A) { return strcmp(class_P(A), "dgeMatrix") ? dup_mMatrix_as_dgeMatrix(A) : A; } static R_INLINE SEXP mMatrix_as_geMatrix(SEXP A) { return strcmp(class_P(A) + 1, "geMatrix") ? dup_mMatrix_as_geMatrix(A) : A; } // Keep centralized --- *and* in sync with ../inst/include/Matrix.h : #define MATRIX_VALID_dense \ "dmatrix", "dgeMatrix", \ "lmatrix", "lgeMatrix", \ "nmatrix", "ngeMatrix", \ "zmatrix", "zgeMatrix" #define MATRIX_VALID_Csparse \ "dgCMatrix", "dsCMatrix", "dtCMatrix", \ "lgCMatrix", "lsCMatrix", "ltCMatrix", \ "ngCMatrix", "nsCMatrix", "ntCMatrix", \ "zgCMatrix", "zsCMatrix", "ztCMatrix" #define MATRIX_VALID_Tsparse \ "dgTMatrix", "dsTMatrix", "dtTMatrix", \ "lgTMatrix", "lsTMatrix", "ltTMatrix", \ "ngTMatrix", "nsTMatrix", "ntTMatrix", \ "zgTMatrix", "zsTMatrix", "ztTMatrix" #define MATRIX_VALID_Rsparse \ "dgRMatrix", "dsRMatrix", "dtRMatrix", \ "lgRMatrix", "lsRMatrix", "ltRMatrix", \ "ngRMatrix", "nsRMatrix", "ntRMatrix", \ "zgRMatrix", "zsRMatrix", "ztRMatrix" #define MATRIX_VALID_CHMfactor "dCHMsuper", "dCHMsimpl", "nCHMsuper", "nCHMsimpl" /** * Return the 0-based index of a string match in a vector of strings * terminated by an empty string. Returns -1 for no match. * * @param class string to match * @param valid vector of possible matches terminated by an empty string * * @return index of match or -1 for no match */ static R_INLINE int Matrix_check_class(char *class, const char **valid) { int ans; for (ans = 0; ; ans++) { if (!strlen(valid[ans])) return -1; if (!strcmp(class, valid[ans])) return ans; } } /** * These are the ones "everyone" should use -- is() versions, also looking * at super classes: */ # define Matrix_check_class_etc R_check_class_etc # define Matrix_check_class_and_super R_check_class_and_super /** Accessing *sparseVectors : fast (and recycling) v[i] for v = ?sparseVector: * -> ./sparseVector.c -> ./t_sparseVector.c : */ // Type_ans sparseVector_sub(int64_t i, int nnz_v, int* v_i, Type_ans* v_x, int len_v): /* Define all of * dsparseVector_sub(....) * isparseVector_sub(....) * lsparseVector_sub(....) * nsparseVector_sub(....) * zsparseVector_sub(....) */ #define _dspV_ #include "t_sparseVector.c" #define _ispV_ #include "t_sparseVector.c" #define _lspV_ #include "t_sparseVector.c" #define _nspV_ #include "t_sparseVector.c" #define _zspV_ #include "t_sparseVector.c" #ifdef __cplusplus } #endif #endif /* MATRIX_MUTILS_H_ */ Matrix/src/lgCMatrix.h0000644000175100001440000000021412271765436014400 0ustar hornikusers#ifndef MATRIX_LGCMATRIX_H #define MATRIX_LGCMATRIX_H #include "Mutils.h" SEXP lgC_to_matrix(SEXP x); SEXP ngC_to_matrix(SEXP x); #endif Matrix/src/dtpMatrix.c0000644000175100001440000001500212271765436014456 0ustar hornikusers/* double (precision) Triangular Packed Matrices * Note: this means *square* {n x n} matrices */ #include "dtpMatrix.h" SEXP dtpMatrix_validate(SEXP obj) { SEXP val = triangularMatrix_validate(obj); if(isString(val)) return(val); else { int d = INTEGER(GET_SLOT(obj, Matrix_DimSym))[0], lx = length(GET_SLOT(obj, Matrix_xSym)); /* packed_ncol() [Mutils.h] checks, but gives *error* .. need string: */ if(lx * 2 != d*(d+1)) return(mkString(_("Incorrect length of 'x' slot"))); return ScalarLogical(1); } } static double get_norm(SEXP obj, const char *typstr) { char typnm[] = {'\0', '\0'}; int *dims = INTEGER(GET_SLOT(obj, Matrix_DimSym)); double *work = (double *) NULL; typnm[0] = La_norm_type(typstr); if (*typnm == 'I') { work = (double *) R_alloc(dims[0], sizeof(double)); } return F77_CALL(dlantp)(typnm, uplo_P(obj), diag_P(obj), dims, REAL(GET_SLOT(obj, Matrix_xSym)), work); } SEXP dtpMatrix_norm(SEXP obj, SEXP type) { return ScalarReal(get_norm(obj, CHAR(asChar(type)))); } SEXP dtpMatrix_rcond(SEXP obj, SEXP type) { int *dims = INTEGER(GET_SLOT(obj, Matrix_DimSym)), info; char typnm[] = {'\0', '\0'}; double rcond; typnm[0] = La_rcond_type(CHAR(asChar(type))); F77_CALL(dtpcon)(typnm, uplo_P(obj), diag_P(obj), dims, REAL(GET_SLOT(obj, Matrix_xSym)), &rcond, (double *) R_alloc(3*dims[0], sizeof(double)), (int *) R_alloc(dims[0], sizeof(int)), &info); return ScalarReal(rcond); } SEXP dtpMatrix_solve(SEXP a) { SEXP val = PROTECT(duplicate(a)); int info, *Dim = INTEGER(GET_SLOT(val, Matrix_DimSym)); F77_CALL(dtptri)(uplo_P(val), diag_P(val), Dim, REAL(GET_SLOT(val, Matrix_xSym)), &info); UNPROTECT(1); return val; } // also applicable to dspMatrix , dppMatrix : SEXP dtpMatrix_getDiag(SEXP x) { int n = *INTEGER(GET_SLOT(x, Matrix_DimSym)); SEXP val = PROTECT(allocVector(REALSXP, n)); tr_d_packed_getDiag(REAL(val), x, n); UNPROTECT(1); return val; } // also applicable to lspMatrix : SEXP ltpMatrix_getDiag(SEXP x) { int n = *INTEGER(GET_SLOT(x, Matrix_DimSym)); SEXP val = PROTECT(allocVector(LGLSXP, n)); tr_l_packed_getDiag(LOGICAL(val), x, n); UNPROTECT(1); return val; } SEXP dtpMatrix_setDiag(SEXP x, SEXP d) { int n = INTEGER(GET_SLOT(x, Matrix_DimSym))[0]; return tr_d_packed_setDiag(REAL(d), LENGTH(d), x, n); } SEXP ltpMatrix_setDiag(SEXP x, SEXP d) { int n = INTEGER(GET_SLOT(x, Matrix_DimSym))[0]; return tr_l_packed_setDiag(INTEGER(d), LENGTH(d), x, n); } SEXP dtpMatrix_addDiag(SEXP x, SEXP d) { int n = INTEGER(GET_SLOT(x, Matrix_DimSym))[0]; return tr_d_packed_addDiag(REAL(d), LENGTH(d), x, n); } SEXP dtpMatrix_matrix_mm(SEXP x, SEXP y, SEXP right, SEXP trans) { SEXP val = PROTECT(dup_mMatrix_as_dgeMatrix(y)); int rt = asLogical(right); // if(rt), compute b %*% op(a), else op(a) %*% b int tr = asLogical(trans); // if(tr), op(a) = t(a), else op(a) = a /* Since 'x' is square (n x n ), dim(x %*% y) = dim(y) */ int *xDim = INTEGER(GET_SLOT(x, Matrix_DimSym)), *yDim = INTEGER(GET_SLOT(val, Matrix_DimSym)); int m = yDim[0], n = yDim[1]; int ione = 1; const char *uplo = uplo_P(x), *diag = diag_P(x); double *xx = REAL(GET_SLOT(x, Matrix_xSym)), *vx = REAL(GET_SLOT(val, Matrix_xSym)); if (yDim[0] != xDim[1]) if ((rt && xDim[0] != n) || (!rt && xDim[1] != m)) error(_("Dimensions of a (%d,%d) and b (%d,%d) do not conform"), xDim[0], xDim[1], yDim[0], yDim[1]); if (m < 1 || n < 1) { /* error(_("Matrices with zero extents cannot be multiplied")); */ } else /* BLAS */ // go via BLAS 2 dtpmv(.); there is no dtpmm in Lapack! if(rt) { error(_("right=TRUE is not yet implemented __ FIXME")); } else { for (int j = 0; j < n; j++) // X %*% y[,j] F77_CALL(dtpmv)(uplo, /*trans = */ tr ? "T" : "N", diag, yDim, xx, vx + j * m, &ione); } UNPROTECT(1); return val; } SEXP dtpMatrix_matrix_solve(SEXP a, SEXP b) { SEXP val = PROTECT(dup_mMatrix_as_dgeMatrix(b)); /* Since 'a' is square (n x n ), dim(a %*% b) = dim(b) */ int *aDim = INTEGER(GET_SLOT(a, Matrix_DimSym)), *bDim = INTEGER(GET_SLOT(val, Matrix_DimSym)); int ione = 1; const char *uplo = uplo_P(a), *diag = diag_P(a); if (bDim[0] != aDim[1]) error(_("Dimensions of a (%d,%d) and b (%d,%d) do not conform"), aDim[0], aDim[1], bDim[0], bDim[1]); #ifdef pre_2013_08_30 double *ax = REAL(GET_SLOT(a, Matrix_xSym)), *vx = REAL(GET_SLOT(val, Matrix_xSym)); for (int j = 0; j < bDim[1]; j++) /* a^{-1} %*% b[,j] via BLAS 2 DTPSV(.) */ F77_CALL(dtpsv)(uplo, "N", diag, bDim, ax, vx + j * bDim[0], &ione); #else F77_CALL(dtptrs)(uplo, "N", diag, /* n= */ aDim, /* nrhs = */ &bDim[1], /* ap = */ REAL(GET_SLOT(a, Matrix_xSym)), /* b = */ REAL(GET_SLOT(val, Matrix_xSym)), bDim, &ione); #endif UNPROTECT(1); return val; } /* FIXME: This function should be removed and a rt argument added to * dtpMatrix_matrix_mm -- also to be more parallel to ./dtrMatrix.c code */ SEXP dgeMatrix_dtpMatrix_mm(SEXP x, SEXP y) { SEXP val = PROTECT(duplicate(x)); /* Since 'y' is square (n x n ), dim(x %*% y) = dim(x) */ int *xDim = INTEGER(GET_SLOT(x, Matrix_DimSym)), *yDim = INTEGER(GET_SLOT(y, Matrix_DimSym)); const char *uplo = uplo_P(y), *diag = diag_P(y); double *yx = REAL(GET_SLOT(y, Matrix_xSym)), *vx = REAL(GET_SLOT(val, Matrix_xSym)); if (yDim[0] != xDim[1]) error(_("Dimensions of a (%d,%d) and b (%d,%d) do not conform"), xDim[0], xDim[1], yDim[0], yDim[1]); for (int i = 0; i < xDim[0]; i++)/* val[i,] := Y' %*% x[i,] */ F77_CALL(dtpmv)(uplo, "T", diag, yDim, yx, vx + i, /* incr = */ xDim); UNPROTECT(1); return val; } SEXP dtpMatrix_as_dtrMatrix(SEXP from) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dtrMatrix"))), uplo = GET_SLOT(from, Matrix_uploSym), diag = GET_SLOT(from, Matrix_diagSym), dimP = GET_SLOT(from, Matrix_DimSym), dmnP = GET_SLOT(from, Matrix_DimNamesSym); int n = *INTEGER(dimP); SET_SLOT(val, Matrix_DimSym, duplicate(dimP)); SET_SLOT(val, Matrix_DimNamesSym, duplicate(dmnP)); SET_SLOT(val, Matrix_diagSym, duplicate(diag)); SET_SLOT(val, Matrix_uploSym, duplicate(uplo)); packed_to_full_double(REAL(ALLOC_SLOT(val, Matrix_xSym, REALSXP, n*n)), REAL(GET_SLOT(from, Matrix_xSym)), n, *CHAR(STRING_ELT(uplo, 0)) == 'U' ? UPP : LOW); SET_SLOT(val, Matrix_DimNamesSym, duplicate(GET_SLOT(from, Matrix_DimNamesSym))); UNPROTECT(1); return val; } Matrix/src/Csparse.h0000644000175100001440000000462312271765436014116 0ustar hornikusers #ifndef MATRIX_CSPARSE_H #define MATRIX_CSPARSE_H #include "Mutils.h" Rboolean isValid_Csparse(SEXP x); SEXP Csparse_Csparse_prod(SEXP a, SEXP b); SEXP Csparse_band(SEXP x, SEXP k1, SEXP k2); SEXP Csparse_crossprod(SEXP x, SEXP trans, SEXP triplet); SEXP Csparse_Csparse_crossprod(SEXP a, SEXP b, SEXP trans); SEXP Csparse_dense_crossprod(SEXP a, SEXP b); SEXP Csparse_dense_prod(SEXP a, SEXP b); SEXP Csparse_diagU2N(SEXP x); SEXP Csparse_diagN2U(SEXP x); SEXP Csparse_drop(SEXP x, SEXP tol); SEXP Csparse_horzcat(SEXP x, SEXP y); SEXP Csparse_submatrix(SEXP x, SEXP i, SEXP j); SEXP dCsparse_subassign(SEXP x, SEXP i_, SEXP j_, SEXP value); SEXP lCsparse_subassign(SEXP x, SEXP i_, SEXP j_, SEXP value); SEXP iCsparse_subassign(SEXP x, SEXP i_, SEXP j_, SEXP value); SEXP nCsparse_subassign(SEXP x, SEXP i_, SEXP j_, SEXP value); SEXP zCsparse_subassign(SEXP x, SEXP i_, SEXP j_, SEXP value); SEXP Csparse_symmetric_to_general(SEXP x); SEXP Csparse_general_to_symmetric(SEXP x, SEXP uplo); SEXP Csparse_MatrixMarket(SEXP x, SEXP fname); SEXP Csparse_sort (SEXP x); SEXP Csparse_to_Tsparse(SEXP x, SEXP tri); SEXP Csparse_to_dense(SEXP x); SEXP Csparse_to_nz_pattern(SEXP x, SEXP tri); SEXP nz_pattern_to_Csparse(SEXP x, SEXP res_kind); SEXP nz2Csparse (SEXP x, enum x_slot_kind r_kind); SEXP Csparse_to_matrix(SEXP x, SEXP chk); SEXP Csparse_to_vector(SEXP x); SEXP Csparse_transpose(SEXP x, SEXP tri); SEXP Csparse_validate (SEXP x); SEXP Csparse_validate2(SEXP x, SEXP maybe_modify); SEXP Csparse_validate_(SEXP x, Rboolean maybe_modify); SEXP Csparse_vertcat(SEXP x, SEXP y); SEXP Rsparse_validate(SEXP x); SEXP diag_tC_ptr(int n, int *x_p, double *x_x, int *perm, SEXP resultKind); SEXP diag_tC(SEXP pslot, SEXP xslot, SEXP perm_slot, SEXP resultKind); // FIXME: these are nowhere used (are they?) SEXP create_Csparse(char* cls, int* i, int* j, int* p, int np, void* x, int nnz, int* dims, SEXP dimnames, int index1); #define DG_I_J(i, j, x, nnz) create_Csparse("dgCMatrix", i, j, (int*)NULL, 0, (void*)x, nnz, (int*)NULL, R_NilValue, 1) #define NG_I_J(i, j, nnz) create_Csparse("ngCMatrix", i, j, (int*)NULL, 0, (void*)NULL, nnz, (int*)NULL, R_NilValue, 1) #define DG_I_P(i, p, np, x, nnz) create_Csparse("dgCMatrix", i, (int*)NULL, p, np, (void*)x, nnz, (int*)NULL, R_NilValue, 1) #define NG_I_P(i, p, np, nnz) create_Csparse("ngCMatrix", i, (int*)NULL, p, np, (void*)NULL, nnz, (int*)NULL, R_NilValue, 1) #endif Matrix/src/dppMatrix.h0000644000175100001440000000055312271765436014464 0ustar hornikusers#ifndef MATRIX_PPMATRIX_H #define MATRIX_PPMATRIX_H #include #include "Mutils.h" #include "dspMatrix.h" SEXP dppMatrix_rcond(SEXP obj, SEXP type); SEXP dppMatrix_validate(SEXP obj); SEXP dppMatrix_solve(SEXP a); SEXP dppMatrix_matrix_solve(SEXP a, SEXP b); SEXP dppMatrix_chol(SEXP x); double get_norm_sp(SEXP obj, const char *typstr); #endif Matrix/src/dtTMatrix.h0000644000175100001440000000030512271765436014427 0ustar hornikusers#ifndef MATRIX_TRT_H #define MATRIX_TRT_H #include "Mutils.h" #include "chm_common.h" SEXP dtTMatrix_as_dtrMatrix(SEXP x); SEXP tTMatrix_validate(SEXP x); SEXP xTMatrix_validate(SEXP x); #endif Matrix/src/chm_common.h0000644000175100001440000000645412271765436014641 0ustar hornikusers#ifndef CHM_COMMON_H #define CHM_COMMON_H #include "SuiteSparse_config/SuiteSparse_config.h" #include "CHOLMOD/Include/cholmod.h" #include "Mutils.h" #ifdef Matrix_with_SPQR # include "SPQR/Include/SuiteSparseQR_C.h" #endif /* typedef struct cholmod_common_struct *CHM_CM ; typedef struct cholmod_dense_struct *CHM_DN ; typedef struct cholmod_factor_struct *CHM_FR ; typedef struct cholmod_sparse_struct *CHM_SP ; typedef struct cholmod_triplet_struct *CHM_TR ; */ typedef cholmod_common* CHM_CM; typedef cholmod_dense* CHM_DN; typedef const cholmod_dense* const_CHM_DN; typedef cholmod_factor* CHM_FR; typedef const cholmod_factor* const_CHM_FR; typedef cholmod_sparse* CHM_SP; typedef const cholmod_sparse* const_CHM_SP; typedef cholmod_triplet* CHM_TR; typedef const cholmod_triplet* const_CHM_TR; extern cholmod_common c; /* structure for int CHM routines */ extern cholmod_common cl; /* structure for UF_long routines */ /* NOTE: Versions of these are *EXPORTED* via ../inst/include/Matrix.h * ---- and used e.g., in the lme4 package */ CHM_SP as_cholmod_sparse (CHM_SP ans, SEXP x, Rboolean check_Udiag, Rboolean sort_in_place); CHM_TR as_cholmod_triplet(CHM_TR ans, SEXP x, Rboolean check_Udiag); CHM_DN as_cholmod_dense (CHM_DN ans, SEXP x); CHM_DN as_cholmod_x_dense(CHM_DN ans, SEXP x); CHM_DN numeric_as_chm_dense(CHM_DN ans, double *v, int nr, int nc); CHM_FR as_cholmod_factor (CHM_FR ans, SEXP x); #define AS_CHM_DN(x) as_cholmod_dense ((CHM_DN)alloca(sizeof(cholmod_dense)), x ) #define AS_CHM_FR(x) as_cholmod_factor ((CHM_FR)alloca(sizeof(cholmod_factor)), x ) #define AS_CHM_SP(x) as_cholmod_sparse ((CHM_SP)alloca(sizeof(cholmod_sparse)), x, TRUE, FALSE) #define AS_CHM_TR(x) as_cholmod_triplet((CHM_TR)alloca(sizeof(cholmod_triplet)),x, TRUE) /* the non-diagU2N-checking versions : */ #define AS_CHM_SP__(x) as_cholmod_sparse ((CHM_SP)alloca(sizeof(cholmod_sparse)), x, FALSE, FALSE) #define AS_CHM_TR__(x) as_cholmod_triplet((CHM_TR)alloca(sizeof(cholmod_triplet)), x, FALSE) // optional diagU2N-checking #define AS_CHM_SP2(x,chk) as_cholmod_sparse ((CHM_SP)alloca(sizeof(cholmod_sparse)), x, chk, FALSE) #define N_AS_CHM_DN(x,nr,nc) M_numeric_as_chm_dense((CHM_DN)alloca(sizeof(cholmod_dense)), x , nr, nc ) static R_INLINE Rboolean chm_factor_ok(CHM_FR f) { return (Rboolean) (f->minor >= f->n); } Rboolean check_sorted_chm(CHM_SP A); int R_cholmod_start(CHM_CM Common); int R_cholmod_l_start(CHM_CM Common); void R_cholmod_error(int status, const char *file, int line, const char *message); SEXP get_SuiteSparse_version(); SEXP chm_factor_to_SEXP(CHM_FR f, int dofree); SEXP chm_sparse_to_SEXP(CHM_SP a, int dofree, int uploT, int Rkind, const char *diag, SEXP dn); SEXP chm_triplet_to_SEXP(CHM_TR a, int dofree, int uploT, int Rkind, const char* diag, SEXP dn); SEXP chm_dense_to_SEXP(CHM_DN a, int dofree, int Rkind, SEXP dn); /* int uploST, char *diag, SEXP dn); */ SEXP chm_dense_to_matrix(CHM_DN a, int dofree, SEXP dn); SEXP chm_dense_to_vector(CHM_DN a, int dofree); void chm_diagN2U(CHM_SP chx, int uploT, Rboolean do_realloc); SEXP CHMfactor_validate(SEXP obj); SEXP CHMsimpl_validate(SEXP obj); SEXP CHMsuper_validate(SEXP obj); SEXP CHM_set_common_env(SEXP rho); void CHM_store_common(); void CHM_restore_common(); #endif Matrix/src/CHOLMOD/0000755000175100001440000000000012271765426013424 5ustar hornikusersMatrix/src/CHOLMOD/Makefile0000644000175100001440000000122312271765436015063 0ustar hornikusers#------------------------------------------------------------------------------- # CHOLMOD Makefile #------------------------------------------------------------------------------- .PHONY : default all library purge clean distclean ccode default: all # Compile the C-callable libraries and the Demo programs. all: ( cd Lib ; $(MAKE) ) # Compile the C-callable libraries only. library: ( cd Lib ; $(MAKE) ) # Remove all files not in the original distribution purge: ( cd Lib ; $(MAKE) purge ) # Remove all files not in the original distribution, except keep the # compiled libraries. clean: ( cd Lib ; $(MAKE) clean ) distclean: purge ccode: all Matrix/src/CHOLMOD/Modify/0000755000175100001440000000000012271765426014653 5ustar hornikusersMatrix/src/CHOLMOD/Modify/License.txt0000644000175100001440000000204611770402705016767 0ustar hornikusersCHOLMOD/Modify Module. Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager CHOLMOD is also available under other licenses; contact authors for details. http://www.suitesparse.com Note that this license is for the CHOLMOD/Modify module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. Matrix/src/CHOLMOD/Modify/t_cholmod_updown_numkr.c0000644000175100001440000005165212271765436021611 0ustar hornikusers/* ========================================================================== */ /* === Modify/t_cholmod_updown_numkr ======================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Modify Module. Copyright (C) 2005-2006, * Timothy A. Davis and William W. Hager. * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Supernodal numerical update/downdate of rank K = RANK, along a single path. * This routine operates on a simplicial factor, but operates on adjacent * columns of L that would fit within a single supernode. "Adjacent" means * along a single path in the elimination tree; they may or may not be * adjacent in the matrix L. * * external defines: NUMERIC, WDIM, RANK. * * WDIM is 1, 2, 4, or 8. RANK can be 1 to WDIM. * * A simple method is included (#define SIMPLE). The code works, but is slow. * It is meant only to illustrate what this routine is doing. * * A rank-K update proceeds along a single path, using single-column, dual- * column, or quad-column updates of L. If a column j and the next column * in the path (its parent) do not have the same nonzero pattern, a single- * column update is used. If they do, but the 3rd and 4th column from j do * not have the same pattern, a dual-column update is used, in which the two * columns are treated as if they were a single supernode of two columns. If * there are 4 columns in the path that all have the same nonzero pattern, then * a quad-column update is used. All three kinds of updates can be used along * a single path, in a single call to this function. * * Single-column update: * * When updating a single column of L, each iteration of the for loop, * below, processes four rows of W (all columns involved) and one column * of L. Suppose we have a rank-5 update, and columns 2 through 6 of W * are involved. In this case, W in this routine is a pointer to column * 2 of the matrix W in the caller. W (in the caller, shown as 'W') is * held in row-major order, and is 8-by-n (a dense matrix storage format), * but shown below in column form to match the column of L. Suppose there * are 13 nonzero entries in column 27 of L, with row indices 27 (the * diagonal, D), 28, 30, 31, 42, 43, 44, 50, 51, 67, 81, 83, and 84. This * pattern is held in Li [Lp [27] ... Lp [27 + Lnz [27] - 1], where * Lnz [27] = 13. The modification of the current column j of L is done * in the following order. A dot (.) means the entry of W is not accessed. * * W0 points to row 27 of W, and G is a 1-by-8 temporary vector. * * G[0] G[4] * G x x x x x . . . * * W0 * | * v * 27 . . x x x x x . W0 points to W (27,2) * * * row 'W' W column j = 27 * | | | of L * v v v | * first iteration of for loop: v * * 28 . . 1 5 9 13 17 . x * 30 . . 2 6 10 14 18 . x * 31 . . 3 7 11 15 19 . x * 42 . . 4 8 12 16 20 . x * * second iteration of for loop: * * 43 . . 1 5 9 13 17 . x * 44 . . 2 6 10 14 18 . x * 50 . . 3 7 11 15 19 . x * 51 . . 4 8 12 16 20 . x * * third iteration of for loop: * * 67 . . 1 5 9 13 17 . x * 81 . . 2 6 10 14 18 . x * 83 . . 3 7 11 15 19 . x * 84 . . 4 8 12 16 20 . x * * If the number of offdiagonal nonzeros in column j of L is not divisible * by 4, then the switch-statement does the work for the first nz % 4 rows. * * Dual-column update: * * In this case, two columns of L that are adjacent in the path are being * updated, by 1 to 8 columns of W. Suppose columns j=27 and j=28 are * adjacent columns in the path (they need not be j and j+1). Two rows * of G and W are used as coefficients during the update: (G0, G1) and * (W0, W1). * * G0 x x x x x . . . * G1 x x x x x . . . * * 27 . . x x x x x . W0 points to W (27,2) * 28 . . x x x x x . W1 points to W (28,2) * * * row 'W' W0,W1 column j = 27 * | | | of L * v v v | * | |-- column j = 28 of L * v v * update L (j1,j): * * 28 . . 1 2 3 4 5 . x - ("-" is not stored in L) * * cleanup iteration since length is odd: * * 30 . . 1 2 3 4 5 . x x * * then each iteration does two rows of both columns of L: * * 31 . . 1 3 5 7 9 . x x * 42 . . 2 4 6 8 10 . x x * * 43 . . 1 3 5 7 9 . x x * 44 . . 2 4 6 8 10 . x x * * 50 . . 1 3 5 7 9 . x x * 51 . . 2 4 6 8 10 . x x * * 67 . . 1 3 5 7 9 . x x * 81 . . 2 4 6 8 10 . x x * * 83 . . 1 3 5 7 9 . x x * 84 . . 2 4 6 8 10 . x x * * If the number of offdiagonal nonzeros in column j of L is not even, * then the cleanup iteration does the work for the first row. * * Quad-column update: * * In this case, four columns of L that are adjacent in the path are being * updated, by 1 to 8 columns of W. Suppose columns j=27, 28, 30, and 31 * are adjacent columns in the path (they need not be j, j+1, ...). Four * rows of G and W are used as coefficients during the update: (G0 through * G3) and (W0 through W3). j=27, j1=28, j2=30, and j3=31. * * G0 x x x x x . . . * G1 x x x x x . . . * G3 x x x x x . . . * G4 x x x x x . . . * * 27 . . x x x x x . W0 points to W (27,2) * 28 . . x x x x x . W1 points to W (28,2) * 30 . . x x x x x . W2 points to W (30,2) * 31 . . x x x x x . W3 points to W (31,2) * * * row 'W' W0,W1,.. column j = 27 * | | | of L * v v v | * | |-- column j = 28 of L * | | |-- column j = 30 of L * | | | |-- column j = 31 of L * v v v v * update L (j1,j): * 28 . . 1 2 3 4 5 . x - - - * * update L (j2,j): * 30 . . 1 2 3 4 5 . # x - - (# denotes modified) * * update L (j2,j1) * 30 . . 1 2 3 4 5 . x # - - * * update L (j3,j) * 31 . . 1 2 3 4 5 . # x x - * * update L (j3,j1) * 31 . . 1 2 3 4 5 . x # x - * * update L (j3,j2) * 31 . . 1 2 3 4 5 . x x # - * * cleanup iteration since length is odd: * 42 . . 1 2 3 4 5 . x x x x * * * ----- CHOLMOD v1.1.1 did the following -------------------------------------- * then each iteration does two rows of all four colummns of L: * * 43 . . 1 3 5 7 9 . x x x x * 44 . . 2 4 6 8 10 . x x x x * * 50 . . 1 3 5 7 9 . x x x x * 51 . . 2 4 6 8 10 . x x x x * * 67 . . 1 3 5 7 9 . x x x x * 81 . . 2 4 6 8 10 . x x x x * * 83 . . 1 3 5 7 9 . x x x x * 84 . . 2 4 6 8 10 . x x x x * * ----- CHOLMOD v1.2.0 does the following ------------------------------------- * then each iteration does one rows of all four colummns of L: * * 43 . . 1 2 3 4 5 . x x x x * 44 . . 1 2 3 4 5 . x x x x * 50 . . 1 3 5 4 5 . x x x x * 51 . . 1 2 3 4 5 . x x x x * 67 . . 1 3 5 4 5 . x x x x * 81 . . 1 2 3 4 5 . x x x x * 83 . . 1 3 5 4 5 . x x x x * 84 . . 1 2 3 4 5 . x x x x * * This file is included in t_cholmod_updown.c, only. * It is not compiled separately. It contains no user-callable routines. * * workspace: Xwork (WDIM*nrow) */ /* ========================================================================== */ /* === loop unrolling macros ================================================ */ /* ========================================================================== */ #undef RANK1 #undef RANK2 #undef RANK3 #undef RANK4 #undef RANK5 #undef RANK6 #undef RANK7 #undef RANK8 #define RANK1(statement) statement #if RANK < 2 #define RANK2(statement) #else #define RANK2(statement) statement #endif #if RANK < 3 #define RANK3(statement) #else #define RANK3(statement) statement #endif #if RANK < 4 #define RANK4(statement) #else #define RANK4(statement) statement #endif #if RANK < 5 #define RANK5(statement) #else #define RANK5(statement) statement #endif #if RANK < 6 #define RANK6(statement) #else #define RANK6(statement) statement #endif #if RANK < 7 #define RANK7(statement) #else #define RANK7(statement) statement #endif #if RANK < 8 #define RANK8(statement) #else #define RANK8(statement) statement #endif #define FOR_ALL_K \ RANK1 (DO (0)) \ RANK2 (DO (1)) \ RANK3 (DO (2)) \ RANK4 (DO (3)) \ RANK5 (DO (4)) \ RANK6 (DO (5)) \ RANK7 (DO (6)) \ RANK8 (DO (7)) /* ========================================================================== */ /* === alpha/gamma ========================================================== */ /* ========================================================================== */ #undef ALPHA_GAMMA #define ALPHA_GAMMA(Dj,Alpha,Gamma,W) \ { \ double dj = Dj ; \ if (update) \ { \ for (k = 0 ; k < RANK ; k++) \ { \ double w = W [k] ; \ double alpha = Alpha [k] ; \ double a = alpha + (w * w) / dj ; \ dj *= a ; \ Alpha [k] = a ; \ Gamma [k] = (- w / dj) ; \ dj /= alpha ; \ } \ } \ else \ { \ for (k = 0 ; k < RANK ; k++) \ { \ double w = W [k] ; \ double alpha = Alpha [k] ; \ double a = alpha - (w * w) / dj ; \ dj *= a ; \ Alpha [k] = a ; \ Gamma [k] = w / dj ; \ dj /= alpha ; \ } \ } \ Dj = ((use_dbound) ? (CHOLMOD(dbound) (dj, Common)) : (dj)) ; \ } /* ========================================================================== */ /* === numeric update/downdate along one path =============================== */ /* ========================================================================== */ static void NUMERIC (WDIM, RANK) ( int update, /* TRUE for update, FALSE for downdate */ Int j, /* first column in the path */ Int e, /* last column in the path */ double Alpha [ ], /* alpha, for each column of W */ double W [ ], /* W is an n-by-WDIM array, stored in row-major order */ cholmod_factor *L, /* with unit diagonal (diagonal not stored) */ cholmod_common *Common ) { #ifdef SIMPLE #define w(row,col) W [WDIM*(row) + (col)] /* ---------------------------------------------------------------------- */ /* concise but slow version for illustration only */ /* ---------------------------------------------------------------------- */ double Gamma [WDIM] ; double *Lx ; Int *Li, *Lp, *Lnz ; Int p, k ; Int use_dbound = IS_GT_ZERO (Common->dbound) ; Li = L->i ; Lx = L->x ; Lp = L->p ; Lnz = L->nz ; /* walk up the etree from node j to its ancestor e */ for ( ; j <= e ; j = (Lnz [j] > 1) ? (Li [Lp [j] + 1]) : Int_max) { /* update the diagonal entry D (j,j) with each column of W */ ALPHA_GAMMA (Lx [Lp [j]], Alpha, Gamma, (&(w (j,0)))) ; /* update column j of L */ for (p = Lp [j] + 1 ; p < Lp [j] + Lnz [j] ; p++) { /* update row Li [p] of column j of L with each column of W */ Int i = Li [p] ; for (k = 0 ; k < RANK ; k++) { w (i,k) -= w (j,k) * Lx [p] ; Lx [p] -= Gamma [k] * w (i,k) ; } } /* clear workspace W */ for (k = 0 ; k < RANK ; k++) { w (j,k) = 0 ; } } #else /* ---------------------------------------------------------------------- */ /* dynamic supernodal version: supernodes detected dynamically */ /* ---------------------------------------------------------------------- */ double G0 [RANK], G1 [RANK], G2 [RANK], G3 [RANK] ; double Z0 [RANK], Z1 [RANK], Z2 [RANK], Z3 [RANK] ; double *W0, *W1, *W2, *W3, *Lx ; Int *Li, *Lp, *Lnz ; Int j1, j2, j3, p0, p1, p2, p3, parent, lnz, pend, k ; Int use_dbound = IS_GT_ZERO (Common->dbound) ; Li = L->i ; Lx = L->x ; Lp = L->p ; Lnz = L->nz ; /* walk up the etree from node j to its ancestor e */ for ( ; j <= e ; j = parent) { p0 = Lp [j] ; /* col j is Li,Lx [p0 ... p0+lnz-1] */ lnz = Lnz [j] ; W0 = W + WDIM * j ; /* pointer to row j of W */ pend = p0 + lnz ; /* for k = 0 to RANK-1 do: */ #define DO(k) Z0 [k] = W0 [k] ; FOR_ALL_K #undef DO /* for k = 0 to RANK-1 do: */ #define DO(k) W0 [k] = 0 ; FOR_ALL_K #undef DO /* update D (j,j) */ ALPHA_GAMMA (Lx [p0], Alpha, G0, Z0) ; p0++ ; /* determine how many columns of L to update at the same time */ parent = (lnz > 1) ? (Li [p0]) : Int_max ; if (parent <= e && lnz == Lnz [parent] + 1) { /* -------------------------------------------------------------- */ /* node j and its parent j1 can be updated at the same time */ /* -------------------------------------------------------------- */ j1 = parent ; j2 = (lnz > 2) ? (Li [p0+1]) : Int_max ; j3 = (lnz > 3) ? (Li [p0+2]) : Int_max ; W1 = W + WDIM * j1 ; /* pointer to row j1 of W */ p1 = Lp [j1] ; /* for k = 0 to RANK-1 do: */ #define DO(k) Z1 [k] = W1 [k] ; FOR_ALL_K #undef DO /* for k = 0 to RANK-1 do: */ #define DO(k) W1 [k] = 0 ; FOR_ALL_K #undef DO /* update L (j1,j) */ { double lx = Lx [p0] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ Z1 [k] -= Z0 [k] * lx ; \ lx -= G0 [k] * Z1 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx ; } /* update D (j1,j1) */ ALPHA_GAMMA (Lx [p1], Alpha, G1, Z1) ; p1++ ; /* -------------------------------------------------------------- */ /* update 2 or 4 columns of L */ /* -------------------------------------------------------------- */ if ((j2 <= e) && /* j2 in the current path */ (j3 <= e) && /* j3 in the current path */ (lnz == Lnz [j2] + 2) && /* column j2 matches */ (lnz == Lnz [j3] + 3)) /* column j3 matches */ { /* ---------------------------------------------------------- */ /* update 4 columns of L */ /* ---------------------------------------------------------- */ /* p0 and p1 currently point to row j2 in cols j and j1 of L */ parent = (lnz > 4) ? (Li [p0+2]) : Int_max ; W2 = W + WDIM * j2 ; /* pointer to row j2 of W */ W3 = W + WDIM * j3 ; /* pointer to row j3 of W */ p2 = Lp [j2] ; p3 = Lp [j3] ; /* for k = 0 to RANK-1 do: */ #define DO(k) Z2 [k] = W2 [k] ; FOR_ALL_K #undef DO /* for k = 0 to RANK-1 do: */ #define DO(k) Z3 [k] = W3 [k] ; FOR_ALL_K #undef DO /* for k = 0 to RANK-1 do: */ #define DO(k) W2 [k] = 0 ; FOR_ALL_K #undef DO /* for k = 0 to RANK-1 do: */ #define DO(k) W3 [k] = 0 ; FOR_ALL_K #undef DO /* update L (j2,j) and update L (j2,j1) */ { double lx [2] ; lx [0] = Lx [p0] ; lx [1] = Lx [p1] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ Z2 [k] -= Z0 [k] * lx [0] ; lx [0] -= G0 [k] * Z2 [k] ; \ Z2 [k] -= Z1 [k] * lx [1] ; lx [1] -= G1 [k] * Z2 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx [0] ; Lx [p1++] = lx [1] ; } /* update D (j2,j2) */ ALPHA_GAMMA (Lx [p2], Alpha, G2, Z2) ; p2++ ; /* update L (j3,j), L (j3,j1), and L (j3,j2) */ { double lx [3] ; lx [0] = Lx [p0] ; lx [1] = Lx [p1] ; lx [2] = Lx [p2] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ Z3 [k] -= Z0 [k] * lx [0] ; lx [0] -= G0 [k] * Z3 [k] ; \ Z3 [k] -= Z1 [k] * lx [1] ; lx [1] -= G1 [k] * Z3 [k] ; \ Z3 [k] -= Z2 [k] * lx [2] ; lx [2] -= G2 [k] * Z3 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx [0] ; Lx [p1++] = lx [1] ; Lx [p2++] = lx [2] ; } /* update D (j3,j3) */ ALPHA_GAMMA (Lx [p3], Alpha, G3, Z3) ; p3++ ; /* each iteration updates L (i, [j j1 j2 j3]) */ for ( ; p0 < pend ; p0++, p1++, p2++, p3++) { double lx [4], *w0 ; lx [0] = Lx [p0] ; lx [1] = Lx [p1] ; lx [2] = Lx [p2] ; lx [3] = Lx [p3] ; w0 = W + WDIM * Li [p0] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w0 [k] -= Z0 [k] * lx [0] ; lx [0] -= G0 [k] * w0 [k] ; \ w0 [k] -= Z1 [k] * lx [1] ; lx [1] -= G1 [k] * w0 [k] ; \ w0 [k] -= Z2 [k] * lx [2] ; lx [2] -= G2 [k] * w0 [k] ; \ w0 [k] -= Z3 [k] * lx [3] ; lx [3] -= G3 [k] * w0 [k] ; FOR_ALL_K #undef DO Lx [p0] = lx [0] ; Lx [p1] = lx [1] ; Lx [p2] = lx [2] ; Lx [p3] = lx [3] ; } } else { /* ---------------------------------------------------------- */ /* update 2 columns of L */ /* ---------------------------------------------------------- */ parent = j2 ; /* cleanup iteration if length is odd */ if ((lnz - 2) % 2) { double lx [2] , *w0 ; lx [0] = Lx [p0] ; lx [1] = Lx [p1] ; w0 = W + WDIM * Li [p0] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w0 [k] -= Z0 [k] * lx [0] ; lx [0] -= G0 [k] * w0 [k] ; \ w0 [k] -= Z1 [k] * lx [1] ; lx [1] -= G1 [k] * w0 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx [0] ; Lx [p1++] = lx [1] ; } for ( ; p0 < pend ; p0 += 2, p1 += 2) { double lx [2][2], w [2], *w0, *w1 ; lx [0][0] = Lx [p0 ] ; lx [1][0] = Lx [p0+1] ; lx [0][1] = Lx [p1 ] ; lx [1][1] = Lx [p1+1] ; w0 = W + WDIM * Li [p0 ] ; w1 = W + WDIM * Li [p0+1] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w [0] = w0 [k] - Z0 [k] * lx [0][0] ; \ w [1] = w1 [k] - Z0 [k] * lx [1][0] ; \ lx [0][0] -= G0 [k] * w [0] ; \ lx [1][0] -= G0 [k] * w [1] ; \ w0 [k] = w [0] -= Z1 [k] * lx [0][1] ; \ w1 [k] = w [1] -= Z1 [k] * lx [1][1] ; \ lx [0][1] -= G1 [k] * w [0] ; \ lx [1][1] -= G1 [k] * w [1] ; FOR_ALL_K #undef DO Lx [p0 ] = lx [0][0] ; Lx [p0+1] = lx [1][0] ; Lx [p1 ] = lx [0][1] ; Lx [p1+1] = lx [1][1] ; } } } else { /* -------------------------------------------------------------- */ /* update one column of L */ /* -------------------------------------------------------------- */ /* cleanup iteration if length is not a multiple of 4 */ switch ((lnz - 1) % 4) { case 1: { double lx , *w0 ; lx = Lx [p0] ; w0 = W + WDIM * Li [p0] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w0 [k] -= Z0 [k] * lx ; lx -= G0 [k] * w0 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx ; } break ; case 2: { double lx [2], *w0, *w1 ; lx [0] = Lx [p0 ] ; lx [1] = Lx [p0+1] ; w0 = W + WDIM * Li [p0 ] ; w1 = W + WDIM * Li [p0+1] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w0 [k] -= Z0 [k] * lx [0] ; \ w1 [k] -= Z0 [k] * lx [1] ; \ lx [0] -= G0 [k] * w0 [k] ; \ lx [1] -= G0 [k] * w1 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx [0] ; Lx [p0++] = lx [1] ; } break ; case 3: { double lx [3], *w0, *w1, *w2 ; lx [0] = Lx [p0 ] ; lx [1] = Lx [p0+1] ; lx [2] = Lx [p0+2] ; w0 = W + WDIM * Li [p0 ] ; w1 = W + WDIM * Li [p0+1] ; w2 = W + WDIM * Li [p0+2] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w0 [k] -= Z0 [k] * lx [0] ; \ w1 [k] -= Z0 [k] * lx [1] ; \ w2 [k] -= Z0 [k] * lx [2] ; \ lx [0] -= G0 [k] * w0 [k] ; \ lx [1] -= G0 [k] * w1 [k] ; \ lx [2] -= G0 [k] * w2 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx [0] ; Lx [p0++] = lx [1] ; Lx [p0++] = lx [2] ; } } for ( ; p0 < pend ; p0 += 4) { double lx [4], *w0, *w1, *w2, *w3 ; lx [0] = Lx [p0 ] ; lx [1] = Lx [p0+1] ; lx [2] = Lx [p0+2] ; lx [3] = Lx [p0+3] ; w0 = W + WDIM * Li [p0 ] ; w1 = W + WDIM * Li [p0+1] ; w2 = W + WDIM * Li [p0+2] ; w3 = W + WDIM * Li [p0+3] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w0 [k] -= Z0 [k] * lx [0] ; \ w1 [k] -= Z0 [k] * lx [1] ; \ w2 [k] -= Z0 [k] * lx [2] ; \ w3 [k] -= Z0 [k] * lx [3] ; \ lx [0] -= G0 [k] * w0 [k] ; \ lx [1] -= G0 [k] * w1 [k] ; \ lx [2] -= G0 [k] * w2 [k] ; \ lx [3] -= G0 [k] * w3 [k] ; FOR_ALL_K #undef DO Lx [p0 ] = lx [0] ; Lx [p0+1] = lx [1] ; Lx [p0+2] = lx [2] ; Lx [p0+3] = lx [3] ; } } } #endif } /* prepare this file for another inclusion in t_cholmod_updown.c: */ #undef RANK Matrix/src/CHOLMOD/Modify/cholmod_updown.c0000644000175100001440000014336112271765436020051 0ustar hornikusers/* ========================================================================== */ /* === Modify/cholmod_updown ================================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Modify Module. * Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager. * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Updates/downdates the LDL' factorization (symbolic, then numeric), by * computing a new factorization of * * Lnew * Dnew * Lnew' = Lold * Dold * Lold' +/- C*C' * * C must be sorted. It can be either packed or unpacked. As in all CHOLMOD * routines, the columns of L are sorted on input, and also on output. * * If the factor is not an unpacked LDL' or dynamic LDL', it is converted * to an LDL' dynamic factor. An unpacked LDL' factor may be updated, but if * any one column runs out of space, the factor is converted to an LDL' * dynamic one. If the initial conversion fails, the factor is returned * unchanged. * * If memory runs out during the update, the factor is returned as a simplicial * symbolic factor. That is, everything is freed except for the fill-reducing * ordering and its corresponding column counts (typically computed by * cholmod_analyze). * * Note that the fill-reducing permutation L->Perm is NOT used. The row * indices of C refer to the rows of L, not A. If your original system is * LDL' = PAP' (where P = L->Perm), and you want to compute the LDL' * factorization of A+CC', then you must permute C first. That is: * * PAP' = LDL' * P(A+CC')P' = PAP'+PCC'P' = LDL' + (PC)(PC)' = LDL' + Cnew*Cnew' * where Cnew = P*C. * * You can use the cholmod_submatrix routine in the MatrixOps module * to permute C, with: * * Cnew = cholmod_submatrix (C, L->Perm, L->n, NULL, -1, TRUE, TRUE, Common) ; * * Note that the sorted input parameter to cholmod_submatrix must be TRUE, * because cholmod_updown requires C with sorted columns. * * The system Lx=b can also be updated/downdated. The old system was Lold*x=b. * The new system is Lnew*xnew = b + deltab. The old solution x is overwritten * with xnew. Note that as in the update/downdate of L itself, the fill- * reducing permutation L->Perm is not used. x and b are in the permuted * ordering, not your original ordering. x and b are n-by-1; this routine * does not handle multiple right-hand-sides. * * workspace: Flag (nrow), Head (nrow+1), W (maxrank*nrow), Iwork (nrow), * where maxrank is 2, 4, or 8. * * Only real matrices are supported. A symbolic L is converted into a * numeric identity matrix. */ #ifndef NMODIFY #include "cholmod_internal.h" #include "cholmod_modify.h" /* ========================================================================== */ /* === cholmod_updown ======================================================= */ /* ========================================================================== */ /* Compute the new LDL' factorization of LDL'+CC' (an update) or LDL'-CC' * (a downdate). The factor object L need not be an LDL' factorization; it * is converted to one if it isn't. */ int CHOLMOD(updown) ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(updown_mask) (update, C, NULL, NULL, L, NULL, NULL, Common)) ; } /* ========================================================================== */ /* === cholmod_updown_solve ================================================= */ /* ========================================================================== */ /* Does the same as cholmod_updown, except that it also updates/downdates the * solution to Lx=b+DeltaB. x and b must be n-by-1 dense matrices. b is not * need as input to this routine, but a sparse change to b is (DeltaB). Only * entries in DeltaB corresponding to columns modified in L are accessed; the * rest are ignored. */ int CHOLMOD(updown_solve) ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(updown_mask) (update, C, NULL, NULL, L, X, DeltaB, Common)) ; } /* ========================================================================== */ /* === Power2 =============================================================== */ /* ========================================================================== */ /* Power2 [i] is smallest power of 2 that is >= i (for i in range 0 to 8) */ static Int Power2 [ ] = { /* 0 1 2 3 4 5 6 7 8 */ 0, 1, 2, 4, 4, 8, 8, 8, 8 } ; /* ========================================================================== */ /* === debug routines ======================================================= */ /* ========================================================================== */ #ifndef NDEBUG static void dump_set (Int s, Int **Set_ps1, Int **Set_ps2, Int j, Int n, cholmod_common *Common) { Int *p, len, i, ilast ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return ; } len = Set_ps2 [s] - Set_ps1 [s] ; PRINT2 (("Set s: "ID" len: "ID":", s, len)) ; ASSERT (len > 0) ; ilast = j ; for (p = Set_ps1 [s] ; p < Set_ps2 [s] ; p++) { i = *p ; PRINT3 ((" "ID"", i)) ; ASSERT (i > ilast && i < n) ; ilast = i ; } PRINT3 (("\n")) ; } static void dump_col ( char *w, Int j, Int p1, Int p2, Int *Li, double *Lx, Int n, cholmod_common *Common ) { Int p, row, lastrow ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return ; } PRINT3 (("\n\nDUMP COL==== j = "ID" %s: p1="ID" p2="ID" \n", j, w, p1,p2)); lastrow = -1 ; for (p = p1 ; p < p2 ; p++) { PRINT3 ((" "ID": ", p)) ; row = Li [p] ; PRINT3 ((""ID" ", Li [p])) ; PRINT3 (("%g ", Lx [p])) ; PRINT3 (("\n")) ; ASSERT (row > lastrow && row < n) ; lastrow = row ; } ASSERT (p1 < p2) ; ASSERT (Li [p1] == j) ; PRINT3 (("\n")) ; } #endif /* ========================================================================== */ /* === a path =============================================================== */ /* ========================================================================== */ /* A path is a set of nodes of the etree which are all affected by the same * columns of C. */ typedef struct Path_struct { Int start ; /* column at which to start, or EMPTY if initial */ Int end ; /* column at which to end, or EMPTY if initial */ Int ccol ; /* column of C to which path refers */ Int parent ; /* parent path */ Int c ; /* child of j along this path */ Int next ; /* next path in link list */ Int rank ; /* number of rank-1 paths merged onto this path */ Int order ; /* dfs order of this path */ Int wfirst ; /* first column of W to affect this path */ Int pending ; /* column at which the path is pending */ Int botrow ; /* for partial update/downdate of solution to Lx=b */ } Path_type ; /* ========================================================================== */ /* === dfs ================================================================== */ /* ========================================================================== */ /* Compute the DFS order of the set of paths. This can be recursive because * there are at most 23 paths to sort: one for each column of C (8 at most), * and one for each node in a balanced binary tree with 8 leaves (15). * Stack overflow is thus not a problem. */ static void dfs ( Path_type *Path, /* the set of Paths */ Int k, /* the rank of the update/downdate */ Int path, /* which path to work on */ Int *path_order, /* the current path order */ Int *w_order, /* the current order of the columns of W */ Int depth, Int npaths /* total number of paths */ ) { Int c ; /* child path */ ASSERT (path >= 0 && path < npaths) ; if (path < k) { /* this is a leaf node, corresponding to column W (:,path) */ /* and column C (:, Path [path].ccol) */ ASSERT (Path [path].ccol >= 0) ; Path [path].wfirst = *w_order ; Path [path].order = *w_order ; (*w_order)++ ; } else { /* this is a non-leaf path, within the tree */ ASSERT (Path [path].c != EMPTY) ; ASSERT (Path [path].ccol == EMPTY) ; /* order each child path */ for (c = Path [path].c ; c != EMPTY ; c = Path [c].next) { dfs (Path, k, c, path_order, w_order, depth+1, npaths) ; if (Path [path].wfirst == EMPTY) { Path [path].wfirst = Path [c].wfirst ; } } /* order this path next */ Path [path].order = (*path_order)++ ; } } /* ========================================================================== */ /* === numeric update/downdate routines ===================================== */ /* ========================================================================== */ #define WDIM 1 #include "t_cholmod_updown.c" #define WDIM 2 #include "t_cholmod_updown.c" #define WDIM 4 #include "t_cholmod_updown.c" #define WDIM 8 #include "t_cholmod_updown.c" /* ========================================================================== */ /* === cholmod_updown_mark ================================================== */ /* ========================================================================== */ /* Update/downdate LDL' +/- C*C', and update/downdate selected portions of the * solution to Lx=b. * * The original system is L*x = b. The new system is Lnew*xnew = b + deltab. * deltab(i) can be nonzero only if column i of L is modified by the update/ * downdate. If column i is not modified, the deltab(i) is not accessed. * * The solution to Lx=b is not modified if either X or DeltaB are NULL. * * Rowmark and colmark: * -------------------- * * rowmark and colmark affect which portions of L take part in the update/ * downdate of the solution to Lx=b. They do not affect how L itself is * updated/downdated. They are both ignored if X or DeltaB are NULL. * * If not NULL, rowmark is an integer array of size n where L is n-by-n. * rowmark [j] defines the part of column j of L that takes part in the update/ * downdate of the forward solve, Lx=b. Specifically, if i = rowmark [j], * then L(j:i-1,j) is used, and L(i:end,j) is ignored. * * If not NULL, colmark is an integer array of size C->ncol. colmark [ccol] * for a column C(:,ccol) redefines those parts of L that take part in the * update/downdate of Lx=b. Each column of C affects a set of columns of L. * If column ccol of C affects column j of L, then the new rowmark [j] of * column j of L is defined as colmark [ccol]. In a multiple-rank update/ * downdate, if two or more columns of C affect column j, its new rowmark [j] * is the colmark of the least-numbered column of C. colmark is ignored if * it is NULL, in which case rowmark is not modified. If colmark [ccol] is * EMPTY (-1), then rowmark is not modified for that particular column of C. * colmark is ignored if it is NULL, or rowmark, X, or DeltaB are NULL. * * The algorithm for modifying the solution to Lx=b when rowmark and colmark * are NULL is as follows: * * for each column j of L that is modified: * deltab (j:end) += L (j:end,j) * x(j) * modify L * for each column j of L that is modified: * x (j) = deltab (j) * deltab (j) = 0 * deltab (j+1:end) -= L (j+1:end,j) * x(j) * * If rowmark is non-NULL but colmark is NULL: * * for each column j of L that is modified: * deltab (j:rowmark(j)-1) += L (j:rowmark(j)-1,j) * x(j) * modify L * for each column j of L that is modified: * x (j) = deltab (j) * deltab (j) = 0 * deltab (j+1:rowmark(j)-1) -= L (j+1:rowmark(j)-1,j) * x(j) * * If both rowmark and colmark are non-NULL: * * for each column j of L that is modified: * deltab (j:rowmark(j)-1) += L (j:rowmark(j)-1,j) * x(j) * modify L * for each column j of L that is modified: * modify rowmark (j) according to colmark * for each column j of L that is modified: * x (j) = deltab (j) * deltab (j) = 0 * deltab (j+1:rowmark(j)-1) -= L (j+1:rowmark(j)-1,j) * x(j) * * Note that if the rank of C exceeds k = Common->maxrank (which is 2, 4, or 8), * then the update/downdate is done as a series of rank-k updates. In this * case, the above algorithm is repeated for each block of k columns of C. * * Unless it leads to no changes in rowmark, colmark should be used only if * C->ncol <= Common->maxrank, because the update/downdate is done with maxrank * columns at a time. Otherwise, the results are undefined. * * This routine is an "expert" routine. It is meant for use in LPDASA only. */ int CHOLMOD(updown_mark) ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ Int *colmark, /* Int array of size n. */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(updown_mask) (update, C, colmark, NULL, L, X, DeltaB, Common)) ; } /* ========================================================================== */ /* === cholmod_updown_mask ================================================== */ /* ========================================================================== */ int CHOLMOD(updown_mask) ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ Int *colmark, /* Int array of size n. See cholmod_updown.c */ Int *mask, /* size n */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { double xj, fl ; double *Lx, *W, *Xx, *Nx ; Int *Li, *Lp, *Lnz, *Cp, *Ci, *Cnz, *Head, *Flag, *Stack, *Lnext, *Iwork, *Set_ps1 [32], *Set_ps2 [32], *ps1, *ps2 ; size_t maxrank ; Path_type OrderedPath [32], Path [32] ; Int n, wdim, k1, k2, npaths, i, j, row, packed, ccol, p, cncol, do_solve, mark, jj, j2, kk, nextj, p1, p2, c, use_colmark, newlnz, k, newpath, path_order, w_order, scattered, path, newparent, pp1, pp2, smax, maxrow, row1, nsets, s, p3, newlnz1, Set [32], top, len, lnz, m, botrow ; size_t w ; int ok = TRUE ; DEBUG (Int oldparent) ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (C, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_REAL, FALSE) ; RETURN_IF_XTYPE_INVALID (C, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; n = L->n ; cncol = C->ncol ; if (!(C->sorted)) { ERROR (CHOLMOD_INVALID, "C must have sorted columns") ; return (FALSE) ; } if (n != (Int) (C->nrow)) { ERROR (CHOLMOD_INVALID, "C and L dimensions do not match") ; return (FALSE) ; } do_solve = (X != NULL) && (DeltaB != NULL) ; if (do_solve) { RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; RETURN_IF_XTYPE_INVALID (DeltaB, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; Xx = X->x ; Nx = DeltaB->x ; if (X->nrow != L->n || X->ncol != 1 || DeltaB->nrow != L->n || DeltaB->ncol != 1 || Xx == NULL || Nx == NULL) { ERROR (CHOLMOD_INVALID, "X and/or DeltaB invalid") ; return (FALSE) ; } } else { Xx = NULL ; Nx = NULL ; } Common->status = CHOLMOD_OK ; Common->modfl = 0 ; fl = 0 ; use_colmark = (colmark != NULL) ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* Note: cholmod_rowadd and cholmod_rowdel use the second n doubles in * Common->Xwork for Cx, and then perform a rank-1 update here, which uses * the first n doubles in Common->Xwork. Both the rowadd and rowdel * routines allocate enough workspace so that Common->Xwork isn't destroyed * below. Also, both cholmod_rowadd and cholmod_rowdel use the second n * ints in Common->Iwork for Ci. */ /* make sure maxrank is in the proper range */ maxrank = CHOLMOD(maxrank) (n, Common) ; k = MIN (cncol, (Int) maxrank) ; /* maximum k is wdim */ wdim = Power2 [k] ; /* number of columns needed in W */ ASSERT (wdim <= (Int) maxrank) ; PRINT1 (("updown wdim final "ID" k "ID"\n", wdim, k)) ; /* w = wdim * n */ w = CHOLMOD(mult_size_t) (n, wdim, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, n, w, Common) ; if (Common->status < CHOLMOD_OK || maxrank == 0) { /* out of memory, L is returned unchanged */ return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* convert to simplicial numeric LDL' factor, if not already */ /* ---------------------------------------------------------------------- */ if (L->xtype == CHOLMOD_PATTERN || L->is_super || L->is_ll) { /* can only update/downdate a simplicial LDL' factorization */ CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, FALSE, FALSE, L, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory, L is returned unchanged */ return (FALSE) ; } } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; PRINT1 (("updown, rank %g update %d\n", (double) C->ncol, update)) ; DEBUG (CHOLMOD(dump_factor) (L, "input L for updown", Common)) ; ASSERT (CHOLMOD(dump_sparse) (C, "input C for updown", Common) >= 0) ; Ci = C->i ; Cp = C->p ; Cnz = C->nz ; packed = C->packed ; ASSERT (IMPLIES (!packed, Cnz != NULL)) ; /* ---------------------------------------------------------------------- */ /* quick return */ /* ---------------------------------------------------------------------- */ if (cncol <= 0 || n == 0) { /* nothing to do */ return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* get L */ /* ---------------------------------------------------------------------- */ Li = L->i ; Lx = L->x ; Lp = L->p ; Lnz = L->nz ; Lnext = L->next ; ASSERT (Lnz != NULL) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Flag = Common->Flag ; /* size n, Flag [i] <= mark must hold */ Head = Common->Head ; /* size n, Head [i] == EMPTY must hold */ W = Common->Xwork ; /* size n-by-wdim, zero on input and output*/ /* note that Iwork [n .. 2*n-1] (i/i/l) may be in use in rowadd/rowdel: */ Iwork = Common->Iwork ; Stack = Iwork ; /* size n, uninitialized (i/i/l) */ /* ---------------------------------------------------------------------- */ /* entire rank-cncol update, done as a sequence of rank-k updates */ /* ---------------------------------------------------------------------- */ ps1 = NULL ; ps2 = NULL ; for (k1 = 0 ; k1 < cncol ; k1 += k) { /* ------------------------------------------------------------------ */ /* get the next k columns of C for the update/downdate */ /* ------------------------------------------------------------------ */ /* the last update/downdate might be less than rank-k */ if (k > cncol - k1) { k = cncol - k1 ; wdim = Power2 [k] ; } k2 = k1 + k - 1 ; /* workspaces are in the following state, on input and output */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, wdim, Common)) ; /* ------------------------------------------------------------------ */ /* create a zero-length path for each column of W */ /* ------------------------------------------------------------------ */ nextj = n ; path = 0 ; for (ccol = k1 ; ccol <= k2 ; ccol++) { PRINT1 (("Column ["ID"]: "ID"\n", path, ccol)) ; ASSERT (ccol >= 0 && ccol <= cncol) ; pp1 = Cp [ccol] ; pp2 = (packed) ? (Cp [ccol+1]) : (pp1 + Cnz [ccol]) ; /* get the row index j of the first entry in C (:,ccol) */ if (pp2 > pp1) { /* Column ccol of C has at least one entry. */ j = Ci [pp1] ; } else { /* Column ccol of C is empty. Pretend it has one entry in * the last column with numerical value of zero. */ j = n-1 ; } ASSERT (j >= 0 && j < n) ; /* find first column to work on */ nextj = MIN (nextj, j) ; Path [path].ccol = ccol ; /* which column of C this path is for */ Path [path].start = EMPTY ; /* paths for C have zero length */ Path [path].end = EMPTY ; Path [path].parent = EMPTY ; /* no parent yet */ Path [path].rank = 1 ; /* one column of W */ Path [path].c = EMPTY ; /* no child of this path (case A) */ Path [path].next = Head [j] ; /* this path is pending at col j */ Path [path].pending = j ; /* this path is pending at col j */ Head [j] = path ; /* this path is pending at col j */ PRINT1(("Path "ID" starts: start "ID" end "ID" parent "ID" c "ID"" "j "ID" ccol "ID"\n", path, Path [path].start, Path [path].end, Path [path].parent, Path [path].c, j, ccol)) ; /* initialize botrow for this path */ Path [path].botrow = (use_colmark) ? colmark [ccol] : n ; path++ ; } /* we start with paths 0 to k-1. Next one (now unused) is npaths */ npaths = k ; j = nextj ; ASSERT (j < n) ; scattered = FALSE ; /* ------------------------------------------------------------------ */ /* symbolic update of columns of L */ /* ------------------------------------------------------------------ */ while (j < n) { ASSERT (j >= 0 && j < n && Lnz [j] > 0) ; /* the old column, Li [p1..p2-1]. D (j,j) is stored in Lx [p1] */ p1 = Lp [j] ; newlnz = Lnz [j] ; p2 = p1 + newlnz ; #ifndef NDEBUG PRINT1 (("\n=========Column j="ID" p1 "ID" p2 "ID" lnz "ID" \n", j, p1, p2, newlnz)) ; dump_col ("Old", j, p1, p2, Li, Lx, n, Common) ; oldparent = (Lnz [j] > 1) ? (Li [p1 + 1]) : EMPTY ; ASSERT (CHOLMOD(dump_work) (TRUE, FALSE, 0, Common)) ; ASSERT (!scattered) ; PRINT1 (("Col "ID": Checking paths, npaths: "ID"\n", j, npaths)) ; for (kk = 0 ; kk < npaths ; kk++) { Int kk2, found, j3 = Path [kk].pending ; PRINT2 (("Path "ID" pending at "ID".\n", kk, j3)) ; if (j3 != EMPTY) { /* Path kk must be somewhere in link list for column j3 */ ASSERT (Head [j3] != EMPTY) ; PRINT3 ((" List at "ID": ", j3)) ; found = FALSE ; for (kk2 = Head [j3] ; kk2 != EMPTY ; kk2 = Path [kk2].next) { PRINT3 ((""ID" ", kk2)) ; ASSERT (Path [kk2].pending == j3) ; found = found || (kk2 == kk) ; } PRINT3 (("\n")) ; ASSERT (found) ; } } PRINT1 (("\nCol "ID": Paths at this column, head "ID"\n", j, Head [j])); ASSERT (Head [j] != EMPTY) ; for (kk = Head [j] ; kk != EMPTY ; kk = Path [kk].next) { PRINT1 (("path "ID": (c="ID" j="ID") npaths "ID"\n", kk, Path[kk].c, j, npaths)) ; ASSERT (kk >= 0 && kk < npaths) ; ASSERT (Path [kk].pending == j) ; } #endif /* -------------------------------------------------------------- */ /* determine the path we're on */ /* -------------------------------------------------------------- */ /* get the first old path at column j */ path = Head [j] ; /* -------------------------------------------------------------- */ /* update/downdate of forward solve, Lx=b */ /* -------------------------------------------------------------- */ if (do_solve) { xj = Xx [j] ; if (IS_NONZERO (xj)) { xj = Xx [j] ; /* This is first time column j has been seen for entire */ /* rank-k update/downdate. */ /* DeltaB += Lold (j:botrow-1,j) * X (j) */ Nx [j] += xj ; /* diagonal of L */ /* find the botrow for this column */ botrow = (use_colmark) ? Path [path].botrow : n ; for (p = p1 + 1 ; p < p2 ; p++) { i = Li [p] ; if (i >= botrow) { break ; } Nx [i] += Lx [p] * xj ; } /* clear X[j] to flag col j of Lold as having been seen. If * X (j) was initially zero, then the above code is never * executed for column j. This is safe, since if xj=0 the * code above does not do anything anyway. */ Xx [j] = 0.0 ; } } /* -------------------------------------------------------------- */ /* start a new path at this column if two or more paths merge */ /* -------------------------------------------------------------- */ newpath = /* start a new path if paths have merged */ (Path [path].next != EMPTY) /* or if j is the first node on a path (case A). */ || (Path [path].c == EMPTY) ; if (newpath) { /* get the botrow of the first path at column j */ botrow = (use_colmark) ? Path [path].botrow : n ; path = npaths++ ; ASSERT (npaths <= 3*k) ; Path [path].ccol = EMPTY ; /* no single col of C for this path*/ Path [path].start = j ; /* path starts at this column j */ Path [path].end = EMPTY ; /* don't know yet where it ends */ Path [path].parent = EMPTY ;/* don't know parent path yet */ Path [path].rank = 0 ; /* rank is sum of child path ranks */ PRINT1 (("Path "ID" starts: start "ID" end "ID" parent "ID"\n", path, Path [path].start, Path [path].end, Path [path].parent)) ; /* set the botrow of the new path */ Path [path].botrow = (use_colmark) ? botrow : n ; } /* -------------------------------------------------------------- */ /* for each path kk pending at column j */ /* -------------------------------------------------------------- */ /* make a list of the sets that need to be merged into column j */ nsets = 0 ; for (kk = Head [j] ; kk != EMPTY ; kk = Path [kk].next) { /* ---------------------------------------------------------- */ /* path kk is at (c,j) */ /* ---------------------------------------------------------- */ c = Path [kk].c ; ASSERT (c < j) ; PRINT1 (("TUPLE on path "ID" (c="ID" j="ID")\n", kk, c, j)) ; ASSERT (Path [kk].pending == j) ; if (newpath) { /* finalize path kk and find rank of this path */ Path [kk].end = c ; /* end of old path is previous node c */ Path [kk].parent = path ; /* parent is this path */ Path [path].rank += Path [kk].rank ; /* sum up ranks */ Path [kk].pending = EMPTY ; PRINT1 (("Path "ID" done:start "ID" end "ID" parent "ID"\n", kk, Path [kk].start, Path [kk].end, Path [kk].parent)) ; } if (c == EMPTY) { /* ------------------------------------------------------ */ /* CASE A: first node in path */ /* ------------------------------------------------------ */ /* update: add pattern of incoming column */ /* Column ccol of C is in Ci [pp1 ... pp2-1] */ ccol = Path [kk].ccol ; pp1 = Cp [ccol] ; pp2 = (packed) ? (Cp [ccol+1]) : (pp1 + Cnz [ccol]) ; PRINT1 (("Case A, ccol = "ID" len "ID"\n", ccol, pp2-pp1)) ; ASSERT (IMPLIES (pp2 > pp1, Ci [pp1] == j)) ; if (!scattered) { /* scatter the original pattern of column j of L */ for (p = p1 ; p < p2 ; p++) { Flag [Li [p]] = mark ; } scattered = TRUE ; } /* scatter column ccol of C (skip first entry, j) */ newlnz1 = newlnz ; for (p = pp1 + 1 ; p < pp2 ; p++) { row = Ci [p] ; if (Flag [row] < mark) { /* this is a new entry in Lj' */ Flag [row] = mark ; newlnz++ ; } } if (newlnz1 != newlnz) { /* column ccol of C adds something to column j of L */ Set [nsets++] = FLIP (ccol) ; } } else if (Head [c] == 1) { /* ------------------------------------------------------ */ /* CASE B: c is old, but changed, child of j */ /* CASE C: new child of j */ /* ------------------------------------------------------ */ /* Head [c] is 1 if col c of L has new entries, * EMPTY otherwise */ Flag [c] = 0 ; Head [c] = EMPTY ; /* update: add Lc' */ /* column c of L is in Li [pp1 .. pp2-1] */ pp1 = Lp [c] ; pp2 = pp1 + Lnz [c] ; PRINT1 (("Case B/C: c = "ID"\n", c)) ; DEBUG (dump_col ("Child", c, pp1, pp2, Li, Lx, n, Common)) ; ASSERT (j == Li [pp1 + 1]) ; /* j is new parent of c */ if (!scattered) { /* scatter the original pattern of column j of L */ for (p = p1 ; p < p2 ; p++) { Flag [Li [p]] = mark ; } scattered = TRUE ; } /* scatter column c of L (skip first two entries, c and j)*/ newlnz1 = newlnz ; for (p = pp1 + 2 ; p < pp2 ; p++) { row = Li [p] ; if (Flag [row] < mark) { /* this is a new entry in Lj' */ Flag [row] = mark ; newlnz++ ; } } PRINT2 (("\n")) ; if (newlnz1 != newlnz) { /* column c of L adds something to column j of L */ Set [nsets++] = c ; } } } /* -------------------------------------------------------------- */ /* update the pattern of column j of L */ /* -------------------------------------------------------------- */ /* Column j of L will be in Li/Lx [p1 .. p3-1] */ p3 = p1 + newlnz ; ASSERT (IMPLIES (nsets == 0, newlnz == Lnz [j])) ; PRINT1 (("p1 "ID" p2 "ID" p3 "ID" nsets "ID"\n", p1, p2, p3,nsets)); /* -------------------------------------------------------------- */ /* ensure we have enough space for the longer column */ /* -------------------------------------------------------------- */ if (nsets > 0 && p3 > Lp [Lnext [j]]) { PRINT1 (("Col realloc: j "ID" newlnz "ID"\n", j, newlnz)) ; if (!CHOLMOD(reallocate_column) (j, newlnz, L, Common)) { /* out of memory, L is now simplicial symbolic */ CHOLMOD(clear_flag) (Common) ; for (j = 0 ; j <= n ; j++) { Head [j] = EMPTY ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, wdim, Common)) ; return (FALSE) ; } /* L->i and L->x may have moved. Column j has moved too */ Li = L->i ; Lx = L->x ; p1 = Lp [j] ; p2 = p1 + Lnz [j] ; p3 = p1 + newlnz ; } /* -------------------------------------------------------------- */ /* create set pointers */ /* -------------------------------------------------------------- */ for (s = 0 ; s < nsets ; s++) { /* Pattern of Set s is *(Set_ps1 [s] ... Set_ps2 [s]-1) */ c = Set [s] ; if (c < EMPTY) { /* column ccol of C, skip first entry (j) */ ccol = FLIP (c) ; pp1 = Cp [ccol] ; pp2 = (packed) ? (Cp [ccol+1]) : (pp1 + Cnz [ccol]) ; ASSERT (pp2 - pp1 > 1) ; Set_ps1 [s] = &(Ci [pp1 + 1]) ; Set_ps2 [s] = &(Ci [pp2]) ; PRINT1 (("set "ID" is ccol "ID"\n", s, ccol)) ; } else { /* column c of L, skip first two entries (c and j) */ pp1 = Lp [c] ; pp2 = pp1 + Lnz [c] ; ASSERT (Lnz [c] > 2) ; Set_ps1 [s] = &(Li [pp1 + 2]) ; Set_ps2 [s] = &(Li [pp2]) ; PRINT1 (("set "ID" is L "ID"\n", s, c)) ; } DEBUG (dump_set (s, Set_ps1, Set_ps2, j, n, Common)) ; } /* -------------------------------------------------------------- */ /* multiset merge */ /* -------------------------------------------------------------- */ /* Merge the sets into a single sorted set, Lj'. Before the merge * starts, column j is located in Li/Lx [p1 ... p2-1] and the * space Li/Lx [p2 ... p3-1] is empty. p1 is Lp [j], p2 is * Lp [j] + Lnz [j] (the old length of the column), and p3 is * Lp [j] + newlnz (the new and longer length of the column). * * The sets 0 to nsets-1 are defined by the Set_ps1 and Set_ps2 * pointers. Set s is located in *(Set_ps1 [s] ... Set_ps2 [s]-1). * It may be a column of C, or a column of L. All row indices i in * the sets are in the range i > j and i < n. All sets are sorted. * * The merge into column j of L is done in place. * * During the merge, p2 and p3 are updated. Li/Lx [p1..p2-1] * reflects the indices of the old column j of L that are yet to * be merged into the new column. Entries in their proper place in * the new column j of L are located in Li/Lx [p3 ... p1+newlnz-1]. * The merge finishes when p2 == p3. * * During the merge, set s consumed as it is merged into column j of * L. Its unconsumed contents are *(Set_ps1 [s] ... Set_ps2 [s]-1). * When a set is completely consumed, it is removed from the set of * sets, and nsets is decremented. * * The multiset merge and 2-set merge finishes when p2 == p3. */ PRINT1 (("Multiset merge p3 "ID" p2 "ID" nsets "ID"\n", p3, p2, nsets)) ; while (p3 > p2 && nsets > 1) { #ifndef NDEBUG PRINT2 (("\nMultiset merge. nsets = "ID"\n", nsets)) ; PRINT2 (("Source col p1 = "ID", p2 = "ID", p3= "ID"\n", p1, p2, p3)) ; for (p = p1 + 1 ; p < p2 ; p++) { PRINT2 ((" p: "ID" source row "ID" %g\n", p, Li[p], Lx[p])) ; ASSERT (Li [p] > j && Li [p] < n) ; } PRINT2 (("---\n")) ; for (p = p3 ; p < p1 + newlnz ; p++) { PRINT2 ((" p: "ID" target row "ID" %g\n", p, Li[p], Lx[p])) ; ASSERT (Li [p] > j && Li [p] < n) ; } for (s = 0 ; s < nsets ; s++) { dump_set (s, Set_ps1, Set_ps2, j, n, Common) ; } #endif /* get the entry at the tail end of source column Lj */ row1 = Li [p2 - 1] ; ASSERT (row1 >= j && p2 >= p1) ; /* find the largest row in all the sets */ maxrow = row1 ; smax = EMPTY ; for (s = nsets-1 ; s >= 0 ; s--) { ASSERT (Set_ps1 [s] < Set_ps2 [s]) ; row = *(Set_ps2 [s] - 1) ; if (row == maxrow) { /* skip past this entry in set s (it is a duplicate) */ Set_ps2 [s]-- ; if (Set_ps1 [s] == Set_ps2 [s]) { /* nothing more in this set */ nsets-- ; Set_ps1 [s] = Set_ps1 [nsets] ; Set_ps2 [s] = Set_ps2 [nsets] ; if (smax == nsets) { /* Set smax redefined; it is now this set */ smax = s ; } } } else if (row > maxrow) { maxrow = row ; smax = s ; } } ASSERT (maxrow > j) ; /* move the row onto the stack of the target column */ if (maxrow == row1) { /* next entry is in Lj, move to the bottom of Lj' */ ASSERT (smax == EMPTY) ; p2-- ; p3-- ; Li [p3] = maxrow ; Lx [p3] = Lx [p2] ; } else { /* new entry in Lj' */ ASSERT (smax >= 0 && smax < nsets) ; Set_ps2 [smax]-- ; p3-- ; Li [p3] = maxrow ; Lx [p3] = 0.0 ; if (Set_ps1 [smax] == Set_ps2 [smax]) { /* nothing more in this set */ nsets-- ; Set_ps1 [smax] = Set_ps1 [nsets] ; Set_ps2 [smax] = Set_ps2 [nsets] ; PRINT1 (("Set "ID" now empty\n", smax)) ; } } } /* -------------------------------------------------------------- */ /* 2-set merge: */ /* -------------------------------------------------------------- */ /* This the same as the multi-set merge, except there is only one * set s = 0 left. The source column j and the set 0 are being * merged into the target column j. */ if (nsets > 0) { ps1 = Set_ps1 [0] ; ps2 = Set_ps2 [0] ; } while (p3 > p2) { #ifndef NDEBUG PRINT2 (("\n2-set merge.\n")) ; ASSERT (nsets == 1) ; PRINT2 (("Source col p1 = "ID", p2 = "ID", p3= "ID"\n", p1, p2, p3)) ; for (p = p1 + 1 ; p < p2 ; p++) { PRINT2 ((" p: "ID" source row "ID" %g\n", p, Li[p], Lx[p])) ; ASSERT (Li [p] > j && Li [p] < n) ; } PRINT2 (("---\n")) ; for (p = p3 ; p < p1 + newlnz ; p++) { PRINT2 ((" p: "ID" target row "ID" %g\n", p, Li[p], Lx[p])) ; ASSERT (Li [p] > j && Li [p] < n) ; } dump_set (0, Set_ps1, Set_ps2, j, n, Common) ; #endif if (p2 == p1 + 1) { /* the top of Lj is empty; copy the set and quit */ while (p3 > p2) { /* new entry in Lj' */ row = *(--ps2) ; p3-- ; Li [p3] = row ; Lx [p3] = 0.0 ; } } else { /* get the entry at the tail end of Lj */ row1 = Li [p2 - 1] ; ASSERT (row1 > j && row1 < n) ; /* get the entry at the tail end of the incoming set */ ASSERT (ps1 < ps2) ; row = *(ps2-1) ; ASSERT (row > j && row1 < n) ; /* move the larger of the two entries to the target set */ if (row1 >= row) { /* next entry is in Lj, move to the bottom */ if (row1 == row) { /* skip past this entry in the set */ ps2-- ; } p2-- ; p3-- ; Li [p3] = row1 ; Lx [p3] = Lx [p2] ; } else { /* new entry in Lj' */ ps2-- ; p3-- ; Li [p3] = row ; Lx [p3] = 0.0 ; } } } /* -------------------------------------------------------------- */ /* The new column j of L is now in Li/Lx [p1 ... p2-1] */ /* -------------------------------------------------------------- */ p2 = p1 + newlnz ; DEBUG (dump_col ("After merge: ", j, p1, p2, Li, Lx, n, Common)) ; fl += Path [path].rank * (6 + 4 * (double) newlnz) ; /* -------------------------------------------------------------- */ /* clear Flag; original pattern of column j L no longer marked */ /* -------------------------------------------------------------- */ mark = CHOLMOD(clear_flag) (Common) ; scattered = FALSE ; /* -------------------------------------------------------------- */ /* find the new parent */ /* -------------------------------------------------------------- */ newparent = (newlnz > 1) ? (Li [p1 + 1]) : EMPTY ; PRINT1 (("\nNew parent, Lnz: "ID": "ID" "ID"\n", j, newparent,newlnz)); ASSERT (oldparent == EMPTY || newparent <= oldparent) ; /* -------------------------------------------------------------- */ /* go to the next node in the path */ /* -------------------------------------------------------------- */ /* path moves to (j,nextj) unless j is a root */ nextj = (newparent == EMPTY) ? n : newparent ; /* place path at head of list for nextj, or terminate the path */ PRINT1 (("\n j = "ID" nextj = "ID"\n\n", j, nextj)) ; Path [path].c = j ; if (nextj < n) { /* put path on link list of pending paths at column nextj */ Path [path].next = Head [nextj] ; Path [path].pending = nextj ; Head [nextj] = path ; PRINT1 (("Path "ID" continues to ("ID","ID"). Rank "ID"\n", path, Path [path].c, nextj, Path [path].rank)) ; } else { /* path has ended here, at a root */ Path [path].next = EMPTY ; Path [path].pending = EMPTY ; Path [path].end = j ; PRINT1 (("Path "ID" ends at root ("ID"). Rank "ID"\n", path, Path [path].end, Path [path].rank)) ; } /* The link list Head [j] can now be emptied. Set Head [j] to 1 * if column j has changed (it is no longer used as a link list). */ PRINT1 (("column "ID", oldlnz = "ID"\n", j, Lnz [j])) ; Head [j] = (Lnz [j] != newlnz) ? 1 : EMPTY ; Lnz [j] = newlnz ; PRINT1 (("column "ID", newlnz = "ID"\n", j, newlnz)) ; DEBUG (dump_col ("New", j, p1, p2, Li, Lx, n, Common)) ; /* move to the next column */ if (k == Path [path].rank) { /* only one path left */ j = nextj ; } else { /* The current path is moving from column j to column nextj * (nextj is n if the path has ended). However, there may be * other paths pending in columns j+1 to nextj-1. There are * two methods for looking for the next column with a pending * update. The first one looks at all columns j+1 to nextj-1 * for a non-empty link list. This can be costly if j and * nextj differ by a large amount (it can be O(n), but this * entire routine may take Omega(1) time). The second method * looks at all paths and finds the smallest column at which any * path is pending. It takes O(# of paths), which is bounded * by 23: one for each column of C (up to 8), and then 15 for a * balanced binary tree with 8 leaves. However, if j and * nextj differ by a tiny amount (nextj is often j+1 near * the end of the matrix), looking at columns j+1 to nextj * would be faster. Both methods give the same answer. */ if (nextj - j < npaths) { /* there are fewer columns to search than paths */ PRINT1 (("check j="ID" to nextj="ID"\n", j, nextj)) ; for (j2 = j + 1 ; j2 < nextj ; j2++) { PRINT1 (("check j="ID" "ID"\n", j2, Head [j2])) ; if (Head [j2] != EMPTY) { PRINT1 (("found, j="ID"\n", j2)) ; ASSERT (Path [Head [j2]].pending == j2) ; break ; } } } else { /* there are fewer paths than columns to search */ j2 = nextj ; for (kk = 0 ; kk < npaths ; kk++) { jj = Path [kk].pending ; PRINT2 (("Path "ID" pending at "ID"\n", kk, jj)) ; if (jj != EMPTY) j2 = MIN (j2, jj) ; } } j = j2 ; } } /* ensure workspaces are back to the values required on input */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, TRUE, Common)) ; /* ------------------------------------------------------------------ */ /* depth-first-search of tree to order the paths */ /* ------------------------------------------------------------------ */ /* create lists of child paths */ PRINT1 (("\n\nDFS search:\n\n")) ; for (path = 0 ; path < npaths ; path++) { Path [path].c = EMPTY ; /* first child of path */ Path [path].next = EMPTY ; /* next sibling of path */ Path [path].order = EMPTY ; /* path is not ordered yet */ Path [path].wfirst = EMPTY ; /* 1st column of W not found yet */ #ifndef NDEBUG j = Path [path].start ; PRINT1 (("Path "ID" : start "ID" end "ID" parent "ID" ccol "ID"\n", path, j, Path [path].end, Path [path].parent, Path [path].ccol)) ; for ( ; ; ) { PRINT1 ((" column "ID"\n", j)) ; ASSERT (j == EMPTY || (j >= 0 && j < n)) ; if (j == Path [path].end) { break ; } ASSERT (j >= 0 && j < n) ; j = (Lnz [j] > 1) ? (Li [Lp [j] + 1]) : EMPTY ; } #endif } for (path = 0 ; path < npaths ; path++) { p = Path [path].parent ; /* add path to child list of parent */ if (p != EMPTY) { ASSERT (p < npaths) ; Path [path].next = Path [p].c ; Path [p].c = path ; } } path_order = k ; w_order = 0 ; for (path = npaths-1 ; path >= 0 ; path--) { if (Path [path].order == EMPTY) { /* this path is the root of a subtree of Tbar */ PRINT1 (("Root path "ID"\n", path)) ; ASSERT (path >= k) ; dfs (Path, k, path, &path_order, &w_order, 0, npaths) ; } } ASSERT (path_order == npaths) ; ASSERT (w_order == k) ; /* reorder the paths */ for (path = 0 ; path < npaths ; path++) { /* old order is path, new order is Path [path].order */ OrderedPath [Path [path].order] = Path [path] ; } #ifndef NDEBUG for (path = 0 ; path < npaths ; path++) { PRINT1 (("Ordered Path "ID": start "ID" end "ID" wfirst "ID" rank " ""ID" ccol "ID"\n", path, OrderedPath [path].start, OrderedPath [path].end, OrderedPath [path].wfirst, OrderedPath [path].rank, OrderedPath [path].ccol)) ; if (path < k) { ASSERT (OrderedPath [path].ccol >= 0) ; } else { ASSERT (OrderedPath [path].ccol == EMPTY) ; } } #endif /* ------------------------------------------------------------------ */ /* numeric update/downdate for all paths */ /* ------------------------------------------------------------------ */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, wdim, Common)) ; switch (wdim) { case 1: updown_1_r (update, C, k, L, W, OrderedPath, npaths, mask, Common) ; break ; case 2: updown_2_r (update, C, k, L, W, OrderedPath, npaths, mask, Common) ; break ; case 4: updown_4_r (update, C, k, L, W, OrderedPath, npaths, mask, Common) ; break ; case 8: updown_8_r (update, C, k, L, W, OrderedPath, npaths, mask, Common) ; break ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, wdim, Common)) ; } /* ---------------------------------------------------------------------- */ /* update/downdate the forward solve */ /* ---------------------------------------------------------------------- */ if (do_solve) { /* We now have DeltaB += Lold (:,j) * X (j) for all columns j in union * of all paths seen during the entire rank-cncol update/downdate. For * each j in path, do DeltaB -= Lnew (:,j)*DeltaB(j) * in topological order. */ #ifndef NDEBUG PRINT1 (("\ndo_solve, DeltaB + Lold(:,Path)*X(Path):\n")) ; for (i = 0 ; i < n ; i++) { PRINT1 (("do_solve: "ID" %30.20e\n", i, Nx [i])) ; } #endif /* Note that the downdate, if it deleted entries, would need to compute * the Stack prior to doing any downdates. */ /* find the union of all the paths in the new L */ top = n ; /* "top" is stack pointer, not a row or column index */ for (ccol = 0 ; ccol < cncol ; ccol++) { /* -------------------------------------------------------------- */ /* j = first row index of C (:,ccol) */ /* -------------------------------------------------------------- */ pp1 = Cp [ccol] ; pp2 = (packed) ? (Cp [ccol+1]) : (pp1 + Cnz [ccol]) ; if (pp2 > pp1) { /* Column ccol of C has at least one entry. */ j = Ci [pp1] ; } else { /* Column ccol of C is empty */ j = n-1 ; } PRINT1 (("\ndo_solve: ccol= "ID"\n", ccol)) ; ASSERT (j >= 0 && j < n) ; len = 0 ; /* -------------------------------------------------------------- */ /* find the new rowmark */ /* -------------------------------------------------------------- */ /* Each column of C can redefine the region of L that takes part in * the update/downdate of the triangular solve Lx=b. If * i = colmark [ccol] for column C(:,ccol), then i = rowmark [j] is * redefined for all columns along the path modified by C(:,ccol). * If more than one column modifies any given column j of L, then * the rowmark of j is determined by the colmark of the least- * numbered column that affects column j. That is, if both * C(:,ccol1) and C(:,ccol2) affect column j of L, then * rowmark [j] = colmark [MIN (ccol1, ccol2)]. * * rowmark [j] is not modified if rowmark or colmark are NULL, * or if colmark [ccol] is EMPTY. */ botrow = (use_colmark) ? (colmark [ccol]) : EMPTY ; /* -------------------------------------------------------------- */ /* traverse from j towards root, stopping if node already visited */ /* -------------------------------------------------------------- */ while (j != EMPTY && Flag [j] < mark) { PRINT1 (("do_solve: subpath j= "ID"\n", j)) ; ASSERT (j >= 0 && j < n) ; Stack [len++] = j ; /* place j on the stack */ Flag [j] = mark ; /* flag j as visited */ /* if using colmark, mark column j with botrow */ ASSERT (Li [Lp [j]] == j) ; /* diagonal is always present */ if (use_colmark) { Li [Lp [j]] = botrow ; /* use the space for botrow */ } /* go up the tree, to the parent of j */ j = (Lnz [j] > 1) ? (Li [Lp [j] + 1]) : EMPTY ; } /* -------------------------------------------------------------- */ /* move the path down to the bottom of the stack */ /* -------------------------------------------------------------- */ ASSERT (len <= top) ; while (len > 0) { Stack [--top] = Stack [--len] ; } } #ifndef NDEBUG /* Union of paths now in Stack [top..n-1] in topological order */ PRINT1 (("\nTopological order:\n")) ; for (i = top ; i < n ; i++) { PRINT1 (("column "ID" in full path\n", Stack [i])) ; } #endif /* Do the forward solve for the full path part of L */ for (m = top ; m < n ; m++) { j = Stack [m] ; ASSERT (j >= 0 && j < n) ; PRINT1 (("do_solve: path j= "ID"\n", j)) ; p1 = Lp [j] ; lnz = Lnz [j] ; p2 = p1 + lnz ; xj = Nx [j] ; /* copy new solution onto old one, for all cols in full path */ Xx [j] = xj ; Nx [j] = 0. ; /* DeltaB -= Lnew (j+1:botrow-1,j) * deltab(j) */ if (use_colmark) { botrow = Li [p1] ; /* get botrow */ Li [p1] = j ; /* restore diagonal entry */ for (p = p1 + 1 ; p < p2 ; p++) { i = Li [p] ; if (i >= botrow) break ; Nx [i] -= Lx [p] * xj ; } } else { for (p = p1 + 1 ; p < p2 ; p++) { Nx [Li [p]] -= Lx [p] * xj ; } } } /* clear the Flag */ mark = CHOLMOD(clear_flag) (Common) ; } /* ---------------------------------------------------------------------- */ /* successful update/downdate */ /* ---------------------------------------------------------------------- */ Common->modfl = fl ; DEBUG (for (j = 0 ; j < n ; j++) ASSERT (IMPLIES (do_solve, Nx[j] == 0.))) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, TRUE, Common)) ; DEBUG (CHOLMOD(dump_factor) (L, "output L for updown", Common)) ; return (TRUE) ; } #endif Matrix/src/CHOLMOD/Modify/t_cholmod_updown.c0000644000175100001440000001504512271765436020371 0ustar hornikusers/* ========================================================================== */ /* === Modify/t_cholmod_updown ============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Modify Module. Copyright (C) 2005-2006, * Timothy A. Davis and William W. Hager. * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Updates/downdates the LDL' factorization, by computing a new factorization of * * Lnew * Dnew * Lnew' = Lold * Dold * Lold' +/- C*C' * * This file is not compiled separately. It is included into * cholmod_updown.c. There are no user-callable routines in this file. * * The next include statements, below, create the numerical update/downdate * kernels from t_cholmod_updown_numkr.c. There are 4 compiled versions of this * file, one for each value of WDIM in the set 1, 2, 4, and 8. Each calls * multiple versions of t_cholmod_updown_numkr; the number of versions of each * is equal to WDIM. Each t_cholmod_updown_numkr version is included as a * static function within its t_cholmod_updown.c caller routine. Thus: * * t*_updown.c creates these versions of t_cholmod_updown_numkr.c: * --------- --------------------------------------------------- * * updown_1_r updown_1_1 * * updown_2_r updown_2_1 updown_2_2 * * updown_4_r updown_4_1 updown_4_2 updown_4_3 updown_4_4 * * updown_8_r updown_8_1 updown_8_2 updown_8_3 updown_8_4 * updown_8_5 updown_8_6 updown_8_7 updown_8_8 * * workspace: Xwork (nrow*wdim) */ /* ========================================================================== */ /* === routines for numeric update/downdate along one path ================== */ /* ========================================================================== */ #undef FORM_NAME #undef NUMERIC #define FORM_NAME(k,rank) updown_ ## k ## _ ## rank #define NUMERIC(k,rank) FORM_NAME(k,rank) #define RANK 1 #include "t_cholmod_updown_numkr.c" #if WDIM >= 2 #define RANK 2 #include "t_cholmod_updown_numkr.c" #endif #if WDIM >= 4 #define RANK 3 #include "t_cholmod_updown_numkr.c" #define RANK 4 #include "t_cholmod_updown_numkr.c" #endif #if WDIM == 8 #define RANK 5 #include "t_cholmod_updown_numkr.c" #define RANK 6 #include "t_cholmod_updown_numkr.c" #define RANK 7 #include "t_cholmod_updown_numkr.c" #define RANK 8 #include "t_cholmod_updown_numkr.c" #endif /* ========================================================================== */ /* === numeric update/downdate for all paths ================================ */ /* ========================================================================== */ static void NUMERIC (WDIM, r) ( int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* in packed or unpacked, and sorted form */ /* no empty columns */ Int rank, /* rank of the update/downdate */ cholmod_factor *L, /* with unit diagonal (diagonal not stored) */ /* temporary workspaces: */ double W [ ], /* n-by-WDIM dense matrix, initially zero */ Path_type Path [ ], Int npaths, Int mask [ ], /* size n */ cholmod_common *Common ) { double Alpha [8] ; double *Cx, *Wpath, *W1, *a ; Int i, j, p, ccol, pend, wfirst, e, path, packed ; Int *Ci, *Cp, *Cnz ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ci = C->i ; Cx = C->x ; Cp = C->p ; Cnz = C->nz ; packed = C->packed ; ASSERT (IMPLIES (!packed, Cnz != NULL)) ; ASSERT (L->n == C->nrow) ; DEBUG (CHOLMOD(dump_real) ("num_d: in W:", W, WDIM, L->n, FALSE, 1,Common)); /* ---------------------------------------------------------------------- */ /* scatter C into W */ /* ---------------------------------------------------------------------- */ for (path = 0 ; path < rank ; path++) { /* W (:, path) = C (:, Path [path].col) */ ccol = Path [path].ccol ; Wpath = W + path ; PRINT1 (("Ordered Columns [path = "ID"] = "ID"\n", path, ccol)) ; p = Cp [ccol] ; pend = (packed) ? (Cp [ccol+1]) : (p + Cnz [ccol]) ; /* column C can be empty */ for ( ; p < pend ; p++) { i = Ci [p] ; ASSERT (i >= 0 && i < (Int) (C->nrow)) ; if (mask == NULL || mask [i] < 0) { Wpath [WDIM * i] = Cx [p] ; } PRINT1 ((" row "ID" : %g mask "ID"\n", i, Cx [p], (mask) ? mask [i] : 0)) ; } Alpha [path] = 1.0 ; } DEBUG (CHOLMOD(dump_real) ("num_d: W:", W, WDIM, L->n, FALSE, 1,Common)) ; /* ---------------------------------------------------------------------- */ /* numeric update/downdate of the paths */ /* ---------------------------------------------------------------------- */ /* for each disjoint subpath in Tbar in DFS order do */ for (path = rank ; path < npaths ; path++) { /* determine which columns of W to use */ wfirst = Path [path].wfirst ; e = Path [path].end ; j = Path [path].start ; ASSERT (e >= 0 && e < (Int) (L->n)) ; ASSERT (j >= 0 && j < (Int) (L->n)) ; W1 = W + wfirst ; /* pointer to row 0, column wfirst of W */ a = Alpha + wfirst ; /* pointer to Alpha [wfirst] */ PRINT1 (("Numerical update/downdate of path "ID"\n", path)) ; PRINT1 (("start "ID" end "ID" wfirst "ID" rank "ID" ccol "ID"\n", j, e, wfirst, Path [path].rank, Path [path].ccol)) ; #if WDIM == 1 NUMERIC (WDIM,1) (update, j, e, a, W1, L, Common) ; #else switch (Path [path].rank) { case 1: NUMERIC (WDIM,1) (update, j, e, a, W1, L, Common) ; break ; #if WDIM >= 2 case 2: NUMERIC (WDIM,2) (update, j, e, a, W1, L, Common) ; break ; #endif #if WDIM >= 4 case 3: NUMERIC (WDIM,3) (update, j, e, a, W1, L, Common) ; break ; case 4: NUMERIC (WDIM,4) (update, j, e, a, W1, L, Common) ; break ; #endif #if WDIM == 8 case 5: NUMERIC (WDIM,5) (update, j, e, a, W1, L, Common) ; break ; case 6: NUMERIC (WDIM,6) (update, j, e, a, W1, L, Common) ; break ; case 7: NUMERIC (WDIM,7) (update, j, e, a, W1, L, Common) ; break ; case 8: NUMERIC (WDIM,8) (update, j, e, a, W1, L, Common) ; break ; #endif } #endif } } /* prepare for the next inclusion of this file in cholmod_updown.c */ #undef WDIM Matrix/src/CHOLMOD/Modify/cholmod_rowdel.c0000644000175100001440000003173012271765436020025 0ustar hornikusers/* ========================================================================== */ /* === Modify/cholmod_rowdel ================================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Modify Module. * Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager. * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Deletes a row and column from an LDL' factorization. The row and column k * is set to the kth row and column of the identity matrix. Optionally * downdates the solution to Lx=b. * * workspace: Flag (nrow), Head (nrow+1), W (nrow*2), Iwork (2*nrow) * * Only real matrices are supported (exception: since only the pattern of R * is used, it can have any valid xtype). */ #ifndef NMODIFY #include "cholmod_internal.h" #include "cholmod_modify.h" /* ========================================================================== */ /* === cholmod_rowdel ======================================================= */ /* ========================================================================== */ /* Sets the kth row and column of L to be the kth row and column of the identity * matrix, and updates L(k+1:n,k+1:n) accordingly. To reduce the running time, * the caller can optionally provide the nonzero pattern (or an upper bound) of * kth row of L, as the sparse n-by-1 vector R. Provide R as NULL if you want * CHOLMOD to determine this itself, which is easier for the caller, but takes * a little more time. */ int CHOLMOD(rowdel) ( /* ---- input ---- */ size_t k, /* row/column index to delete */ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { double yk [2] ; yk [0] = 0. ; yk [1] = 0. ; return (CHOLMOD(rowdel_mark) (k, R, yk, NULL, L, NULL, NULL, Common)) ; } /* ========================================================================== */ /* === cholmod_rowdel_solve ================================================= */ /* ========================================================================== */ /* Does the same as cholmod_rowdel, but also downdates the solution to Lx=b. * When row/column k of A is "deleted" from the system A*y=b, this can induce * a change to x, in addition to changes arising when L and b are modified. * If this is the case, the kth entry of y is required as input (yk) */ int CHOLMOD(rowdel_solve) ( /* ---- input ---- */ size_t k, /* row/column index to delete */ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */ double yk [2], /* kth entry in the solution to A*y=b */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(rowdel_mark) (k, R, yk, NULL, L, X, DeltaB, Common)) ; } /* ========================================================================== */ /* === cholmod_rowdel_mark ================================================== */ /* ========================================================================== */ /* Does the same as cholmod_rowdel_solve, except only part of L is used in * the update/downdate of the solution to Lx=b. This routine is an "expert" * routine. It is meant for use in LPDASA only. * * if R == NULL then columns 0:k-1 of L are searched for row k. Otherwise, it * searches columns in the set defined by the pattern of the first column of R. * This is meant to be the pattern of row k of L (a superset of that pattern is * OK too). R must be a permutation of a subset of 0:k-1. */ int CHOLMOD(rowdel_mark) ( /* ---- input ---- */ size_t kdel, /* row/column index to delete */ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */ double yk [2], /* kth entry in the solution to A*y=b */ Int *colmark, /* Int array of size 1. See cholmod_updown.c */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { double dk, sqrt_dk, xk, dj, fl ; double *Lx, *Cx, *W, *Xx, *Nx ; Int *Li, *Lp, *Lnz, *Ci, *Rj, *Rp, *Iwork ; cholmod_sparse *C, Cmatrix ; Int j, p, pend, kk, lnz, n, Cp [2], do_solve, do_update, left, k, right, middle, i, klast, given_row, rnz ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_REAL, FALSE) ; n = L->n ; k = kdel ; if (kdel >= L->n || k < 0) { ERROR (CHOLMOD_INVALID, "k invalid") ; return (FALSE) ; } if (R == NULL) { Rj = NULL ; rnz = EMPTY ; } else { RETURN_IF_XTYPE_INVALID (R, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (R->ncol != 1 || R->nrow != L->n) { ERROR (CHOLMOD_INVALID, "R invalid") ; return (FALSE) ; } Rj = R->i ; Rp = R->p ; rnz = Rp [1] ; } do_solve = (X != NULL) && (DeltaB != NULL) ; if (do_solve) { RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; RETURN_IF_XTYPE_INVALID (DeltaB, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; Xx = X->x ; Nx = DeltaB->x ; if (X->nrow != L->n || X->ncol != 1 || DeltaB->nrow != L->n || DeltaB->ncol != 1 || Xx == NULL || Nx == NULL) { ERROR (CHOLMOD_INVALID, "X and/or DeltaB invalid") ; return (FALSE) ; } } else { Xx = NULL ; Nx = NULL ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 2*n */ s = CHOLMOD(mult_size_t) (n, 2, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, s, s, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ; /* ---------------------------------------------------------------------- */ /* convert to simplicial numeric LDL' factor, if not already */ /* ---------------------------------------------------------------------- */ if (L->xtype == CHOLMOD_PATTERN || L->is_super || L->is_ll) { /* can only update/downdate a simplicial LDL' factorization */ CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, FALSE, FALSE, L, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory, L is returned unchanged */ return (FALSE) ; } } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* inputs, not modified on output: */ Lp = L->p ; /* size n+1 */ /* outputs, contents defined on input for incremental case only: */ Lnz = L->nz ; /* size n */ Li = L->i ; /* size L->nzmax. Can change in size. */ Lx = L->x ; /* size L->nzmax. Can change in size. */ ASSERT (L->nz != NULL) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ W = Common->Xwork ; /* size n, used only in cholmod_updown */ Cx = W + n ; /* use 2nd column of Xwork for C (size n) */ Iwork = Common->Iwork ; Ci = Iwork + n ; /* size n (i/i/l) */ /* NOTE: cholmod_updown uses Iwork [0..n-1] (i/i/l) as Stack */ /* ---------------------------------------------------------------------- */ /* prune row k from all columns of L */ /* ---------------------------------------------------------------------- */ given_row = (rnz >= 0) ; klast = given_row ? rnz : k ; PRINT2 (("given_row "ID"\n", given_row)) ; for (kk = 0 ; kk < klast ; kk++) { /* either search j = 0:k-1 or j = Rj [0:rnz-1] */ j = given_row ? (Rj [kk]) : (kk) ; if (j < 0 || j >= k) { ERROR (CHOLMOD_INVALID, "R invalid") ; return (FALSE) ; } PRINT2 (("Prune col j = "ID":\n", j)) ; lnz = Lnz [j] ; dj = Lx [Lp [j]] ; ASSERT (Lnz [j] > 0 && Li [Lp [j]] == j) ; if (lnz > 1) { left = Lp [j] ; pend = left + lnz ; right = pend - 1 ; i = Li [right] ; if (i < k) { /* row k is not in column j */ continue ; } else if (i == k) { /* k is the last row index in this column (quick delete) */ if (do_solve) { Xx [j] -= yk [0] * dj * Lx [right] ; } Lx [right] = 0 ; } else { /* binary search for row k in column j */ PRINT2 (("\nBinary search: lnz "ID" k = "ID"\n", lnz, k)) ; while (left < right) { middle = (left + right) / 2 ; PRINT2 (("left "ID" right "ID" middle "ID": ["ID" "ID"" ""ID"]\n", left, right, middle, Li [left], Li [middle], Li [right])) ; if (k > Li [middle]) { left = middle + 1 ; } else { right = middle ; } } ASSERT (left >= Lp [j] && left < pend) ; #ifndef NDEBUG /* brute force, linear-time search */ { Int p3 = Lp [j] ; i = EMPTY ; PRINT2 (("Brute force:\n")) ; for ( ; p3 < pend ; p3++) { i = Li [p3] ; PRINT2 (("p "ID" ["ID"]\n", p3, i)) ; if (i >= k) { break ; } } if (i == k) { ASSERT (k == Li [p3]) ; ASSERT (p3 == left) ; } } #endif if (k == Li [left]) { if (do_solve) { Xx [j] -= yk [0] * dj * Lx [left] ; } /* found row k in column j. Prune it from the column.*/ Lx [left] = 0 ; } } } } #ifndef NDEBUG /* ensure that row k has been deleted from the matrix L */ for (j = 0 ; j < k ; j++) { Int lasti ; lasti = EMPTY ; p = Lp [j] ; pend = p + Lnz [j] ; /* look for row k in column j */ PRINT1 (("Pruned column "ID"\n", j)) ; for ( ; p < pend ; p++) { i = Li [p] ; PRINT2 ((" "ID"", i)) ; PRINT2 ((" %g\n", Lx [p])) ; ASSERT (IMPLIES (i == k, Lx [p] == 0)) ; ASSERT (i > lasti) ; lasti = i ; } PRINT1 (("\n")) ; } #endif /* ---------------------------------------------------------------------- */ /* set diagonal and clear column k of L */ /* ---------------------------------------------------------------------- */ lnz = Lnz [k] - 1 ; ASSERT (Lnz [k] > 0) ; /* ---------------------------------------------------------------------- */ /* update/downdate */ /* ---------------------------------------------------------------------- */ /* update or downdate L (k+1:n, k+1:n) with the vector * C = L (:,k) * sqrt (abs (D [k])) * Do a numeric update if D[k] > 0, numeric downdate otherwise. */ PRINT1 (("rowdel downdate lnz = "ID"\n", lnz)) ; /* store the new unit diagonal */ p = Lp [k] ; pend = p + lnz + 1 ; dk = Lx [p] ; Lx [p++] = 1 ; PRINT2 (("D [k = "ID"] = %g\n", k, dk)) ; ok = TRUE ; fl = 0 ; if (lnz > 0) { /* compute DeltaB for updown (in DeltaB) */ if (do_solve) { xk = Xx [k] - yk [0] * dk ; for ( ; p < pend ; p++) { Nx [Li [p]] += Lx [p] * xk ; } } do_update = IS_GT_ZERO (dk) ; if (!do_update) { dk = -dk ; } sqrt_dk = sqrt (dk) ; p = Lp [k] + 1 ; for (kk = 0 ; kk < lnz ; kk++, p++) { Ci [kk] = Li [p] ; Cx [kk] = Lx [p] * sqrt_dk ; Lx [p] = 0 ; /* clear column k */ } fl = lnz + 1 ; /* create a n-by-1 sparse matrix to hold the single column */ C = &Cmatrix ; C->nrow = n ; C->ncol = 1 ; C->nzmax = lnz ; C->sorted = TRUE ; C->packed = TRUE ; C->p = Cp ; C->i = Ci ; C->x = Cx ; C->nz = NULL ; C->itype = L->itype ; C->xtype = L->xtype ; C->dtype = L->dtype ; C->z = NULL ; C->stype = 0 ; Cp [0] = 0 ; Cp [1] = lnz ; /* numeric update if dk > 0, and with Lx=b change */ /* workspace: Flag (nrow), Head (nrow+1), W (nrow), Iwork (2*nrow) */ ok = CHOLMOD(updown_mark) (do_update ? (1) : (0), C, colmark, L, X, DeltaB, Common) ; /* clear workspace */ for (kk = 0 ; kk < lnz ; kk++) { Cx [kk] = 0 ; } } Common->modfl += fl ; if (do_solve) { /* kth equation becomes identity, so X(k) is now Y(k) */ Xx [k] = yk [0] ; } DEBUG (CHOLMOD(dump_factor) (L, "LDL factorization, L:", Common)) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ; return (ok) ; } #endif Matrix/src/CHOLMOD/Modify/cholmod_rowadd.c0000644000175100001440000004643012271765436020014 0ustar hornikusers/* ========================================================================== */ /* === Modify/cholmod_rowadd ================================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Modify Module. * Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager. * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Adds a row and column to an LDL' factorization, and optionally updates the * solution to Lx=b. * * workspace: Flag (nrow), Head (nrow+1), W (2*nrow), Iwork (2*nrow) * * Only real matrices are supported. A symbolic L is converted into a * numeric identity matrix before the row is added. */ #ifndef NMODIFY #include "cholmod_internal.h" #include "cholmod_modify.h" /* ========================================================================== */ /* === cholmod_rowadd ======================================================= */ /* ========================================================================== */ /* cholmod_rowadd adds a row to the LDL' factorization. It computes the kth * row and kth column of L, and then updates the submatrix L (k+1:n,k+1:n) * accordingly. The kth row and column of L should originally be equal to the * kth row and column of the identity matrix (they are treated as such, if they * are not). The kth row/column of L is computed as the factorization of the * kth row/column of the matrix to factorize, which is provided as a single * n-by-1 sparse matrix R. The sparse vector R need not be sorted. */ int CHOLMOD(rowadd) ( /* ---- input ---- */ size_t k, /* row/column index to add */ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { double bk [2] ; bk [0] = 0. ; bk [1] = 0. ; return (CHOLMOD(rowadd_mark) (k, R, bk, NULL, L, NULL, NULL, Common)) ; } /* ========================================================================== */ /* === cholmod_rowadd_solve ================================================= */ /* ========================================================================== */ /* Does the same as cholmod_rowadd, and also updates the solution to Lx=b * See cholmod_updown for a description of how Lx=b is updated. There is on * additional parameter: bk specifies the new kth entry of b. */ int CHOLMOD(rowadd_solve) ( /* ---- input ---- */ size_t k, /* row/column index to add */ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */ double bk [2], /* kth entry of the right-hand-side b */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(rowadd_mark) (k, R, bk, NULL, L, X, DeltaB, Common)) ; } /* ========================================================================== */ /* === icomp ================================================================ */ /* ========================================================================== */ /* for sorting by qsort */ static int icomp (Int *i, Int *j) { if (*i < *j) { return (-1) ; } else { return (1) ; } } /* ========================================================================== */ /* === cholmod_rowadd_mark ================================================== */ /* ========================================================================== */ /* Does the same as cholmod_rowadd_solve, except only part of L is used in * the update/downdate of the solution to Lx=b. This routine is an "expert" * routine. It is meant for use in LPDASA only. */ int CHOLMOD(rowadd_mark) ( /* ---- input ---- */ size_t kadd, /* row/column index to add */ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */ double bk [2], /* kth entry of the right hand side, b */ Int *colmark, /* Int array of size 1. See cholmod_updown.c */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { double dk, yj, l_kj, lx, l_ij, sqrt_dk, dj, xk, rnz, fl ; double *Lx, *W, *Cx, *Rx, *Xx, *Nx ; Int *Li, *Lp, *Lnz, *Flag, *Stack, *Ci, *Rj, *Rp, *Lnext, *Iwork, *Rnz ; cholmod_sparse *C, Cmatrix ; Int i, j, p, pend, top, len, kk, li, lnz, mark, k, n, parent, Cp [2], do_solve, do_update ; size_t s ; int ok = TRUE ; DEBUG (Int lastrow) ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_NULL (R, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_REAL, FALSE) ; RETURN_IF_XTYPE_INVALID (R, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; n = L->n ; k = kadd ; if (kadd >= L->n || k < 0) { ERROR (CHOLMOD_INVALID, "k invalid") ; return (FALSE) ; } if (R->ncol != 1 || R->nrow != L->n) { ERROR (CHOLMOD_INVALID, "R invalid") ; return (FALSE) ; } Rj = R->i ; Rx = R->x ; Rp = R->p ; Rnz = R->nz ; rnz = (R->packed) ? (Rp [1]) : (Rnz [0]) ; do_solve = (X != NULL) && (DeltaB != NULL) ; if (do_solve) { RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; RETURN_IF_XTYPE_INVALID (DeltaB, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; Xx = X->x ; Nx = DeltaB->x ; if (X->nrow != L->n || X->ncol != 1 || DeltaB->nrow != L->n || DeltaB->ncol != 1 || Xx == NULL || Nx == NULL) { ERROR (CHOLMOD_INVALID, "X and/or DeltaB invalid") ; return (FALSE) ; } } else { Xx = NULL ; Nx = NULL ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 2*n */ s = CHOLMOD(mult_size_t) (n, 2, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, s, s, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, s, Common)) ; /* ---------------------------------------------------------------------- */ /* convert to simplicial numeric LDL' factor, if not already */ /* ---------------------------------------------------------------------- */ if (L->xtype == CHOLMOD_PATTERN || L->is_super || L->is_ll) { /* can only update/downdate a simplicial LDL' factorization */ CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, FALSE, FALSE, L, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory, L is returned unchanged */ return (FALSE) ; } } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* inputs, not modified on output: */ Lp = L->p ; /* size n+1. input, not modified on output */ /* outputs, contents defined on input for incremental case only: */ Lnz = L->nz ; /* size n */ Li = L->i ; /* size L->nzmax. Can change in size. */ Lx = L->x ; /* size L->nzmax. Can change in size. */ Lnext = L->next ; /* size n+2 */ ASSERT (L->nz != NULL) ; PRINT1 (("rowadd:\n")) ; fl = 0 ; #if 0 #ifndef NDEBUG /* column k of L should be zero, except for the diagonal. This test is * overly cautious. */ for (p = Lp [k] + 1 ; p < Lp [k] + Lnz [k] ; p++) ASSERT (Lx [p] == 0) ; #endif #endif /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Flag = Common->Flag ; /* size n */ W = Common->Xwork ; /* size n */ Cx = W + n ; /* size n (use 2nd column of Xwork for C) */ Iwork = Common->Iwork ; Stack = Iwork ; /* size n (i/i/l), also in cholmod_updown */ Ci = Iwork + n ; /* size n (i/i/l) */ /* NOTE: cholmod_updown uses Iwork [0..n-1] (i/i/l) as Stack as well */ mark = Common->mark ; /* copy Rj/Rx into W/Ci */ for (p = 0 ; p < rnz ; p++) { i = Rj [p] ; ASSERT (i >= 0 && i < n) ; W [i] = Rx [p] ; Ci [p] = i ; } /* At this point, W [Ci [0..rnz-1]] holds the sparse vector to add */ /* The nonzero pattern of column W is held in Ci (it may be unsorted). */ /* ---------------------------------------------------------------------- */ /* symbolic factorization to get pattern of kth row of L */ /* ---------------------------------------------------------------------- */ DEBUG (for (p = 0 ; p < rnz ; p++) PRINT1 (("C ("ID",%g)\n", Ci [p], W [Ci [p]]))) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* flag the diagonal */ Flag [k] = mark ; /* find the union of all the paths */ top = n ; lnz = 0 ; /* # of nonzeros in column k of L, excluding diagonal */ for (p = 0 ; p < rnz ; p++) { i = Ci [p] ; if (i < k) { /* walk from i = entry in Ci to root (and stop if i marked)*/ PRINT2 (("\nwalk from i = "ID" towards k = "ID"\n", i, k)) ; len = 0 ; /* walk up tree, but stop if we go below the diagonal */ while (i < k && i != EMPTY && Flag [i] < mark) { PRINT2 ((" Add "ID" to path\n", i)) ; ASSERT (i >= 0 && i < k) ; Stack [len++] = i ; /* place i on the stack */ Flag [i] = mark ; /* mark i as visited */ /* parent is the first entry in the column after the diagonal */ ASSERT (Lnz [i] > 0) ; parent = (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY ; PRINT2 ((" parent: "ID"\n", parent)) ; i = parent ; /* go up the tree */ } ASSERT (len <= top) ; /* move the path down to the bottom of the stack */ /* this shifts Stack [0..len-1] down to [ ... oldtop-1] */ while (len > 0) { Stack [--top] = Stack [--len] ; } } else if (i > k) { /* prune the diagonal and upper triangular entries from Ci */ Ci [lnz++] = i ; Flag [i] = mark ; } } #ifndef NDEBUG PRINT1 (("length of S after prune: "ID"\n", lnz)) ; for (p = 0 ; p < lnz ; p++) { PRINT1 (("After prune Ci ["ID"] = "ID"\n", p, Ci [p])) ; ASSERT (Ci [p] > k) ; } #endif /* ---------------------------------------------------------------------- */ /* ensure each column of L has enough space to grow */ /* ---------------------------------------------------------------------- */ for (kk = top ; kk < n ; kk++) { /* could skip this if we knew column j already included row k */ j = Stack [kk] ; if (Lp [j] + Lnz [j] >= Lp [Lnext [j]]) { PRINT1 (("Col "ID" realloc, old Lnz "ID"\n", j, Lnz [j])) ; if (!CHOLMOD(reallocate_column) (j, Lnz [j] + 1, L, Common)) { /* out of memory, L is now simplicial symbolic */ /* CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; for (i = 0 ; i < n ; i++) { W [i] = 0 ; } return (FALSE) ; } /* L->i and L->x may have moved */ Li = L->i ; Lx = L->x ; } ASSERT (Lp [j] + Lnz [j] < Lp [Lnext [j]] || (Lp [Lnext [j]] - Lp [j] == n-j)) ; } /* ---------------------------------------------------------------------- */ /* compute kth row of L and store in column form */ /* ---------------------------------------------------------------------- */ /* solve L (1:k-1, 1:k-1) * y (1:k-1) = b (1:k-1) */ /* where b (1:k) is in W and Ci */ /* L (k, 1:k-1) = y (1:k-1) ./ D (1:k-1) */ /* D (k) = B (k,k) - L (k, 1:k-1) * y (1:k-1) */ PRINT2 (("\nForward solve: "ID" to "ID"\n", top, n)) ; ASSERT (Lnz [k] >= 1 && Li [Lp [k]] == k) ; DEBUG (for (i = top ; i < n ; i++) PRINT2 ((" Path: "ID"\n", Stack [i]))) ; dk = W [k] ; W [k] = 0.0 ; /* if do_solve: compute x (k) = b (k) - L (k, 1:k-1) * x (1:k-1) */ xk = bk [0] ; PRINT2 (("B [k] = %g\n", xk)) ; for (kk = top ; kk < n ; kk++) { j = Stack [kk] ; i = j ; PRINT2 (("Forward solve col j = "ID":\n", j)) ; ASSERT (j >= 0 && j < k) ; /* forward solve using L (j+1:k-1,j) */ yj = W [j] ; W [j] = 0.0 ; p = Lp [j] ; pend = p + Lnz [j] ; ASSERT (Lnz [j] > 0) ; dj = Lx [p++] ; for ( ; p < pend ; p++) { i = Li [p] ; PRINT2 ((" row "ID"\n", i)) ; ASSERT (i > j) ; ASSERT (i < n) ; /* stop at row k */ if (i >= k) { break ; } W [i] -= Lx [p] * yj ; } /* each iteration of the above for loop did 2 flops, and 3 flops * are done below. so: fl += 2 * (Lp [j] - p - 1) + 3 becomes: */ fl += 2 * (Lp [j] - p) + 1 ; /* scale L (k,1:k-1) and compute dot product for D (k,k) */ l_kj = yj / dj ; dk -= l_kj * yj ; /* compute dot product for X(k) */ if (do_solve) { xk -= l_kj * Xx [j] ; } /* store l_kj in the jth column of L */ /* and shift the rest of the column down */ li = k ; lx = l_kj ; if (i == k) { /* no need to modify the nonzero pattern of L, since it already * contains row index k. */ ASSERT (Li [p] == k) ; Lx [p] = l_kj ; for (p++ ; p < pend ; p++) { i = Li [p] ; l_ij = Lx [p] ; ASSERT (i > k && i < n) ; PRINT2 ((" apply to row "ID" of column k of L\n", i)) ; /* add to the pattern of the kth column of L */ if (Flag [i] < mark) { PRINT2 ((" add Ci["ID"] = "ID"\n", lnz, i)) ; ASSERT (i > k) ; Ci [lnz++] = i ; Flag [i] = mark ; } /* apply the update to the kth column of L */ /* yj is equal to l_kj * d_j */ W [i] -= l_ij * yj ; } } else { PRINT2 (("Shift col j = "ID", apply saxpy to col k of L\n", j)) ; for ( ; p < pend ; p++) { /* swap (Li [p],Lx [p]) with (li,lx) */ i = Li [p] ; l_ij = Lx [p] ; Li [p] = li ; Lx [p] = lx ; li = i ; lx = l_ij ; ASSERT (i > k && i < n) ; PRINT2 ((" apply to row "ID" of column k of L\n", i)) ; /* add to the pattern of the kth column of L */ if (Flag [i] < mark) { PRINT2 ((" add Ci["ID"] = "ID"\n", lnz, i)) ; ASSERT (i > k) ; Ci [lnz++] = i ; Flag [i] = mark ; } /* apply the update to the kth column of L */ /* yj is equal to l_kj * d_j */ W [i] -= l_ij * yj ; } /* store the last value in the jth column of L */ Li [p] = li ; Lx [p] = lx ; Lnz [j]++ ; } } /* ---------------------------------------------------------------------- */ /* merge C with the pattern of the existing column of L */ /* ---------------------------------------------------------------------- */ /* This column should be zero, but it may contain explicit zero entries. * These entries should be kept, not dropped. */ p = Lp [k] ; pend = p + Lnz [k] ; for (p++ ; p < pend ; p++) { i = Li [p] ; /* add to the pattern of the kth column of L */ if (Flag [i] < mark) { PRINT2 ((" add Ci["ID"] = "ID" from existing col k\n", lnz, i)) ; ASSERT (i > k) ; Ci [lnz++] = i ; Flag [i] = mark ; } } /* ---------------------------------------------------------------------- */ if (do_solve) { Xx [k] = xk ; PRINT2 (("Xx [k] = %g\n", Xx [k])) ; } /* ---------------------------------------------------------------------- */ /* ensure abs (dk) >= dbound, if dbound is given */ /* ---------------------------------------------------------------------- */ dk = (IS_GT_ZERO (Common->dbound)) ? (CHOLMOD(dbound) (dk, Common)) : dk ; PRINT2 (("D [k = "ID"] = %g\n", k, dk)) ; /* ---------------------------------------------------------------------- */ /* store the kth column of L */ /* ---------------------------------------------------------------------- */ /* ensure the new column of L has enough space */ if (Lp [k] + lnz + 1 > Lp [Lnext [k]]) { PRINT1 (("New Col "ID" realloc, old Lnz "ID"\n", k, Lnz [k])) ; if (!CHOLMOD(reallocate_column) (k, lnz + 1, L, Common)) { /* out of memory, L is now simplicial symbolic */ CHOLMOD(clear_flag) (Common) ; for (i = 0 ; i < n ; i++) { W [i] = 0 ; } return (FALSE) ; } /* L->i and L->x may have moved */ Li = L->i ; Lx = L->x ; } ASSERT (Lp [k] + lnz + 1 <= Lp [Lnext [k]]) ; #ifndef NDEBUG PRINT2 (("\nPrior to sort: lnz "ID" (excluding diagonal)\n", lnz)) ; for (kk = 0 ; kk < lnz ; kk++) { i = Ci [kk] ; PRINT2 (("L ["ID"] kept: "ID" %e\n", kk, i, W [i] / dk)) ; } #endif /* sort Ci */ qsort (Ci, lnz, sizeof (Int), (int (*) (const void *, const void *)) icomp); /* store the kth column of L */ DEBUG (lastrow = k) ; p = Lp [k] ; Lx [p++] = dk ; Lnz [k] = lnz + 1 ; fl += lnz ; for (kk = 0 ; kk < lnz ; kk++, p++) { i = Ci [kk] ; PRINT2 (("L ["ID"] after sort: "ID", %e\n", kk, i, W [i] / dk)) ; ASSERT (i > lastrow) ; Li [p] = i ; Lx [p] = W [i] / dk ; W [i] = 0.0 ; DEBUG (lastrow = i) ; } /* compute DeltaB for updown (in DeltaB) */ if (do_solve) { p = Lp [k] ; pend = p + Lnz [k] ; for (p++ ; p < pend ; p++) { ASSERT (Li [p] > k) ; Nx [Li [p]] -= Lx [p] * xk ; } } /* clear the flag for the update */ mark = CHOLMOD(clear_flag) (Common) ; /* workspaces are now cleared */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ; /* ---------------------------------------------------------------------- */ /* update/downdate */ /* ---------------------------------------------------------------------- */ /* update or downdate L (k+1:n, k+1:n) with the vector * C = L (:,k) * sqrt (abs (D [k])). * Do a numeric update if D[k] < 0, numeric downdate otherwise. */ ok = TRUE ; Common->modfl = 0 ; PRINT1 (("rowadd update lnz = "ID"\n", lnz)) ; if (lnz > 0) { do_update = IS_LT_ZERO (dk) ; if (do_update) { dk = -dk ; } sqrt_dk = sqrt (dk) ; p = Lp [k] + 1 ; for (kk = 0 ; kk < lnz ; kk++, p++) { Cx [kk] = Lx [p] * sqrt_dk ; } fl += lnz + 1 ; /* create a n-by-1 sparse matrix to hold the single column */ C = &Cmatrix ; C->nrow = n ; C->ncol = 1 ; C->nzmax = lnz ; C->sorted = TRUE ; C->packed = TRUE ; C->p = Cp ; C->i = Ci ; C->x = Cx ; C->nz = NULL ; C->itype = L->itype ; C->xtype = L->xtype ; C->dtype = L->dtype ; C->z = NULL ; C->stype = 0 ; Cp [0] = 0 ; Cp [1] = lnz ; /* numeric downdate if dk > 0, and optional Lx=b change */ /* workspace: Flag (nrow), Head (nrow+1), W (nrow), Iwork (2*nrow) */ ok = CHOLMOD(updown_mark) (do_update ? (1) : (0), C, colmark, L, X, DeltaB, Common) ; /* clear workspace */ for (kk = 0 ; kk < lnz ; kk++) { Cx [kk] = 0 ; } } Common->modfl += fl ; DEBUG (CHOLMOD(dump_factor) (L, "LDL factorization, L:", Common)) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ; return (ok) ; } #endif Matrix/src/CHOLMOD/Cholesky/0000755000175100001440000000000012271765426015205 5ustar hornikusersMatrix/src/CHOLMOD/Cholesky/cholmod_colamd.c0000644000175100001440000001560712271765436020327 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/cholmod_colamd ============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* CHOLMOD interface to the COLAMD ordering routine (version 2.4 or later). * Finds a permutation p such that the Cholesky factorization of PAA'P' is * sparser than AA' using colamd. If the postorder input parameter is TRUE, * the column etree is found and postordered, and the colamd ordering is then * combined with its postordering. A must be unsymmetric. * * There can be no duplicate entries in f. * f can be length 0 to n if A is m-by-n. * * workspace: Iwork (4*nrow+ncol), Head (nrow+1), Flag (nrow) * Allocates a copy of its input matrix, which * is then used as CCOLAMD's workspace. * * Supports any xtype (pattern, real, complex, or zomplex) */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "colamd.h" #include "cholmod_cholesky.h" #if (!defined (COLAMD_VERSION) || (COLAMD_VERSION < COLAMD_VERSION_CODE (2,5))) #error "COLAMD v2.5 or later is required" #endif /* ========================================================================== */ /* === cholmod_colamd ======================================================= */ /* ========================================================================== */ int CHOLMOD(colamd) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int postorder, /* if TRUE, follow with a coletree postorder */ /* ---- output --- */ Int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) { double knobs [COLAMD_KNOBS] ; cholmod_sparse *C ; Int *NewPerm, *Parent, *Post, *Work2n ; Int k, nrow, ncol ; size_t s, alen ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (Perm, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (A->stype != 0) { ERROR (CHOLMOD_INVALID, "matrix must be unsymmetric") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; ncol = A->ncol ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* Note: this is less than the space used in cholmod_analyze, so if * cholmod_colamd is being called by that routine, no space will be * allocated. */ /* s = 4*nrow + ncol */ s = CHOLMOD(mult_size_t) (nrow, 4, &ok) ; s = CHOLMOD(add_size_t) (s, ncol, &ok) ; #ifdef LONG alen = colamd_l_recommended (A->nzmax, ncol, nrow) ; colamd_l_set_defaults (knobs) ; #else alen = colamd_recommended (A->nzmax, ncol, nrow) ; colamd_set_defaults (knobs) ; #endif if (!ok || alen == 0) { ERROR (CHOLMOD_TOO_LARGE, "matrix invalid or too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (0, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* allocate COLAMD workspace */ /* ---------------------------------------------------------------------- */ /* colamd_printf is only available in colamd v2.4 or later */ colamd_printf = Common->print_function ; C = CHOLMOD(allocate_sparse) (ncol, nrow, alen, TRUE, TRUE, 0, CHOLMOD_PATTERN, Common) ; /* ---------------------------------------------------------------------- */ /* copy (and transpose) the input matrix A into the colamd workspace */ /* ---------------------------------------------------------------------- */ /* C = A (:,f)', which also packs A if needed. */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset) */ ok = CHOLMOD(transpose_unsym) (A, 0, NULL, fset, fsize, C, Common) ; /* ---------------------------------------------------------------------- */ /* order the matrix (destroys the contents of C->i and C->p) */ /* ---------------------------------------------------------------------- */ /* get parameters */ if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS) { /* this is the CHOLMOD default, not the COLAMD default */ knobs [COLAMD_DENSE_ROW] = -1 ; } else { /* get the knobs from the Common parameters */ knobs [COLAMD_DENSE_COL] = Common->method[Common->current].prune_dense ; knobs [COLAMD_DENSE_ROW] = Common->method[Common->current].prune_dense2; knobs [COLAMD_AGGRESSIVE] = Common->method[Common->current].aggressive ; } if (ok) { Int *Cp ; Int stats [COLAMD_STATS] ; Cp = C->p ; #ifdef LONG colamd_l (ncol, nrow, alen, C->i, Cp, knobs, stats) ; #else colamd (ncol, nrow, alen, C->i, Cp, knobs, stats) ; #endif ok = stats [COLAMD_STATUS] ; ok = (ok == COLAMD_OK || ok == COLAMD_OK_BUT_JUMBLED) ; /* permutation returned in C->p, if the ordering succeeded */ for (k = 0 ; k < nrow ; k++) { Perm [k] = Cp [k] ; } } CHOLMOD(free_sparse) (&C, Common) ; /* ---------------------------------------------------------------------- */ /* column etree postordering */ /* ---------------------------------------------------------------------- */ if (postorder) { /* use the last 2*n space in Iwork for Parent and Post */ Work2n = Common->Iwork ; Work2n += 2*((size_t) nrow) + ncol ; Parent = Work2n ; /* size nrow (i/i/l) */ Post = Work2n + nrow ; /* size nrow (i/i/l) */ /* workspace: Iwork (2*nrow+ncol), Flag (nrow), Head (nrow+1) */ ok = ok && CHOLMOD(analyze_ordering) (A, CHOLMOD_COLAMD, Perm, fset, fsize, Parent, Post, NULL, NULL, NULL, Common) ; /* combine the colamd permutation with its postordering */ if (ok) { NewPerm = Common->Iwork ; /* size nrow (i/i/l) */ for (k = 0 ; k < nrow ; k++) { NewPerm [k] = Perm [Post [k]] ; } for (k = 0 ; k < nrow ; k++) { Perm [k] = NewPerm [k] ; } } } return (ok) ; } #endif Matrix/src/CHOLMOD/Cholesky/License.txt0000644000175100001440000000204711770402705017322 0ustar hornikusersCHOLMOD/Cholesky module, Copyright (C) 2005-2006, Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.suitesparse.com Note that this license is for the CHOLMOD/Cholesky module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Matrix/src/CHOLMOD/Cholesky/t_cholmod_lsolve.c0000644000175100001440000006371212271765436020717 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/t_cholmod_lsolve ============================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2013, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Template routine to solve Lx=b with unit or non-unit diagonal, or * solve LDx=b. * * The numeric xtype of L and Y must match. Y contains b on input and x on * output, stored in row-form. Y is nrow-by-n, where nrow must equal 1 for the * complex or zomplex cases, and nrow <= 4 for the real case. * * This file is not compiled separately. It is included in t_cholmod_solve.c * instead. It contains no user-callable routines. * * workspace: none * * Supports real, complex, and zomplex factors. */ /* undefine all prior definitions */ #undef FORM_NAME #undef LSOLVE /* -------------------------------------------------------------------------- */ /* define the method */ /* -------------------------------------------------------------------------- */ #ifdef LL /* LL': solve Lx=b with non-unit diagonal */ #define FORM_NAME(prefix,rank) prefix ## ll_lsolve_ ## rank #elif defined (LD) /* LDL': solve LDx=b */ #define FORM_NAME(prefix,rank) prefix ## ldl_ldsolve_ ## rank #else /* LDL': solve Lx=b with unit diagonal */ #define FORM_NAME(prefix,rank) prefix ## ldl_lsolve_ ## rank #endif /* LSOLVE(k) defines the name of a routine for an n-by-k right-hand-side. */ #define LSOLVE(prefix,rank) FORM_NAME(prefix,rank) #ifdef REAL /* ========================================================================== */ /* === LSOLVE (1) =========================================================== */ /* ========================================================================== */ /* Solve Lx=b, where b has 1 column */ static void LSOLVE (PREFIX,1) ( cholmod_factor *L, double X [ ] /* n-by-1 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = 0 ; j < n ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j+1, and j+2) */ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y = X [j] ; #ifdef LL y /= Lx [p] ; X [j] = y ; #elif defined (LD) X [j] = y / Lx [p] ; #endif for (p++ ; p < pend ; p++) { X [Li [p]] -= Lx [p] * y ; } j++ ; /* advance to next column of L */ } else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2] ; Int q = Lp [j+1] ; #ifdef LL y [0] = X [j] / Lx [p] ; y [1] = (X [j+1] - Lx [p+1] * y [0]) / Lx [q] ; X [j ] = y [0] ; X [j+1] = y [1] ; #elif defined (LD) y [0] = X [j] ; y [1] = X [j+1] - Lx [p+1] * y [0] ; X [j ] = y [0] / Lx [p] ; X [j+1] = y [1] / Lx [q] ; #else y [0] = X [j] ; y [1] = X [j+1] - Lx [p+1] * y [0] ; X [j+1] = y [1] ; #endif for (p += 2, q++ ; p < pend ; p++, q++) { X [Li [p]] -= Lx [p] * y [0] + Lx [q] * y [1] ; } j += 2 ; /* advance to next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3] ; Int q = Lp [j+1] ; Int r = Lp [j+2] ; #ifdef LL y [0] = X [j] / Lx [p] ; y [1] = (X [j+1] - Lx [p+1] * y [0]) / Lx [q] ; y [2] = (X [j+2] - Lx [p+2] * y [0] - Lx [q+1] * y [1]) / Lx [r] ; X [j ] = y [0] ; X [j+1] = y [1] ; X [j+2] = y [2] ; #elif defined (LD) y [0] = X [j] ; y [1] = X [j+1] - Lx [p+1] * y [0] ; y [2] = X [j+2] - Lx [p+2] * y [0] - Lx [q+1] * y [1] ; X [j ] = y [0] / Lx [p] ; X [j+1] = y [1] / Lx [q] ; X [j+2] = y [2] / Lx [r] ; #else y [0] = X [j] ; y [1] = X [j+1] - Lx [p+1] * y [0] ; y [2] = X [j+2] - Lx [p+2] * y [0] - Lx [q+1] * y [1] ; X [j+1] = y [1] ; X [j+2] = y [2] ; #endif for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++) { X [Li [p]] -= Lx [p] * y [0] + Lx [q] * y [1] + Lx [r] * y [2] ; } j += 3 ; /* advance to next column of L */ } } } /* ========================================================================== */ /* === LSOLVE (2) =========================================================== */ /* ========================================================================== */ /* Solve Lx=b, where b has 2 columns */ static void LSOLVE (PREFIX,2) ( cholmod_factor *L, double X [ ][2] /* n-by-2 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = 0 ; j < n ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j+1, and j+2) */ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y [2] ; y [0] = X [j][0] ; y [1] = X [j][1] ; #ifdef LL y [0] /= Lx [p] ; y [1] /= Lx [p] ; X [j][0] = y [0] ; X [j][1] = y [1] ; #elif defined (LD) X [j][0] = y [0] / Lx [p] ; X [j][1] = y [1] / Lx [p] ; #endif for (p++ ; p < pend ; p++) { Int i = Li [p] ; X [i][0] -= Lx [p] * y [0] ; X [i][1] -= Lx [p] * y [1] ; } j++ ; /* advance to next column of L */ } else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2][2] ; Int q = Lp [j+1] ; y [0][0] = X [j][0] ; y [0][1] = X [j][1] ; #ifdef LL y [0][0] /= Lx [p] ; y [0][1] /= Lx [p] ; y [1][0] = (X [j+1][0] - Lx [p+1] * y [0][0]) / Lx [q] ; y [1][1] = (X [j+1][1] - Lx [p+1] * y [0][1]) / Lx [q] ; X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; #elif defined (LD) y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; X [j ][0] = y [0][0] / Lx [p] ; X [j ][1] = y [0][1] / Lx [p] ; X [j+1][0] = y [1][0] / Lx [q] ; X [j+1][1] = y [1][1] / Lx [q] ; #else y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; #endif for (p += 2, q++ ; p < pend ; p++, q++) { Int i = Li [p] ; X [i][0] -= Lx [p] * y [0][0] + Lx [q] * y [1][0] ; X [i][1] -= Lx [p] * y [0][1] + Lx [q] * y [1][1] ; } j += 2 ; /* advance to next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3][2] ; Int q = Lp [j+1] ; Int r = Lp [j+2] ; y [0][0] = X [j][0] ; y [0][1] = X [j][1] ; #ifdef LL y [0][0] /= Lx [p] ; y [0][1] /= Lx [p] ; y [1][0] = (X [j+1][0] - Lx[p+1] * y[0][0]) / Lx [q] ; y [1][1] = (X [j+1][1] - Lx[p+1] * y[0][1]) / Lx [q] ; y [2][0] = (X [j+2][0] - Lx[p+2] * y[0][0] - Lx[q+1]*y[1][0])/Lx[r]; y [2][1] = (X [j+2][1] - Lx[p+2] * y[0][1] - Lx[q+1]*y[1][1])/Lx[r]; X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+2][0] = y [2][0] ; X [j+2][1] = y [2][1] ; #elif defined (LD) y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ; y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ; X [j ][0] = y [0][0] / Lx [p] ; X [j ][1] = y [0][1] / Lx [p] ; X [j+1][0] = y [1][0] / Lx [q] ; X [j+1][1] = y [1][1] / Lx [q] ; X [j+2][0] = y [2][0] / Lx [r] ; X [j+2][1] = y [2][1] / Lx [r] ; #else y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ; y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+2][0] = y [2][0] ; X [j+2][1] = y [2][1] ; #endif for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++) { Int i = Li [p] ; X[i][0] -= Lx[p] * y[0][0] + Lx[q] * y[1][0] + Lx[r] * y[2][0] ; X[i][1] -= Lx[p] * y[0][1] + Lx[q] * y[1][1] + Lx[r] * y[2][1] ; } j += 3 ; /* advance to next column of L */ } } } /* ========================================================================== */ /* === LSOLVE (3) =========================================================== */ /* ========================================================================== */ /* Solve Lx=b, where b has 3 columns */ static void LSOLVE (PREFIX,3) ( cholmod_factor *L, double X [ ][3] /* n-by-3 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = 0 ; j < n ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j+1, and j+2) */ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y [3] ; y [0] = X [j][0] ; y [1] = X [j][1] ; y [2] = X [j][2] ; #ifdef LL y [0] /= Lx [p] ; y [1] /= Lx [p] ; y [2] /= Lx [p] ; X [j][0] = y [0] ; X [j][1] = y [1] ; X [j][2] = y [2] ; #elif defined (LD) X [j][0] = y [0] / Lx [p] ; X [j][1] = y [1] / Lx [p] ; X [j][2] = y [2] / Lx [p] ; #endif for (p++ ; p < pend ; p++) { Int i = Li [p] ; double lx = Lx [p] ; X [i][0] -= lx * y [0] ; X [i][1] -= lx * y [1] ; X [i][2] -= lx * y [2] ; } j++ ; /* advance to next column of L */ } else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2][3] ; Int q = Lp [j+1] ; y [0][0] = X [j][0] ; y [0][1] = X [j][1] ; y [0][2] = X [j][2] ; #ifdef LL y [0][0] /= Lx [p] ; y [0][1] /= Lx [p] ; y [0][2] /= Lx [p] ; y [1][0] = (X [j+1][0] - Lx [p+1] * y [0][0]) / Lx [q] ; y [1][1] = (X [j+1][1] - Lx [p+1] * y [0][1]) / Lx [q] ; y [1][2] = (X [j+1][2] - Lx [p+1] * y [0][2]) / Lx [q] ; X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; #elif defined (LD) y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; X [j ][0] = y [0][0] / Lx [p] ; X [j ][1] = y [0][1] / Lx [p] ; X [j ][2] = y [0][2] / Lx [p] ; X [j+1][0] = y [1][0] / Lx [q] ; X [j+1][1] = y [1][1] / Lx [q] ; X [j+1][2] = y [1][2] / Lx [q] ; #else y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; #endif for (p += 2, q++ ; p < pend ; p++, q++) { Int i = Li [p] ; double lx [2] ; lx [0] = Lx [p] ; lx [1] = Lx [q] ; X [i][0] -= lx [0] * y [0][0] + lx [1] * y [1][0] ; X [i][1] -= lx [0] * y [0][1] + lx [1] * y [1][1] ; X [i][2] -= lx [0] * y [0][2] + lx [1] * y [1][2] ; } j += 2 ; /* advance to next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3][3] ; Int q = Lp [j+1] ; Int r = Lp [j+2] ; y [0][0] = X [j][0] ; y [0][1] = X [j][1] ; y [0][2] = X [j][2] ; #ifdef LL y [0][0] /= Lx [p] ; y [0][1] /= Lx [p] ; y [0][2] /= Lx [p] ; y [1][0] = (X [j+1][0] - Lx[p+1] * y[0][0]) / Lx [q] ; y [1][1] = (X [j+1][1] - Lx[p+1] * y[0][1]) / Lx [q] ; y [1][2] = (X [j+1][2] - Lx[p+1] * y[0][2]) / Lx [q] ; y [2][0] = (X [j+2][0] - Lx[p+2] * y[0][0] - Lx[q+1]*y[1][0])/Lx[r]; y [2][1] = (X [j+2][1] - Lx[p+2] * y[0][1] - Lx[q+1]*y[1][1])/Lx[r]; y [2][2] = (X [j+2][2] - Lx[p+2] * y[0][2] - Lx[q+1]*y[1][2])/Lx[r]; X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; X [j+2][0] = y [2][0] ; X [j+2][1] = y [2][1] ; X [j+2][2] = y [2][2] ; #elif defined (LD) y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ; y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ; y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ; X [j ][0] = y [0][0] / Lx [p] ; X [j ][1] = y [0][1] / Lx [p] ; X [j ][2] = y [0][2] / Lx [p] ; X [j+1][0] = y [1][0] / Lx [q] ; X [j+1][1] = y [1][1] / Lx [q] ; X [j+1][2] = y [1][2] / Lx [q] ; X [j+2][0] = y [2][0] / Lx [r] ; X [j+2][1] = y [2][1] / Lx [r] ; X [j+2][2] = y [2][2] / Lx [r] ; #else y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ; y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ; y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; X [j+2][0] = y [2][0] ; X [j+2][1] = y [2][1] ; X [j+2][2] = y [2][2] ; #endif for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++) { Int i = Li [p] ; double lx [3] ; lx [0] = Lx [p] ; lx [1] = Lx [q] ; lx [2] = Lx [r] ; X [i][0] -= lx[0] * y[0][0] + lx[1] * y[1][0] + lx[2] * y[2][0]; X [i][1] -= lx[0] * y[0][1] + lx[1] * y[1][1] + lx[2] * y[2][1]; X [i][2] -= lx[0] * y[0][2] + lx[1] * y[1][2] + lx[2] * y[2][2]; } j += 3 ; /* advance to next column of L */ } } } /* ========================================================================== */ /* === LSOLVE (4) =========================================================== */ /* ========================================================================== */ /* Solve Lx=b, where b has 4 columns */ static void LSOLVE (PREFIX,4) ( cholmod_factor *L, double X [ ][4] /* n-by-4 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = 0 ; j < n ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j+1, and j+2) */ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y [4] ; y [0] = X [j][0] ; y [1] = X [j][1] ; y [2] = X [j][2] ; y [3] = X [j][3] ; #ifdef LL y [0] /= Lx [p] ; y [1] /= Lx [p] ; y [2] /= Lx [p] ; y [3] /= Lx [p] ; X [j][0] = y [0] ; X [j][1] = y [1] ; X [j][2] = y [2] ; X [j][3] = y [3] ; #elif defined (LD) X [j][0] = y [0] / Lx [p] ; X [j][1] = y [1] / Lx [p] ; X [j][2] = y [2] / Lx [p] ; X [j][3] = y [3] / Lx [p] ; #endif for (p++ ; p < pend ; p++) { Int i = Li [p] ; double lx = Lx [p] ; X [i][0] -= lx * y [0] ; X [i][1] -= lx * y [1] ; X [i][2] -= lx * y [2] ; X [i][3] -= lx * y [3] ; } j++ ; /* advance to next column of L */ } else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2][4] ; Int q = Lp [j+1] ; y [0][0] = X [j][0] ; y [0][1] = X [j][1] ; y [0][2] = X [j][2] ; y [0][3] = X [j][3] ; #ifdef LL y [0][0] /= Lx [p] ; y [0][1] /= Lx [p] ; y [0][2] /= Lx [p] ; y [0][3] /= Lx [p] ; y [1][0] = (X [j+1][0] - Lx [p+1] * y [0][0]) / Lx [q] ; y [1][1] = (X [j+1][1] - Lx [p+1] * y [0][1]) / Lx [q] ; y [1][2] = (X [j+1][2] - Lx [p+1] * y [0][2]) / Lx [q] ; y [1][3] = (X [j+1][3] - Lx [p+1] * y [0][3]) / Lx [q] ; X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j ][3] = y [0][3] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; X [j+1][3] = y [1][3] ; #elif defined (LD) y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ; X [j ][0] = y [0][0] / Lx [p] ; X [j ][1] = y [0][1] / Lx [p] ; X [j ][2] = y [0][2] / Lx [p] ; X [j ][3] = y [0][3] / Lx [p] ; X [j+1][0] = y [1][0] / Lx [q] ; X [j+1][1] = y [1][1] / Lx [q] ; X [j+1][2] = y [1][2] / Lx [q] ; X [j+1][3] = y [1][3] / Lx [q] ; #else y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; X [j+1][3] = y [1][3] ; #endif for (p += 2, q++ ; p < pend ; p++, q++) { Int i = Li [p] ; double lx [2] ; lx [0] = Lx [p] ; lx [1] = Lx [q] ; X [i][0] -= lx [0] * y [0][0] + lx [1] * y [1][0] ; X [i][1] -= lx [0] * y [0][1] + lx [1] * y [1][1] ; X [i][2] -= lx [0] * y [0][2] + lx [1] * y [1][2] ; X [i][3] -= lx [0] * y [0][3] + lx [1] * y [1][3] ; } j += 2 ; /* advance to next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3][4] ; Int q = Lp [j+1] ; Int r = Lp [j+2] ; y [0][0] = X [j][0] ; y [0][1] = X [j][1] ; y [0][2] = X [j][2] ; y [0][3] = X [j][3] ; #ifdef LL y [0][0] /= Lx [p] ; y [0][1] /= Lx [p] ; y [0][2] /= Lx [p] ; y [0][3] /= Lx [p] ; y [1][0] = (X [j+1][0] - Lx[p+1] * y[0][0]) / Lx [q] ; y [1][1] = (X [j+1][1] - Lx[p+1] * y[0][1]) / Lx [q] ; y [1][2] = (X [j+1][2] - Lx[p+1] * y[0][2]) / Lx [q] ; y [1][3] = (X [j+1][3] - Lx[p+1] * y[0][3]) / Lx [q] ; y [2][0] = (X [j+2][0] - Lx[p+2] * y[0][0] - Lx[q+1]*y[1][0])/Lx[r]; y [2][1] = (X [j+2][1] - Lx[p+2] * y[0][1] - Lx[q+1]*y[1][1])/Lx[r]; y [2][2] = (X [j+2][2] - Lx[p+2] * y[0][2] - Lx[q+1]*y[1][2])/Lx[r]; y [2][3] = (X [j+2][3] - Lx[p+2] * y[0][3] - Lx[q+1]*y[1][3])/Lx[r]; X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j ][3] = y [0][3] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; X [j+1][3] = y [1][3] ; X [j+2][0] = y [2][0] ; X [j+2][1] = y [2][1] ; X [j+2][2] = y [2][2] ; X [j+2][3] = y [2][3] ; #elif defined (LD) y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ; y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ; y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ; y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ; y [2][3] = X [j+2][3] - Lx [p+2] * y [0][3] - Lx [q+1] * y [1][3] ; X [j ][0] = y [0][0] / Lx [p] ; X [j ][1] = y [0][1] / Lx [p] ; X [j ][2] = y [0][2] / Lx [p] ; X [j ][3] = y [0][3] / Lx [p] ; X [j+1][0] = y [1][0] / Lx [q] ; X [j+1][1] = y [1][1] / Lx [q] ; X [j+1][2] = y [1][2] / Lx [q] ; X [j+1][3] = y [1][3] / Lx [q] ; X [j+2][0] = y [2][0] / Lx [r] ; X [j+2][1] = y [2][1] / Lx [r] ; X [j+2][2] = y [2][2] / Lx [r] ; X [j+2][3] = y [2][3] / Lx [r] ; #else y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ; y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ; y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ; y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ; y [2][3] = X [j+2][3] - Lx [p+2] * y [0][3] - Lx [q+1] * y [1][3] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; X [j+1][3] = y [1][3] ; X [j+2][0] = y [2][0] ; X [j+2][1] = y [2][1] ; X [j+2][2] = y [2][2] ; X [j+2][3] = y [2][3] ; #endif for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++) { Int i = Li [p] ; double lx [3] ; lx [0] = Lx [p] ; lx [1] = Lx [q] ; lx [2] = Lx [r] ; X [i][0] -= lx[0] * y[0][0] + lx[1] * y[1][0] + lx[2] * y[2][0]; X [i][1] -= lx[0] * y[0][1] + lx[1] * y[1][1] + lx[2] * y[2][1]; X [i][2] -= lx[0] * y[0][2] + lx[1] * y[1][2] + lx[2] * y[2][2]; X [i][3] -= lx[0] * y[0][3] + lx[1] * y[1][3] + lx[2] * y[2][3]; } j += 3 ; /* advance to next column of L */ } } } #endif /* ========================================================================== */ /* === LSOLVE (k) =========================================================== */ /* ========================================================================== */ static void LSOLVE (PREFIX,k) ( cholmod_factor *L, cholmod_dense *Y, /* nr-by-n where nr is 1 to 4 */ Int *Yseti, Int ysetlen ) { double yx [2] ; #ifdef ZOMPLEX double yz [1] ; double *Lz = L->z ; double *Xz = Y->z ; #endif double *Lx = L->x ; double *Xx = Y->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int n = L->n, jj, jjiters ; ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */ ASSERT (L->n == Y->ncol) ; /* dimensions must match */ ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */ ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */ ASSERT (!(L->is_super)) ; /* L is simplicial LL' or LDL' */ #ifdef REAL if (Yseti == NULL) { /* ------------------------------------------------------------------ */ /* real case, no Yseti, with 1 to 4 RHS's and dynamic supernodes */ /* ------------------------------------------------------------------ */ ASSERT (Y->nrow <= 4) ; switch (Y->nrow) { case 1: LSOLVE (PREFIX,1) (L, Y->x) ; break ; case 2: LSOLVE (PREFIX,2) (L, Y->x) ; break ; case 3: LSOLVE (PREFIX,3) (L, Y->x) ; break ; case 4: LSOLVE (PREFIX,4) (L, Y->x) ; break ; } } else #endif { /* ------------------------------------------------------------------ */ /* solve a complex linear system or solve with Yseti */ /* ------------------------------------------------------------------ */ ASSERT (Y->nrow == 1) ; jjiters = Yseti ? ysetlen : n ; for (jj = 0 ; jj < jjiters ; jj++) { Int j = Yseti ? Yseti [jj] : jj ; /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* y = X [j] ; */ ASSIGN (yx,yz,0, Xx,Xz,j) ; #ifdef LL /* y /= Lx [p] ; */ /* X [j] = y ; */ DIV_REAL (yx,yz,0, yx,yz,0, Lx,p) ; ASSIGN (Xx,Xz,j, yx,yz,0) ; #elif defined (LD) /* X [j] = y / Lx [p] ; */ DIV_REAL (Xx,Xz,j, yx,yz,0, Lx,p) ; #endif for (p++ ; p < pend ; p++) { /* X [Li [p]] -= Lx [p] * y ; */ Int i = Li [p] ; MULTSUB (Xx,Xz,i, Lx,Lz,p, yx,yz,0) ; } } } } /* prepare for the next inclusion of this file in cholmod_solve.c */ #undef LL #undef LD Matrix/src/CHOLMOD/Cholesky/debug_c0000644000175100001440000000442010312305403016473 0ustar hornikusers#ifndef NDEBUG /* cholmod_print_parent (Lparent, n, "Lparent, w/colcnt", Common) ; cholmod_print_perm (Lperm, n, n, "Lperm, w/colcnt", Common) ; cholmod_print_subset (Lcolcount, n, n, "Colcount, w/colcnt",Common); */ if (symmetric < 0) { /* symmetric lower case: S = tril (A (p,p))' and F = S' */ /* workspace: Iwork (2*nrow) */ C2 = cholmod_transpose (A, FALSE, Lperm, NULL, 0, Common) ; SS = C2 ; /* workspace: Iwork (nrow) */ C1 = cholmod_transpose (C2, FALSE, NULL, NULL, 0, Common) ; FF = C1 ; } else { /* symmetric upper case: F = triu (A (p,p))' and S = F' */ /* unsymmetric case: F = A (p,f)' and S = F' */ /* workspace: symmetric: Iwork (2*nrow), * unsym: Iwork (nrow if no fset, MAX(nrow,ncol) if fset) */ C1 = cholmod_transpose (A, FALSE, Lperm, fset, nf, Common) ; FF = C1 ; /* workspace: Iwork (nrow) */ C2 = cholmod_transpose (C1, FALSE, NULL, NULL, 0, Common) ; SS = C2 ; } /* workspace: symmmetric: Iwork (nrow), * unsymmetric: Iwork (nrow+ncol)*/ ColCount2 = cholmod_malloc (n, sizeof (int), Common) ; Parent2 = cholmod_malloc (n, sizeof (int), Common) ; Post2 = cholmod_malloc (n, sizeof (int), Common) ; /* cholmod_print_parent (Lparent, n, "Lparent, w/colcnt", Common) ; printf (">>>>> finding etree of post-permuted matrix\n") ; */ cholmod_etree (symmetric ? SS:FF, Parent2, Common) ; /* cholmod_print_parent (Parent2, n, "Parent2, w/colcnt", Common) ; for (k = 0 ; k < n ; k++) { printf ("k %d Parent old %d new %d\n", k, Lparent [k], Parent2 [k]) ; } */ for (k = 0 ; k < n ; k++) { ASSERT (Lparent [k] == Parent2 [k]) ; } /* workspace: Iwork (2*nrow) */ cholmod_postorder (Parent2, n, NULL, Post2, Common) ; cholmod_rowcolcounts (symmetric ? FF:SS, fset, nf, Parent2, Post2, NULL, ColCount2, First, Level, Common) ; for (k = 0 ; k < n ; k++) { ASSERT (Lcolcount [k] == ColCount2 [k]) ; } cholmod_free (n, sizeof (int), ColCount2, Common) ; cholmod_free (n, sizeof (int), Parent2, Common) ; cholmod_free (n, sizeof (int), Post2, Common) ; cholmod_free_sparse (&C1, Common) ; cholmod_free_sparse (&C2, Common) ; #endif Matrix/src/CHOLMOD/Cholesky/cholmod_etree.c0000644000175100001440000001577012271765436020175 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/cholmod_etree =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Compute the elimination tree of A or A'*A * * In the symmetric case, the upper triangular part of A is used. Entries not * in this part of the matrix are ignored. Computing the etree of a symmetric * matrix from just its lower triangular entries is not supported. * * In the unsymmetric case, all of A is used, and the etree of A'*A is computed. * * References: * * J. Liu, "A compact row storage scheme for Cholesky factors", ACM Trans. * Math. Software, vol 12, 1986, pp. 127-148. * * J. Liu, "The role of elimination trees in sparse factorization", SIAM J. * Matrix Analysis & Applic., vol 11, 1990, pp. 134-172. * * J. Gilbert, X. Li, E. Ng, B. Peyton, "Computing row and column counts for * sparse QR and LU factorization", BIT, vol 41, 2001, pp. 693-710. * * workspace: symmetric: Iwork (nrow), unsymmetric: Iwork (nrow+ncol) * * Supports any xtype (pattern, real, complex, or zomplex) */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === update_etree ========================================================= */ /* ========================================================================== */ static void update_etree ( /* inputs, not modified */ Int k, /* process the edge (k,i) in the input graph */ Int i, /* inputs, modified on output */ Int Parent [ ], /* Parent [t] = p if p is the parent of t */ Int Ancestor [ ] /* Ancestor [t] is the ancestor of node t in the partially-constructed etree */ ) { Int a ; for ( ; ; ) /* traverse the path from k to the root of the tree */ { a = Ancestor [k] ; if (a == i) { /* final ancestor reached; no change to tree */ return ; } /* perform path compression */ Ancestor [k] = i ; if (a == EMPTY) { /* final ancestor undefined; this is a new edge in the tree */ Parent [k] = i ; return ; } /* traverse up to the ancestor of k */ k = a ; } } /* ========================================================================== */ /* === cholmod_etree ======================================================== */ /* ========================================================================== */ /* Find the elimination tree of A or A'*A */ int CHOLMOD(etree) ( /* ---- input ---- */ cholmod_sparse *A, /* ---- output --- */ Int *Parent, /* size ncol. Parent [j] = p if p is the parent of j */ /* --------------- */ cholmod_common *Common ) { Int *Ap, *Ai, *Anz, *Ancestor, *Prev, *Iwork ; Int i, j, jprev, p, pend, nrow, ncol, packed, stype ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (Parent, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ stype = A->stype ; /* s = A->nrow + (stype ? 0 : A->ncol) */ s = CHOLMOD(add_size_t) (A->nrow, (stype ? 0 : A->ncol), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (0, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } ASSERT (CHOLMOD(dump_sparse) (A, "etree", Common) >= 0) ; Iwork = Common->Iwork ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ncol = A->ncol ; /* the number of columns of A */ nrow = A->nrow ; /* the number of rows of A */ Ap = A->p ; /* size ncol+1, column pointers for A */ Ai = A->i ; /* the row indices of A */ Anz = A->nz ; /* number of nonzeros in each column of A */ packed = A->packed ; Ancestor = Iwork ; /* size ncol (i/i/l) */ for (j = 0 ; j < ncol ; j++) { Parent [j] = EMPTY ; Ancestor [j] = EMPTY ; } /* ---------------------------------------------------------------------- */ /* compute the etree */ /* ---------------------------------------------------------------------- */ if (stype > 0) { /* ------------------------------------------------------------------ */ /* symmetric (upper) case: compute etree (A) */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < ncol ; j++) { /* for each row i in column j of triu(A), excluding the diagonal */ p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i < j) { update_etree (i, j, Parent, Ancestor) ; } } } } else if (stype == 0) { /* ------------------------------------------------------------------ */ /* unsymmetric case: compute etree (A'*A) */ /* ------------------------------------------------------------------ */ Prev = Iwork + ncol ; /* size nrow (i/i/l) */ for (i = 0 ; i < nrow ; i++) { Prev [i] = EMPTY ; } for (j = 0 ; j < ncol ; j++) { /* for each row i in column j of A */ p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { /* a graph is constructed dynamically with one path per row * of A. If the ith row of A contains column indices * (j1,j2,j3,j4) then the new graph has edges (j1,j2), (j2,j3), * and (j3,j4). When at node i of this path-graph, all edges * (jprev,j) are considered, where jprevPerm can be used (or not) to permute the input matrix A. * * These routines are used after a supernodal factorization is converted into * a simplicial one, to remove zero entries that were added due to relaxed * supernode amalgamation. They can also be used after a series of downdates * to remove entries that would no longer be present if the matrix were * factorized from scratch. A downdate (cholmod_updown) does not remove any * entries from L. * * workspace: Flag (nrow), Head (nrow+1), * if symmetric: Iwork (2*nrow) * if unsymmetric: Iwork (2*nrow+ncol). * Allocates up to 2 copies of its input matrix A (pattern only). */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === cholmod_resymbol ===================================================== */ /* ========================================================================== */ /* Remove entries from L that are not in the factorization of P*A*P', P*A*A'*P', * or P*F*F'*P' (depending on A->stype and whether fset is NULL or not). * * cholmod_resymbol is the same as cholmod_resymbol_noperm, except that it * first permutes A according to L->Perm. A can be upper/lower/unsymmetric, * in contrast to cholmod_resymbol_noperm (which can be lower or unsym). */ int CHOLMOD(resymbol) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int pack, /* if TRUE, pack the columns of L */ /* ---- in/out --- */ cholmod_factor *L, /* factorization, entries pruned on output */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *H, *F, *G ; Int stype, nrow, ncol ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; if (L->is_super) { /* cannot operate on a supernodal factorization */ ERROR (CHOLMOD_INVALID, "cannot operate on supernodal L") ; return (FALSE) ; } if (L->n != A->nrow) { /* dimensions must agree */ ERROR (CHOLMOD_INVALID, "A and L dimensions do not match") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ stype = A->stype ; nrow = A->nrow ; ncol = A->ncol ; /* s = 2*nrow + (stype ? 0 : ncol) */ s = CHOLMOD(mult_size_t) (nrow, 2, &ok) ; s = CHOLMOD(add_size_t) (s, (stype ? 0 : ncol), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (nrow, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* permute the input matrix if necessary */ /* ---------------------------------------------------------------------- */ H = NULL ; G = NULL ; if (stype > 0) { if (L->ordering == CHOLMOD_NATURAL) { /* F = triu(A)' */ /* workspace: Iwork (nrow) */ G = CHOLMOD(ptranspose) (A, 0, NULL, NULL, 0, Common) ; } else { /* F = triu(A(p,p))' */ /* workspace: Iwork (2*nrow) */ G = CHOLMOD(ptranspose) (A, 0, L->Perm, NULL, 0, Common) ; } F = G ; } else if (stype < 0) { if (L->ordering == CHOLMOD_NATURAL) { F = A ; } else { /* G = triu(A(p,p))' */ /* workspace: Iwork (2*nrow) */ G = CHOLMOD(ptranspose) (A, 0, L->Perm, NULL, 0, Common) ; /* H = G' */ /* workspace: Iwork (nrow) */ H = CHOLMOD(ptranspose) (G, 0, NULL, NULL, 0, Common) ; F = H ; } } else { if (L->ordering == CHOLMOD_NATURAL) { F = A ; } else { /* G = A(p,f)' */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/ G = CHOLMOD(ptranspose) (A, 0, L->Perm, fset, fsize, Common) ; /* H = G' */ /* workspace: Iwork (ncol) */ H = CHOLMOD(ptranspose) (G, 0, NULL, NULL, 0, Common) ; F = H ; } } /* No need to check for failure here. cholmod_resymbol_noperm will return * FALSE if F is NULL. */ /* ---------------------------------------------------------------------- */ /* resymbol */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(resymbol_noperm) (F, fset, fsize, pack, L, Common) ; /* ---------------------------------------------------------------------- */ /* free the temporary matrices, if they exist */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&H, Common) ; CHOLMOD(free_sparse) (&G, Common) ; return (ok) ; } /* ========================================================================== */ /* === cholmod_resymbol_noperm ============================================== */ /* ========================================================================== */ /* Redo symbolic LDL' or LL' factorization of I + F*F' or I+A, where F=A(:,f). * * L already exists, but is a superset of the true dynamic pattern (simple * column downdates and row deletions haven't pruned anything). Just redo the * symbolic factorization and drop entries that are no longer there. The * diagonal is not modified. The number of nonzeros in column j of L * (L->nz[j]) can decrease. The column pointers (L->p[j]) remain unchanged if * pack is FALSE or if L is not monotonic. Otherwise, the columns of L are * packed in place. * * For the symmetric case, the columns of the lower triangular part of A * are accessed by column. NOTE that this the transpose of the general case. * * For the unsymmetric case, F=A(:,f) is accessed by column. * * A need not be sorted, and can be packed or unpacked. If L->Perm is not * identity, then A must already be permuted according to the permutation used * to factorize L. The advantage of using this routine is that it does not * need to create permuted copies of A first. * * This routine can be called if L is only partially factored via cholmod_rowfac * since all it does is prune. If an entry is in F*F' or A, but not in L, it * isn't added to L. * * L must be simplicial LDL' or LL'; it cannot be supernodal or symbolic. * * The set f is held in fset and fsize. * fset = NULL means ":" in MATLAB. fset is ignored. * fset != NULL means f = fset [0..fset-1]. * fset != NULL and fsize = 0 means f is the empty set. * There can be no duplicates in fset. * Common->status is set to CHOLMOD_INVALID if fset is invalid. * * workspace: Flag (nrow), Head (nrow+1), * if symmetric: Iwork (2*nrow) * if unsymmetric: Iwork (2*nrow+ncol). * Unlike cholmod_resymbol, this routine does not allocate any temporary * copies of its input matrix. */ int CHOLMOD(resymbol_noperm) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int pack, /* if TRUE, pack the columns of L */ /* ---- in/out --- */ cholmod_factor *L, /* factorization, entries pruned on output */ /* --------------- */ cholmod_common *Common ) { double *Lx, *Lz ; Int i, j, k, row, parent, p, pend, pdest, ncol, apacked, sorted, nrow, nf, use_fset, mark, jj, stype, xtype ; Int *Ap, *Ai, *Anz, *Li, *Lp, *Lnz, *Flag, *Head, *Link, *Anext, *Iwork ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; ncol = A->ncol ; nrow = A->nrow ; stype = A->stype ; ASSERT (IMPLIES (stype != 0, nrow == ncol)) ; if (stype > 0) { /* symmetric, with upper triangular part, not supported */ ERROR (CHOLMOD_INVALID, "symmetric upper not supported ") ; return (FALSE) ; } if (L->is_super) { /* cannot operate on a supernodal or symbolic factorization */ ERROR (CHOLMOD_INVALID, "cannot operate on supernodal L") ; return (FALSE) ; } if (L->n != A->nrow) { /* dimensions must agree */ ERROR (CHOLMOD_INVALID, "A and L dimensions do not match") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 2*nrow + (stype ? 0 : ncol) */ s = CHOLMOD(mult_size_t) (nrow, 2, &ok) ; if (stype != 0) { s = CHOLMOD(add_size_t) (s, ncol, &ok) ; } if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (nrow, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ai = A->i ; Ap = A->p ; Anz = A->nz ; apacked = A->packed ; sorted = A->sorted ; Li = L->i ; Lx = L->x ; Lz = L->z ; Lp = L->p ; Lnz = L->nz ; xtype = L->xtype ; /* If L is monotonic on input, then it can be packed or * unpacked on output, depending on the pack input parameter. */ /* cannot pack a non-monotonic matrix */ if (!(L->is_monotonic)) { pack = FALSE ; } ASSERT (L->nzmax >= (size_t) (Lp [L->n])) ; pdest = 0 ; PRINT1 (("\n\n===================== Resymbol pack %d Apacked %d\n", pack, A->packed)) ; ASSERT (CHOLMOD(dump_sparse) (A, "ReSymbol A:", Common) >= 0) ; DEBUG (CHOLMOD(dump_factor) (L, "ReSymbol initial L (i, x):", Common)) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Flag = Common->Flag ; /* size nrow */ Head = Common->Head ; /* size nrow+1 */ Iwork = Common->Iwork ; Link = Iwork ; /* size nrow (i/i/l) [ */ Lnz = Iwork + nrow ; /* size nrow (i/i/l), if L not packed */ Anext = Iwork + 2*((size_t) nrow) ; /* size ncol (i/i/l), unsym. only */ for (j = 0 ; j < nrow ; j++) { Link [j] = EMPTY ; } /* use Lnz in L itself */ Lnz = L->nz ; ASSERT (Lnz != NULL) ; /* ---------------------------------------------------------------------- */ /* for the unsymmetric case, queue each column of A (:,f) */ /* ---------------------------------------------------------------------- */ /* place each column of the basis set on the link list corresponding to */ /* the smallest row index in that column */ if (stype == 0) { use_fset = (fset != NULL) ; if (use_fset) { nf = fsize ; /* This is the only O(ncol) loop in cholmod_resymbol. * It is required only to check the fset. */ for (j = 0 ; j < ncol ; j++) { Anext [j] = -2 ; } for (jj = 0 ; jj < nf ; jj++) { j = fset [jj] ; if (j < 0 || j > ncol || Anext [j] != -2) { /* out-of-range or duplicate entry in fset */ ERROR (CHOLMOD_INVALID, "fset invalid") ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (FALSE) ; } /* flag column j as having been seen */ Anext [j] = EMPTY ; } /* the fset is now valid */ ASSERT (CHOLMOD(dump_perm) (fset, nf, ncol, "fset", Common)) ; } else { nf = ncol ; } for (jj = 0 ; jj < nf ; jj++) { j = (use_fset) ? (fset [jj]) : jj ; /* column j is the fset; find the smallest row (if any) */ p = Ap [j] ; pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ; if (pend > p) { k = Ai [p] ; if (!sorted) { for ( ; p < pend ; p++) { k = MIN (k, Ai [p]) ; } } /* place column j on link list k */ ASSERT (k >= 0 && k < nrow) ; Anext [j] = Head [k] ; Head [k] = j ; } } } /* ---------------------------------------------------------------------- */ /* recompute symbolic LDL' factorization */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < nrow ; k++) { #ifndef NDEBUG PRINT1 (("\n\n================== Initial column k = "ID"\n", k)) ; for (p = Lp [k] ; p < Lp [k] + Lnz [k] ; p++) { PRINT1 ((" row: "ID" value: ", Li [p])) ; PRINT1 (("\n")) ; } PRINT1 (("Recomputing LDL, column k = "ID"\n", k)) ; #endif /* ------------------------------------------------------------------ */ /* compute column k of I+F*F' or I+A */ /* ------------------------------------------------------------------ */ /* flag the diagonal entry */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; Flag [k] = mark ; PRINT1 ((" row: "ID" (diagonal)\n", k)) ; if (stype != 0) { /* merge column k of A into Flag (lower triangular part only) */ p = Ap [k] ; pend = (apacked) ? (Ap [k+1]) : (p + Anz [k]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i > k) { Flag [i] = mark ; } } } else { /* for each column j whos first row index is in row k */ for (j = Head [k] ; j != EMPTY ; j = Anext [j]) { /* merge column j of A into Flag */ PRINT1 ((" ---- A column "ID"\n", j)) ; p = Ap [j] ; pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ; PRINT1 ((" length "ID" adding\n", pend-p)) ; for ( ; p < pend ; p++) { #ifndef NDEBUG ASSERT (Ai [p] >= k && Ai [p] < nrow) ; if (Flag [Ai [p]] < mark) PRINT1 ((" row "ID"\n", Ai [p])) ; #endif Flag [Ai [p]] = mark ; } } /* clear the kth link list */ Head [k] = EMPTY ; } /* ------------------------------------------------------------------ */ /* compute pruned pattern of kth column of L = union of children */ /* ------------------------------------------------------------------ */ /* for each column j of L whose parent is k */ for (j = Link [k] ; j != EMPTY ; j = Link [j]) { /* merge column j of L into Flag */ PRINT1 ((" ---- L column "ID"\n", k)) ; ASSERT (j < k) ; ASSERT (Lnz [j] > 0) ; p = Lp [j] ; pend = p + Lnz [j] ; ASSERT (Li [p] == j && Li [p+1] == k) ; p++ ; /* skip past the diagonal entry */ for ( ; p < pend ; p++) { /* add to pattern */ ASSERT (Li [p] >= k && Li [p] < nrow) ; Flag [Li [p]] = mark ; } } /* ------------------------------------------------------------------ */ /* prune the kth column of L */ /* ------------------------------------------------------------------ */ PRINT1 (("Final column of L:\n")) ; p = Lp [k] ; pend = p + Lnz [k] ; if (pack) { /* shift column k upwards */ Lp [k] = pdest ; } else { /* leave column k in place, just reduce Lnz [k] */ pdest = p ; } for ( ; p < pend ; p++) { ASSERT (pdest < pend) ; ASSERT (pdest <= p) ; row = Li [p] ; ASSERT (row >= k && row < nrow) ; if (Flag [row] == mark) { /* keep this entry */ Li [pdest] = row ; if (xtype == CHOLMOD_REAL) { Lx [pdest] = Lx [p] ; } else if (xtype == CHOLMOD_COMPLEX) { Lx [2*pdest ] = Lx [2*p ] ; Lx [2*pdest+1] = Lx [2*p+1] ; } else if (xtype == CHOLMOD_ZOMPLEX) { Lx [pdest] = Lx [p] ; Lz [pdest] = Lz [p] ; } pdest++ ; } } /* ------------------------------------------------------------------ */ /* prepare this column for its parent */ /* ------------------------------------------------------------------ */ Lnz [k] = pdest - Lp [k] ; PRINT1 ((" L("ID") length "ID"\n", k, Lnz [k])) ; ASSERT (Lnz [k] > 0) ; /* parent is the first entry in the column after the diagonal */ parent = (Lnz [k] > 1) ? (Li [Lp [k] + 1]) : EMPTY ; PRINT1 (("parent ("ID") = "ID"\n", k, parent)) ; ASSERT ((parent > k && parent < nrow) || (parent == EMPTY)) ; if (parent != EMPTY) { Link [k] = Link [parent] ; Link [parent] = k ; } } /* done using Iwork for Link, Lnz (if needed), and Anext ] */ /* ---------------------------------------------------------------------- */ /* convert L to packed, if requested */ /* ---------------------------------------------------------------------- */ if (pack) { /* finalize Lp */ Lp [nrow] = pdest ; /* Shrink L to be just large enough. It cannot fail. */ /* workspace: none */ ASSERT ((size_t) (Lp [nrow]) <= L->nzmax) ; CHOLMOD(reallocate_factor) (Lp [nrow], L, Common) ; ASSERT (Common->status >= CHOLMOD_OK) ; } /* ---------------------------------------------------------------------- */ /* clear workspace */ /* ---------------------------------------------------------------------- */ /* CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; DEBUG (CHOLMOD(dump_factor) (L, "ReSymbol final L (i, x):", Common)) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (TRUE) ; } #endif Matrix/src/CHOLMOD/Cholesky/t_cholmod_ltsolve.c0000644000175100001440000005463312271765436021105 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/t_cholmod_ltsolve =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2013, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Template routine to solve L'x=b with unit or non-unit diagonal, or * solve DL'x=b. * * The numeric xtype of L and Y must match. Y contains b on input and x on * output, stored in row-form. Y is nrow-by-n, where nrow must equal 1 for the * complex or zomplex cases, and nrow <= 4 for the real case. * * This file is not compiled separately. It is included in t_cholmod_solve.c * instead. It contains no user-callable routines. * * workspace: none * * Supports real, complex, and zomplex factors. */ /* undefine all prior definitions */ #undef FORM_NAME #undef LSOLVE #undef DIAG /* -------------------------------------------------------------------------- */ /* define the method */ /* -------------------------------------------------------------------------- */ #ifdef LL /* LL': solve Lx=b with non-unit diagonal */ #define FORM_NAME(prefix,rank) prefix ## ll_ltsolve_ ## rank #define DIAG #elif defined (LD) /* LDL': solve LDx=b */ #define FORM_NAME(prefix,rank) prefix ## ldl_dltsolve_ ## rank #define DIAG #else /* LDL': solve Lx=b with unit diagonal */ #define FORM_NAME(prefix,rank) prefix ## ldl_ltsolve_ ## rank #endif /* LSOLVE(k) defines the name of a routine for an n-by-k right-hand-side. */ #define LSOLVE(prefix,rank) FORM_NAME(prefix,rank) #ifdef REAL /* ========================================================================== */ /* === LSOLVE (1) =========================================================== */ /* ========================================================================== */ /* Solve L'x=b, where b has 1 column */ static void LSOLVE (PREFIX,1) ( cholmod_factor *L, double X [ ] /* n-by-1 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = n-1 ; j >= 0 ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j-1, and j-2) */ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y = X [j] ; #ifdef DIAG double d = Lx [p] ; #endif #ifdef LD y /= d ; #endif for (p++ ; p < pend ; p++) { y -= Lx [p] * X [Li [p]] ; } #ifdef LL X [j] = y / d ; #else X [j] = y ; #endif j-- ; /* advance to the next column of L */ } else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2], t ; Int q = Lp [j-1] ; #ifdef DIAG double d [2] ; d [0] = Lx [p] ; d [1] = Lx [q] ; #endif t = Lx [q+1] ; #ifdef LD y [0] = X [j ] / d [0] ; y [1] = X [j-1] / d [1] ; #else y [0] = X [j ] ; y [1] = X [j-1] ; #endif for (p++, q += 2 ; p < pend ; p++, q++) { Int i = Li [p] ; y [0] -= Lx [p] * X [i] ; y [1] -= Lx [q] * X [i] ; } #ifdef LL y [0] /= d [0] ; y [1] = (y [1] - t * y [0]) / d [1] ; #else y [1] -= t * y [0] ; #endif X [j ] = y [0] ; X [j-1] = y [1] ; j -= 2 ; /* advance to the next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3], t [3] ; Int q = Lp [j-1] ; Int r = Lp [j-2] ; #ifdef DIAG double d [3] ; d [0] = Lx [p] ; d [1] = Lx [q] ; d [2] = Lx [r] ; #endif t [0] = Lx [q+1] ; t [1] = Lx [r+1] ; t [2] = Lx [r+2] ; #ifdef LD y [0] = X [j] / d [0] ; y [1] = X [j-1] / d [1] ; y [2] = X [j-2] / d [2] ; #else y [0] = X [j] ; y [1] = X [j-1] ; y [2] = X [j-2] ; #endif for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++) { Int i = Li [p] ; y [0] -= Lx [p] * X [i] ; y [1] -= Lx [q] * X [i] ; y [2] -= Lx [r] * X [i] ; } #ifdef LL y [0] /= d [0] ; y [1] = (y [1] - t [0] * y [0]) / d [1] ; y [2] = (y [2] - t [2] * y [0] - t [1] * y [1]) / d [2] ; #else y [1] -= t [0] * y [0] ; y [2] -= t [2] * y [0] + t [1] * y [1] ; #endif X [j-2] = y [2] ; X [j-1] = y [1] ; X [j ] = y [0] ; j -= 3 ; /* advance to the next column of L */ } } } /* ========================================================================== */ /* === LSOLVE (2) =========================================================== */ /* ========================================================================== */ /* Solve L'x=b, where b has 2 columns */ static void LSOLVE (PREFIX,2) ( cholmod_factor *L, double X [ ][2] /* n-by-2 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = n-1 ; j >= 0 ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j-1, and j-2) */ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y [2] ; #ifdef DIAG double d = Lx [p] ; #endif #ifdef LD y [0] = X [j][0] / d ; y [1] = X [j][1] / d ; #else y [0] = X [j][0] ; y [1] = X [j][1] ; #endif for (p++ ; p < pend ; p++) { Int i = Li [p] ; y [0] -= Lx [p] * X [i][0] ; y [1] -= Lx [p] * X [i][1] ; } #ifdef LL X [j][0] = y [0] / d ; X [j][1] = y [1] / d ; #else X [j][0] = y [0] ; X [j][1] = y [1] ; #endif j-- ; /* advance to the next column of L */ } else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2][2], t ; Int q = Lp [j-1] ; #ifdef DIAG double d [2] ; d [0] = Lx [p] ; d [1] = Lx [q] ; #endif t = Lx [q+1] ; #ifdef LD y [0][0] = X [j ][0] / d [0] ; y [0][1] = X [j ][1] / d [0] ; y [1][0] = X [j-1][0] / d [1] ; y [1][1] = X [j-1][1] / d [1] ; #else y [0][0] = X [j ][0] ; y [0][1] = X [j ][1] ; y [1][0] = X [j-1][0] ; y [1][1] = X [j-1][1] ; #endif for (p++, q += 2 ; p < pend ; p++, q++) { Int i = Li [p] ; y [0][0] -= Lx [p] * X [i][0] ; y [0][1] -= Lx [p] * X [i][1] ; y [1][0] -= Lx [q] * X [i][0] ; y [1][1] -= Lx [q] * X [i][1] ; } #ifdef LL y [0][0] /= d [0] ; y [0][1] /= d [0] ; y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ; y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ; #else y [1][0] -= t * y [0][0] ; y [1][1] -= t * y [0][1] ; #endif X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j-1][0] = y [1][0] ; X [j-1][1] = y [1][1] ; j -= 2 ; /* advance to the next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3][2], t [3] ; Int q = Lp [j-1] ; Int r = Lp [j-2] ; #ifdef DIAG double d [3] ; d [0] = Lx [p] ; d [1] = Lx [q] ; d [2] = Lx [r] ; #endif t [0] = Lx [q+1] ; t [1] = Lx [r+1] ; t [2] = Lx [r+2] ; #ifdef LD y [0][0] = X [j ][0] / d [0] ; y [0][1] = X [j ][1] / d [0] ; y [1][0] = X [j-1][0] / d [1] ; y [1][1] = X [j-1][1] / d [1] ; y [2][0] = X [j-2][0] / d [2] ; y [2][1] = X [j-2][1] / d [2] ; #else y [0][0] = X [j ][0] ; y [0][1] = X [j ][1] ; y [1][0] = X [j-1][0] ; y [1][1] = X [j-1][1] ; y [2][0] = X [j-2][0] ; y [2][1] = X [j-2][1] ; #endif for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++) { Int i = Li [p] ; y [0][0] -= Lx [p] * X [i][0] ; y [0][1] -= Lx [p] * X [i][1] ; y [1][0] -= Lx [q] * X [i][0] ; y [1][1] -= Lx [q] * X [i][1] ; y [2][0] -= Lx [r] * X [i][0] ; y [2][1] -= Lx [r] * X [i][1] ; } #ifdef LL y [0][0] /= d [0] ; y [0][1] /= d [0] ; y [1][0] = (y [1][0] - t [0] * y [0][0]) / d [1] ; y [1][1] = (y [1][1] - t [0] * y [0][1]) / d [1] ; y [2][0] = (y [2][0] - t [2] * y [0][0] - t [1] * y [1][0]) / d [2]; y [2][1] = (y [2][1] - t [2] * y [0][1] - t [1] * y [1][1]) / d [2]; #else y [1][0] -= t [0] * y [0][0] ; y [1][1] -= t [0] * y [0][1] ; y [2][0] -= t [2] * y [0][0] + t [1] * y [1][0] ; y [2][1] -= t [2] * y [0][1] + t [1] * y [1][1] ; #endif X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j-1][0] = y [1][0] ; X [j-1][1] = y [1][1] ; X [j-2][0] = y [2][0] ; X [j-2][1] = y [2][1] ; j -= 3 ; /* advance to the next column of L */ } } } /* ========================================================================== */ /* === LSOLVE (3) =========================================================== */ /* ========================================================================== */ /* Solve L'x=b, where b has 3 columns */ static void LSOLVE (PREFIX,3) ( cholmod_factor *L, double X [ ][3] /* n-by-3 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = n-1 ; j >= 0 ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j-1, and j-2) */ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y [3] ; #ifdef DIAG double d = Lx [p] ; #endif #ifdef LD y [0] = X [j][0] / d ; y [1] = X [j][1] / d ; y [2] = X [j][2] / d ; #else y [0] = X [j][0] ; y [1] = X [j][1] ; y [2] = X [j][2] ; #endif for (p++ ; p < pend ; p++) { Int i = Li [p] ; y [0] -= Lx [p] * X [i][0] ; y [1] -= Lx [p] * X [i][1] ; y [2] -= Lx [p] * X [i][2] ; } #ifdef LL X [j][0] = y [0] / d ; X [j][1] = y [1] / d ; X [j][2] = y [2] / d ; #else X [j][0] = y [0] ; X [j][1] = y [1] ; X [j][2] = y [2] ; #endif j-- ; /* advance to the next column of L */ } else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2][3], t ; Int q = Lp [j-1] ; #ifdef DIAG double d [2] ; d [0] = Lx [p] ; d [1] = Lx [q] ; #endif t = Lx [q+1] ; #ifdef LD y [0][0] = X [j ][0] / d [0] ; y [0][1] = X [j ][1] / d [0] ; y [0][2] = X [j ][2] / d [0] ; y [1][0] = X [j-1][0] / d [1] ; y [1][1] = X [j-1][1] / d [1] ; y [1][2] = X [j-1][2] / d [1] ; #else y [0][0] = X [j ][0] ; y [0][1] = X [j ][1] ; y [0][2] = X [j ][2] ; y [1][0] = X [j-1][0] ; y [1][1] = X [j-1][1] ; y [1][2] = X [j-1][2] ; #endif for (p++, q += 2 ; p < pend ; p++, q++) { Int i = Li [p] ; y [0][0] -= Lx [p] * X [i][0] ; y [0][1] -= Lx [p] * X [i][1] ; y [0][2] -= Lx [p] * X [i][2] ; y [1][0] -= Lx [q] * X [i][0] ; y [1][1] -= Lx [q] * X [i][1] ; y [1][2] -= Lx [q] * X [i][2] ; } #ifdef LL y [0][0] /= d [0] ; y [0][1] /= d [0] ; y [0][2] /= d [0] ; y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ; y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ; y [1][2] = (y [1][2] - t * y [0][2]) / d [1] ; #else y [1][0] -= t * y [0][0] ; y [1][1] -= t * y [0][1] ; y [1][2] -= t * y [0][2] ; #endif X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j-1][0] = y [1][0] ; X [j-1][1] = y [1][1] ; X [j-1][2] = y [1][2] ; j -= 2 ; /* advance to the next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3][3], t [3] ; Int q = Lp [j-1] ; Int r = Lp [j-2] ; #ifdef DIAG double d [3] ; d [0] = Lx [p] ; d [1] = Lx [q] ; d [2] = Lx [r] ; #endif t [0] = Lx [q+1] ; t [1] = Lx [r+1] ; t [2] = Lx [r+2] ; #ifdef LD y [0][0] = X [j ][0] / d [0] ; y [0][1] = X [j ][1] / d [0] ; y [0][2] = X [j ][2] / d [0] ; y [1][0] = X [j-1][0] / d [1] ; y [1][1] = X [j-1][1] / d [1] ; y [1][2] = X [j-1][2] / d [1] ; y [2][0] = X [j-2][0] / d [2] ; y [2][1] = X [j-2][1] / d [2] ; y [2][2] = X [j-2][2] / d [2] ; #else y [0][0] = X [j ][0] ; y [0][1] = X [j ][1] ; y [0][2] = X [j ][2] ; y [1][0] = X [j-1][0] ; y [1][1] = X [j-1][1] ; y [1][2] = X [j-1][2] ; y [2][0] = X [j-2][0] ; y [2][1] = X [j-2][1] ; y [2][2] = X [j-2][2] ; #endif for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++) { Int i = Li [p] ; y [0][0] -= Lx [p] * X [i][0] ; y [0][1] -= Lx [p] * X [i][1] ; y [0][2] -= Lx [p] * X [i][2] ; y [1][0] -= Lx [q] * X [i][0] ; y [1][1] -= Lx [q] * X [i][1] ; y [1][2] -= Lx [q] * X [i][2] ; y [2][0] -= Lx [r] * X [i][0] ; y [2][1] -= Lx [r] * X [i][1] ; y [2][2] -= Lx [r] * X [i][2] ; } #ifdef LL y [0][0] /= d [0] ; y [0][1] /= d [0] ; y [0][2] /= d [0] ; y [1][0] = (y [1][0] - t [0] * y [0][0]) / d [1] ; y [1][1] = (y [1][1] - t [0] * y [0][1]) / d [1] ; y [1][2] = (y [1][2] - t [0] * y [0][2]) / d [1] ; y [2][0] = (y [2][0] - t [2] * y [0][0] - t [1] * y [1][0]) / d [2]; y [2][1] = (y [2][1] - t [2] * y [0][1] - t [1] * y [1][1]) / d [2]; y [2][2] = (y [2][2] - t [2] * y [0][2] - t [1] * y [1][2]) / d [2]; #else y [1][0] -= t [0] * y [0][0] ; y [1][1] -= t [0] * y [0][1] ; y [1][2] -= t [0] * y [0][2] ; y [2][0] -= t [2] * y [0][0] + t [1] * y [1][0] ; y [2][1] -= t [2] * y [0][1] + t [1] * y [1][1] ; y [2][2] -= t [2] * y [0][2] + t [1] * y [1][2] ; #endif X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j-1][0] = y [1][0] ; X [j-1][1] = y [1][1] ; X [j-1][2] = y [1][2] ; X [j-2][0] = y [2][0] ; X [j-2][1] = y [2][1] ; X [j-2][2] = y [2][2] ; j -= 3 ; /* advance to the next column of L */ } } } /* ========================================================================== */ /* === LSOLVE (4) =========================================================== */ /* ========================================================================== */ /* Solve L'x=b, where b has 4 columns */ static void LSOLVE (PREFIX,4) ( cholmod_factor *L, double X [ ][4] /* n-by-4 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = n-1 ; j >= 0 ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j-1, and j-2) */ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y [4] ; #ifdef DIAG double d = Lx [p] ; #endif #ifdef LD y [0] = X [j][0] / d ; y [1] = X [j][1] / d ; y [2] = X [j][2] / d ; y [3] = X [j][3] / d ; #else y [0] = X [j][0] ; y [1] = X [j][1] ; y [2] = X [j][2] ; y [3] = X [j][3] ; #endif for (p++ ; p < pend ; p++) { Int i = Li [p] ; y [0] -= Lx [p] * X [i][0] ; y [1] -= Lx [p] * X [i][1] ; y [2] -= Lx [p] * X [i][2] ; y [3] -= Lx [p] * X [i][3] ; } #ifdef LL X [j][0] = y [0] / d ; X [j][1] = y [1] / d ; X [j][2] = y [2] / d ; X [j][3] = y [3] / d ; #else X [j][0] = y [0] ; X [j][1] = y [1] ; X [j][2] = y [2] ; X [j][3] = y [3] ; #endif j-- ; /* advance to the next column of L */ } else /* if (j == 1 || lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j) */ { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2][4], t ; Int q = Lp [j-1] ; #ifdef DIAG double d [2] ; d [0] = Lx [p] ; d [1] = Lx [q] ; #endif t = Lx [q+1] ; #ifdef LD y [0][0] = X [j ][0] / d [0] ; y [0][1] = X [j ][1] / d [0] ; y [0][2] = X [j ][2] / d [0] ; y [0][3] = X [j ][3] / d [0] ; y [1][0] = X [j-1][0] / d [1] ; y [1][1] = X [j-1][1] / d [1] ; y [1][2] = X [j-1][2] / d [1] ; y [1][3] = X [j-1][3] / d [1] ; #else y [0][0] = X [j ][0] ; y [0][1] = X [j ][1] ; y [0][2] = X [j ][2] ; y [0][3] = X [j ][3] ; y [1][0] = X [j-1][0] ; y [1][1] = X [j-1][1] ; y [1][2] = X [j-1][2] ; y [1][3] = X [j-1][3] ; #endif for (p++, q += 2 ; p < pend ; p++, q++) { Int i = Li [p] ; y [0][0] -= Lx [p] * X [i][0] ; y [0][1] -= Lx [p] * X [i][1] ; y [0][2] -= Lx [p] * X [i][2] ; y [0][3] -= Lx [p] * X [i][3] ; y [1][0] -= Lx [q] * X [i][0] ; y [1][1] -= Lx [q] * X [i][1] ; y [1][2] -= Lx [q] * X [i][2] ; y [1][3] -= Lx [q] * X [i][3] ; } #ifdef LL y [0][0] /= d [0] ; y [0][1] /= d [0] ; y [0][2] /= d [0] ; y [0][3] /= d [0] ; y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ; y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ; y [1][2] = (y [1][2] - t * y [0][2]) / d [1] ; y [1][3] = (y [1][3] - t * y [0][3]) / d [1] ; #else y [1][0] -= t * y [0][0] ; y [1][1] -= t * y [0][1] ; y [1][2] -= t * y [0][2] ; y [1][3] -= t * y [0][3] ; #endif X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j ][3] = y [0][3] ; X [j-1][0] = y [1][0] ; X [j-1][1] = y [1][1] ; X [j-1][2] = y [1][2] ; X [j-1][3] = y [1][3] ; j -= 2 ; /* advance to the next column of L */ } /* NOTE: with 4 right-hand-sides, it suffices to exploit dynamic * supernodes of just size 1 and 2. 3-column supernodes are not * needed. */ } } #endif /* ========================================================================== */ /* === LSOLVE (k) =========================================================== */ /* ========================================================================== */ static void LSOLVE (PREFIX,k) ( cholmod_factor *L, cholmod_dense *Y, /* nr-by-n where nr is 1 to 4 */ Int *Yseti, Int ysetlen ) { #ifdef DIAG double d [1] ; #endif double yx [2] ; #ifdef ZOMPLEX double yz [1] ; double *Lz = L->z ; double *Xz = Y->z ; #endif double *Lx = L->x ; double *Xx = Y->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int n = L->n, jj, jjiters ; ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */ ASSERT (L->n == Y->ncol) ; /* dimensions must match */ ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */ ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */ ASSERT (!(L->is_super)) ; /* L is simplicial LL' or LDL' */ #ifdef REAL if (Yseti == NULL) { /* ------------------------------------------------------------------ */ /* real case, no Yseti, with 1 to 4 RHS's and dynamic supernodes */ /* ------------------------------------------------------------------ */ ASSERT (Y->nrow <= 4) ; switch (Y->nrow) { case 1: LSOLVE (PREFIX,1) (L, Y->x) ; break ; case 2: LSOLVE (PREFIX,2) (L, Y->x) ; break ; case 3: LSOLVE (PREFIX,3) (L, Y->x) ; break ; case 4: LSOLVE (PREFIX,4) (L, Y->x) ; break ; } } else #endif { /* ------------------------------------------------------------------ */ /* solve a complex linear system or solve with Yseti */ /* ------------------------------------------------------------------ */ ASSERT (Y->nrow == 1) ; jjiters = Yseti ? ysetlen : n ; for (jj = jjiters-1 ; jj >= 0 ; jj--) { Int j = Yseti ? Yseti [jj] : jj ; /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* y = X [j] ; */ ASSIGN (yx,yz,0, Xx,Xz,j) ; #ifdef DIAG /* d = Lx [p] ; */ ASSIGN_REAL (d,0, Lx,p) ; #endif #ifdef LD /* y /= d ; */ DIV_REAL (yx,yz,0, yx,yz,0, d,0) ; #endif for (p++ ; p < pend ; p++) { /* y -= conj (Lx [p]) * X [Li [p]] ; */ Int i = Li [p] ; MULTSUBCONJ (yx,yz,0, Lx,Lz,p, Xx,Xz,i) ; } #ifdef LL /* X [j] = y / d ; */ DIV_REAL (Xx,Xz,j, yx,yz,0, d,0) ; #else /* X [j] = y ; */ ASSIGN (Xx,Xz,j, yx,yz,0) ; #endif } } } /* prepare for the next inclusion of this file in cholmod_solve.c */ #undef LL #undef LD Matrix/src/CHOLMOD/Cholesky/cholmod_rowfac.c0000644000175100001440000005652512271765436020355 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/cholmod_rowfac ============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2013, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Full or incremental numerical LDL' or LL' factorization (simplicial, not * supernodal) cholmod_factorize is the "easy" wrapper for this code, but it * does not provide access to incremental factorization. * * cholmod_rowfac computes the full or incremental LDL' or LL' factorization of * A+beta*I (where A is symmetric) or A*F+beta*I (where A and F are unsymmetric * and only the upper triangular part of A*F+beta*I is used). It computes * L (and D, for LDL') one row at a time. beta is real. * * A is nrow-by-ncol or nrow-by-nrow. In "packed" form it is a conventional * column-oriented sparse matrix. Row indices of column j are in * Ai [Ap [j] ... Ap [j+1]-1] and values in the same locations of Ax. * will be faster if A has sorted columns. In "unpacked" form the column * of A ends at Ap [j] + Anz [j] - 1 instead of Ap [j+1] - 1. * * Row indices in each column of A can be sorted or unsorted, but the routine * routine works fastest if A is sorted, or if only triu(A) is provided * for the symmetric case. * * The unit-diagonal nrow-by-nrow output matrix L is returned in "unpacked" * column form, with row indices of column j in Li [Lp [j] ... * Lp [j] + Lnz [j] - 1] and values in the same location in Lx. The row * indices in each column of L are in sorted order. The unit diagonal of L * is not stored. * * L can be a simplicial symbolic or numeric (L->is_super must be FALSE). * A symbolic factor is converted immediately into a numeric factor containing * the identity matrix. * * For a full factorization, kstart = 0 and kend = nrow. The existing nonzero * entries (numerical values in L->x and L->z for the zomplex case, and indices * in L->i), if any, are overwritten. * * To compute an incremental factorization, select kstart and kend as the range * of rows of L you wish to compute. A correct factorization will be computed * only if all descendants of all nodes k = kstart to kend-1 in the etree have * been factorized by a prior call to this routine, and if rows kstart to kend-1 * have not been factorized. This condition is NOT checked on input. * * --------------- * Symmetric case: * --------------- * * The factorization (in MATLAB notation) is: * * S = beta*I + A * S = triu (S) + triu (S,1)' * L*D*L' = S, or L*L' = S * * A is a conventional sparse matrix in compressed column form. Only the * diagonal and upper triangular part of A is accessed; the lower * triangular part is ignored and assumed to be equal to the upper * triangular part. For an incremental factorization, only columns kstart * to kend-1 of A are accessed. F is not used. * * --------------- * Unsymmetric case: * --------------- * * The factorization (in MATLAB notation) is: * * S = beta*I + A*F * S = triu (S) + triu (S,1)' * L*D*L' = S, or L*L' = S * * The typical case is F=A'. Alternatively, if F=A(:,f)', then this * routine factorizes S = beta*I + A(:,f)*A(:,f)'. * * All of A and F are accessed, but only the upper triangular part of A*F * is used. F must be of size A->ncol by A->nrow. F is used for the * unsymmetric case only. F can be packed or unpacked and it need not be * sorted. * * For a complete factorization of beta*I + A*A', * this routine performs a number of flops exactly equal to: * * sum (for each column j of A) of (Anz (j)^2 + Anz (j)), to form S * + * sum (for each column j of L) of (Lnz (j)^2 + 3*Lnz (j)), to factorize S * * where Anz (j) is the number of nonzeros in column j of A, and Lnz (j) * is the number of nonzero in column j of L below the diagonal. * * * workspace: Flag (nrow), W (nrow if real, 2*nrow if complex/zomplex), * Iwork (nrow) * * Supports any xtype, except a pattern-only input matrix A cannot be * factorized. */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === subtree ============================================================== */ /* ========================================================================== */ /* Compute the nonzero pattern of the sparse triangular solve Lx=b, where L in * this case is L(0:k-1,0:k-1), and b is a column of A. This is done by * traversing the kth row-subtree of the elimination tree of L, starting from * each nonzero entry in b. The pattern is returned postordered, and is valid * for a subsequent numerical triangular solve of Lx=b. The elimination tree * can be provided in a Parent array, or extracted from the pattern of L itself. * * The pattern of x = inv(L)*b is returned in Stack [top...]. * Also scatters b, or a multiple of b, into the work vector W. * * The SCATTER macro is defines how the numerical values of A or A*A' are to be * scattered. * * PARENT(i) is a macro the defines how the etree is accessed. It is either: * #define PARENT(i) Parent [i] * #define PARENT(i) (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY */ #define SUBTREE \ for ( ; p < pend ; p++) \ { \ i = Ai [p] ; \ if (i <= k) \ { \ /* scatter the column of A, or A*A' into Wx and Wz */ \ SCATTER ; \ /* start at node i and traverse up the subtree, stop at node k */ \ for (len = 0 ; i < k && i != EMPTY && Flag [i] < mark ; i = parent) \ { \ /* L(k,i) is nonzero, and seen for the first time */ \ Stack [len++] = i ; /* place i on the stack */ \ Flag [i] = mark ; /* mark i as visited */ \ parent = PARENT (i) ; /* traverse up the etree to the parent */ \ } \ /* move the path down to the bottom of the stack */ \ while (len > 0) \ { \ Stack [--top] = Stack [--len] ; \ } \ } \ else if (sorted) \ { \ break ; \ } \ } /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define REAL #include "t_cholmod_rowfac.c" #define COMPLEX #include "t_cholmod_rowfac.c" #define ZOMPLEX #include "t_cholmod_rowfac.c" #define MASK #define REAL #include "t_cholmod_rowfac.c" #define COMPLEX #include "t_cholmod_rowfac.c" #define ZOMPLEX #include "t_cholmod_rowfac.c" #undef MASK /* ========================================================================== */ /* === cholmod_row_subtree ================================================== */ /* ========================================================================== */ /* Compute the nonzero pattern of the solution to the lower triangular system * L(0:k-1,0:k-1) * x = A (0:k-1,k) if A is symmetric, or * L(0:k-1,0:k-1) * x = A (0:k-1,:) * A (:,k)' if A is unsymmetric. * This gives the nonzero pattern of row k of L (excluding the diagonal). * The pattern is returned postordered. * * The symmetric case requires A to be in symmetric-upper form. * * The result is returned in R, a pre-allocated sparse matrix of size nrow-by-1, * with R->nzmax >= nrow. R is assumed to be packed (Rnz [0] is not updated); * the number of entries in R is given by Rp [0]. * * FUTURE WORK: a very minor change to this routine could allow it to compute * the nonzero pattern of x for any system Lx=b. The SUBTREE macro would need * to change, to eliminate its dependence on k. * * workspace: Flag (nrow) */ int CHOLMOD(row_subtree) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */ size_t krow, /* row k of L */ Int *Parent, /* elimination tree */ /* ---- output --- */ cholmod_sparse *R, /* pattern of L(k,:), 1-by-n with R->nzmax >= n */ /* --------------- */ cholmod_common *Common ) { Int *Rp, *Stack, *Flag, *Ap, *Ai, *Anz, *Fp, *Fi, *Fnz ; Int p, pend, parent, t, stype, nrow, k, pf, pfend, Fpacked, packed, sorted, top, len, i, mark ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (R, FALSE) ; RETURN_IF_NULL (Parent, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (R, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; stype = A->stype ; if (stype == 0) { RETURN_IF_NULL (F, FALSE) ; RETURN_IF_XTYPE_INVALID (F, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; } if (krow >= A->nrow) { ERROR (CHOLMOD_INVALID, "subtree: k invalid") ; return (FALSE) ; } if (R->ncol != 1 || A->nrow != R->nrow || A->nrow > R->nzmax) { ERROR (CHOLMOD_INVALID, "subtree: R invalid") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; CHOLMOD(allocate_work) (nrow, 0, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (stype > 0) { /* symmetric upper case: F is not needed. It may be NULL */ Fp = NULL ; Fi = NULL ; Fnz = NULL ; Fpacked = TRUE ; } else if (stype == 0) { /* unsymmetric case: F is required. */ Fp = F->p ; Fi = F->i ; Fnz = F->nz ; Fpacked = F->packed ; } else { /* symmetric lower triangular form not supported */ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ; return (FALSE) ; } Ap = A->p ; Ai = A->i ; Anz = A->nz ; packed = A->packed ; sorted = A->sorted ; k = krow ; Stack = R->i ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Flag = Common->Flag ; /* size nrow, Flag [i] < mark must hold */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* ---------------------------------------------------------------------- */ /* compute the pattern of L(k,:) */ /* ---------------------------------------------------------------------- */ top = nrow ; /* Stack is empty */ Flag [k] = mark ; /* do not include diagonal entry in Stack */ #define SCATTER /* do not scatter numerical values */ #define PARENT(i) Parent [i] /* use Parent for etree */ if (stype != 0) { /* scatter kth col of triu (A), get pattern L(k,:) */ p = Ap [k] ; pend = (packed) ? (Ap [k+1]) : (p + Anz [k]) ; SUBTREE ; } else { /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */ pf = Fp [k] ; pfend = (Fpacked) ? (Fp [k+1]) : (pf + Fnz [k]) ; for ( ; pf < pfend ; pf++) { /* get nonzero entry F (t,k) */ t = Fi [pf] ; p = Ap [t] ; pend = (packed) ? (Ap [t+1]) : (p + Anz [t]) ; SUBTREE ; } } #undef SCATTER #undef PARENT /* shift the stack upwards, to the first part of R */ len = nrow - top ; for (i = 0 ; i < len ; i++) { Stack [i] = Stack [top + i] ; } Rp = R->p ; Rp [0] = 0 ; Rp [1] = len ; R->sorted = FALSE ; CHOLMOD(clear_flag) (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_lsolve_pattern =============================================== */ /* ========================================================================== */ /* Compute the nonzero pattern of Y=L\B. L must be simplicial, and B * must be a single sparse column vector with B->stype = 0. The values of * B are not used; it just specifies a nonzero pattern. The pattern of * Y is not sorted, but is in topological order instead (suitable for a * sparse forward/backsolve). */ int CHOLMOD(lsolve_pattern) ( /* ---- input ---- */ cholmod_sparse *B, /* sparse right-hand-side (a single sparse column) */ cholmod_factor *L, /* the factor L from which parent(i) is derived */ /* ---- output --- */ cholmod_sparse *Yset, /* pattern of Y=L\B, n-by-1 with Y->nzmax >= n */ /* --------------- */ cholmod_common *Common ) { size_t krow ; RETURN_IF_NULL (B, FALSE) ; krow = B->nrow ; return (CHOLMOD(row_lsubtree) (B, NULL, 0, krow, L, Yset, Common)) ; } /* ========================================================================== */ /* === cholmod_row_lsubtree ================================================= */ /* ========================================================================== */ /* Identical to cholmod_row_subtree, except that the elimination tree is * obtained from L itself, as the first off-diagonal entry in each column. * L must be simplicial, not supernodal. * * If krow = A->nrow, then A must be a single sparse column vector, (A->stype * must be zero), and the nonzero pattern of x=L\b is computed, where b=A(:,0) * is the single sparse right-hand-side. The inputs Fi and fnz are ignored. * See CHOLMOD(lsolve_pattern) above for a simpler interface for this case. */ int CHOLMOD(row_lsubtree) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ Int *Fi, size_t fnz, /* nonzero pattern of kth row of A', not required * for the symmetric case. Need not be sorted. */ size_t krow, /* row k of L */ cholmod_factor *L, /* the factor L from which parent(i) is derived */ /* ---- output --- */ cholmod_sparse *R, /* pattern of L(k,:), n-by-1 with R->nzmax >= n */ /* --------------- */ cholmod_common *Common ) { Int *Rp, *Stack, *Flag, *Ap, *Ai, *Anz, *Lp, *Li, *Lnz ; Int p, pend, parent, t, stype, nrow, k, pf, packed, sorted, top, len, i, mark, ka ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (R, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (R, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; nrow = A->nrow ; stype = A->stype ; if (stype < 0) { /* symmetric lower triangular form not supported */ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ; return (FALSE) ; } if (krow > nrow) { ERROR (CHOLMOD_INVALID, "lsubtree: krow invalid") ; return (FALSE) ; } else if (krow == nrow) { /* find pattern of x=L\b where b=A(:,0) */ k = nrow ; /* compute all of the result; don't stop in SUBTREE */ ka = 0 ; /* use column A(:,0) */ if (stype != 0 || A->ncol != 1) { /* A must be unsymmetric (it's a single sparse column vector) */ ERROR (CHOLMOD_INVALID, "lsubtree: A invalid") ; return (FALSE) ; } } else { /* find pattern of L(k,:) using A(:,k) and Fi if A unsymmetric */ k = krow ; /* which row of L to compute */ ka = k ; /* which column of A to use */ if (stype == 0) { RETURN_IF_NULL (Fi, FALSE) ; } } if (R->ncol != 1 || nrow != R->nrow || nrow > R->nzmax || ka >= A->ncol) { ERROR (CHOLMOD_INVALID, "lsubtree: R invalid") ; return (FALSE) ; } if (L->is_super) { ERROR (CHOLMOD_INVALID, "lsubtree: L invalid (cannot be supernodal)") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ CHOLMOD(allocate_work) (nrow, 0, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; Anz = A->nz ; packed = A->packed ; sorted = A->sorted ; Stack = R->i ; Lp = L->p ; Li = L->i ; Lnz = L->nz ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Flag = Common->Flag ; /* size nrow, Flag [i] < mark must hold */ mark = CHOLMOD(clear_flag) (Common) ; /* ---------------------------------------------------------------------- */ /* compute the pattern of L(k,:) */ /* ---------------------------------------------------------------------- */ top = nrow ; /* Stack is empty */ if (k < nrow) { Flag [k] = mark ; /* do not include diagonal entry in Stack */ } #define SCATTER /* do not scatter numerical values */ #define PARENT(i) (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY if (krow == nrow || stype != 0) { /* scatter kth col of triu (A), get pattern L(k,:) */ p = Ap [ka] ; pend = (packed) ? (Ap [ka+1]) : (p + Anz [ka]) ; SUBTREE ; } else { /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */ for (pf = 0 ; pf < (Int) fnz ; pf++) { /* get nonzero entry F (t,k) */ t = Fi [pf] ; p = Ap [t] ; pend = (packed) ? (Ap [t+1]) : (p + Anz [t]) ; SUBTREE ; } } #undef SCATTER #undef PARENT /* shift the stack upwards, to the first part of R */ len = nrow - top ; for (i = 0 ; i < len ; i++) { Stack [i] = Stack [top + i] ; } Rp = R->p ; Rp [0] = 0 ; Rp [1] = len ; R->sorted = FALSE ; CHOLMOD(clear_flag) (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_rowfac ======================================================= */ /* ========================================================================== */ /* This is the incremental factorization for general purpose usage. */ int CHOLMOD(rowfac) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */ double beta [2], /* factorize beta*I+A or beta*I+AA' */ size_t kstart, /* first row to factorize */ size_t kend, /* last row to factorize is kend-1 */ /* ---- in/out --- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(rowfac_mask) (A, F, beta, kstart, kend, NULL, NULL, L, Common)) ; } /* ========================================================================== */ /* === cholmod_rowfac_mask ================================================== */ /* ========================================================================== */ /* This is meant for use in LPDASA only. */ int CHOLMOD(rowfac_mask) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */ double beta [2], /* factorize beta*I+A or beta*I+AA' */ size_t kstart, /* first row to factorize */ size_t kend, /* last row to factorize is kend-1 */ Int *mask, /* size A->nrow. if mask[i] >= 0 row i is set to zero */ Int *RLinkUp, /* size A->nrow. link list of rows to compute */ /* ---- in/out --- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) { Int n ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (L->xtype != CHOLMOD_PATTERN && A->xtype != L->xtype) { ERROR (CHOLMOD_INVALID, "xtype of A and L do not match") ; return (FALSE) ; } if (L->is_super) { ERROR (CHOLMOD_INVALID, "can only do simplicial factorization"); return (FALSE) ; } if (A->stype == 0) { RETURN_IF_NULL (F, FALSE) ; if (A->xtype != F->xtype) { ERROR (CHOLMOD_INVALID, "xtype of A and F do not match") ; return (FALSE) ; } } if (A->stype < 0) { /* symmetric lower triangular form not supported */ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ; return (FALSE) ; } if (kend > L->n) { ERROR (CHOLMOD_INVALID, "kend invalid") ; return (FALSE) ; } if (A->nrow != L->n) { ERROR (CHOLMOD_INVALID, "dimensions of A and L do not match") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; Common->rowfacfl = 0 ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* Xwork is of size n for the real case, 2*n for complex/zomplex */ n = L->n ; /* s = ((A->xtype != CHOLMOD_REAL) ? 2:1)*n */ s = CHOLMOD(mult_size_t) (n, ((A->xtype != CHOLMOD_REAL) ? 2:1), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, n, s, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, A->nrow, Common)) ; /* ---------------------------------------------------------------------- */ /* factorize the matrix, using template routine */ /* ---------------------------------------------------------------------- */ if (RLinkUp == NULL) { switch (A->xtype) { case CHOLMOD_REAL: ok = r_cholmod_rowfac (A, F, beta, kstart, kend, L, Common) ; break ; case CHOLMOD_COMPLEX: ok = c_cholmod_rowfac (A, F, beta, kstart, kend, L, Common) ; break ; case CHOLMOD_ZOMPLEX: ok = z_cholmod_rowfac (A, F, beta, kstart, kend, L, Common) ; break ; } } else { switch (A->xtype) { case CHOLMOD_REAL: ok = r_cholmod_rowfac_mask (A, F, beta, kstart, kend, mask, RLinkUp, L, Common) ; break ; case CHOLMOD_COMPLEX: ok = c_cholmod_rowfac_mask (A, F, beta, kstart, kend, mask, RLinkUp, L, Common) ; break ; case CHOLMOD_ZOMPLEX: ok = z_cholmod_rowfac_mask (A, F, beta, kstart, kend, mask, RLinkUp, L, Common) ; break ; } } return (ok) ; } #endif Matrix/src/CHOLMOD/Cholesky/cholmod_solve.c0000644000175100001440000014160512271765436020216 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/cholmod_solve =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2013, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Solve one of the following systems. D is identity for an LL' factorization, * in which the D operation is skipped: * * Ax=b 0: CHOLMOD_A x = P' * (L' \ (D \ (L \ (P * b)))) * LDL'x=b 1: CHOLMOD_LDLt x = (L' \ (D \ (L \ ( b)))) * LDx=b 2: CHOLMOD_LD x = ( (D \ (L \ ( b)))) * DL'x=b 3: CHOLMOD_DLt x = (L' \ (D \ ( ( b)))) * Lx=b 4: CHOLMOD_L x = ( ( (L \ ( b)))) * L'x=b 5: CHOLMOD_Lt x = (L' \ ( ( ( b)))) * Dx=b 6: CHOLMOD_D x = ( (D \ ( ( b)))) * x=Pb 7: CHOLMOD_P x = ( ( ( (P * b)))) * x=P'b 8: CHOLMOD_Pt x = P' * ( ( ( ( b)))) * * The factorization can be simplicial LDL', simplicial LL', or supernodal LL'. * For an LL' factorization, D is the identity matrix. Thus CHOLMOD_LD and * CHOLMOD_L solve the same system if an LL' factorization was performed, * for example. * * The supernodal solver uses BLAS routines dtrsv, dgemv, dtrsm, and dgemm, * or their complex counterparts ztrsv, zgemv, ztrsm, and zgemm. * * If both L and B are real, then X is returned real. If either is complex * or zomplex, X is returned as either complex or zomplex, depending on the * Common->prefer_zomplex parameter. * * Supports any numeric xtype (pattern-only matrices not supported). * * This routine does not check to see if the diagonal of L or D is zero, * because sometimes a partial solve can be done with indefinite or singular * matrix. If you wish to check in your own code, test L->minor. If * L->minor == L->n, then the matrix has no zero diagonal entries. * If k = L->minor < L->n, then L(k,k) is zero for an LL' factorization, or * D(k,k) is zero for an LDL' factorization. * * This routine returns X as NULL only if it runs out of memory. If L is * indefinite or singular, then X may contain Inf's or NaN's, but it will * exist on output. */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" #ifndef NSUPERNODAL #include "cholmod_supernodal.h" #endif /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define REAL #include "t_cholmod_solve.c" #define COMPLEX #include "t_cholmod_solve.c" #define ZOMPLEX #include "t_cholmod_solve.c" /* ========================================================================== */ /* === Permutation macro ==================================================== */ /* ========================================================================== */ /* If Perm is NULL, it is interpretted as the identity permutation */ #define P(k) ((Perm == NULL) ? (k) : Perm [k]) /* ========================================================================== */ /* === perm ================================================================= */ /* ========================================================================== */ /* Y = B (P (1:nrow), k1 : min (k1+ncols,ncol)-1) where B is nrow-by-ncol. * * Creates a permuted copy of a contiguous set of columns of B. * Y is already allocated on input. Y must be of sufficient size. Let nk be * the number of columns accessed in B. Y->xtype determines the complexity of * the result. * * If B is real and Y is complex (or zomplex), only the real part of B is * copied into Y. The imaginary part of Y is set to zero. * * If B is complex (or zomplex) and Y is real, both the real and imaginary and * parts of B are returned in Y. Y is returned as nrow-by-2*nk. The even * columns of Y contain the real part of B and the odd columns contain the * imaginary part of B. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is * returned as nrow-by-nk with leading dimension nrow. Y->nzmax must be >= * nrow*nk. * * The case where the input (B) is real and the output (Y) is zomplex is * not used. */ static void perm ( /* ---- input ---- */ cholmod_dense *B, /* input matrix B */ Int *Perm, /* optional input permutation (can be NULL) */ Int k1, /* first column of B to copy */ Int ncols, /* last column to copy is min(k1+ncols,B->ncol)-1 */ /* ---- in/out --- */ cholmod_dense *Y /* output matrix Y, already allocated */ ) { double *Yx, *Yz, *Bx, *Bz ; Int k2, nk, p, k, j, nrow, ncol, d, dual, dj, j2 ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ncol = B->ncol ; nrow = B->nrow ; k2 = MIN (k1+ncols, ncol) ; nk = MAX (k2 - k1, 0) ; dual = (Y->xtype == CHOLMOD_REAL && B->xtype != CHOLMOD_REAL) ? 2 : 1 ; d = B->d ; Bx = B->x ; Bz = B->z ; Yx = Y->x ; Yz = Y->z ; Y->nrow = nrow ; Y->ncol = dual*nk ; Y->d = nrow ; ASSERT (((Int) Y->nzmax) >= nrow*nk*dual) ; /* ---------------------------------------------------------------------- */ /* Y = B (P (1:nrow), k1:k2-1) */ /* ---------------------------------------------------------------------- */ switch (Y->xtype) { case CHOLMOD_REAL: switch (B->xtype) { case CHOLMOD_REAL: /* Y real, B real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [k + j2] = Bx [p] ; /* real */ } } break ; case CHOLMOD_COMPLEX: /* Y real, B complex. Y is nrow-by-2*nk */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [k + j2 ] = Bx [2*p ] ; /* real */ Yx [k + j2 + nrow] = Bx [2*p+1] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y real, B zomplex. Y is nrow-by-2*nk */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [k + j2 ] = Bx [p] ; /* real */ Yx [k + j2 + nrow] = Bz [p] ; /* imag */ } } break ; } break ; case CHOLMOD_COMPLEX: switch (B->xtype) { case CHOLMOD_REAL: /* Y complex, B real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [2*k + j2] = Bx [p] ; /* real */ Yx [2*k+1 + j2] = 0 ; /* imag */ } } break ; case CHOLMOD_COMPLEX: /* Y complex, B complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [2*k + j2] = Bx [2*p ] ; /* real */ Yx [2*k+1 + j2] = Bx [2*p+1] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y complex, B zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [2*k + j2] = Bx [p] ; /* real */ Yx [2*k+1 + j2] = Bz [p] ; /* imag */ } } break ; } break ; case CHOLMOD_ZOMPLEX: switch (B->xtype) { #if 0 case CHOLMOD_REAL: /* this case is not used */ break ; #endif case CHOLMOD_COMPLEX: /* Y zomplex, B complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [k + j2] = Bx [2*p ] ; /* real */ Yz [k + j2] = Bx [2*p+1] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y zomplex, B zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [k + j2] = Bx [p] ; /* real */ Yz [k + j2] = Bz [p] ; /* imag */ } } break ; } break ; } } /* ========================================================================== */ /* === iperm ================================================================ */ /* ========================================================================== */ /* X (P (1:nrow), k1 : min (k1+ncols,ncol)-1) = Y where X is nrow-by-ncol. * * Copies and permutes Y into a contiguous set of columns of X. X is already * allocated on input. Y must be of sufficient size. Let nk be the number * of columns accessed in X. X->xtype determines the complexity of the result. * * If X is real and Y is complex (or zomplex), only the real part of B is * copied into X. The imaginary part of Y is ignored. * * If X is complex (or zomplex) and Y is real, both the real and imaginary and * parts of Y are returned in X. Y is nrow-by-2*nk. The even * columns of Y contain the real part of B and the odd columns contain the * imaginary part of B. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is * nrow-by-nk with leading dimension nrow. Y->nzmax must be >= nrow*nk. * * The case where the input (Y) is complex and the output (X) is real, * and the case where the input (Y) is zomplex and the output (X) is real, * are not used. */ static void iperm ( /* ---- input ---- */ cholmod_dense *Y, /* input matrix Y */ Int *Perm, /* optional input permutation (can be NULL) */ Int k1, /* first column of B to copy */ Int ncols, /* last column to copy is min(k1+ncols,B->ncol)-1 */ /* ---- in/out --- */ cholmod_dense *X /* output matrix X, already allocated */ ) { double *Yx, *Yz, *Xx, *Xz ; Int k2, nk, p, k, j, nrow, ncol, d, dj, j2 ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ncol = X->ncol ; nrow = X->nrow ; k2 = MIN (k1+ncols, ncol) ; nk = MAX (k2 - k1, 0) ; d = X->d ; Xx = X->x ; Xz = X->z ; Yx = Y->x ; Yz = Y->z ; ASSERT (((Int) Y->nzmax) >= nrow*nk* ((X->xtype != CHOLMOD_REAL && Y->xtype == CHOLMOD_REAL) ? 2:1)) ; /* ---------------------------------------------------------------------- */ /* X (P (1:nrow), k1:k2-1) = Y */ /* ---------------------------------------------------------------------- */ switch (Y->xtype) { case CHOLMOD_REAL: switch (X->xtype) { case CHOLMOD_REAL: /* Y real, X real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [k + j2] ; /* real */ } } break ; case CHOLMOD_COMPLEX: /* Y real, X complex. Y is nrow-by-2*nk */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [2*p ] = Yx [k + j2 ] ; /* real */ Xx [2*p+1] = Yx [k + j2 + nrow] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y real, X zomplex. Y is nrow-by-2*nk */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [k + j2 ] ; /* real */ Xz [p] = Yx [k + j2 + nrow] ; /* imag */ } } break ; } break ; case CHOLMOD_COMPLEX: switch (X->xtype) { #if 0 case CHOLMOD_REAL: /* this case is not used */ break ; #endif case CHOLMOD_COMPLEX: /* Y complex, X complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [2*p ] = Yx [2*k + j2] ; /* real */ Xx [2*p+1] = Yx [2*k+1 + j2] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y complex, X zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [2*k + j2] ; /* real */ Xz [p] = Yx [2*k+1 + j2] ; /* imag */ } } break ; } break ; case CHOLMOD_ZOMPLEX: switch (X->xtype) { #if 0 case CHOLMOD_REAL: /* this case is not used */ break ; #endif case CHOLMOD_COMPLEX: /* Y zomplex, X complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [2*p ] = Yx [k + j2] ; /* real */ Xx [2*p+1] = Yz [k + j2] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y zomplex, X zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [k + j2] ; /* real */ Xz [p] = Yz [k + j2] ; /* imag */ } } break ; } break ; } } /* ========================================================================== */ /* === ptrans =============================================================== */ /* ========================================================================== */ /* Y = B (P (1:nrow), k1 : min (k1+ncols,ncol)-1)' where B is nrow-by-ncol. * * Creates a permuted and transposed copy of a contiguous set of columns of B. * Y is already allocated on input. Y must be of sufficient size. Let nk be * the number of columns accessed in B. Y->xtype determines the complexity of * the result. * * If B is real and Y is complex (or zomplex), only the real part of B is * copied into Y. The imaginary part of Y is set to zero. * * If B is complex (or zomplex) and Y is real, both the real and imaginary and * parts of B are returned in Y. Y is returned as 2*nk-by-nrow. The even * rows of Y contain the real part of B and the odd rows contain the * imaginary part of B. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is * returned as nk-by-nrow with leading dimension nk. Y->nzmax must be >= * nrow*nk. * * The array transpose is performed, not the complex conjugate transpose. */ static void ptrans ( /* ---- input ---- */ cholmod_dense *B, /* input matrix B */ Int *Perm, /* optional input permutation (can be NULL) */ Int k1, /* first column of B to copy */ Int ncols, /* last column to copy is min(k1+ncols,B->ncol)-1 */ /* ---- in/out --- */ cholmod_dense *Y /* output matrix Y, already allocated */ ) { double *Yx, *Yz, *Bx, *Bz ; Int k2, nk, p, k, j, nrow, ncol, d, dual, dj, j2 ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ncol = B->ncol ; nrow = B->nrow ; k2 = MIN (k1+ncols, ncol) ; nk = MAX (k2 - k1, 0) ; dual = (Y->xtype == CHOLMOD_REAL && B->xtype != CHOLMOD_REAL) ? 2 : 1 ; d = B->d ; Bx = B->x ; Bz = B->z ; Yx = Y->x ; Yz = Y->z ; Y->nrow = dual*nk ; Y->ncol = nrow ; Y->d = dual*nk ; ASSERT (((Int) Y->nzmax) >= nrow*nk*dual) ; /* ---------------------------------------------------------------------- */ /* Y = B (P (1:nrow), k1:k2-1)' */ /* ---------------------------------------------------------------------- */ switch (Y->xtype) { case CHOLMOD_REAL: switch (B->xtype) { case CHOLMOD_REAL: /* Y real, B real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*nk] = Bx [p] ; /* real */ } } break ; case CHOLMOD_COMPLEX: /* Y real, B complex. Y is 2*nk-by-nrow */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*2*nk] = Bx [2*p ] ; /* real */ Yx [j2+1 + k*2*nk] = Bx [2*p+1] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y real, B zomplex. Y is 2*nk-by-nrow */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*2*nk] = Bx [p] ; /* real */ Yx [j2+1 + k*2*nk] = Bz [p] ; /* imag */ } } break ; } break ; case CHOLMOD_COMPLEX: switch (B->xtype) { case CHOLMOD_REAL: /* Y complex, B real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*2*nk] = Bx [p] ; /* real */ Yx [j2+1 + k*2*nk] = 0 ; /* imag */ } } break ; case CHOLMOD_COMPLEX: /* Y complex, B complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*2*nk] = Bx [2*p ] ; /* real */ Yx [j2+1 + k*2*nk] = Bx [2*p+1] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y complex, B zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*2*nk] = Bx [p] ; /* real */ Yx [j2+1 + k*2*nk] = Bz [p] ; /* imag */ } } break ; } break ; case CHOLMOD_ZOMPLEX: switch (B->xtype) { case CHOLMOD_REAL: /* Y zomplex, B real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*nk] = Bx [p] ; /* real */ Yz [j2 + k*nk] = 0 ; /* imag */ } } break ; case CHOLMOD_COMPLEX: /* Y zomplex, B complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*nk] = Bx [2*p ] ; /* real */ Yz [j2 + k*nk] = Bx [2*p+1] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y zomplex, B zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*nk] = Bx [p] ; /* real */ Yz [j2 + k*nk] = Bz [p] ; /* imag */ } } break ; } break ; } } /* ========================================================================== */ /* === iptrans ============================================================== */ /* ========================================================================== */ /* X (P (1:nrow), k1 : min (k1+ncols,ncol)-1) = Y' where X is nrow-by-ncol. * * Copies into a permuted and transposed contiguous set of columns of X. * X is already allocated on input. Y must be of sufficient size. Let nk be * the number of columns accessed in X. X->xtype determines the complexity of * the result. * * If X is real and Y is complex (or zomplex), only the real part of Y is * copied into X. The imaginary part of Y is ignored. * * If X is complex (or zomplex) and Y is real, both the real and imaginary and * parts of X are returned in Y. Y is 2*nk-by-nrow. The even * rows of Y contain the real part of X and the odd rows contain the * imaginary part of X. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is * nk-by-nrow with leading dimension nk. Y->nzmax must be >= nrow*nk. * * The case where Y is complex or zomplex, and X is real, is not used. * * The array transpose is performed, not the complex conjugate transpose. */ static void iptrans ( /* ---- input ---- */ cholmod_dense *Y, /* input matrix Y */ Int *Perm, /* optional input permutation (can be NULL) */ Int k1, /* first column of X to copy into */ Int ncols, /* last column to copy is min(k1+ncols,X->ncol)-1 */ /* ---- in/out --- */ cholmod_dense *X /* output matrix X, already allocated */ ) { double *Yx, *Yz, *Xx, *Xz ; Int k2, nk, p, k, j, nrow, ncol, d, dj, j2 ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ncol = X->ncol ; nrow = X->nrow ; k2 = MIN (k1+ncols, ncol) ; nk = MAX (k2 - k1, 0) ; d = X->d ; Xx = X->x ; Xz = X->z ; Yx = Y->x ; Yz = Y->z ; ASSERT (((Int) Y->nzmax) >= nrow*nk* ((X->xtype != CHOLMOD_REAL && Y->xtype == CHOLMOD_REAL) ? 2:1)) ; /* ---------------------------------------------------------------------- */ /* X (P (1:nrow), k1:k2-1) = Y' */ /* ---------------------------------------------------------------------- */ switch (Y->xtype) { case CHOLMOD_REAL: switch (X->xtype) { case CHOLMOD_REAL: /* Y real, X real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [j2 + k*nk] ; /* real */ } } break ; case CHOLMOD_COMPLEX: /* Y real, X complex. Y is 2*nk-by-nrow */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [2*p ] = Yx [j2 + k*2*nk] ; /* real */ Xx [2*p+1] = Yx [j2+1 + k*2*nk] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y real, X zomplex. Y is 2*nk-by-nrow */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [j2 + k*2*nk] ; /* real */ Xz [p] = Yx [j2+1 + k*2*nk] ; /* imag */ } } break ; } break ; case CHOLMOD_COMPLEX: switch (X->xtype) { #if 0 case CHOLMOD_REAL: /* this case is not used */ break ; #endif case CHOLMOD_COMPLEX: /* Y complex, X complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [2*p ] = Yx [j2 + k*2*nk] ; /* real */ Xx [2*p+1] = Yx [j2+1 + k*2*nk] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y complex, X zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [j2 + k*2*nk] ; /* real */ Xz [p] = Yx [j2+1 + k*2*nk] ; /* imag */ } } break ; } break ; case CHOLMOD_ZOMPLEX: switch (X->xtype) { #if 0 case CHOLMOD_REAL: /* this case is not used */ break ; #endif case CHOLMOD_COMPLEX: /* Y zomplex, X complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [2*p ] = Yx [j2 + k*nk] ; /* real */ Xx [2*p+1] = Yz [j2 + k*nk] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y zomplex, X zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [j2 + k*nk] ; /* real */ Xz [p] = Yz [j2 + k*nk] ; /* imag */ } } break ; } break ; } } /* ========================================================================== */ /* === cholmod_solve ======================================================== */ /* ========================================================================== */ /* Solve a linear system. * * The factorization can be simplicial LDL', simplicial LL', or supernodal LL'. * The Dx=b solve returns silently for the LL' factorizations (it is implicitly * identity). */ cholmod_dense *CHOLMOD(solve) ( /* ---- input ---- */ int sys, /* system to solve */ cholmod_factor *L, /* factorization to use */ cholmod_dense *B, /* right-hand-side */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *Y = NULL, *X = NULL ; cholmod_dense *E = NULL ; int ok ; /* do the solve, allocating workspaces as needed */ ok = CHOLMOD (solve2) (sys, L, B, NULL, &X, NULL, &Y, &E, Common) ; /* free workspaces if allocated, and free result if an error occured */ CHOLMOD(free_dense) (&Y, Common) ; CHOLMOD(free_dense) (&E, Common) ; if (!ok) { CHOLMOD(free_dense) (&X, Common) ; } return (X) ; } /* ========================================================================== */ /* === cholmod_solve2 ======================================================= */ /* ========================================================================== */ /* This function acts just like cholmod_solve, except that the solution X and * the internal workspace (Y and E) can be passed in preallocated. If the * solution X or any required workspaces are not allocated on input, or if they * are the wrong size or type, then this function frees them and reallocates * them as the proper size and type. Thus, if you have a sequence of solves to * do, you can let this function allocate X, Y, and E on the first call. * Subsequent calls to cholmod_solve2 can then reuse this space. You must * then free the workspaces Y and E (and X if desired) when you are finished. * For example, the first call to cholmod_l_solve2, below, will solve the * requested system. The next 2 calls (with different right-hand-sides but * the same value of "sys") will resuse the workspace and solution X from the * first call. Finally, when all solves are done, you must free the workspaces * Y and E (otherwise you will have a memory leak), and you should also free X * when you are done with it. Note that on input, X, Y, and E must be either * valid cholmod_dense matrices, or initialized to NULL. You cannot pass in an * uninitialized X, Y, or E. * * cholmod_dense *X = NULL, *Y = NULL, *E = NULL ; * ... * cholmod_l_solve2 (sys, L, B1, NULL, &X, NULL, &Y, &E, Common) ; * cholmod_l_solve2 (sys, L, B2, NULL, &X, NULL, &Y, &E, Common) ; * cholmod_l_solve2 (sys, L, B3, NULL, &X, NULL, &Y, &E, Common) ; * cholmod_l_free_dense (&X, Common) ; * cholmod_l_free_dense (&Y, Common) ; * cholmod_l_free_dense (&E, Common) ; * * The equivalent when using cholmod_l_solve is: * * cholmod_dense *X = NULL, *Y = NULL, *E = NULL ; * ... * X = cholmod_l_solve (sys, L, B1, Common) ; * cholmod_l_free_dense (&X, Common) ; * X = cholmod_l_solve (sys, L, B2, Common) ; * cholmod_l_free_dense (&X, Common) ; * X = cholmod_l_solve (sys, L, B3, Common) ; * cholmod_l_free_dense (&X, Common) ; * * Both methods work fine, but in the 2nd method with cholmod_solve, the * internal workspaces (Y and E) are allocated and freed on each call. * * Bset is an optional sparse column (pattern only) that specifies a set * of row indices. It is ignored if NULL, or if sys is CHOLMOD_P or * CHOLMOD_Pt. If it is present and not ignored, B must be a dense column * vector, and only entries B(i) where i is in the pattern of Bset are * considered. All others are treated as if they were zero (they are not * accessed). L must be a simplicial factorization, not supernodal. L is * converted from supernodal to simplicial if necessary. The solution X is * defined only for entries in the output sparse pattern of Xset. * The xtype (real/complex/zomplex) of L and B must match. * * NOTE: If Bset is present and L is supernodal, it is converted to simplicial * on output. */ int CHOLMOD(solve2) /* returns TRUE on success, FALSE on failure */ ( /* ---- input ---- */ int sys, /* system to solve */ cholmod_factor *L, /* factorization to use */ cholmod_dense *B, /* right-hand-side */ cholmod_sparse *Bset, /* ---- output --- */ cholmod_dense **X_Handle, /* solution, allocated if need be */ cholmod_sparse **Xset_Handle, /* ---- workspace */ cholmod_dense **Y_Handle, /* workspace, or NULL */ cholmod_dense **E_Handle, /* workspace, or NULL */ /* --------------- */ cholmod_common *Common ) { double *Yx, *Yz, *Bx, *Bz, *Xx, *Xz ; cholmod_dense *Y = NULL, *X = NULL ; cholmod_sparse *C, *Yset, C_header, Yset_header, *Xset ; Int *Perm = NULL, *IPerm = NULL ; Int n, nrhs, ncols, ctype, xtype, k1, nr, ytype, k, blen, p, i, d, nrow ; Int Cp [2], Ysetp [2], *Ci, *Yseti, ysetlen ; Int *Bsetp, *Bseti, *Bsetnz, *Xseti, *Xsetp, *Iwork ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_NULL (B, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (B, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; if (sys < CHOLMOD_A || sys > CHOLMOD_Pt) { ERROR (CHOLMOD_INVALID, "invalid system") ; return (FALSE) ; } DEBUG (CHOLMOD(dump_factor) (L, "L", Common)) ; DEBUG (CHOLMOD(dump_dense) (B, "B", Common)) ; nrhs = B->ncol ; n = (Int) L->n ; d = (Int) B->d ; nrow = (Int) B->nrow ; if (d < n || nrow != n) { ERROR (CHOLMOD_INVALID, "dimensions of L and B do not match") ; return (FALSE) ; } if (Bset) { if (nrhs != 1) { ERROR (CHOLMOD_INVALID, "Bset requires a single right-hand side") ; return (FALSE) ; } if (L->xtype != B->xtype) { ERROR (CHOLMOD_INVALID, "Bset requires xtype of L and B to match") ; return (FALSE) ; } DEBUG (CHOLMOD(dump_sparse) (Bset, "Bset", Common)) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if ((sys == CHOLMOD_P || sys == CHOLMOD_Pt || sys == CHOLMOD_A) && L->ordering != CHOLMOD_NATURAL) { /* otherwise, Perm is NULL, and the identity permutation is used */ Perm = L->Perm ; } /* ---------------------------------------------------------------------- */ /* allocate the result X (or resuse the space from a prior call) */ /* ---------------------------------------------------------------------- */ ctype = (Common->prefer_zomplex) ? CHOLMOD_ZOMPLEX : CHOLMOD_COMPLEX ; if (Bset) { xtype = L->xtype ; } else if (sys == CHOLMOD_P || sys == CHOLMOD_Pt) { /* x=Pb and x=P'b return X real if B is real; X is the preferred * complex/zcomplex type if B is complex or zomplex */ xtype = (B->xtype == CHOLMOD_REAL) ? CHOLMOD_REAL : ctype ; } else if (L->xtype == CHOLMOD_REAL && B->xtype == CHOLMOD_REAL) { /* X is real if both L and B are real */ xtype = CHOLMOD_REAL ; } else { /* X is complex, use the preferred complex/zomplex type */ xtype = ctype ; } /* ensure X has the right size and type */ X = CHOLMOD(ensure_dense) (X_Handle, n, nrhs, n, xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* solve using L, D, L', P, or some combination */ /* ---------------------------------------------------------------------- */ if (Bset) { /* ------------------------------------------------------------------ */ /* solve for a subset of x, with a sparse b */ /* ------------------------------------------------------------------ */ Int save_realloc_state ; #ifndef NSUPERNODAL /* convert a supernodal L to simplicial when using Bset */ if (L->is_super) { /* Can only use Bset on a simplicial factorization. The supernodal * factor L is converted to simplicial, leaving the xtype unchanged * (real, complex, or zomplex). Since the supernodal factorization * is already LL', it is left in that form. This conversion uses * the ll_super_to_simplicial_numeric function in * cholmod_change_factor. */ CHOLMOD(change_factor) ( CHOLMOD_REAL, /* ignored, since L is already numeric */ TRUE, /* convert to LL' (no change to num. values) */ FALSE, /* convert to simplicial */ FALSE, /* do not pack the columns of L */ FALSE, /* (ignored) */ L, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory, L is returned unchanged */ return (FALSE) ; } } #endif /* L, X, and B are all the same xtype */ /* ensure Y is the the right size */ Y = CHOLMOD(ensure_dense) (Y_Handle, 1, n, 1, L->xtype, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (FALSE) ; } /* ------------------------------------------------------------------ */ /* get the inverse permutation, constructing it if needed */ /* ------------------------------------------------------------------ */ DEBUG (CHOLMOD (dump_perm) (Perm, n,n, "Perm", Common)) ; if ((sys == CHOLMOD_A || sys == CHOLMOD_P) && Perm != NULL) { /* The inverse permutation IPerm is used for the c=Pb step, which is needed only for solving Ax=b or x=Pb. No other steps should use IPerm */ if (L->IPerm == NULL) { /* construct the inverse permutation. This is done only once * and then stored in L permanently. */ L->IPerm = CHOLMOD(malloc) (n, sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (FALSE) ; } IPerm = L->IPerm ; for (k = 0 ; k < n ; k++) { IPerm [Perm [k]] = k ; } } /* x=A\b and x=Pb both need IPerm */ IPerm = L->IPerm ; } if (sys == CHOLMOD_P) { /* x=Pb needs to turn off the subsequent x=P'b permutation */ Perm = NULL ; } DEBUG (CHOLMOD (dump_perm) (Perm, n,n, "Perm", Common)) ; DEBUG (CHOLMOD (dump_perm) (IPerm, n,n, "IPerm", Common)) ; /* ------------------------------------------------------------------ */ /* ensure Xset is the right size and type */ /* ------------------------------------------------------------------ */ /* Xset is n-by-1, nzmax >= n, pattern-only, packed, unsorted */ Xset = *Xset_Handle ; if (Xset == NULL || (Int) Xset->nrow != n || (Int) Xset->ncol != 1 || (Int) Xset->nzmax < n || Xset->itype != CHOLMOD_PATTERN) { /* this is done only once, for the 1st call to cholmod_solve */ CHOLMOD(free_sparse) (Xset_Handle, Common) ; Xset = CHOLMOD(allocate_sparse) (n, 1, n, FALSE, TRUE, 0, CHOLMOD_PATTERN, Common) ; *Xset_Handle = Xset ; } Xset->sorted = FALSE ; Xset->stype = 0 ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (FALSE) ; } /* -------------------------------------------------------------- */ /* ensure Flag of size n, and 3*n Int workspace is available */ /* -------------------------------------------------------------- */ /* does no work if prior calls already allocated enough space */ CHOLMOD(allocate_work) (n, 3*n, 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (FALSE) ; } /* [ use Iwork (n:3n-1) for Ci and Yseti */ Iwork = Common->Iwork ; /* Iwork (0:n-1) is not used because it is used by check_perm, print_perm, check_sparse, and print_sparse */ Ci = Iwork + n ; Yseti = Ci + n ; /* reallocating workspace would break Ci and Yseti */ save_realloc_state = Common->no_workspace_reallocate ; Common->no_workspace_reallocate = TRUE ; /* -------------------------------------------------------------- */ /* C = permuted Bset, to correspond to the permutation of L */ /* -------------------------------------------------------------- */ /* C = IPerm (Bset) */ DEBUG (CHOLMOD(dump_sparse) (Bset, "Bset", Common)) ; Bsetp = Bset->p ; Bseti = Bset->i ; Bsetnz = Bset->nz ; blen = (Bset->packed) ? Bsetp [1] : Bsetnz [0] ; /* C = spones (P*B) or C = spones (B) if IPerm is NULL */ C = &C_header ; C->nrow = n ; C->ncol = 1 ; C->nzmax = n ; C->packed = TRUE ; C->stype = 0 ; C->itype = ITYPE ; C->xtype = CHOLMOD_PATTERN ; C->dtype = CHOLMOD_DOUBLE ; C->nz = NULL ; C->p = Cp ; C->i = Ci ; C->x = NULL ; C->z = NULL ; C->sorted = FALSE ; Cp [0] = 0 ; Cp [1] = blen ; for (p = 0 ; p < blen ; p++) { Int iold = Bseti [p] ; Ci [p] = IPerm ? IPerm [iold] : iold ; } DEBUG (CHOLMOD (dump_sparse) (C, "C", Common)) ; /* create a sparse column Yset from Iwork (n:2n-1) */ Yset = &Yset_header ; Yset->nrow = n ; Yset->ncol = 1 ; Yset->nzmax = n ; Yset->packed = TRUE ; Yset->stype = 0 ; Yset->itype = ITYPE ; Yset->xtype = CHOLMOD_PATTERN ; Yset->dtype = CHOLMOD_DOUBLE ; Yset->nz = NULL ; Yset->p = Ysetp ; Yset->i = Yseti ; Yset->x = NULL ; Yset->z = NULL ; Yset->sorted = FALSE ; Ysetp [0] = 0 ; Ysetp [1] = 0 ; DEBUG (CHOLMOD (dump_sparse) (Yset, "Yset empty", Common)) ; /* -------------------------------------------------------------- */ /* Yset = nonzero pattern of L\C, or just C itself */ /* -------------------------------------------------------------- */ /* this takes O(ysetlen) time */ if (sys == CHOLMOD_P || sys == CHOLMOD_Pt || sys == CHOLMOD_D) { Ysetp [1] = blen ; for (p = 0 ; p < blen ; p++) { Yseti [p] = Ci [p] ; } } else { if (!CHOLMOD(lsolve_pattern) (C, L, Yset, Common)) { Common->no_workspace_reallocate = save_realloc_state ; return (FALSE) ; } } DEBUG (CHOLMOD (dump_sparse) (Yset, "Yset", Common)) ; /* -------------------------------------------------------------- */ /* clear the parts of Y that we will use in the solve */ /* -------------------------------------------------------------- */ Yx = Y->x ; Yz = Y->z ; ysetlen = Ysetp [1] ; switch (L->xtype) { case CHOLMOD_REAL: for (p = 0 ; p < ysetlen ; p++) { i = Yseti [p] ; Yx [i] = 0 ; } break ; case CHOLMOD_COMPLEX: for (p = 0 ; p < ysetlen ; p++) { i = Yseti [p] ; Yx [2*i ] = 0 ; Yx [2*i+1] = 0 ; } break ; case CHOLMOD_ZOMPLEX: for (p = 0 ; p < ysetlen ; p++) { i = Yseti [p] ; Yx [i] = 0 ; Yz [i] = 0 ; } break ; } DEBUG (CHOLMOD (dump_dense) (Y, "Y (Yset) = 0", Common)) ; /* -------------------------------------------------------------- */ /* scatter and permute B into Y */ /* -------------------------------------------------------------- */ /* Y (C) = B (Bset) */ Bx = B->x ; Bz = B->z ; switch (L->xtype) { case CHOLMOD_REAL: for (p = 0 ; p < blen ; p++) { Int iold = Bseti [p] ; Int inew = Ci [p] ; Yx [inew] = Bx [iold] ; } break ; case CHOLMOD_COMPLEX: for (p = 0 ; p < blen ; p++) { Int iold = Bseti [p] ; Int inew = Ci [p] ; Yx [2*inew ] = Bx [2*iold ] ; Yx [2*inew+1] = Bx [2*iold+1] ; } break ; case CHOLMOD_ZOMPLEX: for (p = 0 ; p < blen ; p++) { Int iold = Bseti [p] ; Int inew = Ci [p] ; Yx [inew] = Bx [iold] ; Yz [inew] = Bz [iold] ; } break ; } DEBUG (CHOLMOD (dump_dense) (Y, "Y (C) = B (Bset)", Common)) ; /* -------------------------------------------------------------- */ /* solve Y = (L' \ (L \ Y'))', or other system, with template */ /* -------------------------------------------------------------- */ /* the solve only iterates over columns in Yseti [0...ysetlen-1] */ if (! (sys == CHOLMOD_P || sys == CHOLMOD_Pt)) { switch (L->xtype) { case CHOLMOD_REAL: r_simplicial_solver (sys, L, Y, Yseti, ysetlen) ; break ; case CHOLMOD_COMPLEX: c_simplicial_solver (sys, L, Y, Yseti, ysetlen) ; break ; case CHOLMOD_ZOMPLEX: z_simplicial_solver (sys, L, Y, Yseti, ysetlen) ; break ; } } DEBUG (CHOLMOD (dump_dense) (Y, "Y after solve", Common)) ; /* -------------------------------------------------------------- */ /* X = P'*Y, but only for rows in Yset, and create Xset */ /* -------------------------------------------------------------- */ /* X (Perm (Yset)) = Y (Yset) */ Xx = X->x ; Xz = X->z ; Xseti = Xset->i ; Xsetp = Xset->p ; switch (L->xtype) { case CHOLMOD_REAL: for (p = 0 ; p < ysetlen ; p++) { Int inew = Yseti [p] ; Int iold = Perm ? Perm [inew] : inew ; Xx [iold] = Yx [inew] ; Xseti [p] = iold ; } break ; case CHOLMOD_COMPLEX: for (p = 0 ; p < ysetlen ; p++) { Int inew = Yseti [p] ; Int iold = Perm ? Perm [inew] : inew ; Xx [2*iold ] = Yx [2*inew] ; Xx [2*iold+1] = Yx [2*inew+1] ; Xseti [p] = iold ; } break ; case CHOLMOD_ZOMPLEX: for (p = 0 ; p < ysetlen ; p++) { Int inew = Yseti [p] ; Int iold = Perm ? Perm [inew] : inew ; Xx [iold] = Yx [inew] ; Xz [iold] = Yz [inew] ; Xseti [p] = iold ; } break ; } Xsetp [0] = 0 ; Xsetp [1] = ysetlen ; DEBUG (CHOLMOD(dump_sparse) (Xset, "Xset", Common)) ; DEBUG (CHOLMOD(dump_dense) (X, "X", Common)) ; Common->no_workspace_reallocate = save_realloc_state ; /* done using Iwork (n:3n-1) for Ci and Yseti ] */ } else if (sys == CHOLMOD_P) { /* ------------------------------------------------------------------ */ /* x = P*b */ /* ------------------------------------------------------------------ */ perm (B, Perm, 0, nrhs, X) ; } else if (sys == CHOLMOD_Pt) { /* ------------------------------------------------------------------ */ /* x = P'*b */ /* ------------------------------------------------------------------ */ iperm (B, Perm, 0, nrhs, X) ; } else if (L->is_super) { /* ------------------------------------------------------------------ */ /* solve using a supernodal LL' factorization */ /* ------------------------------------------------------------------ */ #ifndef NSUPERNODAL /* allocate workspace */ cholmod_dense *E ; Int dual ; Common->blas_ok = TRUE ; dual = (L->xtype == CHOLMOD_REAL && B->xtype != CHOLMOD_REAL) ? 2 : 1 ; Y = CHOLMOD(ensure_dense) (Y_Handle, n, dual*nrhs, n, L->xtype, Common); E = CHOLMOD(ensure_dense) (E_Handle, dual*nrhs, L->maxesize, dual*nrhs, L->xtype, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (FALSE) ; } perm (B, Perm, 0, nrhs, Y) ; /* Y = P*B */ if (sys == CHOLMOD_A || sys == CHOLMOD_LDLt) { CHOLMOD(super_lsolve) (L, Y, E, Common) ; /* Y = L\Y */ CHOLMOD(super_ltsolve) (L, Y, E, Common) ; /* Y = L'\Y*/ } else if (sys == CHOLMOD_L || sys == CHOLMOD_LD) { CHOLMOD(super_lsolve) (L, Y, E, Common) ; /* Y = L\Y */ } else if (sys == CHOLMOD_Lt || sys == CHOLMOD_DLt) { CHOLMOD(super_ltsolve) (L, Y, E, Common) ; /* Y = L'\Y*/ } iperm (Y, Perm, 0, nrhs, X) ; /* X = P'*Y */ if (CHECK_BLAS_INT && !Common->blas_ok) { /* Integer overflow in the BLAS. This is probably impossible, * since the BLAS were used to create the supernodal factorization. * It might be possible for the calls to the BLAS to differ between * factorization and forward/backsolves, however. This statement * is untested; it does not appear in the compiled code if * CHECK_BLAS_INT is true (when the same integer is used in * CHOLMOD and the BLAS. */ return (FALSE) ; } #else /* CHOLMOD Supernodal module not installed */ ERROR (CHOLMOD_NOT_INSTALLED,"Supernodal module not installed") ; #endif } else { /* ------------------------------------------------------------------ */ /* solve using a simplicial LL' or LDL' factorization */ /* ------------------------------------------------------------------ */ if (L->xtype == CHOLMOD_REAL && B->xtype == CHOLMOD_REAL) { /* L, B, and Y are all real */ /* solve with up to 4 columns of B at a time */ ncols = 4 ; nr = MAX (4, nrhs) ; ytype = CHOLMOD_REAL ; } else if (L->xtype == CHOLMOD_REAL) { /* L is real and B is complex or zomplex */ /* solve with one column of B (real/imag), at a time */ ncols = 1 ; nr = 2 ; ytype = CHOLMOD_REAL ; } else { /* L is complex or zomplex, B is real/complex/zomplex, Y has the * same complexity as L. Solve with one column of B at a time. */ ncols = 1 ; nr = 1 ; ytype = L->xtype ; } Y = CHOLMOD(ensure_dense) (Y_Handle, nr, n, nr, ytype, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (FALSE) ; } for (k1 = 0 ; k1 < nrhs ; k1 += ncols) { /* -------------------------------------------------------------- */ /* Y = B (P, k1:k1+ncols-1)' = (P * B (:,...))' */ /* -------------------------------------------------------------- */ ptrans (B, Perm, k1, ncols, Y) ; /* -------------------------------------------------------------- */ /* solve Y = (L' \ (L \ Y'))', or other system, with template */ /* -------------------------------------------------------------- */ switch (L->xtype) { case CHOLMOD_REAL: r_simplicial_solver (sys, L, Y, NULL, 0) ; break ; case CHOLMOD_COMPLEX: c_simplicial_solver (sys, L, Y, NULL, 0) ; break ; case CHOLMOD_ZOMPLEX: z_simplicial_solver (sys, L, Y, NULL, 0) ; break ; } /* -------------------------------------------------------------- */ /* X (P, k1:k2+ncols-1) = Y' */ /* -------------------------------------------------------------- */ iptrans (Y, Perm, k1, ncols, X) ; } } /* printf ("bye from solve2\n") ; */ DEBUG (CHOLMOD(dump_dense) (X, "X result", Common)) ; return (TRUE) ; } #endif Matrix/src/CHOLMOD/Cholesky/cholmod_rcond.c0000644000175100001440000001144212271765436020166 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/cholmod_rcond =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Return a rough estimate of the reciprocal of the condition number: * the minimum entry on the diagonal of L (or absolute entry of D for an LDL' * factorization) divided by the maximum entry (squared for LL'). L can be * real, complex, or zomplex. Returns -1 on error, 0 if the matrix is singular * or has a zero entry on the diagonal of L, 1 if the matrix is 0-by-0, or * min(diag(L))/max(diag(L)) otherwise. Never returns NaN; if L has a NaN on * the diagonal it returns zero instead. * * For an LL' factorization, (min(diag(L))/max(diag(L)))^2 is returned. * For an LDL' factorization, (min(diag(D))/max(diag(D))) is returned. */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === LMINMAX ============================================================== */ /* ========================================================================== */ /* Update lmin and lmax for one entry L(j,j) */ #define FIRST_LMINMAX(Ljj,lmin,lmax) \ { \ double ljj = Ljj ; \ if (IS_NAN (ljj)) \ { \ return (0) ; \ } \ lmin = ljj ; \ lmax = ljj ; \ } #define LMINMAX(Ljj,lmin,lmax) \ { \ double ljj = Ljj ; \ if (IS_NAN (ljj)) \ { \ return (0) ; \ } \ if (ljj < lmin) \ { \ lmin = ljj ; \ } \ else if (ljj > lmax) \ { \ lmax = ljj ; \ } \ } /* ========================================================================== */ /* === cholmod_rcond ======================================================== */ /* ========================================================================== */ double CHOLMOD(rcond) /* return min(diag(L)) / max(diag(L)) */ ( /* ---- input ---- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) { double lmin, lmax, rcond ; double *Lx ; Int *Lpi, *Lpx, *Super, *Lp ; Int n, e, nsuper, s, k1, k2, psi, psend, psx, nsrow, nscol, jj, j ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (L, EMPTY) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ n = L->n ; if (n == 0) { return (1) ; } if (L->minor < L->n) { return (0) ; } e = (L->xtype == CHOLMOD_COMPLEX) ? 2 : 1 ; if (L->is_super) { /* L is supernodal */ nsuper = L->nsuper ; /* number of supernodes in L */ Lpi = L->pi ; /* column pointers for integer pattern */ Lpx = L->px ; /* column pointers for numeric values */ Super = L->super ; /* supernode sizes */ Lx = L->x ; /* numeric values */ FIRST_LMINMAX (Lx [0], lmin, lmax) ; /* first diagonal entry of L */ for (s = 0 ; s < nsuper ; s++) { k1 = Super [s] ; /* first column in supernode s */ k2 = Super [s+1] ; /* last column in supernode is k2-1 */ psi = Lpi [s] ; /* first row index is L->s [psi] */ psend = Lpi [s+1] ; /* last row index is L->s [psend-1] */ psx = Lpx [s] ; /* first numeric entry is Lx [psx] */ nsrow = psend - psi ; /* supernode is nsrow-by-nscol */ nscol = k2 - k1 ; for (jj = 0 ; jj < nscol ; jj++) { LMINMAX (Lx [e * (psx + jj + jj*nsrow)], lmin, lmax) ; } } } else { /* L is simplicial */ Lp = L->p ; Lx = L->x ; if (L->is_ll) { /* LL' factorization */ FIRST_LMINMAX (Lx [Lp [0]], lmin, lmax) ; for (j = 1 ; j < n ; j++) { LMINMAX (Lx [e * Lp [j]], lmin, lmax) ; } } else { /* LDL' factorization, the diagonal might be negative */ FIRST_LMINMAX (fabs (Lx [Lp [0]]), lmin, lmax) ; for (j = 1 ; j < n ; j++) { LMINMAX (fabs (Lx [e * Lp [j]]), lmin, lmax) ; } } } rcond = lmin / lmax ; if (L->is_ll) { rcond = rcond*rcond ; } return (rcond) ; } #endif Matrix/src/CHOLMOD/Cholesky/cholmod_spsolve.c0000644000175100001440000002364312271765436020562 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/cholmod_spsolve ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Given an LL' or LDL' factorization of A, solve one of the following systems: * * Ax=b 0: CHOLMOD_A also applies the permutation L->Perm * LDL'x=b 1: CHOLMOD_LDLt does not apply L->Perm * LDx=b 2: CHOLMOD_LD * DL'x=b 3: CHOLMOD_DLt * Lx=b 4: CHOLMOD_L * L'x=b 5: CHOLMOD_Lt * Dx=b 6: CHOLMOD_D * x=Pb 7: CHOLMOD_P apply a permutation (P is L->Perm) * x=P'b 8: CHOLMOD_Pt apply an inverse permutation * * where b and x are sparse. If L and b are real, then x is real. Otherwise, * x is complex or zomplex, depending on the Common->prefer_zomplex parameter. * All xtypes of x and b are supported (real, complex, and zomplex). */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === EXPAND_AS_NEEDED ===================================================== */ /* ========================================================================== */ /* Double the size of the sparse matrix X, if we have run out of space. */ #define EXPAND_AS_NEEDED \ if (xnz >= nzmax) \ { \ nzmax *= 2 ; \ CHOLMOD(reallocate_sparse) (nzmax, X, Common) ; \ if (Common->status < CHOLMOD_OK) \ { \ CHOLMOD(free_sparse) (&X, Common) ; \ CHOLMOD(free_dense) (&X4, Common) ; \ CHOLMOD(free_dense) (&B4, Common) ; \ return (NULL) ; \ } \ Xi = X->i ; \ Xx = X->x ; \ Xz = X->z ; \ } /* ========================================================================== */ /* === cholmod_spolve ======================================================= */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(spsolve) /* returns the sparse solution X */ ( /* ---- input ---- */ int sys, /* system to solve */ cholmod_factor *L, /* factorization to use */ cholmod_sparse *B, /* right-hand-side */ /* --------------- */ cholmod_common *Common ) { double x, z ; cholmod_dense *X4, *B4 ; cholmod_sparse *X ; double *Bx, *Bz, *Xx, *Xz, *B4x, *B4z, *X4x, *X4z ; Int *Bi, *Bp, *Xp, *Xi, *Bnz ; Int n, nrhs, q, p, i, j, jfirst, jlast, packed, block, pend, j_n, xtype ; size_t xnz, nzmax ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (L, NULL) ; RETURN_IF_NULL (B, NULL) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ; RETURN_IF_XTYPE_INVALID (B, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ; if (L->n != B->nrow) { ERROR (CHOLMOD_INVALID, "dimensions of L and B do not match") ; return (NULL) ; } if (B->stype) { ERROR (CHOLMOD_INVALID, "B cannot be stored in symmetric mode") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace B4 and initial result X */ /* ---------------------------------------------------------------------- */ n = L->n ; nrhs = B->ncol ; /* X is real if both L and B are real, complex/zomplex otherwise */ xtype = (L->xtype == CHOLMOD_REAL && B->xtype == CHOLMOD_REAL) ? CHOLMOD_REAL : (Common->prefer_zomplex ? CHOLMOD_ZOMPLEX : CHOLMOD_COMPLEX) ; /* solve up to 4 columns at a time */ block = MIN (nrhs, 4) ; /* initial size of X is at most 4*n */ nzmax = n*block ; X = CHOLMOD(spzeros) (n, nrhs, nzmax, xtype, Common) ; B4 = CHOLMOD(zeros) (n, block, B->xtype, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&X, Common) ; CHOLMOD(free_dense) (&B4, Common) ; return (NULL) ; } Bp = B->p ; Bi = B->i ; Bx = B->x ; Bz = B->z ; Bnz = B->nz ; packed = B->packed ; Xp = X->p ; Xi = X->i ; Xx = X->x ; Xz = X->z ; xnz = 0 ; B4x = B4->x ; B4z = B4->z ; /* ---------------------------------------------------------------------- */ /* solve in chunks of 4 columns at a time */ /* ---------------------------------------------------------------------- */ for (jfirst = 0 ; jfirst < nrhs ; jfirst += block) { /* ------------------------------------------------------------------ */ /* adjust the number of columns of B4 */ /* ------------------------------------------------------------------ */ jlast = MIN (nrhs, jfirst + block) ; B4->ncol = jlast - jfirst ; /* ------------------------------------------------------------------ */ /* scatter B(jfirst:jlast-1) into B4 */ /* ------------------------------------------------------------------ */ for (j = jfirst ; j < jlast ; j++) { p = Bp [j] ; pend = (packed) ? (Bp [j+1]) : (p + Bnz [j]) ; j_n = (j-jfirst)*n ; switch (B->xtype) { case CHOLMOD_REAL: for ( ; p < pend ; p++) { B4x [Bi [p] + j_n] = Bx [p] ; } break ; case CHOLMOD_COMPLEX: for ( ; p < pend ; p++) { q = Bi [p] + j_n ; B4x [2*q ] = Bx [2*p ] ; B4x [2*q+1] = Bx [2*p+1] ; } break ; case CHOLMOD_ZOMPLEX: for ( ; p < pend ; p++) { q = Bi [p] + j_n ; B4x [q] = Bx [p] ; B4z [q] = Bz [p] ; } break ; } } /* ------------------------------------------------------------------ */ /* solve the system (X4 = A\B4 or other system) */ /* ------------------------------------------------------------------ */ X4 = CHOLMOD(solve) (sys, L, B4, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&X, Common) ; CHOLMOD(free_dense) (&B4, Common) ; CHOLMOD(free_dense) (&X4, Common) ; return (NULL) ; } ASSERT (X4->xtype == xtype) ; X4x = X4->x ; X4z = X4->z ; /* ------------------------------------------------------------------ */ /* append the solution onto X */ /* ------------------------------------------------------------------ */ for (j = jfirst ; j < jlast ; j++) { Xp [j] = xnz ; j_n = (j-jfirst)*n ; if ( xnz + n <= nzmax) { /* ---------------------------------------------------------- */ /* X is guaranteed to be large enough */ /* ---------------------------------------------------------- */ switch (xtype) { case CHOLMOD_REAL: for (i = 0 ; i < n ; i++) { x = X4x [i + j_n] ; if (IS_NONZERO (x)) { Xi [xnz] = i ; Xx [xnz] = x ; xnz++ ; } } break ; case CHOLMOD_COMPLEX: for (i = 0 ; i < n ; i++) { x = X4x [2*(i + j_n) ] ; z = X4x [2*(i + j_n)+1] ; if (IS_NONZERO (x) || IS_NONZERO (z)) { Xi [xnz] = i ; Xx [2*xnz ] = x ; Xx [2*xnz+1] = z ; xnz++ ; } } break ; case CHOLMOD_ZOMPLEX: for (i = 0 ; i < n ; i++) { x = X4x [i + j_n] ; z = X4z [i + j_n] ; if (IS_NONZERO (x) || IS_NONZERO (z)) { Xi [xnz] = i ; Xx [xnz] = x ; Xz [xnz] = z ; xnz++ ; } } break ; } } else { /* ---------------------------------------------------------- */ /* X may need to increase in size */ /* ---------------------------------------------------------- */ switch (xtype) { case CHOLMOD_REAL: for (i = 0 ; i < n ; i++) { x = X4x [i + j_n] ; if (IS_NONZERO (x)) { EXPAND_AS_NEEDED ; Xi [xnz] = i ; Xx [xnz] = x ; xnz++ ; } } break ; case CHOLMOD_COMPLEX: for (i = 0 ; i < n ; i++) { x = X4x [2*(i + j_n) ] ; z = X4x [2*(i + j_n)+1] ; if (IS_NONZERO (x) || IS_NONZERO (z)) { EXPAND_AS_NEEDED ; Xi [xnz] = i ; Xx [2*xnz ] = x ; Xx [2*xnz+1] = z ; xnz++ ; } } break ; case CHOLMOD_ZOMPLEX: for (i = 0 ; i < n ; i++) { x = X4x [i + j_n] ; z = X4z [i + j_n] ; if (IS_NONZERO (x) || IS_NONZERO (z)) { EXPAND_AS_NEEDED ; Xi [xnz] = i ; Xx [xnz] = x ; Xz [xnz] = z ; xnz++ ; } } break ; } } } CHOLMOD(free_dense) (&X4, Common) ; /* ------------------------------------------------------------------ */ /* clear B4 for next iteration */ /* ------------------------------------------------------------------ */ if (jlast < nrhs) { for (j = jfirst ; j < jlast ; j++) { p = Bp [j] ; pend = (packed) ? (Bp [j+1]) : (p + Bnz [j]) ; j_n = (j-jfirst)*n ; switch (B->xtype) { case CHOLMOD_REAL: for ( ; p < pend ; p++) { B4x [Bi [p] + j_n] = 0 ; } break ; case CHOLMOD_COMPLEX: for ( ; p < pend ; p++) { q = Bi [p] + j_n ; B4x [2*q ] = 0 ; B4x [2*q+1] = 0 ; } break ; case CHOLMOD_ZOMPLEX: for ( ; p < pend ; p++) { q = Bi [p] + j_n ; B4x [q] = 0 ; B4z [q] = 0 ; } break ; } } } } Xp [nrhs] = xnz ; /* ---------------------------------------------------------------------- */ /* reduce X in size, free workspace, and return result */ /* ---------------------------------------------------------------------- */ ASSERT (xnz <= X->nzmax) ; CHOLMOD(reallocate_sparse) (xnz, X, Common) ; ASSERT (Common->status == CHOLMOD_OK) ; CHOLMOD(free_dense) (&B4, Common) ; return (X) ; } #endif Matrix/src/CHOLMOD/Cholesky/cholmod_amd.c0000644000175100001440000001606212271765436017625 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/cholmod_amd ================================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* CHOLMOD interface to the AMD ordering routine. Orders A if the matrix is * symmetric. On output, Perm [k] = i if row/column i of A is the kth * row/column of P*A*P'. This corresponds to A(p,p) in MATLAB notation. * * If A is unsymmetric, cholmod_amd orders A*A'. On output, Perm [k] = i if * row/column i of A*A' is the kth row/column of P*A*A'*P'. This corresponds to * A(p,:)*A(p,:)' in MATLAB notation. If f is present, A(p,f)*A(p,f)' is * ordered. * * Computes the flop count for a subsequent LL' factorization, the number * of nonzeros in L, and the number of nonzeros in the matrix ordered (A, * A*A' or A(:,f)*A(:,f)'). * * workspace: Iwork (6*nrow). Head (nrow). * * Allocates a temporary copy of A+A' or A*A' (with * both upper and lower triangular parts) as input to AMD. * * Supports any xtype (pattern, real, complex, or zomplex) */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "amd.h" #include "cholmod_cholesky.h" #if (!defined (AMD_VERSION) || (AMD_VERSION < AMD_VERSION_CODE (2,0))) #error "AMD v2.0 or later is required" #endif /* ========================================================================== */ /* === cholmod_amd ========================================================== */ /* ========================================================================== */ int CHOLMOD(amd) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ Int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) { double Info [AMD_INFO], Control2 [AMD_CONTROL], *Control ; Int *Cp, *Len, *Nv, *Head, *Elen, *Degree, *Wi, *Iwork, *Next ; cholmod_sparse *C ; Int j, n, cnz ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; n = A->nrow ; RETURN_IF_NULL (Perm, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; if (n == 0) { /* nothing to do */ Common->fl = 0 ; Common->lnz = 0 ; Common->anz = 0 ; return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ /* Note: this is less than the space used in cholmod_analyze, so if * cholmod_amd is being called by that routine, no space will be * allocated. */ /* s = MAX (6*n, A->ncol) */ s = CHOLMOD(mult_size_t) (n, 6, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } s = MAX (s, A->ncol) ; CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } Iwork = Common->Iwork ; Degree = Iwork ; /* size n */ Wi = Iwork + n ; /* size n */ Len = Iwork + 2*((size_t) n) ; /* size n */ Nv = Iwork + 3*((size_t) n) ; /* size n */ Next = Iwork + 4*((size_t) n) ; /* size n */ Elen = Iwork + 5*((size_t) n) ; /* size n */ Head = Common->Head ; /* size n+1, but only n is used */ /* ---------------------------------------------------------------------- */ /* construct the input matrix for AMD */ /* ---------------------------------------------------------------------- */ if (A->stype == 0) { /* C = A*A' or A(:,f)*A(:,f)', add extra space of nnz(C)/2+n to C */ C = CHOLMOD(aat) (A, fset, fsize, -2, Common) ; } else { /* C = A+A', but use only the upper triangular part of A if A->stype = 1 * and only the lower part of A if A->stype = -1. Add extra space of * nnz(C)/2+n to C. */ C = CHOLMOD(copy) (A, 0, -2, Common) ; } if (Common->status < CHOLMOD_OK) { /* out of memory, fset invalid, or other error */ return (FALSE) ; } Cp = C->p ; for (j = 0 ; j < n ; j++) { Len [j] = Cp [j+1] - Cp [j] ; } /* C does not include the diagonal, and both upper and lower parts. * Common->anz includes the diagonal, and just the lower part of C */ cnz = Cp [n] ; Common->anz = cnz / 2 + n ; /* ---------------------------------------------------------------------- */ /* order C using AMD */ /* ---------------------------------------------------------------------- */ /* get parameters */ if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS) { /* use AMD defaults */ Control = NULL ; } else { Control = Control2 ; Control [AMD_DENSE] = Common->method [Common->current].prune_dense ; Control [AMD_AGGRESSIVE] = Common->method [Common->current].aggressive ; } /* AMD_2 does not use amd_malloc and amd_free, but set these pointers just * be safe. */ amd_malloc = Common->malloc_memory ; amd_free = Common->free_memory ; amd_calloc = Common->calloc_memory ; amd_realloc = Common->realloc_memory ; /* AMD_2 doesn't print anything either, but future versions might, * so set the amd_printf pointer too. */ amd_printf = Common->print_function ; #ifdef LONG amd_l2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen, Degree, Wi, Control, Info) ; #else amd_2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen, Degree, Wi, Control, Info) ; #endif /* LL' flop count. Need to subtract n for LL' flop count. Note that this * is a slight upper bound which is often exact (see AMD/Source/amd_2.c for * details). cholmod_analyze computes an exact flop count and fill-in. */ Common->fl = Info [AMD_NDIV] + 2 * Info [AMD_NMULTSUBS_LDL] + n ; /* Info [AMD_LNZ] excludes the diagonal */ Common->lnz = n + Info [AMD_LNZ] ; /* ---------------------------------------------------------------------- */ /* free the AMD workspace and clear the persistent workspace in Common */ /* ---------------------------------------------------------------------- */ ASSERT (IMPLIES (Common->status == CHOLMOD_OK, CHOLMOD(dump_perm) (Perm, n, n, "AMD2 perm", Common))) ; CHOLMOD(free_sparse) (&C, Common) ; for (j = 0 ; j <= n ; j++) { Head [j] = EMPTY ; } return (TRUE) ; } #endif Matrix/src/CHOLMOD/Cholesky/cholmod_factorize.c0000644000175100001440000003430112271765436021046 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/cholmod_factorize =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Computes the numerical factorization of a symmetric matrix. The primary * inputs to this routine are a sparse matrix A and the symbolic factor L from * cholmod_analyze or a prior numerical factor L. If A is symmetric, this * routine factorizes A(p,p)+beta*I (beta can be zero), where p is the * fill-reducing permutation (L->Perm). If A is unsymmetric, either * A(p,:)*A(p,:)'+beta*I or A(p,f)*A(p,f)'+beta*I is factorized. The set f and * the nonzero pattern of the matrix A must be the same as the matrix passed to * cholmod_analyze for the supernodal case. For the simplicial case, it can * be different, but it should be the same for best performance. beta is real. * * A simplicial factorization or supernodal factorization is chosen, based on * the type of the factor L. If L->is_super is TRUE, a supernodal LL' * factorization is computed. Otherwise, a simplicial numeric factorization * is computed, either LL' or LDL', depending on Common->final_ll. * * Once the factorization is complete, it can be left as is or optionally * converted into any simplicial numeric type, depending on the * Common->final_* parameters. If converted from a supernodal to simplicial * type, and the Common->final_resymbol parameter is true, then numerically * zero entries in L due to relaxed supernodal amalgamation are removed from * the simplicial factor (they are always left in the supernodal form of L). * Entries that are numerically zero but present in the simplicial symbolic * pattern of L are left in place (that is, the graph of L remains chordal). * This is required for the update/downdate/rowadd/rowdel routines to work * properly. * * workspace: Flag (nrow), Head (nrow+1), * if symmetric: Iwork (2*nrow+2*nsuper) * if unsymmetric: Iwork (2*nrow+MAX(2*nsuper,ncol)) * where nsuper is 0 if simplicial, or the # of relaxed supernodes in * L otherwise (nsuper <= nrow). * if simplicial: W (nrow). * Allocates up to two temporary copies of its input matrix (including * both pattern and numerical values). * * If the matrix is not positive definite the routine returns TRUE, but * sets Common->status to CHOLMOD_NOT_POSDEF and L->minor is set to the * column at which the failure occurred. Columns L->minor to L->n-1 are * set to zero. * * Supports any xtype (pattern, real, complex, or zomplex), except that the * input matrix A cannot be pattern-only. If L is simplicial, its numeric * xtype matches A on output. If L is supernodal, its xtype is real if A is * real, or complex if A is complex or zomplex. */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" #ifndef NSUPERNODAL #include "cholmod_supernodal.h" #endif /* ========================================================================== */ /* === cholmod_factorize ==================================================== */ /* ========================================================================== */ /* Factorizes PAP' (or PAA'P' if A->stype is 0), using a factor obtained * from cholmod_analyze. The analysis can be re-used simply by calling this * routine a second time with another matrix. A must have the same nonzero * pattern as that passed to cholmod_analyze. */ int CHOLMOD(factorize) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ /* ---- in/out --- */ cholmod_factor *L, /* resulting factorization */ /* --------------- */ cholmod_common *Common ) { double zero [2] ; zero [0] = 0 ; zero [1] = 0 ; return (CHOLMOD(factorize_p) (A, zero, NULL, 0, L, Common)) ; } /* ========================================================================== */ /* === cholmod_factorize_p ================================================== */ /* ========================================================================== */ /* Same as cholmod_factorize, but with more options. */ int CHOLMOD(factorize_p) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ double beta [2], /* factorize beta*I+A or beta*I+A'*A */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- in/out --- */ cholmod_factor *L, /* resulting factorization */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *S, *F, *A1, *A2 ; Int nrow, ncol, stype, convert, n, nsuper, grow2, status ; size_t s, t, uncol ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; nrow = A->nrow ; ncol = A->ncol ; n = L->n ; stype = A->stype ; if (L->n != A->nrow) { ERROR (CHOLMOD_INVALID, "A and L dimensions do not match") ; return (FALSE) ; } if (stype != 0 && nrow != ncol) { ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (FALSE) ; } DEBUG (CHOLMOD(dump_sparse) (A, "A for cholmod_factorize", Common)) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ nsuper = (L->is_super ? L->nsuper : 0) ; uncol = ((stype != 0) ? 0 : ncol) ; /* s = 2*nrow + MAX (uncol, 2*nsuper) */ s = CHOLMOD(mult_size_t) (nsuper, 2, &ok) ; s = MAX (uncol, s) ; t = CHOLMOD(mult_size_t) (nrow, 2, &ok) ; s = CHOLMOD(add_size_t) (s, t, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (nrow, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } S = NULL ; F = NULL ; A1 = NULL ; A2 = NULL ; /* convert to another form when done, if requested */ convert = !(Common->final_asis) ; /* ---------------------------------------------------------------------- */ /* perform supernodal LL' or simplicial LDL' factorization */ /* ---------------------------------------------------------------------- */ if (L->is_super) { #ifndef NSUPERNODAL /* ------------------------------------------------------------------ */ /* supernodal factorization */ /* ------------------------------------------------------------------ */ if (L->ordering == CHOLMOD_NATURAL) { /* -------------------------------------------------------------- */ /* natural ordering */ /* -------------------------------------------------------------- */ if (stype > 0) { /* S = tril (A'), F not needed */ /* workspace: Iwork (nrow) */ A1 = CHOLMOD(ptranspose) (A, 2, NULL, NULL, 0, Common) ; S = A1 ; } else if (stype < 0) { /* This is the fastest option for the natural ordering */ /* S = A; F not needed */ S = A ; } else { /* F = A(:,f)' */ /* workspace: Iwork (nrow) */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/ A1 = CHOLMOD(ptranspose) (A, 2, NULL, fset, fsize, Common) ; F = A1 ; /* S = A */ S = A ; } } else { /* -------------------------------------------------------------- */ /* permute the input matrix before factorization */ /* -------------------------------------------------------------- */ if (stype > 0) { /* This is the fastest option for factoring a permuted matrix */ /* S = tril (PAP'); F not needed */ /* workspace: Iwork (2*nrow) */ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ; S = A1 ; } else if (stype < 0) { /* A2 = triu (PAP') */ /* workspace: Iwork (2*nrow) */ A2 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ; /* S = tril (A2'); F not needed */ /* workspace: Iwork (nrow) */ A1 = CHOLMOD(ptranspose) (A2, 2, NULL, NULL, 0, Common) ; S = A1 ; CHOLMOD(free_sparse) (&A2, Common) ; ASSERT (A2 == NULL) ; } else { /* F = A(p,f)' */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, fset, fsize, Common) ; F = A1 ; /* S = F' */ /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (F, 2, NULL, NULL, 0, Common) ; S = A2 ; } } /* ------------------------------------------------------------------ */ /* supernodal factorization */ /* ------------------------------------------------------------------ */ /* workspace: Flag (nrow), Head (nrow+1), Iwork (2*nrow+2*nsuper) */ if (Common->status == CHOLMOD_OK) { CHOLMOD(super_numeric) (S, F, beta, L, Common) ; } status = Common->status ; ASSERT (IMPLIES (status >= CHOLMOD_OK, L->xtype != CHOLMOD_PATTERN)) ; /* ------------------------------------------------------------------ */ /* convert to final form, if requested */ /* ------------------------------------------------------------------ */ if (Common->status >= CHOLMOD_OK && convert) { /* workspace: none */ ok = CHOLMOD(change_factor) (L->xtype, Common->final_ll, Common->final_super, Common->final_pack, Common->final_monotonic, L, Common) ; if (ok && Common->final_resymbol && !(L->is_super)) { /* workspace: Flag (nrow), Head (nrow+1), * if symmetric: Iwork (2*nrow) * if unsymmetric: Iwork (2*nrow+ncol) */ CHOLMOD(resymbol_noperm) (S, fset, fsize, Common->final_pack, L, Common) ; } } #else /* ------------------------------------------------------------------ */ /* CHOLMOD Supernodal module not installed */ /* ------------------------------------------------------------------ */ status = CHOLMOD_NOT_INSTALLED ; ERROR (CHOLMOD_NOT_INSTALLED,"Supernodal module not installed") ; #endif } else { /* ------------------------------------------------------------------ */ /* simplicial LDL' factorization */ /* ------------------------------------------------------------------ */ /* Permute the input matrix A if necessary. cholmod_rowfac requires * triu(A) in column form for the symmetric case, and A in column form * for the unsymmetric case (the matrix S). The unsymmetric case * requires A in row form, or equivalently A' in column form (the * matrix F). */ if (L->ordering == CHOLMOD_NATURAL) { /* -------------------------------------------------------------- */ /* natural ordering */ /* -------------------------------------------------------------- */ if (stype > 0) { /* F is not needed, S = A */ S = A ; } else if (stype < 0) { /* F is not needed, S = A' */ /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (A, 2, NULL, NULL, 0, Common) ; S = A2 ; } else { /* F = A (:,f)' */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/ A1 = CHOLMOD(ptranspose) (A, 2, NULL, fset, fsize, Common) ; F = A1 ; S = A ; } } else { /* -------------------------------------------------------------- */ /* permute the input matrix before factorization */ /* -------------------------------------------------------------- */ if (stype > 0) { /* F = tril (A (p,p)') */ /* workspace: Iwork (2*nrow) */ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ; /* A2 = triu (F') */ /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (A1, 2, NULL, NULL, 0, Common) ; /* the symmetric case does not need F, free it and set to NULL*/ CHOLMOD(free_sparse) (&A1, Common) ; } else if (stype < 0) { /* A2 = triu (A (p,p)'), F not needed. This is the fastest * way to factorize a matrix using the simplicial routine * (cholmod_rowfac). */ /* workspace: Iwork (2*nrow) */ A2 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ; } else { /* F = A (p,f)' */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, fset, fsize, Common) ; F = A1 ; /* A2 = F' */ /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (F, 2, NULL, NULL, 0, Common) ; } S = A2 ; } /* ------------------------------------------------------------------ */ /* simplicial LDL' or LL' factorization */ /* ------------------------------------------------------------------ */ /* factorize beta*I+S (symmetric) or beta*I+F*F' (unsymmetric) */ /* workspace: Flag (nrow), W (nrow), Iwork (2*nrow) */ if (Common->status == CHOLMOD_OK) { grow2 = Common->grow2 ; L->is_ll = BOOLEAN (Common->final_ll) ; if (L->xtype == CHOLMOD_PATTERN && Common->final_pack) { /* allocate a factor with exactly the space required */ Common->grow2 = 0 ; } CHOLMOD(rowfac) (S, F, beta, 0, nrow, L, Common) ; Common->grow2 = grow2 ; } status = Common->status ; /* ------------------------------------------------------------------ */ /* convert to final form, if requested */ /* ------------------------------------------------------------------ */ if (Common->status >= CHOLMOD_OK && convert) { /* workspace: none */ CHOLMOD(change_factor) (L->xtype, L->is_ll, FALSE, Common->final_pack, Common->final_monotonic, L, Common) ; } } /* ---------------------------------------------------------------------- */ /* free A1 and A2 if they exist */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&A1, Common) ; CHOLMOD(free_sparse) (&A2, Common) ; Common->status = MAX (Common->status, status) ; return (Common->status >= CHOLMOD_OK) ; } #endif Matrix/src/CHOLMOD/Cholesky/cholmod_postorder.c0000644000175100001440000002275012271765436021106 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/cholmod_postorder =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Compute the postorder of a tree. */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === dfs ================================================================== */ /* ========================================================================== */ /* The code below includes both a recursive and non-recursive depth-first-search * of a tree. The recursive code is simpler, but can lead to stack overflow. * It is left here for reference, to understand what the non-recursive code * is computing. To try the recursive version, uncomment the following * #define, or compile the code with -DRECURSIVE. Be aware that stack * overflow may occur. #define RECURSIVE */ #ifdef RECURSIVE /* recursive version: a working code for reference only, not actual use */ static Int dfs /* return the new value of k */ ( Int p, /* start a DFS at node p */ Int k, /* start the node numbering at k */ Int Post [ ], /* Post ordering, modified on output */ Int Head [ ], /* Head [p] = youngest child of p; EMPTY on output */ Int Next [ ], /* Next [j] = sibling of j; unmodified */ Int Pstack [ ] /* unused */ ) { Int j ; /* start a DFS at each child of node p */ for (j = Head [p] ; j != EMPTY ; j = Next [j]) { /* start a DFS at child node j */ k = dfs (j, k, Post, Head, Next, Pstack) ; } Post [k++] = p ; /* order node p as the kth node */ Head [p] = EMPTY ; /* link list p no longer needed */ return (k) ; /* the next node will be numbered k */ } #else /* non-recursive version for actual use */ static Int dfs /* return the new value of k */ ( Int p, /* start the DFS at a root node p */ Int k, /* start the node numbering at k */ Int Post [ ], /* Post ordering, modified on output */ Int Head [ ], /* Head [p] = youngest child of p; EMPTY on output */ Int Next [ ], /* Next [j] = sibling of j; unmodified */ Int Pstack [ ] /* workspace of size n, undefined on input or output */ ) { Int j, phead ; /* put the root node on the stack */ Pstack [0] = p ; phead = 0 ; /* while the stack is not empty, do: */ while (phead >= 0) { /* grab the node p from top of the stack and get its youngest child j */ p = Pstack [phead] ; j = Head [p] ; if (j == EMPTY) { /* all children of p ordered. remove p from stack and order it */ phead-- ; Post [k++] = p ; /* order node p as the kth node */ } else { /* leave p on the stack. Start a DFS at child node j by putting * j on the stack and removing j from the list of children of p. */ Head [p] = Next [j] ; Pstack [++phead] = j ; } } return (k) ; /* the next node will be numbered k */ } #endif /* ========================================================================== */ /* === cholmod_postorder ==================================================== */ /* ========================================================================== */ /* Postorder a tree. The tree is either an elimination tree (the output from * from cholmod_etree) or a component tree (from cholmod_nested_dissection). * * An elimination tree is a complete tree of n nodes with Parent [j] > j or * Parent [j] = EMPTY if j is a root. On output Post [0..n-1] is a complete * permutation vector. * * A component tree is a subset of 0..n-1. Parent [j] = -2 if node j is not * in the component tree. Parent [j] = EMPTY if j is a root of the component * tree, and Parent [j] is in the range 0 to n-1 if j is in the component * tree but not a root. On output, Post [k] is defined only for nodes in * the component tree. Post [k] = j if node j is the kth node in the * postordered component tree, where k is in the range 0 to the number of * components minus 1. * * Node j is ignored and not included in the postorder if Parent [j] < EMPTY. * * As a result, check_parent (Parent, n,...) may fail on input, since * cholmod_check_parent assumes Parent is an elimination tree. Similarly, * cholmod_check_perm (Post, ...) may fail on output, since Post is a partial * permutation if Parent is a component tree. * * An optional node weight can be given. When starting a postorder at node j, * the children of j are ordered in increasing order of their weight. * If no weights are given (Weight is NULL) then children are ordered in * increasing order of their node number. The weight of a node must be in the * range 0 to n-1. Weights outside that range are silently converted to that * range (weights < 0 are treated as zero, and weights >= n are treated as n-1). * * * workspace: Head (n), Iwork (2*n) */ SuiteSparse_long CHOLMOD(postorder) /* return # of nodes postordered */ ( /* ---- input ---- */ Int *Parent, /* size n. Parent [j] = p if p is the parent of j */ size_t n, Int *Weight, /* size n, optional. Weight [j] is weight of node j */ /* ---- output --- */ Int *Post, /* size n. Post [k] = j is kth in postordered tree */ /* --------------- */ cholmod_common *Common ) { Int *Head, *Next, *Pstack, *Iwork ; Int j, p, k, w, nextj ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (Parent, EMPTY) ; RETURN_IF_NULL (Post, EMPTY) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 2*n */ s = CHOLMOD(mult_size_t) (n, 2, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (EMPTY) ; } CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (EMPTY) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Head = Common->Head ; /* size n+1, initially all EMPTY */ Iwork = Common->Iwork ; Next = Iwork ; /* size n (i/i/l) */ Pstack = Iwork + n ; /* size n (i/i/l) */ /* ---------------------------------------------------------------------- */ /* construct a link list of children for each node */ /* ---------------------------------------------------------------------- */ if (Weight == NULL) { /* in reverse order so children are in ascending order in each list */ for (j = n-1 ; j >= 0 ; j--) { p = Parent [j] ; if (p >= 0 && p < ((Int) n)) { /* add j to the list of children for node p */ Next [j] = Head [p] ; Head [p] = j ; } } /* Head [p] = j if j is the youngest (least-numbered) child of p */ /* Next [j1] = j2 if j2 is the next-oldest sibling of j1 */ } else { /* First, construct a set of link lists according to Weight. * * Whead [w] = j if node j is the first node in bucket w. * Next [j1] = j2 if node j2 follows j1 in a link list. */ Int *Whead = Pstack ; /* use Pstack as workspace for Whead [ */ for (w = 0 ; w < ((Int) n) ; w++) { Whead [w] = EMPTY ; } /* do in forward order, so nodes that ties are ordered by node index */ for (j = 0 ; j < ((Int) n) ; j++) { p = Parent [j] ; if (p >= 0 && p < ((Int) n)) { w = Weight [j] ; w = MAX (0, w) ; w = MIN (w, ((Int) n) - 1) ; /* place node j at the head of link list for weight w */ Next [j] = Whead [w] ; Whead [w] = j ; } } /* traverse weight buckets, placing each node in its parent's list */ for (w = n-1 ; w >= 0 ; w--) { for (j = Whead [w] ; j != EMPTY ; j = nextj) { nextj = Next [j] ; /* put node j in the link list of its parent */ p = Parent [j] ; ASSERT (p >= 0 && p < ((Int) n)) ; Next [j] = Head [p] ; Head [p] = j ; } } /* Whead no longer needed ] */ /* Head [p] = j if j is the lightest child of p */ /* Next [j1] = j2 if j2 is the next-heaviest sibling of j1 */ } /* ---------------------------------------------------------------------- */ /* start a DFS at each root node of the etree */ /* ---------------------------------------------------------------------- */ k = 0 ; for (j = 0 ; j < ((Int) n) ; j++) { if (Parent [j] == EMPTY) { /* j is the root of a tree; start a DFS here */ k = dfs (j, k, Post, Head, Next, Pstack) ; } } /* this would normally be EMPTY already, unless Parent is invalid */ for (j = 0 ; j < ((Int) n) ; j++) { Head [j] = EMPTY ; } PRINT1 (("postordered "ID" nodes\n", k)) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (k) ; } #endif Matrix/src/CHOLMOD/Cholesky/cholmod_analyze.c0000644000175100001440000010023012271765436020516 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/cholmod_analyze ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2013, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Order and analyze a matrix (either simplicial or supernodal), in prepartion * for numerical factorization via cholmod_factorize or via the "expert" * routines cholmod_rowfac and cholmod_super_numeric. * * symmetric case: A or A(p,p) * unsymmetric case: AA', A(p,:)*A(p,:)', A(:,f)*A(:,f)', or A(p,f)*A(p,f)' * * For the symmetric case, only the upper or lower triangular part of A is * accessed (depending on the type of A). LL'=A (or permuted A) is analzed. * For the unsymmetric case (LL'=AA' or permuted A). * * There can be no duplicate entries in p or f. p is of length m if A is * m-by-n. f can be length 0 to n. * * In both cases, the columns of A need not be sorted. A can be in packed * or unpacked form. * * Ordering options include: * * natural: A is not permuted to reduce fill-in * given: a permutation can be provided to this routine (UserPerm) * AMD: approximate minumum degree (AMD for the symmetric case, * COLAMD for the AA' case). * METIS: nested dissection with METIS_NodeND * NESDIS: nested dissection using METIS_NodeComputeSeparator, * typically followed by a constrained minimum degree * (CAMD for the symmetric case, CCOLAMD for the AA' case). * * Multiple ordering options can be tried (up to 9 of them), and the best one * is selected (the one that gives the smallest number of nonzeros in the * simplicial factor L). If one method fails, cholmod_analyze keeps going, and * picks the best among the methods that succeeded. This routine fails (and * returns NULL) if either initial memory allocation fails, all ordering methods * fail, or the supernodal analysis (if requested) fails. By default, the 9 * methods available are: * * 1) given permutation (skipped if UserPerm is NULL) * 2) AMD (symmetric case) or COLAMD (unsymmetric case) * 3) METIS with default parameters * 4) NESDIS with default parameters (stopping the partitioning when * the graph is of size nd_small = 200 or less, remove nodes with * more than max (16, prune_dense * sqrt (n)) nodes where * prune_dense = 10, and follow partitioning with CCOLAMD, a * constrained minimum degree ordering). * 5) natural * 6) NESDIS, nd_small = 20000, prune_dense = 10 * 7) NESDIS, nd_small = 4, prune_dense = 10, no min degree * 8) NESDIS, nd_small = 200, prune_dense = 0 * 9) COLAMD for A*A' or AMD for A * * By default, the first two are tried, and METIS is tried if AMD reports a high * flop count and fill-in. Let fl denote the flop count for the AMD, ordering, * nnz(L) the # of nonzeros in L, and nnz(tril(A)) (or A*A'). If * fl/nnz(L) >= 500 and nnz(L)/nnz(tril(A)) >= 5, then METIS is attempted. The * best ordering is used (UserPerm if given, AMD, and METIS if attempted). If * you do not have METIS, only the first two will be tried (user permutation, * if provided, and AMD/COLAMD). This default behavior is obtained when * Common->nmethods is zero. In this case, methods 0, 1, and 2 in * Common->method [..] are reset to User-provided, AMD, and METIS (or NESDIS * if Common->default_nesdis is set to the non-default value of TRUE), * respectively. * * You can modify these 9 methods and the number of methods tried by changing * parameters in the Common argument. If you know the best ordering for your * matrix, set Common->nmethods to 1 and set Common->method[0].ordering to the * requested ordering method. Parameters for each method can also be modified * (refer to cholmod.h for details). * * Note that it is possible for METIS to terminate your program if it runs out * of memory. This is not the case for any CHOLMOD or minimum degree ordering * routine (AMD, COLAMD, CAMD, CCOLAMD, or CSYMAMD). Since NESDIS relies on * METIS, it too can terminate your program. * * The factor L is returned as simplicial symbolic (L->is_super FALSE) if * Common->supernodal <= CHOLMOD_SIMPLICIAL (0) or as supernodal symbolic if * Common->supernodal >= CHOLMOD_SUPERNODAL (2). If Common->supernodal is * equal to CHOLMOD_AUTO (1), then L is simplicial if the flop count per * nonzero in L is less than Common->supernodal_switch (default: 40), and * is returned as a supernodal factor otherwise. * * In both cases, L->xtype is CHOLMOD_PATTERN. * A subsequent call to cholmod_factorize will perform a * simplicial or supernodal factorization, depending on the type of L. * * For the simplicial case, L contains the fill-reducing permutation (L->Perm) * and the counts of nonzeros in each column of L (L->ColCount). For the * supernodal case, L also contains the nonzero pattern of each supernode. * * workspace: Flag (nrow), Head (nrow+1) * if symmetric: Iwork (6*nrow) * if unsymmetric: Iwork (6*nrow+ncol). * calls various ordering routines, which typically allocate O(nnz(A)) * temporary workspace ((2 to 3)*nnz(A) * sizeof (Int) is typical, but it * can be much higher if A*A' must be explicitly formed for METIS). Also * allocates up to 2 temporary (permuted/transpose) copies of the nonzero * pattern of A, and up to 3*n*sizeof(Int) additional workspace. * * Supports any xtype (pattern, real, complex, or zomplex) */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" #ifndef NSUPERNODAL #include "cholmod_supernodal.h" #endif #ifndef NPARTITION #include "cholmod_partition.h" #endif /* ========================================================================== */ /* === cholmod_analyze ====================================================== */ /* ========================================================================== */ /* Orders and analyzes A, AA', PAP', or PAA'P' and returns a symbolic factor * that can later be passed to cholmod_factorize. */ cholmod_factor *CHOLMOD(analyze) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order and analyze */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(analyze_p2) (TRUE, A, NULL, NULL, 0, Common)) ; } /* ========================================================================== */ /* === cholmod_analyze_p ==================================================== */ /* ========================================================================== */ /* Orders and analyzes A, AA', PAP', PAA'P', FF', or PFF'P and returns a * symbolic factor that can later be passed to cholmod_factorize, where * F = A(:,fset) if fset is not NULL and A->stype is zero. * UserPerm is tried if non-NULL. */ cholmod_factor *CHOLMOD(analyze_p) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order and analyze */ Int *UserPerm, /* user-provided permutation, size A->nrow */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(analyze_p2) (TRUE, A, UserPerm, fset, fsize, Common)) ; } /* ========================================================================== */ /* === permute_matrices ===================================================== */ /* ========================================================================== */ /* Permute and transpose a matrix. Allocates the A1 and A2 matrices, if needed, * or returns them as NULL if not needed. */ static int permute_matrices ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to permute */ Int ordering, /* ordering method used */ Int *Perm, /* fill-reducing permutation */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ Int do_rowcolcounts,/* if TRUE, compute both S and F. If FALSE, only * S is needed for the symmetric case, and only F for * the unsymmetric case */ /* ---- output --- */ cholmod_sparse **A1_handle, /* see comments below for A1, A2, S, F */ cholmod_sparse **A2_handle, cholmod_sparse **S_handle, cholmod_sparse **F_handle, /* --------------- */ cholmod_common *Common ) { cholmod_sparse *A1, *A2, *S, *F ; *A1_handle = NULL ; *A2_handle = NULL ; *S_handle = NULL ; *F_handle = NULL ; A1 = NULL ; A2 = NULL ; if (ordering == CHOLMOD_NATURAL) { /* ------------------------------------------------------------------ */ /* natural ordering of A */ /* ------------------------------------------------------------------ */ if (A->stype < 0) { /* symmetric lower case: A already in lower form, so S=A' */ /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (A, 0, NULL, NULL, 0, Common) ; F = A ; S = A2 ; } else if (A->stype > 0) { /* symmetric upper case: F = pattern of triu (A)', S = A */ /* workspace: Iwork (nrow) */ if (do_rowcolcounts) { /* F not needed for symmetric case if do_rowcolcounts FALSE */ A1 = CHOLMOD(ptranspose) (A, 0, NULL, fset, fsize, Common) ; } F = A1 ; S = A ; } else { /* unsymmetric case: F = pattern of A (:,f)', S = A */ /* workspace: Iwork (nrow if no fset, MAX(nrow,ncol) if fset) */ A1 = CHOLMOD(ptranspose) (A, 0, NULL, fset, fsize, Common) ; F = A1 ; S = A ; } } else { /* ------------------------------------------------------------------ */ /* A is permuted */ /* ------------------------------------------------------------------ */ if (A->stype < 0) { /* symmetric lower case: S = tril (A (p,p))' and F = S' */ /* workspace: Iwork (2*nrow) */ A2 = CHOLMOD(ptranspose) (A, 0, Perm, NULL, 0, Common) ; S = A2 ; /* workspace: Iwork (nrow) */ if (do_rowcolcounts) { /* F not needed for symmetric case if do_rowcolcounts FALSE */ A1 = CHOLMOD(ptranspose) (A2, 0, NULL, NULL, 0, Common) ; } F = A1 ; } else if (A->stype > 0) { /* symmetric upper case: F = triu (A (p,p))' and S = F' */ /* workspace: Iwork (2*nrow) */ A1 = CHOLMOD(ptranspose) (A, 0, Perm, NULL, 0, Common) ; F = A1 ; /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (A1, 0, NULL, NULL, 0, Common) ; S = A2 ; } else { /* unsymmetric case: F = A (p,f)' and S = F' */ /* workspace: Iwork (nrow if no fset, MAX(nrow,ncol) if fset) */ A1 = CHOLMOD(ptranspose) (A, 0, Perm, fset, fsize, Common) ; F = A1 ; if (do_rowcolcounts) { /* S not needed for unsymmetric case if do_rowcolcounts FALSE */ /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (A1, 0, NULL, NULL, 0, Common) ; } S = A2 ; } } /* If any cholmod_*transpose fails, one or more matrices will be NULL */ *A1_handle = A1 ; *A2_handle = A2 ; *S_handle = S ; *F_handle = F ; return (Common->status == CHOLMOD_OK) ; } /* ========================================================================== */ /* === cholmod_analyze_ordering ============================================= */ /* ========================================================================== */ /* Given a matrix A and its fill-reducing permutation, compute the elimination * tree, its (non-weighted) postordering, and the number of nonzeros in each * column of L. Also computes the flop count, the total nonzeros in L, and * the nonzeros in A (Common->fl, Common->lnz, and Common->anz). * * The column counts of L, flop count, and other statistics from * cholmod_rowcolcounts are not computed if ColCount is NULL. * * workspace: Iwork (2*nrow if symmetric, 2*nrow+ncol if unsymmetric), * Flag (nrow), Head (nrow+1) */ int CHOLMOD(analyze_ordering) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ int ordering, /* ordering method used */ Int *Perm, /* size n, fill-reducing permutation to analyze */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ Int *Parent, /* size n, elimination tree */ Int *Post, /* size n, postordering of elimination tree */ Int *ColCount, /* size n, nnz in each column of L */ /* ---- workspace */ Int *First, /* size n workspace for cholmod_postorder */ Int *Level, /* size n workspace for cholmod_postorder */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *A1, *A2, *S, *F ; Int n, ok, do_rowcolcounts ; /* check inputs */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; n = A->nrow ; do_rowcolcounts = (ColCount != NULL) ; /* permute A according to Perm and fset */ ok = permute_matrices (A, ordering, Perm, fset, fsize, do_rowcolcounts, &A1, &A2, &S, &F, Common) ; /* find etree of S (symmetric upper/lower case) or F (unsym case) */ /* workspace: symmmetric: Iwork (nrow), unsym: Iwork (nrow+ncol) */ ok = ok && CHOLMOD(etree) (A->stype ? S:F, Parent, Common) ; /* postorder the etree (required by cholmod_rowcolcounts) */ /* workspace: Iwork (2*nrow) */ ok = ok && (CHOLMOD(postorder) (Parent, n, NULL, Post, Common) == n) ; /* cholmod_postorder doesn't set Common->status if it returns < n */ Common->status = (!ok && Common->status == CHOLMOD_OK) ? CHOLMOD_INVALID : Common->status ; /* analyze LL'=S or SS' or S(:,f)*S(:,f)' */ /* workspace: * if symmetric: Flag (nrow), Iwork (2*nrow) * if unsymmetric: Flag (nrow), Iwork (2*nrow+ncol), Head (nrow+1) */ if (do_rowcolcounts) { ok = ok && CHOLMOD(rowcolcounts) (A->stype ? F:S, fset, fsize, Parent, Post, NULL, ColCount, First, Level, Common) ; } /* free temporary matrices and return result */ CHOLMOD(free_sparse) (&A1, Common) ; CHOLMOD(free_sparse) (&A2, Common) ; return (ok) ; } /* ========================================================================== */ /* === Free workspace and return L ========================================== */ /* ========================================================================== */ #define FREE_WORKSPACE_AND_RETURN \ { \ Common->no_workspace_reallocate = FALSE ; \ CHOLMOD(free) (n, sizeof (Int), Lparent, Common) ; \ CHOLMOD(free) (n, sizeof (Int), Perm, Common) ; \ CHOLMOD(free) (n, sizeof (Int), ColCount, Common) ; \ if (Common->status < CHOLMOD_OK) \ { \ CHOLMOD(free_factor) (&L, Common) ; \ } \ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; \ return (L) ; \ } /* ========================================================================== */ /* === cholmod_analyze_p2 =================================================== */ /* ========================================================================== */ /* Ordering and analysis for sparse Cholesky or sparse QR. CHOLMOD itself * always uses for_cholesky = TRUE. The for_cholesky = FALSE option is * for SuiteSparseQR only. */ cholmod_factor *CHOLMOD(analyze_p2) ( /* ---- input ---- */ int for_cholesky, /* if TRUE, then analyze for Cholesky; else for QR */ cholmod_sparse *A, /* matrix to order and analyze */ Int *UserPerm, /* user-provided permutation, size A->nrow */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* --------------- */ cholmod_common *Common ) { double lnz_best ; Int *First, *Level, *Work4n, *Cmember, *CParent, *ColCount, *Lperm, *Parent, *Post, *Perm, *Lparent, *Lcolcount ; cholmod_factor *L ; Int k, n, ordering, method, nmethods, status, default_strategy, ncol, uncol, skip_analysis, skip_best ; Int amd_backup ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; Common->status = CHOLMOD_OK ; status = CHOLMOD_OK ; Common->selected = EMPTY ; Common->called_nd = FALSE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ n = A->nrow ; ncol = A->ncol ; uncol = (A->stype == 0) ? (A->ncol) : 0 ; /* ---------------------------------------------------------------------- */ /* set the default strategy */ /* ---------------------------------------------------------------------- */ lnz_best = (double) EMPTY ; skip_best = FALSE ; nmethods = MIN (Common->nmethods, CHOLMOD_MAXMETHODS) ; nmethods = MAX (0, nmethods) ; #ifndef NDEBUG PRINT1 (("cholmod_analyze_p2 :: nmethods "ID"\n", nmethods)) ; for (method = 0 ; method < nmethods ; method++) { PRINT1 ((" "ID": ordering "ID"\n", method, Common->method [method].ordering)) ; } #endif default_strategy = (nmethods == 0) ; if (default_strategy) { /* default strategy: try UserPerm, if given. Try AMD for A, or AMD * to order A*A'. Try METIS for the symmetric case only if AMD reports * a high degree of fill-in and flop count. METIS is not tried if the * Partition Module isn't installed. If Common->default_nesdis is * TRUE, then NESDIS is used as the 3rd ordering instead. */ Common->method [0].ordering = CHOLMOD_GIVEN ;/* skip if UserPerm NULL */ Common->method [1].ordering = CHOLMOD_AMD ; Common->method [2].ordering = (Common->default_nesdis ? CHOLMOD_NESDIS : CHOLMOD_METIS) ; amd_backup = FALSE ; #ifndef NPARTITION nmethods = 3 ; #else nmethods = 2 ; #endif } else { /* If only METIS and NESDIS are selected, or if 2 or more methods are * being tried, then enable AMD backup */ amd_backup = (nmethods > 1) || (nmethods == 1 && (Common->method [0].ordering == CHOLMOD_METIS || Common->method [0].ordering == CHOLMOD_NESDIS)) ; } #ifdef NSUPERNODAL /* CHOLMOD Supernodal module not installed, just do simplicial analysis */ Common->supernodal = CHOLMOD_SIMPLICIAL ; #endif /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* Note: enough space needs to be allocated here so that routines called by * cholmod_analyze do not reallocate the space. */ /* s = 6*n + uncol */ s = CHOLMOD(mult_size_t) (n, 6, &ok) ; s = CHOLMOD(add_size_t) (s, uncol, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ensure that subsequent routines, called by cholmod_analyze, do not * reallocate any workspace. This is set back to FALSE in the * FREE_WORKSPACE_AND_RETURN macro, which is the only way this function * returns to its caller. */ Common->no_workspace_reallocate = TRUE ; /* Use the last 4*n Int's in Iwork for Parent, First, Level, and Post, since * other CHOLMOD routines will use the first 2n+uncol space. The ordering * routines (cholmod_amd, cholmod_colamd, cholmod_ccolamd, cholmod_metis) * are an exception. They can use all 6n + ncol space, since the contents * of Parent, First, Level, and Post are not needed across calls to those * routines. */ Work4n = Common->Iwork ; Work4n += 2*((size_t) n) + uncol ; Parent = Work4n ; First = Work4n + n ; Level = Work4n + 2*((size_t) n) ; Post = Work4n + 3*((size_t) n) ; /* note that this assignment means that cholmod_nested_dissection, * cholmod_ccolamd, and cholmod_camd can use only the first 4n+uncol * space in Common->Iwork */ Cmember = Post ; CParent = Level ; /* ---------------------------------------------------------------------- */ /* allocate more workspace, and an empty simplicial symbolic factor */ /* ---------------------------------------------------------------------- */ L = CHOLMOD(allocate_factor) (n, Common) ; Lparent = CHOLMOD(malloc) (n, sizeof (Int), Common) ; Perm = CHOLMOD(malloc) (n, sizeof (Int), Common) ; ColCount = CHOLMOD(malloc) (n, sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ FREE_WORKSPACE_AND_RETURN ; } Lperm = L->Perm ; Lcolcount = L->ColCount ; Common->anz = EMPTY ; /* ---------------------------------------------------------------------- */ /* try all the requested ordering options and backup to AMD if needed */ /* ---------------------------------------------------------------------- */ /* turn off error handling [ */ Common->try_catch = TRUE ; for (method = 0 ; method <= nmethods ; method++) { /* ------------------------------------------------------------------ */ /* determine the method to try */ /* ------------------------------------------------------------------ */ Common->fl = EMPTY ; Common->lnz = EMPTY ; skip_analysis = FALSE ; if (method == nmethods) { /* All methods failed: backup to AMD */ if (Common->selected == EMPTY && amd_backup) { PRINT1 (("All methods requested failed: backup to AMD\n")) ; ordering = CHOLMOD_AMD ; } else { break ; } } else { ordering = Common->method [method].ordering ; } Common->current = method ; PRINT1 (("method "ID": Try method: "ID"\n", method, ordering)) ; /* ------------------------------------------------------------------ */ /* find the fill-reducing permutation */ /* ------------------------------------------------------------------ */ if (ordering == CHOLMOD_NATURAL) { /* -------------------------------------------------------------- */ /* natural ordering */ /* -------------------------------------------------------------- */ for (k = 0 ; k < n ; k++) { Perm [k] = k ; } } else if (ordering == CHOLMOD_GIVEN) { /* -------------------------------------------------------------- */ /* use given ordering of A, if provided */ /* -------------------------------------------------------------- */ if (UserPerm == NULL) { /* this is not an error condition */ PRINT1 (("skip, no user perm given\n")) ; continue ; } for (k = 0 ; k < n ; k++) { /* UserPerm is checked in cholmod_ptranspose */ Perm [k] = UserPerm [k] ; } } else if (ordering == CHOLMOD_AMD) { /* -------------------------------------------------------------- */ /* AMD ordering of A, A*A', or A(:,f)*A(:,f)' */ /* -------------------------------------------------------------- */ amd_backup = FALSE ; /* no need to try AMD twice ... */ CHOLMOD(amd) (A, fset, fsize, Perm, Common) ; skip_analysis = TRUE ; } else if (ordering == CHOLMOD_COLAMD) { /* -------------------------------------------------------------- */ /* AMD for symmetric case, COLAMD for A*A' or A(:,f)*A(:,f)' */ /* -------------------------------------------------------------- */ if (A->stype) { CHOLMOD(amd) (A, fset, fsize, Perm, Common) ; skip_analysis = TRUE ; } else { /* Alternative: CHOLMOD(ccolamd) (A, fset, fsize, NULL, Perm, Common) ; */ /* do not postorder, it is done later, below */ /* workspace: Iwork (4*nrow+uncol), Flag (nrow), Head (nrow+1)*/ CHOLMOD(colamd) (A, fset, fsize, FALSE, Perm, Common) ; } } else if (ordering == CHOLMOD_METIS) { /* -------------------------------------------------------------- */ /* use METIS_NodeND directly (via a CHOLMOD wrapper) */ /* -------------------------------------------------------------- */ #ifndef NPARTITION /* postorder parameter is false, because it will be later, below */ /* workspace: Iwork (4*nrow+uncol), Flag (nrow), Head (nrow+1) */ Common->called_nd = TRUE ; CHOLMOD(metis) (A, fset, fsize, FALSE, Perm, Common) ; #else Common->status = CHOLMOD_NOT_INSTALLED ; #endif } else if (ordering == CHOLMOD_NESDIS) { /* -------------------------------------------------------------- */ /* use CHOLMOD's nested dissection */ /* -------------------------------------------------------------- */ /* this method is based on METIS' node bissection routine * (METIS_NodeComputeSeparator). In contrast to METIS_NodeND, * it calls CAMD or CCOLAMD on the whole graph, instead of MMD * on just the leaves. */ #ifndef NPARTITION /* workspace: Flag (nrow), Head (nrow+1), Iwork (2*nrow) */ Common->called_nd = TRUE ; CHOLMOD(nested_dissection) (A, fset, fsize, Perm, CParent, Cmember, Common) ; #else Common->status = CHOLMOD_NOT_INSTALLED ; #endif } else { /* -------------------------------------------------------------- */ /* invalid ordering method */ /* -------------------------------------------------------------- */ Common->status = CHOLMOD_INVALID ; PRINT1 (("No such ordering: "ID"\n", ordering)) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; if (Common->status < CHOLMOD_OK) { /* out of memory, or method failed */ status = MIN (status, Common->status) ; Common->status = CHOLMOD_OK ; continue ; } /* ------------------------------------------------------------------ */ /* analyze the ordering */ /* ------------------------------------------------------------------ */ if (!skip_analysis) { if (!CHOLMOD(analyze_ordering) (A, ordering, Perm, fset, fsize, Parent, Post, ColCount, First, Level, Common)) { /* ordering method failed; clear status and try next method */ status = MIN (status, Common->status) ; Common->status = CHOLMOD_OK ; continue ; } } ASSERT (Common->fl >= 0 && Common->lnz >= 0) ; Common->method [method].fl = Common->fl ; Common->method [method].lnz = Common->lnz ; PRINT1 (("lnz %g fl %g\n", Common->lnz, Common->fl)) ; /* ------------------------------------------------------------------ */ /* pick the best method */ /* ------------------------------------------------------------------ */ /* fl.pt. compare, but lnz can never be NaN */ if (Common->selected == EMPTY || Common->lnz < lnz_best) { Common->selected = method ; PRINT1 (("this is best so far, method "ID"\n", method)) ; L->ordering = ordering ; lnz_best = Common->lnz ; for (k = 0 ; k < n ; k++) { Lperm [k] = Perm [k] ; } /* save the results of cholmod_analyze_ordering, if it was called */ skip_best = skip_analysis ; if (!skip_analysis) { /* save the column count; becomes permanent part of L */ for (k = 0 ; k < n ; k++) { Lcolcount [k] = ColCount [k] ; } /* Parent is needed for weighted postordering and for supernodal * analysis. Does not become a permanent part of L */ for (k = 0 ; k < n ; k++) { Lparent [k] = Parent [k] ; } } } /* ------------------------------------------------------------------ */ /* determine if METIS is to be skipped */ /* ------------------------------------------------------------------ */ if (default_strategy && ordering == CHOLMOD_AMD) { if ((Common->fl < 500 * Common->lnz) || (Common->lnz < 5 * Common->anz)) { /* AMD found an ordering with less than 500 flops per nonzero in * L, or one with a fill-in ratio (nnz(L)/nnz(A)) of less than * 5. This is pretty good, and it's unlikely that METIS will do * better (this heuristic is based on tests on all symmetric * positive definite matrices in the UF sparse matrix * collection, and it works well across a wide range of * problems). METIS can take much more time than AMD. */ break ; } } } /* turn error printing back on ] */ Common->try_catch = FALSE ; /* ---------------------------------------------------------------------- */ /* return if no ordering method succeeded */ /* ---------------------------------------------------------------------- */ if (Common->selected == EMPTY) { /* All methods failed. * If two or more methods failed, they may have failed for different * reasons. Both would clear Common->status and skip to the next * method. Common->status needs to be restored here to the worst error * obtained in any of the methods. CHOLMOD_INVALID is worse * than CHOLMOD_OUT_OF_MEMORY, since the former implies something may * be wrong with the user's input. CHOLMOD_OUT_OF_MEMORY is simply an * indication of lack of resources. */ if (status >= CHOLMOD_OK) { /* this can occur if nmethods = 1, ordering = CHOLMOD_GIVEN, but UserPerm is NULL */ status = CHOLMOD_INVALID ; } ERROR (status, "all methods failed") ; FREE_WORKSPACE_AND_RETURN ; } /* ---------------------------------------------------------------------- */ /* do the analysis for AMD, if skipped */ /* ---------------------------------------------------------------------- */ Common->fl = Common->method [Common->selected].fl ; Common->lnz = Common->method [Common->selected].lnz ; ASSERT (Common->lnz >= 0) ; if (skip_best) { if (!CHOLMOD(analyze_ordering) (A, L->ordering, Lperm, fset, fsize, Lparent, Post, Lcolcount, First, Level, Common)) { /* out of memory, or method failed */ FREE_WORKSPACE_AND_RETURN ; } } /* ---------------------------------------------------------------------- */ /* postorder the etree, weighted by the column counts */ /* ---------------------------------------------------------------------- */ if (Common->postorder) { /* combine the fill-reducing ordering with the weighted postorder */ /* workspace: Iwork (2*nrow) */ if (CHOLMOD(postorder) (Lparent, n, Lcolcount, Post, Common) == n) { /* use First and Level as workspace [ */ Int *Wi = First, *InvPost = Level ; Int newchild, oldchild, newparent, oldparent ; for (k = 0 ; k < n ; k++) { Wi [k] = Lperm [Post [k]] ; } for (k = 0 ; k < n ; k++) { Lperm [k] = Wi [k] ; } for (k = 0 ; k < n ; k++) { Wi [k] = Lcolcount [Post [k]] ; } for (k = 0 ; k < n ; k++) { Lcolcount [k] = Wi [k] ; } for (k = 0 ; k < n ; k++) { InvPost [Post [k]] = k ; } /* updated Lparent needed only for supernodal case */ for (newchild = 0 ; newchild < n ; newchild++) { oldchild = Post [newchild] ; oldparent = Lparent [oldchild] ; newparent = (oldparent == EMPTY) ? EMPTY : InvPost [oldparent] ; Wi [newchild] = newparent ; } for (k = 0 ; k < n ; k++) { Lparent [k] = Wi [k] ; } /* done using Iwork as workspace ] */ /* L is now postordered, no longer in natural ordering */ if (L->ordering == CHOLMOD_NATURAL) { L->ordering = CHOLMOD_POSTORDERED ; } } } /* ---------------------------------------------------------------------- */ /* supernodal analysis, if requested or if selected automatically */ /* ---------------------------------------------------------------------- */ #ifndef NSUPERNODAL if (Common->supernodal > CHOLMOD_AUTO || (Common->supernodal == CHOLMOD_AUTO && Common->lnz > 0 && (Common->fl / Common->lnz) >= Common->supernodal_switch)) { cholmod_sparse *S, *F, *A2, *A1 ; permute_matrices (A, L->ordering, Lperm, fset, fsize, TRUE, &A1, &A2, &S, &F, Common) ; /* workspace: Flag (nrow), Head (nrow), Iwork (5*nrow) */ CHOLMOD(super_symbolic2) (for_cholesky, S, F, Lparent, L, Common) ; PRINT1 (("status %d\n", Common->status)) ; CHOLMOD(free_sparse) (&A1, Common) ; CHOLMOD(free_sparse) (&A2, Common) ; } #endif /* ---------------------------------------------------------------------- */ /* free temporary matrices and workspace, and return result L */ /* ---------------------------------------------------------------------- */ FREE_WORKSPACE_AND_RETURN ; } #endif Matrix/src/CHOLMOD/Cholesky/cholmod_rowcolcounts.c0000644000175100001440000004365612271765436021636 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/cholmod_rowcolcounts ======================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Compute the row and column counts of the Cholesky factor L of the matrix * A or A*A'. The etree and its postordering must already be computed (see * cholmod_etree and cholmod_postorder) and given as inputs to this routine. * * For the symmetric case (LL'=A), A is accessed by column. Only the lower * triangular part of A is used. Entries not in this part of the matrix are * ignored. This is the same as storing the upper triangular part of A by * rows, with entries in the lower triangular part being ignored. NOTE: this * representation is the TRANSPOSE of the input to cholmod_etree. * * For the unsymmetric case (LL'=AA'), A is accessed by column. Equivalently, * if A is viewed as a matrix in compressed-row form, this routine computes * the row and column counts for L where LL'=A'A. If the input vector f is * present, then F*F' is analyzed instead, where F = A(:,f). * * The set f is held in fset and fsize. * fset = NULL means ":" in MATLAB. fset is ignored. * fset != NULL means f = fset [0..fset-1]. * fset != NULL and fsize = 0 means f is the empty set. * Common->status is set to CHOLMOD_INVALID if fset is invalid. * * In both cases, the columns of A need not be sorted. * A can be packed or unpacked. * * References: * J. Gilbert, E. Ng, B. Peyton, "An efficient algorithm to compute row and * column counts for sparse Cholesky factorization", SIAM J. Matrix Analysis & * Applic., vol 15, 1994, pp. 1075-1091. * * J. Gilbert, X. Li, E. Ng, B. Peyton, "Computing row and column counts for * sparse QR and LU factorization", BIT, vol 41, 2001, pp. 693-710. * * workspace: * if symmetric: Flag (nrow), Iwork (2*nrow) * if unsymmetric: Flag (nrow), Iwork (2*nrow+ncol), Head (nrow+1) * * Supports any xtype (pattern, real, complex, or zomplex). */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === initialize_node ====================================================== */ /* ========================================================================== */ static int initialize_node /* initial work for kth node in postordered etree */ ( Int k, /* at the kth step of the algorithm (and kth node) */ Int Post [ ], /* Post [k] = i, the kth node in postordered etree */ Int Parent [ ], /* Parent [i] is the parent of i in the etree */ Int ColCount [ ], /* ColCount [c] is the current weight of node c */ Int PrevNbr [ ] /* PrevNbr [u] = k if u was last considered at step k */ ) { Int p, parent ; /* determine p, the kth node in the postordered etree */ p = Post [k] ; /* adjust the weight if p is not a root of the etree */ parent = Parent [p] ; if (parent != EMPTY) { ColCount [parent]-- ; } /* flag node p to exclude self edges (p,p) */ PrevNbr [p] = k ; return (p) ; } /* ========================================================================== */ /* === process_edge ========================================================= */ /* ========================================================================== */ /* edge (p,u) is being processed. p < u is a descendant of its ancestor u in * the etree. node p is the kth node in the postordered etree. */ static void process_edge ( Int p, /* process edge (p,u) of the matrix */ Int u, Int k, /* we are at the kth node in the postordered etree */ Int First [ ], /* First [i] = k if the postordering of first * descendent of node i is k */ Int PrevNbr [ ], /* u was last considered at step k = PrevNbr [u] */ Int ColCount [ ], /* ColCount [c] is the current weight of node c */ Int PrevLeaf [ ], /* s = PrevLeaf [u] means that s was the last leaf * seen in the subtree rooted at u. */ Int RowCount [ ], /* RowCount [i] is # of nonzeros in row i of L, * including the diagonal. Not computed if NULL. */ Int SetParent [ ], /* the FIND/UNION data structure, which forms a set * of trees. A root i has i = SetParent [i]. Following * a path from i to the root q of the subtree containing * i means that q is the SetParent representative of i. * All nodes in the tree could have their SetParent * equal to the root q; the tree representation is used * to save time. When a path is traced from i to its * root q, the path is re-traversed to set the SetParent * of the whole path to be the root q. */ Int Level [ ] /* Level [i] = length of path from node i to root */ ) { Int prevleaf, q, s, sparent ; if (First [p] > PrevNbr [u]) { /* p is a leaf of the subtree of u */ ColCount [p]++ ; prevleaf = PrevLeaf [u] ; if (prevleaf == EMPTY) { /* p is the first leaf of subtree of u; RowCount will be incremented * by the length of the path in the etree from p up to u. */ q = u ; } else { /* q = FIND (prevleaf): find the root q of the * SetParent tree containing prevleaf */ for (q = prevleaf ; q != SetParent [q] ; q = SetParent [q]) { ; } /* the root q has been found; re-traverse the path and * perform path compression */ s = prevleaf ; for (s = prevleaf ; s != q ; s = sparent) { sparent = SetParent [s] ; SetParent [s] = q ; } /* adjust the RowCount and ColCount; RowCount will be incremented by * the length of the path from p to the SetParent root q, and * decrement the ColCount of q by one. */ ColCount [q]-- ; } if (RowCount != NULL) { /* if RowCount is being computed, increment it by the length of * the path from p to q */ RowCount [u] += (Level [p] - Level [q]) ; } /* p is a leaf of the subtree of u, so mark PrevLeaf [u] to be p */ PrevLeaf [u] = p ; } /* flag u has having been processed at step k */ PrevNbr [u] = k ; } /* ========================================================================== */ /* === finalize_node ======================================================== */ /* ========================================================================== */ static void finalize_node /* compute UNION (p, Parent [p]) */ ( Int p, Int Parent [ ], /* Parent [p] is the parent of p in the etree */ Int SetParent [ ] /* see process_edge, above */ ) { /* all nodes in the SetParent tree rooted at p now have as their final * root the node Parent [p]. This computes UNION (p, Parent [p]) */ if (Parent [p] != EMPTY) { SetParent [p] = Parent [p] ; } } /* ========================================================================== */ /* === cholmod_rowcolcounts ================================================= */ /* ========================================================================== */ int CHOLMOD(rowcolcounts) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ Int *Parent, /* size nrow. Parent [i] = p if p is the parent of i */ Int *Post, /* size nrow. Post [k] = i if i is the kth node in * the postordered etree. */ /* ---- output --- */ Int *RowCount, /* size nrow. RowCount [i] = # entries in the ith row of * L, including the diagonal. */ Int *ColCount, /* size nrow. ColCount [i] = # entries in the ith * column of L, including the diagonal. */ Int *First, /* size nrow. First [i] = k is the least postordering * of any descendant of i. */ Int *Level, /* size nrow. Level [i] is the length of the path from * i to the root, with Level [root] = 0. */ /* --------------- */ cholmod_common *Common ) { double fl, ff ; Int *Ap, *Ai, *Anz, *PrevNbr, *SetParent, *Head, *PrevLeaf, *Anext, *Ipost, *Iwork ; Int i, j, r, k, len, s, p, pend, inew, stype, nf, anz, inode, parent, nrow, ncol, packed, use_fset, jj ; size_t w ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (Parent, FALSE) ; RETURN_IF_NULL (Post, FALSE) ; RETURN_IF_NULL (ColCount, FALSE) ; RETURN_IF_NULL (First, FALSE) ; RETURN_IF_NULL (Level, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; stype = A->stype ; if (stype > 0) { /* symmetric with upper triangular part not supported */ ERROR (CHOLMOD_INVALID, "symmetric upper not supported") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; /* the number of rows of A */ ncol = A->ncol ; /* the number of columns of A */ /* w = 2*nrow + (stype ? 0 : ncol) */ w = CHOLMOD(mult_size_t) (nrow, 2, &ok) ; w = CHOLMOD(add_size_t) (w, (stype ? 0 : ncol), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (nrow, w, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_perm) (Post, nrow, nrow, "Post", Common)) ; ASSERT (CHOLMOD(dump_parent) (Parent, nrow, "Parent", Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; /* size ncol+1, column pointers for A */ Ai = A->i ; /* the row indices of A, of size nz=Ap[ncol+1] */ Anz = A->nz ; packed = A->packed ; ASSERT (IMPLIES (!packed, Anz != NULL)) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; SetParent = Iwork ; /* size nrow (i/i/l) */ PrevNbr = Iwork + nrow ; /* size nrow (i/i/l) */ Anext = Iwork + 2*((size_t) nrow) ; /* size ncol (i/i/l) (unsym only) */ PrevLeaf = Common->Flag ; /* size nrow */ Head = Common->Head ; /* size nrow+1 (unsym only)*/ /* ---------------------------------------------------------------------- */ /* find the first descendant and level of each node in the tree */ /* ---------------------------------------------------------------------- */ /* First [i] = k if the postordering of first descendent of node i is k */ /* Level [i] = length of path from node i to the root (Level [root] = 0) */ for (i = 0 ; i < nrow ; i++) { First [i] = EMPTY ; } /* postorder traversal of the etree */ for (k = 0 ; k < nrow ; k++) { /* node i of the etree is the kth node in the postordered etree */ i = Post [k] ; /* i is a leaf if First [i] is still EMPTY */ /* ColCount [i] starts at 1 if i is a leaf, zero otherwise */ ColCount [i] = (First [i] == EMPTY) ? 1 : 0 ; /* traverse the path from node i to the root, stopping if we find a * node r whose First [r] is already defined. */ len = 0 ; for (r = i ; (r != EMPTY) && (First [r] == EMPTY) ; r = Parent [r]) { First [r] = k ; len++ ; } if (r == EMPTY) { /* we hit a root node, the level of which is zero */ len-- ; } else { /* we stopped at node r, where Level [r] is already defined */ len += Level [r] ; } /* re-traverse the path from node i to r; set the level of each node */ for (s = i ; s != r ; s = Parent [s]) { Level [s] = len-- ; } } /* ---------------------------------------------------------------------- */ /* AA' case: sort columns of A according to first postordered row index */ /* ---------------------------------------------------------------------- */ fl = 0.0 ; if (stype == 0) { /* [ use PrevNbr [0..nrow-1] as workspace for Ipost */ Ipost = PrevNbr ; /* Ipost [i] = k if i is the kth node in the postordered etree. */ for (k = 0 ; k < nrow ; k++) { Ipost [Post [k]] = k ; } use_fset = (fset != NULL) ; if (use_fset) { nf = fsize ; /* clear Anext to check fset */ for (j = 0 ; j < ncol ; j++) { Anext [j] = -2 ; } /* find the first postordered row in each column of A (post,f) * and place the column in the corresponding link list */ for (jj = 0 ; jj < nf ; jj++) { j = fset [jj] ; if (j < 0 || j > ncol || Anext [j] != -2) { /* out-of-range or duplicate entry in fset */ ERROR (CHOLMOD_INVALID, "fset invalid") ; return (FALSE) ; } /* flag column j as having been seen */ Anext [j] = EMPTY ; } /* fset is now valid */ ASSERT (CHOLMOD(dump_perm) (fset, nf, ncol, "fset", Common)) ; } else { nf = ncol ; } for (jj = 0 ; jj < nf ; jj++) { j = (use_fset) ? (fset [jj]) : jj ; /* column j is in the fset; find the smallest row (if any) */ p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; ff = (double) MAX (0, pend - p) ; fl += ff*ff + ff ; if (pend > p) { k = Ipost [Ai [p]] ; for ( ; p < pend ; p++) { inew = Ipost [Ai [p]] ; k = MIN (k, inew) ; } /* place column j in link list k */ ASSERT (k >= 0 && k < nrow) ; Anext [j] = Head [k] ; Head [k] = j ; } } /* Ipost no longer needed for inverse postordering ] * Head [k] contains a link list of all columns whose first * postordered row index is equal to k, for k = 0 to nrow-1. */ } /* ---------------------------------------------------------------------- */ /* compute the row counts and node weights */ /* ---------------------------------------------------------------------- */ if (RowCount != NULL) { for (i = 0 ; i < nrow ; i++) { RowCount [i] = 1 ; } } for (i = 0 ; i < nrow ; i++) { PrevLeaf [i] = EMPTY ; PrevNbr [i] = EMPTY ; SetParent [i] = i ; /* every node is in its own set, by itself */ } if (stype != 0) { /* ------------------------------------------------------------------ */ /* symmetric case: LL' = A */ /* ------------------------------------------------------------------ */ /* also determine the number of entries in triu(A) */ anz = nrow ; for (k = 0 ; k < nrow ; k++) { /* j is the kth node in the postordered etree */ j = initialize_node (k, Post, Parent, ColCount, PrevNbr) ; /* for all nonzeros A(i,j) below the diagonal, in column j of A */ p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i > j) { /* j is a descendant of i in etree(A) */ anz++ ; process_edge (j, i, k, First, PrevNbr, ColCount, PrevLeaf, RowCount, SetParent, Level) ; } } /* update SetParent: UNION (j, Parent [j]) */ finalize_node (j, Parent, SetParent) ; } Common->anz = anz ; } else { /* ------------------------------------------------------------------ */ /* unsymmetric case: LL' = AA' */ /* ------------------------------------------------------------------ */ for (k = 0 ; k < nrow ; k++) { /* inode is the kth node in the postordered etree */ inode = initialize_node (k, Post, Parent, ColCount, PrevNbr) ; /* for all cols j whose first postordered row is k: */ for (j = Head [k] ; j != EMPTY ; j = Anext [j]) { /* k is the first postordered row in column j of A */ /* for all rows i in column j: */ p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* has i already been considered at this step k */ if (PrevNbr [i] < k) { /* inode is a descendant of i in etree(AA') */ /* process edge (inode,i) and set PrevNbr[i] to k */ process_edge (inode, i, k, First, PrevNbr, ColCount, PrevLeaf, RowCount, SetParent, Level) ; } } } /* clear link list k */ Head [k] = EMPTY ; /* update SetParent: UNION (inode, Parent [inode]) */ finalize_node (inode, Parent, SetParent) ; } } /* ---------------------------------------------------------------------- */ /* finish computing the column counts */ /* ---------------------------------------------------------------------- */ for (j = 0 ; j < nrow ; j++) { parent = Parent [j] ; if (parent != EMPTY) { /* add the ColCount of j to its parent */ ColCount [parent] += ColCount [j] ; } } /* ---------------------------------------------------------------------- */ /* clear workspace */ /* ---------------------------------------------------------------------- */ Common->mark = EMPTY ; /* CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* flop count and nnz(L) for subsequent LL' numerical factorization */ /* ---------------------------------------------------------------------- */ /* use double to avoid integer overflow. lnz cannot be NaN. */ Common->aatfl = fl ; Common->lnz = 0. ; fl = 0 ; for (j = 0 ; j < nrow ; j++) { ff = (double) (ColCount [j]) ; Common->lnz += ff ; fl += ff*ff ; } Common->fl = fl ; PRINT1 (("rowcol fl %g lnz %g\n", Common->fl, Common->lnz)) ; return (TRUE) ; } #endif Matrix/src/CHOLMOD/Cholesky/t_cholmod_rowfac.c0000644000175100001440000003227012271765436020667 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/t_cholmod_rowfac ============================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Template routine for cholmod_rowfac. Supports any numeric xtype * (real, complex, or zomplex). * * workspace: Iwork (n), Flag (n), Xwork (n if real, 2*n if complex) */ #include "cholmod_template.h" #ifdef MASK static int TEMPLATE (cholmod_rowfac_mask) #else static int TEMPLATE (cholmod_rowfac) #endif ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */ double beta [2], /* factorize beta*I+A or beta*I+AA' (beta [0] only) */ size_t kstart, /* first row to factorize */ size_t kend, /* last row to factorize is kend-1 */ #ifdef MASK /* These inputs are used for cholmod_rowfac_mask only */ Int *mask, /* size A->nrow. if mask[i] then W(i) is set to zero */ Int *RLinkUp, /* size A->nrow. link list of rows to compute */ #endif /* ---- in/out --- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) { double yx [2], lx [2], fx [2], dk [1], di [1], fl = 0 ; #ifdef ZOMPLEX double yz [1], lz [1], fz [1] ; #endif double *Ax, *Az, *Lx, *Lz, *Wx, *Wz, *Fx, *Fz ; Int *Ap, *Anz, *Ai, *Lp, *Lnz, *Li, *Lnext, *Flag, *Stack, *Fp, *Fi, *Fnz, *Iwork ; Int i, p, k, t, pf, pfend, top, s, mark, pend, n, lnz, is_ll, multadds, use_dbound, packed, stype, Fpacked, sorted, nzmax, len, parent ; #ifndef REAL Int dk_imaginary ; #endif /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ PRINT1 (("\nin cholmod_rowfac, kstart %d kend %d stype %d\n", kstart, kend, A->stype)) ; DEBUG (CHOLMOD(dump_factor) (L, "Initial L", Common)) ; n = A->nrow ; stype = A->stype ; if (stype > 0) { /* symmetric upper case: F is not needed. It may be NULL */ Fp = NULL ; Fi = NULL ; Fx = NULL ; Fz = NULL ; Fnz = NULL ; Fpacked = TRUE ; } else { /* unsymmetric case: F is required. */ Fp = F->p ; Fi = F->i ; Fx = F->x ; Fz = F->z ; Fnz = F->nz ; Fpacked = F->packed ; } Ap = A->p ; /* size A->ncol+1, column pointers of A */ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */ Ax = A->x ; /* size nz, numeric values of A */ Az = A->z ; Anz = A->nz ; packed = A->packed ; sorted = A->sorted ; use_dbound = IS_GT_ZERO (Common->dbound) ; /* get the current factors L (and D for LDL'); allocate space if needed */ is_ll = L->is_ll ; if (L->xtype == CHOLMOD_PATTERN) { /* ------------------------------------------------------------------ */ /* L is symbolic only; allocate and initialize L (and D for LDL') */ /* ------------------------------------------------------------------ */ /* workspace: none */ CHOLMOD(change_factor) (A->xtype, is_ll, FALSE, FALSE, TRUE, L, Common); if (Common->status < CHOLMOD_OK) { /* out of memory */ return (FALSE) ; } ASSERT (L->minor == (size_t) n) ; } else if (kstart == 0 && kend == (size_t) n) { /* ------------------------------------------------------------------ */ /* refactorization; reset L->nz and L->minor to restart factorization */ /* ------------------------------------------------------------------ */ L->minor = n ; Lnz = L->nz ; for (k = 0 ; k < n ; k++) { Lnz [k] = 1 ; } } ASSERT (is_ll == L->is_ll) ; ASSERT (L->xtype != CHOLMOD_PATTERN) ; DEBUG (CHOLMOD(dump_factor) (L, "L ready", Common)) ; DEBUG (CHOLMOD(dump_sparse) (A, "A ready", Common)) ; DEBUG (if (stype == 0) CHOLMOD(dump_sparse) (F, "F ready", Common)) ; /* inputs, can be modified on output: */ Lp = L->p ; /* size n+1 */ ASSERT (Lp != NULL) ; /* outputs, contents defined on input for incremental case only: */ Lnz = L->nz ; /* size n */ Lnext = L->next ; /* size n+2 */ Li = L->i ; /* size L->nzmax, can change in size */ Lx = L->x ; /* size L->nzmax or 2*L->nzmax, can change in size */ Lz = L->z ; /* size L->nzmax for zomplex case, can change in size */ nzmax = L->nzmax ; ASSERT (Lnz != NULL && Li != NULL && Lx != NULL) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; Stack = Iwork ; /* size n (i/i/l) */ Flag = Common->Flag ; /* size n, Flag [i] < mark must hold */ Wx = Common->Xwork ; /* size n if real, 2*n if complex or * zomplex. Xwork [i] == 0 must hold. */ Wz = Wx + n ; /* size n for zomplex case only */ mark = Common->mark ; ASSERT ((Int) Common->xworksize >= (L->xtype == CHOLMOD_REAL ? 1:2)*n) ; /* ---------------------------------------------------------------------- */ /* compute LDL' or LL' factorization by rows */ /* ---------------------------------------------------------------------- */ #ifdef MASK #define NEXT(k) k = RLinkUp [k] #else #define NEXT(k) k++ #endif for (k = kstart ; k < ((Int) kend) ; NEXT(k)) { PRINT1 (("\n===============K "ID" Lnz [k] "ID"\n", k, Lnz [k])) ; /* ------------------------------------------------------------------ */ /* compute pattern of kth row of L and scatter kth input column */ /* ------------------------------------------------------------------ */ /* column k of L is currently empty */ ASSERT (Lnz [k] == 1) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ; top = n ; /* Stack is empty */ Flag [k] = mark ; /* do not include diagonal entry in Stack */ /* use Li [Lp [i]+1] for etree */ #define PARENT(i) (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY if (stype > 0) { /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */ p = Ap [k] ; pend = (packed) ? (Ap [k+1]) : (p + Anz [k]) ; /* W [i] = Ax [i] ; scatter column of A */ #define SCATTER ASSIGN(Wx,Wz,i, Ax,Az,p) SUBTREE ; #undef SCATTER } else { /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */ pf = Fp [k] ; pfend = (Fpacked) ? (Fp [k+1]) : (pf + Fnz [k]) ; for ( ; pf < pfend ; pf++) { /* get nonzero entry F (t,k) */ t = Fi [pf] ; /* fk = Fx [pf] */ ASSIGN (fx, fz, 0, Fx, Fz, pf) ; p = Ap [t] ; pend = (packed) ? (Ap [t+1]) : (p + Anz [t]) ; multadds = 0 ; /* W [i] += Ax [p] * fx ; scatter column of A*A' */ #define SCATTER MULTADD (Wx,Wz,i, Ax,Az,p, fx,fz,0) ; multadds++ ; SUBTREE ; #undef SCATTER #ifdef REAL fl += 2 * ((double) multadds) ; #else fl += 8 * ((double) multadds) ; #endif } } #undef PARENT /* ------------------------------------------------------------------ */ /* if mask is present, set the corresponding entries in W to zero */ /* ------------------------------------------------------------------ */ #ifdef MASK /* remove the dead element of Wx */ if (mask != NULL) { #if 0 /* older version */ for (p = n; p > top;) { i = Stack [--p] ; if ( mask [i] >= 0 ) { CLEAR (Wx,Wz,i) ; /* set W(i) to zero */ } } #endif for (s = top ; s < n ; s++) { i = Stack [s] ; if (mask [i] >= 0) { CLEAR (Wx,Wz,i) ; /* set W(i) to zero */ } } } #endif /* nonzero pattern of kth row of L is now in Stack [top..n-1]. * Flag [Stack [top..n-1]] is equal to mark, but no longer needed */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* ------------------------------------------------------------------ */ /* compute kth row of L and store in column form */ /* ------------------------------------------------------------------ */ /* Solve L (0:k-1, 0:k-1) * y (0:k-1) = b (0:k-1) where * b (0:k) = A (0:k,k) or A(0:k,:) * F(:,k) is in W and Stack. * * For LDL' factorization: * L (k, 0:k-1) = y (0:k-1) ./ D (0:k-1) * D (k) = b (k) - L (k, 0:k-1) * y (0:k-1) * * For LL' factorization: * L (k, 0:k-1) = y (0:k-1) * L (k,k) = sqrt (b (k) - L (k, 0:k-1) * L (0:k-1, k)) */ /* dk = W [k] + beta */ ADD_REAL (dk,0, Wx,k, beta,0) ; #ifndef REAL /* In the unsymmetric case, the imaginary part of W[k] must be real, * since F is assumed to be the complex conjugate transpose of A. In * the symmetric case, W[k] is the diagonal of A. If the imaginary part * of W[k] is nonzero, then the Cholesky factorization cannot be * computed; A is not positive definite */ dk_imaginary = (stype > 0) ? (IMAG_IS_NONZERO (Wx,Wz,k)) : FALSE ; #endif /* W [k] = 0.0 ; */ CLEAR (Wx,Wz,k) ; for (s = top ; s < n ; s++) { /* get i for each nonzero entry L(k,i) */ i = Stack [s] ; /* y = W [i] ; */ ASSIGN (yx,yz,0, Wx,Wz,i) ; /* W [i] = 0.0 ; */ CLEAR (Wx,Wz,i) ; lnz = Lnz [i] ; p = Lp [i] ; ASSERT (lnz > 0 && Li [p] == i) ; pend = p + lnz ; /* di = Lx [p] ; the diagonal entry L or D(i,i), which is real */ ASSIGN_REAL (di,0, Lx,p) ; if (i >= (Int) L->minor || IS_ZERO (di [0])) { /* For the LL' factorization, L(i,i) is zero. For the LDL', * D(i,i) is zero. Skip column i of L, and set L(k,i) = 0. */ CLEAR (lx,lz,0) ; p = pend ; } else if (is_ll) { #ifdef REAL fl += 2 * ((double) (pend - p - 1)) + 3 ; #else fl += 8 * ((double) (pend - p - 1)) + 6 ; #endif /* forward solve using L (i:(k-1),i) */ /* divide by L(i,i), which must be real and nonzero */ /* y /= di [0] */ DIV_REAL (yx,yz,0, yx,yz,0, di,0) ; for (p++ ; p < pend ; p++) { /* W [Li [p]] -= Lx [p] * y ; */ MULTSUB (Wx,Wz,Li[p], Lx,Lz,p, yx,yz,0) ; } /* do not scale L; compute dot product for L(k,k) */ /* L(k,i) = conj(y) ; */ ASSIGN_CONJ (lx,lz,0, yx,yz,0) ; /* d -= conj(y) * y ; */ LLDOT (dk,0, yx,yz,0) ; } else { #ifdef REAL fl += 2 * ((double) (pend - p - 1)) + 3 ; #else fl += 8 * ((double) (pend - p - 1)) + 6 ; #endif /* forward solve using D (i,i) and L ((i+1):(k-1),i) */ for (p++ ; p < pend ; p++) { /* W [Li [p]] -= Lx [p] * y ; */ MULTSUB (Wx,Wz,Li[p], Lx,Lz,p, yx,yz,0) ; } /* Scale L (k,0:k-1) for LDL' factorization, compute D (k,k)*/ #ifdef REAL /* L(k,i) = y/d */ lx [0] = yx [0] / di [0] ; /* d -= L(k,i) * y */ dk [0] -= lx [0] * yx [0] ; #else /* L(k,i) = conj(y) ; */ ASSIGN_CONJ (lx,lz,0, yx,yz,0) ; /* L(k,i) /= di ; */ DIV_REAL (lx,lz,0, lx,lz,0, di,0) ; /* d -= conj(y) * y / di */ LDLDOT (dk,0, yx,yz,0, di,0) ; #endif } /* determine if column i of L can hold the new L(k,i) entry */ if (p >= Lp [Lnext [i]]) { /* column i needs to grow */ PRINT1 (("Factor Colrealloc "ID", old Lnz "ID"\n", i, Lnz [i])); if (!CHOLMOD(reallocate_column) (i, lnz + 1, L, Common)) { /* out of memory, L is now simplicial symbolic */ for (i = 0 ; i < n ; i++) { /* W [i] = 0 ; */ CLEAR (Wx,Wz,i) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, n, Common)) ; return (FALSE) ; } Li = L->i ; /* L->i, L->x, L->z may have moved */ Lx = L->x ; Lz = L->z ; p = Lp [i] + lnz ; /* contents of L->p changed */ ASSERT (p < Lp [Lnext [i]]) ; } /* store L (k,i) in the column form matrix of L */ Li [p] = k ; /* Lx [p] = L(k,i) ; */ ASSIGN (Lx,Lz,p, lx,lz,0) ; Lnz [i]++ ; } /* ------------------------------------------------------------------ */ /* ensure abs (d) >= dbound if dbound is given, and store it in L */ /* ------------------------------------------------------------------ */ p = Lp [k] ; Li [p] = k ; if (k >= (Int) L->minor) { /* the matrix is already not positive definite */ dk [0] = 0 ; } else if (use_dbound) { /* modify the diagonal to force LL' or LDL' to exist */ dk [0] = CHOLMOD(dbound) (is_ll ? fabs (dk [0]) : dk [0], Common) ; } else if ((is_ll ? (IS_LE_ZERO (dk [0])) : (IS_ZERO (dk [0]))) #ifndef REAL || dk_imaginary #endif ) { /* the matrix has just been found to be not positive definite */ dk [0] = 0 ; L->minor = k ; ERROR (CHOLMOD_NOT_POSDEF, "not positive definite") ; } if (is_ll) { /* this is counted as one flop, below */ dk [0] = sqrt (dk [0]) ; } /* Lx [p] = D(k,k) = d ; real part only */ ASSIGN_REAL (Lx,p, dk,0) ; CLEAR_IMAG (Lx,Lz,p) ; } #undef NEXT if (is_ll) fl += MAX ((Int) kend - (Int) kstart, 0) ; /* count sqrt's */ Common->rowfacfl = fl ; DEBUG (CHOLMOD(dump_factor) (L, "final cholmod_rowfac", Common)) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, n, Common)) ; return (TRUE) ; } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX Matrix/src/CHOLMOD/Cholesky/t_cholmod_solve.c0000644000175100001440000001242312271765436020534 0ustar hornikusers/* ========================================================================== */ /* === Cholesky/t_cholmod_solve ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2013, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Template routine for cholmod_solve. Supports any numeric xtype (real, * complex, or zomplex). The xtypes of all matrices (L and Y) must match. */ #include "cholmod_template.h" /* ========================================================================== */ /* === simplicial template solvers ========================================== */ /* ========================================================================== */ /* LL': solve Lx=b with non-unit diagonal */ #define LL #include "t_cholmod_lsolve.c" /* LDL': solve LDx=b */ #define LD #include "t_cholmod_lsolve.c" /* LDL': solve Lx=b with unit diagonal */ #include "t_cholmod_lsolve.c" /* LL': solve L'x=b with non-unit diagonal */ #define LL #include "t_cholmod_ltsolve.c" /* LDL': solve DL'x=b */ #define LD #include "t_cholmod_ltsolve.c" /* LDL': solve L'x=b with unit diagonal */ #include "t_cholmod_ltsolve.c" /* ========================================================================== */ /* === t_ldl_dsolve ========================================================= */ /* ========================================================================== */ /* Solve Dx=b for an LDL' factorization, where Y holds b' on input and x' on * output. * * The number of right-hand-sides (nrhs) is not restricted, even if Yseti * is present. */ static void TEMPLATE (ldl_dsolve) ( cholmod_factor *L, cholmod_dense *Y, /* nr-by-n with leading dimension nr */ Int *Yseti, Int ysetlen ) { double d [1] ; double *Lx, *Yx, *Yz ; Int *Lp ; Int n, nrhs, k, p, k1, k2, kk, kkiters ; ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */ ASSERT (L->n == Y->ncol) ; /* dimensions must match */ ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */ ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */ ASSERT (!(L->is_super) && !(L->is_ll)) ; /* L is simplicial LDL' */ nrhs = Y->nrow ; n = L->n ; Lp = L->p ; Lx = L->x ; Yx = Y->x ; Yz = Y->z ; kkiters = Yseti ? ysetlen : n ; for (kk = 0 ; kk < kkiters ; kk++) { k = Yseti ? Yseti [kk] : kk ; k1 = k*nrhs ; k2 = (k+1)*nrhs ; ASSIGN_REAL (d,0, Lx,Lp[k]) ; for (p = k1 ; p < k2 ; p++) { DIV_REAL (Yx,Yz,p, Yx,Yz,p, d,0) ; } } } /* ========================================================================== */ /* === t_simplicial_solver ================================================== */ /* ========================================================================== */ /* Solve a linear system, where Y' contains the (array-transposed) right-hand * side on input, and the solution on output. No permutations are applied; * these must have already been applied to Y on input. * * Yseti [0..ysetlen-1] is an optional list of indices from * cholmod_lsolve_pattern. The solve is performed only on the columns of L * corresponding to entries in Yseti. Ignored if NULL. If present, most * functions require that Y' consist of a single dense column. */ static void TEMPLATE (simplicial_solver) ( int sys, /* system to solve */ cholmod_factor *L, /* factor to use, a simplicial LL' or LDL' */ cholmod_dense *Y, /* right-hand-side on input, solution on output */ Int *Yseti, Int ysetlen ) { if (L->is_ll) { /* The factorization is LL' */ if (sys == CHOLMOD_A || sys == CHOLMOD_LDLt) { /* Solve Ax=b or LL'x=b */ TEMPLATE (ll_lsolve_k) (L, Y, Yseti, ysetlen) ; TEMPLATE (ll_ltsolve_k) (L, Y, Yseti, ysetlen) ; } else if (sys == CHOLMOD_L || sys == CHOLMOD_LD) { /* Solve Lx=b */ TEMPLATE (ll_lsolve_k) (L, Y, Yseti, ysetlen) ; } else if (sys == CHOLMOD_Lt || sys == CHOLMOD_DLt) { /* Solve L'x=b */ TEMPLATE (ll_ltsolve_k) (L, Y, Yseti, ysetlen) ; } } else { /* The factorization is LDL' */ if (sys == CHOLMOD_A || sys == CHOLMOD_LDLt) { /* Solve Ax=b or LDL'x=b */ TEMPLATE (ldl_lsolve_k) (L, Y, Yseti, ysetlen) ; TEMPLATE (ldl_dltsolve_k) (L, Y, Yseti, ysetlen) ; } else if (sys == CHOLMOD_LD) { /* Solve LDx=b */ TEMPLATE (ldl_ldsolve_k) (L, Y, Yseti, ysetlen) ; } else if (sys == CHOLMOD_L) { /* Solve Lx=b */ TEMPLATE (ldl_lsolve_k) (L, Y, Yseti, ysetlen) ; } else if (sys == CHOLMOD_Lt) { /* Solve L'x=b */ TEMPLATE (ldl_ltsolve_k) (L, Y, Yseti, ysetlen) ; } else if (sys == CHOLMOD_DLt) { /* Solve DL'x=b */ TEMPLATE (ldl_dltsolve_k) (L, Y, Yseti, ysetlen) ; } else if (sys == CHOLMOD_D) { /* Solve Dx=b */ TEMPLATE (ldl_dsolve) (L, Y, Yseti, ysetlen) ; } } } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX Matrix/src/CHOLMOD/Lib/0000755000175100001440000000000012271765426014132 5ustar hornikusersMatrix/src/CHOLMOD/Lib/Makefile0000644000175100001440000004407512271765436015605 0ustar hornikusers#=============================================================================== # CHOLOMD/Lib/Makefile: for compiling the CHOLMOD library #=============================================================================== include ${MkInclude} default: lib PKG_CPPFLAGS = -I../../AMD/Include -I../../AMD/Source \ -I../../COLAMD/Include \ -I../Include -I../../SuiteSparse_config -DNPARTITION -DNPRINT # -I../../CCOLAMD \ # -I../../CAMD/Include -I../../CAMD/Source \ # -I../../Metis \ #------------------------------------------------------------------------------- # ../Include/ directory contains all include files: #------------------------------------------------------------------------------- INC = ../Include/cholmod.h \ ../Include/cholmod_blas.h \ ../Include/cholmod_check.h \ ../Include/cholmod_cholesky.h \ ../Include/cholmod_complexity.h \ ../Include/cholmod_config.h \ ../Include/cholmod_core.h \ ../Include/cholmod_internal.h \ ../Include/cholmod_matrixops.h \ ../Include/cholmod_modify.h \ ../Include/cholmod_partition.h \ ../Include/cholmod_supernodal.h \ ../Include/cholmod_template.h #------------------------------------------------------------------------------- # The 7 CHOLMOD library modules (int, double) #------------------------------------------------------------------------------- CORE = cholmod_aat.o cholmod_add.o cholmod_band.o \ cholmod_change_factor.o cholmod_common.o cholmod_complex.o \ cholmod_copy.o cholmod_dense.o cholmod_error.o cholmod_factor.o \ cholmod_memory.o cholmod_sparse.o \ cholmod_transpose.o cholmod_triplet.o \ cholmod_version.o CHECK = cholmod_check.o cholmod_read.o cholmod_write.o CHOLESKY = cholmod_amd.o cholmod_analyze.o cholmod_colamd.o \ cholmod_etree.o cholmod_factorize.o cholmod_postorder.o \ cholmod_rcond.o cholmod_resymbol.o cholmod_rowcolcounts.o \ cholmod_rowfac.o cholmod_solve.o cholmod_spsolve.o MATRIXOPS = cholmod_drop.o cholmod_horzcat.o cholmod_norm.o \ cholmod_scale.o cholmod_sdmult.o cholmod_ssmult.o \ cholmod_submatrix.o cholmod_vertcat.o cholmod_symmetry.o PARTITION = cholmod_ccolamd.o cholmod_csymamd.o \ cholmod_metis.o cholmod_nesdis.o cholmod_camd.o MODIFY = cholmod_rowadd.o cholmod_rowdel.o cholmod_updown.o SUPERNODAL = cholmod_super_numeric.o cholmod_super_solve.o \ cholmod_super_symbolic.o DI = $(CORE) $(CHECK) $(CHOLESKY) $(MATRIXOPS) $(MODIFY) $(SUPERNODAL) # $(PARTITION) #------------------------------------------------------------------------------- # CHOLMOD library modules (long, double) #------------------------------------------------------------------------------- LCORE = cholmod_l_aat.o cholmod_l_add.o cholmod_l_band.o \ cholmod_l_change_factor.o cholmod_l_common.o cholmod_l_complex.o \ cholmod_l_copy.o cholmod_l_dense.o cholmod_l_error.o \ cholmod_l_factor.o cholmod_l_memory.o \ cholmod_l_sparse.o cholmod_l_transpose.o cholmod_l_triplet.o \ cholmod_l_version.o LCHECK = cholmod_l_check.o cholmod_l_read.o cholmod_l_write.o LCHOLESKY = cholmod_l_amd.o cholmod_l_analyze.o cholmod_l_colamd.o \ cholmod_l_etree.o cholmod_l_factorize.o cholmod_l_postorder.o \ cholmod_l_rcond.o cholmod_l_resymbol.o cholmod_l_rowcolcounts.o \ cholmod_l_rowfac.o cholmod_l_solve.o cholmod_l_spsolve.o LMATRIXOPS = cholmod_l_drop.o cholmod_l_horzcat.o cholmod_l_norm.o \ cholmod_l_scale.o cholmod_l_sdmult.o cholmod_l_ssmult.o \ cholmod_l_submatrix.o cholmod_l_vertcat.o cholmod_l_symmetry.o LPARTITION = cholmod_l_ccolamd.o cholmod_l_csymamd.o \ cholmod_l_metis.o cholmod_l_nesdis.o cholmod_l_camd.o LMODIFY = cholmod_l_rowadd.o cholmod_l_rowdel.o cholmod_l_updown.o LSUPERNODAL = cholmod_l_super_numeric.o cholmod_l_super_solve.o \ cholmod_l_super_symbolic.o DL = $(LCORE) $(LCHECK) $(LCHOLESKY) $(LMATRIXOPS) $(LMODIFY) $(LSUPERNODAL) #$(LPARTITION) #------------------------------------------------------------------------------- OBJS = $(DI) $(DL) # ^^ FIXME? MM thinks we should be able to only use $(DI) # well, Doug thought so, too .. but it's currently wrong: # --> ../../chm_common.c has a few 'cholmod_l_' left LIB = ../../CHOLMOD.a C = $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) lib: $(LIB) $(LIB): $(OBJS) $(AR) -rucs $(LIB) $(OBJS) mostlyclean: clean clean: @-rm -rf .libs _libs $(LIB) @-rm -f $(OBJS) $(OBJ): $(INC) #------------------------------------------------------------------------------- # Check Module: #------------------------------------------------------------------------------- cholmod_check.o: ../Check/cholmod_check.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Check/cholmod_check.c -o $@ cholmod_read.o: ../Check/cholmod_read.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Check/cholmod_read.c -o $@ cholmod_write.o: ../Check/cholmod_write.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Check/cholmod_write.c -o $@ #------------------------------------------------------------------------------- cholmod_l_check.o: ../Check/cholmod_check.c $(C) -DDLONG -c $(I) ../Check/cholmod_check.c -o $@ cholmod_l_read.o: ../Check/cholmod_read.c $(C) -DDLONG -c $(I) ../Check/cholmod_read.c -o $@ cholmod_l_write.o: ../Check/cholmod_write.c $(C) -DDLONG -c $(I) ../Check/cholmod_write.c -o $@ #------------------------------------------------------------------------------- # Core Module: #------------------------------------------------------------------------------- cholmod_common.o: ../Core/cholmod_common.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_common.c -o $@ cholmod_dense.o: ../Core/cholmod_dense.c ../Core/t_cholmod_dense.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_dense.c -o $@ cholmod_factor.o: ../Core/cholmod_factor.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_factor.c -o $@ cholmod_change_factor.o: ../Core/cholmod_change_factor.c \ ../Core/t_cholmod_change_factor.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_change_factor.c -o $@ cholmod_memory.o: ../Core/cholmod_memory.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_memory.c -o $@ cholmod_sparse.o: ../Core/cholmod_sparse.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_sparse.c -o $@ cholmod_complex.o: ../Core/cholmod_complex.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_complex.c -o $@ cholmod_transpose.o: ../Core/cholmod_transpose.c ../Core/t_cholmod_transpose.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_transpose.c -o $@ cholmod_band.o: ../Core/cholmod_band.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_band.c -o $@ cholmod_copy.o: ../Core/cholmod_copy.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_copy.c -o $@ cholmod_triplet.o: ../Core/cholmod_triplet.c ../Core/t_cholmod_triplet.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_triplet.c -o $@ cholmod_error.o: ../Core/cholmod_error.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_error.c -o $@ cholmod_aat.o: ../Core/cholmod_aat.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_aat.c -o $@ cholmod_add.o: ../Core/cholmod_add.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_add.c -o $@ cholmod_version.o: ../Core/cholmod_version.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Core/cholmod_version.c -o $@ #------------------------------------------------------------------------------- cholmod_l_common.o: ../Core/cholmod_common.c $(C) -DDLONG -c $(I) ../Core/cholmod_common.c -o $@ cholmod_l_dense.o: ../Core/cholmod_dense.c ../Core/t_cholmod_dense.c $(C) -DDLONG -c $(I) ../Core/cholmod_dense.c -o $@ cholmod_l_factor.o: ../Core/cholmod_factor.c $(C) -DDLONG -c $(I) ../Core/cholmod_factor.c -o $@ cholmod_l_change_factor.o: ../Core/cholmod_change_factor.c \ ../Core/t_cholmod_change_factor.c $(C) -DDLONG -c $(I) ../Core/cholmod_change_factor.c -o $@ cholmod_l_memory.o: ../Core/cholmod_memory.c $(C) -DDLONG -c $(I) ../Core/cholmod_memory.c -o $@ cholmod_l_sparse.o: ../Core/cholmod_sparse.c $(C) -DDLONG -c $(I) ../Core/cholmod_sparse.c -o $@ cholmod_l_complex.o: ../Core/cholmod_complex.c $(C) -DDLONG -c $(I) ../Core/cholmod_complex.c -o $@ cholmod_l_transpose.o: ../Core/cholmod_transpose.c ../Core/t_cholmod_transpose.c $(C) -DDLONG -c $(I) ../Core/cholmod_transpose.c -o $@ cholmod_l_band.o: ../Core/cholmod_band.c $(C) -DDLONG -c $(I) ../Core/cholmod_band.c -o $@ cholmod_l_copy.o: ../Core/cholmod_copy.c $(C) -DDLONG -c $(I) ../Core/cholmod_copy.c -o $@ cholmod_l_triplet.o: ../Core/cholmod_triplet.c ../Core/t_cholmod_triplet.c $(C) -DDLONG -c $(I) ../Core/cholmod_triplet.c -o $@ cholmod_l_error.o: ../Core/cholmod_error.c $(C) -DDLONG -c $(I) ../Core/cholmod_error.c -o $@ cholmod_l_aat.o: ../Core/cholmod_aat.c $(C) -DDLONG -c $(I) ../Core/cholmod_aat.c -o $@ cholmod_l_add.o: ../Core/cholmod_add.c $(C) -DDLONG -c $(I) ../Core/cholmod_add.c -o $@ cholmod_l_version.o: ../Core/cholmod_version.c $(C) -DDLONG -c $(I) ../Core/cholmod_version.c -o $@ #------------------------------------------------------------------------------- # Cholesky Module: #------------------------------------------------------------------------------- cholmod_amd.o: ../Cholesky/cholmod_amd.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Cholesky/cholmod_amd.c -o $@ cholmod_analyze.o: ../Cholesky/cholmod_analyze.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Cholesky/cholmod_analyze.c -o $@ cholmod_colamd.o: ../Cholesky/cholmod_colamd.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Cholesky/cholmod_colamd.c -o $@ cholmod_etree.o: ../Cholesky/cholmod_etree.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Cholesky/cholmod_etree.c -o $@ cholmod_factorize.o: ../Cholesky/cholmod_factorize.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Cholesky/cholmod_factorize.c -o $@ cholmod_postorder.o: ../Cholesky/cholmod_postorder.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Cholesky/cholmod_postorder.c -o $@ cholmod_rcond.o: ../Cholesky/cholmod_rcond.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Cholesky/cholmod_rcond.c -o $@ cholmod_resymbol.o: ../Cholesky/cholmod_resymbol.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Cholesky/cholmod_resymbol.c -o $@ cholmod_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Cholesky/cholmod_rowcolcounts.c -o $@ cholmod_solve.o: ../Cholesky/cholmod_solve.c ../Cholesky/t_cholmod_lsolve.c \ ../Cholesky/t_cholmod_ltsolve.c ../Cholesky/t_cholmod_solve.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Cholesky/cholmod_solve.c -o $@ cholmod_spsolve.o: ../Cholesky/cholmod_spsolve.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Cholesky/cholmod_spsolve.c -o $@ cholmod_rowfac.o: ../Cholesky/cholmod_rowfac.c ../Cholesky/t_cholmod_rowfac.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Cholesky/cholmod_rowfac.c -o $@ #------------------------------------------------------------------------------- cholmod_l_amd.o: ../Cholesky/cholmod_amd.c $(C) -DDLONG -c $(I) ../Cholesky/cholmod_amd.c -o $@ cholmod_l_analyze.o: ../Cholesky/cholmod_analyze.c $(C) -DDLONG -c $(I) ../Cholesky/cholmod_analyze.c -o $@ cholmod_l_colamd.o: ../Cholesky/cholmod_colamd.c $(C) -DDLONG -c $(I) ../Cholesky/cholmod_colamd.c -o $@ cholmod_l_etree.o: ../Cholesky/cholmod_etree.c $(C) -DDLONG -c $(I) ../Cholesky/cholmod_etree.c -o $@ cholmod_l_factorize.o: ../Cholesky/cholmod_factorize.c $(C) -DDLONG -c $(I) ../Cholesky/cholmod_factorize.c -o $@ cholmod_l_postorder.o: ../Cholesky/cholmod_postorder.c $(C) -DDLONG -c $(I) ../Cholesky/cholmod_postorder.c -o $@ cholmod_l_rcond.o: ../Cholesky/cholmod_rcond.c $(C) -DDLONG -c $(I) ../Cholesky/cholmod_rcond.c -o $@ cholmod_l_resymbol.o: ../Cholesky/cholmod_resymbol.c $(C) -DDLONG -c $(I) ../Cholesky/cholmod_resymbol.c -o $@ cholmod_l_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c $(C) -DDLONG -c $(I) ../Cholesky/cholmod_rowcolcounts.c -o $@ cholmod_l_solve.o: ../Cholesky/cholmod_solve.c ../Cholesky/t_cholmod_lsolve.c \ ../Cholesky/t_cholmod_ltsolve.c ../Cholesky/t_cholmod_solve.c $(C) -DDLONG -c $(I) ../Cholesky/cholmod_solve.c -o $@ cholmod_l_spsolve.o: ../Cholesky/cholmod_spsolve.c $(C) -DDLONG -c $(I) ../Cholesky/cholmod_spsolve.c -o $@ cholmod_l_rowfac.o: ../Cholesky/cholmod_rowfac.c ../Cholesky/t_cholmod_rowfac.c $(C) -DDLONG -c $(I) ../Cholesky/cholmod_rowfac.c -o $@ #------------------------------------------------------------------------------- # Partition Module: #------------------------------------------------------------------------------- cholmod_ccolamd.o: ../Partition/cholmod_ccolamd.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Partition/cholmod_ccolamd.c -o $@ cholmod_csymamd.o: ../Partition/cholmod_csymamd.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Partition/cholmod_csymamd.c -o $@ cholmod_camd.o: ../Partition/cholmod_camd.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Partition/cholmod_camd.c -o $@ cholmod_metis.o: ../Partition/cholmod_metis.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Partition/cholmod_metis.c -o $@ cholmod_nesdis.o: ../Partition/cholmod_nesdis.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Partition/cholmod_nesdis.c -o $@ #------------------------------------------------------------------------------- cholmod_l_ccolamd.o: ../Partition/cholmod_ccolamd.c $(C) -DDLONG -c $(I) ../Partition/cholmod_ccolamd.c -o $@ cholmod_l_csymamd.o: ../Partition/cholmod_csymamd.c $(C) -DDLONG -c $(I) ../Partition/cholmod_csymamd.c -o $@ cholmod_l_camd.o: ../Partition/cholmod_camd.c $(C) -DDLONG -c $(I) ../Partition/cholmod_camd.c -o $@ cholmod_l_metis.o: ../Partition/cholmod_metis.c $(C) -DDLONG -c $(I) ../Partition/cholmod_metis.c -o $@ cholmod_l_nesdis.o: ../Partition/cholmod_nesdis.c $(C) -DDLONG -c $(I) ../Partition/cholmod_nesdis.c -o $@ #------------------------------------------------------------------------------- # MatrixOps Module: #------------------------------------------------------------------------------- cholmod_horzcat.o: ../MatrixOps/cholmod_horzcat.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../MatrixOps/cholmod_horzcat.c -o $@ cholmod_norm.o: ../MatrixOps/cholmod_norm.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../MatrixOps/cholmod_norm.c -o $@ cholmod_scale.o: ../MatrixOps/cholmod_scale.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../MatrixOps/cholmod_scale.c -o $@ cholmod_drop.o: ../MatrixOps/cholmod_drop.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../MatrixOps/cholmod_drop.c -o $@ cholmod_sdmult.o: ../MatrixOps/cholmod_sdmult.c \ ../MatrixOps/t_cholmod_sdmult.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../MatrixOps/cholmod_sdmult.c -o $@ cholmod_ssmult.o: ../MatrixOps/cholmod_ssmult.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../MatrixOps/cholmod_ssmult.c -o $@ cholmod_submatrix.o: ../MatrixOps/cholmod_submatrix.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../MatrixOps/cholmod_submatrix.c -o $@ cholmod_vertcat.o: ../MatrixOps/cholmod_vertcat.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../MatrixOps/cholmod_vertcat.c -o $@ cholmod_symmetry.o: ../MatrixOps/cholmod_symmetry.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../MatrixOps/cholmod_symmetry.c -o $@ #------------------------------------------------------------------------------- cholmod_l_horzcat.o: ../MatrixOps/cholmod_horzcat.c $(C) -DDLONG -c $(I) ../MatrixOps/cholmod_horzcat.c -o $@ cholmod_l_norm.o: ../MatrixOps/cholmod_norm.c $(C) -DDLONG -c $(I) ../MatrixOps/cholmod_norm.c -o $@ cholmod_l_scale.o: ../MatrixOps/cholmod_scale.c $(C) -DDLONG -c $(I) ../MatrixOps/cholmod_scale.c -o $@ cholmod_l_drop.o: ../MatrixOps/cholmod_drop.c $(C) -DDLONG -c $(I) ../MatrixOps/cholmod_drop.c -o $@ cholmod_l_sdmult.o: ../MatrixOps/cholmod_sdmult.c \ ../MatrixOps/t_cholmod_sdmult.c $(C) -DDLONG -c $(I) ../MatrixOps/cholmod_sdmult.c -o $@ cholmod_l_ssmult.o: ../MatrixOps/cholmod_ssmult.c $(C) -DDLONG -c $(I) ../MatrixOps/cholmod_ssmult.c -o $@ cholmod_l_submatrix.o: ../MatrixOps/cholmod_submatrix.c $(C) -DDLONG -c $(I) ../MatrixOps/cholmod_submatrix.c -o $@ cholmod_l_vertcat.o: ../MatrixOps/cholmod_vertcat.c $(C) -DDLONG -c $(I) ../MatrixOps/cholmod_vertcat.c -o $@ cholmod_l_symmetry.o: ../MatrixOps/cholmod_symmetry.c $(C) -DDLONG -c $(I) ../MatrixOps/cholmod_symmetry.c -o $@ #------------------------------------------------------------------------------- # Modify Module: #------------------------------------------------------------------------------- cholmod_rowadd.o: ../Modify/cholmod_rowadd.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Modify/cholmod_rowadd.c -o $@ cholmod_rowdel.o: ../Modify/cholmod_rowdel.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Modify/cholmod_rowdel.c -o $@ cholmod_updown.o: ../Modify/cholmod_updown.c \ ../Modify/t_cholmod_updown.c ../Modify/t_cholmod_updown_numkr.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Modify/cholmod_updown.c -o $@ #------------------------------------------------------------------------------- cholmod_l_rowadd.o: ../Modify/cholmod_rowadd.c $(C) -DDLONG -c $(I) ../Modify/cholmod_rowadd.c -o $@ cholmod_l_rowdel.o: ../Modify/cholmod_rowdel.c $(C) -DDLONG -c $(I) ../Modify/cholmod_rowdel.c -o $@ cholmod_l_updown.o: ../Modify/cholmod_updown.c \ ../Modify/t_cholmod_updown.c ../Modify/t_cholmod_updown_numkr.c $(C) -DDLONG -c $(I) ../Modify/cholmod_updown.c -o $@ #------------------------------------------------------------------------------- # Supernodal Module: #------------------------------------------------------------------------------- cholmod_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \ ../Supernodal/t_cholmod_gpu.c \ ../Supernodal/t_cholmod_super_numeric.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Supernodal/cholmod_super_numeric.c -o $@ cholmod_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Supernodal/cholmod_super_symbolic.c -o $@ cholmod_super_solve.o: ../Supernodal/cholmod_super_solve.c \ ../Supernodal/t_cholmod_super_solve.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -c ../Supernodal/cholmod_super_solve.c -o $@ #------------------------------------------------------------------------------- cholmod_l_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \ ../Supernodal/t_cholmod_super_numeric.c $(C) -DDLONG -c $(I) ../Supernodal/cholmod_super_numeric.c -o $@ cholmod_l_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c $(C) -DDLONG -c $(I) ../Supernodal/cholmod_super_symbolic.c -o $@ cholmod_l_super_solve.o: ../Supernodal/cholmod_super_solve.c \ ../Supernodal/t_cholmod_super_solve.c $(C) -DDLONG -c $(I) ../Supernodal/cholmod_super_solve.c -o $@ Matrix/src/CHOLMOD/Check/0000755000175100001440000000000012271765426014441 5ustar hornikusersMatrix/src/CHOLMOD/Check/License.txt0000644000175100001440000000204211770402705016551 0ustar hornikusersCHOLMOD/Check Module. Copyright (C) 2005-2006, Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.suitesparse.com Note that this license is for the CHOLMOD/Check module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Matrix/src/CHOLMOD/Check/cholmod_write.c0000644000175100001440000005124212271765436017451 0ustar hornikusers/* ========================================================================== */ /* === Check/cholmod_write ================================================== */ /* ========================================================================== */ /* Write a matrix to a file in Matrix Market form. * * A can be sparse or full. * * If present and non-empty, A and Z must have the same dimension. Z contains * the explicit zero entries in the matrix (which MATLAB drops). The entries * of Z appear as explicit zeros in the output file. Z is optional. If it is * an empty matrix it is ignored. Z must be sparse or empty, if present. * It is ignored if A is full. * * filename is the name of the output file. comments is file whose * contents are include after the Matrix Market header and before the first * data line. Ignored if an empty string or not present. * * Except for the workspace used by cholmod_symmetry (ncol integers) for * the sparse case, these routines use no workspace at all. */ #ifndef NCHECK #include "cholmod_internal.h" #include "cholmod_check.h" #include "cholmod_matrixops.h" #include #include #define MMLEN 1024 #define MAXLINE MMLEN+6 /* ========================================================================== */ /* === include_comments ===================================================== */ /* ========================================================================== */ /* Read in the comments file, if it exists, and copy it to the Matrix Market * file. A "%" is prepended to each line. Returns TRUE if successful, FALSE * otherwise. */ static int include_comments (FILE *f, const char *comments) { FILE *cf = NULL ; char buffer [MAXLINE] ; int ok = TRUE ; if (comments != NULL && comments [0] != '\0') { cf = fopen (comments, "r") ; if (cf == NULL) { return (FALSE) ; } while (ok && fgets (buffer, MAXLINE, cf) != NULL) { /* ensure the line is not too long */ buffer [MMLEN-1] = '\0' ; buffer [MMLEN-2] = '\n' ; ok = ok && (fprintf (f, "%%%s", buffer) > 0) ; } fclose (cf) ; } return (ok) ; } /* ========================================================================== */ /* === get_value ============================================================ */ /* ========================================================================== */ /* Get the pth value in the matrix. */ static void get_value ( double *Ax, /* real values, or real/imag. for CHOLMOD_COMPLEX type */ double *Az, /* imaginary values for CHOLMOD_ZOMPLEX type */ Int p, /* get the pth entry */ Int xtype, /* A->xtype: pattern, real, complex, or zomplex */ double *x, /* the real part */ double *z /* the imaginary part */ ) { switch (xtype) { case CHOLMOD_PATTERN: *x = 1 ; *z = 0 ; break ; case CHOLMOD_REAL: *x = Ax [p] ; *z = 0 ; break ; case CHOLMOD_COMPLEX: *x = Ax [2*p] ; *z = Ax [2*p+1] ; break ; case CHOLMOD_ZOMPLEX: *x = Ax [p] ; *z = Az [p] ; break ; } } /* ========================================================================== */ /* === print_value ========================================================== */ /* ========================================================================== */ /* Print a numeric value to the file, using the shortest format that ensures * the value is written precisely. Returns TRUE if successful, FALSE otherwise. */ static int print_value ( FILE *f, /* file to print to */ double x, /* value to print */ Int is_integer /* TRUE if printing as an integer */ ) { double y ; char s [MAXLINE], *p ; Int i, dest = 0, src = 0 ; int width, ok ; if (is_integer) { i = (Int) x ; ok = (fprintf (f, ID, i) > 0) ; return (ok) ; } /* ---------------------------------------------------------------------- */ /* handle Inf and NaN */ /* ---------------------------------------------------------------------- */ /* change -inf to -HUGE_DOUBLE, and change +inf and nan to +HUGE_DOUBLE */ if (CHOLMOD_IS_NAN (x) || x >= HUGE_DOUBLE) { x = HUGE_DOUBLE ; } else if (x <= -HUGE_DOUBLE) { x = -HUGE_DOUBLE ; } /* ---------------------------------------------------------------------- */ /* find the smallest acceptable precision */ /* ---------------------------------------------------------------------- */ for (width = 6 ; width < 20 ; width++) { sprintf (s, "%.*g", width, x) ; sscanf (s, "%lg", &y) ; if (x == y) break ; } /* ---------------------------------------------------------------------- */ /* shorten the string */ /* ---------------------------------------------------------------------- */ /* change "e+0" to "e", change "e+" to "e", and change "e-0" to "e-" */ for (i = 0 ; i < MAXLINE && s [i] != '\0' ; i++) { if (s [i] == 'e') { if (s [i+1] == '+') { dest = i+1 ; if (s [i+2] == '0') { /* delete characters s[i+1] and s[i+2] */ src = i+3 ; } else { /* delete characters s[i+1] */ src = i+2 ; } } else if (s [i+1] == '-') { dest = i+2 ; if (s [i+2] == '0') { /* delete character s[i+2] */ src = i+3 ; } else { /* no change */ break ; } } while (s [src] != '\0') { s [dest++] = s [src++] ; } s [dest] = '\0' ; break ; } } /* delete the leading "0" if present and not necessary */ p = s ; s [MAXLINE-1] = '\0' ; i = strlen (s) ; if (i > 2 && s [0] == '0' && s [1] == '.') { /* change "0.x" to ".x" */ p = s + 1 ; } else if (i > 3 && s [0] == '-' && s [1] == '0' && s [2] == '.') { /* change "-0.x" to "-.x" */ s [1] = '-' ; p = s + 1 ; } #if 0 /* double-check */ i = sscanf (p, "%lg", &z) ; if (i != 1 || y != z) { /* oops! something went wrong in the "e+0" edit, above. */ /* this "cannot" happen */ sprintf (s, "%.*g", width, x) ; p = s ; } #endif /* ---------------------------------------------------------------------- */ /* print the value to the file */ /* ---------------------------------------------------------------------- */ ok = (fprintf (f, "%s", p) > 0) ; return (ok) ; } /* ========================================================================== */ /* === print_triplet ======================================================== */ /* ========================================================================== */ /* Print a triplet, converting it to one-based. Returns TRUE if successful, * FALSE otherwise. */ static int print_triplet ( FILE *f, /* file to print to */ Int is_binary, /* TRUE if file is "pattern" */ Int is_complex, /* TRUE if file is "complex" */ Int is_integer, /* TRUE if file is "integer" */ Int i, /* row index (zero-based) */ Int j, /* column index (zero-based) */ double x, /* real part */ double z /* imaginary part */ ) { int ok ; ok = (fprintf (f, ID " " ID, 1+i, 1+j) > 0) ; if (!is_binary) { fprintf (f, " ") ; ok = ok && print_value (f, x, is_integer) ; if (is_complex) { fprintf (f, " ") ; ok = ok && print_value (f, z, is_integer) ; } } ok = ok && (fprintf (f, "\n") > 0) ; return (ok) ; } /* ========================================================================== */ /* === ntriplets ============================================================ */ /* ========================================================================== */ /* Compute the number of triplets that will be printed to the file * from the matrix A. */ static Int ntriplets ( cholmod_sparse *A, /* matrix that will be printed */ Int is_sym /* TRUE if the file is symmetric (lower part only)*/ ) { Int *Ap, *Ai, *Anz, packed, i, j, p, pend, ncol, stype, nz = 0 ; if (A == NULL) { /* the Z matrix is NULL */ return (0) ; } stype = A->stype ; Ap = A->p ; Ai = A->i ; Anz = A->nz ; packed = A->packed ; ncol = A->ncol ; for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? Ap [j+1] : p + Anz [j] ; for ( ; p < pend ; p++) { i = Ai [p] ; if ((stype < 0 && i >= j) || (stype == 0 && (i >= j || !is_sym))) { /* CHOLMOD matrix is symmetric-lower (and so is the file); * or CHOLMOD matrix is unsymmetric and either A(i,j) is in * the lower part or the file is unsymmetric. */ nz++ ; } else if (stype > 0 && i <= j) { /* CHOLMOD matrix is symmetric-upper, but the file is * symmetric-lower. Need to transpose the entry. */ nz++ ; } } } return (nz) ; } /* ========================================================================== */ /* === cholmod_write_sparse ================================================= */ /* ========================================================================== */ /* Write a sparse matrix to a file in Matrix Market format. Optionally include * comments, and print explicit zero entries given by the pattern of the Z * matrix. If not NULL, the Z matrix must have the same dimensions and stype * as A. * * Returns the symmetry in which the matrix was printed (1 to 7, see the * CHOLMOD_MM_* codes in CHOLMOD/Include/cholmod_core.h), or -1 on failure. * * If A and Z are sorted on input, and either unsymmetric (stype = 0) or * symmetric-lower (stype < 0), and if A and Z do not overlap, then the triplets * are sorted, first by column and then by row index within each column, with * no duplicate entries. If all the above holds except stype > 0, then the * triplets are sorted by row first and then column. */ int CHOLMOD(write_sparse) ( /* ---- input ---- */ FILE *f, /* file to write to, must already be open */ cholmod_sparse *A, /* matrix to print */ cholmod_sparse *Z, /* optional matrix with pattern of explicit zeros */ const char *comments, /* optional filename of comments to include */ /* --------------- */ cholmod_common *Common ) { double x = 0, z = 0 ; double *Ax, *Az ; Int *Ap, *Ai, *Anz, *Zp, *Zi, *Znz ; Int nrow, ncol, is_complex, symmetry, i, j, q, iz, p, nz, is_binary, stype, is_integer, asym, is_sym, xtype, apacked, zpacked, pend, qend, zsym ; int ok ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (f, EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; if (Z != NULL && (Z->nrow == 0 || Z->ncol == 0)) { /* Z is non-NULL but empty, so treat it as a NULL matrix */ Z = NULL ; } if (Z != NULL) { RETURN_IF_XTYPE_INVALID (Z, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; if (Z->nrow != A->nrow || Z->ncol != A->ncol || Z->stype != A->stype) { ERROR (CHOLMOD_INVALID, "dimension or type of A and Z mismatch") ; return (EMPTY) ; } } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get the A matrix */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; nrow = A->nrow ; ncol = A->ncol ; xtype = A->xtype ; apacked = A->packed ; if (xtype == CHOLMOD_PATTERN) { /* a CHOLMOD pattern matrix is printed as "pattern" in the file */ is_binary = TRUE ; is_integer = FALSE ; is_complex = FALSE ; } else if (xtype == CHOLMOD_REAL) { /* determine if a real matrix is in fact binary or integer */ is_binary = TRUE ; is_integer = TRUE ; is_complex = FALSE ; for (j = 0 ; (is_binary || is_integer) && j < ncol ; j++) { p = Ap [j] ; pend = (apacked) ? Ap [j+1] : p + Anz [j] ; for ( ; (is_binary || is_integer) && p < pend ; p++) { x = Ax [p] ; if (x != 1) { is_binary = FALSE ; } /* convert to Int and then back to double */ i = (Int) x ; z = (double) i ; if (z != x) { is_integer = FALSE ; } } } } else { /* a CHOLMOD complex matrix is printed as "complex" in the file */ is_binary = FALSE ; is_integer = FALSE ; is_complex = TRUE ; } /* ---------------------------------------------------------------------- */ /* get the Z matrix (only consider the pattern) */ /* ---------------------------------------------------------------------- */ Zp = NULL ; Zi = NULL ; Znz = NULL ; zpacked = TRUE ; if (Z != NULL) { Zp = Z->p ; Zi = Z->i ; Znz = Z->nz ; zpacked = Z->packed ; } /* ---------------------------------------------------------------------- */ /* determine the symmetry of A and Z */ /* ---------------------------------------------------------------------- */ stype = A->stype ; if (A->nrow != A->ncol) { asym = CHOLMOD_MM_RECTANGULAR ; } else if (stype != 0) { /* CHOLMOD's A and Z matrices have a symmetric (and matching) stype. * Note that the diagonal is not checked. */ asym = is_complex ? CHOLMOD_MM_HERMITIAN : CHOLMOD_MM_SYMMETRIC ; } else if (!A->sorted) { /* A is in unsymmetric storage, but unsorted */ asym = CHOLMOD_MM_UNSYMMETRIC ; } else { /* CHOLMOD's stype is zero (stored in unsymmetric form) */ asym = EMPTY ; zsym = EMPTY ; #ifndef NMATRIXOPS /* determine if the matrices are in fact symmetric or Hermitian */ asym = CHOLMOD(symmetry) (A, 1, NULL, NULL, NULL, NULL, Common) ; zsym = (Z == NULL) ? 999 : CHOLMOD(symmetry) (Z, 1, NULL, NULL, NULL, NULL, Common) ; #endif if (asym == EMPTY || zsym <= CHOLMOD_MM_UNSYMMETRIC) { /* not computed, out of memory, or Z is unsymmetric */ asym = CHOLMOD_MM_UNSYMMETRIC ; } } /* ---------------------------------------------------------------------- */ /* write the Matrix Market header */ /* ---------------------------------------------------------------------- */ ok = fprintf (f, "%%%%MatrixMarket matrix coordinate") > 0 ; if (is_complex) { ok = ok && (fprintf (f, " complex") > 0) ; } else if (is_binary) { ok = ok && (fprintf (f, " pattern") > 0) ; } else if (is_integer) { ok = ok && (fprintf (f, " integer") > 0) ; } else { ok = ok && (fprintf (f, " real") > 0) ; } is_sym = FALSE ; switch (asym) { case CHOLMOD_MM_RECTANGULAR: case CHOLMOD_MM_UNSYMMETRIC: /* A is rectangular or unsymmetric */ ok = ok && (fprintf (f, " general\n") > 0) ; is_sym = FALSE ; symmetry = CHOLMOD_MM_UNSYMMETRIC ; break ; case CHOLMOD_MM_SYMMETRIC: case CHOLMOD_MM_SYMMETRIC_POSDIAG: /* A is symmetric */ ok = ok && (fprintf (f, " symmetric\n") > 0) ; is_sym = TRUE ; symmetry = CHOLMOD_MM_SYMMETRIC ; break ; case CHOLMOD_MM_HERMITIAN: case CHOLMOD_MM_HERMITIAN_POSDIAG: /* A is Hermitian */ ok = ok && (fprintf (f, " Hermitian\n") > 0) ; is_sym = TRUE ; symmetry = CHOLMOD_MM_HERMITIAN ; break ; case CHOLMOD_MM_SKEW_SYMMETRIC: /* A is skew symmetric */ ok = ok && (fprintf (f, " skew-symmetric\n") > 0) ; is_sym = TRUE ; symmetry = CHOLMOD_MM_SKEW_SYMMETRIC ; break ; } /* ---------------------------------------------------------------------- */ /* include the comments if present */ /* ---------------------------------------------------------------------- */ ok = ok && include_comments (f, comments) ; /* ---------------------------------------------------------------------- */ /* write a sparse matrix (A and Z) */ /* ---------------------------------------------------------------------- */ nz = ntriplets (A, is_sym) + ntriplets (Z, is_sym) ; /* write the first data line, with nrow, ncol, and # of triplets */ ok = ok && (fprintf (f, ID " " ID " " ID "\n", nrow, ncol, nz) > 0) ; for (j = 0 ; ok && j < ncol ; j++) { /* merge column of A and Z */ p = Ap [j] ; pend = (apacked) ? Ap [j+1] : p + Anz [j] ; q = (Z == NULL) ? 0 : Zp [j] ; qend = (Z == NULL) ? 0 : ((zpacked) ? Zp [j+1] : q + Znz [j]) ; while (ok) { /* get the next row index from A and Z */ i = (p < pend) ? Ai [p] : (nrow+1) ; iz = (q < qend) ? Zi [q] : (nrow+2) ; if (i <= iz) { /* get A(i,j), or quit if both A and Z are exhausted */ if (i == nrow+1) break ; get_value (Ax, Az, p, xtype, &x, &z) ; p++ ; } else { /* get Z(i,j) */ i = iz ; x = 0 ; z = 0 ; q++ ; } if ((stype < 0 && i >= j) || (stype == 0 && (i >= j || !is_sym))) { /* CHOLMOD matrix is symmetric-lower (and so is the file); * or CHOLMOD matrix is unsymmetric and either A(i,j) is in * the lower part or the file is unsymmetric. */ ok = ok && print_triplet (f, is_binary, is_complex, is_integer, i,j, x,z) ; } else if (stype > 0 && i <= j) { /* CHOLMOD matrix is symmetric-upper, but the file is * symmetric-lower. Need to transpose the entry. If the * matrix is real, the complex part is ignored. If the matrix * is complex, it Hermitian. */ ASSERT (IMPLIES (is_complex, asym == CHOLMOD_MM_HERMITIAN)) ; if (z != 0) { z = -z ; } ok = ok && print_triplet (f, is_binary, is_complex, is_integer, j,i, x,z) ; } } } if (!ok) { ERROR (CHOLMOD_INVALID, "error reading/writing file") ; return (EMPTY) ; } return (asym) ; } /* ========================================================================== */ /* === cholmod_write_dense ================================================== */ /* ========================================================================== */ /* Write a dense matrix to a file in Matrix Market format. Optionally include * comments. Returns > 0 if successful, -1 otherwise (1 if rectangular, 2 if * square). Future versions may return 1 to 7 on success (a CHOLMOD_MM_* code, * just as cholmod_write_sparse does). * * A dense matrix is written in "general" format; symmetric formats in the * Matrix Market standard are not exploited. */ int CHOLMOD(write_dense) ( /* ---- input ---- */ FILE *f, /* file to write to, must already be open */ cholmod_dense *X, /* matrix to print */ const char *comments, /* optional filename of comments to include */ /* --------------- */ cholmod_common *Common ) { double x = 0, z = 0 ; double *Xx, *Xz ; Int nrow, ncol, is_complex, i, j, xtype, p ; int ok ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (f, EMPTY) ; RETURN_IF_NULL (X, EMPTY) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get the X matrix */ /* ---------------------------------------------------------------------- */ Xx = X->x ; Xz = X->z ; nrow = X->nrow ; ncol = X->ncol ; xtype = X->xtype ; is_complex = (xtype == CHOLMOD_COMPLEX) || (xtype == CHOLMOD_ZOMPLEX) ; /* ---------------------------------------------------------------------- */ /* write the Matrix Market header */ /* ---------------------------------------------------------------------- */ ok = (fprintf (f, "%%%%MatrixMarket matrix array") > 0) ; if (is_complex) { ok = ok && (fprintf (f, " complex general\n") > 0) ; } else { ok = ok && (fprintf (f, " real general\n") > 0) ; } /* ---------------------------------------------------------------------- */ /* include the comments if present */ /* ---------------------------------------------------------------------- */ ok = ok && include_comments (f, comments) ; /* ---------------------------------------------------------------------- */ /* write a dense matrix */ /* ---------------------------------------------------------------------- */ /* write the first data line, with nrow and ncol */ ok = ok && (fprintf (f, ID " " ID "\n", nrow, ncol) > 0) ; Xx = X->x ; Xz = X->z ; for (j = 0 ; ok && j < ncol ; j++) { for (i = 0 ; ok && i < nrow ; i++) { p = i + j*nrow ; get_value (Xx, Xz, p, xtype, &x, &z) ; ok = ok && print_value (f, x, FALSE) ; if (is_complex) { ok = ok && (fprintf (f, " ") > 0) ; ok = ok && print_value (f, z, FALSE) ; } ok = ok && (fprintf (f, "\n") > 0) ; } } if (!ok) { ERROR (CHOLMOD_INVALID, "error reading/writing file") ; return (EMPTY) ; } return ((nrow == ncol) ? CHOLMOD_MM_UNSYMMETRIC : CHOLMOD_MM_RECTANGULAR) ; } #endif Matrix/src/CHOLMOD/Check/cholmod_check.c0000644000175100001440000020250412271765436017373 0ustar hornikusers/* ========================================================================== */ /* === Check/cholmod_check ================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Check Module. Copyright (C) 2005-2013, Timothy A. Davis * The CHOLMOD/Check Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Routines to check and print the contents of the 5 CHOLMOD objects: * * No CHOLMOD routine calls the check or print routines. If a user wants to * check CHOLMOD's input parameters, a separate call to the appropriate check * routine should be used before calling other CHOLMOD routines. * * cholmod_check_common check statistics and workspace in Common * cholmod_check_sparse check sparse matrix in compressed column form * cholmod_check_dense check dense matrix * cholmod_check_factor check factorization * cholmod_check_triplet check sparse matrix in triplet form * * cholmod_print_common print statistics in Common * cholmod_print_sparse print sparse matrix in compressed column form * cholmod_print_dense print dense matrix * cholmod_print_factor print factorization * cholmod_print_triplet print sparse matrix in triplet form * * In addition, this file contains routines to check and print three types of * integer vectors: * * cholmod_check_perm check a permutation of 0:n-1 (no duplicates) * cholmod_check_subset check a subset of 0:n-1 (duplicates OK) * cholmod_check_parent check an elimination tree * * cholmod_print_perm print a permutation * cholmod_print_subset print a subset * cholmod_print_parent print an elimination tree * * Each Common->print level prints the items at or below the given level: * * 0: print nothing; just check the data structures and return TRUE/FALSE * 1: error messages * 2: warning messages * 3: one-line summary of each object printed * 4: short summary of each object (first and last few entries) * 5: entire contents of the object * * No CHOLMOD routine calls these routines, so no printing occurs unless * the user specifically calls a cholmod_print_* routine. Thus, the default * print level is 3. * * Common->precise controls the # of digits printed for numerical entries * (5 if FALSE, 15 if TRUE). * * If Common->print_function is NULL, then no printing occurs. The * cholmod_check_* and cholmod_print_* routines still check their inputs and * return TRUE/FALSE if the object is valid or not. * * This file also includes debugging routines that are enabled only when * NDEBUG is defined in cholmod_internal.h (cholmod_dump_*). */ #ifndef NCHECK #include "cholmod_internal.h" #include "cholmod_check.h" /* ========================================================================== */ /* === printing definitions ================================================= */ /* ========================================================================== */ #ifdef LONG #define I8 "%8ld" #define I_8 "%-8ld" #else #define I8 "%8d" #define I_8 "%-8d" #endif #define PR(i,format,arg) \ { \ if (print >= i && Common->print_function != NULL) \ { \ (Common->print_function) (format, arg) ; \ } \ } #define P1(format,arg) PR(1,format,arg) #define P2(format,arg) PR(2,format,arg) #define P3(format,arg) PR(3,format,arg) #define P4(format,arg) PR(4,format,arg) #define ERR(msg) \ { \ P1 ("\nCHOLMOD ERROR: %s: ", type) ; \ if (name != NULL) \ { \ P1 ("%s", name) ; \ } \ P1 (": %s\n", msg) ; \ ERROR (CHOLMOD_INVALID, "invalid") ; \ return (FALSE) ; \ } /* print a numerical value */ #define PRINTVALUE(value) \ { \ if (Common->precise) \ { \ P4 (" %23.15e", value) ; \ } \ else \ { \ P4 (" %.5g", value) ; \ } \ } /* start printing */ #define ETC_START(count,limit) \ { \ count = (init_print == 4) ? (limit) : (-1) ; \ } /* re-enable printing if condition is met */ #define ETC_ENABLE(condition,count,limit) \ { \ if ((condition) && init_print == 4) \ { \ count = limit ; \ print = 4 ; \ } \ } /* turn off printing if limit is reached */ #define ETC_DISABLE(count) \ { \ if ((count >= 0) && (count-- == 0) && print == 4) \ { \ P4 ("%s", " ...\n") ; \ print = 3 ; \ } \ } /* re-enable printing, or turn if off after limit is reached */ #define ETC(condition,count,limit) \ { \ ETC_ENABLE (condition, count, limit) ; \ ETC_DISABLE (count) ; \ } #define BOOLSTR(x) ((x) ? "true " : "false") /* ========================================================================== */ /* === print_value ========================================================== */ /* ========================================================================== */ static void print_value ( Int print, Int xtype, double *Xx, double *Xz, Int p, cholmod_common *Common) { if (xtype == CHOLMOD_REAL) { PRINTVALUE (Xx [p]) ; } else if (xtype == CHOLMOD_COMPLEX) { P4 ("%s", "(") ; PRINTVALUE (Xx [2*p ]) ; P4 ("%s", " , ") ; PRINTVALUE (Xx [2*p+1]) ; P4 ("%s", ")") ; } else if (xtype == CHOLMOD_ZOMPLEX) { P4 ("%s", "(") ; PRINTVALUE (Xx [p]) ; P4 ("%s", " , ") ; PRINTVALUE (Xz [p]) ; P4 ("%s", ")") ; } } /* ========================================================================== */ /* === cholmod_check_common ================================================= */ /* ========================================================================== */ /* Print and verify the contents of Common */ static int check_common ( Int print, const char *name, cholmod_common *Common ) { double fl, lnz ; double *Xwork ; Int *Flag, *Head ; SuiteSparse_long mark ; Int i, nrow, nmethods, ordering, xworksize, amd_backup, init_print ; const char *type = "common" ; /* ---------------------------------------------------------------------- */ /* print control parameters and statistics */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; init_print = print ; P2 ("%s", "\n") ; P1 ("CHOLMOD version %d", CHOLMOD_MAIN_VERSION) ; P1 (".%d", CHOLMOD_SUB_VERSION) ; P1 (".%d", CHOLMOD_SUBSUB_VERSION) ; P1 (", %s: ", CHOLMOD_DATE) ; if (name != NULL) { P1 ("%s: ", name) ; } switch (Common->status) { case CHOLMOD_OK: P1 ("%s", "status: OK\n") ; break ; case CHOLMOD_OUT_OF_MEMORY: P1 ("%s", "status: ERROR, out of memory\n") ; break ; case CHOLMOD_INVALID: P1 ("%s", "status: ERROR, invalid parameter\n") ; break ; case CHOLMOD_TOO_LARGE: P1 ("%s", "status: ERROR, problem too large\n") ; break ; case CHOLMOD_NOT_INSTALLED: P1 ("%s", "status: ERROR, method not installed\n") ; break ; #if GPU_BLAS case CHOLMOD_GPU_PROBLEM: P1 ("%s", "status: ERROR, GPU had a fatal error\n") ; break ; #endif case CHOLMOD_NOT_POSDEF: P1 ("%s", "status: warning, matrix not positive definite\n") ; break ; case CHOLMOD_DSMALL: P1 ("%s", "status: warning, diagonal entry has tiny abs. value\n") ; break ; default: ERR ("unknown status") ; } P2 (" Architecture: %s\n", CHOLMOD_ARCHITECTURE) ; P3 (" sizeof(int): %d\n", (int) sizeof (int)) ; P3 (" sizeof(SuiteSparse_long): %d\n", (int) sizeof (SuiteSparse_long)); P3 (" sizeof(void *): %d\n", (int) sizeof (void *)) ; P3 (" sizeof(double): %d\n", (int) sizeof (double)) ; P3 (" sizeof(Int): %d (CHOLMOD's basic integer)\n", (int) sizeof (Int)) ; P3 (" sizeof(BLAS_INT): %d (integer used in the BLAS)\n", (int) sizeof (BLAS_INT)) ; if (Common->fl != EMPTY) { P2 ("%s", " Results from most recent analysis:\n") ; P2 (" Cholesky flop count: %.5g\n", Common->fl) ; P2 (" Nonzeros in L: %.5g\n", Common->lnz) ; } if (Common->modfl != EMPTY) { P2 (" Update/downdate flop count: %.5g\n", Common->modfl) ; } P2 (" memory blocks in use: %8.0f\n", (double) (Common->malloc_count)) ; P2 (" memory in use (MB): %8.1f\n", (double) (Common->memory_inuse) / 1048576.) ; P2 (" peak memory usage (MB): %8.1f\n", (double) (Common->memory_usage) / 1048576.) ; /* ---------------------------------------------------------------------- */ /* primary control parameters and related ordering statistics */ /* ---------------------------------------------------------------------- */ P3 (" maxrank: update/downdate rank: "ID"\n", (Int) CHOLMOD(maxrank) (0, Common)) ; P3 (" supernodal control: %d", Common->supernodal) ; P3 (" %g ", Common->supernodal_switch) ; if (Common->supernodal <= CHOLMOD_SIMPLICIAL) { P3 ("%s", "(always do simplicial)\n") ; } else if (Common->supernodal == CHOLMOD_AUTO) { P3 ("(supernodal if flops/lnz >= %g)\n", Common->supernodal_switch) ; } else { P3 ("%s", "(always do supernodal)\n") ; } nmethods = MIN (Common->nmethods, CHOLMOD_MAXMETHODS) ; nmethods = MAX (0, nmethods) ; if (nmethods > 0) { P3 ("%s", " nmethods: number of ordering methods to try: ") ; P3 (""ID"\n", nmethods) ; amd_backup = (nmethods > 1) || (nmethods == 1 && (Common->method [0].ordering == CHOLMOD_METIS || Common->method [0].ordering == CHOLMOD_NESDIS)) ; } else { P3 ("%s", " nmethods=0: default strategy: Try user permutation if " "given. Try AMD.\n") ; #ifndef NPARTITION if (Common->default_nesdis) { P3 ("%s", " Try NESDIS if AMD reports flops/nnz(L) >= 500 and " "nnz(L)/nnz(A) >= 5.\n") ; } else { P3 ("%s", " Try METIS if AMD reports flops/nnz(L) >= 500 and " "nnz(L)/nnz(A) >= 5.\n") ; } #endif P3 ("%s", " Select best ordering tried.\n") ; Common->method [0].ordering = CHOLMOD_GIVEN ; Common->method [1].ordering = CHOLMOD_AMD ; Common->method [2].ordering = (Common->default_nesdis ? CHOLMOD_NESDIS : CHOLMOD_METIS) ; amd_backup = FALSE ; #ifndef NPARTITION nmethods = 3 ; #else nmethods = 2 ; #endif } for (i = 0 ; i < nmethods ; i++) { P3 (" method "ID": ", i) ; ordering = Common->method [i].ordering ; fl = Common->method [i].fl ; lnz = Common->method [i].lnz ; switch (ordering) { case CHOLMOD_NATURAL: P3 ("%s", "natural\n") ; break ; case CHOLMOD_GIVEN: P3 ("%s", "user permutation (if given)\n") ; break ; case CHOLMOD_AMD: P3 ("%s", "AMD (or COLAMD if factorizing AA')\n") ; amd_backup = FALSE ; break ; case CHOLMOD_COLAMD: P3 ("%s", "AMD if factorizing A, COLAMD if factorizing AA')\n"); amd_backup = FALSE ; break ; case CHOLMOD_METIS: P3 ("%s", "METIS_NodeND nested dissection\n") ; break ; case CHOLMOD_NESDIS: P3 ("%s", "CHOLMOD nested dissection\n") ; P3 (" nd_small: # nodes in uncut subgraph: "ID"\n", (Int) (Common->method [i].nd_small)) ; P3 (" nd_compress: compress the graph: %s\n", BOOLSTR (Common->method [i].nd_compress)) ; P3 (" nd_camd: use constrained min degree: %s\n", BOOLSTR (Common->method [i].nd_camd)) ; break ; default: P3 (ID, ordering) ; ERR ("unknown ordering method") ; break ; } if (!(ordering == CHOLMOD_NATURAL || ordering == CHOLMOD_GIVEN)) { if (Common->method [i].prune_dense < 0) { P3 (" prune_dense: for pruning dense nodes: %s\n", " none pruned") ; } else { P3 (" prune_dense: for pruning dense nodes: " "%.5g\n", Common->method [i].prune_dense) ; P3 (" a dense node has degree " ">= max(16,(%.5g)*sqrt(n))\n", Common->method [i].prune_dense) ; } } if (ordering == CHOLMOD_COLAMD || ordering == CHOLMOD_NESDIS) { if (Common->method [i].prune_dense2 < 0) { P3 (" prune_dense2: for pruning dense rows for AA':" " %s\n", " none pruned") ; } else { P3 (" prune_dense2: for pruning dense rows for AA':" " %.5g\n", Common->method [i].prune_dense2) ; P3 (" a dense row has degree " ">= max(16,(%.5g)*sqrt(ncol))\n", Common->method [i].prune_dense2) ; } } if (fl != EMPTY) P3 (" flop count: %.5g\n", fl) ; if (lnz != EMPTY) P3 (" nnz(L): %.5g\n", lnz) ; } /* backup AMD results, if any */ if (amd_backup) { P3 ("%s", " backup method: ") ; P3 ("%s", "AMD (or COLAMD if factorizing AA')\n") ; fl = Common->method [nmethods].fl ; lnz = Common->method [nmethods].lnz ; if (fl != EMPTY) P3 (" AMD flop count: %.5g\n", fl) ; if (lnz != EMPTY) P3 (" AMD nnz(L): %.5g\n", lnz) ; } /* ---------------------------------------------------------------------- */ /* arcane control parameters */ /* ---------------------------------------------------------------------- */ if (Common->final_asis) { P4 ("%s", " final_asis: TRUE, leave as is\n") ; } else { P4 ("%s", " final_asis: FALSE, convert when done\n") ; if (Common->final_super) { P4 ("%s", " final_super: TRUE, leave in supernodal form\n") ; } else { P4 ("%s", " final_super: FALSE, convert to simplicial form\n") ; } if (Common->final_ll) { P4 ("%s", " final_ll: TRUE, convert to LL' form\n") ; } else { P4 ("%s", " final_ll: FALSE, convert to LDL' form\n") ; } if (Common->final_pack) { P4 ("%s", " final_pack: TRUE, pack when done\n") ; } else { P4 ("%s", " final_pack: FALSE, do not pack when done\n") ; } if (Common->final_monotonic) { P4 ("%s", " final_monotonic: TRUE, ensure L is monotonic\n") ; } else { P4 ("%s", " final_monotonic: FALSE, do not ensure L is monotonic\n") ; } P4 (" final_resymbol: remove zeros from amalgamation: %s\n", BOOLSTR (Common->final_resymbol)) ; } P4 (" dbound: LDL' diagonal threshold: % .5g\n Entries with abs. value" " less than dbound are replaced with +/- dbound.\n", Common->dbound) ; P4 (" grow0: memory reallocation: % .5g\n", Common->grow0) ; P4 (" grow1: memory reallocation: % .5g\n", Common->grow1) ; P4 (" grow2: memory reallocation: %g\n", (double) (Common->grow2)) ; P4 ("%s", " nrelax, zrelax: supernodal amalgamation rule:\n") ; P4 ("%s", " s = # columns in two adjacent supernodes\n") ; P4 ("%s", " z = % of zeros in new supernode if they are merged.\n") ; P4 ("%s", " Two supernodes are merged if") ; P4 (" (s <= %g) or (no new zero entries) or\n", (double) (Common->nrelax [0])) ; P4 (" (s <= %g and ", (double) (Common->nrelax [1])) ; P4 ("z < %.5g%%) or", Common->zrelax [0] * 100) ; P4 (" (s <= %g and ", (double) (Common->nrelax [2])) ; P4 ("z < %.5g%%) or", Common->zrelax [1] * 100) ; P4 (" (z < %.5g%%)\n", Common->zrelax [2] * 100) ; /* ---------------------------------------------------------------------- */ /* check workspace */ /* ---------------------------------------------------------------------- */ mark = Common->mark ; nrow = Common->nrow ; Flag = Common->Flag ; Head = Common->Head ; if (nrow > 0) { if (mark < 0 || Flag == NULL || Head == NULL) { ERR ("workspace corrupted (Flag and/or Head missing)") ; } for (i = 0 ; i < nrow ; i++) { if (Flag [i] >= mark) { PRINT0 (("Flag ["ID"]="ID", mark = %ld\n", i, Flag [i], mark)) ; ERR ("workspace corrupted (Flag)") ; } } for (i = 0 ; i <= nrow ; i++) { if (Head [i] != EMPTY) { PRINT0 (("Head ["ID"] = "ID",\n", i, Head [i])) ; ERR ("workspace corrupted (Head)") ; } } } xworksize = Common->xworksize ; Xwork = Common->Xwork ; if (xworksize > 0) { if (Xwork == NULL) { ERR ("workspace corrupted (Xwork missing)") ; } for (i = 0 ; i < xworksize ; i++) { if (Xwork [i] != 0.) { PRINT0 (("Xwork ["ID"] = %g\n", i, Xwork [i])) ; ERR ("workspace corrupted (Xwork)") ; } } } /* workspace and parameters are valid */ P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } int CHOLMOD(check_common) ( cholmod_common *Common ) { return (check_common (0, NULL, Common)) ; } int CHOLMOD(print_common) ( /* ---- input ---- */ const char *name, /* printed name of Common object */ /* --------------- */ cholmod_common *Common ) { Int print = (Common == NULL) ? 3 : (Common->print) ; return (check_common (print, name, Common)) ; } /* ========================================================================== */ /* === cholmod_gpu_stats ==================================================== */ /* ========================================================================== */ /* Print CPU / GPU statistics. If the timer is not installed, the times are reported as zero, but this function still works. Likewise, the function still works if the GPU BLAS is not installed. */ int CHOLMOD(gpu_stats) ( cholmod_common *Common /* input */ ) { double cpu_time, gpu_time ; int print ; RETURN_IF_NULL_COMMON (FALSE) ; print = Common->print ; P2 ("%s", "\nCHOLMOD GPU/CPU statistics:\n") ; P2 ("SYRK CPU calls %12.0f", (double) Common->CHOLMOD_CPU_SYRK_CALLS) ; P2 (" time %12.4e\n", Common->CHOLMOD_CPU_SYRK_TIME) ; P2 (" GPU calls %12.0f", (double) Common->CHOLMOD_GPU_SYRK_CALLS) ; P2 (" time %12.4e\n", Common->CHOLMOD_GPU_SYRK_TIME) ; P2 ("GEMM CPU calls %12.0f", (double) Common->CHOLMOD_CPU_GEMM_CALLS) ; P2 (" time %12.4e\n", Common->CHOLMOD_CPU_GEMM_TIME) ; P2 (" GPU calls %12.0f", (double) Common->CHOLMOD_GPU_GEMM_CALLS) ; P2 (" time %12.4e\n", Common->CHOLMOD_GPU_GEMM_TIME) ; P2 ("POTRF CPU calls %12.0f", (double) Common->CHOLMOD_CPU_POTRF_CALLS) ; P2 (" time %12.4e\n", Common->CHOLMOD_CPU_POTRF_TIME) ; P2 (" GPU calls %12.0f", (double) Common->CHOLMOD_GPU_POTRF_CALLS) ; P2 (" time %12.4e\n", Common->CHOLMOD_GPU_POTRF_TIME) ; P2 ("TRSM CPU calls %12.0f", (double) Common->CHOLMOD_CPU_TRSM_CALLS) ; P2 (" time %12.4e\n", Common->CHOLMOD_CPU_TRSM_TIME) ; P2 (" GPU calls %12.0f", (double) Common->CHOLMOD_GPU_TRSM_CALLS) ; P2 (" time %12.4e\n", Common->CHOLMOD_GPU_TRSM_TIME) ; cpu_time = Common->CHOLMOD_CPU_SYRK_TIME + Common->CHOLMOD_CPU_TRSM_TIME + Common->CHOLMOD_CPU_GEMM_TIME + Common->CHOLMOD_CPU_POTRF_TIME ; gpu_time = Common->CHOLMOD_GPU_SYRK_TIME + Common->CHOLMOD_GPU_TRSM_TIME + Common->CHOLMOD_GPU_GEMM_TIME + Common->CHOLMOD_GPU_POTRF_TIME ; P2 ("time in the BLAS: CPU %12.4e", cpu_time) ; P2 (" GPU %12.4e", gpu_time) ; P2 (" total: %12.4e\n", cpu_time + gpu_time) ; P2 ("assembly time %12.4e", Common->CHOLMOD_ASSEMBLE_TIME) ; P2 (" %12.4e\n", Common->CHOLMOD_ASSEMBLE_TIME2) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_check_sparse ================================================= */ /* ========================================================================== */ /* Ensure that a sparse matrix in column-oriented form is valid, and optionally * print it. Returns the number of entries on the diagonal or -1 if error. * * workspace: Iwork (nrow) */ static SuiteSparse_long check_sparse ( Int *Wi, Int print, const char *name, cholmod_sparse *A, SuiteSparse_long *nnzdiag, cholmod_common *Common ) { double *Ax, *Az ; Int *Ap, *Ai, *Anz ; Int nrow, ncol, nzmax, sorted, packed, j, p, pend, i, nz, ilast, space, init_print, dnz, count, xtype ; const char *type = "sparse" ; /* ---------------------------------------------------------------------- */ /* print header information */ /* ---------------------------------------------------------------------- */ P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD sparse: ") ; if (name != NULL) { P3 ("%s: ", name) ; } if (A == NULL) { ERR ("null") ; } nrow = A->nrow ; ncol = A->ncol ; nzmax = A->nzmax ; sorted = A->sorted ; packed = A->packed ; xtype = A->xtype ; Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; nz = CHOLMOD(nnz) (A, Common) ; P3 (" "ID"", nrow) ; P3 ("-by-"ID", ", ncol) ; P3 ("nz "ID",", nz) ; if (A->stype > 0) { P3 ("%s", " upper.") ; } else if (A->stype < 0) { P3 ("%s", " lower.") ; } else { P3 ("%s", " up/lo.") ; } P4 ("\n nzmax "ID", ", nzmax) ; if (nz > nzmax) { ERR ("nzmax too small") ; } if (!sorted) { P4 ("%s", "un") ; } P4 ("%s", "sorted, ") ; if (!packed) { P4 ("%s", "un") ; } P4 ("%s", "packed, ") ; switch (A->itype) { case CHOLMOD_INT: P4 ("%s", "\n scalar types: int, ") ; break ; case CHOLMOD_INTLONG: ERR ("mixed int/long type unsupported") ; case CHOLMOD_LONG: P4 ("%s", "\n scalar types: SuiteSparse_long, "); break ; default: ERR ("unknown itype") ; } switch (A->xtype) { case CHOLMOD_PATTERN: P4 ("%s", "pattern") ; break ; case CHOLMOD_REAL: P4 ("%s", "real") ; break ; case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ; case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ; default: ERR ("unknown xtype") ; } switch (A->dtype) { case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ; case CHOLMOD_SINGLE: ERR ("float unsupported") ; default: ERR ("unknown dtype") ; } if (A->itype != ITYPE || A->dtype != DTYPE) { ERR ("integer and real type must match routine") ; } if (A->stype && nrow != ncol) { ERR ("symmetric but not square") ; } /* check for existence of Ap, Ai, Anz, Ax, and Az arrays */ if (Ap == NULL) { ERR ("p array not present") ; } if (Ai == NULL) { ERR ("i array not present") ; } if (!packed && Anz == NULL) { ERR ("nz array not present") ; } if (xtype != CHOLMOD_PATTERN && Ax == NULL) { ERR ("x array not present") ; } if (xtype == CHOLMOD_ZOMPLEX && Az == NULL) { ERR ("z array not present") ; } /* packed matrices must start at Ap [0] = 0 */ if (packed && Ap [0] != 0) { ERR ("p [0] must be zero") ; } if (packed && (Ap [ncol] < Ap [0] || Ap [ncol] > nzmax)) { ERR ("p [ncol] invalid") ; } /* ---------------------------------------------------------------------- */ /* allocate workspace if needed */ /* ---------------------------------------------------------------------- */ if (!sorted) { if (Wi == NULL) { CHOLMOD(allocate_work) (0, nrow, 0, Common) ; Wi = Common->Iwork ; /* size nrow, (i/i/l) */ } if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } for (i = 0 ; i < nrow ; i++) { Wi [i] = EMPTY ; } } /* ---------------------------------------------------------------------- */ /* check and print each column */ /* ---------------------------------------------------------------------- */ init_print = print ; dnz = 0 ; ETC_START (count, 8) ; for (j = 0 ; j < ncol ; j++) { ETC (j == ncol-1, count, 4) ; p = Ap [j] ; if (packed) { pend = Ap [j+1] ; nz = pend - p ; } else { /* Note that Anz [j] < 0 is treated as zero */ nz = MAX (0, Anz [j]) ; pend = p + nz ; } /* Note that space can be negative if the matrix is non-monotonic */ space = Ap [j+1] - p ; P4 (" col "ID":", j) ; P4 (" nz "ID"", nz) ; P4 (" start "ID"", p) ; P4 (" end "ID"", pend) ; if (!packed) { P4 (" space "ID"", space) ; } P4 ("%s", ":\n") ; if (p < 0 || pend > nzmax) { ERR ("pointer invalid") ; } if (nz < 0 || nz > nrow) { ERR ("nz invalid") ; } ilast = EMPTY ; for ( ; p < pend ; p++) { ETC (j == ncol-1 && p >= pend-4, count, -1) ; i = Ai [p] ; P4 (" "I8":", i) ; print_value (print, xtype, Ax, Az, p, Common) ; if (i == j) { dnz++ ; } if (i < 0 || i >= nrow) { ERR ("row index out of range") ; } if (sorted && i <= ilast) { ERR ("row indices out of order") ; } if (!sorted && Wi [i] == j) { ERR ("duplicate row index") ; } P4 ("%s", "\n") ; ilast = i ; if (!sorted) { Wi [i] = j ; } } } /* matrix is valid */ P4 (" nnz on diagonal: "ID"\n", dnz) ; P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; *nnzdiag = dnz ; return (TRUE) ; } int CHOLMOD(check_sparse) ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to check */ /* --------------- */ cholmod_common *Common ) { SuiteSparse_long nnzdiag ; RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_sparse (NULL, 0, NULL, A, &nnzdiag, Common)) ; } int CHOLMOD(print_sparse) ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to print */ const char *name, /* printed name of sparse matrix */ /* --------------- */ cholmod_common *Common ) { SuiteSparse_long nnzdiag ; RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_sparse (NULL, Common->print, name, A, &nnzdiag, Common)) ; } /* ========================================================================== */ /* === cholmod_check_dense ================================================== */ /* ========================================================================== */ /* Ensure a dense matrix is valid, and optionally print it. */ static int check_dense ( Int print, const char *name, cholmod_dense *X, cholmod_common *Common ) { double *Xx, *Xz ; Int i, j, d, nrow, ncol, nzmax, nz, init_print, count, xtype ; const char *type = "dense" ; /* ---------------------------------------------------------------------- */ /* print header information */ /* ---------------------------------------------------------------------- */ P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD dense: ") ; if (name != NULL) { P3 ("%s: ", name) ; } if (X == NULL) { ERR ("null") ; } nrow = X->nrow ; ncol = X->ncol ; nzmax = X->nzmax ; d = X->d ; Xx = X->x ; Xz = X->z ; xtype = X->xtype ; P3 (" "ID"", nrow) ; P3 ("-by-"ID", ", ncol) ; P4 ("\n leading dimension "ID", ", d) ; P4 ("nzmax "ID", ", nzmax) ; if (d * ncol > nzmax) { ERR ("nzmax too small") ; } if (d < nrow) { ERR ("leading dimension must be >= # of rows") ; } if (Xx == NULL) { ERR ("null") ; } switch (X->xtype) { case CHOLMOD_PATTERN: ERR ("pattern unsupported") ; break ; case CHOLMOD_REAL: P4 ("%s", "real") ; break ; case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ; case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ; default: ERR ("unknown xtype") ; } switch (X->dtype) { case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ; case CHOLMOD_SINGLE: ERR ("single unsupported") ; default: ERR ("unknown dtype") ; } /* ---------------------------------------------------------------------- */ /* check and print each entry */ /* ---------------------------------------------------------------------- */ if (print >= 4) { init_print = print ; ETC_START (count, 9) ; nz = nrow * ncol ; for (j = 0 ; j < ncol ; j++) { ETC (j == ncol-1, count, 5) ; P4 (" col "ID":\n", j) ; for (i = 0 ; i < nrow ; i++) { ETC (j == ncol-1 && i >= nrow-4, count, -1) ; P4 (" "I8":", i) ; print_value (print, xtype, Xx, Xz, i+j*d, Common) ; P4 ("%s", "\n") ; } } } /* dense is valid */ P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } int CHOLMOD(check_dense) ( /* ---- input ---- */ cholmod_dense *X, /* dense matrix to check */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_dense (0, NULL, X, Common)) ; } int CHOLMOD(print_dense) ( /* ---- input ---- */ cholmod_dense *X, /* dense matrix to print */ const char *name, /* printed name of dense matrix */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_dense (Common->print, name, X, Common)) ; } /* ========================================================================== */ /* === cholmod_check_subset ================================================= */ /* ========================================================================== */ /* Ensure S (0:len-1) is a subset of 0:n-1. Duplicates are allowed. S may be * NULL. A negative len denotes the set 0:n-1. * * To check the rset and cset for A(rset,cset), where nc and nr are the length * of cset and rset respectively: * * cholmod_check_subset (cset, nc, A->ncol, Common) ; * cholmod_check_subset (rset, nr, A->nrow, Common) ; * * workspace: none */ static int check_subset ( Int *S, SuiteSparse_long len, size_t n, Int print, const char *name, cholmod_common *Common ) { Int i, k, init_print, count ; const char *type = "subset" ; init_print = print ; if (S == NULL) { /* zero len denotes S = [ ], negative len denotes S = 0:n-1 */ len = (len < 0) ? (-1) : 0 ; } P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD subset: ") ; if (name != NULL) { P3 ("%s: ", name) ; } P3 (" len: %ld ", len) ; if (len < 0) { P3 ("%s", "(denotes 0:n-1) ") ; } P3 ("n: "ID"", (Int) n) ; P4 ("%s", "\n") ; if (len <= 0 || S == NULL) { P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } if (print >= 4) { ETC_START (count, 8) ; for (k = 0 ; k < ((Int) len) ; k++) { ETC (k == ((Int) len) - 4, count, -1) ; i = S [k] ; P4 (" "I8":", k) ; P4 (" "ID"\n", i) ; if (i < 0 || i >= ((Int) n)) { ERR ("entry out range") ; } } } else { for (k = 0 ; k < ((Int) len) ; k++) { i = S [k] ; if (i < 0 || i >= ((Int) n)) { ERR ("entry out range") ; } } } P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } int CHOLMOD(check_subset) ( /* ---- input ---- */ Int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */ SuiteSparse_long len, /* size of Set (an integer array), or < 0 if 0:n-1 */ size_t n, /* 0:n-1 is valid range */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_subset (Set, len, n, 0, NULL, Common)) ; } int CHOLMOD(print_subset) ( /* ---- input ---- */ Int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */ SuiteSparse_long len, /* size of Set (an integer array), or < 0 if 0:n-1 */ size_t n, /* 0:n-1 is valid range */ const char *name, /* printed name of Set */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_subset (Set, len, n, Common->print, name, Common)) ; } /* ========================================================================== */ /* === cholmod_check_perm =================================================== */ /* ========================================================================== */ /* Ensure that Perm [0..len-1] is a permutation of a subset of 0:n-1. Perm * may be NULL, which is interpreted as the identity permutation. There can * be no duplicate entries (len must be <= n). * * If n <= Common->nrow, then this routine takes O(len) time and does not * allocate any memory, by using Common->Flag. Otherwise, it takes O(n) time * and ensures that Common->Iwork is at least n*sizeof(Int) in size. * * To check the fset: cholmod_check_perm (fset, fsize, ncol, Common) ; * To check a permutation: cholmod_check_perm (Perm, n, n, Common) ; * * workspace: Flag (n) if n <= Common->nrow, Iwork (n) otherwise. */ static int check_perm ( Int *Wi, Int print, const char *name, Int *Perm, size_t len, size_t n, cholmod_common *Common ) { Int *Flag ; Int i, k, mark, init_print, count ; const char *type = "perm" ; /* ---------------------------------------------------------------------- */ /* checks that take O(1) time */ /* ---------------------------------------------------------------------- */ if (Perm == NULL || n == 0) { /* Perm is valid implicit identity, or empty */ return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* checks that take O(n) time or require memory allocation */ /* ---------------------------------------------------------------------- */ init_print = print ; ETC_START (count, 8) ; if (Wi == NULL && n <= Common->nrow) { /* use the Common->Flag array if it's big enough */ mark = CHOLMOD(clear_flag) (Common) ; Flag = Common->Flag ; ASSERT (CHOLMOD(dump_work) (TRUE, FALSE, 0, Common)) ; if (print >= 4) { for (k = 0 ; k < ((Int) len) ; k++) { ETC (k >= ((Int) len) - 4, count, -1) ; i = Perm [k] ; P4 (" "I8":", k) ; P4 (""ID"\n", i) ; if (i < 0 || i >= ((Int) n) || Flag [i] == mark) { CHOLMOD(clear_flag) (Common) ; ERR ("invalid permutation") ; } Flag [i] = mark ; } } else { for (k = 0 ; k < ((Int) len) ; k++) { i = Perm [k] ; if (i < 0 || i >= ((Int) n) || Flag [i] == mark) { CHOLMOD(clear_flag) (Common) ; ERR ("invalid permutation") ; } Flag [i] = mark ; } } CHOLMOD(clear_flag) (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, FALSE, 0, Common)) ; } else { if (Wi == NULL) { /* use Common->Iwork instead, but initialize it first */ CHOLMOD(allocate_work) (0, n, 0, Common) ; Wi = Common->Iwork ; /* size n, (i/i/i) is OK */ } if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } for (i = 0 ; i < ((Int) n) ; i++) { Wi [i] = FALSE ; } if (print >= 4) { for (k = 0 ; k < ((Int) len) ; k++) { ETC (k >= ((Int) len) - 4, count, -1) ; i = Perm [k] ; P4 (" "I8":", k) ; P4 (""ID"\n", i) ; if (i < 0 || i >= ((Int) n) || Wi [i]) { ERR ("invalid permutation") ; } Wi [i] = TRUE ; } } else { for (k = 0 ; k < ((Int) len) ; k++) { i = Perm [k] ; if (i < 0 || i >= ((Int) n) || Wi [i]) { ERR ("invalid permutation") ; } Wi [i] = TRUE ; } } } /* perm is valid */ return (TRUE) ; } int CHOLMOD(check_perm) ( /* ---- input ---- */ Int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */ size_t len, /* size of Perm (an integer array) */ size_t n, /* 0:n-1 is valid range */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_perm (NULL, 0, NULL, Perm, len, n, Common)) ; } int CHOLMOD(print_perm) ( /* ---- input ---- */ Int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */ size_t len, /* size of Perm (an integer array) */ size_t n, /* 0:n-1 is valid range */ const char *name, /* printed name of Perm */ /* --------------- */ cholmod_common *Common ) { Int ok, print ; RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; print = Common->print ; P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD perm: ") ; if (name != NULL) { P3 ("%s: ", name) ; } P3 (" len: "ID"", (Int) len) ; P3 (" n: "ID"", (Int) n) ; P4 ("%s", "\n") ; ok = check_perm (NULL, print, name, Perm, len, n, Common) ; if (ok) { P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; } return (ok) ; } /* ========================================================================== */ /* === cholmod_check_parent ================================================= */ /* ========================================================================== */ /* Ensure that Parent is a valid elimination tree of nodes 0 to n-1. * If j is a root of the tree then Parent [j] is EMPTY (-1). * * NOTE: this check will fail if applied to the component tree (CParent) in * cholmod_nested_dissection, unless it has been postordered and renumbered. * * workspace: none */ static int check_parent ( Int *Parent, size_t n, Int print, const char *name, cholmod_common *Common ) { Int j, p, init_print, count ; const char *type = "parent" ; init_print = print ; P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD parent: ") ; if (name != NULL) { P3 ("%s: ", name) ; } P3 (" n: "ID"", (Int) n) ; P4 ("%s", "\n") ; if (Parent == NULL) { ERR ("null") ; } /* ---------------------------------------------------------------------- */ /* checks that take O(n) time */ /* ---------------------------------------------------------------------- */ ETC_START (count, 8) ; for (j = 0 ; j < ((Int) n) ; j++) { ETC (j == ((Int) n) - 4, count, -1) ; p = Parent [j] ; P4 (" "I8":", j) ; P4 (" "ID"\n", p) ; if (!(p == EMPTY || p > j)) { ERR ("invalid") ; } } P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } int CHOLMOD(check_parent) ( /* ---- input ---- */ Int *Parent, /* Parent [0:n-1] is an elimination tree */ size_t n, /* size of Parent */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_parent (Parent, n, 0, NULL, Common)) ; } int CHOLMOD(print_parent) ( /* ---- input ---- */ Int *Parent, /* Parent [0:n-1] is an elimination tree */ size_t n, /* size of Parent */ const char *name, /* printed name of Parent */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_parent (Parent, n, Common->print, name, Common)) ; } /* ========================================================================== */ /* === cholmod_check_factor ================================================= */ /* ========================================================================== */ static int check_factor ( Int *Wi, Int print, const char *name, cholmod_factor *L, cholmod_common *Common ) { double *Lx, *Lz ; Int *Lp, *Li, *Lnz, *Lnext, *Lprev, *Perm, *ColCount, *Lpi, *Lpx, *Super, *Ls ; Int n, nzmax, j, p, pend, i, nz, ordering, space, is_monotonic, minor, count, precise, init_print, ilast, lnz, head, tail, jprev, plast, jnext, examine_super, nsuper, s, k1, k2, psi, psend, psx, nsrow, nscol, ps2, psxend, ssize, xsize, maxcsize, maxesize, nsrow2, jj, ii, xtype ; Int for_cholesky ; const char *type = "factor" ; /* ---------------------------------------------------------------------- */ /* print header information */ /* ---------------------------------------------------------------------- */ P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD factor: ") ; if (name != NULL) { P3 ("%s: ", name) ; } if (L == NULL) { ERR ("null") ; } n = L->n ; minor = L->minor ; ordering = L->ordering ; xtype = L->xtype ; Perm = L->Perm ; ColCount = L->ColCount ; lnz = 0 ; precise = Common->precise ; P3 (" "ID"", n) ; P3 ("-by-"ID"", n) ; if (minor < n) { P3 (" not positive definite (column "ID")", minor) ; } switch (L->itype) { case CHOLMOD_INT: P4 ("%s", "\n scalar types: int, ") ; break ; case CHOLMOD_INTLONG: ERR ("mixed int/long type unsupported") ; case CHOLMOD_LONG: P4 ("%s", "\n scalar types: SuiteSparse_long, "); break ; default: ERR ("unknown itype") ; } switch (L->xtype) { case CHOLMOD_PATTERN: P4 ("%s", "pattern") ; break ; case CHOLMOD_REAL: P4 ("%s", "real") ; break ; case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ; case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ; default: ERR ("unknown xtype") ; } switch (L->dtype) { case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ; case CHOLMOD_SINGLE: ERR ("single unsupported") ; default: ERR ("unknown dtype") ; } if (L->itype != ITYPE || L->dtype != DTYPE) { ERR ("integer and real type must match routine") ; } if (L->is_super) { P3 ("%s", " supernodal") ; } else { P3 ("%s", " simplicial") ; } if (L->is_ll) { P3 ("%s", ", LL'.") ; } else { P3 ("%s", ", LDL'.") ; } P4 ("%s", "\n ordering method used: ") ; switch (L->ordering) { case CHOLMOD_POSTORDERED:P4 ("%s", "natural (postordered)") ; break ; case CHOLMOD_NATURAL: P4 ("%s", "natural") ; break ; case CHOLMOD_GIVEN: P4 ("%s", "user-provided") ; break ; case CHOLMOD_AMD: P4 ("%s", "AMD") ; break ; case CHOLMOD_COLAMD: P4 ("%s", "AMD for A, COLAMD for A*A'") ;break ; #ifndef NPARTITION case CHOLMOD_METIS: P4 ("%s", "METIS NodeND") ; break ; case CHOLMOD_NESDIS: P4 ("%s", "CHOLMOD nested dissection") ; break ; #endif default: ERR ("unknown ordering") ; } P4 ("%s", "\n") ; init_print = print ; if (L->is_super && L->xtype == CHOLMOD_ZOMPLEX) { ERR ("Supernodal zomplex L not supported") ; } /* ---------------------------------------------------------------------- */ /* check L->Perm */ /* ---------------------------------------------------------------------- */ if (!check_perm (Wi, print, name, Perm, n, n, Common)) { return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* check L->ColCount */ /* ---------------------------------------------------------------------- */ if (ColCount == NULL) { ERR ("ColCount vector invalid") ; } ETC_START (count, 8) ; for (j = 0 ; j < n ; j++) { ETC (j >= n-4, count, -1) ; P4 (" col: "ID" ", j) ; nz = ColCount [j] ; P4 ("colcount: "ID"\n", nz) ; if (nz < 0 || nz > n-j) { ERR ("ColCount out of range") ; } } /* ---------------------------------------------------------------------- */ /* check factor */ /* ---------------------------------------------------------------------- */ if (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) { /* ------------------------------------------------------------------ */ /* check simplicial symbolic factor */ /* ------------------------------------------------------------------ */ /* nothing else to do */ ; } else if (L->xtype != CHOLMOD_PATTERN && !(L->is_super)) { /* ------------------------------------------------------------------ */ /* check simplicial numerical factor */ /* ------------------------------------------------------------------ */ P4 ("monotonic: %d\n", L->is_monotonic) ; nzmax = L->nzmax ; P3 (" nzmax "ID".", nzmax) ; P4 ("%s", "\n") ; Lp = L->p ; Li = L->i ; Lx = L->x ; Lz = L->z ; Lnz = L->nz ; Lnext = L->next ; Lprev = L->prev ; /* check for existence of Lp, Li, Lnz, Lnext, Lprev, and Lx arrays */ if (Lp == NULL) { ERR ("p array not present") ; } if (Li == NULL) { ERR ("i array not present") ; } if (Lnz == NULL) { ERR ("nz array not present") ; } if (Lx == NULL) { ERR ("x array not present") ; } if (xtype == CHOLMOD_ZOMPLEX && Lz == NULL) { ERR ("z array not present") ; } if (Lnext == NULL) { ERR ("next array not present") ; } if (Lprev == NULL) { ERR ("prev array not present") ; } ETC_START (count, 8) ; /* check each column of L */ plast = 0 ; is_monotonic = TRUE ; for (j = 0 ; j < n ; j++) { ETC (j >= n-3, count, -1) ; p = Lp [j] ; nz = Lnz [j] ; pend = p + nz ; lnz += nz ; P4 (" col "ID":", j) ; P4 (" nz "ID"", nz) ; P4 (" start "ID"", p) ; P4 (" end "ID"", pend) ; if (Lnext [j] < 0 || Lnext [j] > n) { ERR ("invalid link list") ; } space = Lp [Lnext [j]] - p ; P4 (" space "ID"", space) ; P4 (" free "ID":\n", space - nz) ; if (p < 0 || pend > nzmax || space < 1) { ERR ("pointer invalid") ; } if (nz < 1 || nz > (n-j) || nz > space) { ERR ("nz invalid") ; } ilast = j-1 ; if (p < plast) { is_monotonic = FALSE ; } plast = p ; i = Li [p] ; P4 (" "I8":", i) ; if (i != j) { ERR ("diagonal missing") ; } print_value (print, xtype, Lx, Lz, p, Common) ; P4 ("%s", "\n") ; ilast = j ; for (p++ ; p < pend ; p++) { ETC_DISABLE (count) ; i = Li [p] ; P4 (" "I8":", i) ; if (i < j || i >= n) { ERR ("row index out of range") ; } if (i <= ilast) { ERR ("row indices out of order") ; } print_value (print, xtype, Lx, Lz, p, Common) ; P4 ("%s", "\n") ; ilast = i ; } } if (L->is_monotonic && !is_monotonic) { ERR ("columns not monotonic") ; } /* check the link list */ head = n+1 ; tail = n ; j = head ; jprev = EMPTY ; count = 0 ; for ( ; ; ) { if (j < 0 || j > n+1 || count > n+2) { ERR ("invalid link list") ; } jnext = Lnext [j] ; if (j >= 0 && j < n) { if (jprev != Lprev [j]) { ERR ("invalid link list") ; } } count++ ; if (j == tail) { break ; } jprev = j ; j = jnext ; } if (Lnext [tail] != EMPTY || count != n+2) { ERR ("invalid link list") ; } } else { /* ------------------------------------------------------------------ */ /* check supernodal numeric or symbolic factor */ /* ------------------------------------------------------------------ */ nsuper = L->nsuper ; ssize = L->ssize ; xsize = L->xsize ; maxcsize = L->maxcsize ; maxesize = L->maxesize ; Ls = L->s ; Lpi = L->pi ; Lpx = L->px ; Super = L->super ; Lx = L->x ; ETC_START (count, 8) ; P4 (" ssize "ID" ", ssize) ; P4 ("xsize "ID" ", xsize) ; P4 ("maxcsize "ID" ", maxcsize) ; P4 ("maxesize "ID"\n", maxesize) ; if (Ls == NULL) { ERR ("invalid: L->s missing") ; } if (Lpi == NULL) { ERR ("invalid: L->pi missing") ; } if (Lpx == NULL) { ERR ("invalid: L->px missing") ; } if (Super == NULL) { ERR ("invalid: L->super missing") ; } if (L->xtype != CHOLMOD_PATTERN) { /* numerical supernodal factor */ if (Lx == NULL) { ERR ("invalid: L->x missing") ; } if (Ls [0] == EMPTY) { ERR ("invalid: L->s not defined") ; } examine_super = TRUE ; } else { /* symbolic supernodal factor, but only if it has been computed */ examine_super = (Ls [0] != EMPTY) ; } if (examine_super) { if (Lpi [0] != 0 || MAX (1, Lpi [nsuper]) != ssize) { PRINT0 (("Lpi [0] "ID", Lpi [nsuper = "ID"] = "ID"\n", Lpi [0], nsuper, Lpi [nsuper])) ; ERR ("invalid: L->pi invalid") ; } for_cholesky = (Lpx [0] != 123456) ; if (for_cholesky && (Lpx [0] != 0 || MAX (1, Lpx[nsuper]) != xsize)) { ERR ("invalid: L->px invalid") ; } /* check and print each supernode */ for (s = 0 ; s < nsuper ; s++) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; nsrow = psend - psi ; nscol = k2 - k1 ; nsrow2 = nsrow - nscol ; ps2 = psi + nscol ; if (for_cholesky) { psx = Lpx [s] ; psxend = Lpx [s+1] ; } ETC (s == nsuper-1, count, 4) ; P4 (" supernode "ID", ", s) ; P4 ("col "ID" ", k1) ; P4 ("to "ID". ", k2-1) ; P4 ("nz in first col: "ID".\n", nsrow) ; if (for_cholesky) { P4 (" values start "ID", ", psx) ; P4 ("end "ID"\n", psxend) ; } if (k1 > k2 || k1 < 0 || k2 > n || nsrow < nscol || nsrow2 < 0 || (for_cholesky && psxend - psx != nsrow * nscol)) { ERR ("invalid supernode") ; } lnz += nscol * nsrow - (nscol*nscol - nscol)/2 ; if (L->xtype != CHOLMOD_PATTERN) { /* print each column of the supernode */ for (jj = 0 ; jj < nscol ; jj++) { ETC_ENABLE (s == nsuper-1 && jj >= nscol-3, count, -1) ; j = k1 + jj ; P4 (" col "ID"\n", j) ; ilast = j ; i = Ls [psi + jj] ; P4 (" "I8":", i) ; if (i != j) { ERR ("row index invalid") ; } /* PRINTVALUE (Lx [psx + jj + jj*nsrow]) ; */ print_value (print, xtype, Lx, NULL, psx + jj + jj*nsrow, Common) ; P4 ("%s", "\n") ; for (ii = jj + 1 ; ii < nsrow ; ii++) { ETC_DISABLE (count) ; i = Ls [psi + ii] ; P4 (" "I8":", i) ; if (i <= ilast || i > n) { ERR ("row index out of range") ; } /* PRINTVALUE (Lx [psx + ii + jj*nsrow]) ; */ print_value (print, xtype, Lx, NULL, psx + ii + jj*nsrow, Common) ; P4 ("%s", "\n") ; ilast = i ; } } } else { /* just print the leading column of the supernode */ P4 (" col "ID"\n", k1) ; for (jj = 0 ; jj < nscol ; jj++) { ETC (s == nsuper-1 && jj >= nscol-3, count, -1) ; j = k1 + jj ; i = Ls [psi + jj] ; P4 (" "I8"", i) ; if (i != j) { ERR ("row index invalid") ; } P4 ("%s", "\n") ; } ilast = j ; for (ii = nscol ; ii < nsrow ; ii++) { ETC_DISABLE (count) ; i = Ls [psi + ii] ; P4 (" "I8"", i) ; if (i <= ilast || i > n) { ERR ("row index out of range") ; } P4 ("%s", "\n") ; ilast = i ; } } } } } /* factor is valid */ P3 (" nz "ID"", lnz) ; P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } int CHOLMOD(check_factor) ( /* ---- input ---- */ cholmod_factor *L, /* factor to check */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_factor (NULL, 0, NULL, L, Common)) ; } int CHOLMOD(print_factor) ( /* ---- input ---- */ cholmod_factor *L, /* factor to print */ const char *name, /* printed name of factor */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_factor (NULL, Common->print, name, L, Common)) ; } /* ========================================================================== */ /* === cholmod_check_triplet ================================================ */ /* ========================================================================== */ /* Ensure a triplet matrix is valid, and optionally print it. */ static int check_triplet ( Int print, const char *name, cholmod_triplet *T, cholmod_common *Common ) { double *Tx, *Tz ; Int *Ti, *Tj ; Int i, j, p, nrow, ncol, nzmax, nz, xtype, init_print, count ; const char *type = "triplet" ; /* ---------------------------------------------------------------------- */ /* print header information */ /* ---------------------------------------------------------------------- */ P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD triplet: ") ; if (name != NULL) { P3 ("%s: ", name) ; } if (T == NULL) { ERR ("null") ; } nrow = T->nrow ; ncol = T->ncol ; nzmax = T->nzmax ; nz = T->nnz ; Ti = T->i ; Tj = T->j ; Tx = T->x ; Tz = T->z ; xtype = T->xtype ; P3 (" "ID"", nrow) ; P3 ("-by-"ID", ", ncol) ; P3 ("nz "ID",", nz) ; if (T->stype > 0) { P3 ("%s", " upper.") ; } else if (T->stype < 0) { P3 ("%s", " lower.") ; } else { P3 ("%s", " up/lo.") ; } P4 ("\n nzmax "ID", ", nzmax) ; if (nz > nzmax) { ERR ("nzmax too small") ; } switch (T->itype) { case CHOLMOD_INT: P4 ("%s", "\n scalar types: int, ") ; break ; case CHOLMOD_INTLONG: ERR ("mixed int/long type unsupported") ; case CHOLMOD_LONG: P4 ("%s", "\n scalar types: SuiteSparse_long, "); break ; default: ERR ("unknown itype") ; } switch (T->xtype) { case CHOLMOD_PATTERN: P4 ("%s", "pattern") ; break ; case CHOLMOD_REAL: P4 ("%s", "real") ; break ; case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ; case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ; default: ERR ("unknown xtype") ; } switch (T->dtype) { case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ; case CHOLMOD_SINGLE: ERR ("single unsupported") ; default: ERR ("unknown dtype") ; } if (T->itype != ITYPE || T->dtype != DTYPE) { ERR ("integer and real type must match routine") ; } if (T->stype && nrow != ncol) { ERR ("symmetric but not square") ; } /* check for existence of Ti, Tj, Tx arrays */ if (Tj == NULL) { ERR ("j array not present") ; } if (Ti == NULL) { ERR ("i array not present") ; } if (xtype != CHOLMOD_PATTERN && Tx == NULL) { ERR ("x array not present") ; } if (xtype == CHOLMOD_ZOMPLEX && Tz == NULL) { ERR ("z array not present") ; } /* ---------------------------------------------------------------------- */ /* check and print each entry */ /* ---------------------------------------------------------------------- */ init_print = print ; ETC_START (count, 8) ; for (p = 0 ; p < nz ; p++) { ETC (p >= nz-4, count, -1) ; i = Ti [p] ; P4 (" "I8":", p) ; P4 (" "I_8"", i) ; if (i < 0 || i >= nrow) { ERR ("row index out of range") ; } j = Tj [p] ; P4 (" "I_8"", j) ; if (j < 0 || j >= ncol) { ERR ("column index out of range") ; } print_value (print, xtype, Tx, Tz, p, Common) ; P4 ("%s", "\n") ; } /* triplet matrix is valid */ P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } int CHOLMOD(check_triplet) ( /* ---- input ---- */ cholmod_triplet *T, /* triplet matrix to check */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_triplet (0, NULL, T, Common)) ; } int CHOLMOD(print_triplet) ( /* ---- input ---- */ cholmod_triplet *T, /* triplet matrix to print */ const char *name, /* printed name of triplet matrix */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_triplet (Common->print, name, T, Common)) ; } /* ========================================================================== */ /* === CHOLMOD debugging routines =========================================== */ /* ========================================================================== */ #ifndef NDEBUG /* The global variables present only when debugging enabled. */ int CHOLMOD(dump) = 0 ; int CHOLMOD(dump_malloc) = -1 ; /* workspace: no debug routines use workspace in Common */ /* ========================================================================== */ /* === cholmod_dump_init ==================================================== */ /* ========================================================================== */ void CHOLMOD(dump_init) (const char *s, cholmod_common *Common) { int i = 0 ; FILE *f ; f = fopen ("debug", "r") ; CHOLMOD(dump) = 0 ; if (f != NULL) { i = fscanf (f, "%d", &CHOLMOD(dump)) ; fclose (f) ; } PRINT1 (("%s: cholmod_dump_init, D = %d\n", s, CHOLMOD(dump))) ; } /* ========================================================================== */ /* === cholmod_dump_sparse ================================================== */ /* ========================================================================== */ /* returns nnz (diag (A)) or EMPTY if error */ SuiteSparse_long CHOLMOD(dump_sparse) ( cholmod_sparse *A, const char *name, cholmod_common *Common ) { Int *Wi ; SuiteSparse_long nnzdiag ; Int ok ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (0) ; } RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; Wi = malloc (MAX (1, A->nrow) * sizeof (Int)) ; ok = check_sparse (Wi, CHOLMOD(dump), name, A, &nnzdiag, Common) ; if (Wi != NULL) free (Wi) ; return (ok ? nnzdiag : EMPTY) ; } /* ========================================================================== */ /* === cholmod_dump_factor ================================================== */ /* ========================================================================== */ int CHOLMOD(dump_factor) ( cholmod_factor *L, const char *name, cholmod_common *Common ) { Int *Wi ; int ok ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; Wi = malloc (MAX (1, L->n) * sizeof (Int)) ; ok = check_factor (Wi, CHOLMOD(dump), name, L, Common) ; if (Wi != NULL) free (Wi) ; return (ok) ; } /* ========================================================================== */ /* === cholmod_dump_perm ==================================================== */ /* ========================================================================== */ int CHOLMOD(dump_perm) ( Int *Perm, size_t len, size_t n, const char *name, cholmod_common *Common ) { Int *Wi ; int ok ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; Wi = malloc (MAX (1, n) * sizeof (Int)) ; ok = check_perm (Wi, CHOLMOD(dump), name, Perm, len, n,Common) ; if (Wi != NULL) free (Wi) ; return (ok) ; } /* ========================================================================== */ /* === cholmod_dump_dense =================================================== */ /* ========================================================================== */ int CHOLMOD(dump_dense) ( cholmod_dense *X, const char *name, cholmod_common *Common ) { if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; return (check_dense (CHOLMOD(dump), name, X, Common)) ; } /* ========================================================================== */ /* === cholmod_dump_triplet ================================================= */ /* ========================================================================== */ int CHOLMOD(dump_triplet) ( cholmod_triplet *T, const char *name, cholmod_common *Common ) { if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; return (check_triplet (CHOLMOD(dump), name, T, Common)) ; } /* ========================================================================== */ /* === cholmod_dump_subset ================================================== */ /* ========================================================================== */ int CHOLMOD(dump_subset) ( Int *S, size_t len, size_t n, const char *name, cholmod_common *Common ) { if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; return (check_subset (S, len, n, CHOLMOD(dump), name, Common)) ; } /* ========================================================================== */ /* === cholmod_dump_parent ================================================== */ /* ========================================================================== */ int CHOLMOD(dump_parent) ( Int *Parent, size_t n, const char *name, cholmod_common *Common ) { if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; return (check_parent (Parent, n, CHOLMOD(dump), name, Common)) ; } /* ========================================================================== */ /* === cholmod_dump_real ==================================================== */ /* ========================================================================== */ void CHOLMOD(dump_real) ( const char *name, Real *X, SuiteSparse_long nrow, SuiteSparse_long ncol, int lower, int xentry, cholmod_common *Common ) { /* dump an nrow-by-ncol real dense matrix */ SuiteSparse_long i, j ; double x, z ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return ; } PRINT1 (("%s: dump_real, nrow: %ld ncol: %ld lower: %d\n", name, nrow, ncol, lower)) ; for (j = 0 ; j < ncol ; j++) { PRINT2 ((" col %ld\n", j)) ; for (i = 0 ; i < nrow ; i++) { /* X is stored in column-major form */ if (lower && i < j) { PRINT2 ((" %5ld: -", i)) ; } else { x = *X ; PRINT2 ((" %5ld: %e", i, x)) ; if (xentry == 2) { z = *(X+1) ; PRINT2 ((", %e", z)) ; } } PRINT2 (("\n")) ; X += xentry ; } } } /* ========================================================================== */ /* === cholmod_dump_super =================================================== */ /* ========================================================================== */ void CHOLMOD(dump_super) ( SuiteSparse_long s, Int *Super, Int *Lpi, Int *Ls, Int *Lpx, double *Lx, int xentry, cholmod_common *Common ) { Int k1, k2, do_values, psi, psx, nsrow, nscol, psend, ilast, p, i ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return ; } k1 = Super [s] ; k2 = Super [s+1] ; nscol = k2 - k1 ; do_values = (Lpx != NULL) && (Lx != NULL) ; psi = Lpi [s] ; psend = Lpi [s+1] ; nsrow = psend - psi ; PRINT1 (("\nSuper %ld, columns "ID" to "ID", "ID" rows "ID" cols\n", s, k1, k2-1, nsrow, nscol)) ; ilast = -1 ; for (p = psi ; p < psend ; p++) { i = Ls [p] ; PRINT2 ((" "ID" : p-psi "ID"\n", i, p-psi)) ; ASSERT (IMPLIES (p-psi < nscol, i == k1 + (p-psi))) ; if (p-psi == nscol-1) PRINT2 (("------\n")) ; ASSERT (i > ilast) ; ilast = i ; } if (do_values) { psx = Lpx [s] ; CHOLMOD(dump_real) ("Supernode", Lx + xentry*psx, nsrow, nscol, TRUE, xentry, Common) ; } } /* ========================================================================== */ /* === cholmod_dump_mem ===================================================== */ /* ========================================================================== */ int CHOLMOD(dump_mem) ( const char *where, SuiteSparse_long should, cholmod_common *Common ) { SuiteSparse_long diff = should - Common->memory_inuse ; if (diff != 0) { PRINT0 (("mem: %-15s peak %10g inuse %10g should %10g\n", where, (double) Common->memory_usage, (double) Common->memory_inuse, (double) should)) ; PRINT0 (("mem: %s diff %ld !\n", where, diff)) ; } return (diff == 0) ; } /* ========================================================================== */ /* === cholmod_dump_partition =============================================== */ /* ========================================================================== */ /* make sure we have a proper separator (for debugging only) * * workspace: none */ int CHOLMOD(dump_partition) ( SuiteSparse_long n, Int *Cp, Int *Ci, Int *Cnw, Int *Part, SuiteSparse_long sepsize, cholmod_common *Common ) { Int chek [3], which, ok, i, j, p ; PRINT1 (("bisect sepsize %ld\n", sepsize)) ; ok = TRUE ; chek [0] = 0 ; chek [1] = 0 ; chek [2] = 0 ; for (j = 0 ; j < n ; j++) { PRINT2 (("--------j "ID" in part "ID" nw "ID"\n", j, Part [j], Cnw[j])); which = Part [j] ; for (p = Cp [j] ; p < Cp [j+1] ; p++) { i = Ci [p] ; PRINT3 (("i "ID", part "ID"\n", i, Part [i])) ; if (which == 0) { if (Part [i] == 1) { PRINT0 (("Error! "ID" "ID"\n", i, j)) ; ok = FALSE ; } } else if (which == 1) { if (Part [i] == 0) { PRINT0 (("Error! "ID" "ID"\n", i, j)) ; ok = FALSE ; } } } if (which < 0 || which > 2) { PRINT0 (("Part out of range\n")) ; ok = FALSE ; } chek [which] += Cnw [j] ; } PRINT1 (("sepsize %ld check "ID" "ID" "ID"\n", sepsize, chek[0], chek[1],chek[2])); if (sepsize != chek[2]) { PRINT0 (("mismatch!\n")) ; ok = FALSE ; } return (ok) ; } /* ========================================================================== */ /* === cholmod_dump_work ==================================================== */ /* ========================================================================== */ int CHOLMOD(dump_work) (int flag, int head, SuiteSparse_long wsize, cholmod_common *Common) { double *W ; Int *Flag, *Head ; Int k, nrow, mark ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; nrow = Common->nrow ; Flag = Common->Flag ; Head = Common->Head ; W = Common->Xwork ; mark = Common->mark ; if (wsize < 0) { /* check all of Xwork */ wsize = Common->xworksize ; } else { /* check on the first wsize doubles in Xwork */ wsize = MIN (wsize, (Int) (Common->xworksize)) ; } if (flag) { for (k = 0 ; k < nrow ; k++) { if (Flag [k] >= mark) { PRINT0 (("Flag invalid, Flag ["ID"] = "ID", mark = "ID"\n", k, Flag [k], mark)) ; ASSERT (0) ; return (FALSE) ; } } } if (head) { for (k = 0 ; k < nrow ; k++) { if (Head [k] != EMPTY) { PRINT0 (("Head invalid, Head ["ID"] = "ID"\n", k, Head [k])) ; ASSERT (0) ; return (FALSE) ; } } } for (k = 0 ; k < wsize ; k++) { if (W [k] != 0.) { PRINT0 (("W invalid, W ["ID"] = %g\n", k, W [k])) ; ASSERT (0) ; return (FALSE) ; } } return (TRUE) ; } #endif #endif Matrix/src/CHOLMOD/Check/cholmod_read.c0000644000175100001440000011740112271765436017232 0ustar hornikusers/* ========================================================================== */ /* === Check/cholmod_read =================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Check Module. Copyright (C) 2005-2006, Timothy A. Davis. * The CHOLMOD/Check Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Read a sparse matrix in triplet or dense form. A triplet matrix can be * returned as compressed-column sparse matrix. The file format is compatible * with all variations of the Matrix Market "coordinate" and "array" format * (http://www.nist.gov/MatrixMarket). The format supported by these routines * also allow other formats, where the Matrix Market header is optional. * * Although the Matrix Market header is optional, I recommend that users stick * with the strict Matrix Market format. The optional format appears here to * support the reading of symmetric matrices stored with just their upper * triangular parts present, for testing and development of the A->stype > 0 * format in CHOLMOD. That format is not included in the Matrix Market format. * * If the first line of the file starts with %%MatrixMarket, then it is * interpretted as a file in Matrix Market format. This line must have * the following format: * * %%MatrixMarket matrix * * is one of: coordinate or array. The former is a sparse matrix in * triplet form. The latter is a dense matrix in column-major form. * * is one of: real, complex, pattern, or integer. * The functions here convert the "integer" and "pattern" types to real. * * is one of: general, hermitian, symmetric, or skew-symmetric * * The strings are case-insensitive. Only the first character is * significant (or the first two for skew-symmetric). * * is ignored for all matrices; the actual type (real, complex, * or pattern) is inferred from the number of tokens in each line of the * file. For a "coordinate" matrix: 2: pattern, 3: real, 4: complex; for * a dense "array" matrix: 1: real, 2: complex. This is compatible with * the Matrix Market format, since pattern matrices must have two tokens * per line, real matrices must have 3, and complex matrices must have 4. * A storage of "general" implies an stype of zero (see below). * "symmetric" and "hermitian" imply an stype of -1. Skew-symmetric and * complex symmetric matrices are always returned with both upper and lower * triangular parts present, with an stype of zero, since CHOLMOD does not * have a method for representing skew-symmetric and complex symmetric * matrices. Real symmetric and complex Hermitian matrices may optionally * be returned with both parts present. * * Any other lines starting with "%" are treated as comments, and are ignored. * Blank lines are ignored. The Matrix Market header is optional in this * routine (it is not optional in the Matrix Market format). * * Note that complex matrices are always returned in CHOLMOD_COMPLEX format, * not CHOLMOD_ZOMPLEX. * * ----------------------------------------------------------------------------- * Triplet matrices: * ----------------------------------------------------------------------------- * * The first data line of a triplet matrix contains 3 or 4 integers: * * nrow ncol nnz stype * * where stype is optional (stype does not appear in the Matrix Market format). * The matrix is nrow-by-ncol. The following nnz lines (excluding comments * and blank lines) each contain a single entry. Duplicates are permitted, * and are summed in the output matrix. * * The stype is first derived from the Matrix Market header. If the stype * appears as the fourth integer in the first data line, it is determined from * that line. * * If stype is present, it denotes the storage format for the matrix. * stype = 0 denotes an unsymmetric matrix (same as Matrix Market "general"). * stype = -1 denotes a real symmetric or complex Hermitian matrix whose lower * triangular entries are stored. Entries may be present in the upper * triangular part, but these are ignored (same as Matrix Market * "real symmetric" and "complex Hermitian"). * stype = 1 denotes a real symmetric or complex Hermitian matrix whose upper * triangular entries are stored. Entries may be present in the lower * triangular part, but these are ignored. This option is not present * in the Matrix Market format. * * If stype is not present (no Matrix Market header and not in the first data * line) it is inferred from the rest of the data. If the matrix is * rectangular, or has entries in both the upper and lower triangular parts, * then it is assumed to be unsymmetric (stype=0). If only entries in the * lower triangular part are present, the matrix is assumed to have stype = -1. * If only entries in the upper triangular part are present, the matrix is * assumed to have stype = 1. * * After the first data line (with nrow, ncol, nnz, and optionally stype), * each nonzero consists of one line with 2, 3, or 4 entries. All lines must * have the same number of entries. The first two entries are the row and * column indices of the nonzero. If 3 entries are present, the 3rd entry is * the numerical value, and the matrix is real. If 4 entries are present, * the 3rd and 4th entries in the line are the real and imaginary parts of * a complex value. * * The matrix can be either 0-based or 1-based. It is first assumed to be * one-based (all matrices in the Matrix Market are one-based), with row indices * in the range 1 to ncol and column indices in the range 1 to nrow. If a row * or column index of zero is found, the matrix is assumed to be zero-based * (with row indices in the range 0 to ncol-1 and column indices in the range 0 * to nrow-1). * * If Common->prefer_binary is set to its default value of FALSE, then * for symmetric pattern-only matrices, the kth diagonal (if present) is set to * one plus the degree of the row/column k, and the off-diagonal entries are set * to -1. A symmetric pattern-only matrix with a zero-free diagonal is thus * converted into a symmetric positive definite matrix. All entries are set to * one for an unsymmetric pattern-only matrix. This differs from the * Matrix Market format (A = mmread ('file') returns a binary pattern for A for * symmetric pattern-only matrices). If Common->prefer_binary is TRUE, then * this function returns a binary matrix (just like mmread('file')). * * ----------------------------------------------------------------------------- * Dense matrices: * ----------------------------------------------------------------------------- * * A dense matrix is specified by the Matrix Market "array" format. The * Matrix Market header is optional; if not present, the matrix is assumed to * be in the Matrix Market "general" format. The first data line contains just * two integers: * * nrow ncol * * The can be real, integer, or complex (not pattern). These functions * convert an integer type to real. The entries in the matrix are stored in * column-major format, with one line per entry. Two entries are present in * each line for complex matrices, one for real and integer matrices. In * rectangular and unsymmetric matrices, all entries are present. For real * symmetric or complex Hermitian matrices, only entries in the lower triangular * part appear. For skew-symmetric matrices, only entries in the strictly * lower triangular part appear. * * Since CHOLMOD does not have a data structure for presenting dense symmetric/ * Hermitian matrices, these functions always return a dense matrix in its * general form, with both upper and lower parts present. */ #ifndef NCHECK #include "cholmod_internal.h" #include "cholmod_check.h" #include #include /* The MatrixMarket format specificies a maximum line length of 1024 */ #define MAXLINE 1030 /* ========================================================================== */ /* === get_line ============================================================= */ /* ========================================================================== */ /* Read one line of the file, return TRUE if successful, FALSE if EOF. */ static int get_line (FILE *f, char *buf) { buf [0] = '\0' ; buf [1] = '\0' ; buf [MAXLINE] = '\0' ; return (fgets (buf, MAXLINE, f) != NULL) ; } /* ========================================================================== */ /* === fix_inf ============================================================== */ /* ========================================================================== */ /* Replace huge values with +/- Inf's, since scanf and printf don't deal * with Inf's properly. */ static double fix_inf (double x) { if ((x >= HUGE_DOUBLE) || (x <= -HUGE_DOUBLE)) { /* treat this as +/- Inf (assume 2*x leads to overflow) */ x = 2*x ; } return (x) ; } /* ========================================================================== */ /* === is_blank_line ======================================================== */ /* ========================================================================== */ /* TRUE if s is a blank line or comment, FALSE otherwise */ static int is_blank_line ( char *s ) { int c, k ; if (s [0] == '%') { /* a comment line */ return (TRUE) ; } for (k = 0 ; k <= MAXLINE ; k++) { c = s [k] ; if (c == '\0') { /* end of line */ break ; } if (!isspace (c)) { /* non-space character */ return (FALSE) ; } } return (TRUE) ; } /* ========================================================================== */ /* === read_header ========================================================== */ /* ========================================================================== */ /* Read the header. This consists of zero or more comment lines (blank, or * starting with a "%" in the first column), followed by a single data line * containing up to four numerical values. * * The first line may optionally be a Matrix Market header line, of the form * * %%MatrixMarket matrix * * The first data line of a sparse matrix in triplet form consists of 3 or 4 * numerical values: * * nrow ncol nnz stype * * where stype is optional (it does not appear in the Matrix Market file * format). The first line of a dense matrix in column-major form consists of * two numerical values: * * nrow ncol * * The stype of the matrix is determine either from the Matrix Market header, * or (optionally) from the first data line. stypes of 0 to -3 directly * correlate with the Matrix Market format; stype = 1 is an extension to that * format. * * 999: unknown (will be inferred from the data) * 1: real symmetric or complex Hermitian with upper part stored * (not in the Matrix Market format) * 0: unsymmetric (same as Matrix Market "general") * -1: real symmetric or complex Hermitian, with lower part stored * (Matrix Market "real symmetric" or "complex hermitian") * -2: real or complex skew symmetric (lower part stored, can only be * specified by Matrix Market header) * -3: complex symmetric (lower part stored) * specified by Matrix Market header) * * The Matrix Market header is optional. If stype appears in the first data * line, it is determine by that data line. Otherwise, if the Matrix Market * header appears, stype is determined from that header. If stype does not * appear, it is set to "unknown" (999). */ #define STYPE_UNKNOWN 999 #define STYPE_SYMMETRIC_UPPER 1 #define STYPE_UNSYMMETRIC 0 #define STYPE_SYMMETRIC_LOWER -1 #define STYPE_SKEW_SYMMETRIC -2 #define STYPE_COMPLEX_SYMMETRIC_LOWER -3 static int read_header /* returns TRUE if successful, FALSE on error */ ( /* ---- input ---- */ FILE *f, /* file to read from */ /* ---- output --- */ char *buf, /* a character array of size MAXLINE+1 */ int *mtype, /* CHOLMOD_TRIPLET or CHOLMOD_DENSE */ size_t *nrow, /* number of rows in the matrix */ size_t *ncol, /* number of columns in the matrix */ size_t *nnz, /* number of entries in a triplet matrix (0 for dense)*/ int *stype /* stype (see above) */ ) { char *p ; int first = TRUE, got_mm_header = FALSE, c, c2, is_complex, nitems ; double l1, l2, l3, l4 ; *mtype = CHOLMOD_TRIPLET ; *nrow = 0 ; *ncol = 0 ; *nnz = 0 ; *stype = STYPE_UNKNOWN ; for ( ; ; ) { /* ------------------------------------------------------------------ */ /* get the next line */ /* ------------------------------------------------------------------ */ if (!get_line (f, buf)) { /* premature end of file */ return (FALSE) ; } if (first && (strncmp (buf, "%%MatrixMarket", 14) == 0)) { /* -------------------------------------------------------------- */ /* read a Matrix Market header */ /* -------------------------------------------------------------- */ got_mm_header = TRUE ; p = buf ; /* -------------------------------------------------------------- */ /* get "matrix" token */ /* -------------------------------------------------------------- */ while (*p && !isspace (*p)) p++ ; while (*p && isspace (*p)) p++ ; c = tolower (*p) ; if (c != 'm') { /* bad format */ return (FALSE) ; } /* -------------------------------------------------------------- */ /* get the fmt token ("coord" or "array") */ /* -------------------------------------------------------------- */ while (*p && !isspace (*p)) p++ ; while (*p && isspace (*p)) p++ ; c = tolower (*p) ; if (c == 'c') { *mtype = CHOLMOD_TRIPLET ; } else if (c == 'a') { *mtype = CHOLMOD_DENSE ; } else { /* bad format, neither "coordinate" nor "array" */ return (FALSE) ; } /* -------------------------------------------------------------- */ /* get type token (real, pattern, complex, integer) */ /* -------------------------------------------------------------- */ while (*p && !isspace (*p)) p++ ; while (*p && isspace (*p)) p++ ; c = tolower (*p) ; if (!(c == 'r' || c == 'p' || c == 'c' || c == 'i')) { /* bad format */ return (FALSE) ; } is_complex = (c == 'c') ; /* -------------------------------------------------------------- */ /* get storage token (general, hermitian, symmetric, skew) */ /* -------------------------------------------------------------- */ while (*p && !isspace (*p)) p++ ; while (*p && isspace (*p)) p++ ; c = tolower (*p) ; c2 = tolower (*(p+1)) ; if (c == 'g') { /* "general" storage (unsymmetric matrix), both parts present */ *stype = STYPE_UNSYMMETRIC ; } else if (c == 's' && c2 == 'y') { /* "symmetric" */ if (is_complex) { /* complex symmetric, lower triangular part present */ *stype = STYPE_COMPLEX_SYMMETRIC_LOWER ; } else { /* real symmetric, lower triangular part present */ *stype = STYPE_SYMMETRIC_LOWER ; } } else if (c == 'h') { /* "hermitian" matrix, lower triangular part present */ *stype = STYPE_SYMMETRIC_LOWER ; } else if (c == 's' && c2 == 'k') { /* "skew-symmetric" (real or complex), lower part present */ *stype = STYPE_SKEW_SYMMETRIC ; } else { /* bad format */ return (FALSE) ; } } else if (is_blank_line (buf)) { /* -------------------------------------------------------------- */ /* blank line or comment line */ /* -------------------------------------------------------------- */ continue ; } else { /* -------------------------------------------------------------- */ /* read the first data line and return */ /* -------------------------------------------------------------- */ /* format: nrow ncol nnz stype */ l1 = EMPTY ; l2 = EMPTY ; l3 = 0 ; l4 = 0 ; nitems = sscanf (buf, "%lg %lg %lg %lg\n", &l1, &l2, &l3, &l4) ; if (nitems < 2 || nitems > 4 || l1 > Int_max || l2 > Int_max) { /* invalid matrix */ return (FALSE) ; } *nrow = l1 ; *ncol = l2 ; if (nitems == 2) { /* a dense matrix */ if (!got_mm_header) { *mtype = CHOLMOD_DENSE ; *stype = STYPE_UNSYMMETRIC ; } } if (nitems == 3 || nitems == 4) { /* a sparse triplet matrix */ *nnz = l3 ; if (!got_mm_header) { *mtype = CHOLMOD_TRIPLET ; } } if (nitems == 4) { /* an stype specified here can only be 1, 0, or -1 */ if (l4 < 0) { *stype = STYPE_SYMMETRIC_LOWER ; } else if (l4 > 0) { *stype = STYPE_SYMMETRIC_UPPER ; } else { *stype = STYPE_UNSYMMETRIC ; } } if (*nrow != *ncol) { /* a rectangular matrix must be unsymmetric */ *stype = STYPE_UNSYMMETRIC ; } return (TRUE) ; } first = FALSE ; } } /* ========================================================================== */ /* === read_triplet ========================================================= */ /* ========================================================================== */ /* Header has already been read in, including first line (nrow ncol nnz stype). * Read the triplets. */ static cholmod_triplet *read_triplet ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ size_t nrow, /* number of rows */ size_t ncol, /* number of columns */ size_t nnz, /* number of triplets in file to read */ int stype, /* stype from header, or "unknown" */ int prefer_unsym, /* if TRUE, always return T->stype of zero */ /* ---- workspace */ char *buf, /* of size MAXLINE+1 */ /* --------------- */ cholmod_common *Common ) { double x, z ; double *Tx ; Int *Ti, *Tj, *Rdeg, *Cdeg ; cholmod_triplet *T ; double l1, l2 ; Int nitems, xtype, unknown, k, nshould, is_lower, is_upper, one_based, i, j, imax, jmax, skew_symmetric, p, complex_symmetric ; size_t s, nnz2, extra ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* quick return for empty matrix */ /* ---------------------------------------------------------------------- */ if (nrow == 0 || ncol == 0 || nnz == 0) { /* return an empty matrix */ return (CHOLMOD(allocate_triplet) (nrow, ncol, 0, 0, CHOLMOD_REAL, Common)) ; } /* ---------------------------------------------------------------------- */ /* special stype cases: unknown, skew symmetric, and complex symmetric */ /* ---------------------------------------------------------------------- */ unknown = (stype == STYPE_UNKNOWN) ; skew_symmetric = (stype == STYPE_SKEW_SYMMETRIC) ; complex_symmetric = (stype == STYPE_COMPLEX_SYMMETRIC_LOWER) ; extra = 0 ; if (stype < STYPE_SYMMETRIC_LOWER || (prefer_unsym && stype != STYPE_UNSYMMETRIC)) { /* 999: unknown might be converted to unsymmetric */ /* 1: symmetric upper converted to unsym. if prefer_unsym is TRUE */ /* -1: symmetric lower converted to unsym. if prefer_unsym is TRUE */ /* -2: real or complex skew symmetric converted to unsymmetric */ /* -3: complex symmetric converted to unsymmetric */ stype = STYPE_UNSYMMETRIC ; extra = nnz ; } nnz2 = CHOLMOD(add_size_t) (nnz, extra, &ok) ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = nrow + ncol */ s = CHOLMOD(add_size_t) (nrow, ncol, &ok) ; if (!ok || nrow > Int_max || ncol > Int_max || nnz > Int_max) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } CHOLMOD(allocate_work) (0, s, 0, Common) ; Rdeg = Common->Iwork ; /* size nrow */ Cdeg = Rdeg + nrow ; /* size ncol */ /* ---------------------------------------------------------------------- */ /* read the triplets */ /* ---------------------------------------------------------------------- */ is_lower = TRUE ; is_upper = TRUE ; one_based = TRUE ; imax = 0 ; jmax = 0 ; Tx = NULL ; Ti = NULL ; Tj = NULL ; xtype = 999 ; nshould = 0 ; for (k = 0 ; k < (Int) nnz ; k++) { /* ------------------------------------------------------------------ */ /* get the next triplet, skipping blank lines and comment lines */ /* ------------------------------------------------------------------ */ l1 = EMPTY ; l2 = EMPTY ; x = 0 ; z = 0 ; for ( ; ; ) { if (!get_line (f, buf)) { /* premature end of file - not enough triplets read in */ ERROR (CHOLMOD_INVALID, "premature EOF") ; return (NULL) ; } if (is_blank_line (buf)) { /* blank line or comment */ continue ; } nitems = sscanf (buf, "%lg %lg %lg %lg\n", &l1, &l2, &x, &z) ; x = fix_inf (x) ; z = fix_inf (z) ; break ; } nitems = (nitems == EOF) ? 0 : nitems ; i = l1 ; j = l2 ; /* ------------------------------------------------------------------ */ /* for first triplet: determine type and allocate triplet matrix */ /* ------------------------------------------------------------------ */ if (k == 0) { if (nitems < 2 || nitems > 4) { /* invalid matrix */ ERROR (CHOLMOD_INVALID, "invalid format") ; return (NULL) ; } else if (nitems == 2) { /* this will be converted into a real matrix later */ xtype = CHOLMOD_PATTERN ; } else if (nitems == 3) { xtype = CHOLMOD_REAL ; } else if (nitems == 4) { xtype = CHOLMOD_COMPLEX ; } /* the rest of the lines should have the same number of entries */ nshould = nitems ; /* allocate triplet matrix */ T = CHOLMOD(allocate_triplet) (nrow, ncol, nnz2, stype, (xtype == CHOLMOD_PATTERN ? CHOLMOD_REAL : xtype), Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } Ti = T->i ; Tj = T->j ; Tx = T->x ; T->nnz = nnz ; } /* ------------------------------------------------------------------ */ /* save the entry in the triplet matrix */ /* ------------------------------------------------------------------ */ if (nitems != nshould || i < 0 || j < 0) { /* wrong format, premature end-of-file, or negative indices */ CHOLMOD(free_triplet) (&T, Common) ; ERROR (CHOLMOD_INVALID, "invalid matrix file") ; return (NULL) ; } Ti [k] = i ; Tj [k] = j ; if (i < j) { /* this entry is in the upper triangular part */ is_lower = FALSE ; } if (i > j) { /* this entry is in the lower triangular part */ is_upper = FALSE ; } if (xtype == CHOLMOD_REAL) { Tx [k] = x ; } else if (xtype == CHOLMOD_COMPLEX) { Tx [2*k ] = x ; /* real part */ Tx [2*k+1] = z ; /* imaginary part */ } if (i == 0 || j == 0) { one_based = FALSE ; } imax = MAX (i, imax) ; jmax = MAX (j, jmax) ; } /* ---------------------------------------------------------------------- */ /* convert to zero-based */ /* ---------------------------------------------------------------------- */ if (one_based) { /* input matrix is one-based; convert matrix to zero-based */ for (k = 0 ; k < (Int) nnz ; k++) { Ti [k]-- ; Tj [k]-- ; } } if (one_based ? (imax > (Int) nrow || jmax > (Int) ncol) : (imax >= (Int) nrow || jmax >= (Int) ncol)) { /* indices out of range */ CHOLMOD(free_triplet) (&T, Common) ; ERROR (CHOLMOD_INVALID, "indices out of range") ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* determine the stype, if not yet known */ /* ---------------------------------------------------------------------- */ if (unknown) { if (is_lower && is_upper) { /* diagonal matrix, symmetric with upper part present */ stype = STYPE_SYMMETRIC_UPPER ; } else if (is_lower && !is_upper) { /* symmetric, lower triangular part present */ stype = STYPE_SYMMETRIC_LOWER ; } else if (!is_lower && is_upper) { /* symmetric, upper triangular part present */ stype = STYPE_SYMMETRIC_UPPER ; } else { /* unsymmetric */ stype = STYPE_UNSYMMETRIC ; extra = 0 ; } } /* ---------------------------------------------------------------------- */ /* add the remainder of symmetric, skew-symmetric or Hermitian matrices */ /* ---------------------------------------------------------------------- */ /* note that this step is not done for real symmetric or complex Hermitian * matrices, unless prefer_unsym is TRUE */ if (extra > 0) { p = nnz ; for (k = 0 ; k < (Int) nnz ; k++) { i = Ti [k] ; j = Tj [k] ; if (i != j) { Ti [p] = j ; Tj [p] = i ; if (xtype == CHOLMOD_REAL) { if (skew_symmetric) { Tx [p] = -Tx [k] ; } else { Tx [p] = Tx [k] ; } } else if (xtype == CHOLMOD_COMPLEX) { if (skew_symmetric) { Tx [2*p ] = -Tx [2*k ] ; Tx [2*p+1] = -Tx [2*k+1] ; } else if (complex_symmetric) { Tx [2*p ] = Tx [2*k ] ; Tx [2*p+1] = Tx [2*k+1] ; } else /* Hermitian */ { Tx [2*p ] = Tx [2*k ] ; Tx [2*p+1] = -Tx [2*k+1] ; } } p++ ; } } T->nnz = p ; nnz = p ; } T->stype = stype ; /* ---------------------------------------------------------------------- */ /* create values for a pattern-only matrix */ /* ---------------------------------------------------------------------- */ if (xtype == CHOLMOD_PATTERN) { if (stype == STYPE_UNSYMMETRIC || Common->prefer_binary) { /* unsymmetric case, or binary case */ for (k = 0 ; k < (Int) nnz ; k++) { Tx [k] = 1 ; } } else { /* compute the row and columm degrees (excluding the diagonal) */ for (i = 0 ; i < (Int) nrow ; i++) { Rdeg [i] = 0 ; } for (j = 0 ; j < (Int) ncol ; j++) { Cdeg [j] = 0 ; } for (k = 0 ; k < (Int) nnz ; k++) { i = Ti [k] ; j = Tj [k] ; if ((stype < 0 && i > j) || (stype > 0 && i < j)) { /* both a(i,j) and a(j,i) appear in the matrix */ Rdeg [i]++ ; Cdeg [j]++ ; Rdeg [j]++ ; Cdeg [i]++ ; } } /* assign the numerical values */ for (k = 0 ; k < (Int) nnz ; k++) { i = Ti [k] ; j = Tj [k] ; Tx [k] = (i == j) ? (1 + MAX (Rdeg [i], Cdeg [j])) : (-1) ; } } } /* ---------------------------------------------------------------------- */ /* return the new triplet matrix */ /* ---------------------------------------------------------------------- */ return (T) ; } /* ========================================================================== */ /* === read_dense =========================================================== */ /* ========================================================================== */ /* Header has already been read in, including first line (nrow ncol). * Read a dense matrix. */ static cholmod_dense *read_dense ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ size_t nrow, /* number of rows */ size_t ncol, /* number of columns */ int stype, /* stype from header */ /* ---- workspace */ char *buf, /* of size MAXLINE+1 */ /* --------------- */ cholmod_common *Common ) { double x, z ; double *Xx = NULL ; cholmod_dense *X ; Int nitems, xtype = -1, nshould = 0, i, j, k, kup, first ; /* ---------------------------------------------------------------------- */ /* quick return for empty matrix */ /* ---------------------------------------------------------------------- */ if (nrow == 0 || ncol == 0) { /* return an empty dense matrix */ return (CHOLMOD(zeros) (nrow, ncol, CHOLMOD_REAL, Common)) ; } /* ---------------------------------------------------------------------- */ /* read the entries */ /* ---------------------------------------------------------------------- */ first = TRUE ; for (j = 0 ; j < (Int) ncol ; j++) { /* ------------------------------------------------------------------ */ /* get the row index of the first entry in the file for column j */ /* ------------------------------------------------------------------ */ if (stype == STYPE_UNSYMMETRIC) { i = 0 ; } else if (stype == STYPE_SKEW_SYMMETRIC) { i = j+1 ; } else /* real symmetric or complex Hermitian lower */ { i = j ; } /* ------------------------------------------------------------------ */ /* get column j */ /* ------------------------------------------------------------------ */ for ( ; i < (Int) nrow ; i++) { /* -------------------------------------------------------------- */ /* get the next entry, skipping blank lines and comment lines */ /* -------------------------------------------------------------- */ x = 0 ; z = 0 ; for ( ; ; ) { if (!get_line (f, buf)) { /* premature end of file - not enough entries read in */ ERROR (CHOLMOD_INVALID, "premature EOF") ; return (NULL) ; } if (is_blank_line (buf)) { /* blank line or comment */ continue ; } nitems = sscanf (buf, "%lg %lg\n", &x, &z) ; x = fix_inf (x) ; z = fix_inf (z) ; break ; } nitems = (nitems == EOF) ? 0 : nitems ; /* -------------------------------------------------------------- */ /* for first entry: determine type and allocate dense matrix */ /* -------------------------------------------------------------- */ if (first) { first = FALSE ; if (nitems < 1 || nitems > 2) { /* invalid matrix */ ERROR (CHOLMOD_INVALID, "invalid format") ; return (NULL) ; } else if (nitems == 1) { /* a real matrix */ xtype = CHOLMOD_REAL ; } else if (nitems == 2) { /* a complex matrix */ xtype = CHOLMOD_COMPLEX ; } /* the rest of the lines should have same number of entries */ nshould = nitems ; /* allocate the result */ X = CHOLMOD(zeros) (nrow, ncol, xtype, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } Xx = X->x ; } /* -------------------------------------------------------------- */ /* save the entry in the dense matrix */ /* -------------------------------------------------------------- */ if (nitems != nshould) { /* wrong format or premature end-of-file */ CHOLMOD(free_dense) (&X, Common) ; ERROR (CHOLMOD_INVALID, "invalid matrix file") ; return (NULL) ; } k = i + j*nrow ; kup = j + i*nrow ; if (xtype == CHOLMOD_REAL) { /* real matrix */ Xx [k] = x ; if (k != kup) { if (stype == STYPE_SYMMETRIC_LOWER) { /* real symmetric matrix */ Xx [kup] = x ; } else if (stype == STYPE_SKEW_SYMMETRIC) { /* real skew symmetric matrix */ Xx [kup] = -x ; } } } else if (xtype == CHOLMOD_COMPLEX) { Xx [2*k ] = x ; /* real part */ Xx [2*k+1] = z ; /* imaginary part */ if (k != kup) { if (stype == STYPE_SYMMETRIC_LOWER) { /* complex Hermitian */ Xx [2*kup ] = x ; /* real part */ Xx [2*kup+1] = -z ; /* imaginary part */ } else if (stype == STYPE_SKEW_SYMMETRIC) { /* complex skew symmetric */ Xx [2*kup ] = -x ; /* real part */ Xx [2*kup+1] = -z ; /* imaginary part */ } if (stype == STYPE_COMPLEX_SYMMETRIC_LOWER) { /* complex symmetric */ Xx [2*kup ] = x ; /* real part */ Xx [2*kup+1] = z ; /* imaginary part */ } } } } } /* ---------------------------------------------------------------------- */ /* return the new dense matrix */ /* ---------------------------------------------------------------------- */ return (X) ; } /* ========================================================================== */ /* === cholmod_read_triplet ================================================= */ /* ========================================================================== */ /* Read in a triplet matrix from a file. */ cholmod_triplet *CHOLMOD(read_triplet) ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ /* --------------- */ cholmod_common *Common ) { char buf [MAXLINE+1] ; size_t nrow, ncol, nnz ; int stype, mtype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (f, NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* read the header and first data line */ /* ---------------------------------------------------------------------- */ if (!read_header (f, buf, &mtype, &nrow, &ncol, &nnz, &stype) || mtype != CHOLMOD_TRIPLET) { /* invalid matrix - this function can only read in a triplet matrix */ ERROR (CHOLMOD_INVALID, "invalid format") ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* read the triplet matrix */ /* ---------------------------------------------------------------------- */ return (read_triplet (f, nrow, ncol, nnz, stype, FALSE, buf, Common)) ; } /* ========================================================================== */ /* === cholmod_read_sparse ================================================== */ /* ========================================================================== */ /* Read a sparse matrix from a file. See cholmod_read_triplet for a discussion * of the file format. * * If Common->prefer_upper is TRUE (the default case), a symmetric matrix is * returned stored in upper-triangular form (A->stype == 1). */ cholmod_sparse *CHOLMOD(read_sparse) ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *A, *A2 ; cholmod_triplet *T ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (f, NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* convert to a sparse matrix in compressed-column form */ /* ---------------------------------------------------------------------- */ T = CHOLMOD(read_triplet) (f, Common) ; A = CHOLMOD(triplet_to_sparse) (T, 0, Common) ; CHOLMOD(free_triplet) (&T, Common) ; if (Common->prefer_upper && A != NULL && A->stype == -1) { /* A=A' */ A2 = CHOLMOD(transpose) (A, 2, Common) ; CHOLMOD(free_sparse) (&A, Common) ; A = A2 ; } return (A) ; } /* ========================================================================== */ /* === cholmod_read_dense =================================================== */ /* ========================================================================== */ /* Read a dense matrix from a file. */ cholmod_dense *CHOLMOD(read_dense) ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ /* --------------- */ cholmod_common *Common ) { char buf [MAXLINE+1] ; size_t nrow, ncol, nnz ; int stype, mtype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (f, NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* read the header and first data line */ /* ---------------------------------------------------------------------- */ if (!read_header (f, buf, &mtype, &nrow, &ncol, &nnz, &stype) || mtype != CHOLMOD_DENSE) { /* invalid matrix - this function can only read in a dense matrix */ ERROR (CHOLMOD_INVALID, "invalid format") ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* read the dense matrix */ /* ---------------------------------------------------------------------- */ return (read_dense (f, nrow, ncol, stype, buf, Common)) ; } /* ========================================================================== */ /* === cholmod_read_matrix ================================================== */ /* ========================================================================== */ /* Read a triplet matrix, sparse matrix or a dense matrix from a file. Returns * a void pointer to either a cholmod_triplet, cholmod_sparse, or cholmod_dense * object. The type of object is passed back to the caller as the mtype * argument. */ void *CHOLMOD(read_matrix) ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ int prefer, /* If 0, a sparse matrix is always return as a * cholmod_triplet form. It can have any stype * (symmetric-lower, unsymmetric, or * symmetric-upper). * If 1, a sparse matrix is returned as an unsymmetric * cholmod_sparse form (A->stype == 0), with both * upper and lower triangular parts present. * This is what the MATLAB mread mexFunction does, * since MATLAB does not have an stype. * If 2, a sparse matrix is returned with an stype of 0 * or 1 (unsymmetric, or symmetric with upper part * stored). * This argument has no effect for dense matrices. */ /* ---- output---- */ int *mtype, /* CHOLMOD_TRIPLET, CHOLMOD_SPARSE or CHOLMOD_DENSE */ /* --------------- */ cholmod_common *Common ) { void *G = NULL ; cholmod_sparse *A, *A2 ; cholmod_triplet *T ; char buf [MAXLINE+1] ; size_t nrow, ncol, nnz ; int stype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (f, NULL) ; RETURN_IF_NULL (mtype, NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* read the header to determine the mtype */ /* ---------------------------------------------------------------------- */ if (!read_header (f, buf, mtype, &nrow, &ncol, &nnz, &stype)) { /* invalid matrix */ ERROR (CHOLMOD_INVALID, "invalid format") ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* read a matrix */ /* ---------------------------------------------------------------------- */ if (*mtype == CHOLMOD_TRIPLET) { /* read in the triplet matrix, converting to unsymmetric format if * prefer == 1 */ T = read_triplet (f, nrow, ncol, nnz, stype, prefer == 1, buf, Common) ; if (prefer == 0) { /* return matrix in its original triplet form */ G = T ; } else { /* return matrix in a compressed-column form */ A = CHOLMOD(triplet_to_sparse) (T, 0, Common) ; CHOLMOD(free_triplet) (&T, Common) ; if (A != NULL && prefer == 2 && A->stype == -1) { /* convert A from symmetric-lower to symmetric-upper */ A2 = CHOLMOD(transpose) (A, 2, Common) ; CHOLMOD(free_sparse) (&A, Common) ; A = A2 ; } *mtype = CHOLMOD_SPARSE ; G = A ; } } else if (*mtype == CHOLMOD_DENSE) { /* return a dense matrix */ G = read_dense (f, nrow, ncol, stype, buf, Common) ; } return (G) ; } #endif Matrix/src/CHOLMOD/Supernodal/0000755000175100001440000000000012271765426015540 5ustar hornikusersMatrix/src/CHOLMOD/Supernodal/cholmod_super_symbolic.c0000644000175100001440000007176112271765436022465 0ustar hornikusers/* ========================================================================== */ /* === Supernodal/cholmod_super_symbolic ==================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Supernodal symbolic analysis of the LL' factorization of A, A*A', * A(:,f)*A(:,f)'. * * This routine must be preceded by a simplicial symbolic analysis * (cholmod_rowcolcounts). See cholmod_analyze.c for an example of how to use * this routine. * * The user need not call this directly; cholmod_analyze is a "simple" wrapper * for this routine. * * Symmetric case: * * A is stored in column form, with entries stored in the upper triangular * part. Entries in the lower triangular part are ignored. * * Unsymmetric case: * * A is stored in column form. If F is equal to the transpose of A, then * A*A' is analyzed. F can include a subset of the columns of A * (F=A(:,f)'), in which case F*F' is analyzed. * * Requires Parent and L->ColCount to be defined on input; these are the * simplicial Parent and ColCount arrays as computed by cholmod_rowcolcounts. * Does not use L->Perm; the input matrices A and F must already be properly * permuted. Allocates and computes the supernodal pattern of L (L->super, * L->pi, L->px, and L->s). Does not allocate the real part (L->x). * * Supports any xtype (pattern, real, complex, or zomplex). */ #ifndef NSUPERNODAL #include "cholmod_internal.h" #include "cholmod_supernodal.h" /* ========================================================================== */ /* === subtree ============================================================== */ /* ========================================================================== */ /* In the symmetric case, traverse the kth row subtree from the nonzeros in * A (0:k1-1,k) and add the new entries found to the pattern of the kth row * of L. The current supernode s contains the diagonal block k1:k2-1, so it * can be skipped. * * In the unsymmetric case, the nonzero pattern of A*F is computed one column * at a time (thus, the total time spent in this function is bounded below by * the time taken to multiply A*F, which can be high if A is tall and thin). * The kth column is A*F(:,k), or the set union of all columns A(:,j) for which * F(j,k) is nonzero. This routine is called once for each entry j. Only the * upper triangular part is needed, so only A (0:k1-1,j) is accessed, where * k1:k2-1 are the columns of the current supernode s (k is in the range k1 to * k2-1). * * If A is sorted, then the total time taken by this function is proportional * to the number of nonzeros in the strictly block upper triangular part of A, * plus the number of entries in the strictly block lower triangular part of * the supernodal part of L. This excludes entries in the diagonal blocks * corresponding to the columns in each supernode. That is, if k1:k2-1 are * in a single supernode, then only A (0:k1-1,k1:k2-1) are accessed. * * For the unsymmetric case, only the strictly block upper triangular part * of A*F is constructed. * * Only adds column indices corresponding to the leading columns of each * relaxed supernode. */ static void subtree ( /* inputs, not modified: */ Int j, /* j = k for symmetric case */ Int k, Int Ap [ ], Int Ai [ ], Int Anz [ ], Int SuperMap [ ], Int Sparent [ ], Int mark, Int sorted, /* true if the columns of A are sorted */ Int k1, /* only consider A (0:k1-1,k) */ /* input/output: */ Int Flag [ ], Int Ls [ ], Int Lpi2 [ ] ) { Int p, pend, i, si ; p = Ap [j] ; pend = (Anz == NULL) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i < k1) { /* (i,k) is an entry in the upper triangular part of A or A*F'. * symmetric case: A(i,k) is nonzero (j=k). * unsymmetric case: A(i,j) and F(j,k) are both nonzero. * * Column i is in supernode si = SuperMap [i]. Follow path from si * to root of supernodal etree, stopping at the first flagged * supernode. The root of the row subtree is supernode SuperMap[k], * which is flagged already. This traversal will stop there, or it * might stop earlier if supernodes have been flagged by previous * calls to this routine for the same k. */ for (si = SuperMap [i] ; Flag [si] < mark ; si = Sparent [si]) { ASSERT (si <= SuperMap [k]) ; Ls [Lpi2 [si]++] = k ; Flag [si] = mark ; } } else if (sorted) { break ; } } } /* clear workspace used by cholmod_super_symbolic */ #define FREE_WORKSPACE \ { \ /* CHOLMOD(clear_flag) (Common) ; */ \ CHOLMOD_CLEAR_FLAG (Common) ; \ for (k = 0 ; k <= nfsuper ; k++) \ { \ Head [k] = EMPTY ; \ } \ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; \ } \ /* ========================================================================== */ /* === cholmod_super_symbolic2 ============================================== */ /* ========================================================================== */ /* Analyze for supernodal Cholesky or multifrontal QR. CHOLMOD itself always * analyzes for supernodal Cholesky, of course. The "for_cholesky = TRUE" * option is used by SuiteSparseQR only. */ int CHOLMOD(super_symbolic2) ( /* ---- input ---- */ int for_cholesky, /* Cholesky if TRUE, QR if FALSE */ cholmod_sparse *A, /* matrix to analyze */ cholmod_sparse *F, /* F = A' or A(:,f)' */ Int *Parent, /* elimination tree */ /* ---- in/out --- */ cholmod_factor *L, /* simplicial symbolic on input, * supernodal symbolic on output */ /* --------------- */ cholmod_common *Common ) { double zrelax0, zrelax1, zrelax2, xxsize ; Int *Wi, *Wj, *Super, *Snz, *Ap, *Ai, *Flag, *Head, *Ls, *Lpi, *Lpx, *Fnz, *Sparent, *Anz, *SuperMap, *Merged, *Nscol, *Zeros, *Fp, *Fj, *ColCount, *Lpi2, *Lsuper, *Iwork ; Int nsuper, d, n, j, k, s, mark, parent, p, pend, k1, k2, packed, nscol, nsrow, ndrow1, ndrow2, stype, ssize, xsize, sparent, plast, slast, csize, maxcsize, ss, nscol0, nscol1, ns, nfsuper, newzeros, totzeros, merge, snext, esize, maxesize, nrelax0, nrelax1, nrelax2, Asorted ; size_t w ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_NULL (Parent, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_PATTERN, FALSE) ; stype = A->stype ; if (stype < 0) { /* invalid symmetry; symmetric lower form not supported */ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ; return (FALSE) ; } if (stype == 0) { /* F must be present in the unsymmetric case */ RETURN_IF_NULL (F, FALSE) ; } if (L->is_super) { /* L must be a simplicial symbolic factor */ ERROR (CHOLMOD_INVALID, "L must be symbolic on input") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ n = A->nrow ; /* w = 5*n */ w = CHOLMOD(mult_size_t) (n, 5, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, w, 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* A is now either A or triu(A(p,p)) for the symmetric case. It is either * A or A(p,f) for the unsymmetric case (both in column form). It can be * either packed or unpacked, and either sorted or unsorted. Entries in * the lower triangular part may be present if A is symmetric, but these * are ignored. */ Ap = A->p ; Ai = A->i ; Anz = A->nz ; if (stype != 0) { /* F not accessed */ Fp = NULL ; Fj = NULL ; Fnz = NULL ; packed = TRUE ; } else { /* F = A(:,f) or A(p,f) in packed row form, either sorted or unsorted */ Fp = F->p ; Fj = F->i ; Fnz = F->nz ; packed = F->packed ; } ColCount = L->ColCount ; nrelax0 = Common->nrelax [0] ; nrelax1 = Common->nrelax [1] ; nrelax2 = Common->nrelax [2] ; zrelax0 = Common->zrelax [0] ; zrelax1 = Common->zrelax [1] ; zrelax2 = Common->zrelax [2] ; zrelax0 = IS_NAN (zrelax0) ? 0 : zrelax0 ; zrelax1 = IS_NAN (zrelax1) ? 0 : zrelax1 ; zrelax2 = IS_NAN (zrelax2) ? 0 : zrelax2 ; ASSERT (CHOLMOD(dump_parent) (Parent, n, "Parent", Common)) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ /* Sparent, Snz, and Merged could be allocated later, of size nfsuper */ Iwork = Common->Iwork ; Wi = Iwork ; /* size n (i/l/l). Lpi2 is i/l/l */ Wj = Iwork + n ; /* size n (i/l/l). Zeros is i/l/l */ Sparent = Iwork + 2*((size_t) n) ; /* size nfsuper <= n [ */ Snz = Iwork + 3*((size_t) n) ; /* size nfsuper <= n [ */ Merged = Iwork + 4*((size_t) n) ; /* size nfsuper <= n [ */ Flag = Common->Flag ; /* size n */ Head = Common->Head ; /* size n+1 */ /* ---------------------------------------------------------------------- */ /* find the fundamental supernodes */ /* ---------------------------------------------------------------------- */ /* count the number of children of each node, using Wi [ */ for (j = 0 ; j < n ; j++) { Wi [j] = 0 ; } for (j = 0 ; j < n ; j++) { parent = Parent [j] ; if (parent != EMPTY) { Wi [parent]++ ; } } Super = Head ; /* use Head [0..nfsuper] as workspace for Super list ( */ /* column 0 always starts a new supernode */ nfsuper = (n == 0) ? 0 : 1 ; /* number of fundamental supernodes */ Super [0] = 0 ; for (j = 1 ; j < n ; j++) { /* check if j starts new supernode, or in the same supernode as j-1 */ if (Parent [j-1] != j /* parent of j-1 is not j */ || (ColCount [j-1] != ColCount [j] + 1) /* j-1 not subset of j*/ || Wi [j] > 1) /* j has more than one child */ { /* j is the leading node of a supernode */ Super [nfsuper++] = j ; } } Super [nfsuper] = n ; /* contents of Wi no longer needed for child count ] */ Nscol = Wi ; /* use Wi as size-nfsuper workspace for Nscol [ */ /* ---------------------------------------------------------------------- */ /* find the mapping of fundamental nodes to supernodes */ /* ---------------------------------------------------------------------- */ SuperMap = Wj ; /* use Wj as workspace for SuperMap [ */ /* SuperMap [k] = s if column k is contained in supernode s */ for (s = 0 ; s < nfsuper ; s++) { for (k = Super [s] ; k < Super [s+1] ; k++) { SuperMap [k] = s ; } } /* ---------------------------------------------------------------------- */ /* construct the fundamental supernodal etree */ /* ---------------------------------------------------------------------- */ for (s = 0 ; s < nfsuper ; s++) { j = Super [s+1] - 1 ; /* last node in supernode s */ parent = Parent [j] ; /* parent of last node */ Sparent [s] = (parent == EMPTY) ? EMPTY : SuperMap [parent] ; PRINT1 (("Sparent ["ID"] = "ID"\n", s, Sparent [s])) ; } /* contents of Wj no longer needed as workspace for SuperMap ] * SuperMap will be recomputed below, for the relaxed supernodes. */ Zeros = Wj ; /* use Wj for Zeros, workspace of size nfsuper [ */ /* ---------------------------------------------------------------------- */ /* relaxed amalgamation */ /* ---------------------------------------------------------------------- */ for (s = 0 ; s < nfsuper ; s++) { Merged [s] = EMPTY ; /* s not merged into another */ Nscol [s] = Super [s+1] - Super [s] ; /* # of columns in s */ Zeros [s] = 0 ; /* # of zero entries in s */ ASSERT (s <= Super [s]) ; Snz [s] = ColCount [Super [s]] ; /* # of entries in leading col of s */ PRINT2 (("lnz ["ID"] "ID"\n", s, Snz [s])) ; } for (s = nfsuper-2 ; s >= 0 ; s--) { /* should supernodes s and s+1 merge into a new node s? */ PRINT1 (("\n========= Check relax of s "ID" and s+1 "ID"\n", s, s+1)) ; ss = Sparent [s] ; if (ss == EMPTY) { PRINT1 (("s "ID" is a root, no merge with s+1 = "ID"\n", s, s+1)) ; continue ; } /* find the current parent of s (perform path compression as needed) */ for (ss = Sparent [s] ; Merged [ss] != EMPTY ; ss = Merged [ss]) ; sparent = ss ; PRINT2 (("Current sparent of s "ID" is "ID"\n", s, sparent)) ; /* ss is the current parent of s */ for (ss = Sparent [s] ; Merged [ss] != EMPTY ; ss = snext) { snext = Merged [ss] ; PRINT2 (("ss "ID" is dead, merged into snext "ID"\n", ss, snext)) ; Merged [ss] = sparent ; } /* if s+1 is not the current parent of s, do not merge */ if (sparent != s+1) { continue ; } nscol0 = Nscol [s] ; /* # of columns in s */ nscol1 = Nscol [s+1] ; /* # of columns in s+1 */ ns = nscol0 + nscol1 ; PRINT2 (("ns "ID" nscol0 "ID" nscol1 "ID"\n", ns, nscol0, nscol1)) ; totzeros = Zeros [s+1] ; /* current # of zeros in s+1 */ /* determine if supernodes s and s+1 should merge */ if (ns <= nrelax0) { PRINT2 (("ns is tiny ("ID"), so go ahead and merge\n", ns)) ; merge = TRUE ; } else { /* use double to avoid integer overflow */ double lnz0 = Snz [s] ; /* # entries in leading column of s */ double lnz1 = Snz [s+1] ; /* # entries in leading column of s+1 */ double xnewzeros = nscol0 * (lnz1 + nscol0 - lnz0) ; /* use Int for the final update of Zeros [s] below */ newzeros = nscol0 * (Snz [s+1] + nscol0 - Snz [s]) ; ASSERT (newzeros == xnewzeros) ; PRINT2 (("lnz0 %g lnz1 %g xnewzeros %g\n", lnz0, lnz1, xnewzeros)) ; if (xnewzeros == 0) { /* no new zeros, so go ahead and merge */ PRINT2 (("no new fillin, so go ahead and merge\n")) ; merge = TRUE ; } else { /* # of zeros if merged */ double xtotzeros = ((double) totzeros) + xnewzeros ; /* xtotsize: total size of merged supernode, if merged: */ double xns = (double) ns ; double xtotsize = (xns * (xns+1) / 2) + xns * (lnz1 - nscol1) ; double z = xtotzeros / xtotsize ; Int totsize ; totsize = (ns * (ns+1) / 2) + ns * (Snz [s+1] - nscol1) ; PRINT2 (("oldzeros "ID" newzeros "ID" xtotsize %g z %g\n", Zeros [s+1], newzeros, xtotsize, z)) ; /* use Int for the final update of Zeros [s] below */ totzeros += newzeros ; /* do not merge if supernode would become too big * (Int overflow). Continue computing; not (yet) an error. */ /* fl.pt. compare, but no NaN's can occur here */ merge = ((ns <= nrelax1 && z < zrelax0) || (ns <= nrelax2 && z < zrelax1) || (z < zrelax2)) && (xtotsize < Int_max / sizeof (double)) ; } } if (merge) { PRINT1 (("Merge node s ("ID") and s+1 ("ID")\n", s, s+1)) ; Zeros [s] = totzeros ; Merged [s+1] = s ; Snz [s] = nscol0 + Snz [s+1] ; Nscol [s] += Nscol [s+1] ; } } /* contents of Wj no longer needed for Zeros ] */ /* contents of Wi no longer needed for Nscol ] */ /* contents of Sparent no longer needed (recomputed below) */ /* ---------------------------------------------------------------------- */ /* construct the relaxed supernode list */ /* ---------------------------------------------------------------------- */ nsuper = 0 ; for (s = 0 ; s < nfsuper ; s++) { if (Merged [s] == EMPTY) { PRINT1 (("live supernode: "ID" snz "ID"\n", s, Snz [s])) ; Super [nsuper] = Super [s] ; Snz [nsuper] = Snz [s] ; nsuper++ ; } } Super [nsuper] = n ; PRINT1 (("Fundamental supernodes: "ID" relaxed "ID"\n", nfsuper, nsuper)) ; /* Merged no longer needed ] */ /* ---------------------------------------------------------------------- */ /* find the mapping of relaxed nodes to supernodes */ /* ---------------------------------------------------------------------- */ /* use Wj as workspace for SuperMap { */ /* SuperMap [k] = s if column k is contained in supernode s */ for (s = 0 ; s < nsuper ; s++) { for (k = Super [s] ; k < Super [s+1] ; k++) { SuperMap [k] = s ; } } /* ---------------------------------------------------------------------- */ /* construct the relaxed supernodal etree */ /* ---------------------------------------------------------------------- */ for (s = 0 ; s < nsuper ; s++) { j = Super [s+1] - 1 ; /* last node in supernode s */ parent = Parent [j] ; /* parent of last node */ Sparent [s] = (parent == EMPTY) ? EMPTY : SuperMap [parent] ; PRINT1 (("new Sparent ["ID"] = "ID"\n", s, Sparent [s])) ; } /* ---------------------------------------------------------------------- */ /* determine the size of L->s and L->x */ /* ---------------------------------------------------------------------- */ ssize = 0 ; xsize = 0 ; xxsize = 0 ; for (s = 0 ; s < nsuper ; s++) { nscol = Super [s+1] - Super [s] ; nsrow = Snz [s] ; ASSERT (nscol > 0) ; ssize += nsrow ; if (for_cholesky) { xsize += nscol * nsrow ; /* also compute xsize in double to guard against Int overflow */ xxsize += ((double) nscol) * ((double) nsrow) ; } if (ssize < 0 || (for_cholesky && xxsize > Int_max)) { /* Int overflow, clear workspace and return. QR factorization will not use xxsize, so that error is ignored. For Cholesky factorization, however, memory of space xxsize will be allocated, so this is a failure. Both QR and Cholesky fail if ssize overflows. */ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; FREE_WORKSPACE ; return (FALSE) ; } ASSERT (ssize > 0) ; ASSERT (IMPLIES (for_cholesky, xsize > 0)) ; } xsize = MAX (1, xsize) ; ssize = MAX (1, ssize) ; PRINT1 (("ix sizes: "ID" "ID" nsuper "ID"\n", ssize, xsize, nsuper)) ; /* ---------------------------------------------------------------------- */ /* allocate L (all except real part L->x) */ /* ---------------------------------------------------------------------- */ L->ssize = ssize ; L->xsize = xsize ; L->nsuper = nsuper ; CHOLMOD(change_factor) (CHOLMOD_PATTERN, TRUE, TRUE, TRUE, TRUE, L, Common); if (Common->status < CHOLMOD_OK) { /* out of memory; L is still a valid simplicial symbolic factor */ FREE_WORKSPACE ; return (FALSE) ; } DEBUG (CHOLMOD(dump_factor) (L, "L to symbolic super", Common)) ; ASSERT (L->is_ll && L->xtype == CHOLMOD_PATTERN && L->is_super) ; Lpi = L->pi ; Lpx = L->px ; Ls = L->s ; Ls [0] = 0 ; /* flag for cholmod_check_factor; supernodes are defined */ Lpx [0] = for_cholesky ? 0 : 123456 ; /* magic number for sparse QR */ Lsuper = L->super ; /* copy the list of relaxed supernodes into the final list in L */ for (s = 0 ; s <= nsuper ; s++) { Lsuper [s] = Super [s] ; } /* Head no longer needed as workspace for fundamental Super list ) */ Super = Lsuper ; /* Super is now the list of relaxed supernodes */ /* ---------------------------------------------------------------------- */ /* construct column pointers of relaxed supernodal pattern (L->pi) */ /* ---------------------------------------------------------------------- */ p = 0 ; for (s = 0 ; s < nsuper ; s++) { Lpi [s] = p ; p += Snz [s] ; PRINT1 (("Snz ["ID"] = "ID", Super ["ID"] = "ID"\n", s, Snz [s], s, Super[s])) ; } Lpi [nsuper] = p ; ASSERT ((Int) (L->ssize) == MAX (1,p)) ; /* ---------------------------------------------------------------------- */ /* construct pointers for supernodal values (L->px) */ /* ---------------------------------------------------------------------- */ if (for_cholesky) { /* L->px is not needed for QR factorization (it may lead to Int overflow, anyway, if xsize caused Int overflow above) */ p = 0 ; for (s = 0 ; s < nsuper ; s++) { nscol = Super [s+1] - Super [s] ; /* number of columns in s */ nsrow = Snz [s] ; /* # of rows, incl triangular part*/ Lpx [s] = p ; /* pointer to numerical part of s */ p += nscol * nsrow ; } Lpx [s] = p ; ASSERT ((Int) (L->xsize) == MAX (1,p)) ; } /* Snz no longer needed ] */ /* ---------------------------------------------------------------------- */ /* symbolic analysis to construct the relaxed supernodal pattern (L->s) */ /* ---------------------------------------------------------------------- */ Lpi2 = Wi ; /* copy Lpi into Lpi2, using Wi as workspace for Lpi2 [ */ for (s = 0 ; s < nsuper ; s++) { Lpi2 [s] = Lpi [s] ; } Asorted = A->sorted ; for (s = 0 ; s < nsuper ; s++) { /* sth supernode is in columns k1 to k2-1. * compute nonzero pattern of L (k1:k2-1,:). */ /* place rows k1 to k2-1 in leading column of supernode s */ k1 = Super [s] ; k2 = Super [s+1] ; PRINT1 (("=========>>> Supernode "ID" k1 "ID" k2-1 "ID"\n", s, k1, k2-1)) ; for (k = k1 ; k < k2 ; k++) { Ls [Lpi2 [s]++] = k ; } /* compute nonzero pattern each row k1 to k2-1 */ for (k = k1 ; k < k2 ; k++) { /* compute row k of L. In the symmetric case, the pattern of L(k,:) * is the set of nodes reachable in the supernodal etree from any * row i in the nonzero pattern of A(0:k,k). In the unsymmetric * case, the pattern of the kth column of A*A' is the set union * of all columns A(0:k,j) for each nonzero F(j,k). */ /* clear the Flag array and mark the current supernode */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; Flag [s] = mark ; ASSERT (s == SuperMap [k]) ; /* traverse the row subtree for each nonzero in A or AA' */ if (stype != 0) { subtree (k, k, Ap, Ai, Anz, SuperMap, Sparent, mark, Asorted, k1, Flag, Ls, Lpi2) ; } else { /* for each j nonzero in F (:,k) do */ p = Fp [k] ; pend = (packed) ? (Fp [k+1]) : (p + Fnz [k]) ; for ( ; p < pend ; p++) { subtree (Fj [p], k, Ap, Ai, Anz, SuperMap, Sparent, mark, Asorted, k1, Flag, Ls, Lpi2) ; } } } } #ifndef NDEBUG for (s = 0 ; s < nsuper ; s++) { PRINT1 (("Lpi2[s] "ID" Lpi[s+1] "ID"\n", Lpi2 [s], Lpi [s+1])) ; ASSERT (Lpi2 [s] == Lpi [s+1]) ; CHOLMOD(dump_super) (s, Super, Lpi, Ls, NULL, NULL, 0, Common) ; } #endif /* contents of Wi no longer needed for Lpi2 ] */ /* Sparent no longer needed ] */ /* ---------------------------------------------------------------------- */ /* determine the largest update matrix (L->maxcsize) */ /* ---------------------------------------------------------------------- */ /* maxcsize could be determined before L->s is allocated and defined, which * would mean that all memory requirements for both the symbolic and numeric * factorizations could be computed using O(nnz(A)+O(n)) space. However, it * would require a lot of extra work. The analysis phase, above, would need * to be duplicated, but with Ls not kept; instead, the algorithm would keep * track of the current s and slast for each supernode d, and update them * when a new row index appears in supernode d. An alternative would be to * do this computation only if the allocation of L->s failed, in which case * the following code would be skipped. * * The csize for a supernode is the size of its largest contribution to * a subsequent ancestor supernode. For example, suppose the rows of #'s * in the figure below correspond to the columns of a subsequent supernode, * and the dots are the entries in that ancestore. * * c * c c * c c c * x x x * x x x * # # # . * # # # . . * * * * . . * * * * . . * * * * . . * . . * * Then for this update, the csize is 3-by-2, or 6, because there are 3 * rows of *'s which is the number of rows in the update, and there are * 2 rows of #'s, which is the number columns in the update. The csize * of a supernode is the largest such contribution for any ancestor * supernode. maxcsize, for the whole matrix, has a rough upper bound of * the maximum size of any supernode. This bound is loose, because the * the contribution must be less than the size of the ancestor supernodal * that it's updating. maxcsize of a completely dense matrix, with one * supernode, is zero. * * maxesize is the column dimension for the workspace E needed for the * solve. E is of size nrhs-by-maxesize, where the nrhs is the number of * columns in the right-hand-side. The maxesize is the largest esize of * any supernode. The esize of a supernode is the number of row indices * it contains, excluding the column indices of the supernode itself. * For the following example, esize is 4: * * c * c c * c c c * x x x * x x x * x x x * x x x * * maxesize can be no bigger than n. */ maxcsize = 1 ; maxesize = 1 ; /* Do not need to guard csize against Int overflow since xsize is OK. */ if (for_cholesky) { /* this is not needed for QR factorization */ for (d = 0 ; d < nsuper ; d++) { nscol = Super [d+1] - Super [d] ; p = Lpi [d] + nscol ; plast = p ; pend = Lpi [d+1] ; esize = pend - p ; maxesize = MAX (maxesize, esize) ; slast = (p == pend) ? (EMPTY) : (SuperMap [Ls [p]]) ; for ( ; p <= pend ; p++) { s = (p == pend) ? (EMPTY) : (SuperMap [Ls [p]]) ; if (s != slast) { /* row i is the start of a new supernode */ ndrow1 = p - plast ; ndrow2 = pend - plast ; csize = ndrow2 * ndrow1 ; PRINT1 (("Supernode "ID" ancestor "ID" C: "ID"-by-"ID " csize "ID"\n", d, slast, ndrow1, ndrow2, csize)) ; maxcsize = MAX (maxcsize, csize) ; plast = p ; slast = s ; } } } PRINT1 (("max csize "ID"\n", maxcsize)) ; } /* Wj no longer needed for SuperMap } */ L->maxcsize = maxcsize ; L->maxesize = maxesize ; L->is_super = TRUE ; ASSERT (L->xtype == CHOLMOD_PATTERN && L->is_ll) ; /* ---------------------------------------------------------------------- */ /* supernodal symbolic factorization is complete */ /* ---------------------------------------------------------------------- */ FREE_WORKSPACE ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_super_symbolic =============================================== */ /* ========================================================================== */ /* Analyzes A, AA', or A(:,f)*A(:,f)' in preparation for a supernodal numeric * factorization. The user need not call this directly; cholmod_analyze is * a "simple" wrapper for this routine. * * This function does all the analysis for a supernodal Cholesky factorization. * * workspace: Flag (nrow), Head (nrow), Iwork (2*nrow), * and temporary space of size 3*nfsuper*sizeof(Int), where nfsuper <= n * is the number of fundamental supernodes. */ int CHOLMOD(super_symbolic) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ cholmod_sparse *F, /* F = A' or A(:,f)' */ Int *Parent, /* elimination tree */ /* ---- in/out --- */ cholmod_factor *L, /* simplicial symbolic on input, * supernodal symbolic on output */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(super_symbolic2) (TRUE, A, F, Parent, L, Common)) ; } #endif Matrix/src/CHOLMOD/Supernodal/License.txt0000644000175100001440000000203111770402705017646 0ustar hornikusersCHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.suitesparse.com Note that this license is for the CHOLMOD/Supernodal module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. Matrix/src/CHOLMOD/Supernodal/t_cholmod_gpu.c0000644000175100001440000010374612271765436020543 0ustar hornikusers/* ========================================================================== */ /* === Supernodal/t_cholmod_gpu ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Supernodal Module. Copyright (C) 2005-2012, Timothy A. Davis * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* GPU BLAS template routine for cholmod_super_numeric. */ /* ========================================================================== */ /* === include files and definitions ======================================== */ /* ========================================================================== */ #include "cholmod_template.h" #undef L_ENTRY #ifdef REAL #define L_ENTRY 1 #else #define L_ENTRY 2 #endif /* #define GPU_Printf printf */ #define GPU_Printf #define PAGE_SIZE (4*1024) #define OK(cuda_operation) ((cuda_operation) == cudaSuccess) /* ========================================================================== */ /* === gpu_init ============================================================= */ /* ========================================================================== */ void TEMPLATE (CHOLMOD (gpu_init)) ( void *Cwork, Int maxSize, cholmod_common *Common ) { Int i ; cublasStatus_t cublasError ; cudaError_t cudaErr ; size_t maxBytesSize, HostPinnedSize ; Common->GemmUsed = 0 ; GPU_Printf ("gpu_init : %p\n", (void *) ((size_t) Cwork & ~(PAGE_SIZE-1))) ; if (!(Common->cublasHandle)) { /* ------------------------------------------------------------------ */ /* create the CUDA BLAS handle */ /* ------------------------------------------------------------------ */ cublasError = cublasCreate (&(Common->cublasHandle)) ; if (cublasError != CUBLAS_STATUS_SUCCESS) { ERROR (CHOLMOD_GPU_PROBLEM, "CUBLAS initialization") ; return ; } /* ------------------------------------------------------------------ */ /* create each CUDA stream */ /* ------------------------------------------------------------------ */ cudaErr = cudaStreamCreate (&(Common->cudaStreamSyrk)) ; if (cudaErr != cudaSuccess) { ERROR (CHOLMOD_GPU_PROBLEM, "CUDA stream initialization") ; return ; } cudaErr = cudaStreamCreate (&(Common->cudaStreamGemm)) ; if (cudaErr != cudaSuccess) { ERROR (CHOLMOD_GPU_PROBLEM, "CUDA stream initialization") ; return ; } cudaErr = cudaStreamCreate (&(Common->cudaStreamTrsm)) ; if (cudaErr != cudaSuccess) { ERROR (CHOLMOD_GPU_PROBLEM, "CUDA stream initialization") ; return ; } for (i = 0 ; i < 3 ; i++) { cudaErr = cudaStreamCreate (&(Common->cudaStreamPotrf [i])) ; if (cudaErr != cudaSuccess) { ERROR (CHOLMOD_GPU_PROBLEM, "CUDA stream initialization") ; return ; } } /* ------------------------------------------------------------------ */ /* create each CUDA event */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < 2 ; i++) { cudaErr = cudaEventCreateWithFlags (&(Common->cublasEventPotrf [i]), cudaEventDisableTiming) ; if (cudaErr != cudaSuccess) { ERROR (CHOLMOD_GPU_PROBLEM, "CUDA event") ; return ; } } } /* ---------------------------------------------------------------------- */ /* pin the Host memory */ /* ---------------------------------------------------------------------- */ Common->HostPinnedMemory = (void *) ((size_t) Cwork & ~(PAGE_SIZE-1)) ; maxBytesSize = sizeof (double)*L_ENTRY*maxSize ; /* Align on a 4K page boundary (it is no more necessary in 4.1 */ HostPinnedSize = (((size_t) Cwork + maxBytesSize + PAGE_SIZE-1) & ~(PAGE_SIZE-1)) - (size_t) (Common->HostPinnedMemory) ; GPU_Printf ("gpu HostPinnedSize: %g %p\n", (double) HostPinnedSize, Common->HostPinnedMemory) ; cudaErr = cudaHostRegister (Common->HostPinnedMemory, HostPinnedSize, 0) ; if (cudaErr != cudaSuccess) { ERROR (CHOLMOD_GPU_PROBLEM, "CUDA Pinning Memory") ; Common->HostPinnedMemory = NULL ; } } /* ========================================================================== */ /* === gpu_end ============================================================== */ /* ========================================================================== */ void TEMPLATE (CHOLMOD (gpu_end)) ( cholmod_common *Common ) { int i; /* unpin the Host memory */ GPU_Printf ("gpu_end %p\n", Common->HostPinnedMemory) ; cudaError_t cudaErr = cudaHostUnregister (Common->HostPinnedMemory) ; if (cudaErr != cudaSuccess) { ERROR (CHOLMOD_GPU_PROBLEM, "CUDA Unpinning Memory") ; Common->HostPinnedMemory = NULL ; } /* ------------------------------------------------------------------ */ /* destroy Cublas Handle */ /* ------------------------------------------------------------------ */ if (Common->cublasHandle) { cublasDestroy(Common->cublasHandle); Common->cublasHandle = NULL ; } /* ------------------------------------------------------------------ */ /* destroy each CUDA stream */ /* ------------------------------------------------------------------ */ if (Common->cudaStreamSyrk) { cudaStreamDestroy (Common->cudaStreamSyrk) ; Common->cudaStreamSyrk = NULL ; } if (Common->cudaStreamGemm) { cudaStreamDestroy (Common->cudaStreamGemm) ; } if (Common->cudaStreamTrsm) { cudaStreamDestroy (Common->cudaStreamTrsm) ; Common->cudaStreamTrsm = NULL ; } for (i = 0 ; i < 3 ; i++) { if (Common->cudaStreamPotrf [i]) { cudaStreamDestroy(Common->cudaStreamPotrf [i]) ; Common->cudaStreamPotrf [i] = NULL ; } } /* ------------------------------------------------------------------ */ /* destroy each CUDA event */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < 2 ; i++) { if (Common->cublasEventPotrf [i]) { cudaEventDestroy( Common->cublasEventPotrf [i] ) ; Common->cublasEventPotrf [i] = NULL ; } } } /* ========================================================================== */ /* === gpu_updateC ========================================================== */ /* ========================================================================== */ /* C = L (k1:n-1, kd1:kd2-1) * L (k1:k2-1, kd1:kd2-1)', except that k1:n-1 * refers to all of the rows in L, but many of the rows are all zero. * Supernode d holds columns kd1 to kd2-1 of L. Nonzero rows in the range * k1:k2-1 are in the list Ls [pdi1 ... pdi2-1], of size ndrow1. Nonzero rows * in the range k2:n-1 are in the list Ls [pdi2 ... pdend], of size ndrow2. * Let L1 = L (Ls [pdi1 ... pdi2-1], kd1:kd2-1), and let L2 = L (Ls [pdi2 ... * pdend], kd1:kd2-1). C is ndrow2-by-ndrow1. Let C1 be the first ndrow1 * rows of C and let C2 be the last ndrow2-ndrow1 rows of C. Only the lower * triangular part of C1 needs to be computed since C1 is symmetric. */ int TEMPLATE (CHOLMOD (gpu_updateC)) ( Int ndrow1, /* C is ndrow2-by-ndrow2 */ Int ndrow2, Int ndrow, /* leading dimension of Lx */ Int ndcol, /* L1 is ndrow1-by-ndcol */ Int pdx1, /* L1 starts at Lx + L_ENTRY*pdx1 */ /* L2 starts at Lx + L_ENTRY*(pdx1 + ndrow1) */ double *Lx, double *C, cholmod_common *Common ) { double *devPtrLx, *devPtrC ; double alpha, beta ; cublasStatus_t cublasStatus ; cudaError_t cudaStat [2] ; Int ndrow3 ; Common->SyrkUsed = 0 ; Common->GemmUsed = 0 ; if ((ndrow2 < 512) || (ndcol < 128)) { /* too small for the CUDA BLAS; use the CPU instead */ return (0) ; } ndrow3 = ndrow2 - ndrow1 ; #ifndef NTIMER Common->syrkStart = SuiteSparse_time ( ) ; #endif /* ---------------------------------------------------------------------- */ /* allocate workspace on the GPU */ /* ---------------------------------------------------------------------- */ cudaStat [0] = cudaMalloc ((void **) &devPtrLx, ndrow2 * ndcol * L_ENTRY * sizeof (devPtrLx [0])) ; cudaStat [1] = cudaMalloc ((void **) &devPtrC, ndrow2 * ndrow1 * L_ENTRY * sizeof (devPtrC [0])) ; Common->devSyrkGemmPtrLx = devPtrLx ; Common->devSyrkGemmPtrC = devPtrC ; if (cudaStat [0] || cudaStat [1]) { /* one or both cudaMalloc's failed */ if (devPtrLx) cudaFree (devPtrLx) ; if (devPtrC) cudaFree (devPtrC) ; GPU_Printf ("gpu malloc failed =%d,%d ndrow1=%d ndrow2=%d ndcol=%d\n", cudaStat [0], cudaStat [1], (int) ndrow1, (int) ndrow2, (int) ndcol) ; /* cudaMalloc failure is not an error, just bypass the GPU */ return (0) ; } Common->SyrkUsed = 1 ; #ifndef NTIMER Common->CHOLMOD_GPU_SYRK_CALLS++ ; #endif /* ---------------------------------------------------------------------- */ /* copy Lx to the GPU */ /* ---------------------------------------------------------------------- */ /* copy Lx in two steps on different streams. * (ldLx is shortened from ndrow to ndrow2) */ cudaStat [0] = cudaMemcpy2DAsync (devPtrLx, ndrow2 * L_ENTRY * sizeof (devPtrLx [0]), Lx + L_ENTRY * pdx1, ndrow * L_ENTRY * sizeof (Lx [0]), ndrow1 * L_ENTRY * sizeof (devPtrLx [0]), ndcol, cudaMemcpyHostToDevice, Common->cudaStreamSyrk) ; if (cudaStat [0]) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy to device") ; } if (ndrow3 > 0) { Common->GemmUsed = 1 ; cudaStat [1] = cudaMemcpy2DAsync (devPtrLx + L_ENTRY*ndrow1, ndrow2 * L_ENTRY * sizeof (devPtrLx [0]), Lx + L_ENTRY * (pdx1 + ndrow1), ndrow * L_ENTRY * sizeof (Lx [0]), ndrow3 * L_ENTRY * sizeof (devPtrLx [0]), ndcol, cudaMemcpyHostToDevice, Common->cudaStreamGemm) ; if (cudaStat [1]) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy to device") ; } } /* ---------------------------------------------------------------------- */ /* do the CUDA SYRK */ /* ---------------------------------------------------------------------- */ cublasStatus = cublasSetStream (Common->cublasHandle, Common->cudaStreamSyrk) ; if (cublasStatus != CUBLAS_STATUS_SUCCESS) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS stream") ; } alpha = 1.0 ; beta = 0.0 ; #ifdef REAL cublasStatus = cublasDsyrk (Common->cublasHandle, CUBLAS_FILL_MODE_LOWER, CUBLAS_OP_N, (int) ndrow1, (int) ndcol, /* N, K: L1 is ndrow1-by-ndcol */ &alpha, /* ALPHA: 1 */ devPtrLx, ndrow2, /* A, LDA: L1, ndrow2 */ &beta, /* BETA: 0 */ devPtrC, ndrow2) ; /* C, LDC: C1 */ #else cublasStatus = cublasZherk (Common->cublasHandle, CUBLAS_FILL_MODE_LOWER, CUBLAS_OP_N, (int) ndrow1, (int) ndcol, /* N, K: L1 is ndrow1-by-ndcol*/ &alpha, /* ALPHA: 1 */ (const cuDoubleComplex *) devPtrLx, ndrow2, /* A, LDA: L1, ndrow2 */ &beta, /* BETA: 0 */ (cuDoubleComplex *) devPtrC, ndrow2) ; /* C, LDC: C1 */ #endif if (cublasStatus != CUBLAS_STATUS_SUCCESS) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS routine failure") ; } /* ---------------------------------------------------------------------- */ /* partial copy of C to the GPU */ /* ---------------------------------------------------------------------- */ cudaStat [0] = cudaMemcpy2DAsync (C, ndrow2 * L_ENTRY * sizeof (C [0]), devPtrC, ndrow2 * L_ENTRY * sizeof (devPtrC [0]), ndrow1 * L_ENTRY * sizeof (devPtrC [0]), ndrow1, cudaMemcpyDeviceToHost, Common->cudaStreamSyrk) ; if (cudaStat [0]) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy from device") ; } /* ---------------------------------------------------------------------- */ /* compute remaining (ndrow2-ndrow1)-by-ndrow1 block of C, C2 = L2*L1' */ /* ---------------------------------------------------------------------- */ if (ndrow3 > 0) { #ifndef REAL cuDoubleComplex calpha = {1.0,0.0} ; cuDoubleComplex cbeta = {0.0,0.0} ; #endif #ifndef NTIMER Common->CHOLMOD_GPU_GEMM_CALLS++ ; #endif cublasStatus = cublasSetStream (Common->cublasHandle, Common->cudaStreamGemm) ; if (cublasStatus != CUBLAS_STATUS_SUCCESS) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS stream") ; } /* ------------------------------------------------------------------ */ /* do the CUDA BLAS dgemm */ /* ------------------------------------------------------------------ */ #ifdef REAL alpha = 1.0 ; beta = 0.0 ; cublasStatus = cublasDgemm (Common->cublasHandle, CUBLAS_OP_N, CUBLAS_OP_T, ndrow3, ndrow1, ndcol, /* M, N, K */ &alpha, /* ALPHA: 1 */ devPtrLx + L_ENTRY*(ndrow1), /* A, LDA: L2, ndrow */ ndrow2, devPtrLx, /* B, LDB: L1, ndrow */ ndrow2, &beta, /* BETA: 0 */ devPtrC + L_ENTRY*ndrow1, /* C, LDC: C2 */ ndrow2) ; #else cublasStatus = cublasZgemm (Common->cublasHandle, CUBLAS_OP_N, CUBLAS_OP_C, ndrow3, ndrow1, ndcol, /* M, N, K */ &calpha, /* ALPHA: 1 */ (const cuDoubleComplex *) devPtrLx + ndrow1, /* A, LDA: L2, ndrow */ ndrow2, (const cuDoubleComplex *) devPtrLx, /* B, LDB: L1, ndrow */ ndrow2, &cbeta, /* BETA: 0 */ (cuDoubleComplex *)devPtrC + ndrow1, /* C, LDC: C2 */ ndrow2) ; #endif if (cublasStatus != CUBLAS_STATUS_SUCCESS) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS routine failure") ; } /* ------------------------------------------------------------------ */ /* finish copy of C */ /* ------------------------------------------------------------------ */ cudaStat [0] = cudaMemcpy2DAsync (C + L_ENTRY*ndrow1, ndrow2 * L_ENTRY * sizeof (C [0]), devPtrC+ L_ENTRY*ndrow1, ndrow2 * L_ENTRY * sizeof (devPtrC [0]), ndrow3 * L_ENTRY * sizeof (devPtrC [0]), ndrow1, cudaMemcpyDeviceToHost, Common->cudaStreamGemm) ; if (cudaStat [0]) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy from device") ; } } return (1) ; } /* ========================================================================== */ /* === gpu_syncSyrk ========================================================= */ /* ========================================================================== */ /* synchronize with the CUDA BLAS dsyrk stream */ void TEMPLATE (CHOLMOD (gpu_syncSyrk)) ( cholmod_common *Common ) { if (Common->SyrkUsed) { cudaStreamSynchronize (Common->cudaStreamSyrk) ; if (!Common->GemmUsed) { cudaFree (Common->devSyrkGemmPtrLx) ; cudaFree (Common->devSyrkGemmPtrC) ; Common->devSyrkGemmPtrLx = NULL ; Common->devSyrkGemmPtrC = NULL ; #ifndef NTIMER /* this actually sums time spend on Syrk and Gemm */ Common->CHOLMOD_GPU_SYRK_TIME += SuiteSparse_time ( ) - Common->syrkStart ; #endif } } } /* ========================================================================== */ /* === gpu_syncGemm ========================================================= */ /* ========================================================================== */ /* synchronize with the CUDA BLAS dgemm stream */ void TEMPLATE (CHOLMOD (gpu_syncGemm)) ( cholmod_common *Common ) { if (Common->GemmUsed) { cudaStreamSynchronize (Common->cudaStreamGemm) ; cudaFree (Common->devSyrkGemmPtrLx) ; cudaFree (Common->devSyrkGemmPtrC) ; Common->devSyrkGemmPtrLx = NULL ; Common->devSyrkGemmPtrC = NULL ; #ifndef NTIMER /* this actually sums time spend on Syrk and Gemm */ Common->CHOLMOD_GPU_SYRK_TIME += SuiteSparse_time ( ) - Common->syrkStart ; #endif } } /* ========================================================================== */ /* === gpu_lower_potrf ====================================================== */ /* ========================================================================== */ /* Cholesky factorzation (dpotrf) of a matrix S, operating on the lower * triangular part only. S is nscol2-by-nscol2 with leading dimension nsrow. * * S is the top part of the supernode (the lower triangular matrx). * This function also copies the bottom rectangular part of the supernode (B) * onto the GPU, in preparation for gpu_triangular_solve. */ int TEMPLATE (CHOLMOD (gpu_lower_potrf)) ( Int nscol2, /* S is nscol2-by-nscol2 */ Int nsrow, /* leading dimension of S */ Int psx, /* S is located at Lx + L_Entry*psx */ double *Lx, /* contains S; overwritten with Cholesky factor */ Int *info, /* BLAS info return value */ cholmod_common *Common ) { double *devPtrA, *devPtrB, *A ; double alpha, beta ; cudaError_t cudaStat ; cublasStatus_t cublasStatus ; Int j, nsrow2, nb, n, gpu_lda, lda, gpu_ldb ; int ilda, ijb, iinfo ; #ifndef NTIMER double tstart = SuiteSparse_time ( ) ; #endif if (nscol2 < 256) { /* too small for the CUDA BLAS; use the CPU instead */ return (0) ; } nsrow2 = nsrow - nscol2 ; /* ---------------------------------------------------------------------- */ /* heuristic to get the block size depending of the problem size */ /* ---------------------------------------------------------------------- */ nb = 128 ; if (nscol2 > 4096) nb = 256 ; if (nscol2 > 8192) nb = 384 ; n = nscol2 ; gpu_lda = ((nscol2+31)/32)*32 ; lda = nsrow ; A = Lx + L_ENTRY*psx ; /* ---------------------------------------------------------------------- */ /* free the dpotrf workspace, if allocated */ /* ---------------------------------------------------------------------- */ if (Common->devPotrfWork) { cudaFree (Common->devPotrfWork) ; Common->devPotrfWork = NULL ; } /* ---------------------------------------------------------------------- */ /* determine the GPU leading dimension of B */ /* ---------------------------------------------------------------------- */ gpu_ldb = 0 ; if (nsrow2 > 0) { gpu_ldb = ((nsrow2+31)/32)*32 ; } /* ---------------------------------------------------------------------- */ /* allocate device memory for the factorization and for potential solve */ /* ---------------------------------------------------------------------- */ cudaStat = cudaMalloc ((void **) &devPtrA, gpu_lda * (gpu_lda + gpu_ldb) * L_ENTRY * sizeof (devPtrA [0])) ; if (cudaStat) { GPU_Printf ("@@gpu_lower_potrf cudaMalloc failed =%d gpu_lda=%d\n", cudaStat, (int) (gpu_lda)) ; /* cudaMalloc failure not fatal, GPU bypassed */ return (0) ; } #ifndef NTIMER Common->CHOLMOD_GPU_POTRF_CALLS++ ; #endif /* ---------------------------------------------------------------------- */ /* remember where device memory is, to be used by triangular solve later */ /* ---------------------------------------------------------------------- */ Common->devPotrfWork = devPtrA ; devPtrB = devPtrA + gpu_lda * gpu_lda * L_ENTRY ; /* ---------------------------------------------------------------------- */ /* copy B in advance, for gpu_triangular_solve */ /* ---------------------------------------------------------------------- */ if (nsrow2 > 0) { cudaStat = cudaMemcpy2DAsync (devPtrB, gpu_ldb * L_ENTRY * sizeof (devPtrB [0]), Lx + L_ENTRY * (psx + nscol2), nsrow * L_ENTRY * sizeof (Lx [0]), nsrow2 * L_ENTRY * sizeof (devPtrB [0]), nscol2, cudaMemcpyHostToDevice, Common->cudaStreamTrsm) ; if (cudaStat) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy to device") ; } } /* ---------------------------------------------------------------------- */ /* block Cholesky factorization of S */ /* ---------------------------------------------------------------------- */ for (j = 0 ; j < n ; j += nb) { Int jb = nb < (n-j) ? nb : (n-j) ; /* ------------------------------------------------------------------ */ /* copy jb columns starting at the diagonal to the GPU */ /* ------------------------------------------------------------------ */ cudaStat = cudaMemcpy2DAsync (devPtrA + (j + j*gpu_lda)*L_ENTRY, gpu_lda * L_ENTRY * sizeof (devPtrA [0]), A + L_ENTRY*(j + j*lda), lda * L_ENTRY * sizeof (A [0]), (n-j) * L_ENTRY * sizeof (devPtrA [0]), jb, cudaMemcpyHostToDevice, Common->cudaStreamPotrf [0]) ; if (cudaStat) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy to device") ; } /* ------------------------------------------------------------------ */ /* define the dpotrf stream */ /* ------------------------------------------------------------------ */ cublasStatus = cublasSetStream (Common->cublasHandle, Common->cudaStreamPotrf [0]) ; if (cublasStatus != CUBLAS_STATUS_SUCCESS) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS stream") ; } /* ------------------------------------------------------------------ */ /* record the end of the copy of block L22 | L32 */ /* ------------------------------------------------------------------ */ cudaStat = cudaEventRecord (Common->cublasEventPotrf [0], Common->cudaStreamPotrf [0]) ; if (cudaStat) { ERROR (CHOLMOD_GPU_PROBLEM, "CUDA event failure") ; } /* ------------------------------------------------------------------ */ /* do the CUDA BLAS dsyrk */ /* ------------------------------------------------------------------ */ alpha = -1.0 ; beta = 1.0 ; #ifdef REAL cublasStatus = cublasDsyrk (Common->cublasHandle, CUBLAS_FILL_MODE_LOWER, CUBLAS_OP_N, jb, j, &alpha, devPtrA + j, gpu_lda, &beta, devPtrA + j + j*gpu_lda, gpu_lda) ; #else cublasStatus = cublasZherk (Common->cublasHandle, CUBLAS_FILL_MODE_LOWER, CUBLAS_OP_N, jb, j, &alpha, (cuDoubleComplex*)devPtrA + j, gpu_lda, &beta, (cuDoubleComplex*)devPtrA + j + j*gpu_lda, gpu_lda) ; #endif if (cublasStatus != CUBLAS_STATUS_SUCCESS) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS routine failure") ; } /* ------------------------------------------------------------------ */ cudaStat = cudaEventRecord (Common->cublasEventPotrf [1], Common->cudaStreamPotrf [0]) ; if (cudaStat) { ERROR (CHOLMOD_GPU_PROBLEM, "CUDA event failure") ; } cudaStat = cudaStreamWaitEvent (Common->cudaStreamPotrf [1], Common->cublasEventPotrf [1], 0) ; if (cudaStat) { ERROR (CHOLMOD_GPU_PROBLEM, "CUDA event failure") ; } /* ------------------------------------------------------------------ */ /* copy back the jb columns on two different streams */ /* ------------------------------------------------------------------ */ cudaStat = cudaMemcpy2DAsync (A + L_ENTRY*(j + j*lda), lda * L_ENTRY * sizeof (double), devPtrA + L_ENTRY*(j + j*gpu_lda), gpu_lda * L_ENTRY * sizeof (double), L_ENTRY * sizeof (double)*jb, jb, cudaMemcpyDeviceToHost, Common->cudaStreamPotrf [1]) ; if (cudaStat) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy from device") ; } cudaStat = cudaMemcpy2DAsync (A + L_ENTRY*j, lda * L_ENTRY * sizeof (double), devPtrA + L_ENTRY*j, gpu_lda * L_ENTRY * sizeof (double), L_ENTRY * sizeof (double)*jb, j, cudaMemcpyDeviceToHost, Common->cudaStreamPotrf [0]) ; if (cudaStat) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy to device") ; } /* ------------------------------------------------------------------ */ /* do the CUDA BLAS dgemm */ /* ------------------------------------------------------------------ */ if ((j+jb) < n) { #ifdef REAL alpha = -1.0 ; beta = 1.0 ; cublasStatus = cublasDgemm (Common->cublasHandle, CUBLAS_OP_N, CUBLAS_OP_T, (n-j-jb), jb, j, &alpha, devPtrA + (j+jb), gpu_lda, devPtrA + (j) , gpu_lda, &beta, devPtrA + (j+jb + j*gpu_lda), gpu_lda) ; #else cuDoubleComplex calpha = {-1.0,0.0} ; cuDoubleComplex cbeta = { 1.0,0.0} ; cublasStatus = cublasZgemm (Common->cublasHandle, CUBLAS_OP_N, CUBLAS_OP_C, (n-j-jb), jb, j, &calpha, (cuDoubleComplex*)devPtrA + (j+jb), gpu_lda, (cuDoubleComplex*)devPtrA + (j) , gpu_lda, &cbeta, (cuDoubleComplex*)devPtrA + (j+jb + j*gpu_lda), gpu_lda) ; #endif if (cublasStatus != CUBLAS_STATUS_SUCCESS) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS routine failure") ; } } cudaStat = cudaStreamSynchronize (Common->cudaStreamPotrf [1]) ; if (cudaStat) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy to device") ; } /* ------------------------------------------------------------------ */ /* compute the Cholesky factorization of the jbxjb block on the CPU */ /* ------------------------------------------------------------------ */ ilda = (int) lda ; ijb = jb ; #ifdef REAL LAPACK_DPOTRF ("L", &ijb, A + L_ENTRY * (j + j*lda), &ilda, &iinfo) ; #else LAPACK_ZPOTRF ("L", &ijb, A + L_ENTRY * (j + j*lda), &ilda, &iinfo) ; #endif *info = iinfo ; if (*info != 0) { *info = *info + j ; break ; } /* ------------------------------------------------------------------ */ /* copy the result back to the GPU */ /* ------------------------------------------------------------------ */ cudaStat = cudaMemcpy2DAsync (devPtrA + L_ENTRY*(j + j*gpu_lda), gpu_lda * L_ENTRY * sizeof (double), A + L_ENTRY * (j + j*lda), lda * L_ENTRY * sizeof (double), L_ENTRY * sizeof (double) * jb, jb, cudaMemcpyHostToDevice, Common->cudaStreamPotrf [0]) ; if (cudaStat) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy to device") ; } /* ------------------------------------------------------------------ */ /* do the CUDA BLAS dtrsm */ /* ------------------------------------------------------------------ */ if ((j+jb) < n) { #ifdef REAL alpha = 1.0 ; cublasStatus = cublasDtrsm (Common->cublasHandle, CUBLAS_SIDE_RIGHT, CUBLAS_FILL_MODE_LOWER, CUBLAS_OP_T, CUBLAS_DIAG_NON_UNIT, (n-j-jb), jb, &alpha, devPtrA + (j + j*gpu_lda), gpu_lda, devPtrA + (j+jb + j*gpu_lda), gpu_lda) ; #else cuDoubleComplex calpha = {1.0,0.0}; cublasStatus = cublasZtrsm (Common->cublasHandle, CUBLAS_SIDE_RIGHT, CUBLAS_FILL_MODE_LOWER, CUBLAS_OP_C, CUBLAS_DIAG_NON_UNIT, (n-j-jb), jb, &calpha, (cuDoubleComplex *)devPtrA + (j + j*gpu_lda), gpu_lda, (cuDoubleComplex *)devPtrA + (j+jb + j*gpu_lda), gpu_lda) ; #endif if (cublasStatus != CUBLAS_STATUS_SUCCESS) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS routine failure") ; } } } if (nsrow2 <= 0) { /* No TRSM necessary */ cudaFree (Common->devPotrfWork) ; Common->devPotrfWork = NULL ; } #ifndef NTIMER Common->CHOLMOD_GPU_POTRF_TIME += SuiteSparse_time ( ) - tstart ; #endif return (1) ; } /* ========================================================================== */ /* === gpu_triangular_solve ================================================= */ /* ========================================================================== */ /* The current supernode is columns k1 to k2-1 of L. Let L1 be the diagonal * block (factorized by dpotrf/zpotrf above; rows/cols k1:k2-1), and L2 be rows * k2:n-1 and columns k1:k2-1 of L. The triangular system to solve is L2*L1' = * S2, where S2 is overwritten with L2. More precisely, L2 = S2 / L1' in * MATLAB notation. */ /* Version with pre-allocation in POTRF */ int TEMPLATE (CHOLMOD (gpu_triangular_solve)) ( Int nsrow2, /* L1 and S2 are nsrow2-by-nscol2 */ Int nscol2, /* L1 is nscol2-by-nscol2 */ Int nsrow, /* leading dimension of L1, L2, and S2 */ Int psx, /* L1 is at Lx+L_ENTRY*psx; L2 at Lx+L_ENTRY*(psx+nscol2)*/ double *Lx, /* holds L1, L2, and S2 */ cholmod_common *Common ) { double *devPtrA, *devPtrB ; cudaError_t cudaStat ; cublasStatus_t cublasStatus ; Int gpu_lda, gpu_ldb ; #ifdef REAL double alpha = 1.0 ; #else cuDoubleComplex calpha = {1.0,0.0} ; #endif if (!Common->devPotrfWork) { /* no workspace for triangular solve */ return (0) ; } #ifndef NTIMER double tstart = SuiteSparse_time ( ) ; Common->CHOLMOD_GPU_TRSM_CALLS++ ; #endif gpu_lda = ((nscol2+31)/32)*32 ; gpu_ldb = ((nsrow2+31)/32)*32 ; devPtrA = Common->devPotrfWork ; devPtrB = devPtrA + gpu_lda * gpu_lda * L_ENTRY ; /* ---------------------------------------------------------------------- */ /* start the trsm stream */ /* ---------------------------------------------------------------------- */ cublasStatus = cublasSetStream (Common->cublasHandle, Common->cudaStreamTrsm) ; if (cublasStatus != CUBLAS_STATUS_SUCCESS) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS stream") ; } /* ---------------------------------------------------------------------- */ /* do the CUDA BLAS dtrsm */ /* ---------------------------------------------------------------------- */ #ifdef REAL cublasStatus = cublasDtrsm (Common->cublasHandle, CUBLAS_SIDE_RIGHT, CUBLAS_FILL_MODE_LOWER, CUBLAS_OP_T, CUBLAS_DIAG_NON_UNIT, nsrow2, nscol2, /* M, N */ &alpha, /* ALPHA: 1 */ devPtrA, gpu_lda, /* A, LDA */ devPtrB, gpu_ldb) ; /* B, LDB */ #else cublasStatus = cublasZtrsm (Common->cublasHandle, CUBLAS_SIDE_RIGHT, CUBLAS_FILL_MODE_LOWER, CUBLAS_OP_C, CUBLAS_DIAG_NON_UNIT, nsrow2, nscol2, /* M, N */ &calpha, /* ALPHA: 1 */ (const cuDoubleComplex *) devPtrA, gpu_lda, /* A, LDA */ (cuDoubleComplex *) devPtrB, gpu_ldb) ; /* B, LDB: nsrow2 */ #endif if (cublasStatus != CUBLAS_STATUS_SUCCESS) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS routine failure") ; } /* ---------------------------------------------------------------------- */ /* copy result back to the CPU */ /* ---------------------------------------------------------------------- */ cudaStat = cudaMemcpy2DAsync (Lx + L_ENTRY*(psx + nscol2), nsrow * L_ENTRY * sizeof (Lx [0]), devPtrB, gpu_ldb * L_ENTRY * sizeof (devPtrB [0]), nsrow2 * L_ENTRY * sizeof (devPtrB [0]), nscol2, cudaMemcpyDeviceToHost, Common->cudaStreamTrsm) ; if (cudaStat) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy from device") ; } /* ---------------------------------------------------------------------- */ /* synchronize with the GPU */ /* ---------------------------------------------------------------------- */ cudaStat = cudaThreadSynchronize ( ) ; if (cudaStat) { ERROR (CHOLMOD_GPU_PROBLEM, "GPU synchronization failure") ; } /* ---------------------------------------------------------------------- */ /* free workspace and return */ /* ---------------------------------------------------------------------- */ cudaFree (Common->devPotrfWork) ; Common->devPotrfWork = NULL ; #ifndef NTIMER Common->CHOLMOD_GPU_TRSM_TIME += SuiteSparse_time ( ) - tstart ; #endif return (1) ; } #undef REAL #undef COMPLEX #undef ZOMPLEX Matrix/src/CHOLMOD/Supernodal/t_cholmod_super_numeric.c0000644000175100001440000007577112271765436022636 0ustar hornikusers/* ========================================================================== */ /* === Supernodal/t_cholmod_super_numeric =================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Supernodal Module. Copyright (C) 2005-2012, Timothy A. Davis * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Template routine for cholmod_super_numeric. All xtypes supported, except * that a zomplex A and F result in a complex L (there is no supernodal * zomplex L). */ /* ========================================================================== */ /* === complex arithmetic =================================================== */ /* ========================================================================== */ #include "cholmod_template.h" #undef L_ENTRY #undef L_CLEAR #undef L_ASSIGN #undef L_MULTADD #undef L_ASSEMBLE #undef L_ASSEMBLESUB #ifdef REAL /* -------------------------------------------------------------------------- */ /* A, F, and L are all real */ /* -------------------------------------------------------------------------- */ #define L_ENTRY 1 #define L_CLEAR(Lx,p) Lx [p] = 0 #define L_ASSIGN(Lx,q, Ax,Az,p) Lx [q] = Ax [p] #define L_MULTADD(Lx,q, Ax,Az,p, f) Lx [q] += Ax [p] * f [0] #define L_ASSEMBLE(Lx,q,b) Lx [q] += b [0] #define L_ASSEMBLESUB(Lx,q,C,p) Lx [q] -= C [p] #else /* -------------------------------------------------------------------------- */ /* A and F are complex or zomplex, L and C are complex */ /* -------------------------------------------------------------------------- */ #define L_ENTRY 2 #define L_CLEAR(Lx,p) Lx [2*(p)] = 0 ; Lx [2*(p)+1] = 0 #define L_ASSEMBLE(Lx,q,b) Lx [2*(q)] += b [0] ; #define L_ASSEMBLESUB(Lx,q,C,p) \ Lx [2*(q) ] -= C [2*(p) ] ; \ Lx [2*(q)+1] -= C [2*(p)+1] ; #ifdef COMPLEX /* -------------------------------------------------------------------------- */ /* A, F, L, and C are all complex */ /* -------------------------------------------------------------------------- */ #define L_ASSIGN(Lx,q, Ax,Az,p) \ Lx [2*(q) ] = Ax [2*(p) ] ; \ Lx [2*(q)+1] = Ax [2*(p)+1] #define L_MULTADD(Lx,q, Ax,Az,p, f) \ Lx [2*(q) ] += Ax [2*(p) ] * f [0] - Ax [2*(p)+1] * f [1] ; \ Lx [2*(q)+1] += Ax [2*(p)+1] * f [0] + Ax [2*(p) ] * f [1] #else /* -------------------------------------------------------------------------- */ /* A and F are zomplex, L and C is complex */ /* -------------------------------------------------------------------------- */ #define L_ASSIGN(Lx,q, Ax,Az,p) \ Lx [2*(q) ] = Ax [p] ; \ Lx [2*(q)+1] = Az [p] ; #define L_MULTADD(Lx,q, Ax,Az,p, f) \ Lx [2*(q) ] += Ax [p] * f [0] - Az [p] * f [1] ; \ Lx [2*(q)+1] += Az [p] * f [0] + Ax [p] * f [1] #endif #endif /* ========================================================================== */ /* === t_cholmod_super_numeric ============================================== */ /* ========================================================================== */ /* This function returns FALSE only if integer overflow occurs in the BLAS. * It returns TRUE otherwise whether or not the matrix is positive definite. */ static int TEMPLATE (cholmod_super_numeric) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* F = A' or A(:,f)' */ double beta [2], /* beta*I is added to diagonal of matrix to factorize */ /* ---- in/out --- */ cholmod_factor *L, /* factorization */ /* -- workspace -- */ cholmod_dense *Cwork, /* size (L->maxcsize)-by-1 */ /* --------------- */ cholmod_common *Common ) { double one [2], zero [2], fjk [2], tstart ; double *Lx, *Ax, *Fx, *Az, *Fz, *C ; Int *Super, *Head, *Ls, *Lpi, *Lpx, *Map, *SuperMap, *RelativeMap, *Next, *Lpos, *Fp, *Fi, *Fnz, *Ap, *Ai, *Anz, *Iwork, *Next_save, *Lpos_save ; Int nsuper, n, j, i, k, s, p, pend, k1, k2, nscol, psi, psx, psend, nsrow, pj, d, kd1, kd2, info, ndcol, ndrow, pdi, pdx, pdend, pdi1, pdi2, pdx1, ndrow1, ndrow2, px, dancestor, sparent, dnext, nsrow2, ndrow3, pk, pf, pfend, stype, Apacked, Fpacked, q, imap, repeat_supernode, nscol2, ss, nscol_new = 0 ; /* If integer overflow occurs in the BLAS, Common->status is set to * CHOLMOD_TOO_LARGE, and the contents of Lx are undefined. */ Common->blas_ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nsuper = L->nsuper ; n = L->n ; C = Cwork->x ; /* workspace of size L->maxcsize */ one [0] = 1.0 ; /* ALPHA for *syrk, *herk, *gemm, and *trsm */ one [1] = 0. ; zero [0] = 0. ; /* BETA for *syrk, *herk, and *gemm */ zero [1] = 0. ; Iwork = Common->Iwork ; SuperMap = Iwork ; /* size n (i/i/l) */ RelativeMap = Iwork + n ; /* size n (i/i/l) */ Next = Iwork + 2*((size_t) n) ; /* size nsuper*/ Lpos = Iwork + 2*((size_t) n) + nsuper ; /* size nsuper*/ Next_save = Iwork + 2*((size_t) n) + 2*((size_t) nsuper) ;/* size nsuper*/ Lpos_save = Iwork + 2*((size_t) n) + 3*((size_t) nsuper) ;/* size nsuper*/ Map = Common->Flag ; /* size n, use Flag as workspace for Map array */ Head = Common->Head ; /* size n+1, only Head [0..nsuper-1] used */ Ls = L->s ; Lpi = L->pi ; Lpx = L->px ; Super = L->super ; Lx = L->x ; #ifdef GPU_BLAS TEMPLATE (CHOLMOD (gpu_init)) (C, L->maxcsize, Common) ; #endif #ifndef NTIMER /* clear GPU / CPU statistics */ Common->CHOLMOD_CPU_GEMM_CALLS = 0 ; Common->CHOLMOD_CPU_SYRK_CALLS = 0 ; Common->CHOLMOD_CPU_TRSM_CALLS = 0 ; Common->CHOLMOD_CPU_POTRF_CALLS = 0 ; Common->CHOLMOD_GPU_GEMM_CALLS = 0 ; Common->CHOLMOD_GPU_SYRK_CALLS = 0 ; Common->CHOLMOD_GPU_TRSM_CALLS = 0 ; Common->CHOLMOD_GPU_POTRF_CALLS = 0 ; Common->CHOLMOD_CPU_GEMM_TIME = 0 ; Common->CHOLMOD_CPU_SYRK_TIME = 0 ; Common->CHOLMOD_CPU_TRSM_TIME = 0 ; Common->CHOLMOD_CPU_POTRF_TIME = 0 ; Common->CHOLMOD_GPU_GEMM_TIME = 0 ; Common->CHOLMOD_GPU_SYRK_TIME = 0 ; Common->CHOLMOD_GPU_TRSM_TIME = 0 ; Common->CHOLMOD_GPU_POTRF_TIME = 0 ; Common->CHOLMOD_ASSEMBLE_TIME = 0 ; Common->CHOLMOD_ASSEMBLE_TIME2 = 0 ; #endif stype = A->stype ; if (stype != 0) { /* F not accessed */ Fp = NULL ; Fi = NULL ; Fx = NULL ; Fz = NULL ; Fnz = NULL ; Fpacked = TRUE ; } else { Fp = F->p ; Fi = F->i ; Fx = F->x ; Fz = F->z ; Fnz = F->nz ; Fpacked = F->packed ; } Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; Apacked = A->packed ; /* clear the Map so that changes in the pattern of A can be detected */ for (i = 0 ; i < n ; i++) { Map [i] = EMPTY ; } /* If the matrix is not positive definite, the supernode s containing the * first zero or negative diagonal entry of L is repeated (but factorized * only up to just before the problematic diagonal entry). The purpose is * to provide MATLAB with [R,p]=chol(A); columns 1 to p-1 of L=R' are * required, where L(p,p) is the problematic diagonal entry. The * repeat_supernode flag tells us whether this is the repeated supernode. * Once supernode s is repeated, the factorization is terminated. */ repeat_supernode = FALSE ; /* ---------------------------------------------------------------------- */ /* supernodal numerical factorization */ /* ---------------------------------------------------------------------- */ for (s = 0 ; s < nsuper ; s++) { /* ------------------------------------------------------------------ */ /* get the size of supernode s */ /* ------------------------------------------------------------------ */ k1 = Super [s] ; /* s contains columns k1 to k2-1 of L */ k2 = Super [s+1] ; nscol = k2 - k1 ; /* # of columns in all of s */ psi = Lpi [s] ; /* pointer to first row of s in Ls */ psx = Lpx [s] ; /* pointer to first row of s in Lx */ psend = Lpi [s+1] ; /* pointer just past last row of s in Ls */ nsrow = psend - psi ; /* # of rows in all of s */ PRINT1 (("====================================================\n" "S "ID" k1 "ID" k2 "ID" nsrow "ID" nscol "ID" psi "ID" psend " ""ID" psx "ID"\n", s, k1, k2, nsrow, nscol, psi, psend, psx)) ; /* ------------------------------------------------------------------ */ /* zero the supernode s */ /* ------------------------------------------------------------------ */ ASSERT ((size_t) (psx + nsrow*nscol) <= L->xsize) ; pend = psx + nsrow * nscol ; /* s is nsrow-by-nscol */ for (p = psx ; p < pend ; p++) { /* Lx [p] = 0 ; */ L_CLEAR (Lx,p) ; } /* ------------------------------------------------------------------ */ /* construct the scattered Map for supernode s */ /* ------------------------------------------------------------------ */ /* If row i is the kth row in s, then Map [i] = k. Similarly, if * column j is the kth column in s, then Map [j] = k. */ for (k = 0 ; k < nsrow ; k++) { PRINT1 ((" "ID" map "ID"\n", Ls [psi+k], k)) ; Map [Ls [psi + k]] = k ; } /* ------------------------------------------------------------------ */ /* copy matrix into supernode s (lower triangular part only) */ /* ------------------------------------------------------------------ */ pk = psx ; for (k = k1 ; k < k2 ; k++) { if (stype != 0) { /* copy the kth column of A into the supernode */ p = Ap [k] ; pend = (Apacked) ? (Ap [k+1]) : (p + Anz [k]) ; for ( ; p < pend ; p++) { /* row i of L is located in row Map [i] of s */ i = Ai [p] ; if (i >= k) { /* This test is here simply to avoid a segfault. If * the test is false, the numeric factorization of A * is undefined. It does not detect all invalid * entries, only some of them (when debugging is * enabled, and Map is cleared after each step, then * all entries not in the pattern of L are detected). */ imap = Map [i] ; if (imap >= 0 && imap < nsrow) { /* Lx [Map [i] + pk] = Ax [p] ; */ L_ASSIGN (Lx,(imap+pk), Ax,Az,p) ; } } } } else { /* copy the kth column of A*F into the supernode */ pf = Fp [k] ; pfend = (Fpacked) ? (Fp [k+1]) : (p + Fnz [k]) ; for ( ; pf < pfend ; pf++) { j = Fi [pf] ; /* fjk = Fx [pf] ; */ L_ASSIGN (fjk,0, Fx,Fz,pf) ; p = Ap [j] ; pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= k) { /* See the discussion of imap above. */ imap = Map [i] ; if (imap >= 0 && imap < nsrow) { /* Lx [Map [i] + pk] += Ax [p] * fjk ; */ L_MULTADD (Lx,(imap+pk), Ax,Az,p, fjk) ; } } } } } pk += nsrow ; /* advance to the next column of the supernode */ } /* add beta to the diagonal of the supernode, if nonzero */ if (beta [0] != 0.0) { /* note that only the real part of beta is used */ pk = psx ; for (k = k1 ; k < k2 ; k++) { /* Lx [pk] += beta [0] ; */ L_ASSEMBLE (Lx,pk, beta) ; pk += nsrow + 1 ; /* advance to the next diagonal entry */ } } PRINT1 (("Supernode with just A: repeat: "ID"\n", repeat_supernode)) ; DEBUG (CHOLMOD(dump_super) (s, Super, Lpi, Ls, Lpx, Lx, L_ENTRY, Common)) ; PRINT1 (("\n\n")) ; /* ------------------------------------------------------------------ */ /* save/restore the list of supernodes */ /* ------------------------------------------------------------------ */ if (!repeat_supernode) { /* Save the list of pending descendants in case s is not positive * definite. Also save Lpos for each descendant d, so that we can * find which part of d is used to update s. */ for (d = Head [s] ; d != EMPTY ; d = Next [d]) { Lpos_save [d] = Lpos [d] ; Next_save [d] = Next [d] ; } } else { /* s is not positive definite, and is being repeated. Restore * the list of supernodes. This can be done with pointer assignment * because all 4 arrays are held within Common->Iwork. */ Lpos = Lpos_save ; Next = Next_save ; } /* ------------------------------------------------------------------ */ /* update supernode s with each pending descendant d */ /* ------------------------------------------------------------------ */ #ifndef NDEBUG for (d = Head [s] ; d != EMPTY ; d = Next [d]) { PRINT1 (("\nWill update "ID" with Child: "ID"\n", s, d)) ; DEBUG (CHOLMOD(dump_super) (d, Super, Lpi, Ls, Lpx, Lx, L_ENTRY, Common)) ; } PRINT1 (("\nNow factorizing supernode "ID":\n", s)) ; #endif for (d = Head [s] ; d != EMPTY ; d = dnext) { /* -------------------------------------------------------------- */ /* get the size of supernode d */ /* -------------------------------------------------------------- */ kd1 = Super [d] ; /* d contains cols kd1 to kd2-1 of L */ kd2 = Super [d+1] ; ndcol = kd2 - kd1 ; /* # of columns in all of d */ pdi = Lpi [d] ; /* pointer to first row of d in Ls */ pdx = Lpx [d] ; /* pointer to first row of d in Lx */ pdend = Lpi [d+1] ; /* pointer just past last row of d in Ls */ ndrow = pdend - pdi ; /* # rows in all of d */ PRINT1 (("Child: ")) ; DEBUG (CHOLMOD(dump_super) (d, Super, Lpi, Ls, Lpx, Lx, L_ENTRY, Common)) ; /* -------------------------------------------------------------- */ /* find the range of rows of d that affect rows k1 to k2-1 of s */ /* -------------------------------------------------------------- */ p = Lpos [d] ; /* offset of 1st row of d affecting s */ pdi1 = pdi + p ; /* ptr to 1st row of d affecting s in Ls */ pdx1 = pdx + p ; /* ptr to 1st row of d affecting s in Lx */ /* there must be at least one row remaining in d to update s */ ASSERT (pdi1 < pdend) ; PRINT1 (("Lpos[d] "ID" pdi1 "ID" Ls[pdi1] "ID"\n", Lpos[d], pdi1, Ls [pdi1])) ; ASSERT (Ls [pdi1] >= k1 && Ls [pdi1] < k2) ; for (pdi2 = pdi1 ; pdi2 < pdend && Ls [pdi2] < k2 ; pdi2++) ; ndrow1 = pdi2 - pdi1 ; /* # rows in first part of d */ ndrow2 = pdend - pdi1 ; /* # rows in remaining d */ /* rows Ls [pdi1 ... pdi2-1] are in the range k1 to k2-1. Since d * affects s, this set cannot be empty. */ ASSERT (pdi1 < pdi2 && pdi2 <= pdend) ; PRINT1 (("ndrow1 "ID" ndrow2 "ID"\n", ndrow1, ndrow2)) ; DEBUG (for (p = pdi1 ; p < pdi2 ; p++) PRINT1 (("Ls["ID"] "ID"\n", p, Ls[p]))) ; /* -------------------------------------------------------------- */ /* construct the update matrix C for this supernode d */ /* -------------------------------------------------------------- */ /* C = L (k1:n-1, kd1:kd2-1) * L (k1:k2-1, kd1:kd2-1)', except * that k1:n-1 refers to all of the rows in L, but many of the * rows are all zero. Supernode d holds columns kd1 to kd2-1 of L. * Nonzero rows in the range k1:k2-1 are in the list * Ls [pdi1 ... pdi2-1], of size ndrow1. Nonzero rows in the range * k2:n-1 are in the list Ls [pdi2 ... pdend], of size ndrow2. Let * L1 = L (Ls [pdi1 ... pdi2-1], kd1:kd2-1), and let * L2 = L (Ls [pdi2 ... pdend], kd1:kd2-1). C is ndrow2-by-ndrow1. * Let C1 be the first ndrow1 rows of C and let C2 be the last * ndrow2-ndrow1 rows of C. Only the lower triangular part of C1 * needs to be computed since C1 is symmetric. */ /* maxcsize is the largest size of C for all pairs (d,s) */ ASSERT (ndrow2 * ndrow1 <= ((Int) L->maxcsize)) ; /* compute leading ndrow1-by-ndrow1 lower triangular block of C, * C1 = L1*L1' */ ndrow3 = ndrow2 - ndrow1 ; /* number of rows of C2 */ ASSERT (ndrow3 >= 0) ; #ifdef GPU_BLAS if (!TEMPLATE (CHOLMOD (gpu_updateC)) (ndrow1, ndrow2, ndrow, ndcol, pdx1, Lx, C, Common)) #endif { #ifndef NTIMER Common->CHOLMOD_CPU_SYRK_CALLS++ ; tstart = SuiteSparse_time () ; #endif #ifdef REAL BLAS_dsyrk ("L", "N", ndrow1, ndcol, /* N, K: L1 is ndrow1-by-ndcol*/ one, /* ALPHA: 1 */ Lx + L_ENTRY*pdx1, ndrow, /* A, LDA: L1, ndrow */ zero, /* BETA: 0 */ C, ndrow2) ; /* C, LDC: C1 */ #else BLAS_zherk ("L", "N", ndrow1, ndcol, /* N, K: L1 is ndrow1-by-ndcol*/ one, /* ALPHA: 1 */ Lx + L_ENTRY*pdx1, ndrow, /* A, LDA: L1, ndrow */ zero, /* BETA: 0 */ C, ndrow2) ; /* C, LDC: C1 */ #endif #ifndef NTIMER Common->CHOLMOD_CPU_SYRK_TIME += SuiteSparse_time () - tstart ; #endif /* compute remaining (ndrow2-ndrow1)-by-ndrow1 block of C, * C2 = L2*L1' */ if (ndrow3 > 0) { #ifndef NTIMER Common->CHOLMOD_CPU_GEMM_CALLS++ ; tstart = SuiteSparse_time () ; #endif #ifdef REAL BLAS_dgemm ("N", "C", ndrow3, ndrow1, ndcol, /* M, N, K */ one, /* ALPHA: 1 */ Lx + L_ENTRY*(pdx1 + ndrow1), /* A, LDA: L2, ndrow */ ndrow, Lx + L_ENTRY*pdx1, /* B, LDB: L1, ndrow */ ndrow, zero, /* BETA: 0 */ C + L_ENTRY*ndrow1, /* C, LDC: C2 */ ndrow2) ; #else BLAS_zgemm ("N", "C", ndrow3, ndrow1, ndcol, /* M, N, K */ one, /* ALPHA: 1 */ Lx + L_ENTRY*(pdx1 + ndrow1),/* A, LDA: L2, ndrow */ ndrow, Lx + L_ENTRY*pdx1, /* B, LDB: L1, ndrow */ ndrow, zero, /* BETA: 0 */ C + L_ENTRY*ndrow1, /* C, LDC: C2 */ ndrow2) ; #endif #ifndef NTIMER Common->CHOLMOD_CPU_GEMM_TIME += SuiteSparse_time () - tstart ; #endif } } DEBUG (CHOLMOD(dump_real) ("C", C, ndrow2, ndrow1, TRUE, L_ENTRY, Common)) ; /* -------------------------------------------------------------- */ /* construct relative map to assemble d into s */ /* -------------------------------------------------------------- */ for (i = 0 ; i < ndrow2 ; i++) { RelativeMap [i] = Map [Ls [pdi1 + i]] ; ASSERT (RelativeMap [i] >= 0 && RelativeMap [i] < nsrow) ; } /* -------------------------------------------------------------- */ /* assemble C into supernode s using the relative map */ /* -------------------------------------------------------------- */ #ifdef GPU_BLAS TEMPLATE (CHOLMOD (gpu_syncSyrk)) (Common) ; if (ndrow3 <= 0) { #endif /* non-GPU version, or GPU version when ndrow3 is zero */ pj = 0 ; for (j = 0 ; j < ndrow1 ; j++) /* cols k1:k2-1 */ { ASSERT (RelativeMap [j] == Map [Ls [pdi1 + j]]) ; ASSERT (RelativeMap [j] >= 0 && RelativeMap [j] < nscol) ; px = psx + RelativeMap [j] * nsrow ; for (i = j ; i < ndrow2 ; i++) /* rows k1:n-1 */ { ASSERT (RelativeMap [i] == Map [Ls [pdi1 + i]]) ; ASSERT (RelativeMap [i] >= j && RelativeMap[i] < nsrow); /* Lx [px + RelativeMap [i]] -= C [i + pj] ; */ q = px + RelativeMap [i] ; L_ASSEMBLESUB (Lx,q, C, i+pj) ; } pj += ndrow2 ; } #ifdef GPU_BLAS } else { /* GPU version when ndrow3 > zero, splits into two parts */ #ifndef NTIMER tstart = SuiteSparse_time () ; #endif pj = 0 ; for (j = 0 ; j < ndrow1 ; j++) /* cols k1:k2-1 */ { ASSERT (RelativeMap [j] == Map [Ls [pdi1 + j]]) ; ASSERT (RelativeMap [j] >= 0 && RelativeMap [j] < nscol) ; px = psx + RelativeMap [j] * nsrow ; for (i = j ; i < ndrow1 ; i++) /* rows k1:k2-1 */ { ASSERT (RelativeMap [i] == Map [Ls [pdi1 + i]]) ; ASSERT (RelativeMap [i] >= j && RelativeMap[i] < nsrow); /* Lx [px + RelativeMap [i]] -= C [i + pj] ; */ q = px + RelativeMap [i] ; L_ASSEMBLESUB (Lx,q, C, i+pj) ; } pj += ndrow2 ; } #ifndef NTIMER Common->CHOLMOD_ASSEMBLE_TIME2 += SuiteSparse_time () - tstart ; #endif /* wait for dgemm to finish */ TEMPLATE (CHOLMOD (gpu_syncGemm)) (Common) ; pj = 0 ; for (j = 0 ; j < ndrow1 ; j++) /* cols k1:k2-1 */ { ASSERT (RelativeMap [j] == Map [Ls [pdi1 + j]]) ; ASSERT (RelativeMap [j] >= 0 && RelativeMap [j] < nscol) ; px = psx + RelativeMap [j] * nsrow ; for (i = ndrow1 ; i < ndrow2 ; i++) /* rows k2:n-1 */ { ASSERT (RelativeMap [i] == Map [Ls [pdi1 + i]]) ; ASSERT (RelativeMap [i] >= j && RelativeMap[i] < nsrow); /* Lx [px + RelativeMap [i]] -= C [i + pj] ; */ q = px + RelativeMap [i] ; L_ASSEMBLESUB (Lx,q, C, i+pj) ; } pj += ndrow2 ; } #ifndef NTIMER Common->CHOLMOD_ASSEMBLE_TIME += SuiteSparse_time () - tstart ; #endif } #endif /* -------------------------------------------------------------- */ /* prepare this supernode d for its next ancestor */ /* -------------------------------------------------------------- */ dnext = Next [d] ; if (!repeat_supernode) { /* If node s is being repeated, Head [dancestor] has already * been cleared (set to EMPTY). It must remain EMPTY. The * dancestor will not be factorized since the factorization * terminates at node s. */ Lpos [d] = pdi2 - pdi ; if (Lpos [d] < ndrow) { dancestor = SuperMap [Ls [pdi2]] ; ASSERT (dancestor > s && dancestor < nsuper) ; /* place d in the link list of its next ancestor */ Next [d] = Head [dancestor] ; Head [dancestor] = d ; } } } PRINT1 (("\nSupernode with contributions A: repeat: "ID"\n", repeat_supernode)) ; DEBUG (CHOLMOD(dump_super) (s, Super, Lpi, Ls, Lpx, Lx, L_ENTRY, Common)) ; PRINT1 (("\n\n")) ; /* ------------------------------------------------------------------ */ /* factorize diagonal block of supernode s in LL' */ /* ------------------------------------------------------------------ */ /* The current supernode s is ready to factorize. It has been updated * by all descendant supernodes. Let S = the current supernode, which * holds rows k1:n-1 and columns k1:k2-1 of the updated matrix. It * splits into two parts: the square diagonal block S1, and the * rectangular part S2. Here, S1 is factorized into L1*L1' and * overwritten by L1. * * If supernode s is being repeated, only factorize it up to but not * including the column containing the problematic entry. */ nscol2 = (repeat_supernode) ? (nscol_new) : (nscol) ; #ifdef GPU_BLAS if (!TEMPLATE (CHOLMOD (gpu_lower_potrf)) (nscol2, nsrow, psx, Lx, &info, Common)) #endif { #ifndef NTIMER Common->CHOLMOD_CPU_POTRF_CALLS++ ; tstart = SuiteSparse_time () ; #endif #ifdef REAL LAPACK_dpotrf ("L", nscol2, /* N: nscol2 */ Lx + L_ENTRY*psx, nsrow, /* A, LDA: S1, nsrow */ info) ; /* INFO */ #else LAPACK_zpotrf ("L", nscol2, /* N: nscol2 */ Lx + L_ENTRY*psx, nsrow, /* A, LDA: S1, nsrow */ info) ; /* INFO */ #endif #ifndef NTIMER Common->CHOLMOD_CPU_POTRF_TIME += SuiteSparse_time ()- tstart ; #endif } /* ------------------------------------------------------------------ */ /* check if the matrix is not positive definite */ /* ------------------------------------------------------------------ */ if (repeat_supernode) { /* the leading part has been refactorized; it must have succeeded */ info = 0 ; /* zero out the rest of this supernode */ p = psx + nsrow * nscol_new ; pend = psx + nsrow * nscol ; /* s is nsrow-by-nscol */ for ( ; p < pend ; p++) { /* Lx [p] = 0 ; */ L_CLEAR (Lx,p) ; } } /* info is set to one in LAPACK_*potrf if blas_ok is FALSE. It is * set to zero in dpotrf/zpotrf if the factorization was successful. */ if (CHECK_BLAS_INT && !Common->blas_ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ; } if (info != 0) { /* Matrix is not positive definite. dpotrf/zpotrf do NOT report an * error if the diagonal of L has NaN's, only if it has a zero. */ if (Common->status == CHOLMOD_OK) { ERROR (CHOLMOD_NOT_POSDEF, "matrix not positive definite") ; } /* L->minor is the column of L that contains a zero or negative * diagonal term. */ L->minor = k1 + info - 1 ; /* clear the link lists of all subsequent supernodes */ for (ss = s+1 ; ss < nsuper ; ss++) { Head [ss] = EMPTY ; } /* zero this supernode, and all remaining supernodes */ pend = L->xsize ; for (p = psx ; p < pend ; p++) { /* Lx [p] = 0. ; */ L_CLEAR (Lx,p) ; } /* If L is indefinite, it still contains useful information. * Supernodes 0 to s-1 are valid, similar to MATLAB [R,p]=chol(A), * where the 1-based p is identical to the 0-based L->minor. Since * L->minor is in the current supernode s, it and any columns to the * left of it in supernode s are also all zero. This differs from * [R,p]=chol(A), which contains nonzero rows 1 to p-1. Fix this * by setting repeat_supernode to TRUE, and repeating supernode s. * * If Common->quick_return_if_not_posdef is true, then the entire * supernode s is not factorized; it is left as all zero. */ if (info == 1 || Common->quick_return_if_not_posdef) { /* If the first column of supernode s contains a zero or * negative diagonal entry, then it is already properly set to * zero. Also, info will be 1 if integer overflow occured in * the BLAS. */ Head [s] = EMPTY ; #ifdef GPU_BLAS TEMPLATE (CHOLMOD (gpu_end)) (Common) ; #endif return (Common->status >= CHOLMOD_OK) ; } else { /* Repeat supernode s, but only factorize it up to but not * including the column containing the problematic diagonal * entry. */ repeat_supernode = TRUE ; s-- ; nscol_new = info - 1 ; continue ; } } /* ------------------------------------------------------------------ */ /* compute the subdiagonal block and prepare supernode for its parent */ /* ------------------------------------------------------------------ */ nsrow2 = nsrow - nscol2 ; if (nsrow2 > 0) { /* The current supernode is columns k1 to k2-1 of L. Let L1 be the * diagonal block (factorized by dpotrf/zpotrf above; rows/cols * k1:k2-1), and L2 be rows k2:n-1 and columns k1:k2-1 of L. The * triangular system to solve is L2*L1' = S2, where S2 is * overwritten with L2. More precisely, L2 = S2 / L1' in MATLAB * notation. */ #ifdef GPU_BLAS if (!TEMPLATE (CHOLMOD (gpu_triangular_solve)) (nsrow2, nscol2, nsrow, psx, Lx, Common)) #endif { #ifndef NTIMER Common->CHOLMOD_CPU_TRSM_CALLS++ ; tstart = SuiteSparse_time () ; #endif #ifdef REAL BLAS_dtrsm ("R", "L", "C", "N", nsrow2, nscol2, /* M, N */ one, /* ALPHA: 1 */ Lx + L_ENTRY*psx, nsrow, /* A, LDA: L1, nsrow */ Lx + L_ENTRY*(psx + nscol2), /* B, LDB, L2, nsrow */ nsrow) ; #else BLAS_ztrsm ("R", "L", "C", "N", nsrow2, nscol2, /* M, N */ one, /* ALPHA: 1 */ Lx + L_ENTRY*psx, nsrow, /* A, LDA: L1, nsrow */ Lx + L_ENTRY*(psx + nscol2), /* B, LDB, L2, nsrow */ nsrow) ; #endif #ifndef NTIMER Common->CHOLMOD_CPU_TRSM_TIME += SuiteSparse_time () - tstart ; #endif } if (CHECK_BLAS_INT && !Common->blas_ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ; } if (!repeat_supernode) { /* Lpos [s] is offset of first row of s affecting its parent */ Lpos [s] = nscol ; sparent = SuperMap [Ls [psi + nscol]] ; ASSERT (sparent != EMPTY) ; ASSERT (Ls [psi + nscol] >= Super [sparent]) ; ASSERT (Ls [psi + nscol] < Super [sparent+1]) ; ASSERT (SuperMap [Ls [psi + nscol]] == sparent) ; ASSERT (sparent > s && sparent < nsuper) ; /* place s in link list of its parent */ Next [s] = Head [sparent] ; Head [sparent] = s ; } } Head [s] = EMPTY ; /* link list for supernode s no longer needed */ /* clear the Map (debugging only, to detect changes in pattern of A) */ DEBUG (for (k = 0 ; k < nsrow ; k++) Map [Ls [psi + k]] = EMPTY) ; DEBUG (CHOLMOD(dump_super) (s, Super, Lpi, Ls, Lpx, Lx, L_ENTRY, Common)) ; if (repeat_supernode) { /* matrix is not positive definite; finished clean-up for supernode * containing negative diagonal */ #ifdef GPU_BLAS TEMPLATE (CHOLMOD (gpu_end)) (Common) ; #endif return (Common->status >= CHOLMOD_OK) ; } } /* success; matrix is positive definite */ L->minor = n ; #ifdef GPU_BLAS TEMPLATE (CHOLMOD (gpu_end)) (Common) ; #endif return (Common->status >= CHOLMOD_OK) ; } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX Matrix/src/CHOLMOD/Supernodal/cholmod_super_solve.c0000644000175100001440000001570212271765436021765 0ustar hornikusers/* ========================================================================== */ /* === Supernodal/cholmod_super_solve ======================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Solve Lx=b or L'x=b for a supernodal factorization. These routines do not * apply the permutation L->Perm. See cholmod_solve for a more general * interface that performs that operation. */ #ifndef NSUPERNODAL #include "cholmod_internal.h" #include "cholmod_supernodal.h" /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define REAL #include "t_cholmod_super_solve.c" #define COMPLEX #include "t_cholmod_super_solve.c" /* ========================================================================== */ /* === cholmod_super_lsolve ================================================= */ /* ========================================================================== */ /* Solve Lx=b where x and b are of size n-by-nrhs. b is overwritten by the * solution x. On input, b is stored in col-major order with leading dimension * of d, and on output x is stored in the same manner. * * The contents of the workspace E are undefined on both input and output. * * workspace: none */ int CHOLMOD(super_lsolve) /* TRUE if OK, FALSE if BLAS overflow occured */ ( /* ---- input ---- */ cholmod_factor *L, /* factor to use for the forward solve */ /* ---- output ---- */ cholmod_dense *X, /* b on input, solution to Lx=b on output */ /* ---- workspace ---- */ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_NULL (X, FALSE) ; RETURN_IF_NULL (E, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (E, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ; if (L->xtype != X->xtype) { ERROR (CHOLMOD_INVALID, "L and X must have the same xtype") ; return (FALSE) ; } if (L->xtype != E->xtype) { ERROR (CHOLMOD_INVALID, "L and E must have the same xtype") ; return (FALSE) ; } if (X->d < X->nrow || L->n != X->nrow) { ERROR (CHOLMOD_INVALID, "X and L dimensions must match") ; return (FALSE) ; } if (E->nzmax < X->ncol * (L->maxesize)) { ERROR (CHOLMOD_INVALID, "workspace E not large enough") ; return (FALSE) ; } if (!(L->is_ll) || !(L->is_super)) { ERROR (CHOLMOD_INVALID, "L not supernodal") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; ASSERT (IMPLIES (L->n == 0, L->nsuper == 0)) ; if (L->n == 0 || X->ncol == 0) { /* nothing to do */ return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* solve Lx=b using template routine */ /* ---------------------------------------------------------------------- */ switch (L->xtype) { case CHOLMOD_REAL: r_cholmod_super_lsolve (L, X, E, Common) ; break ; case CHOLMOD_COMPLEX: c_cholmod_super_lsolve (L, X, E, Common) ; break ; } if (CHECK_BLAS_INT && !Common->blas_ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ; } return (Common->blas_ok) ; } /* ========================================================================== */ /* === cholmod_super_ltsolve ================================================ */ /* ========================================================================== */ /* Solve L'x=b where x and b are of size n-by-nrhs. b is overwritten by the * solution x. On input, b is stored in col-major order with leading dimension * of d, and on output x is stored in the same manner. * * The contents of the workspace E are undefined on both input and output. * * workspace: none */ int CHOLMOD(super_ltsolve) /* TRUE if OK, FALSE if BLAS overflow occured */ ( /* ---- input ---- */ cholmod_factor *L, /* factor to use for the backsolve */ /* ---- output ---- */ cholmod_dense *X, /* b on input, solution to L'x=b on output */ /* ---- workspace ---- */ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_NULL (X, FALSE) ; RETURN_IF_NULL (E, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (E, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ; if (L->xtype != X->xtype) { ERROR (CHOLMOD_INVALID, "L and X must have the same xtype") ; return (FALSE) ; } if (L->xtype != E->xtype) { ERROR (CHOLMOD_INVALID, "L and E must have the same xtype") ; return (FALSE) ; } if (X->d < X->nrow || L->n != X->nrow) { ERROR (CHOLMOD_INVALID, "X and L dimensions must match") ; return (FALSE) ; } if (E->nzmax < X->ncol * (L->maxesize)) { ERROR (CHOLMOD_INVALID, "workspace E not large enough") ; return (FALSE) ; } if (!(L->is_ll) || !(L->is_super)) { ERROR (CHOLMOD_INVALID, "L not supernodal") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; ASSERT (IMPLIES (L->n == 0, L->nsuper == 0)) ; if (L->n == 0 || X->ncol == 0) { /* nothing to do */ return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* solve Lx=b using template routine */ /* ---------------------------------------------------------------------- */ switch (L->xtype) { case CHOLMOD_REAL: r_cholmod_super_ltsolve (L, X, E, Common) ; break ; case CHOLMOD_COMPLEX: c_cholmod_super_ltsolve (L, X, E, Common) ; break ; } if (CHECK_BLAS_INT && !Common->blas_ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ; } return (Common->blas_ok) ; } #endif Matrix/src/CHOLMOD/Supernodal/cholmod_super_numeric.c0000644000175100001440000002537712271765436022310 0ustar hornikusers/* ========================================================================== */ /* === Supernodal/cholmod_super_numeric ===================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Computes the Cholesky factorization of A+beta*I or A*F+beta*I. Only the * the lower triangular part of A+beta*I or A*F+beta*I is accessed. The * matrices A and F must already be permuted according to the fill-reduction * permutation L->Perm. cholmod_factorize is an "easy" wrapper for this code * which applies that permutation. beta is real. * * Symmetric case: A is a symmetric (lower) matrix. F is not accessed. * With a fill-reducing permutation, A(p,p) should be passed instead, where is * p is L->Perm. * * Unsymmetric case: A is unsymmetric, and F must be present. Normally, F=A'. * With a fill-reducing permutation, A(p,f) and A(p,f)' should be passed as A * and F, respectively, where f is a list of the subset of the columns of A. * * The input factorization L must be supernodal (L->is_super is TRUE). It can * either be symbolic or numeric. In the first case, L has been analyzed by * cholmod_analyze or cholmod_super_symbolic, but the matrix has not yet been * numerically factorized. The numerical values are allocated here and the * factorization is computed. In the second case, a prior matrix has been * analyzed and numerically factorized, and a new matrix is being factorized. * The numerical values of L are replaced with the new numerical factorization. * * L->is_ll is ignored, and set to TRUE. This routine always computes an LL' * factorization. Supernodal LDL' factorization is not (yet) supported. * FUTURE WORK: perform a supernodal LDL' factorization if L->is_ll is FALSE. * * Uses BLAS routines dsyrk, dgemm, dtrsm, and the LAPACK routine dpotrf. * The supernodal solver uses BLAS routines dtrsv, dgemv, dtrsm, and dgemm. * * If the matrix is not positive definite the routine returns TRUE, but sets * Common->status to CHOLMOD_NOT_POSDEF and L->minor is set to the column at * which the failure occurred. The supernode containing the non-positive * diagonal entry is set to zero (this includes columns to the left of L->minor * in the same supernode), as are all subsequent supernodes. * * workspace: Flag (nrow), Head (nrow+1), Iwork (2*nrow + 4*nsuper). * Allocates temporary space of size L->maxcsize * sizeof(double) * (twice that for the complex/zomplex case). * * If L is supernodal symbolic on input, it is converted to a supernodal numeric * factor on output, with an xtype of real if A is real, or complex if A is * complex or zomplex. If L is supernodal numeric on input, its xtype must * match A (except that L can be complex and A zomplex). The xtype of A and F * must match. */ #ifndef NSUPERNODAL #include "cholmod_internal.h" #include "cholmod_supernodal.h" /* ========================================================================== */ /* === TEMPLATE codes for GPU and regular numeric factorization ============= */ /* ========================================================================== */ #ifdef GPU_BLAS #define REAL #include "t_cholmod_gpu.c" #define COMPLEX #include "t_cholmod_gpu.c" #define ZOMPLEX #include "t_cholmod_gpu.c" #endif #define REAL #include "t_cholmod_super_numeric.c" #define COMPLEX #include "t_cholmod_super_numeric.c" #define ZOMPLEX #include "t_cholmod_super_numeric.c" /* ========================================================================== */ /* === cholmod_super_numeric ================================================ */ /* ========================================================================== */ /* Returns TRUE if successful, or if the matrix is not positive definite. * Returns FALSE if out of memory, inputs are invalid, or other fatal error * occurs. */ int CHOLMOD(super_numeric) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* F = A' or A(:,f)' */ double beta [2], /* beta*I is added to diagonal of matrix to factorize */ /* ---- in/out --- */ cholmod_factor *L, /* factorization */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *C ; Int *Super, *Map, *SuperMap ; size_t maxcsize ; Int nsuper, n, i, k, s, stype, nrow ; int ok = TRUE, symbolic ; size_t t, w ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_COMPLEX, FALSE) ; stype = A->stype ; if (stype < 0) { if (A->nrow != A->ncol || A->nrow != L->n) { ERROR (CHOLMOD_INVALID, "invalid dimensions") ; return (FALSE) ; } } else if (stype == 0) { if (A->nrow != L->n) { ERROR (CHOLMOD_INVALID, "invalid dimensions") ; return (FALSE) ; } RETURN_IF_NULL (F, FALSE) ; RETURN_IF_XTYPE_INVALID (F, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; if (A->nrow != F->ncol || A->ncol != F->nrow || F->stype != 0) { ERROR (CHOLMOD_INVALID, "F invalid") ; return (FALSE) ; } if (A->xtype != F->xtype) { ERROR (CHOLMOD_INVALID, "A and F must have same xtype") ; return (FALSE) ; } } else { /* symmetric upper case not suppored */ ERROR (CHOLMOD_INVALID, "symmetric upper case not supported") ; return (FALSE) ; } if (!(L->is_super)) { ERROR (CHOLMOD_INVALID, "L not supernodal") ; return (FALSE) ; } if (L->xtype != CHOLMOD_PATTERN) { if (! ((A->xtype == CHOLMOD_REAL && L->xtype == CHOLMOD_REAL) || (A->xtype == CHOLMOD_COMPLEX && L->xtype == CHOLMOD_COMPLEX) || (A->xtype == CHOLMOD_ZOMPLEX && L->xtype == CHOLMOD_COMPLEX))) { ERROR (CHOLMOD_INVALID, "complex type mismatch") ; return (FALSE) ; } } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace in Common */ /* ---------------------------------------------------------------------- */ nsuper = L->nsuper ; maxcsize = L->maxcsize ; nrow = A->nrow ; n = nrow ; PRINT1 (("nsuper "ID" maxcsize %g\n", nsuper, (double) maxcsize)) ; ASSERT (nsuper >= 0 && maxcsize > 0) ; /* w = 2*n + 4*nsuper */ w = CHOLMOD(mult_size_t) (n, 2, &ok) ; t = CHOLMOD(mult_size_t) (nsuper, 4, &ok) ; w = CHOLMOD(add_size_t) (w, t, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, w, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get the current factor L and allocate numerical part, if needed */ /* ---------------------------------------------------------------------- */ Super = L->super ; symbolic = (L->xtype == CHOLMOD_PATTERN) ; if (symbolic) { /* convert to supernodal numeric by allocating L->x */ CHOLMOD(change_factor) ( (A->xtype == CHOLMOD_REAL) ? CHOLMOD_REAL : CHOLMOD_COMPLEX, TRUE, TRUE, TRUE, TRUE, L, Common) ; if (Common->status < CHOLMOD_OK) { /* the factor L remains in symbolic supernodal form */ return (FALSE) ; } } ASSERT (L->dtype == DTYPE) ; ASSERT (L->xtype == CHOLMOD_REAL || L->xtype == CHOLMOD_COMPLEX) ; /* supernodal LDL' is not supported */ L->is_ll = TRUE ; /* ---------------------------------------------------------------------- */ /* get more workspace */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_dense) (maxcsize, 1, maxcsize, L->xtype, Common) ; if (Common->status < CHOLMOD_OK) { int status = Common->status ; if (symbolic) { /* Change L back to symbolic, since the numeric values are not * initialized. This cannot fail. */ CHOLMOD(change_factor) (CHOLMOD_PATTERN, TRUE, TRUE, TRUE, TRUE, L, Common) ; } /* the factor L is now back to the form it had on input */ Common->status = status ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ SuperMap = Common->Iwork ; /* size n (i/i/l) */ Map = Common->Flag ; /* size n, use Flag as workspace for Map array */ for (i = 0 ; i < n ; i++) { Map [i] = EMPTY ; } /* ---------------------------------------------------------------------- */ /* find the mapping of nodes to relaxed supernodes */ /* ---------------------------------------------------------------------- */ /* SuperMap [k] = s if column k is contained in supernode s */ for (s = 0 ; s < nsuper ; s++) { PRINT1 (("Super ["ID"] "ID" ncols "ID"\n", s, Super[s], Super[s+1]-Super[s])); for (k = Super [s] ; k < Super [s+1] ; k++) { SuperMap [k] = s ; PRINT2 (("relaxed SuperMap ["ID"] = "ID"\n", k, SuperMap [k])) ; } } /* ---------------------------------------------------------------------- */ /* supernodal numerical factorization, using template routine */ /* ---------------------------------------------------------------------- */ switch (A->xtype) { case CHOLMOD_REAL: ok = r_cholmod_super_numeric (A, F, beta, L, C, Common) ; break ; case CHOLMOD_COMPLEX: ok = c_cholmod_super_numeric (A, F, beta, L, C, Common) ; break ; case CHOLMOD_ZOMPLEX: /* This operates on complex L, not zomplex */ ok = z_cholmod_super_numeric (A, F, beta, L, C, Common) ; break ; } /* ---------------------------------------------------------------------- */ /* clear Common workspace, free temp workspace C, and return */ /* ---------------------------------------------------------------------- */ /* Flag array was used as workspace, clear it */ Common->mark = EMPTY ; /* CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; CHOLMOD(free_dense) (&C, Common) ; return (ok) ; } #endif Matrix/src/CHOLMOD/Supernodal/t_cholmod_super_solve.c0000644000175100001440000002556512271765436022320 0ustar hornikusers/* ========================================================================== */ /* === Supernodal/t_cholmod_super_solve ===================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Template routine for cholmod_super_solve. Supports real or complex L. */ #include "cholmod_template.h" static void TEMPLATE (cholmod_super_lsolve) ( /* ---- input ---- */ cholmod_factor *L, /* factor to use for the forward solve */ /* ---- output ---- */ cholmod_dense *X, /* b on input, solution to Lx=b on output */ /* ---- workspace ---- */ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */ /* --------------- */ cholmod_common *Common ) { double *Lx, *Xx, *Ex ; double minus_one [2], one [2] ; Int *Lpi, *Lpx, *Ls, *Super ; Int nsuper, k1, k2, psi, psend, psx, nsrow, nscol, ii, s, nsrow2, n, ps2, j, i, d, nrhs ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrhs = X->ncol ; Ex = E->x ; Xx = X->x ; n = L->n ; d = X->d ; nsuper = L->nsuper ; Lpi = L->pi ; Lpx = L->px ; Ls = L->s ; Super = L->super ; Lx = L->x ; minus_one [0] = -1.0 ; minus_one [1] = 0 ; one [0] = 1.0 ; one [1] = 0 ; /* ---------------------------------------------------------------------- */ /* solve Lx=b */ /* ---------------------------------------------------------------------- */ if (nrhs == 1) { for (s = 0 ; s < nsuper ; s++) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; psx = Lpx [s] ; nsrow = psend - psi ; nscol = k2 - k1 ; nsrow2 = nsrow - nscol ; ps2 = psi + nscol ; ASSERT ((size_t) nsrow2 <= L->maxesize) ; /* L1 is nscol-by-nscol, lower triangular with non-unit diagonal. * L2 is nsrow2-by-nscol. L1 and L2 have leading dimension of * nsrow. x1 is nscol-by-nsrow, with leading dimension n. * E is nsrow2-by-1, with leading dimension nsrow2. */ /* gather X into E */ for (ii = 0 ; ii < nsrow2 ; ii++) { /* Ex [ii] = Xx [Ls [ps2 + ii]] ; */ ASSIGN (Ex,-,ii, Xx,-,Ls [ps2 + ii]) ; } #ifdef REAL /* solve L1*x1 (that is, x1 = L1\x1) */ BLAS_dtrsv ("L", "N", "N", nscol, /* N: L1 is nscol-by-nscol */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */ /* E = E - L2*x1 */ BLAS_dgemv ("N", nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Xx + ENTRY_SIZE*k1, 1, /* X, INCX: x1 */ one, /* BETA: 1 */ Ex, 1) ; /* Y, INCY: E */ #else /* solve L1*x1 (that is, x1 = L1\x1) */ BLAS_ztrsv ("L", "N", "N", nscol, /* N: L1 is nscol-by-nscol */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */ /* E = E - L2*x1 */ BLAS_zgemv ("N", nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Xx + ENTRY_SIZE*k1, 1, /* X, INCX: x1 */ one, /* BETA: 1 */ Ex, 1) ; /* Y, INCY: E */ #endif /* scatter E back into X */ for (ii = 0 ; ii < nsrow2 ; ii++) { /* Xx [Ls [ps2 + ii]] = Ex [ii] ; */ ASSIGN (Xx,-,Ls [ps2 + ii], Ex,-,ii) ; } } } else { for (s = 0 ; s < nsuper ; s++) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; psx = Lpx [s] ; nsrow = psend - psi ; nscol = k2 - k1 ; nsrow2 = nsrow - nscol ; ps2 = psi + nscol ; ASSERT ((size_t) nsrow2 <= L->maxesize) ; /* E is nsrow2-by-nrhs, with leading dimension nsrow2. */ /* gather X into E */ for (ii = 0 ; ii < nsrow2 ; ii++) { i = Ls [ps2 + ii] ; for (j = 0 ; j < nrhs ; j++) { /* Ex [ii + j*nsrow2] = Xx [i + j*d] ; */ ASSIGN (Ex,-,ii+j*nsrow2, Xx,-,i+j*d) ; } } #ifdef REAL /* solve L1*x1 */ BLAS_dtrsm ("L", "L", "N", "N", nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */ one, /* ALPHA: 1 */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */ /* E = E - L2*x1 */ if (nsrow2 > 0) { BLAS_dgemm ("N", "N", nsrow2, nrhs, nscol, /* M, N, K */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Xx + ENTRY_SIZE*k1, d, /* B, LDB: X1 */ one, /* BETA: 1 */ Ex, nsrow2) ; /* C, LDC: E */ } #else /* solve L1*x1 */ BLAS_ztrsm ("L", "L", "N", "N", nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */ one, /* ALPHA: 1 */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */ /* E = E - L2*x1 */ if (nsrow2 > 0) { BLAS_zgemm ("N", "N", nsrow2, nrhs, nscol, /* M, N, K */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Xx + ENTRY_SIZE*k1, d, /* B, LDB: X1 */ one, /* BETA: 1 */ Ex, nsrow2) ; /* C, LDC: E */ } #endif /* scatter E back into X */ for (ii = 0 ; ii < nsrow2 ; ii++) { i = Ls [ps2 + ii] ; for (j = 0 ; j < nrhs ; j++) { /* Xx [i + j*d] = Ex [ii + j*nsrow2] ; */ ASSIGN (Xx,-,i+j*d, Ex,-,ii+j*nsrow2) ; } } } } } static void TEMPLATE (cholmod_super_ltsolve) ( /* ---- input ---- */ cholmod_factor *L, /* factor to use for the forward solve */ /* ---- output ---- */ cholmod_dense *X, /* b on input, solution to Lx=b on output */ /* ---- workspace ---- */ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */ /* --------------- */ cholmod_common *Common ) { double *Lx, *Xx, *Ex ; double minus_one [2], one [2] ; Int *Lpi, *Lpx, *Ls, *Super ; Int nsuper, k1, k2, psi, psend, psx, nsrow, nscol, ii, s, nsrow2, n, ps2, j, i, d, nrhs ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrhs = X->ncol ; Ex = E->x ; Xx = X->x ; n = L->n ; d = X->d ; nsuper = L->nsuper ; Lpi = L->pi ; Lpx = L->px ; Ls = L->s ; Super = L->super ; Lx = L->x ; minus_one [0] = -1.0 ; minus_one [1] = 0 ; one [0] = 1.0 ; one [1] = 0 ; /* ---------------------------------------------------------------------- */ /* solve L'x=b */ /* ---------------------------------------------------------------------- */ if (nrhs == 1) { for (s = nsuper-1 ; s >= 0 ; s--) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; psx = Lpx [s] ; nsrow = psend - psi ; nscol = k2 - k1 ; nsrow2 = nsrow - nscol ; ps2 = psi + nscol ; ASSERT ((size_t) nsrow2 <= L->maxesize) ; /* L1 is nscol-by-nscol, lower triangular with non-unit diagonal. * L2 is nsrow2-by-nscol. L1 and L2 have leading dimension of * nsrow. x1 is nscol-by-nsrow, with leading dimension n. * E is nsrow2-by-1, with leading dimension nsrow2. */ /* gather X into E */ for (ii = 0 ; ii < nsrow2 ; ii++) { /* Ex [ii] = Xx [Ls [ps2 + ii]] ; */ ASSIGN (Ex,-,ii, Xx,-,Ls [ps2 + ii]) ; } #ifdef REAL /* x1 = x1 - L2'*E */ BLAS_dgemv ("C", nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Ex, 1, /* X, INCX: Ex */ one, /* BETA: 1 */ Xx + ENTRY_SIZE*k1, 1) ; /* Y, INCY: x1 */ /* solve L1'*x1 */ BLAS_dtrsv ("L", "C", "N", nscol, /* N: L1 is nscol-by-nscol */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */ #else /* x1 = x1 - L2'*E */ BLAS_zgemv ("C", nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Ex, 1, /* X, INCX: Ex */ one, /* BETA: 1 */ Xx + ENTRY_SIZE*k1, 1) ; /* Y, INCY: x1 */ /* solve L1'*x1 */ BLAS_ztrsv ("L", "C", "N", nscol, /* N: L1 is nscol-by-nscol */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */ #endif } } else { for (s = nsuper-1 ; s >= 0 ; s--) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; psx = Lpx [s] ; nsrow = psend - psi ; nscol = k2 - k1 ; nsrow2 = nsrow - nscol ; ps2 = psi + nscol ; ASSERT ((size_t) nsrow2 <= L->maxesize) ; /* E is nsrow2-by-nrhs, with leading dimension nsrow2. */ /* gather X into E */ for (ii = 0 ; ii < nsrow2 ; ii++) { i = Ls [ps2 + ii] ; for (j = 0 ; j < nrhs ; j++) { /* Ex [ii + j*nsrow2] = Xx [i + j*d] ; */ ASSIGN (Ex,-,ii+j*nsrow2, Xx,-,i+j*d) ; } } #ifdef REAL /* x1 = x1 - L2'*E */ if (nsrow2 > 0) { BLAS_dgemm ("C", "N", nscol, nrhs, nsrow2, /* M, N, K */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Ex, nsrow2, /* B, LDB: E */ one, /* BETA: 1 */ Xx + ENTRY_SIZE*k1, d) ; /* C, LDC: x1 */ } /* solve L1'*x1 */ BLAS_dtrsm ("L", "L", "C", "N", nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */ one, /* ALPHA: 1 */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */ #else /* x1 = x1 - L2'*E */ if (nsrow2 > 0) { BLAS_zgemm ("C", "N", nscol, nrhs, nsrow2, /* M, N, K */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Ex, nsrow2, /* B, LDB: E */ one, /* BETA: 1 */ Xx + ENTRY_SIZE*k1, d) ; /* C, LDC: x1 */ } /* solve L1'*x1 */ BLAS_ztrsm ("L", "L", "C", "N", nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */ one, /* ALPHA: 1 */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */ #endif } } } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX Matrix/src/CHOLMOD/Partition/0000755000175100001440000000000012271765426015375 5ustar hornikusersMatrix/src/CHOLMOD/Partition/License.txt0000644000175100001440000000210411770402705017504 0ustar hornikusersCHOLMOD/Partition Module. Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.suitesparse.com Note that this license is for the CHOLMOD/Partition module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Matrix/src/CHOLMOD/Partition/cholmod_nesdis.c0000644000175100001440000020702712271765436020544 0ustar hornikusers/* ========================================================================== */ /* === Partition/cholmod_nesdis ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Partition Module. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* CHOLMOD nested dissection and graph partitioning. * * cholmod_bisect: * * Finds a set of nodes that partitions the graph into two parts. * Compresses the graph first. Requires METIS. * * cholmod_nested_dissection: * * Nested dissection, using its own compression and connected-commponents * algorithms, an external graph partitioner (METIS), and a constrained * minimum degree ordering algorithm (CCOLAMD or CSYMAMD). Typically * gives better orderings than METIS_NodeND (about 5% to 10% fewer * nonzeros in L). * * cholmod_collapse_septree: * * Prune the separator tree returned by cholmod_nested_dissection. * * This file contains several routines private to this file: * * partition compress and partition a graph * clear_flag clear Common->Flag, but do not modify negative entries * find_components find the connected components of a graph * * Supports any xtype (pattern, real, complex, or zomplex). */ #ifndef NPARTITION #include "cholmod_internal.h" #include "cholmod_partition.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === partition ============================================================ */ /* ========================================================================== */ /* Find a set of nodes that partition a graph. The graph must be symmetric * with no diagonal entries. To compress the graph first, compress is TRUE * and on input Hash [j] holds the hash key for node j, which must be in the * range 0 to csize-1. The input graph (Cp, Ci) is destroyed. Cew is all 1's * on input and output. Cnw [j] > 0 is the initial weight of node j. On * output, Cnw [i] = 0 if node i is absorbed into j and the original weight * Cnw [i] is added to Cnw [j]. If compress is FALSE, the graph is not * compressed and Cnw and Hash are unmodified. The partition itself is held in * the output array Part of size n. Part [j] is 0, 1, or 2, depending on * whether node j is in the left part of the graph, the right part, or the * separator, respectively. Note that the input graph need not be connected, * and the output subgraphs (the three parts) may also be unconnected. * * Returns the size of the separator, in terms of the sum of the weights of * the nodes. It is guaranteed to be between 1 and the total weight of all * the nodes. If it is of size less than the total weight, then both the left * and right parts are guaranteed to be non-empty (this guarantee depends on * cholmod_metis_bisector). */ static SuiteSparse_long partition /* size of separator or -1 if failure */ ( /* inputs, not modified on output */ #ifndef NDEBUG Int csize, /* upper bound on # of edges in the graph; * csize >= MAX (n, nnz(C)) must hold. */ #endif int compress, /* if TRUE the compress the graph first */ /* input/output */ Int Hash [ ], /* Hash [i] = hash >= 0 is the hash function for node * i on input. On output, Hash [i] = FLIP (j) if node * i is absorbed into j. Hash [i] >= 0 if i has not * been absorbed. */ /* input graph, compressed graph of cn nodes on output */ cholmod_sparse *C, /* input/output */ Int Cnw [ ], /* size n. Cnw [j] > 0 is the weight of node j on * input. On output, if node i is absorbed into * node j, then Cnw [i] = 0 and the original weight of * node i is added to Cnw [j]. The sum of Cnw [0..n-1] * is not modified. */ /* workspace */ Int Cew [ ], /* size csize, all 1's on input and output */ /* more workspace, undefined on input and output */ Int Cmap [ ], /* size n (i/i/l) */ /* output */ Int Part [ ], /* size n, Part [j] = 0, 1, or 2. */ cholmod_common *Common ) { Int n, hash, head, i, j, k, p, pend, ilen, ilast, pi, piend, jlen, ok, cn, csep, pdest, nodes_pruned, nz, total_weight, jscattered ; Int *Cp, *Ci, *Next, *Hhead ; #ifndef NDEBUG Int cnt, pruned ; double work = 0, goodwork = 0 ; #endif /* ---------------------------------------------------------------------- */ /* quick return for small or empty graphs */ /* ---------------------------------------------------------------------- */ n = C->nrow ; Cp = C->p ; Ci = C->i ; nz = Cp [n] ; PRINT2 (("Partition start, n "ID" nz "ID"\n", n, nz)) ; total_weight = 0 ; for (j = 0 ; j < n ; j++) { ASSERT (Cnw [j] > 0) ; total_weight += Cnw [j] ; } if (n <= 2) { /* very small graph */ for (j = 0 ; j < n ; j++) { Part [j] = 2 ; } return (total_weight) ; } else if (nz <= 0) { /* no edges, this is easy */ PRINT2 (("diagonal matrix\n")) ; k = n/2 ; for (j = 0 ; j < k ; j++) { Part [j] = 0 ; } for ( ; j < n ; j++) { Part [j] = 1 ; } /* ensure the separator is not empty (required by nested dissection) */ Part [n-1] = 2 ; return (Cnw [n-1]) ; } #ifndef NDEBUG ASSERT (n > 1 && nz > 0) ; PRINT2 (("original graph:\n")) ; for (j = 0 ; j < n ; j++) { PRINT2 ((""ID": ", j)) ; for (p = Cp [j] ; p < Cp [j+1] ; p++) { i = Ci [p] ; PRINT3 ((""ID" ", i)) ; ASSERT (i >= 0 && i < n && i != j) ; } PRINT2 (("hash: "ID"\n", Hash [j])) ; } DEBUG (for (p = 0 ; p < csize ; p++) ASSERT (Cew [p] == 1)) ; #endif nodes_pruned = 0 ; if (compress) { /* ------------------------------------------------------------------ */ /* get workspace */ /* ------------------------------------------------------------------ */ Next = Part ; /* use Part as workspace for Next [ */ Hhead = Cew ; /* use Cew as workspace for Hhead [ */ /* ------------------------------------------------------------------ */ /* create the hash buckets */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < n ; j++) { /* get the hash key for node j */ hash = Hash [j] ; ASSERT (hash >= 0 && hash < csize) ; head = Hhead [hash] ; if (head > EMPTY) { /* hash bucket for this hash key is empty. */ head = EMPTY ; } else { /* hash bucket for this hash key is not empty. get old head */ head = FLIP (head) ; ASSERT (head >= 0 && head < n) ; } /* node j becomes the new head of the hash bucket. FLIP it so that * we can tell the difference between an empty or non-empty hash * bucket. */ Hhead [hash] = FLIP (j) ; Next [j] = head ; ASSERT (head >= EMPTY && head < n) ; } #ifndef NDEBUG for (cnt = 0, k = 0 ; k < n ; k++) { ASSERT (Hash [k] >= 0 && Hash [k] < csize) ; /* k is alive */ hash = Hash [k] ; ASSERT (hash >= 0 && hash < csize) ; head = Hhead [hash] ; ASSERT (head < EMPTY) ; /* hash bucket not empty */ j = FLIP (head) ; ASSERT (j >= 0 && j < n) ; if (j == k) { PRINT2 (("hash "ID": ", hash)) ; for ( ; j != EMPTY ; j = Next [j]) { PRINT3 ((" "ID"", j)) ; ASSERT (j >= 0 && j < n) ; ASSERT (Hash [j] == hash) ; cnt++ ; ASSERT (cnt <= n) ; } PRINT2 (("\n")) ; } } ASSERT (cnt == n) ; #endif /* ------------------------------------------------------------------ */ /* scan the non-empty hash buckets for indistinguishable nodes */ /* ------------------------------------------------------------------ */ /* If there are no hash collisions and no compression occurs, this takes * O(n) time. If no hash collisions, but some nodes are removed, this * takes time O(n+e) where e is the sum of the degress of the nodes * that are removed. Even with many hash collisions (a rare case), * this algorithm has never been observed to perform more than nnz(A) * useless work. * * Cmap is used as workspace to mark nodes of the graph, [ * for comparing the nonzero patterns of two nodes i and j. */ #define Cmap_MARK(i) Cmap [i] = j #define Cmap_MARKED(i) (Cmap [i] == j) for (i = 0 ; i < n ; i++) { Cmap [i] = EMPTY ; } for (k = 0 ; k < n ; k++) { hash = Hash [k] ; ASSERT (hash >= FLIP (n-1) && hash < csize) ; if (hash < 0) { /* node k has already been absorbed into some other node */ ASSERT (FLIP (Hash [k]) >= 0 && FLIP (Hash [k] < n)) ; continue ; } head = Hhead [hash] ; ASSERT (head < EMPTY || head == 1) ; if (head == 1) { /* hash bucket is already empty */ continue ; } PRINT2 (("\n--------------------hash "ID":\n", hash)) ; for (j = FLIP (head) ; j != EMPTY && Next[j] > EMPTY ; j = Next [j]) { /* compare j with all nodes i following it in hash bucket */ ASSERT (j >= 0 && j < n && Hash [j] == hash) ; p = Cp [j] ; pend = Cp [j+1] ; jlen = pend - p ; jscattered = FALSE ; DEBUG (for (i = 0 ; i < n ; i++) ASSERT (!Cmap_MARKED (i))) ; DEBUG (pruned = FALSE) ; ilast = j ; for (i = Next [j] ; i != EMPTY ; i = Next [i]) { ASSERT (i >= 0 && i < n && Hash [i] == hash && i != j) ; pi = Cp [i] ; piend = Cp [i+1] ; ilen = piend - pi ; DEBUG (work++) ; if (ilen != jlen) { /* i and j have different degrees */ ilast = i ; continue ; } /* scatter the pattern of node j, if not already */ if (!jscattered) { Cmap_MARK (j) ; for ( ; p < pend ; p++) { Cmap_MARK (Ci [p]) ; } jscattered = TRUE ; DEBUG (work += jlen) ; } for (ok = Cmap_MARKED (i) ; ok && pi < piend ; pi++) { ok = Cmap_MARKED (Ci [pi]) ; DEBUG (work++) ; } if (ok) { /* found it. kill node i and merge it into j */ PRINT2 (("found "ID" absorbed into "ID"\n", i, j)) ; Hash [i] = FLIP (j) ; Cnw [j] += Cnw [i] ; Cnw [i] = 0 ; ASSERT (ilast != i && ilast >= 0 && ilast < n) ; Next [ilast] = Next [i] ; /* delete i from bucket */ nodes_pruned++ ; DEBUG (goodwork += (ilen+1)) ; DEBUG (pruned = TRUE) ; } else { /* i and j are different */ ilast = i ; } } DEBUG (if (pruned) goodwork += jlen) ; } /* empty the hash bucket, restoring Cew */ Hhead [hash] = 1 ; } DEBUG (if (((work - goodwork) / (double) nz) > 0.20) PRINT0 (( "work %12g good %12g nz %12g (wasted work/nz: %6.2f )\n", work, goodwork, (double) nz, (work - goodwork) / ((double) nz)))) ; /* All hash buckets now empty. Cmap no longer needed as workspace. ] * Cew no longer needed as Hhead; Cew is now restored to all ones. ] * Part no longer needed as workspace for Next. ] */ } /* Edge weights are all one, node weights reflect node absorption */ DEBUG (for (p = 0 ; p < csize ; p++) ASSERT (Cew [p] == 1)) ; DEBUG (for (cnt = 0, j = 0 ; j < n ; j++) cnt += Cnw [j]) ; ASSERT (cnt == total_weight) ; /* ---------------------------------------------------------------------- */ /* compress and partition the graph */ /* ---------------------------------------------------------------------- */ if (nodes_pruned == 0) { /* ------------------------------------------------------------------ */ /* no pruning done at all. Do not create the compressed graph */ /* ------------------------------------------------------------------ */ /* FUTURE WORK: could call CHACO, SCOTCH, ... here too */ csep = CHOLMOD(metis_bisector) (C, Cnw, Cew, Part, Common) ; } else if (nodes_pruned == n-1) { /* ------------------------------------------------------------------ */ /* only one node left. This is a dense graph */ /* ------------------------------------------------------------------ */ PRINT2 (("completely dense graph\n")) ; csep = total_weight ; for (j = 0 ; j < n ; j++) { Part [j] = 2 ; } } else { /* ------------------------------------------------------------------ */ /* compress the graph and partition the compressed graph */ /* ------------------------------------------------------------------ */ /* ------------------------------------------------------------------ */ /* create the map from the uncompressed graph to the compressed graph */ /* ------------------------------------------------------------------ */ /* Cmap [j] = k if node j is alive and the kth node of compressed graph. * The mapping is done monotonically (that is, k <= j) to simplify the * uncompression later on. Cmap [j] = EMPTY if node j is dead. */ for (j = 0 ; j < n ; j++) { Cmap [j] = EMPTY ; } k = 0 ; for (j = 0 ; j < n ; j++) { if (Cnw [j] > 0) { ASSERT (k <= j) ; Cmap [j] = k++ ; } } cn = k ; /* # of nodes in compressed graph */ PRINT2 (("compressed graph from "ID" to "ID" nodes\n", n, cn)) ; ASSERT (cn > 1 && cn == n - nodes_pruned) ; /* ------------------------------------------------------------------ */ /* create the compressed graph */ /* ------------------------------------------------------------------ */ k = 0 ; pdest = 0 ; for (j = 0 ; j < n ; j++) { if (Cnw [j] > 0) { /* node j in the full graph is node k in the compressed graph */ ASSERT (k <= j && Cmap [j] == k) ; p = Cp [j] ; pend = Cp [j+1] ; Cp [k] = pdest ; Cnw [k] = Cnw [j] ; for ( ; p < pend ; p++) { /* prune dead nodes, and remap to new node numbering */ i = Ci [p] ; ASSERT (i >= 0 && i < n && i != j) ; i = Cmap [i] ; ASSERT (i >= EMPTY && i < cn && i != k) ; if (i > EMPTY) { ASSERT (pdest <= p) ; Ci [pdest++] = i ; } } k++ ; } } Cp [cn] = pdest ; C->nrow = cn ; C->ncol = cn ; /* affects mem stats unless restored when C free'd */ #ifndef NDEBUG PRINT2 (("pruned graph ("ID"/"ID") nodes, ("ID"/"ID") edges\n", cn, n, pdest, nz)) ; PRINT2 (("compressed graph:\n")) ; for (cnt = 0, j = 0 ; j < cn ; j++) { PRINT2 ((""ID": ", j)) ; for (p = Cp [j] ; p < Cp [j+1] ; p++) { i = Ci [p] ; PRINT3 ((""ID" ", i)) ; ASSERT (i >= 0 && i < cn && i != j) ; } PRINT2 (("weight: "ID"\n", Cnw [j])) ; ASSERT (Cnw [j] > 0) ; cnt += Cnw [j] ; } ASSERT (cnt == total_weight) ; for (j = 0 ; j < n ; j++) PRINT2 (("Cmap ["ID"] = "ID"\n", j, Cmap[j])); ASSERT (k == cn) ; #endif /* ------------------------------------------------------------------ */ /* find the separator of the compressed graph */ /* ------------------------------------------------------------------ */ /* FUTURE WORK: could call CHACO, SCOTCH, ... here too */ csep = CHOLMOD(metis_bisector) (C, Cnw, Cew, Part, Common) ; if (csep < 0) { /* failed */ return (-1) ; } PRINT2 (("Part: ")) ; DEBUG (for (j = 0 ; j < cn ; j++) PRINT2 ((""ID" ", Part [j]))) ; PRINT2 (("\n")) ; /* Cp and Ci no longer needed */ /* ------------------------------------------------------------------ */ /* find the separator of the uncompressed graph */ /* ------------------------------------------------------------------ */ /* expand the separator to live nodes in the uncompressed graph */ for (j = n-1 ; j >= 0 ; j--) { /* do this in reverse order so that Cnw can be expanded in place */ k = Cmap [j] ; ASSERT (k >= EMPTY && k < n) ; if (k > EMPTY) { /* node k in compressed graph and is node j in full graph */ ASSERT (k <= j) ; ASSERT (Hash [j] >= EMPTY) ; Part [j] = Part [k] ; Cnw [j] = Cnw [k] ; } else { /* node j is a dead node */ Cnw [j] = 0 ; DEBUG (Part [j] = EMPTY) ; ASSERT (Hash [j] < EMPTY) ; } } /* find the components for the dead nodes */ for (i = 0 ; i < n ; i++) { if (Hash [i] < EMPTY) { /* node i has been absorbed into node j */ j = FLIP (Hash [i]) ; ASSERT (Part [i] == EMPTY && j >= 0 && j < n && Cnw [i] == 0) ; Part [i] = Part [j] ; } ASSERT (Part [i] >= 0 && Part [i] <= 2) ; } #ifndef NDEBUG PRINT2 (("Part: ")) ; for (cnt = 0, j = 0 ; j < n ; j++) { ASSERT (Part [j] != EMPTY) ; PRINT2 ((""ID" ", Part [j])) ; if (Part [j] == 2) cnt += Cnw [j] ; } PRINT2 (("\n")) ; PRINT2 (("csep "ID" "ID"\n", cnt, csep)) ; ASSERT (cnt == csep) ; for (cnt = 0, j = 0 ; j < n ; j++) cnt += Cnw [j] ; ASSERT (cnt == total_weight) ; #endif } /* ---------------------------------------------------------------------- */ /* return the separator (or -1 if error) */ /* ---------------------------------------------------------------------- */ PRINT2 (("Partition done, n "ID" csep "ID"\n", n, csep)) ; return (csep) ; } /* ========================================================================== */ /* === clear_flag =========================================================== */ /* ========================================================================== */ /* A node j has been removed from the graph if Flag [j] < EMPTY. * If Flag [j] >= EMPTY && Flag [j] < mark, then node j is alive but unmarked. * Flag [j] == mark means that node j is alive and marked. Incrementing mark * means that all nodes are either (still) dead, or live but unmarked. * * If Map is NULL, then on output, Common->mark < Common->Flag [i] for all i * from 0 to Common->nrow. This is the same output condition as * cholmod_clear_flag, except that this routine maintains the Flag [i] < EMPTY * condition as well, if that condition was true on input. * * If Map is non-NULL, then on output, Common->mark < Common->Flag [i] for all * i in the set Map [0..cn-1]. * * workspace: Flag (nrow) */ static SuiteSparse_long clear_flag (Int *Map, Int cn, cholmod_common *Common) { Int nrow, i ; Int *Flag ; PRINT2 (("old mark %ld\n", Common->mark)) ; Common->mark++ ; PRINT2 (("new mark %ld\n", Common->mark)) ; if (Common->mark <= 0) { nrow = Common->nrow ; Flag = Common->Flag ; if (Map != NULL) { for (i = 0 ; i < cn ; i++) { /* if Flag [Map [i]] < EMPTY, leave it alone */ if (Flag [Map [i]] >= EMPTY) { Flag [Map [i]] = EMPTY ; } } /* now Flag [Map [i]] <= EMPTY for all i */ } else { for (i = 0 ; i < nrow ; i++) { /* if Flag [i] < EMPTY, leave it alone */ if (Flag [i] >= EMPTY) { Flag [i] = EMPTY ; } } /* now Flag [i] <= EMPTY for all i */ } Common->mark = 0 ; } return (Common->mark) ; } /* ========================================================================== */ /* === find_components ====================================================== */ /* ========================================================================== */ /* Find all connected components of the current subgraph C. The subgraph C * consists of the nodes of B that appear in the set Map [0..cn-1]. If Map * is NULL, then it is assumed to be the identity mapping * (Map [0..cn-1] = 0..cn-1). * * A node j does not appear in B if it has been ordered (Flag [j] < EMPTY, * which means that j has been ordered and is "deleted" from B). * * If the size of a component is large, it is placed on the component stack, * Cstack. Otherwise, its nodes are ordered and it is not placed on the Cstack. * * A component S is defined by a "representative node" (repnode for short) * called the snode, which is one of the nodes in the subgraph. Likewise, the * subgraph C is defined by its repnode, called cnode. * * If Part is not NULL on input, then Part [i] determines how the components * are placed on the stack. Components containing nodes i with Part [i] == 0 * are placed first, followed by components with Part [i] == 1. * * The first node placed in each of the two parts is flipped when placed in * the Cstack. This allows the components of the two parts to be found simply * by traversing the Cstack. * * workspace: Flag (nrow) */ static void find_components ( /* inputs, not modified on output */ cholmod_sparse *B, Int Map [ ], /* size n, only Map [0..cn-1] used */ Int cn, /* # of nodes in C */ Int cnode, /* root node of component C, or EMPTY if C is the * entire graph B */ Int Part [ ], /* size cn, optional */ /* input/output */ Int Bnz [ ], /* size n. Bnz [j] = # nonzeros in column j of B. * Reduce since B is pruned of dead nodes. */ Int CParent [ ], /* CParent [i] = j if component with repnode j is * the parent of the component with repnode i. * CParent [i] = EMPTY if the component with * repnode i is a root of the separator tree. * CParent [i] is -2 if i is not a repnode. */ Int Cstack [ ], /* component stack for nested dissection */ Int *top, /* Cstack [0..top] contains root nodes of the * the components currently in the stack */ /* workspace, undefined on input and output: */ Int Queue [ ], /* size n, for breadth-first search */ cholmod_common *Common ) { Int n, mark, cj, j, sj, sn, p, i, snode, pstart, pdest, pend, nd_components, part, first, save_mark ; Int *Bp, *Bi, *Flag ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ PRINT2 (("find components: cn %d\n", cn)) ; Flag = Common->Flag ; /* size n */ /* force initialization of Flag [Map [0..cn-1]] */ save_mark = Common->mark ; /* save the current mark */ Common->mark = EMPTY ; /* clear Flag; preserve Flag [Map [i]] if Flag [Map [i]] already < EMPTY */ /* this takes O(cn) time */ mark = clear_flag (Map, cn, Common) ; Bp = B->p ; Bi = B->i ; n = B->nrow ; ASSERT (cnode >= EMPTY && cnode < n) ; ASSERT (IMPLIES (cnode >= 0, Flag [cnode] < EMPTY)) ; /* get ordering parameters */ nd_components = Common->method [Common->current].nd_components ; /* ---------------------------------------------------------------------- */ /* find the connected components of C via a breadth-first search */ /* ---------------------------------------------------------------------- */ part = (Part == NULL) ? 0 : 1 ; /* examine each part (part 1 and then part 0) */ for (part = (Part == NULL) ? 0 : 1 ; part >= 0 ; part--) { /* first is TRUE for the first connected component in each part */ first = TRUE ; /* find all connected components in the current part */ for (cj = 0 ; cj < cn ; cj++) { /* get node snode, which is node cj of C. It might already be in * the separator of C (and thus ordered, with Flag [snode] < EMPTY) */ snode = (Map == NULL) ? (cj) : (Map [cj]) ; ASSERT (snode >= 0 && snode < n) ; if (Flag [snode] >= EMPTY && Flag [snode] < mark && ((Part == NULL) || Part [cj] == part)) { /* ---------------------------------------------------------- */ /* find new connected component S */ /* ---------------------------------------------------------- */ /* node snode is the repnode of a connected component S, the * parent of which is cnode, the repnode of C. If cnode is * EMPTY then C is the original graph B. */ PRINT2 (("----------:::snode "ID" cnode "ID"\n", snode, cnode)); ASSERT (CParent [snode] == -2) ; if (first || nd_components) { /* If this is the first node in this part, then it becomes * the repnode of all components in this part, and all * components in this part form a single node in the * separator tree. If nd_components is TRUE, then all * connected components form their own node in the * separator tree. */ CParent [snode] = cnode ; } /* place j in the queue and mark it */ Queue [0] = snode ; Flag [snode] = mark ; sn = 1 ; /* breadth-first traversal, starting at node j */ for (sj = 0 ; sj < sn ; sj++) { /* get node j from head of Queue and traverse its edges */ j = Queue [sj] ; PRINT2 ((" j: "ID"\n", j)) ; ASSERT (j >= 0 && j < n) ; ASSERT (Flag [j] == mark) ; pstart = Bp [j] ; pdest = pstart ; pend = pstart + Bnz [j] ; for (p = pstart ; p < pend ; p++) { i = Bi [p] ; if (i != j && Flag [i] >= EMPTY) { /* node is still in the graph */ Bi [pdest++] = i ; if (Flag [i] < mark) { /* node i is in this component S, and unflagged * (first time node i has been seen in this BFS) * place node i in the queue and mark it */ Queue [sn++] = i ; Flag [i] = mark ; } } } /* edges to dead nodes have been removed */ Bnz [j] = pdest - pstart ; } /* ---------------------------------------------------------- */ /* order S if it is small; place it on Cstack otherwise */ /* ---------------------------------------------------------- */ PRINT2 (("sn "ID"\n", sn)) ; /* place the new component on the Cstack. Flip the node if * is the first connected component of the current part, * or if all components are treated as their own node in * the separator tree. */ Cstack [++(*top)] = (first || nd_components) ? FLIP (snode) : snode ; first = FALSE ; } } } /* restore the flag (normally taking O(1) time except for Int overflow) */ Common->mark = save_mark++ ; clear_flag (NULL, 0, Common) ; DEBUG (for (i = 0 ; i < n ; i++) ASSERT (Flag [i] < Common->mark)) ; } /* ========================================================================== */ /* === cholmod_bisect ======================================================= */ /* ========================================================================== */ /* Finds a node bisector of A, A*A', A(:,f)*A(:,f)'. * * workspace: Flag (nrow), * Iwork (nrow if symmetric, max (nrow,ncol) if unsymmetric). * Allocates a temporary matrix B=A*A' or B=A, * and O(nnz(A)) temporary memory space. */ SuiteSparse_long CHOLMOD(bisect) /* returns # of nodes in separator */ ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to bisect */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int compress, /* if TRUE, compress the graph first */ /* ---- output --- */ Int *Partition, /* size A->nrow. Node i is in the left graph if * Partition [i] = 0, the right graph if 1, and in the * separator if 2. */ /* --------------- */ cholmod_common *Common ) { Int *Bp, *Bi, *Hash, *Cmap, *Bnw, *Bew, *Iwork ; cholmod_sparse *B ; unsigned Int hash ; Int j, n, bnz, sepsize, p, pend ; size_t csize, s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_NULL (Partition, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* quick return */ /* ---------------------------------------------------------------------- */ n = A->nrow ; if (n == 0) { return (0) ; } /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = n + MAX (n, A->ncol) */ s = CHOLMOD(add_size_t) (A->nrow, MAX (A->nrow, A->ncol), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (EMPTY) ; } CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (EMPTY) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; Iwork = Common->Iwork ; Hash = Iwork ; /* size n, (i/l/l) */ Cmap = Iwork + n ; /* size n, (i/i/l) */ /* ---------------------------------------------------------------------- */ /* convert the matrix to adjacency list form */ /* ---------------------------------------------------------------------- */ /* The input graph to must be symmetric, with no diagonal entries * present. The columns need not be sorted. */ /* B = A, A*A', or A(:,f)*A(:,f)', upper and lower parts present */ if (A->stype) { /* Add the upper/lower part to a symmetric lower/upper matrix by * converting to unsymmetric mode */ /* workspace: Iwork (nrow) */ B = CHOLMOD(copy) (A, 0, -1, Common) ; } else { /* B = A*A' or A(:,f)*A(:,f)', no diagonal */ /* workspace: Flag (nrow), Iwork (max (nrow,ncol)) */ B = CHOLMOD(aat) (A, fset, fsize, -1, Common) ; } if (Common->status < CHOLMOD_OK) { return (EMPTY) ; } Bp = B->p ; Bi = B->i ; bnz = Bp [n] ; ASSERT ((Int) (B->nrow) == n && (Int) (B->ncol) == n) ; /* B does not include the diagonal, and both upper and lower parts. * Common->anz includes the diagonal, and just the lower part of B */ Common->anz = bnz / 2 + ((double) n) ; /* Bew should be at least size n for the hash function to work well */ /* this cannot cause overflow, because the matrix is already created */ csize = MAX (((size_t) n) + 1, (size_t) bnz) ; /* create the graph using Flag as workspace for node weights [ */ Bnw = Common->Flag ; /* size n workspace */ /* compute hash for each node if compression requested */ if (compress) { for (j = 0 ; j < n ; j++) { hash = j ; pend = Bp [j+1] ; for (p = Bp [j] ; p < pend ; p++) { hash += Bi [p] ; ASSERT (Bi [p] != j) ; } /* finalize the hash key for node j */ hash %= csize ; Hash [j] = (Int) hash ; ASSERT (Hash [j] >= 0 && Hash [j] < csize) ; } } /* allocate edge weights */ Bew = CHOLMOD(malloc) (csize, sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&B, Common) ; CHOLMOD(free) (csize, sizeof (Int), Bew, Common) ; return (EMPTY) ; } /* graph has unit node and edge weights */ for (j = 0 ; j < n ; j++) { Bnw [j] = 1 ; } for (s = 0 ; s < csize ; s++) { Bew [s] = 1 ; } /* ---------------------------------------------------------------------- */ /* compress and partition the graph */ /* ---------------------------------------------------------------------- */ sepsize = partition ( #ifndef NDEBUG csize, #endif compress, Hash, B, Bnw, Bew, Cmap, Partition, Common) ; /* contents of Bp, Bi, Bnw, and Bew no longer needed ] */ /* If partition fails, free the workspace below and return sepsize < 0 */ /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ B->ncol = n ; /* restore size for memory usage statistics */ CHOLMOD(free_sparse) (&B, Common) ; Common->mark = EMPTY ; CHOLMOD_CLEAR_FLAG (Common) ; CHOLMOD(free) (csize, sizeof (Int), Bew, Common) ; return (sepsize) ; } /* ========================================================================== */ /* === cholmod_nested_dissection ============================================ */ /* ========================================================================== */ /* This method uses a node bisector, applied recursively (but using a * non-recursive algorithm). Once the graph is partitioned, it calls a * constrained min degree code (CAMD or CSYMAMD for A+A', and CCOLAMD for A*A') * to order all the nodes in the graph - but obeying the constraints determined * by the separators. This routine is similar to METIS_NodeND, except for how * it treats the leaf nodes. METIS_NodeND orders the leaves of the separator * tree with MMD, ignoring the rest of the matrix when ordering a single leaf. * This routine orders the whole matrix with CSYMAMD or CCOLAMD, all at once, * when the graph partitioning is done. * * This function also returns a postorderd separator tree (CParent), and a * mapping of nodes in the graph to nodes in the separator tree (Cmember). * * workspace: Flag (nrow), Head (nrow+1), Iwork (4*nrow + (ncol if unsymmetric)) * Allocates a temporary matrix B=A*A' or B=A, * and O(nnz(A)) temporary memory space. * Allocates an additional 3*n*sizeof(Int) temporary workspace */ SuiteSparse_long CHOLMOD(nested_dissection) /* returns # of components, or -1 if error */ ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ Int *Perm, /* size A->nrow, output permutation */ Int *CParent, /* size A->nrow. On output, CParent [c] is the parent * of component c, or EMPTY if c is a root, and where * c is in the range 0 to # of components minus 1 */ Int *Cmember, /* size A->nrow. Cmember [j] = c if node j of A is * in component c */ /* --------------- */ cholmod_common *Common ) { double prune_dense, nd_oksep ; Int *Bp, *Bi, *Bnz, *Cstack, *Imap, *Map, *Flag, *Head, *Next, *Bnw, *Iwork, *Ipost, *NewParent, *Hash, *Cmap, *Cp, *Ci, *Cew, *Cnw, *Part, *Post, *Work3n ; unsigned Int hash ; Int n, bnz, top, i, j, k, cnode, cdense, p, cj, cn, ci, cnz, mark, c, uncol, sepsize, parent, ncomponents, threshold, ndense, pstart, pdest, pend, nd_compress, nd_camd, csize, jnext, nd_small, total_weight, nchild, child = EMPTY ; cholmod_sparse *B, *C ; size_t s ; int ok = TRUE ; DEBUG (Int cnt) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_NULL (Perm, EMPTY) ; RETURN_IF_NULL (CParent, EMPTY) ; RETURN_IF_NULL (Cmember, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* quick return */ /* ---------------------------------------------------------------------- */ n = A->nrow ; if (n == 0) { return (1) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* get ordering parameters */ prune_dense = Common->method [Common->current].prune_dense ; nd_compress = Common->method [Common->current].nd_compress ; nd_oksep = Common->method [Common->current].nd_oksep ; nd_oksep = MAX (0, nd_oksep) ; nd_oksep = MIN (1, nd_oksep) ; nd_camd = Common->method [Common->current].nd_camd ; nd_small = Common->method [Common->current].nd_small ; nd_small = MAX (4, nd_small) ; PRINT0 (("nd_components %d nd_small %d nd_oksep %g\n", Common->method [Common->current].nd_components, nd_small, nd_oksep)) ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 4*n + uncol */ uncol = (A->stype == 0) ? A->ncol : 0 ; s = CHOLMOD(mult_size_t) (n, 4, &ok) ; s = CHOLMOD(add_size_t) (s, uncol, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (EMPTY) ; } CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (EMPTY) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Flag = Common->Flag ; /* size n */ Head = Common->Head ; /* size n+1, all equal to -1 */ Iwork = Common->Iwork ; Imap = Iwork ; /* size n, same as Queue in find_components */ Map = Iwork + n ; /* size n */ Bnz = Iwork + 2*((size_t) n) ; /* size n */ Hash = Iwork + 3*((size_t) n) ; /* size n */ Work3n = CHOLMOD(malloc) (n, 3*sizeof (Int), Common) ; Part = Work3n ; /* size n */ Bnw = Part + n ; /* size n */ Cnw = Bnw + n ; /* size n */ Cstack = Perm ; /* size n, use Perm as workspace for Cstack [ */ Cmap = Cmember ; /* size n, use Cmember as workspace [ */ if (Common->status < CHOLMOD_OK) { return (EMPTY) ; } /* ---------------------------------------------------------------------- */ /* convert B to symmetric form with both upper/lower parts present */ /* ---------------------------------------------------------------------- */ /* B = A+A', A*A', or A(:,f)*A(:,f)', upper and lower parts present */ if (A->stype) { /* Add the upper/lower part to a symmetric lower/upper matrix by * converting to unsymmetric mode */ /* workspace: Iwork (nrow) */ B = CHOLMOD(copy) (A, 0, -1, Common) ; } else { /* B = A*A' or A(:,f)*A(:,f)', no diagonal */ /* workspace: Flag (nrow), Iwork (max (nrow,ncol)) */ B = CHOLMOD(aat) (A, fset, fsize, -1, Common) ; } if (Common->status < CHOLMOD_OK) { CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ; return (EMPTY) ; } Bp = B->p ; Bi = B->i ; bnz = CHOLMOD(nnz) (B, Common) ; ASSERT ((Int) (B->nrow) == n && (Int) (B->ncol) == n) ; csize = MAX (n, bnz) ; ASSERT (CHOLMOD(dump_sparse) (B, "B for nd:", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* initializations */ /* ---------------------------------------------------------------------- */ /* all nodes start out unmarked and unordered (Type 4, see below) */ Common->mark = EMPTY ; CHOLMOD_CLEAR_FLAG (Common) ; ASSERT (Flag == Common->Flag) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; for (j = 0 ; j < n ; j++) { CParent [j] = -2 ; } /* prune dense nodes from B */ if (IS_NAN (prune_dense) || prune_dense < 0) { /* only remove completely dense nodes */ threshold = n-2 ; } else { /* remove nodes with degree more than threshold */ threshold = (Int) (MAX (16, prune_dense * sqrt ((double) (n)))) ; threshold = MIN (n, threshold) ; } ndense = 0 ; cnode = EMPTY ; cdense = EMPTY ; for (j = 0 ; j < n ; j++) { Bnz [j] = Bp [j+1] - Bp [j] ; if (Bnz [j] > threshold) { /* node j is dense, prune it from B */ PRINT2 (("j is dense %d\n", j)) ; ndense++ ; if (cnode == EMPTY) { /* first dense node found becomes root of this component, * which contains all of the dense nodes found here */ cdense = j ; cnode = j ; CParent [cnode] = EMPTY ; } Flag [j] = FLIP (cnode) ; } } B->packed = FALSE ; ASSERT (B->nz == NULL) ; if (ndense == n) { /* all nodes removed: Perm is identity, all nodes in component zero, * and the separator tree has just one node. */ PRINT2 (("all nodes are dense\n")) ; for (k = 0 ; k < n ; k++) { Perm [k] = k ; Cmember [k] = 0 ; } CParent [0] = EMPTY ; CHOLMOD(free_sparse) (&B, Common) ; CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ; Common->mark = EMPTY ; CHOLMOD_CLEAR_FLAG (Common) ; return (1) ; } /* Cp and Ci are workspace to construct the subgraphs to partition */ C = CHOLMOD(allocate_sparse) (n, n, csize, FALSE, TRUE, 0, CHOLMOD_PATTERN, Common) ; Cew = CHOLMOD(malloc) (csize, sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&C, Common) ; CHOLMOD(free_sparse) (&B, Common) ; CHOLMOD(free) (csize, sizeof (Int), Cew, Common) ; CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ; Common->mark = EMPTY ; CHOLMOD_CLEAR_FLAG (Common) ; PRINT2 (("out of memory for C, etc\n")) ; return (EMPTY) ; } Cp = C->p ; Ci = C->i ; /* create initial unit node and edge weights */ for (j = 0 ; j < n ; j++) { Bnw [j] = 1 ; } for (p = 0 ; p < csize ; p++) { Cew [p] = 1 ; } /* push the initial connnected components of B onto the Cstack */ top = EMPTY ; /* Cstack is empty */ /* workspace: Flag (nrow), Iwork (nrow); use Imap as workspace for Queue [*/ find_components (B, NULL, n, cnode, NULL, Bnz, CParent, Cstack, &top, Imap, Common) ; /* done using Imap as workspace for Queue ] */ /* Nodes can now be of Type 0, 1, 2, or 4 (see definition below) */ /* ---------------------------------------------------------------------- */ /* while Cstack is not empty, do: */ /* ---------------------------------------------------------------------- */ while (top >= 0) { /* clear the Flag array, but do not modify negative entries in Flag */ mark = clear_flag (NULL, 0, Common) ; DEBUG (for (i = 0 ; i < n ; i++) Imap [i] = EMPTY) ; /* ------------------------------------------------------------------ */ /* get node(s) from the top of the Cstack */ /* ------------------------------------------------------------------ */ /* i is the repnode of its (unordered) connected component. Get * all repnodes for all connected components of a single part. If * each connected component is to be ordered separately (nd_components * is TRUE), then this while loop iterates just once. */ cnode = EMPTY ; cn = 0 ; while (cnode == EMPTY) { i = Cstack [top--] ; if (i < 0) { /* this is the last node in this component */ i = FLIP (i) ; cnode = i ; } ASSERT (i >= 0 && i < n && Flag [i] >= EMPTY) ; /* place i in the queue and mark it */ Map [cn] = i ; Flag [i] = mark ; Imap [i] = cn ; cn++ ; } ASSERT (cnode != EMPTY) ; /* During ordering, there are five kinds of nodes in the graph of B, * based on Flag [j] and CParent [j] for nodes j = 0 to n-1: * * Type 0: If cnode is a repnode of an unordered component, then * CParent [cnode] is in the range EMPTY to n-1 and * Flag [cnode] >= EMPTY. This is a "live" node. * * Type 1: If cnode is a repnode of an ordered separator component, * then Flag [cnode] < EMPTY and FLAG [cnode] = FLIP (cnode). * CParent [cnode] is in the range EMPTY to n-1. cnode is a root of * the separator tree if CParent [cnode] == EMPTY. This node is dead. * * Type 2: If node j isn't a repnode, has not been absorbed via * graph compression into another node, but is in an ordered separator * component, then cnode = FLIP (Flag [j]) gives the repnode of the * component that contains j and CParent [j] is -2. This node is dead. * Note that Flag [j] < EMPTY. * * Type 3: If node i has been absorbed via graph compression into some * other node j = FLIP (Flag [i]) where j is not a repnode. * CParent [j] is -2. Node i may or may not be in an ordered * component. This node is dead. Note that Flag [j] < EMPTY. * * Type 4: If node j is "live" (not in an ordered component, and not * absorbed into any other node), then Flag [j] >= EMPTY. * * Only "live" nodes (of type 0 or 4) are placed in a subgraph to be * partitioned. Node j is alive if Flag [j] >= EMPTY, and dead if * Flag [j] < EMPTY. */ /* ------------------------------------------------------------------ */ /* create the subgraph for this connected component C */ /* ------------------------------------------------------------------ */ /* Do a breadth-first search of the graph starting at cnode. * use Map [0..cn-1] for nodes in the component C [ * use Cnw and Cew for node and edge weights of the resulting subgraph [ * use Cp and Ci for the resulting subgraph [ * use Imap [i] for all nodes i in B that are in the component C [ */ cnz = 0 ; total_weight = 0 ; for (cj = 0 ; cj < cn ; cj++) { /* get node j from the head of the queue; it is node cj of C */ j = Map [cj] ; ASSERT (Flag [j] == mark) ; Cp [cj] = cnz ; Cnw [cj] = Bnw [j] ; ASSERT (Cnw [cj] >= 0) ; total_weight += Cnw [cj] ; pstart = Bp [j] ; pdest = pstart ; pend = pstart + Bnz [j] ; hash = cj ; for (p = pstart ; p < pend ; p++) { i = Bi [p] ; /* prune diagonal entries and dead edges from B */ if (i != j && Flag [i] >= EMPTY) { /* live node i is in the current component */ Bi [pdest++] = i ; if (Flag [i] != mark) { /* First time node i has been seen, it is a new node * of C. place node i in the queue and mark it */ Map [cn] = i ; Flag [i] = mark ; Imap [i] = cn ; cn++ ; } /* place the edge (cj,ci) in the adjacency list of cj */ ci = Imap [i] ; ASSERT (ci >= 0 && ci < cn && ci != cj && cnz < csize) ; Ci [cnz++] = ci ; hash += ci ; } } /* edges to dead nodes have been removed */ Bnz [j] = pdest - pstart ; /* finalize the hash key for column j */ hash %= csize ; Hash [cj] = (Int) hash ; ASSERT (Hash [cj] >= 0 && Hash [cj] < csize) ; } Cp [cn] = cnz ; C->nrow = cn ; C->ncol = cn ; /* affects mem stats unless restored when C free'd */ /* contents of Imap no longer needed ] */ #ifndef NDEBUG for (cj = 0 ; cj < cn ; cj++) { j = Map [cj] ; PRINT2 (("----------------------------C column cj: "ID" j: "ID"\n", cj, j)) ; ASSERT (j >= 0 && j < n) ; ASSERT (Flag [j] >= EMPTY) ; for (p = Cp [cj] ; p < Cp [cj+1] ; p++) { ci = Ci [p] ; i = Map [ci] ; PRINT3 (("ci: "ID" i: "ID"\n", ci, i)) ; ASSERT (ci != cj && ci >= 0 && ci < cn) ; ASSERT (i != j && i >= 0 && i < n) ; ASSERT (Flag [i] >= EMPTY) ; } } #endif PRINT0 (("consider cn %d nd_small %d ", cn, nd_small)) ; if (cn < nd_small) /* could be 'total_weight < nd_small' instead */ { /* place all nodes in the separator */ PRINT0 ((" too small\n")) ; sepsize = total_weight ; } else { /* Cp and Ci now contain the component, with cn nodes and cnz * nonzeros. The mapping of a node cj into node j the main graph * B is given by Map [cj] = j */ PRINT0 ((" cut\n")) ; /* -------------------------------------------------------------- */ /* compress and partition the graph C */ /* -------------------------------------------------------------- */ /* The edge weights Cew [0..csize-1] are all 1's on input to and * output from the partition routine. */ sepsize = partition ( #ifndef NDEBUG csize, #endif nd_compress, Hash, C, Cnw, Cew, Cmap, Part, Common) ; /* contents of Cp and Ci no longer needed ] */ if (sepsize < 0) { /* failed */ C->ncol = n ; /* restore size for memory usage statistics */ CHOLMOD(free_sparse) (&C, Common) ; CHOLMOD(free_sparse) (&B, Common) ; CHOLMOD(free) (csize, sizeof (Int), Cew, Common) ; CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ; Common->mark = EMPTY ; CHOLMOD_CLEAR_FLAG (Common) ; return (EMPTY) ; } /* -------------------------------------------------------------- */ /* compress B based on how C was compressed */ /* -------------------------------------------------------------- */ for (ci = 0 ; ci < cn ; ci++) { if (Hash [ci] < EMPTY) { /* ci is dead in C, having been absorbed into cj */ cj = FLIP (Hash [ci]) ; PRINT2 (("In C, "ID" absorbed into "ID" (wgt now "ID")\n", ci, cj, Cnw [cj])) ; /* i is dead in B, having been absorbed into j */ i = Map [ci] ; j = Map [cj] ; PRINT2 (("In B, "ID" (wgt "ID") => "ID" (wgt "ID")\n", i, Bnw [i], j, Bnw [j], Cnw [cj])) ; /* more than one node may be absorbed into j. This is * accounted for in Cnw [cj]. Assign it here rather * than += Bnw [i] */ Bnw [i] = 0 ; Bnw [j] = Cnw [cj] ; Flag [i] = FLIP (j) ; } } DEBUG (for (cnt = 0, j = 0 ; j < n ; j++) cnt += Bnw [j]) ; ASSERT (cnt == n) ; } /* contents of Cnw [0..cn-1] no longer needed ] */ /* ------------------------------------------------------------------ */ /* order the separator, and stack the components when C is split */ /* ------------------------------------------------------------------ */ /* one more component has been found: either the separator of C, * or all of C */ ASSERT (sepsize >= 0 && sepsize <= total_weight) ; PRINT0 (("sepsize %d tot %d : %8.4f ", sepsize, total_weight, ((double) sepsize) / ((double) total_weight))) ; if (sepsize == total_weight || sepsize == 0 || sepsize > nd_oksep * total_weight) { /* Order the nodes in the component. The separator is too large, * or empty. Note that the partition routine cannot return a * sepsize of zero, but it can return a separator consisting of the * whole graph. The "sepsize == 0" test is kept, above, in case the * partition routine changes. In either case, this component * remains unsplit, and becomes a leaf of the separator tree. */ PRINT2 (("cnode %d sepsize zero or all of graph: "ID"\n", cnode, sepsize)) ; for (cj = 0 ; cj < cn ; cj++) { j = Map [cj] ; Flag [j] = FLIP (cnode) ; PRINT2 ((" node cj: "ID" j: "ID" ordered\n", cj, j)) ; } ASSERT (Flag [cnode] == FLIP (cnode)) ; ASSERT (cnode != EMPTY && Flag [cnode] < EMPTY) ; PRINT0 (("discarded\n")) ; } else { /* Order the nodes in the separator of C and find a new repnode * cnode that is in the separator of C. This requires the separator * to be non-empty. */ PRINT0 (("sepsize not tiny: "ID"\n", sepsize)) ; parent = CParent [cnode] ; ASSERT (parent >= EMPTY && parent < n) ; CParent [cnode] = -2 ; cnode = EMPTY ; for (cj = 0 ; cj < cn ; cj++) { j = Map [cj] ; if (Part [cj] == 2) { /* All nodes in the separator become part of a component * whose repnode is cnode */ PRINT2 (("node cj: "ID" j: "ID" ordered\n", cj, j)) ; if (cnode == EMPTY) { PRINT2(("------------new cnode: cj "ID" j "ID"\n", cj, j)) ; cnode = j ; } Flag [j] = FLIP (cnode) ; } else { PRINT2 ((" node cj: "ID" j: "ID" not ordered\n", cj, j)) ; } } ASSERT (cnode != EMPTY && Flag [cnode] < EMPTY) ; ASSERT (CParent [cnode] == -2) ; CParent [cnode] = parent ; /* find the connected components when C is split, and push * them on the Cstack. Use Imap as workspace for Queue. [ */ /* workspace: Flag (nrow) */ find_components (B, Map, cn, cnode, Part, Bnz, CParent, Cstack, &top, Imap, Common) ; /* done using Imap as workspace for Queue ] */ } /* contents of Map [0..cn-1] no longer needed ] */ } /* done using Cmember as workspace for Cmap ] */ /* done using Perm as workspace for Cstack ] */ /* ---------------------------------------------------------------------- */ /* place nodes removed via compression into their proper component */ /* ---------------------------------------------------------------------- */ /* At this point, all nodes are of Type 1, 2, or 3, as defined above. */ for (i = 0 ; i < n ; i++) { /* find the repnode cnode that contains node i */ j = FLIP (Flag [i]) ; PRINT2 (("\nfind component for "ID", in: "ID"\n", i, j)) ; ASSERT (j >= 0 && j < n) ; DEBUG (cnt = 0) ; while (CParent [j] == -2) { j = FLIP (Flag [j]) ; PRINT2 ((" walk up to "ID" ", j)) ; ASSERT (j >= 0 && j < n) ; PRINT2 ((" CParent "ID"\n", CParent [j])) ; ASSERT (cnt < n) ; DEBUG (cnt++) ; } cnode = j ; ASSERT (cnode >= 0 && cnode < n) ; ASSERT (CParent [cnode] >= EMPTY && CParent [cnode] < n) ; PRINT2 (("i "ID" is in component with cnode "ID"\n", i, cnode)) ; ASSERT (Flag [cnode] == FLIP (cnode)) ; /* Mark all nodes along the path from i to cnode as being in the * component whos repnode is cnode. Perform path compression. */ j = FLIP (Flag [i]) ; Flag [i] = FLIP (cnode) ; DEBUG (cnt = 0) ; while (CParent [j] == -2) { ASSERT (j >= 0 && j < n) ; jnext = FLIP (Flag [j]) ; PRINT2 ((" "ID" walk "ID" set cnode to "ID"\n", i, j, cnode)) ; ASSERT (cnt < n) ; DEBUG (cnt++) ; Flag [j] = FLIP (cnode) ; j = jnext ; } } /* At this point, all nodes fall into Types 1 or 2, as defined above. */ #ifndef NDEBUG for (j = 0 ; j < n ; j++) { PRINT2 (("j %d CParent %d ", j, CParent [j])) ; if (CParent [j] >= EMPTY && CParent [j] < n) { /* case 1: j is a repnode of a component */ cnode = j ; PRINT2 ((" a repnode\n")) ; } else { /* case 2: j is not a repnode of a component */ cnode = FLIP (Flag [j]) ; PRINT2 ((" repnode is %d\n", cnode)) ; ASSERT (cnode >= 0 && cnode < n) ; ASSERT (CParent [cnode] >= EMPTY && CParent [cnode] < n) ; } ASSERT (Flag [cnode] == FLIP (cnode)) ; /* case 3 no longer holds */ } #endif /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ C->ncol = n ; /* restore size for memory usage statistics */ CHOLMOD(free_sparse) (&C, Common) ; CHOLMOD(free_sparse) (&B, Common) ; CHOLMOD(free) (csize, sizeof (Int), Cew, Common) ; CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ; /* ---------------------------------------------------------------------- */ /* handle dense nodes */ /* ---------------------------------------------------------------------- */ /* The separator tree has nodes with either no children or two or more * children - with one exception. There may exist a single root node with * exactly one child, which holds the dense rows/columns of the matrix. * Delete this node if it exists. */ if (ndense > 0) { ASSERT (CParent [cdense] == EMPTY) ; /* cdense has no parent */ /* find the children of cdense */ nchild = 0 ; for (j = 0 ; j < n ; j++) { if (CParent [j] == cdense) { nchild++ ; child = j ; } } if (nchild == 1) { /* the cdense node has just one child; merge the two nodes */ PRINT1 (("root has one child\n")) ; CParent [cdense] = -2 ; /* cdense is deleted */ CParent [child] = EMPTY ; /* child becomes a root */ for (j = 0 ; j < n ; j++) { if (Flag [j] == FLIP (cdense)) { /* j is a dense node */ PRINT1 (("dense %d\n", j)) ; Flag [j] = FLIP (child) ; } } } } /* ---------------------------------------------------------------------- */ /* postorder the components */ /* ---------------------------------------------------------------------- */ DEBUG (for (cnt = 0, j = 0 ; j < n ; j++) if (CParent [j] != -2) cnt++) ; /* use Cmember as workspace for Post [ */ Post = Cmember ; /* cholmod_postorder uses Head and Iwork [0..2n]. It does not use Flag, * which here holds the mapping of nodes to repnodes. It ignores all nodes * for which CParent [j] < -1, so it operates just on the repnodes. */ /* workspace: Head (n), Iwork (2*n) */ ncomponents = CHOLMOD(postorder) (CParent, n, NULL, Post, Common) ; ASSERT (cnt == ncomponents) ; /* use Iwork [0..n-1] as workspace for Ipost ( */ Ipost = Iwork ; DEBUG (for (j = 0 ; j < n ; j++) Ipost [j] = EMPTY) ; /* compute inverse postorder */ for (c = 0 ; c < ncomponents ; c++) { cnode = Post [c] ; ASSERT (cnode >= 0 && cnode < n) ; Ipost [cnode] = c ; ASSERT (Head [c] == EMPTY) ; } /* adjust the parent array */ /* Iwork [n..2n-1] used for NewParent [ */ NewParent = Iwork + n ; for (c = 0 ; c < ncomponents ; c++) { parent = CParent [Post [c]] ; NewParent [c] = (parent == EMPTY) ? EMPTY : (Ipost [parent]) ; } for (c = 0 ; c < ncomponents ; c++) { CParent [c] = NewParent [c] ; } ASSERT (CHOLMOD(dump_parent) (CParent, ncomponents, "CParent", Common)) ; /* Iwork [n..2n-1] no longer needed for NewParent ] */ /* Cmember no longer needed for Post ] */ #ifndef NDEBUG /* count the number of children of each node */ for (c = 0 ; c < ncomponents ; c++) { Cmember [c] = 0 ; } for (c = 0 ; c < ncomponents ; c++) { if (CParent [c] != EMPTY) Cmember [CParent [c]]++ ; } for (c = 0 ; c < ncomponents ; c++) { /* a node is either a leaf, or has 2 or more children */ ASSERT (Cmember [c] == 0 || Cmember [c] >= 2) ; } #endif /* ---------------------------------------------------------------------- */ /* place each node in its component */ /* ---------------------------------------------------------------------- */ for (j = 0 ; j < n ; j++) { /* node j is in the cth component, whose repnode is cnode */ cnode = FLIP (Flag [j]) ; PRINT2 (("j "ID" flag "ID" cnode "ID"\n", j, Flag [j], FLIP (Flag [j]))) ; ASSERT (cnode >= 0 && cnode < n) ; c = Ipost [cnode] ; ASSERT (c >= 0 && c < ncomponents) ; Cmember [j] = c ; } /* Flag no longer needed for the node-to-component mapping */ /* done using Iwork [0..n-1] as workspace for Ipost ) */ /* ---------------------------------------------------------------------- */ /* clear the Flag array */ /* ---------------------------------------------------------------------- */ Common->mark = EMPTY ; CHOLMOD_CLEAR_FLAG (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* find the permutation */ /* ---------------------------------------------------------------------- */ PRINT1 (("nd_camd: %d A->stype %d\n", nd_camd, A->stype)) ; if (nd_camd) { /* ------------------------------------------------------------------ */ /* apply camd, csymamd, or ccolamd using the Cmember constraints */ /* ------------------------------------------------------------------ */ if (A->stype != 0) { /* ordering A+A', so fset and fsize are ignored. * Add the upper/lower part to a symmetric lower/upper matrix by * converting to unsymmetric mode * workspace: Iwork (nrow) */ B = CHOLMOD(copy) (A, 0, -1, Common) ; if (Common->status < CHOLMOD_OK) { PRINT0 (("make symmetric failed\n")) ; return (EMPTY) ; } ASSERT ((Int) (B->nrow) == n && (Int) (B->ncol) == n) ; PRINT2 (("nested dissection (2)\n")) ; B->stype = -1 ; if (nd_camd == 2) { /* workspace: Head (nrow+1), Iwork (nrow) if symmetric-upper */ ok = CHOLMOD(csymamd) (B, Cmember, Perm, Common) ; } else { /* workspace: Head (nrow), Iwork (4*nrow) */ ok = CHOLMOD(camd) (B, NULL, 0, Cmember, Perm, Common) ; } CHOLMOD(free_sparse) (&B, Common) ; if (!ok) { /* failed */ PRINT0 (("camd/csymamd failed\n")) ; return (EMPTY) ; } } else { /* ordering A*A' or A(:,f)*A(:,f)' */ /* workspace: Iwork (nrow if no fset; MAX(nrow,ncol) if fset) */ if (!CHOLMOD(ccolamd) (A, fset, fsize, Cmember, Perm, Common)) { /* ccolamd failed */ PRINT2 (("ccolamd failed\n")) ; return (EMPTY) ; } } } else { /* ------------------------------------------------------------------ */ /* natural ordering of each component */ /* ------------------------------------------------------------------ */ /* use Iwork [0..n-1] for Next [ */ Next = Iwork ; /* ------------------------------------------------------------------ */ /* place the nodes in link lists, one list per component */ /* ------------------------------------------------------------------ */ /* do so in reverse order, to preserve original ordering */ for (j = n-1 ; j >= 0 ; j--) { /* node j is in the cth component */ c = Cmember [j] ; ASSERT (c >= 0 && c < ncomponents) ; /* place node j in link list for component c */ Next [j] = Head [c] ; Head [c] = j ; } /* ------------------------------------------------------------------ */ /* order each node in each component */ /* ------------------------------------------------------------------ */ k = 0 ; for (c = 0 ; c < ncomponents ; c++) { for (j = Head [c] ; j != EMPTY ; j = Next [j]) { Perm [k++] = j ; } Head [c] = EMPTY ; } ASSERT (k == n) ; /* done using Iwork [0..n-1] for Next ] */ } /* ---------------------------------------------------------------------- */ /* clear workspace and return number of components */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (ncomponents) ; } /* ========================================================================== */ /* === cholmod_collapse_septree ============================================= */ /* ========================================================================== */ /* cholmod_nested_dissection returns the separator tree that was used in the * constrained minimum degree algorithm. Parameter settings (nd_small, * nd_oksep, etc) that give a good fill-reducing ordering may give too fine of * a separator tree for other uses (parallelism, multi-level LPDASA, etc). This * function takes as input the separator tree computed by * cholmod_nested_dissection, and collapses selected subtrees into single * nodes. A subtree is collapsed if its root node (the separator) is large * compared to the total number of nodes in the subtree, or if the subtree is * small. Note that the separator tree may actually be a forest. * * nd_oksep and nd_small act just like the ordering parameters in Common. * Returns the new number of nodes in the separator tree. */ SuiteSparse_long CHOLMOD(collapse_septree) ( /* ---- input ---- */ size_t n, /* # of nodes in the graph */ size_t ncomponents, /* # of nodes in the separator tree (must be <= n) */ double nd_oksep, /* collapse if #sep >= nd_oksep * #nodes in subtree */ size_t nd_small, /* collapse if #nodes in subtree < nd_small */ /* ---- in/out --- */ Int *CParent, /* size ncomponents; from cholmod_nested_dissection */ Int *Cmember, /* size n; from cholmod_nested_dissection */ /* --------------- */ cholmod_common *Common ) { Int *First, *Count, *Csubtree, *W, *Map ; Int c, j, k, nc, sepsize, total_weight, parent, nc_new, first ; int collapse = FALSE, ok = TRUE ; size_t s ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (CParent, EMPTY) ; RETURN_IF_NULL (Cmember, EMPTY) ; if (n < ncomponents) { ERROR (CHOLMOD_INVALID, "invalid separator tree") ; return (EMPTY) ; } Common->status = CHOLMOD_OK ; nc = ncomponents ; if (n <= 1 || ncomponents <= 1) { /* no change; tree is one node already */ return (nc) ; } nd_oksep = MAX (0, nd_oksep) ; nd_oksep = MIN (1, nd_oksep) ; nd_small = MAX (4, nd_small) ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 3*ncomponents */ s = CHOLMOD(mult_size_t) (ncomponents, 3, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (EMPTY) ; } CHOLMOD(allocate_work) (0, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (EMPTY) ; } W = Common->Iwork ; Count = W ; W += ncomponents ; /* size ncomponents */ Csubtree = W ; W += ncomponents ; /* size ncomponents */ First = W ; W += ncomponents ; /* size ncomponents */ /* ---------------------------------------------------------------------- */ /* find the first descendant of each node of the separator tree */ /* ---------------------------------------------------------------------- */ for (c = 0 ; c < nc ; c++) { First [c] = EMPTY ; } for (k = 0 ; k < nc ; k++) { for (c = k ; c != EMPTY && First [c] == -1 ; c = CParent [c]) { ASSERT (c >= 0 && c < nc) ; First [c] = k ; } } /* ---------------------------------------------------------------------- */ /* find the number of nodes of the graph in each node of the tree */ /* ---------------------------------------------------------------------- */ for (c = 0 ; c < nc ; c++) { Count [c] = 0 ; } for (j = 0 ; j < (Int) n ; j++) { ASSERT (Cmember [j] >= 0 && Cmember [j] < nc) ; Count [Cmember [j]]++ ; } /* ---------------------------------------------------------------------- */ /* find the number of nodes in each subtree */ /* ---------------------------------------------------------------------- */ for (c = 0 ; c < nc ; c++) { /* each subtree includes its root */ Csubtree [c] = Count [c] ; PRINT1 ((ID" size "ID" parent "ID" first "ID"\n", c, Count [c], CParent [c], First [c])) ; } for (c = 0 ; c < nc ; c++) { /* add the subtree of the child, c, into the count of its parent */ parent = CParent [c] ; ASSERT (parent >= EMPTY && parent < nc) ; if (parent != EMPTY) { Csubtree [parent] += Csubtree [c] ; } } #ifndef NDEBUG /* the sum of the roots should be n */ j = 0 ; for (c = 0 ; c < nc ; c++) if (CParent [c] == EMPTY) j += Csubtree [c] ; ASSERT (j == (Int) n) ; #endif /* ---------------------------------------------------------------------- */ /* find subtrees to collapse */ /* ---------------------------------------------------------------------- */ /* consider all nodes in reverse post-order */ for (c = nc-1 ; c >= 0 ; c--) { /* consider the subtree rooted at node c */ sepsize = Count [c] ; total_weight = Csubtree [c] ; PRINT1 (("Node "ID" sepsize "ID" subtree "ID" ratio %g\n", c, sepsize, total_weight, ((double) sepsize)/((double) total_weight))) ; first = First [c] ; if (first < c && /* c must not be a leaf */ (sepsize > nd_oksep * total_weight || total_weight < (int) nd_small)) { /* this separator is too large, or the subtree is too small. * collapse the tree, by converting the entire subtree rooted at * c into a single node. The subtree consists of all nodes from * First[c] to the root c. Flag all nodes from First[c] to c-1 * as dead. */ collapse = TRUE ; for (k = first ; k < c ; k++) { CParent [k] = -2 ; PRINT1 ((" collapse node "ID"\n", k)) ; } /* continue at the next node, first-1 */ c = first ; } } PRINT1 (("collapse: %d\n", collapse)) ; /* ---------------------------------------------------------------------- */ /* compress the tree */ /* ---------------------------------------------------------------------- */ Map = Count ; /* Count no longer needed */ nc_new = nc ; if (collapse) { nc_new = 0 ; for (c = 0 ; c < nc ; c++) { Map [c] = nc_new ; if (CParent [c] >= EMPTY) { /* node c is alive, and becomes node Map[c] in the new tree. * Increment nc_new for the next node c. */ nc_new++ ; } } PRINT1 (("Collapse the tree from "ID" to "ID" nodes\n", nc, nc_new)) ; ASSERT (nc_new > 0) ; for (c = 0 ; c < nc ; c++) { parent = CParent [c] ; if (parent >= EMPTY) { /* node c is alive */ CParent [Map [c]] = (parent == EMPTY) ? EMPTY : Map [parent] ; } } for (j = 0 ; j < (Int) n ; j++) { PRINT1 (("j "ID" Cmember[j] "ID" Map[Cmember[j]] "ID"\n", j, Cmember [j], Map [Cmember [j]])) ; Cmember [j] = Map [Cmember [j]] ; } } /* ---------------------------------------------------------------------- */ /* return new size of separator tree */ /* ---------------------------------------------------------------------- */ return (nc_new) ; } #endif Matrix/src/CHOLMOD/Partition/cholmod_csymamd.c0000644000175100001440000001114512271765436020706 0ustar hornikusers/* ========================================================================== */ /* === Partition/cholmod_csymamd ============================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Partition Module. * Copyright (C) 2005-2013, Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* CHOLMOD interface to the CSYMAMD ordering routine. Finds a permutation * p such that the Cholesky factorization of PAP' is sparser than A. * The column etree is found and postordered, and the CSYMAMD * ordering is then combined with its postordering. If A is unsymmetric, * A+A' is ordered (A must be square). * * workspace: Head (nrow+1) * * Supports any xtype (pattern, real, complex, or zomplex). */ #ifndef NCAMD #include "cholmod_internal.h" #include "ccolamd.h" #include "cholmod_camd.h" #if (CCOLAMD_VERSION < CCOLAMD_VERSION_CODE (2,5)) #error "CCOLAMD v2.0 or later is required" #endif /* ========================================================================== */ /* === cholmod_csymamd ====================================================== */ /* ========================================================================== */ int CHOLMOD(csymamd) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ /* ---- output --- */ Int *Cmember, /* size nrow. see cholmod_ccolamd.c for description */ Int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) { double knobs [CCOLAMD_KNOBS] ; Int *perm, *Head ; Int ok, i, nrow, stats [CCOLAMD_STATS] ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (Perm, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; if (A->nrow != A->ncol || !(A->packed)) { ERROR (CHOLMOD_INVALID, "matrix must be square and packed") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ CHOLMOD(allocate_work) (nrow, 0, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* order the matrix (does not affect A->p or A->i) */ /* ---------------------------------------------------------------------- */ perm = Common->Head ; /* size nrow+1 (i/l/l) */ /* get parameters */ #ifdef LONG ccolamd_l_set_defaults (knobs) ; #else ccolamd_set_defaults (knobs) ; #endif if (Common->current >= 0 && Common->current < CHOLMOD_MAXMETHODS) { /* get the knobs from the Common parameters */ knobs [CCOLAMD_DENSE_ROW] =Common->method[Common->current].prune_dense ; knobs [CCOLAMD_AGGRESSIVE]=Common->method[Common->current].aggressive ; } { #ifdef LONG csymamd_l (nrow, A->i, A->p, perm, knobs, stats, Common->calloc_memory, Common->free_memory, Cmember, A->stype) ; #else csymamd (nrow, A->i, A->p, perm, knobs, stats, Common->calloc_memory, Common->free_memory, Cmember, A->stype) ; #endif ok = stats [CCOLAMD_STATUS] ; } if (ok == CCOLAMD_ERROR_out_of_memory) { ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ; } ok = (ok == CCOLAMD_OK || ok == CCOLAMD_OK_BUT_JUMBLED) ; /* ---------------------------------------------------------------------- */ /* free the workspace and return result */ /* ---------------------------------------------------------------------- */ /* permutation returned in perm [0..n-1] */ for (i = 0 ; i < nrow ; i++) { Perm [i] = perm [i] ; } /* clear Head workspace (used for perm, in csymamd): */ Head = Common->Head ; for (i = 0 ; i <= nrow ; i++) { Head [i] = EMPTY ; } return (ok) ; } #endif Matrix/src/CHOLMOD/Partition/cholmod_camd.c0000644000175100001440000001724612271765436020165 0ustar hornikusers/* ========================================================================== */ /* === Partition/cholmod_camd =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Partition Module. Copyright (C) 2005-2013, Timothy A. Davis * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* CHOLMOD interface to the CAMD ordering routine. Orders A if the matrix is * symmetric. On output, Perm [k] = i if row/column i of A is the kth * row/column of P*A*P'. This corresponds to A(p,p) in MATLAB notation. * * If A is unsymmetric, cholmod_camd orders A*A'. On output, Perm [k] = i if * row/column i of A*A' is the kth row/column of P*A*A'*P'. This corresponds to * A(p,:)*A(p,:)' in MATLAB notation. If f is present, A(p,f)*A(p,f)' is * ordered. * * Computes the flop count for a subsequent LL' factorization, the number * of nonzeros in L, and the number of nonzeros in the matrix ordered (A, * A*A' or A(:,f)*A(:,f)'). * * workspace: Iwork (4*nrow). Head (nrow). * * Allocates a temporary copy of A+A' or A*A' (with * both upper and lower triangular parts) as input to CAMD. * Also allocates 3*(n+1) additional integer workspace (not in Common). * * Supports any xtype (pattern, real, complex, or zomplex) */ #ifndef NCAMD #include "cholmod_internal.h" #include "camd.h" #include "cholmod_camd.h" #if (CAMD_VERSION < CAMD_VERSION_CODE (2,0)) #error "CAMD v2.0 or later is required" #endif /* ========================================================================== */ /* === cholmod_camd ========================================================= */ /* ========================================================================== */ int CHOLMOD(camd) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ Int *Cmember, /* size nrow. see cholmod_ccolamd.c for description.*/ /* ---- output ---- */ Int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) { double Info [CAMD_INFO], Control2 [CAMD_CONTROL], *Control ; Int *Cp, *Len, *Nv, *Head, *Elen, *Degree, *Wi, *Next, *BucketSet, *Work3n, *p ; cholmod_sparse *C ; Int j, n, cnz ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; n = A->nrow ; /* s = 4*n */ s = CHOLMOD(mult_size_t) (n, 4, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } RETURN_IF_NULL (Perm, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; if (n == 0) { /* nothing to do */ Common->fl = 0 ; Common->lnz = 0 ; Common->anz = 0 ; return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ /* cholmod_analyze has allocated Cmember at Common->Iwork + 5*n+uncol, and * CParent at Common->Iwork + 4*n+uncol, where uncol is 0 if A is symmetric * or A->ncol otherwise. Thus, only the first 4n integers in Common->Iwork * can be used here. */ CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } p = Common->Iwork ; Degree = p ; p += n ; /* size n */ Elen = p ; p += n ; /* size n */ Len = p ; p += n ; /* size n */ Nv = p ; p += n ; /* size n */ Work3n = CHOLMOD(malloc) (n+1, 3*sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } p = Work3n ; Next = p ; p += n ; /* size n */ Wi = p ; p += (n+1) ; /* size n+1 */ BucketSet = p ; /* size n */ Head = Common->Head ; /* size n+1 */ /* ---------------------------------------------------------------------- */ /* construct the input matrix for CAMD */ /* ---------------------------------------------------------------------- */ if (A->stype == 0) { /* C = A*A' or A(:,f)*A(:,f)', add extra space of nnz(C)/2+n to C */ C = CHOLMOD(aat) (A, fset, fsize, -2, Common) ; } else { /* C = A+A', but use only the upper triangular part of A if A->stype = 1 * and only the lower part of A if A->stype = -1. Add extra space of * nnz(C)/2+n to C. */ C = CHOLMOD(copy) (A, 0, -2, Common) ; } if (Common->status < CHOLMOD_OK) { /* out of memory, fset invalid, or other error */ CHOLMOD(free) (n+1, 3*sizeof (Int), Work3n, Common) ; return (FALSE) ; } Cp = C->p ; for (j = 0 ; j < n ; j++) { Len [j] = Cp [j+1] - Cp [j] ; } /* C does not include the diagonal, and both upper and lower parts. * Common->anz includes the diagonal, and just the lower part of C */ cnz = Cp [n] ; Common->anz = cnz / 2 + n ; /* ---------------------------------------------------------------------- */ /* order C using CAMD */ /* ---------------------------------------------------------------------- */ /* get parameters */ if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS) { /* use CAMD defaults */ Control = NULL ; } else { Control = Control2 ; Control [CAMD_DENSE] = Common->method [Common->current].prune_dense ; Control [CAMD_AGGRESSIVE] = Common->method [Common->current].aggressive; } /* CAMD_2 does not use camd_malloc and camd_free, but set these pointers * just be safe. */ camd_malloc = Common->malloc_memory ; camd_free = Common->free_memory ; camd_calloc = Common->calloc_memory ; camd_realloc = Common->realloc_memory ; /* CAMD_2 doesn't print anything either, but future versions might, * so set the camd_printf pointer too. */ camd_printf = Common->print_function ; #ifdef LONG /* DEBUG (camd_l_debug_init ("cholmod_l_camd")) ; */ camd_l2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen, Degree, Wi, Control, Info, Cmember, BucketSet) ; #else /* DEBUG (camd_debug_init ("cholmod_camd")) ; */ camd_2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen, Degree, Wi, Control, Info, Cmember, BucketSet) ; #endif /* LL' flop count. Need to subtract n for LL' flop count. Note that this * is a slight upper bound which is often exact (see CAMD/Source/camd_2.c * for details). cholmod_analyze computes an exact flop count and * fill-in. */ Common->fl = Info [CAMD_NDIV] + 2 * Info [CAMD_NMULTSUBS_LDL] + n ; /* Info [CAMD_LNZ] excludes the diagonal */ Common->lnz = n + Info [CAMD_LNZ] ; /* ---------------------------------------------------------------------- */ /* free the CAMD workspace and clear the persistent workspace in Common */ /* ---------------------------------------------------------------------- */ ASSERT (IMPLIES (Common->status == CHOLMOD_OK, CHOLMOD(dump_perm) (Perm, n, n, "CAMD2 perm", Common))) ; CHOLMOD(free_sparse) (&C, Common) ; for (j = 0 ; j <= n ; j++) { Head [j] = EMPTY ; } CHOLMOD(free) (n+1, 3*sizeof (Int), Work3n, Common) ; return (TRUE) ; } #endif Matrix/src/CHOLMOD/Partition/cholmod_ccolamd.c0000644000175100001440000001504012271765436020651 0ustar hornikusers/* ========================================================================== */ /* === Partition/cholmod_ccolamd ============================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Partition Module. * Copyright (C) 2005-2013, Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* CHOLMOD interface to the CCOLAMD ordering routine. Finds a permutation * p such that the Cholesky factorization of PAA'P' is sparser than AA'. * The column etree is found and postordered, and the ccolamd ordering is then * combined with its postordering. A must be unsymmetric. * * workspace: Iwork (MAX (nrow,ncol)) * Allocates a copy of its input matrix, which is * then used as CCOLAMD's workspace. * * Supports any xtype (pattern, real, complex, or zomplex). */ #ifndef NCAMD #include "cholmod_internal.h" #include "ccolamd.h" #include "cholmod_camd.h" #if (CCOLAMD_VERSION < CCOLAMD_VERSION_CODE (2,5)) #error "CCOLAMD v2.0 or later is required" #endif /* ========================================================================== */ /* === ccolamd_interface ==================================================== */ /* ========================================================================== */ /* Order with ccolamd */ static int ccolamd_interface ( cholmod_sparse *A, size_t alen, Int *Perm, Int *Cmember, Int *fset, Int fsize, cholmod_sparse *C, cholmod_common *Common ) { double knobs [CCOLAMD_KNOBS] ; Int *Cp = NULL ; Int ok, k, nrow, ncol, stats [CCOLAMD_STATS] ; nrow = A->nrow ; ncol = A->ncol ; /* ---------------------------------------------------------------------- */ /* copy (and transpose) the input matrix A into the ccolamd workspace */ /* ---------------------------------------------------------------------- */ /* C = A (:,f)', which also packs A if needed. */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset non-NULL) */ ok = CHOLMOD(transpose_unsym) (A, 0, NULL, fset, fsize, C, Common) ; /* ---------------------------------------------------------------------- */ /* order the matrix (destroys the contents of C->i and C->p) */ /* ---------------------------------------------------------------------- */ /* get parameters */ #ifdef LONG ccolamd_l_set_defaults (knobs) ; #else ccolamd_set_defaults (knobs) ; #endif if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS) { /* this is the CHOLMOD default, not the CCOLAMD default */ knobs [CCOLAMD_DENSE_ROW] = -1 ; } else { /* get the knobs from the Common parameters */ knobs [CCOLAMD_DENSE_COL] =Common->method[Common->current].prune_dense ; knobs [CCOLAMD_DENSE_ROW] =Common->method[Common->current].prune_dense2; knobs [CCOLAMD_AGGRESSIVE]=Common->method[Common->current].aggressive ; knobs [CCOLAMD_LU] =Common->method[Common->current].order_for_lu; } if (ok) { #ifdef LONG ccolamd_l (ncol, nrow, alen, C->i, C->p, knobs, stats, Cmember) ; #else ccolamd (ncol, nrow, alen, C->i, C->p, knobs, stats, Cmember) ; #endif ok = stats [CCOLAMD_STATUS] ; ok = (ok == CCOLAMD_OK || ok == CCOLAMD_OK_BUT_JUMBLED) ; /* permutation returned in C->p, if the ordering succeeded */ Cp = C->p ; for (k = 0 ; k < nrow ; k++) { Perm [k] = Cp [k] ; } } return (ok) ; } /* ========================================================================== */ /* === cholmod_ccolamd ====================================================== */ /* ========================================================================== */ /* Order AA' or A(:,f)*A(:,f)' using CCOLAMD. */ int CHOLMOD(ccolamd) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ Int *Cmember, /* size A->nrow. Cmember [i] = c if row i is in the * constraint set c. c must be >= 0. The # of * constraint sets is max (Cmember) + 1. If Cmember is * NULL, then it is interpretted as Cmember [i] = 0 for * all i */ /* ---- output --- */ Int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *C ; Int ok, nrow, ncol ; size_t alen ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (Perm, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (A->stype != 0) { ERROR (CHOLMOD_INVALID, "matrix must be unsymmetric") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; ncol = A->ncol ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ #ifdef LONG alen = ccolamd_l_recommended (A->nzmax, ncol, nrow) ; #else alen = ccolamd_recommended (A->nzmax, ncol, nrow) ; #endif if (alen == 0) { ERROR (CHOLMOD_TOO_LARGE, "matrix invalid or too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (0, MAX (nrow,ncol), 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } C = CHOLMOD(allocate_sparse) (ncol, nrow, alen, TRUE, TRUE, 0, CHOLMOD_PATTERN, Common) ; /* ---------------------------------------------------------------------- */ /* order with ccolamd */ /* ---------------------------------------------------------------------- */ ok = ccolamd_interface (A, alen, Perm, Cmember, fset, fsize, C, Common) ; /* ---------------------------------------------------------------------- */ /* free the workspace and return result */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&C, Common) ; return (ok) ; } #endif Matrix/src/CHOLMOD/Partition/cholmod_metis.c0000644000175100001440000006376712271765436020413 0ustar hornikusers/* ========================================================================== */ /* === Partition/cholmod_metis ============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Partition Module. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* CHOLMOD interface to the METIS package (Version 4.0.1): * * cholmod_metis_bisector: * * Wrapper for METIS_NodeComputeSeparator. Finds a set of nodes that * partitions the graph into two parts. * * cholmod_metis: * * Wrapper for METIS_NodeND, METIS's own nested dissection algorithm. * Typically faster than cholmod_nested_dissection, mostly because it * uses minimum degree on just the leaves of the separator tree, rather * than the whole matrix. * * Note that METIS does not return an error if it runs out of memory. Instead, * it terminates the program. This interface attempts to avoid that problem * by preallocating space that should be large enough for any memory allocations * within METIS, and then freeing that space, just before the call to METIS. * While this is not guaranteed to work, it is very unlikely to fail. If you * encounter this problem, increase Common->metis_memory. If you don't mind * having your program terminated, set Common->metis_memory to zero (a value of * 2.0 is usually safe). Several other METIS workarounds are made in the * routines in this file. See the description of metis_memory_ok, just below, * for more details. * * FUTURE WORK: interfaces to other partitioners (CHACO, SCOTCH, JOSTLE, ... ) * * workspace: several size-nz and size-n temporary arrays. Uses no workspace * in Common. * * Supports any xtype (pattern, real, complex, or zomplex). */ #ifndef NPARTITION #include "cholmod_internal.h" #undef ASSERT #include "metis.h" /* METIS has its own ASSERT that it reveals to the user, so remove it here: */ #undef ASSERT /* and redefine it back again */ #ifndef NDEBUG #define ASSERT(expression) (assert (expression)) #else #define ASSERT(expression) #endif #include "cholmod_partition.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === dumpgraph ============================================================ */ /* ========================================================================== */ /* For dumping the input graph to METIS_NodeND, to check with METIS's onmetis * and graphchk programs. For debugging only. To use, uncomment this #define: #define DUMP_GRAPH */ #ifdef DUMP_GRAPH #include /* After dumping the graph with this routine, run "onmetis metisgraph" */ static void dumpgraph (idxtype *Mp, idxtype *Mi, SuiteSparse_long n, cholmod_common *Common) { SuiteSparse_long i, j, p, nz ; FILE *f ; nz = Mp [n] ; printf ("Dumping METIS graph n %ld nz %ld\n", n, nz) ; /* DUMP_GRAPH */ f = fopen ("metisgraph", "w") ; if (f == NULL) { ERROR (-99, "cannot open metisgraph") ; return ; } fprintf (f, "%ld %ld\n", n, nz/2) ; /* DUMP_GRAPH */ for (j = 0 ; j < n ; j++) { for (p = Mp [j] ; p < Mp [j+1] ; p++) { i = Mi [p] ; fprintf (f, " %ld", i+1) ; /* DUMP_GRAPH */ } fprintf (f, "\n") ; /* DUMP_GRAPH */ } fclose (f) ; } #endif /* ========================================================================== */ /* === metis_memory_ok ====================================================== */ /* ========================================================================== */ /* METIS_NodeND and METIS_NodeComputeSeparator will terminate your program it * they run out of memory. In an attempt to workaround METIS' behavior, this * routine allocates a single block of memory of size equal to an observed * upper bound on METIS' memory usage. It then immediately deallocates the * block. If the allocation fails, METIS is not called. * * Median memory usage for a graph with n nodes and nz edges (counting each * edge twice, or both upper and lower triangular parts of a matrix) is * 4*nz + 40*n + 4096 integers. A "typical" upper bound is 10*nz + 50*n + 4096 * integers. Nearly all matrices tested fit within that upper bound, with the * exception two in the UF sparse matrix collection: Schenk_IBMNA/c-64 and * Gupta/gupta2. The latter exceeds the "upper bound" by a factor of just less * than 2. * * If you do not mind having your program terminated if it runs out of memory, * set Common->metis_memory to zero. Its default value is 2, which allows for * some memory fragmentation, and also accounts for the Gupta/gupta2 matrix. * * An alternative, if CHOLMOD is used in MATLAB, is to use a version of METIS * (4.0.2, perhaps) proposed to George Karypis. This version uses function * pointer for malloc and free. They can be set to mxMalloc and mxFree * (see sputil_config in MATLAB/sputil.c). On Linux, with gcc, you must also * compile CHOLMOD, METIS, AMD, COLAMD, and CCOLAMD with the -fexceptions * compiler flag. With this configuration, mxMalloc safely aborts the * mexFunction, frees all memory allocted by METIS, and safely returns to * MATLAB. You may then set Common->metis_memory = 0. */ #define GUESS(nz,n) (10 * (nz) + 50 * (n) + 4096) static int metis_memory_ok ( Int n, Int nz, cholmod_common *Common ) { double s ; void *p ; size_t metis_guard ; if (Common->metis_memory <= 0) { /* do not prevent METIS from running out of memory */ return (TRUE) ; } n = MAX (1, n) ; nz = MAX (0, nz) ; /* compute in double, to avoid integer overflow */ s = GUESS ((double) nz, (double) n) ; s *= Common->metis_memory ; if (s * sizeof (idxtype) >= ((double) Size_max)) { /* don't even attempt to malloc such a large block */ return (FALSE) ; } /* recompute in size_t */ metis_guard = GUESS ((size_t) nz, (size_t) n) ; metis_guard *= Common->metis_memory ; /* attempt to malloc the block */ p = CHOLMOD(malloc) (metis_guard, sizeof (idxtype), Common) ; if (p == NULL) { /* failure - return out-of-memory condition */ return (FALSE) ; } /* success - free the block */ CHOLMOD(free) (metis_guard, sizeof (idxtype), p, Common) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_metis_bisector =============================================== */ /* ========================================================================== */ /* Finds a set of nodes that bisects the graph of A or AA' (direct interface * to METIS_NodeComputeSeparator). * * The input matrix A must be square, symmetric (with both upper and lower * parts present) and with no diagonal entries. These conditions are NOT * checked. */ SuiteSparse_long CHOLMOD(metis_bisector) /* returns separator size */ ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to bisect */ Int *Anw, /* size A->nrow, node weights */ Int *Aew, /* size nz, edge weights */ /* ---- output --- */ Int *Partition, /* size A->nrow */ /* --------------- */ cholmod_common *Common ) { Int *Ap, *Ai ; idxtype *Mp, *Mi, *Mnw, *Mew, *Mpart ; Int n, nleft, nright, j, p, csep, total_weight, lightest, nz ; int Opt [8], nn, csp ; size_t n1 ; DEBUG (Int nsep) ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_NULL (Anw, EMPTY) ; RETURN_IF_NULL (Aew, EMPTY) ; RETURN_IF_NULL (Partition, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; if (A->stype || A->nrow != A->ncol) { /* A must be square, with both upper and lower parts present */ ERROR (CHOLMOD_INVALID, "matrix must be square, symmetric," " and with both upper/lower parts present") ; return (EMPTY) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* quick return */ /* ---------------------------------------------------------------------- */ n = A->nrow ; if (n == 0) { return (0) ; } n1 = ((size_t) n) + 1 ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; nz = Ap [n] ; /* ---------------------------------------------------------------------- */ /* METIS does not have a 64-bit integer version */ /* ---------------------------------------------------------------------- */ #ifdef LONG if (sizeof (Int) > sizeof (idxtype) && MAX (n,nz) > INT_MAX / sizeof (int)) { /* CHOLMOD's matrix is too large for METIS */ return (EMPTY) ; } #endif /* ---------------------------------------------------------------------- */ /* set default options */ /* ---------------------------------------------------------------------- */ Opt [0] = 0 ; /* use defaults */ Opt [1] = 3 ; /* matching type */ Opt [2] = 1 ; /* init. partitioning algo*/ Opt [3] = 2 ; /* refinement algorithm */ Opt [4] = 0 ; /* no debug */ Opt [5] = 0 ; /* unused */ Opt [6] = 0 ; /* unused */ Opt [7] = -1 ; /* random seed */ DEBUG (for (j = 0 ; j < n ; j++) ASSERT (Anw [j] > 0)) ; /* ---------------------------------------------------------------------- */ /* copy Int to METIS idxtype, if necessary */ /* ---------------------------------------------------------------------- */ DEBUG (for (j = 0 ; j < nz ; j++) ASSERT (Aew [j] > 0)) ; if (sizeof (Int) == sizeof (idxtype)) { /* this is the typical case */ Mi = (idxtype *) Ai ; Mew = (idxtype *) Aew ; Mp = (idxtype *) Ap ; Mnw = (idxtype *) Anw ; Mpart = (idxtype *) Partition ; } else { /* idxtype and Int differ; copy the graph into the METIS idxtype */ Mi = CHOLMOD(malloc) (nz, sizeof (idxtype), Common) ; Mew = CHOLMOD(malloc) (nz, sizeof (idxtype), Common) ; Mp = CHOLMOD(malloc) (n1, sizeof (idxtype), Common) ; Mnw = CHOLMOD(malloc) (n, sizeof (idxtype), Common) ; Mpart = CHOLMOD(malloc) (n, sizeof (idxtype), Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ; CHOLMOD(free) (nz, sizeof (idxtype), Mew, Common) ; CHOLMOD(free) (n1, sizeof (idxtype), Mp, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mnw, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mpart, Common) ; return (EMPTY) ; } for (p = 0 ; p < nz ; p++) { Mi [p] = Ai [p] ; } for (p = 0 ; p < nz ; p++) { Mew [p] = Aew [p] ; } for (j = 0 ; j <= n ; j++) { Mp [j] = Ap [j] ; } for (j = 0 ; j < n ; j++) { Mnw [j] = Anw [j] ; } } /* ---------------------------------------------------------------------- */ /* METIS workaround: try to ensure METIS doesn't run out of memory */ /* ---------------------------------------------------------------------- */ if (!metis_memory_ok (n, nz, Common)) { /* METIS might ask for too much memory and thus terminate the program */ if (sizeof (Int) != sizeof (idxtype)) { CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ; CHOLMOD(free) (nz, sizeof (idxtype), Mew, Common) ; CHOLMOD(free) (n1, sizeof (idxtype), Mp, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mnw, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mpart, Common) ; } return (EMPTY) ; } /* ---------------------------------------------------------------------- */ /* partition the graph */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG PRINT1 (("Metis graph, n = "ID"\n", n)) ; for (j = 0 ; j < n ; j++) { Int ppp ; PRINT2 (("M(:,"ID") node weight "ID"\n", j, (Int) Mnw [j])) ; ASSERT (Mnw [j] > 0) ; for (ppp = Mp [j] ; ppp < Mp [j+1] ; ppp++) { PRINT3 ((" "ID" : "ID"\n", (Int) Mi [ppp], (Int) Mew [ppp])) ; ASSERT (Mi [ppp] != j) ; ASSERT (Mew [ppp] > 0) ; } } #endif nn = n ; METIS_NodeComputeSeparator (&nn, Mp, Mi, Mnw, Mew, Opt, &csp, Mpart) ; n = nn ; csep = csp ; PRINT1 (("METIS csep "ID"\n", csep)) ; /* ---------------------------------------------------------------------- */ /* copy the results back from idxtype, if required */ /* ---------------------------------------------------------------------- */ if (sizeof (Int) != sizeof (idxtype)) { for (j = 0 ; j < n ; j++) { Partition [j] = Mpart [j] ; } CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ; CHOLMOD(free) (nz, sizeof (idxtype), Mew, Common) ; CHOLMOD(free) (n1, sizeof (idxtype), Mp, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mnw, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mpart, Common) ; } /* ---------------------------------------------------------------------- */ /* ensure a reasonable separator */ /* ---------------------------------------------------------------------- */ /* METIS can return a valid separator with no nodes in (for example) the * left part. In this case, there really is no separator. CHOLMOD * prefers, in this case, for all nodes to be in the separator (and both * left and right parts to be empty). Also, if the graph is unconnected, * METIS can return a valid empty separator. CHOLMOD prefers at least one * node in the separator. Note that cholmod_nested_dissection only calls * this routine on connected components, but cholmod_bisect can call this * routine for any graph. */ if (csep == 0) { /* The separator is empty, select lightest node as separator. If * ties, select the highest numbered node. */ lightest = 0 ; for (j = 0 ; j < n ; j++) { if (Anw [j] <= Anw [lightest]) { lightest = j ; } } PRINT1 (("Force "ID" as sep\n", lightest)) ; Partition [lightest] = 2 ; csep = Anw [lightest] ; } /* determine the node weights in the left and right part of the graph */ nleft = 0 ; nright = 0 ; DEBUG (nsep = 0) ; for (j = 0 ; j < n ; j++) { PRINT1 (("Partition ["ID"] = "ID"\n", j, Partition [j])) ; if (Partition [j] == 0) { nleft += Anw [j] ; } else if (Partition [j] == 1) { nright += Anw [j] ; } #ifndef NDEBUG else { ASSERT (Partition [j] == 2) ; nsep += Anw [j] ; } #endif } ASSERT (csep == nsep) ; total_weight = nleft + nright + csep ; if (csep < total_weight) { /* The separator is less than the whole graph. Make sure the left and * right parts are either both empty or both non-empty. */ PRINT1 (("nleft "ID" nright "ID" csep "ID" tot "ID"\n", nleft, nright, csep, total_weight)) ; ASSERT (nleft + nright + csep == total_weight) ; ASSERT (nleft > 0 || nright > 0) ; if ((nleft == 0 && nright > 0) || (nleft > 0 && nright == 0)) { /* left or right is empty; put all nodes in the separator */ PRINT1 (("Force all in sep\n")) ; csep = total_weight ; for (j = 0 ; j < n ; j++) { Partition [j] = 2 ; } } } ASSERT (CHOLMOD(dump_partition) (n, Ap, Ai, Anw, Partition, csep, Common)) ; /* ---------------------------------------------------------------------- */ /* return the sum of the weights of nodes in the separator */ /* ---------------------------------------------------------------------- */ return (csep) ; } /* ========================================================================== */ /* === cholmod_metis ======================================================== */ /* ========================================================================== */ /* CHOLMOD wrapper for the METIS_NodeND ordering routine. Creates A+A', * A*A' or A(:,f)*A(:,f)' and then calls METIS_NodeND on the resulting graph. * This routine is comparable to cholmod_nested_dissection, except that it * calls METIS_NodeND directly, and it does not return the separator tree. * * workspace: Flag (nrow), Iwork (4*n+uncol) * Allocates a temporary matrix B=A*A' or B=A. */ int CHOLMOD(metis) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int postorder, /* if TRUE, follow with etree or coletree postorder */ /* ---- output --- */ Int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) { double d ; Int *Iperm, *Iwork, *Bp, *Bi ; idxtype *Mp, *Mi, *Mperm, *Miperm ; cholmod_sparse *B ; Int i, j, n, nz, p, identity, uncol ; int Opt [8], nn, zero = 0 ; size_t n1, s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (Perm, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* quick return */ /* ---------------------------------------------------------------------- */ n = A->nrow ; if (n == 0) { return (TRUE) ; } n1 = ((size_t) n) + 1 ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 4*n + uncol */ uncol = (A->stype == 0) ? A->ncol : 0 ; s = CHOLMOD(mult_size_t) (n, 4, &ok) ; s = CHOLMOD(add_size_t) (s, uncol, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* convert the matrix to adjacency list form */ /* ---------------------------------------------------------------------- */ /* The input graph for METIS must be symmetric, with both upper and lower * parts present, and with no diagonal entries. The columns need not be * sorted. * B = A+A', A*A', or A(:,f)*A(:,f)', upper and lower parts present */ if (A->stype) { /* Add the upper/lower part to a symmetric lower/upper matrix by * converting to unsymmetric mode */ /* workspace: Iwork (nrow) */ B = CHOLMOD(copy) (A, 0, -1, Common) ; } else { /* B = A*A' or A(:,f)*A(:,f)', no diagonal */ /* workspace: Flag (nrow), Iwork (max (nrow,ncol)) */ B = CHOLMOD(aat) (A, fset, fsize, -1, Common) ; } ASSERT (CHOLMOD(dump_sparse) (B, "B for NodeND", Common) >= 0) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (B->nrow == A->nrow) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; Iperm = Iwork ; /* size n (i/i/l) */ Bp = B->p ; Bi = B->i ; nz = Bp [n] ; /* ---------------------------------------------------------------------- */ /* METIS does not have a SuiteSparse_long integer version */ /* ---------------------------------------------------------------------- */ #ifdef LONG if (sizeof (Int) > sizeof (idxtype) && MAX (n,nz) > INT_MAX / sizeof (int)) { /* CHOLMOD's matrix is too large for METIS */ CHOLMOD(free_sparse) (&B, Common) ; return (FALSE) ; } #endif /* B does not include the diagonal, and both upper and lower parts. * Common->anz includes the diagonal, and just the lower part of B */ Common->anz = nz / 2 + n ; /* ---------------------------------------------------------------------- */ /* set control parameters for METIS_NodeND */ /* ---------------------------------------------------------------------- */ Opt [0] = 0 ; /* use defaults */ Opt [1] = 3 ; /* matching type */ Opt [2] = 1 ; /* init. partitioning algo*/ Opt [3] = 2 ; /* refinement algorithm */ Opt [4] = 0 ; /* no debug */ Opt [5] = 1 ; /* initial compression */ Opt [6] = 0 ; /* no dense node removal */ Opt [7] = 1 ; /* number of separators @ each step */ /* ---------------------------------------------------------------------- */ /* allocate the METIS input arrays, if needed */ /* ---------------------------------------------------------------------- */ if (sizeof (Int) == sizeof (idxtype)) { /* This is the typical case. */ Miperm = (idxtype *) Iperm ; Mperm = (idxtype *) Perm ; Mp = (idxtype *) Bp ; Mi = (idxtype *) Bi ; } else { /* allocate graph for METIS only if Int and idxtype differ */ Miperm = CHOLMOD(malloc) (n, sizeof (idxtype), Common) ; Mperm = CHOLMOD(malloc) (n, sizeof (idxtype), Common) ; Mp = CHOLMOD(malloc) (n1, sizeof (idxtype), Common) ; Mi = CHOLMOD(malloc) (nz, sizeof (idxtype), Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&B, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Miperm, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mperm, Common) ; CHOLMOD(free) (n1, sizeof (idxtype), Mp, Common) ; CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ; return (FALSE) ; } for (j = 0 ; j <= n ; j++) { Mp [j] = Bp [j] ; } for (p = 0 ; p < nz ; p++) { Mi [p] = Bi [p] ; } } /* ---------------------------------------------------------------------- */ /* METIS workarounds */ /* ---------------------------------------------------------------------- */ identity = FALSE ; if (nz == 0) { /* The matrix has no off-diagonal entries. METIS_NodeND fails in this * case, so avoid using it. The best permutation is identity anyway, * so this is an easy fix. */ identity = TRUE ; PRINT1 (("METIS:: no nz\n")) ; } else if (Common->metis_nswitch > 0) { /* METIS_NodeND in METIS 4.0.1 gives a seg fault with one matrix of * order n = 3005 and nz = 6,036,025, including the diagonal entries. * The workaround is to return the identity permutation instead of using * METIS for matrices of dimension 3000 or more and with density of 66% * or more - admittedly an uncertain fix, but such matrices are so dense * that any reasonable ordering will do, even identity (n^2 is only 50% * higher than nz in this case). CHOLMOD's nested dissection method * (cholmod_nested_dissection) has no problems with the same matrix, * even though it too uses METIS_NodeComputeSeparator. The matrix is * derived from LPnetlib/lpi_cplex1 in the UF sparse matrix collection. * If C is the lpi_cplex matrix (of order 3005-by-5224), A = (C*C')^2 * results in the seg fault. The seg fault also occurs in the stand- * alone onmetis program that comes with METIS. If a future version of * METIS fixes this problem, then set Common->metis_nswitch to zero. */ d = ((double) nz) / (((double) n) * ((double) n)) ; if (n > (Int) (Common->metis_nswitch) && d > Common->metis_dswitch) { identity = TRUE ; PRINT1 (("METIS:: nswitch/dswitch activated\n")) ; } } if (!identity && !metis_memory_ok (n, nz, Common)) { /* METIS might ask for too much memory and thus terminate the program */ identity = TRUE ; } /* ---------------------------------------------------------------------- */ /* find the permutation */ /* ---------------------------------------------------------------------- */ if (identity) { /* no need to do the postorder */ postorder = FALSE ; for (i = 0 ; i < n ; i++) { Mperm [i] = i ; } } else { #ifdef DUMP_GRAPH /* DUMP_GRAPH */ printf ("Calling METIS_NodeND n "ID" nz "ID"" "density %g\n", n, nz, ((double) nz) / (((double) n) * ((double) n))); dumpgraph (Mp, Mi, n, Common) ; #endif nn = n ; METIS_NodeND (&nn, Mp, Mi, &zero, Opt, Mperm, Miperm) ; n = nn ; PRINT0 (("METIS_NodeND done\n")) ; } /* ---------------------------------------------------------------------- */ /* free the METIS input arrays */ /* ---------------------------------------------------------------------- */ if (sizeof (Int) != sizeof (idxtype)) { for (i = 0 ; i < n ; i++) { Perm [i] = (Int) (Mperm [i]) ; } CHOLMOD(free) (n, sizeof (idxtype), Miperm, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mperm, Common) ; CHOLMOD(free) (n+1, sizeof (idxtype), Mp, Common) ; CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ; } CHOLMOD(free_sparse) (&B, Common) ; /* ---------------------------------------------------------------------- */ /* etree or column-etree postordering, using the Cholesky Module */ /* ---------------------------------------------------------------------- */ if (postorder) { Int *Parent, *Post, *NewPerm ; Int k ; Parent = Iwork + 2*((size_t) n) + uncol ; /* size n = nrow */ Post = Parent + n ; /* size n */ /* workspace: Iwork (2*nrow+uncol), Flag (nrow), Head (nrow+1) */ CHOLMOD(analyze_ordering) (A, CHOLMOD_METIS, Perm, fset, fsize, Parent, Post, NULL, NULL, NULL, Common) ; if (Common->status == CHOLMOD_OK) { /* combine the METIS permutation with its postordering */ NewPerm = Parent ; /* use Parent as workspace */ for (k = 0 ; k < n ; k++) { NewPerm [k] = Perm [Post [k]] ; } for (k = 0 ; k < n ; k++) { Perm [k] = NewPerm [k] ; } } } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; PRINT1 (("cholmod_metis done\n")) ; return (Common->status == CHOLMOD_OK) ; } #endif Matrix/src/CHOLMOD/Core/0000755000175100001440000000000012271765426014314 5ustar hornikusersMatrix/src/CHOLMOD/Core/cholmod_change_factor.c0000644000175100001440000011335512271765436020761 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_change_factor =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Change the numeric/symbolic, LL/LDL, simplicial/super, packed/unpacked, * monotonic/non-monotonic status of a cholmod_factor object. * * There are four basic classes of factor types: * * (1) simplicial symbolic: Consists of two size-n arrays: the fill-reducing * permutation (L->Perm) and the nonzero count for each column of L * (L->ColCount). All other factor types also include this information. * L->ColCount may be exact (obtained from the analysis routines), or * it may be a guess. During factorization, and certainly after update/ * downdate, the columns of L can have a different number of nonzeros. * L->ColCount is used to allocate space. L->ColCount is exact for the * supernodal factorizations. The nonzero pattern of L is not kept. * * (2) simplicial numeric: These represent L in a compressed column form. The * variants of this type are: * * LDL': L is unit diagonal. Row indices in column j are located in * L->i [L->p [j] ... L->p [j] + L->nz [j]], and corresponding numeric * values are in the same locations in L->x. The total number of * entries is the sum of L->nz [j]. The unit diagonal is not stored; * D is stored on the diagonal of L instead. L->p may or may not be * monotonic. The order of storage of the columns in L->i and L->x is * given by a doubly-linked list (L->prev and L->next). L->p is of * size n+1, but only the first n entries are used (it is used if L * is converted to a sparse matrix via cholmod_factor_to_sparse). * * For the complex case, L->x is stored interleaved with real/imag * parts, and is of size 2*lnz*sizeof(double). For the zomplex case, * L->x is of size lnz*sizeof(double) and holds the real part; L->z * is the same size and holds the imaginary part. * * LL': This is identical to the LDL' form, except that the non-unit * diagonal of L is stored as the first entry in each column of L. * * (3) supernodal symbolic: A representation of the nonzero pattern of the * supernodes for a supernodal factorization. There are L->nsuper * supernodes. Columns L->super [k] to L->super [k+1]-1 are in the kth * supernode. The row indices for the kth supernode are in * L->s [L->pi [k] ... L->pi [k+1]-1]. The numerical values are not * allocated (L->x), but when they are they will be located in * L->x [L->px [k] ... L->px [k+1]-1], and the L->px array is defined * in this factor type. * * For the complex case, L->x is stored interleaved with real/imag parts, * and is of size 2*L->xsize*sizeof(double). The zomplex supernodal case * is not supported, since it is not compatible with LAPACK and the BLAS. * * (4) supernodal numeric: Always an LL' factorization. L is non-unit * diagonal. L->x contains the numerical values of the supernodes, as * described above for the supernodal symbolic factor. * For the complex case, L->x is stored interleaved, and is of size * 2*L->xsize*sizeof(double). The zomplex supernodal case is not * supported, since it is not compatible with LAPACK and the BLAS. * * FUTURE WORK: support a supernodal LDL' factor. * * * In all cases, the row indices in each column (L->i for simplicial L and * L->s for supernodal L) are kept sorted from low indices to high indices. * This means the diagonal of L (or D for LDL' factors) is always kept as the * first entry in each column. * * The cholmod_change_factor routine can do almost all possible conversions. * It cannot do the following conversions: * * (1) Simplicial numeric types cannot be converted to a supernodal * symbolic type. This would simultaneously deallocate the * simplicial pattern and numeric values and reallocate uninitialized * space for the supernodal pattern. This isn't useful for the user, * and not needed by CHOLMOD's own routines either. * * (2) Only a symbolic factor (simplicial to supernodal) can be converted * to a supernodal numeric factor. * * Some conversions are meant only to be used internally by other CHOLMOD * routines, and should not be performed by the end user. They allocate space * whose contents are undefined: * * (1) converting from simplicial symbolic to supernodal symbolic. * (2) converting any factor to supernodal numeric. * * workspace: no conversion routine uses workspace in Common. No temporary * workspace is allocated. * * Supports all xtypes, except that there is no supernodal zomplex L. * * The to_xtype parameter is used only when converting from symbolic to numeric * or numeric to symbolic. It cannot be used to convert a numeric xtype (real, * complex, or zomplex) to a different numeric xtype. For that conversion, * use cholmod_factor_xtype instead. */ #include "cholmod_internal.h" #include "cholmod_core.h" static void natural_list (cholmod_factor *L) ; /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define REAL #include "t_cholmod_change_factor.c" #define COMPLEX #include "t_cholmod_change_factor.c" #define ZOMPLEX #include "t_cholmod_change_factor.c" /* ========================================================================== */ /* === L_is_packed ========================================================== */ /* ========================================================================== */ /* Return TRUE if the columns of L are packed, FALSE otherwise. For debugging * only. */ #ifndef NDEBUG static int L_is_packed (cholmod_factor *L, cholmod_common *Common) { Int j ; Int *Lnz = L->nz ; Int *Lp = L->p ; Int n = L->n ; if (L->xtype == CHOLMOD_PATTERN || L->is_super) { return (TRUE) ; } if (Lnz == NULL || Lp == NULL) { return (TRUE) ; } for (j = 0 ; j < n ; j++) { PRINT3 (("j: "ID" Lnz "ID" Lp[j+1] "ID" Lp[j] "ID"\n", j, Lnz [j], Lp [j+1], Lp [j])) ; if (Lnz [j] != (Lp [j+1] - Lp [j])) { PRINT2 (("L is not packed\n")) ; return (FALSE) ; } } return (TRUE) ; } #endif /* ========================================================================== */ /* === natural_list ========================================================= */ /* ========================================================================== */ /* Create a naturally-ordered doubly-linked list of columns. */ static void natural_list (cholmod_factor *L) { Int head, tail, n, j ; Int *Lnext, *Lprev ; Lnext = L->next ; Lprev = L->prev ; ASSERT (Lprev != NULL && Lnext != NULL) ; n = L->n ; head = n+1 ; tail = n ; Lnext [head] = 0 ; Lprev [head] = EMPTY ; Lnext [tail] = EMPTY ; Lprev [tail] = n-1 ; for (j = 0 ; j < n ; j++) { Lnext [j] = j+1 ; Lprev [j] = j-1 ; } Lprev [0] = head ; L->is_monotonic = TRUE ; } /* ========================================================================== */ /* === allocate_simplicial_numeric ========================================== */ /* ========================================================================== */ /* Allocate O(n) arrays for simplicial numeric factorization. Initializes * the link lists only. Does not allocate the L->i, L->x, or L->z arrays. */ static int allocate_simplicial_numeric ( cholmod_factor *L, cholmod_common *Common ) { Int n ; Int *Lp, *Lnz, *Lprev, *Lnext ; size_t n1, n2 ; PRINT1 (("Allocate simplicial\n")) ; ASSERT (L->xtype == CHOLMOD_PATTERN || L->is_super) ; ASSERT (L->p == NULL) ; ASSERT (L->nz == NULL) ; ASSERT (L->prev == NULL) ; ASSERT (L->next == NULL) ; n = L->n ; /* this cannot cause size_t overflow */ n1 = ((size_t) n) + 1 ; n2 = ((size_t) n) + 2 ; Lp = CHOLMOD(malloc) (n1, sizeof (Int), Common) ; Lnz = CHOLMOD(malloc) (n, sizeof (Int), Common) ; Lprev = CHOLMOD(malloc) (n2, sizeof (Int), Common) ; Lnext = CHOLMOD(malloc) (n2, sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free) (n1, sizeof (Int), Lp, Common) ; CHOLMOD(free) (n, sizeof (Int), Lnz, Common) ; CHOLMOD(free) (n2, sizeof (Int), Lprev, Common) ; CHOLMOD(free) (n2, sizeof (Int), Lnext, Common) ; PRINT1 (("Allocate simplicial failed\n")) ; return (FALSE) ; /* out of memory */ } /* ============================================== commit the changes to L */ L->p = Lp ; L->nz = Lnz ; L->prev = Lprev ; L->next = Lnext ; /* initialize a doubly linked list for columns in natural order */ natural_list (L) ; PRINT1 (("Allocate simplicial done\n")) ; return (TRUE) ; } /* ========================================================================== */ /* === simplicial_symbolic_to_super_symbolic ================================ */ /* ========================================================================== */ /* Convert a simplicial symbolic factor supernodal symbolic factor. Does not * initialize the new space. */ static int simplicial_symbolic_to_super_symbolic ( cholmod_factor *L, cholmod_common *Common ) { Int nsuper, xsize, ssize ; Int *Lsuper, *Lpi, *Lpx, *Ls ; size_t nsuper1 ; ASSERT (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) ; xsize = L->xsize ; ssize = L->ssize ; nsuper = L->nsuper ; nsuper1 = ((size_t) nsuper) + 1 ; PRINT1 (("simple sym to super sym: ssize "ID" xsize "ID" nsuper "ID"" " status %d\n", ssize, xsize, nsuper, Common->status)) ; /* O(nsuper) arrays, where nsuper <= n */ Lsuper = CHOLMOD(malloc) (nsuper1, sizeof (Int), Common) ; Lpi = CHOLMOD(malloc) (nsuper1, sizeof (Int), Common) ; Lpx = CHOLMOD(malloc) (nsuper1, sizeof (Int), Common) ; /* O(ssize) array, where ssize <= nnz(L), and usually much smaller */ Ls = CHOLMOD(malloc) (ssize, sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free) (nsuper1, sizeof (Int), Lsuper, Common) ; CHOLMOD(free) (nsuper1, sizeof (Int), Lpi, Common) ; CHOLMOD(free) (nsuper1, sizeof (Int), Lpx, Common) ; CHOLMOD(free) (ssize, sizeof (Int), Ls, Common) ; return (FALSE) ; /* out of memory */ } /* ============================================== commit the changes to L */ ASSERT (Lsuper != NULL && Lpi != NULL && Lpx != NULL && Ls != NULL) ; L->maxcsize = 0 ; L->maxesize = 0 ; L->super = Lsuper ; L->pi = Lpi ; L->px = Lpx ; L->s = Ls ; Ls [0] = EMPTY ; /* supernodal pattern undefined */ L->is_super = TRUE ; L->is_ll = TRUE ; /* supernodal LDL' not supported */ L->xtype = CHOLMOD_PATTERN ; L->dtype = DTYPE ; L->minor = L->n ; return (TRUE) ; } /* ========================================================================== */ /* === any_to_simplicial_symbolic =========================================== */ /* ========================================================================== */ /* Convert any factor L to a simplicial symbolic factor, leaving only L->Perm * and L->ColCount. Cannot fail. Any of the components of L (except Perm and * ColCount) may already be free'd. */ static void any_to_simplicial_symbolic ( cholmod_factor *L, int to_ll, cholmod_common *Common ) { Int n, lnz, xs, ss, s, e ; size_t n1, n2 ; /* ============================================== commit the changes to L */ n = L->n ; lnz = L->nzmax ; s = L->nsuper + 1 ; xs = (L->is_super) ? ((Int) (L->xsize)) : (lnz) ; e = (L->xtype == CHOLMOD_COMPLEX ? 2 : 1) ; ss = L->ssize ; /* this cannot cause size_t overflow */ n1 = ((size_t) n) + 1 ; n2 = ((size_t) n) + 2 ; /* free all but the symbolic analysis (Perm and ColCount) */ L->p = CHOLMOD(free) (n1, sizeof (Int), L->p, Common) ; L->i = CHOLMOD(free) (lnz, sizeof (Int), L->i, Common) ; L->x = CHOLMOD(free) (xs, e*sizeof (double), L->x, Common) ; L->z = CHOLMOD(free) (lnz, sizeof (double), L->z, Common) ; L->nz = CHOLMOD(free) (n, sizeof (Int), L->nz, Common) ; L->next = CHOLMOD(free) (n2, sizeof (Int), L->next, Common) ; L->prev = CHOLMOD(free) (n2, sizeof (Int), L->prev, Common) ; L->super = CHOLMOD(free) (s, sizeof (Int), L->super, Common) ; L->pi = CHOLMOD(free) (s, sizeof (Int), L->pi, Common) ; L->px = CHOLMOD(free) (s, sizeof (Int), L->px, Common) ; L->s = CHOLMOD(free) (ss, sizeof (Int), L->s, Common) ; L->nzmax = 0 ; L->is_super = FALSE ; L->xtype = CHOLMOD_PATTERN ; L->dtype = DTYPE ; L->minor = n ; L->is_ll = to_ll ; } /* ========================================================================== */ /* === ll_super_to_super_symbolic =========================================== */ /* ========================================================================== */ /* Convert a numerical supernodal L to symbolic supernodal. Cannot fail. */ static void ll_super_to_super_symbolic ( cholmod_factor *L, cholmod_common *Common ) { /* ============================================== commit the changes to L */ /* free all but the supernodal numerical factor */ ASSERT (L->xtype != CHOLMOD_PATTERN && L->is_super && L->is_ll) ; DEBUG (CHOLMOD(dump_factor) (L, "start to super symbolic", Common)) ; L->x = CHOLMOD(free) (L->xsize, (L->xtype == CHOLMOD_COMPLEX ? 2 : 1) * sizeof (double), L->x, Common) ; L->xtype = CHOLMOD_PATTERN ; L->dtype = DTYPE ; L->minor = L->n ; L->is_ll = TRUE ; /* supernodal LDL' not supported */ DEBUG (CHOLMOD(dump_factor) (L, "done to super symbolic", Common)) ; } /* ========================================================================== */ /* === simplicial_symbolic_to_simplicial_numeric ============================ */ /* ========================================================================== */ /* Convert a simplicial symbolic L to a simplicial numeric L; allocate space * for L using L->ColCount from symbolic analysis, and set L to identity. * * If packed < 0, then this routine is creating a copy of another factor * (via cholmod_copy_factor). In this case, the space is not initialized. */ static void simplicial_symbolic_to_simplicial_numeric ( cholmod_factor *L, int to_ll, int packed, int to_xtype, cholmod_common *Common ) { double grow0, grow1, xlen, xlnz ; double *Lx, *Lz ; Int *Li, *Lp, *Lnz, *ColCount ; Int n, grow, grow2, p, j, lnz, len, ok, e ; ASSERT (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) ; if (!allocate_simplicial_numeric (L, Common)) { PRINT1 (("out of memory, allocate simplicial numeric\n")) ; return ; /* out of memory */ } ASSERT (L->ColCount != NULL && L->nz != NULL && L->p != NULL) ; ASSERT (L->x == NULL && L->z == NULL && L->i == NULL) ; ColCount = L->ColCount ; Lnz = L->nz ; Lp = L->p ; ok = TRUE ; n = L->n ; if (packed < 0) { /* ------------------------------------------------------------------ */ /* used by cholmod_copy_factor to allocate a copy of a factor object */ /* ------------------------------------------------------------------ */ lnz = L->nzmax ; L->nzmax = 0 ; } else if (packed) { /* ------------------------------------------------------------------ */ /* LDL' or LL' packed */ /* ------------------------------------------------------------------ */ PRINT1 (("convert to packed LL' or LDL'\n")) ; lnz = 0 ; for (j = 0 ; ok && j < n ; j++) { /* ensure len is in the range 1 to n-j */ len = ColCount [j] ; len = MAX (1, len) ; len = MIN (len, n-j) ; lnz += len ; ok = (lnz >= 0) ; } for (j = 0 ; j <= n ; j++) { Lp [j] = j ; } for (j = 0 ; j < n ; j++) { Lnz [j] = 1 ; } } else { /* ------------------------------------------------------------------ */ /* LDL' unpacked */ /* ------------------------------------------------------------------ */ PRINT1 (("convert to unpacked\n")) ; /* compute new lnzmax */ /* if any parameter is NaN, grow is false */ grow0 = Common->grow0 ; grow1 = Common->grow1 ; grow2 = Common->grow2 ; grow0 = IS_NAN (grow0) ? 1 : grow0 ; grow1 = IS_NAN (grow1) ? 1 : grow1 ; /* fl.pt. compare, but no NaN's: */ grow = (grow0 >= 1.0) && (grow1 >= 1.0) && (grow2 > 0) ; PRINT1 (("init, grow1 %g grow2 "ID"\n", grow1, grow2)) ; /* initialize Lp and Lnz for each column */ lnz = 0 ; for (j = 0 ; ok && j < n ; j++) { Lp [j] = lnz ; Lnz [j] = 1 ; /* ensure len is in the range 1 to n-j */ len = ColCount [j] ; len = MAX (1, len) ; len = MIN (len, n-j) ; /* compute len in double to avoid integer overflow */ PRINT1 (("ColCount ["ID"] = "ID"\n", j, len)) ; if (grow) { xlen = (double) len ; xlen = grow1 * xlen + grow2 ; xlen = MIN (xlen, n-j) ; len = (Int) xlen ; } ASSERT (len >= 1 && len <= n-j) ; lnz += len ; ok = (lnz >= 0) ; } if (ok) { Lp [n] = lnz ; if (grow) { /* add extra space */ xlnz = (double) lnz ; xlnz *= grow0 ; xlnz = MIN (xlnz, Size_max) ; xlnz = MIN (xlnz, ((double) n * (double) n + (double) n) / 2) ; lnz = (Int) xlnz ; } } } lnz = MAX (1, lnz) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; } /* allocate L->i, L->x, and L->z */ PRINT1 (("resizing from zero size to lnz "ID"\n", lnz)) ; ASSERT (L->nzmax == 0) ; e = (to_xtype == CHOLMOD_COMPLEX ? 2 : 1) ; if (!ok || !CHOLMOD(realloc_multiple) (lnz, 1, to_xtype, &(L->i), NULL, &(L->x), &(L->z), &(L->nzmax), Common)) { L->p = CHOLMOD(free) (n+1, sizeof (Int), L->p, Common) ; L->nz = CHOLMOD(free) (n, sizeof (Int), L->nz, Common) ; L->prev = CHOLMOD(free) (n+2, sizeof (Int), L->prev, Common) ; L->next = CHOLMOD(free) (n+2, sizeof (Int), L->next, Common) ; L->i = CHOLMOD(free) (lnz, sizeof (Int), L->i, Common) ; L->x = CHOLMOD(free) (lnz, e*sizeof (double), L->x, Common) ; L->z = CHOLMOD(free) (lnz, sizeof (double), L->z, Common) ; PRINT1 (("cannot realloc simplicial numeric\n")) ; return ; /* out of memory */ } /* ============================================== commit the changes to L */ /* initialize L to be the identity matrix */ L->xtype = to_xtype ; L->dtype = DTYPE ; L->minor = n ; Li = L->i ; Lx = L->x ; Lz = L->z ; #if 0 if (lnz == 1) { /* the user won't expect to access this entry, but some CHOLMOD * routines may. Set it to zero so that valgrind doesn't complain. */ switch (to_xtype) { case CHOLMOD_REAL: Lx [0] = 0 ; break ; case CHOLMOD_COMPLEX: Lx [0] = 0 ; Lx [1] = 0 ; break ; case CHOLMOD_ZOMPLEX: Lx [0] = 0 ; Lz [0] = 0 ; break ; } } #endif if (packed >= 0) { /* create the unit diagonal for either the LL' or LDL' case */ switch (L->xtype) { case CHOLMOD_REAL: for (j = 0 ; j < n ; j++) { ASSERT (Lp [j] < Lp [j+1]) ; p = Lp [j] ; Li [p] = j ; Lx [p] = 1 ; } break ; case CHOLMOD_COMPLEX: for (j = 0 ; j < n ; j++) { ASSERT (Lp [j] < Lp [j+1]) ; p = Lp [j] ; Li [p] = j ; Lx [2*p ] = 1 ; Lx [2*p+1] = 0 ; } break ; case CHOLMOD_ZOMPLEX: for (j = 0 ; j < n ; j++) { ASSERT (Lp [j] < Lp [j+1]) ; p = Lp [j] ; Li [p] = j ; Lx [p] = 1 ; Lz [p] = 0 ; } break ; } } L->is_ll = to_ll ; PRINT1 (("done convert simplicial symbolic to numeric\n")) ; } /* ========================================================================== */ /* === change_simplicial_numeric ============================================ */ /* ========================================================================== */ /* Change LL' to LDL', LDL' to LL', or leave as-is. * * If to_packed is TRUE, then the columns of L are packed and made monotonic * (to_monotonic is ignored; it is implicitly TRUE). * * If to_monotonic is TRUE but to_packed is FALSE, the columns of L are made * monotonic but not packed. * * If both to_packed and to_monotonic are FALSE, then the columns of L are * left as-is, and the conversion is done in place. * * If L is already monotonic, or if it is to be left non-monotonic, then this * conversion always succeeds. * * When converting an LDL' to LL' factorization, any column with a negative * or zero diagonal entry is not modified so that conversion back to LDL' will * succeed. This can result in a matrix L with a negative entry on the diagonal * If the kth entry on the diagonal of D is negative, it and the kth column of * L are left unchanged. A subsequent conversion back to an LDL' form will also * leave the column unchanged, so the correct LDL' factorization will be * restored. L->minor is set to the smallest k for which D (k,k) is negative. */ static void change_simplicial_numeric ( cholmod_factor *L, int to_ll, int to_packed, int to_monotonic, cholmod_common *Common ) { double grow0, grow1, xlen, xlnz ; void *newLi, *newLx, *newLz ; double *Lx, *Lz ; Int *Lp, *Li, *Lnz ; Int make_monotonic, grow2, n, j, lnz, len, grow, ok, make_ll, make_ldl ; size_t nzmax0 ; PRINT1 (("\n===Change simplicial numeric: %d %d %d\n", to_ll, to_packed, to_monotonic)) ; DEBUG (CHOLMOD(dump_factor) (L, "change simplicial numeric", Common)) ; ASSERT (L->xtype != CHOLMOD_PATTERN && !(L->is_super)) ; make_monotonic = ((to_packed || to_monotonic) && !(L->is_monotonic)) ; make_ll = (to_ll && !(L->is_ll)) ; make_ldl = (!to_ll && L->is_ll) ; n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ; Lz = L->z ; Lnz = L->nz ; grow = FALSE ; grow0 = Common->grow0 ; grow1 = Common->grow1 ; grow2 = Common->grow2 ; grow0 = IS_NAN (grow0) ? 1 : grow0 ; grow1 = IS_NAN (grow1) ? 1 : grow1 ; ok = TRUE ; newLi = NULL ; newLx = NULL ; newLz = NULL ; lnz = 0 ; if (make_monotonic) { /* ------------------------------------------------------------------ */ /* Columns out of order, but will be reordered and optionally packed. */ /* ------------------------------------------------------------------ */ PRINT1 (("L is non-monotonic\n")) ; /* compute new L->nzmax */ if (!to_packed) { /* if any parameter is NaN, grow is false */ /* fl.pt. comparisons below are false if any parameter is NaN */ grow = (grow0 >= 1.0) && (grow1 >= 1.0) && (grow2 > 0) ; } for (j = 0 ; ok && j < n ; j++) { len = Lnz [j] ; ASSERT (len >= 1 && len <= n-j) ; /* compute len in double to avoid integer overflow */ if (grow) { xlen = (double) len ; xlen = grow1 * xlen + grow2 ; xlen = MIN (xlen, n-j) ; len = (Int) xlen ; } ASSERT (len >= Lnz [j] && len <= n-j) ; PRINT2 (("j: "ID" Lnz[j] "ID" len "ID" p "ID"\n", j, Lnz [j], len, lnz)) ; lnz += len ; ok = (lnz >= 0) ; } if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return ; } if (grow) { xlnz = (double) lnz ; xlnz *= grow0 ; xlnz = MIN (xlnz, Size_max) ; xlnz = MIN (xlnz, ((double) n * (double) n + (double) n) / 2) ; lnz = (Int) xlnz ; } lnz = MAX (1, lnz) ; PRINT1 (("final lnz "ID"\n", lnz)) ; nzmax0 = 0 ; CHOLMOD(realloc_multiple) (lnz, 1, L->xtype, &newLi, NULL, &newLx, &newLz, &nzmax0, Common) ; if (Common->status < CHOLMOD_OK) { return ; /* out of memory */ } } /* ============================================== commit the changes to L */ /* ---------------------------------------------------------------------- */ /* convert the simplicial L, using template routine */ /* ---------------------------------------------------------------------- */ switch (L->xtype) { case CHOLMOD_REAL: r_change_simplicial_numeric (L, to_ll, to_packed, newLi, newLx, newLz, lnz, grow, grow1, grow2, make_ll, make_monotonic, make_ldl, Common) ; break ; case CHOLMOD_COMPLEX: c_change_simplicial_numeric (L, to_ll, to_packed, newLi, newLx, newLz, lnz, grow, grow1, grow2, make_ll, make_monotonic, make_ldl, Common) ; break ; case CHOLMOD_ZOMPLEX: z_change_simplicial_numeric (L, to_ll, to_packed, newLi, newLx, newLz, lnz, grow, grow1, grow2, make_ll, make_monotonic, make_ldl, Common) ; break ; } DEBUG (CHOLMOD(dump_factor) (L, "L simplicial changed", Common)) ; } /* ========================================================================== */ /* === ll_super_to_simplicial_numeric ======================================= */ /* ========================================================================== */ /* Convert a supernodal numeric factorization to any simplicial numeric one. * Leaves L->xtype unchanged (real or complex, not zomplex since there is * no supernodal zomplex L). */ static void ll_super_to_simplicial_numeric ( cholmod_factor *L, int to_packed, int to_ll, cholmod_common *Common ) { Int *Ls, *Lpi, *Lpx, *Super, *Li ; Int n, lnz, s, nsuper, psi, psend, nsrow, nscol, k1, k2, erows ; DEBUG (CHOLMOD(dump_factor) (L, "start LL super to simplicial", Common)) ; PRINT1 (("super -> simplicial (%d %d)\n", to_packed, to_ll)) ; ASSERT (L->xtype != CHOLMOD_PATTERN && L->is_ll && L->is_super) ; ASSERT (L->x != NULL && L->i == NULL) ; n = L->n ; nsuper = L->nsuper ; Lpi = L->pi ; Lpx = L->px ; Ls = L->s ; Super = L->super ; /* Int overflow cannot occur since supernodal L already exists */ if (to_packed) { /* count the number of nonzeros in L. Each supernode is of the form * * l . . . For this example, nscol = 4 (# columns). nsrow = 9. * l l . . The "." entries are allocated in the supernodal * l l l . factor, but not used. They are not copied to the * l l l l simplicial factor. Some "l" and "e" entries may be * e e e e numerically zero and even symbolically zero if a * e e e e tight simplicial factorization or resymbol were * e e e e done, because of numerical cancellation and relaxed * e e e e supernode amalgamation, respectively. * e e e e */ lnz = 0 ; for (s = 0 ; s < nsuper ; s++) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; nsrow = psend - psi ; nscol = k2 - k1 ; ASSERT (nsrow >= nscol) ; erows = nsrow - nscol ; /* lower triangular part, including the diagonal, * counting the "l" terms in the figure above. */ lnz += nscol * (nscol+1) / 2 ; /* rectangular part, below the diagonal block (the "e" terms) */ lnz += nscol * erows ; } ASSERT (lnz <= (Int) (L->xsize)) ; } else { /* Li will be the same size as Lx */ lnz = L->xsize ; } ASSERT (lnz >= 0) ; PRINT1 (("simplicial lnz = "ID" to_packed: %d to_ll: %d L->xsize %g\n", lnz, to_ll, to_packed, (double) L->xsize)) ; Li = CHOLMOD(malloc) (lnz, sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { return ; /* out of memory */ } if (!allocate_simplicial_numeric (L, Common)) { CHOLMOD(free) (lnz, sizeof (Int), Li, Common) ; return ; /* out of memory */ } /* ============================================== commit the changes to L */ L->i = Li ; L->nzmax = lnz ; /* ---------------------------------------------------------------------- */ /* convert the supernodal L, using template routine */ /* ---------------------------------------------------------------------- */ switch (L->xtype) { case CHOLMOD_REAL: r_ll_super_to_simplicial_numeric (L, to_packed, to_ll, Common) ; break ; case CHOLMOD_COMPLEX: c_ll_super_to_simplicial_numeric (L, to_packed, to_ll, Common) ; break ; } /* ---------------------------------------------------------------------- */ /* free unused parts of L */ /* ---------------------------------------------------------------------- */ L->super = CHOLMOD(free) (nsuper+1, sizeof (Int), L->super, Common) ; L->pi = CHOLMOD(free) (nsuper+1, sizeof (Int), L->pi, Common) ; L->px = CHOLMOD(free) (nsuper+1, sizeof (Int), L->px, Common) ; L->s = CHOLMOD(free) (L->ssize, sizeof (Int), L->s, Common) ; L->ssize = 0 ; L->xsize = 0 ; L->nsuper = 0 ; L->maxesize = 0 ; L->maxcsize = 0 ; L->is_super = FALSE ; DEBUG (CHOLMOD(dump_factor) (L, "done LL super to simplicial", Common)) ; } /* ========================================================================== */ /* === super_symbolic_to_ll_super =========================================== */ /* ========================================================================== */ /* Convert a supernodal symbolic factorization to a supernodal numeric * factorization by allocating L->x. Contents of L->x are undefined. */ static int super_symbolic_to_ll_super ( int to_xtype, cholmod_factor *L, cholmod_common *Common ) { double *Lx ; Int wentry = (to_xtype == CHOLMOD_REAL) ? 1 : 2 ; PRINT1 (("convert super sym to num\n")) ; ASSERT (L->xtype == CHOLMOD_PATTERN && L->is_super) ; Lx = CHOLMOD(malloc) (L->xsize, wentry * sizeof (double), Common) ; PRINT1 (("xsize %g\n", (double) L->xsize)) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } /* ============================================== commit the changes to L */ if (L->xsize == 1) { /* the caller won't expect to access this entry, but some CHOLMOD * routines may. Set it to zero so that valgrind doesn't complain. */ switch (to_xtype) { case CHOLMOD_REAL: Lx [0] = 0 ; break ; case CHOLMOD_COMPLEX: Lx [0] = 0 ; Lx [1] = 0 ; break ; } } L->x = Lx ; L->xtype = to_xtype ; L->dtype = DTYPE ; L->minor = L->n ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_change_factor ================================================ */ /* ========================================================================== */ /* Convert a factor L. Some conversions simply allocate uninitialized space * that meant to be filled later. * * If the conversion fails, the factor is left in its original form, with one * exception. Converting a supernodal symbolic factor to a simplicial numeric * one (with L=D=I) may leave the factor in simplicial symbolic form. * * Memory allocated for each conversion is listed below. */ int CHOLMOD(change_factor) ( /* ---- input ---- */ int to_xtype, /* convert to CHOLMOD_PATTERN, _REAL, _COMPLEX, or * _ZOMPLEX */ int to_ll, /* TRUE: convert to LL', FALSE: LDL' */ int to_super, /* TRUE: convert to supernodal, FALSE: simplicial */ int to_packed, /* TRUE: pack simplicial columns, FALSE: do not pack */ int to_monotonic, /* TRUE: put simplicial columns in order, FALSE: not */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (to_xtype < CHOLMOD_PATTERN || to_xtype > CHOLMOD_ZOMPLEX) { ERROR (CHOLMOD_INVALID, "xtype invalid") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; PRINT1 (("-----convert from (%d,%d,%d,%d,%d) to (%d,%d,%d,%d,%d)\n", L->xtype, L->is_ll, L->is_super, L_is_packed (L, Common), L->is_monotonic, to_xtype, to_ll, to_super, to_packed, to_monotonic)) ; /* ensure all parameters are TRUE/FALSE */ to_ll = BOOLEAN (to_ll) ; to_super = BOOLEAN (to_super) ; ASSERT (BOOLEAN (L->is_ll) == L->is_ll) ; ASSERT (BOOLEAN (L->is_super) == L->is_super) ; if (to_super && to_xtype == CHOLMOD_ZOMPLEX) { ERROR (CHOLMOD_INVALID, "supernodal zomplex L not supported") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* convert */ /* ---------------------------------------------------------------------- */ if (to_xtype == CHOLMOD_PATTERN) { /* ------------------------------------------------------------------ */ /* convert to symbolic */ /* ------------------------------------------------------------------ */ if (!to_super) { /* -------------------------------------------------------------- */ /* convert any factor into a simplicial symbolic factor */ /* -------------------------------------------------------------- */ any_to_simplicial_symbolic (L, to_ll, Common) ; /* cannot fail */ } else { /* -------------------------------------------------------------- */ /* convert to a supernodal symbolic factor */ /* -------------------------------------------------------------- */ if (L->xtype != CHOLMOD_PATTERN && L->is_super) { /* convert from supernodal numeric to supernodal symbolic. * this preserves symbolic pattern of L, discards numeric * values */ ll_super_to_super_symbolic (L, Common) ; /* cannot fail */ } else if (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) { /* convert from simplicial symbolic to supernodal symbolic. * contents of supernodal pattern are uninitialized. Not meant * for the end user. */ simplicial_symbolic_to_super_symbolic (L, Common) ; } else { /* cannot convert from simplicial numeric to supernodal * symbolic */ ERROR (CHOLMOD_INVALID, "cannot convert L to supernodal symbolic") ; } } } else { /* ------------------------------------------------------------------ */ /* convert to numeric */ /* ------------------------------------------------------------------ */ if (to_super) { /* -------------------------------------------------------------- */ /* convert to supernodal numeric factor */ /* -------------------------------------------------------------- */ if (L->xtype == CHOLMOD_PATTERN) { if (L->is_super) { /* Convert supernodal symbolic to supernodal numeric. * Contents of supernodal numeric values are uninitialized. * This is used by cholmod_super_numeric. Not meant for * the end user. */ super_symbolic_to_ll_super (to_xtype, L, Common) ; } else { /* Convert simplicial symbolic to supernodal numeric. * Contents not defined. This is used by * Core/cholmod_copy_factor only. Not meant for the end * user. */ if (!simplicial_symbolic_to_super_symbolic (L, Common)) { /* failure, convert back to simplicial symbolic */ any_to_simplicial_symbolic (L, to_ll, Common) ; } else { /* conversion to super symbolic OK, allocate numeric * part */ super_symbolic_to_ll_super (to_xtype, L, Common) ; } } } else { /* nothing to do if L is already in supernodal numeric form */ if (!(L->is_super)) { ERROR (CHOLMOD_INVALID, "cannot convert simplicial L to supernodal") ; } /* FUTURE WORK: convert to/from supernodal LL' and LDL' */ } } else { /* -------------------------------------------------------------- */ /* convert any factor to simplicial numeric */ /* -------------------------------------------------------------- */ if (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) { /* ---------------------------------------------------------- */ /* convert simplicial symbolic to simplicial numeric (L=I,D=I)*/ /* ---------------------------------------------------------- */ simplicial_symbolic_to_simplicial_numeric (L, to_ll, to_packed, to_xtype, Common) ; } else if (L->xtype != CHOLMOD_PATTERN && L->is_super) { /* ---------------------------------------------------------- */ /* convert a supernodal LL' to simplicial numeric */ /* ---------------------------------------------------------- */ ll_super_to_simplicial_numeric (L, to_packed, to_ll, Common) ; } else if (L->xtype == CHOLMOD_PATTERN && L->is_super) { /* ---------------------------------------------------------- */ /* convert a supernodal symbolic to simplicial numeric (L=D=I)*/ /* ---------------------------------------------------------- */ any_to_simplicial_symbolic (L, to_ll, Common) ; /* if the following fails, it leaves the factor in simplicial * symbolic form */ simplicial_symbolic_to_simplicial_numeric (L, to_ll, to_packed, to_xtype, Common) ; } else { /* ---------------------------------------------------------- */ /* change a simplicial numeric factor */ /* ---------------------------------------------------------- */ /* change LL' to LDL', LDL' to LL', or leave as-is. pack the * columns of L, or leave as-is. Ensure the columns are * monotonic, or leave as-is. */ change_simplicial_numeric (L, to_ll, to_packed, to_monotonic, Common) ; } } } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ return (Common->status >= CHOLMOD_OK) ; } Matrix/src/CHOLMOD/Core/cholmod_aat.c0000644000175100001440000002071512271765436016740 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_aat ===================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* C = A*A' or C = A(:,f)*A(:,f)' * * A can be packed or unpacked, sorted or unsorted, but must be stored with * both upper and lower parts (A->stype of zero). C is returned as packed, * C->stype of zero (both upper and lower parts present), and unsorted. See * cholmod_ssmult in the MatrixOps Module for a more general matrix-matrix * multiply. * * You can trivially convert C into a symmetric upper/lower matrix by * changing C->stype = 1 or -1 after calling this routine. * * workspace: * Flag (A->nrow), * Iwork (max (A->nrow, A->ncol)) if fset present, * Iwork (A->nrow) if no fset, * W (A->nrow) if mode > 0, * allocates temporary copy for A'. * * A can be pattern or real. Complex or zomplex cases are supported only * if the mode is <= 0 (in which case the numerical values are ignored). */ #include "cholmod_internal.h" #include "cholmod_core.h" cholmod_sparse *CHOLMOD(aat) ( /* ---- input ---- */ cholmod_sparse *A, /* input matrix; C=A*A' is constructed */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) * -2: pattern only, no diagonal, add 50% + n extra * space to C */ /* --------------- */ cholmod_common *Common ) { double fjt ; double *Ax, *Fx, *Cx, *W ; Int *Ap, *Anz, *Ai, *Fp, *Fi, *Cp, *Ci, *Flag ; cholmod_sparse *C, *F ; Int packed, j, i, pa, paend, pf, pfend, n, mark, cnz, t, p, values, diag, extra ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; if (A->stype) { ERROR (CHOLMOD_INVALID, "matrix cannot be symmetric") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ diag = (mode >= 0) ; n = A->nrow ; CHOLMOD(allocate_work) (n, MAX (A->ncol, A->nrow), values ? n : 0, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n : 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ; /* get the A matrix */ Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; packed = A->packed ; /* get workspace */ W = Common->Xwork ; /* size n, unused if values is FALSE */ Flag = Common->Flag ; /* size n, Flag [0..n-1] < mark on input*/ /* ---------------------------------------------------------------------- */ /* F = A' or A(:,f)' */ /* ---------------------------------------------------------------------- */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/ F = CHOLMOD(ptranspose) (A, values, NULL, fset, fsize, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } Fp = F->p ; Fi = F->i ; Fx = F->x ; /* ---------------------------------------------------------------------- */ /* count the number of entries in the result C */ /* ---------------------------------------------------------------------- */ cnz = 0 ; for (j = 0 ; j < n ; j++) { /* clear the Flag array */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* exclude the diagonal, if requested */ if (!diag) { Flag [j] = mark ; } /* for each nonzero F(t,j) in column j, do: */ pfend = Fp [j+1] ; for (pf = Fp [j] ; pf < pfend ; pf++) { /* F(t,j) is nonzero */ t = Fi [pf] ; /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */ pa = Ap [t] ; paend = (packed) ? (Ap [t+1]) : (pa + Anz [t]) ; for ( ; pa < paend ; pa++) { i = Ai [pa] ; if (Flag [i] != mark) { Flag [i] = mark ; cnz++ ; } } } if (cnz < 0) { break ; /* integer overflow case */ } } extra = (mode == -2) ? (cnz/2 + n) : 0 ; mark = CHOLMOD(clear_flag) (Common) ; /* ---------------------------------------------------------------------- */ /* check for integer overflow */ /* ---------------------------------------------------------------------- */ if (cnz < 0 || (cnz + extra) < 0) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; CHOLMOD(clear_flag) (Common) ; CHOLMOD(free_sparse) (&F, Common) ; return (NULL) ; /* problem too large */ } /* ---------------------------------------------------------------------- */ /* allocate C */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_sparse) (n, n, cnz + extra, FALSE, TRUE, 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&F, Common) ; return (NULL) ; /* out of memory */ } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* C = A*A' */ /* ---------------------------------------------------------------------- */ cnz = 0 ; if (values) { /* pattern and values */ for (j = 0 ; j < n ; j++) { /* clear the Flag array */ mark = CHOLMOD(clear_flag) (Common) ; /* start column j of C */ Cp [j] = cnz ; /* for each nonzero F(t,j) in column j, do: */ pfend = Fp [j+1] ; for (pf = Fp [j] ; pf < pfend ; pf++) { /* F(t,j) is nonzero */ t = Fi [pf] ; fjt = Fx [pf] ; /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) * and scatter the values into W */ pa = Ap [t] ; paend = (packed) ? (Ap [t+1]) : (pa + Anz [t]) ; for ( ; pa < paend ; pa++) { i = Ai [pa] ; if (Flag [i] != mark) { Flag [i] = mark ; Ci [cnz++] = i ; } W [i] += Ax [pa] * fjt ; } } /* gather the values into C(:,j) */ for (p = Cp [j] ; p < cnz ; p++) { i = Ci [p] ; Cx [p] = W [i] ; W [i] = 0 ; } } } else { /* pattern only */ for (j = 0 ; j < n ; j++) { /* clear the Flag array */ mark = CHOLMOD(clear_flag) (Common) ; /* exclude the diagonal, if requested */ if (!diag) { Flag [j] = mark ; } /* start column j of C */ Cp [j] = cnz ; /* for each nonzero F(t,j) in column j, do: */ pfend = Fp [j+1] ; for (pf = Fp [j] ; pf < pfend ; pf++) { /* F(t,j) is nonzero */ t = Fi [pf] ; /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */ pa = Ap [t] ; paend = (packed) ? (Ap [t+1]) : (pa + Anz [t]) ; for ( ; pa < paend ; pa++) { i = Ai [pa] ; if (Flag [i] != mark) { Flag [i] = mark ; Ci [cnz++] = i ; } } } } } Cp [n] = cnz ; ASSERT (IMPLIES (mode != -2, MAX (1,cnz) == C->nzmax)) ; /* ---------------------------------------------------------------------- */ /* clear workspace and free temporary matrices and return result */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&F, Common) ; CHOLMOD(clear_flag) (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n : 0, Common)) ; DEBUG (i = CHOLMOD(dump_sparse) (C, "aat", Common)) ; ASSERT (IMPLIES (mode < 0, i == 0)) ; return (C) ; } Matrix/src/CHOLMOD/Core/License.txt0000644000175100001440000000207211770402705016427 0ustar hornikusersCHOLMOD/Core Module. Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.suitesparse.com Note that this license is for the CHOLMOD/Core module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Matrix/src/CHOLMOD/Core/cholmod_transpose.c0000644000175100001440000007533712271765436020223 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_transpose =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Core utility routines for the cholmod_sparse object to * compute the transpose or permuted transpose of a matrix: * * Primary routines: * ----------------- * cholmod_transpose transpose sparse matrix * cholmod_ptranspose transpose and permute sparse matrix * cholmod_sort sort row indices in each column of sparse matrix * * Secondary routines: * ------------------- * cholmod_transpose_unsym transpose unsymmetric sparse matrix * cholmod_transpose_sym transpose symmetric sparse matrix * * All xtypes (pattern, real, complex, and zomplex) are supported. * * --------------------------------------- * Unsymmetric case: A->stype is zero. * --------------------------------------- * * Computes F = A', F = A (:,f)' or F = A (p,f)', except that the indexing by * f does not work the same as the MATLAB notation (see below). A->stype * is zero, which denotes that both the upper and lower triangular parts of * A are present (and used). A may in fact be symmetric in pattern and/or * value; A->stype just denotes which part of A are stored. A may be * rectangular. * * p is a permutation of 0:m-1, and f is a subset of 0:n-1, where A is m-by-n. * There can be no duplicate entries in p or f. * * The set f is held in fset and fsize. * fset = NULL means ":" in MATLAB. fsize is ignored. * fset != NULL means f = fset [0..fsize-1]. * fset != NULL and fsize = 0 means f is the empty set. * * Columns not in the set f are considered to be zero. That is, * if A is 5-by-10 then F = A (:,[3 4])' is not 2-by-5, but 10-by-5, and rows * 3 and 4 of F are equal to columns 3 and 4 of A (the other rows of F are * zero). More precisely, in MATLAB notation: * * [m n] = size (A) ; * F = A ; * notf = ones (1,n) ; * notf (f) = 0 ; * F (:, find (notf)) = 0 * F = F' * * If you want the MATLAB equivalent F=A(p,f) operation, use cholmod_submatrix * instead (which does not compute the transpose). * * F->nzmax must be large enough to hold the matrix F. It is not modified. * If F->nz is present then F->nz [j] = # of entries in column j of F. * * A can be sorted or unsorted, with packed or unpacked columns. * * If f is present and not sorted in ascending order, then F is unsorted * (that is, it may contain columns whose row indices do not appear in * ascending order). Otherwise, F is sorted (the row indices in each * column of F appear in strictly ascending order). * * F is returned in packed or unpacked form, depending on F->packed on input. * If F->packed is false, then F is returned in unpacked form (F->nz must be * present). Each row i of F is large enough to hold all the entries in row i * of A, even if f is provided. That is, F->i and * F->x [F->p [i] .. F->p [i] + F->nz [i] - 1] contain all entries in A (i,f), * but F->p [i+1] - F->p [i] is equal to the number of nonzeros in A (i,:), * not just A (i,f). * * The cholmod_transpose_unsym routine is the only operation in CHOLMOD that * can produce an unpacked matrix. * * --------------------------------------- * Symmetric case: A->stype is nonzero. * --------------------------------------- * * Computes F = A' or F = A(p,p)', the transpose or permuted transpose, where * A->stype is nonzero. * * If A->stype > 0, then A is a symmetric matrix where just the upper part * of the matrix is stored. Entries in the lower triangular part may be * present, but are ignored. A must be square. If F=A', then F is returned * sorted; otherwise F is unsorted for the F=A(p,p)' case. * * There can be no duplicate entries in p. * The fset and fsize parameters are not used. * * Three kinds of transposes are available, depending on the "values" parameter: * 0: do not transpose the numerical values; create a CHOLMOD_PATTERN matrix * 1: array transpose * 2: complex conjugate transpose (same as 2 if input is real or pattern) * * ----------------------------------------------------------------------------- * * For cholmod_transpose_unsym and cholmod_transpose_sym, the output matrix * F must already be pre-allocated by the caller, with the correct dimensions. * If F is not valid or has the wrong dimensions, it is not modified. * Otherwise, if F is too small, the transpose is not computed; the contents * of F->p contain the column pointers of the resulting matrix, where * F->p [F->ncol] > F->nzmax. In this case, the remaining contents of F are * not modified. F can still be properly free'd with cholmod_free_sparse. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define PATTERN #include "t_cholmod_transpose.c" #define REAL #include "t_cholmod_transpose.c" #define COMPLEX #include "t_cholmod_transpose.c" #define COMPLEX #define NCONJUGATE #include "t_cholmod_transpose.c" #define ZOMPLEX #include "t_cholmod_transpose.c" #define ZOMPLEX #define NCONJUGATE #include "t_cholmod_transpose.c" /* ========================================================================== */ /* === cholmod_transpose_unsym ============================================== */ /* ========================================================================== */ /* Compute F = A', A (:,f)', or A (p,f)', where A is unsymmetric and F is * already allocated. See cholmod_transpose for a simpler routine. * * workspace: * Iwork (MAX (nrow,ncol)) if fset is present * Iwork (nrow) if fset is NULL * * The xtype of A and F must match, unless values is zero or F->xtype is * CHOLMOD_PATTERN (in which case only the pattern of A is transpose into F). */ int CHOLMOD(transpose_unsym) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 2: complex conj. transpose, 1: array transpose, 0: do not transpose the numerical values */ Int *Perm, /* size nrow, if present (can be NULL) */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ cholmod_sparse *F, /* F = A', A(:,f)', or A(p,f)' */ /* --------------- */ cholmod_common *Common ) { Int *Fp, *Fnz, *Ap, *Ai, *Anz, *Wi ; Int nrow, ncol, permute, use_fset, Apacked, Fpacked, p, pend, i, j, k, Fsorted, nf, jj, jlast ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (F, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (F, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (A->nrow != F->ncol || A->ncol != F->nrow) { ERROR (CHOLMOD_INVALID, "F has the wrong dimensions") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nf = fsize ; use_fset = (fset != NULL) ; nrow = A->nrow ; ncol = A->ncol ; Ap = A->p ; /* size A->ncol+1, column pointers of A */ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */ Anz = A->nz ; Apacked = A->packed ; ASSERT (IMPLIES (!Apacked, Anz != NULL)) ; permute = (Perm != NULL) ; Fp = F->p ; /* size A->nrow+1, row pointers of F */ Fnz = F->nz ; Fpacked = F->packed ; ASSERT (IMPLIES (!Fpacked, Fnz != NULL)) ; nf = (use_fset) ? nf : ncol ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = nrow + ((fset != NULL) ? ncol : 0) */ s = CHOLMOD(add_size_t) (nrow, ((fset != NULL) ? ncol : 0), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (0, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } Wi = Common->Iwork ; /* size nrow (i/l/l) */ /* ---------------------------------------------------------------------- */ /* check Perm and fset */ /* ---------------------------------------------------------------------- */ if (permute) { for (i = 0 ; i < nrow ; i++) { Wi [i] = 1 ; } for (k = 0 ; k < nrow ; k++) { i = Perm [k] ; if (i < 0 || i > nrow || Wi [i] == 0) { ERROR (CHOLMOD_INVALID, "invalid permutation") ; return (FALSE) ; } Wi [i] = 0 ; } } if (use_fset) { for (j = 0 ; j < ncol ; j++) { Wi [j] = 1 ; } for (k = 0 ; k < nf ; k++) { j = fset [k] ; if (j < 0 || j > ncol || Wi [j] == 0) { ERROR (CHOLMOD_INVALID, "invalid fset") ; return (FALSE) ; } Wi [j] = 0 ; } } /* Perm and fset are now valid */ ASSERT (CHOLMOD(dump_perm) (Perm, nrow, nrow, "Perm", Common)) ; ASSERT (CHOLMOD(dump_perm) (fset, nf, ncol, "fset", Common)) ; /* ---------------------------------------------------------------------- */ /* count the entries in each row of A or A(:,f) */ /* ---------------------------------------------------------------------- */ for (i = 0 ; i < nrow ; i++) { Wi [i] = 0 ; } jlast = EMPTY ; Fsorted = TRUE ; if (use_fset) { /* count entries in each row of A(:,f) */ for (jj = 0 ; jj < nf ; jj++) { j = fset [jj] ; if (j <= jlast) { Fsorted = FALSE ; } p = Ap [j] ; pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Wi [Ai [p]]++ ; } jlast = j ; } /* save the nz counts if F is unpacked, and recount all of A */ if (!Fpacked) { if (permute) { for (i = 0 ; i < nrow ; i++) { Fnz [i] = Wi [Perm [i]] ; } } else { for (i = 0 ; i < nrow ; i++) { Fnz [i] = Wi [i] ; } } for (i = 0 ; i < nrow ; i++) { Wi [i] = 0 ; } /* count entries in each row of A */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Wi [Ai [p]]++ ; } } } } else { /* count entries in each row of A */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Wi [Ai [p]]++ ; } } /* save the nz counts if F is unpacked */ if (!Fpacked) { if (permute) { for (i = 0 ; i < nrow ; i++) { Fnz [i] = Wi [Perm [i]] ; } } else { for (i = 0 ; i < nrow ; i++) { Fnz [i] = Wi [i] ; } } } } /* ---------------------------------------------------------------------- */ /* compute the row pointers */ /* ---------------------------------------------------------------------- */ p = 0 ; if (permute) { for (i = 0 ; i < nrow ; i++) { Fp [i] = p ; p += Wi [Perm [i]] ; } for (i = 0 ; i < nrow ; i++) { Wi [Perm [i]] = Fp [i] ; } } else { for (i = 0 ; i < nrow ; i++) { Fp [i] = p ; p += Wi [i] ; } for (i = 0 ; i < nrow ; i++) { Wi [i] = Fp [i] ; } } Fp [nrow] = p ; if (p > (Int) (F->nzmax)) { ERROR (CHOLMOD_INVALID, "F is too small") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* transpose matrix, using template routine */ /* ---------------------------------------------------------------------- */ ok = FALSE ; if (values == 0 || F->xtype == CHOLMOD_PATTERN) { ok = p_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ; } else if (F->xtype == CHOLMOD_REAL) { ok = r_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ; } else if (F->xtype == CHOLMOD_COMPLEX) { if (values == 1) { /* array transpose */ ok = ct_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ; } else { /* complex conjugate transpose */ ok = c_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ; } } else if (F->xtype == CHOLMOD_ZOMPLEX) { if (values == 1) { /* array transpose */ ok = zt_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ; } else { /* complex conjugate transpose */ ok = z_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ; } } /* ---------------------------------------------------------------------- */ /* finalize result F */ /* ---------------------------------------------------------------------- */ if (ok) { F->sorted = Fsorted ; } ASSERT (CHOLMOD(dump_sparse) (F, "output F unsym", Common) >= 0) ; return (ok) ; } /* ========================================================================== */ /* === cholmod_transpose_sym ================================================ */ /* ========================================================================== */ /* Compute F = A' or A (p,p)', where A is symmetric and F is already allocated. * See cholmod_transpose for a simpler routine. * * workspace: Iwork (nrow) if Perm NULL, Iwork (2*nrow) if Perm non-NULL. */ int CHOLMOD(transpose_sym) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 2: complex conj. transpose, 1: array transpose, 0: do not transpose the numerical values */ Int *Perm, /* size nrow, if present (can be NULL) */ /* ---- output --- */ cholmod_sparse *F, /* F = A' or A(p,p)' */ /* --------------- */ cholmod_common *Common ) { Int *Ap, *Anz, *Ai, *Fp, *Wi, *Pinv, *Iwork ; Int p, pend, packed, upper, permute, jold, n, i, j, k, iold ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (F, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (F, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (A->nrow != A->ncol || A->stype == 0) { /* this routine handles square symmetric matrices only */ ERROR (CHOLMOD_INVALID, "matrix must be symmetric") ; return (FALSE) ; } if (A->nrow != F->ncol || A->ncol != F->nrow) { ERROR (CHOLMOD_INVALID, "F has the wrong dimensions") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ permute = (Perm != NULL) ; n = A->nrow ; Ap = A->p ; /* size A->ncol+1, column pointers of A */ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */ Anz = A->nz ; packed = A->packed ; ASSERT (IMPLIES (!packed, Anz != NULL)) ; upper = (A->stype > 0) ; Fp = F->p ; /* size A->nrow+1, row pointers of F */ /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = (Perm != NULL) ? 2*n : n */ s = CHOLMOD(add_size_t) (n, ((Perm != NULL) ? n : 0), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (0, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; Wi = Iwork ; /* size n (i/l/l) */ Pinv = Iwork + n ; /* size n (i/i/l) , unused if Perm NULL */ /* ---------------------------------------------------------------------- */ /* check Perm and construct inverse permutation */ /* ---------------------------------------------------------------------- */ if (permute) { for (i = 0 ; i < n ; i++) { Pinv [i] = EMPTY ; } for (k = 0 ; k < n ; k++) { i = Perm [k] ; if (i < 0 || i > n || Pinv [i] != EMPTY) { ERROR (CHOLMOD_INVALID, "invalid permutation") ; return (FALSE) ; } Pinv [i] = k ; } } /* Perm is now valid */ ASSERT (CHOLMOD(dump_perm) (Perm, n, n, "Perm", Common)) ; /* ---------------------------------------------------------------------- */ /* count the entries in each row of F */ /* ---------------------------------------------------------------------- */ for (i = 0 ; i < n ; i++) { Wi [i] = 0 ; } if (packed) { if (permute) { if (upper) { /* packed, permuted, upper */ for (j = 0 ; j < n ; j++) { jold = Perm [j] ; pend = Ap [jold+1] ; for (p = Ap [jold] ; p < pend ; p++) { iold = Ai [p] ; if (iold <= jold) { i = Pinv [iold] ; Wi [MIN (i, j)]++ ; } } } } else { /* packed, permuted, lower */ for (j = 0 ; j < n ; j++) { jold = Perm [j] ; pend = Ap [jold+1] ; for (p = Ap [jold] ; p < pend ; p++) { iold = Ai [p] ; if (iold >= jold) { i = Pinv [iold] ; Wi [MAX (i, j)]++ ; } } } } } else { if (upper) { /* packed, unpermuted, upper */ for (j = 0 ; j < n ; j++) { pend = Ap [j+1] ; for (p = Ap [j] ; p < pend ; p++) { i = Ai [p] ; if (i <= j) { Wi [i]++ ; } } } } else { /* packed, unpermuted, lower */ for (j = 0 ; j < n ; j++) { pend = Ap [j+1] ; for (p = Ap [j] ; p < pend ; p++) { i = Ai [p] ; if (i >= j) { Wi [i]++ ; } } } } } } else { if (permute) { if (upper) { /* unpacked, permuted, upper */ for (j = 0 ; j < n ; j++) { jold = Perm [j] ; p = Ap [jold] ; pend = p + Anz [jold] ; for ( ; p < pend ; p++) { iold = Ai [p] ; if (iold <= jold) { i = Pinv [iold] ; Wi [MIN (i, j)]++ ; } } } } else { /* unpacked, permuted, lower */ for (j = 0 ; j < n ; j++) { jold = Perm [j] ; p = Ap [jold] ; pend = p + Anz [jold] ; for ( ; p < pend ; p++) { iold = Ai [p] ; if (iold >= jold) { i = Pinv [iold] ; Wi [MAX (i, j)]++ ; } } } } } else { if (upper) { /* unpacked, unpermuted, upper */ for (j = 0 ; j < n ; j++) { p = Ap [j] ; pend = p + Anz [j] ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i <= j) { Wi [i]++ ; } } } } else { /* unpacked, unpermuted, lower */ for (j = 0 ; j < n ; j++) { p = Ap [j] ; pend = p + Anz [j] ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= j) { Wi [i]++ ; } } } } } } /* ---------------------------------------------------------------------- */ /* compute the row pointers */ /* ---------------------------------------------------------------------- */ p = 0 ; for (i = 0 ; i < n ; i++) { Fp [i] = p ; p += Wi [i] ; } Fp [n] = p ; for (i = 0 ; i < n ; i++) { Wi [i] = Fp [i] ; } if (p > (Int) (F->nzmax)) { ERROR (CHOLMOD_INVALID, "F is too small") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* transpose matrix, using template routine */ /* ---------------------------------------------------------------------- */ ok = FALSE ; if (values == 0 || F->xtype == CHOLMOD_PATTERN) { PRINT2 (("\n:::: p_transpose_sym Perm %p\n", Perm)) ; ok = p_cholmod_transpose_sym (A, Perm, F, Common) ; } else if (F->xtype == CHOLMOD_REAL) { PRINT2 (("\n:::: r_transpose_sym Perm %p\n", Perm)) ; ok = r_cholmod_transpose_sym (A, Perm, F, Common) ; } else if (F->xtype == CHOLMOD_COMPLEX) { if (values == 1) { /* array transpose */ PRINT2 (("\n:::: ct_transpose_sym Perm %p\n", Perm)) ; ok = ct_cholmod_transpose_sym (A, Perm, F, Common) ; } else { /* complex conjugate transpose */ PRINT2 (("\n:::: c_transpose_sym Perm %p\n", Perm)) ; ok = c_cholmod_transpose_sym (A, Perm, F, Common) ; } } else if (F->xtype == CHOLMOD_ZOMPLEX) { if (values == 1) { /* array transpose */ PRINT2 (("\n:::: zt_transpose_sym Perm %p\n", Perm)) ; ok = zt_cholmod_transpose_sym (A, Perm, F, Common) ; } else { /* complex conjugate transpose */ PRINT2 (("\n:::: z_transpose_sym Perm %p\n", Perm)) ; ok = z_cholmod_transpose_sym (A, Perm, F, Common) ; } } /* ---------------------------------------------------------------------- */ /* finalize result F */ /* ---------------------------------------------------------------------- */ /* F is sorted if there is no permutation vector */ if (ok) { F->sorted = !permute ; F->packed = TRUE ; F->stype = - SIGN (A->stype) ; /* flip the stype */ ASSERT (CHOLMOD(dump_sparse) (F, "output F sym", Common) >= 0) ; } return (ok) ; } /* ========================================================================== */ /* === cholmod_transpose ==================================================== */ /* ========================================================================== */ /* Returns A'. See also cholmod_ptranspose below. */ cholmod_sparse *CHOLMOD(transpose) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 2: complex conj. transpose, 1: array transpose, 0: do not transpose the numerical values (returns its result as CHOLMOD_PATTERN) */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(ptranspose) (A, values, NULL, NULL, 0, Common)) ; } /* ========================================================================== */ /* === cholmod_ptranspose =================================================== */ /* ========================================================================== */ /* Return A' or A(p,p)' if A is symmetric. Return A', A(:,f)', or A(p,f)' if * A is unsymmetric. * * workspace: * Iwork (MAX (nrow,ncol)) if unsymmetric and fset is non-NULL * Iwork (nrow) if unsymmetric and fset is NULL * Iwork (2*nrow) if symmetric and Perm is non-NULL. * Iwork (nrow) if symmetric and Perm is NULL. * * A simple worst-case upper bound on the workspace is nrow+ncol. */ cholmod_sparse *CHOLMOD(ptranspose) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 2: complex conj. transpose, 1: array transpose, 0: do not transpose the numerical values */ Int *Perm, /* if non-NULL, F = A(p,f) or A(p,p) */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* --------------- */ cholmod_common *Common ) { Int *Ap, *Anz ; cholmod_sparse *F ; Int nrow, ncol, use_fset, j, jj, fnz, packed, stype, nf, xtype ; size_t ineed ; int ok = TRUE ; nf = fsize ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; stype = A->stype ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; ncol = A->ncol ; if (stype != 0) { use_fset = FALSE ; if (Perm != NULL) { ineed = CHOLMOD(mult_size_t) (A->nrow, 2, &ok) ; } else { ineed = A->nrow ; } } else { use_fset = (fset != NULL) ; if (use_fset) { ineed = MAX (A->nrow, A->ncol) ; } else { ineed = A->nrow ; } } if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } CHOLMOD(allocate_work) (0, ineed, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Anz = A->nz ; packed = A->packed ; ASSERT (IMPLIES (!packed, Anz != NULL)) ; xtype = values ? A->xtype : CHOLMOD_PATTERN ; /* ---------------------------------------------------------------------- */ /* allocate F */ /* ---------------------------------------------------------------------- */ /* determine # of nonzeros in F */ if (stype != 0) { /* F=A' or F=A(p,p)', fset is ignored */ fnz = CHOLMOD(nnz) (A, Common) ; } else { nf = (use_fset) ? nf : ncol ; if (use_fset) { fnz = 0 ; /* F=A(:,f)' or F=A(p,f)' */ for (jj = 0 ; jj < nf ; jj++) { /* The fset is not yet checked; it will be thoroughly checked * in cholmod_transpose_unsym. For now, just make sure we don't * access Ap and Anz out of bounds. */ j = fset [jj] ; if (j >= 0 && j < ncol) { fnz += packed ? (Ap [j+1] - Ap [j]) : MAX (0, Anz [j]) ; } } } else { /* F=A' or F=A(p,:)' */ fnz = CHOLMOD(nnz) (A, Common) ; } } /* F is ncol-by-nrow, fnz nonzeros, sorted unless f is present and unsorted, * packed, of opposite stype as A, and with/without numerical values */ F = CHOLMOD(allocate_sparse) (ncol, nrow, fnz, TRUE, TRUE, -SIGN(stype), xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* transpose and optionally permute the matrix A */ /* ---------------------------------------------------------------------- */ if (stype != 0) { /* F = A (p,p)', using upper or lower triangular part of A only */ ok = CHOLMOD(transpose_sym) (A, values, Perm, F, Common) ; } else { /* F = A (p,f)' */ ok = CHOLMOD(transpose_unsym) (A, values, Perm, fset, nf, F, Common) ; } /* ---------------------------------------------------------------------- */ /* return the matrix F, or NULL if an error occured */ /* ---------------------------------------------------------------------- */ if (!ok) { CHOLMOD(free_sparse) (&F, Common) ; } return (F) ; } /* ========================================================================== */ /* === cholmod_sort ========================================================= */ /* ========================================================================== */ /* Sort the columns of A, in place. Returns A in packed form, even if it * starts as unpacked. Removes entries in the ignored part of a symmetric * matrix. * * workspace: Iwork (max (nrow,ncol)). Allocates additional workspace for a * temporary copy of A'. */ int CHOLMOD(sort) ( /* ---- in/out --- */ cholmod_sparse *A, /* matrix to sort */ /* --------------- */ cholmod_common *Common ) { Int *Ap ; cholmod_sparse *F ; Int anz, ncol, nrow, stype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; nrow = A->nrow ; if (nrow <= 1) { /* a 1-by-n sparse matrix must be sorted */ A->sorted = TRUE ; return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ ncol = A->ncol ; CHOLMOD(allocate_work) (0, MAX (nrow, ncol), 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ anz = CHOLMOD(nnz) (A, Common) ; stype = A->stype ; /* ---------------------------------------------------------------------- */ /* sort the columns of the matrix */ /* ---------------------------------------------------------------------- */ /* allocate workspace for transpose: ncol-by-nrow, same # of nonzeros as A, * sorted, packed, same stype as A, and of the same numeric type as A. */ F = CHOLMOD(allocate_sparse) (ncol, nrow, anz, TRUE, TRUE, stype, A->xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } if (stype != 0) { /* F = A', upper or lower triangular part only */ CHOLMOD(transpose_sym) (A, 1, NULL, F, Common) ; A->packed = TRUE ; /* A = F' */ CHOLMOD(transpose_sym) (F, 1, NULL, A, Common) ; } else { /* F = A' */ CHOLMOD(transpose_unsym) (A, 1, NULL, NULL, 0, F, Common) ; A->packed = TRUE ; /* A = F' */ CHOLMOD(transpose_unsym) (F, 1, NULL, NULL, 0, A, Common) ; } ASSERT (A->sorted && A->packed) ; ASSERT (CHOLMOD(dump_sparse) (A, "Asorted", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* reduce A in size, if needed. This must succeed. */ /* ---------------------------------------------------------------------- */ Ap = A->p ; anz = Ap [ncol] ; ASSERT ((size_t) anz <= A->nzmax) ; CHOLMOD(reallocate_sparse) (anz, A, Common) ; ASSERT (Common->status >= CHOLMOD_OK) ; /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&F, Common) ; return (TRUE) ; } Matrix/src/CHOLMOD/Core/cholmod_add.c0000644000175100001440000002024012271765436016714 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_add ===================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* C = alpha*A + beta*B, or spones(A+B). Result is packed, with sorted or * unsorted columns. This routine is much faster and takes less memory if C * is allowed to have unsorted columns. * * If A and B are both symmetric (in upper form) then C is the same. Likewise, * if A and B are both symmetric (in lower form) then C is the same. * Otherwise, C is unsymmetric. A and B must have the same dimension. * * workspace: Flag (nrow), W (nrow) if values, Iwork (max (nrow,ncol)). * allocates temporary copies for A and B if they are symmetric. * allocates temporary copy of C if it is to be returned sorted. * * A and B can have an xtype of pattern or real. Complex or zomplex cases * are supported only if the "values" input parameter is FALSE. */ #include "cholmod_internal.h" #include "cholmod_core.h" cholmod_sparse *CHOLMOD(add) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to add */ cholmod_sparse *B, /* matrix to add */ double alpha [2], /* scale factor for A */ double beta [2], /* scale factor for B */ int values, /* if TRUE compute the numerical values of C */ int sorted, /* if TRUE, sort columns of C */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Bx, *Cx, *W ; Int apacked, up, lo, nrow, ncol, bpacked, nzmax, pa, paend, pb, pbend, i, j, p, mark, nz ; Int *Ap, *Ai, *Anz, *Bp, *Bi, *Bnz, *Flag, *Cp, *Ci ; cholmod_sparse *A2, *B2, *C ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_NULL (B, NULL) ; values = values && (A->xtype != CHOLMOD_PATTERN) && (B->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; RETURN_IF_XTYPE_INVALID (B, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; if (A->nrow != B->nrow || A->ncol != B->ncol) { /* A and B must have the same dimensions */ ERROR (CHOLMOD_INVALID, "A and B dimesions do not match") ; return (NULL) ; } /* A and B must have the same numerical type if values is TRUE (both must * be CHOLMOD_REAL, this is implicitly checked above) */ Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; ncol = A->ncol ; CHOLMOD(allocate_work) (nrow, MAX (nrow,ncol), values ? nrow : 0, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nrow <= 1) { /* C will be implicitly sorted, so no need to sort it here */ sorted = FALSE ; } /* convert A or B to unsymmetric, if necessary */ A2 = NULL ; B2 = NULL ; if (A->stype != B->stype) { if (A->stype) { /* workspace: Iwork (max (nrow,ncol)) */ A2 = CHOLMOD(copy) (A, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } A = A2 ; } if (B->stype) { /* workspace: Iwork (max (nrow,ncol)) */ B2 = CHOLMOD(copy) (B, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&A2, Common) ; return (NULL) ; /* out of memory */ } B = B2 ; } } /* get the A matrix */ ASSERT (A->stype == B->stype) ; up = (A->stype > 0) ; lo = (A->stype < 0) ; Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; apacked = A->packed ; /* get the B matrix */ Bp = B->p ; Bnz = B->nz ; Bi = B->i ; Bx = B->x ; bpacked = B->packed ; /* get workspace */ W = Common->Xwork ; /* size nrow, used if values is TRUE */ Flag = Common->Flag ; /* size nrow, Flag [0..nrow-1] < mark on input */ /* ---------------------------------------------------------------------- */ /* allocate the result C */ /* ---------------------------------------------------------------------- */ /* If integer overflow occurs, nzmax < 0 and the allocate fails properly * (likewise in most other matrix manipulation routines). */ nzmax = CHOLMOD(nnz) (A, Common) + CHOLMOD(nnz) (B, Common) ; C = CHOLMOD(allocate_sparse) (nrow, ncol, nzmax, FALSE, TRUE, SIGN (A->stype), values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; return (NULL) ; /* out of memory */ } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* compute C = alpha*A + beta*B */ /* ---------------------------------------------------------------------- */ nz = 0 ; for (j = 0 ; j < ncol ; j++) { Cp [j] = nz ; /* clear the Flag array */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* scatter B into W */ pb = Bp [j] ; pbend = (bpacked) ? (Bp [j+1]) : (pb + Bnz [j]) ; for (p = pb ; p < pbend ; p++) { i = Bi [p] ; if ((up && i > j) || (lo && i < j)) { continue ; } Flag [i] = mark ; if (values) { W [i] = beta [0] * Bx [p] ; } } /* add A and gather from W into C(:,j) */ pa = Ap [j] ; paend = (apacked) ? (Ap [j+1]) : (pa + Anz [j]) ; for (p = pa ; p < paend ; p++) { i = Ai [p] ; if ((up && i > j) || (lo && i < j)) { continue ; } Flag [i] = EMPTY ; Ci [nz] = i ; if (values) { Cx [nz] = W [i] + alpha [0] * Ax [p] ; W [i] = 0 ; } nz++ ; } /* gather remaining entries into C(:,j), using pattern of B */ for (p = pb ; p < pbend ; p++) { i = Bi [p] ; if ((up && i > j) || (lo && i < j)) { continue ; } if (Flag [i] == mark) { Ci [nz] = i ; if (values) { Cx [nz] = W [i] ; W [i] = 0 ; } nz++ ; } } } Cp [ncol] = nz ; /* ---------------------------------------------------------------------- */ /* reduce C in size and free temporary matrices */ /* ---------------------------------------------------------------------- */ ASSERT (MAX (1,nz) <= C->nzmax) ; CHOLMOD(reallocate_sparse) (nz, C, Common) ; ASSERT (Common->status >= CHOLMOD_OK) ; /* clear the Flag array */ mark = CHOLMOD(clear_flag) (Common) ; CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; /* ---------------------------------------------------------------------- */ /* sort C, if requested */ /* ---------------------------------------------------------------------- */ if (sorted) { /* workspace: Iwork (max (nrow,ncol)) */ if (!CHOLMOD(sort) (C, Common)) { CHOLMOD(free_sparse) (&C, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } } } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (C, "add", Common) >= 0) ; return (C) ; } Matrix/src/CHOLMOD/Core/cholmod_copy.c0000644000175100001440000002731512271765436017150 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_copy ==================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* C = A, which allocates C and copies A into C, with possible change of * stype. The diagonal can optionally be removed. The numerical entries * can optionally be copied. This routine differs from cholmod_copy_sparse, * which makes an exact copy of a sparse matrix. * * A can be of any type (packed/unpacked, upper/lower/unsymmetric). C is * packed and can be of any stype (upper/lower/unsymmetric), except that if * A is rectangular C can only be unsymmetric. If the stype of A and C * differ, then the appropriate conversion is made. * * Symmetry of A (A->stype): * <0: lower: assume A is symmetric with just tril(A); the rest of A is ignored * 0 unsym: assume A is unsymmetric; consider all entries in A * >0 upper: assume A is symmetric with just triu(A); the rest of A is ignored * * Symmetry of C (stype parameter): * <0 lower: return just tril(C) * 0 unsym: return all of C * >0 upper: return just triu(C) * * In MATLAB: Using cholmod_copy: * ---------- ---------------------------- * C = A ; A unsymmetric, C unsymmetric * C = tril (A) ; A unsymmetric, C lower * C = triu (A) ; A unsymmetric, C upper * U = triu (A) ; L = tril (U',-1) ; C = L+U ; A upper, C unsymmetric * C = triu (A)' ; A upper, C lower * C = triu (A) ; A upper, C upper * L = tril (A) ; U = triu (L',1) ; C = L+U ; A lower, C unsymmetric * C = tril (A) ; A lower, C lower * C = tril (A)' ; A lower, C upper * * workspace: Iwork (max (nrow,ncol)) * * A can have an xtype of pattern or real. Complex and zomplex cases only * supported when mode <= 0 (in which case the numerical values are ignored). */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === copy_sym_to_unsym ==================================================== */ /* ========================================================================== */ /* Construct an unsymmetric copy of a symmetric sparse matrix. This does the * work for as C = cholmod_copy (A, 0, mode, Common) when A is symmetric. * In this case, extra space can be added to C. */ static cholmod_sparse *copy_sym_to_unsym ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) * -2: pattern only, no diagonal, add 50% + n extra * space to C */ /* --------------- */ cholmod_common *Common ) { double aij ; double *Ax, *Cx ; Int *Ap, *Ai, *Anz, *Cp, *Ci, *Wj, *Iwork ; cholmod_sparse *C ; Int nrow, ncol, nz, packed, j, p, pend, i, pc, up, lo, values, diag, astype, extra ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; ncol = A->ncol ; Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; packed = A->packed ; values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ; diag = (mode >= 0) ; astype = SIGN (A->stype) ; up = (astype > 0) ; lo = (astype < 0) ; ASSERT (astype != 0) ; /* ---------------------------------------------------------------------- */ /* create an unsymmetric copy of a symmetric matrix */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; Wj = Iwork ; /* size ncol (i/i/l) */ /* In MATLAB notation, for converting a symmetric/upper matrix: * U = triu (A) ; * L = tril (U',-1) ; * C = L + U ; * * For converting a symmetric/lower matrix to unsymmetric: * L = tril (A) ; * U = triu (L',1) ; * C = L + U ; */ ASSERT (up || lo) ; PRINT1 (("copy: convert symmetric to unsym\n")) ; /* count the number of entries in each column of C */ for (j = 0 ; j < ncol ; j++) { Wj [j] = 0 ; } for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i == j) { /* the diagonal entry A(i,i) will appear just once * (unless it is excluded with mode < 0) */ if (diag) { Wj [j]++ ; } } else if ((up && i < j) || (lo && i > j)) { /* upper case: A(i,j) is in the strictly upper part; * A(j,i) will be added to the strictly lower part of C. * lower case is the opposite. */ Wj [j]++ ; Wj [i]++ ; } } } nz = 0 ; for (j = 0 ; j < ncol ; j++) { nz += Wj [j] ; } extra = (mode == -2) ? (nz/2 + ncol) : 0 ; /* allocate C. C is sorted if and only if A is sorted */ C = CHOLMOD(allocate_sparse) (nrow, ncol, nz + extra, A->sorted, TRUE, 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* construct the column pointers for C */ p = 0 ; for (j = 0 ; j < ncol ; j++) { Cp [j] = p ; p += Wj [j] ; } Cp [ncol] = p ; for (j = 0 ; j < ncol ; j++) { Wj [j] = Cp [j] ; } /* construct C */ if (values) { /* pattern and values */ ASSERT (diag) ; for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; aij = Ax [p] ; if (i == j) { /* add diagonal entry A(i,i) to column i */ pc = Wj [i]++ ; Ci [pc] = i ; Cx [pc] = aij ; } else if ((up && i < j) || (lo && i > j)) { /* add A(i,j) to column j */ pc = Wj [j]++ ; Ci [pc] = i ; Cx [pc] = aij ; /* add A(j,i) to column i */ pc = Wj [i]++ ; Ci [pc] = j ; Cx [pc] = aij ; } } } } else { /* pattern only, possibly excluding the diagonal */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i == j) { /* add diagonal entry A(i,i) to column i * (unless it is excluded with mode < 0) */ if (diag) { Ci [Wj [i]++] = i ; } } else if ((up && i < j) || (lo && i > j)) { /* add A(i,j) to column j */ Ci [Wj [j]++] = i ; /* add A(j,i) to column i */ Ci [Wj [i]++] = j ; } } } } /* ---------------------------------------------------------------------- */ /* return the result */ /* ---------------------------------------------------------------------- */ DEBUG (i = CHOLMOD(dump_sparse) (C, "copy_sym_to_unsym", Common)) ; PRINT1 (("mode %d nnzdiag "ID"\n", mode, i)) ; ASSERT (IMPLIES (mode < 0, i == 0)) ; return (C) ; } /* ========================================================================== */ /* === cholmod_copy ========================================================= */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(copy) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ int stype, /* requested stype of C */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *C ; Int nrow, ncol, up, lo, values, diag, astype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; nrow = A->nrow ; ncol = A->ncol ; if ((stype || A->stype) && nrow != ncol) { /* inputs invalid */ ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ CHOLMOD(allocate_work) (0, MAX (nrow,ncol), 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ diag = (mode >= 0) ; astype = SIGN (A->stype) ; stype = SIGN (stype) ; up = (astype > 0) ; lo = (astype < 0) ; /* ---------------------------------------------------------------------- */ /* copy the matrix */ /* ---------------------------------------------------------------------- */ if (astype == stype) { /* ------------------------------------------------------------------ */ /* symmetry of A and C are the same */ /* ------------------------------------------------------------------ */ /* copy A into C, keeping the same symmetry. If A is symmetric * entries in the ignored part of A are not copied into C */ C = CHOLMOD(band) (A, -nrow, ncol, mode, Common) ; } else if (!astype) { /* ------------------------------------------------------------------ */ /* convert unsymmetric matrix A into a symmetric matrix C */ /* ------------------------------------------------------------------ */ if (stype > 0) { /* C = triu (A) */ C = CHOLMOD(band) (A, 0, ncol, mode, Common) ; } else { /* C = tril (A) */ C = CHOLMOD(band) (A, -nrow, 0, mode, Common) ; } if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } C->stype = stype ; } else if (astype == -stype) { /* ------------------------------------------------------------------ */ /* transpose a symmetric matrix */ /* ------------------------------------------------------------------ */ /* converting upper to lower or lower to upper */ /* workspace: Iwork (nrow) */ C = CHOLMOD(transpose) (A, values, Common) ; if (!diag) { /* remove diagonal, if requested */ CHOLMOD(band_inplace) (-nrow, ncol, -1, C, Common) ; } } else { /* ------------------------------------------------------------------ */ /* create an unsymmetric copy of a symmetric matrix */ /* ------------------------------------------------------------------ */ C = copy_sym_to_unsym (A, mode, Common) ; } /* ---------------------------------------------------------------------- */ /* return if error */ /* ---------------------------------------------------------------------- */ if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } /* ---------------------------------------------------------------------- */ /* return the result */ /* ---------------------------------------------------------------------- */ DEBUG (diag = CHOLMOD(dump_sparse) (C, "copy", Common)) ; PRINT1 (("mode %d nnzdiag "ID"\n", mode, diag)) ; ASSERT (IMPLIES (mode < 0, diag == 0)) ; return (C) ; } Matrix/src/CHOLMOD/Core/cholmod_dense.c0000644000175100001440000005042512271765436017272 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_dense =================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2013, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Core utility routines for the cholmod_dense object: * * The solve routines and some of the MatrixOps and Modify routines use dense * matrices as inputs. These are held in column-major order. With a leading * dimension of d, the entry in row i and column j is held in x [i+j*d]. * * Primary routines: * ----------------- * cholmod_allocate_dense allocate a dense matrix * cholmod_free_dense free a dense matrix * * Secondary routines: * ------------------- * cholmod_zeros allocate a dense matrix of all zeros * cholmod_ones allocate a dense matrix of all ones * cholmod_eye allocate a dense identity matrix * cholmod_sparse_to_dense create a dense matrix copy of a sparse matrix * cholmod_dense_to_sparse create a sparse matrix copy of a dense matrix * cholmod_copy_dense create a copy of a dense matrix * cholmod_copy_dense2 copy a dense matrix (pre-allocated) * * All routines in this file can handle the real, complex, and zomplex cases. * Pattern-only dense matrices are not supported. cholmod_sparse_to_dense can * take a pattern-only input sparse matrix, however, and cholmod_dense_to_sparse * can generate a pattern-only output sparse matrix. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define PATTERN #include "t_cholmod_dense.c" #define REAL #include "t_cholmod_dense.c" #define COMPLEX #include "t_cholmod_dense.c" #define ZOMPLEX #include "t_cholmod_dense.c" /* ========================================================================== */ /* === cholmod_allocate_dense =============================================== */ /* ========================================================================== */ /* Allocate a dense matrix with leading dimension d. The space is not * initialized. */ cholmod_dense *CHOLMOD(allocate_dense) ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ size_t d, /* leading dimension */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *X ; size_t nzmax, nzmax0 ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; if (d < nrow) { ERROR (CHOLMOD_INVALID, "leading dimension invalid") ; return (NULL) ; } if (xtype < CHOLMOD_REAL || xtype > CHOLMOD_ZOMPLEX) { ERROR (CHOLMOD_INVALID, "xtype invalid") ; return (NULL) ; } /* ensure the dimensions do not cause integer overflow */ (void) CHOLMOD(add_size_t) (ncol, 2, &ok) ; /* nzmax = MAX (1, d*ncol) ; */ nzmax = CHOLMOD(mult_size_t) (d, ncol, &ok) ; nzmax = MAX (1, nzmax) ; if (!ok || nrow > Int_max || ncol > Int_max || nzmax > Int_max) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate header */ /* ---------------------------------------------------------------------- */ X = CHOLMOD(malloc) (sizeof (cholmod_dense), 1, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } PRINT1 (("cholmod_allocate_dense %d-by-%d nzmax %d xtype %d\n", nrow, ncol, nzmax, xtype)) ; X->nrow = nrow ; X->ncol = ncol ; X->nzmax = nzmax ; X->xtype = xtype ; X->dtype = DTYPE ; X->x = NULL ; X->z = NULL ; X->d = d ; /* ---------------------------------------------------------------------- */ /* allocate the matrix itself */ /* ---------------------------------------------------------------------- */ nzmax0 = 0 ; CHOLMOD(realloc_multiple) (nzmax, 0, xtype, NULL, NULL, &(X->x), &(X->z), &nzmax0, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_dense) (&X, Common) ; return (NULL) ; /* out of memory */ } return (X) ; } /* ========================================================================== */ /* === cholmod_zeros ======================================================== */ /* ========================================================================== */ /* Allocate a dense matrix and set it to zero */ cholmod_dense *CHOLMOD(zeros) ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *X ; double *Xx, *Xz ; Int i, nz ; /* ---------------------------------------------------------------------- */ /* allocate a dense matrix and set it to zero */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; X = CHOLMOD(allocate_dense) (nrow, ncol, nrow, xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* NULL Common, out of memory, or inputs invalid */ } Xx = X->x ; Xz = X->z ; nz = MAX (1, X->nzmax) ; switch (xtype) { case CHOLMOD_REAL: for (i = 0 ; i < nz ; i++) { Xx [i] = 0 ; } break ; case CHOLMOD_COMPLEX: for (i = 0 ; i < 2*nz ; i++) { Xx [i] = 0 ; } break ; case CHOLMOD_ZOMPLEX: for (i = 0 ; i < nz ; i++) { Xx [i] = 0 ; } for (i = 0 ; i < nz ; i++) { Xz [i] = 0 ; } break ; } return (X) ; } /* ========================================================================== */ /* === cholmod_ones ========================================================= */ /* ========================================================================== */ /* Allocate a dense matrix and set it to zero */ cholmod_dense *CHOLMOD(ones) ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *X ; double *Xx, *Xz ; Int i, nz ; /* ---------------------------------------------------------------------- */ /* allocate a dense matrix and set it to all ones */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; X = CHOLMOD(allocate_dense) (nrow, ncol, nrow, xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* NULL Common, out of memory, or inputs invalid */ } Xx = X->x ; Xz = X->z ; nz = MAX (1, X->nzmax) ; switch (xtype) { case CHOLMOD_REAL: for (i = 0 ; i < nz ; i++) { Xx [i] = 1 ; } break ; case CHOLMOD_COMPLEX: for (i = 0 ; i < nz ; i++) { Xx [2*i ] = 1 ; Xx [2*i+1] = 0 ; } break ; case CHOLMOD_ZOMPLEX: for (i = 0 ; i < nz ; i++) { Xx [i] = 1 ; } for (i = 0 ; i < nz ; i++) { Xz [i] = 0 ; } break ; } return (X) ; } /* ========================================================================== */ /* === cholmod_eye ========================================================== */ /* ========================================================================== */ /* Allocate a dense matrix and set it to the identity matrix */ cholmod_dense *CHOLMOD(eye) ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *X ; double *Xx, *Xz ; Int i, n, nz ; /* ---------------------------------------------------------------------- */ /* allocate a dense matrix and set it to the identity matrix */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; X = CHOLMOD(zeros) (nrow, ncol, xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* NULL Common, out of memory, or inputs invalid */ } nz = MAX (1, nrow*ncol) ; Xx = X->x ; Xz = X->z ; n = MIN (nrow, ncol) ; switch (xtype) { case CHOLMOD_REAL: case CHOLMOD_ZOMPLEX: for (i = 0 ; i < n ; i++) { Xx [i + i*nrow] = 1 ; } break ; case CHOLMOD_COMPLEX: for (i = 0 ; i < n ; i++) { Xx [2 * (i + i*nrow)] = 1 ; } break ; } return (X) ; } /* ========================================================================== */ /* === cholmod_free_dense =================================================== */ /* ========================================================================== */ /* free a dense matrix * * workspace: none */ int CHOLMOD(free_dense) ( /* ---- in/out --- */ cholmod_dense **XHandle, /* dense matrix to deallocate, NULL on output */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *X ; RETURN_IF_NULL_COMMON (FALSE) ; if (XHandle == NULL) { /* nothing to do */ return (TRUE) ; } X = *XHandle ; if (X == NULL) { /* nothing to do */ return (TRUE) ; } switch (X->xtype) { case CHOLMOD_REAL: X->x = CHOLMOD(free) (X->nzmax, sizeof (double), X->x, Common) ; break ; case CHOLMOD_COMPLEX: X->x = CHOLMOD(free) (X->nzmax, 2*sizeof (double), X->x, Common) ; break ; case CHOLMOD_ZOMPLEX: X->x = CHOLMOD(free) (X->nzmax, sizeof (double), X->x, Common) ; X->z = CHOLMOD(free) (X->nzmax, sizeof (double), X->z, Common) ; break ; } *XHandle = CHOLMOD(free) (1, sizeof (cholmod_dense), (*XHandle), Common) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_ensure_dense ================================================= */ /* ========================================================================== */ /* Ensure that the input matrix has a certain size and type. If not, free * the existing matrix and reallocate one of the right size and type. * Returns a pointer to the cholmod_dense matrix, possibly reallocated. * Also modifies the input matrix handle, XHandle, if necessary. */ cholmod_dense *CHOLMOD(ensure_dense) ( /* ---- input/output ---- */ cholmod_dense **XHandle, /* matrix handle to check */ /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ size_t d, /* leading dimension */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *X ; RETURN_IF_NULL_COMMON (NULL) ; if (XHandle == NULL) { ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (NULL) ; } X = *XHandle ; if (X == NULL || X->nrow != nrow || X->ncol != ncol || X->d != d || X->xtype != xtype) { /* Matrix X is not allocated, or has the wrong size. Free it and * reallocate it in the right size and shape. If an error occurs * (out of memory or inputs nrow, etc invalid), then the error is * set in cholmod_allocate_dense and X is returned as NULL. */ #if 0 if (X == NULL) { printf ("oops, X was null\n") ; } else { printf ("oops, nrow %g %g ncol %g %g d %g %g xtype %g %g\n", (double) X->nrow, (double) nrow, (double) X->ncol, (double) ncol, (double) X->d, (double) d, (double) X->xtype, (double) xtype ) ; } #endif CHOLMOD(free_dense) (XHandle, Common) ; X = CHOLMOD(allocate_dense) (nrow, ncol, d, xtype, Common) ; *XHandle = X ; } return (X) ; } /* ========================================================================== */ /* === cholmod_sparse_to_dense ============================================== */ /* ========================================================================== */ /* Convert a sparse matrix to a dense matrix. * The output dense matrix has the same xtype as the input sparse matrix, * except that a pattern-only sparse matrix A is converted into a real dense * matrix X, with 1's and 0's. All xtypes are supported. */ cholmod_dense *CHOLMOD(sparse_to_dense) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *X = NULL ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; if (A->stype && A->nrow != A->ncol) { ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (NULL) ; } Common->status = CHOLMOD_OK ; ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* convert the matrix, using template routine */ /* ---------------------------------------------------------------------- */ switch (A->xtype) { case CHOLMOD_PATTERN: X = p_cholmod_sparse_to_dense (A, Common) ; break ; case CHOLMOD_REAL: X = r_cholmod_sparse_to_dense (A, Common) ; break ; case CHOLMOD_COMPLEX: X = c_cholmod_sparse_to_dense (A, Common) ; break ; case CHOLMOD_ZOMPLEX: X = z_cholmod_sparse_to_dense (A, Common) ; break ; } return (X) ; } /* ========================================================================== */ /* === cholmod_dense_to_sparse ============================================== */ /* ========================================================================== */ /* Convert a dense matrix to a sparse matrix, similar to the MATLAB statements: * * C = sparse (X) values = TRUE * C = spones (sparse (X)) values = FALSE * * except that X must be double (it can be of many different types in MATLAB) * * The resulting sparse matrix C has the same numeric xtype as the input dense * matrix X, unless "values" is FALSE (in which case C is real, where C(i,j)=1 * if (i,j) is an entry in X. */ cholmod_sparse *CHOLMOD(dense_to_sparse) ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ int values, /* TRUE if values to be copied, FALSE otherwise */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *C = NULL ; DEBUG (CHOLMOD(dump_dense) (X, "X", Common)) ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (X, NULL) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ; if (X->d < X->nrow) { ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* convert the matrix, using template routine */ /* ---------------------------------------------------------------------- */ switch (X->xtype) { case CHOLMOD_REAL: C = r_cholmod_dense_to_sparse (X, values, Common) ; break ; case CHOLMOD_COMPLEX: C = c_cholmod_dense_to_sparse (X, values, Common) ; break ; case CHOLMOD_ZOMPLEX: C = z_cholmod_dense_to_sparse (X, values, Common) ; break ; } return (C) ; } /* ========================================================================== */ /* === cholmod_copy_dense2 ================================================== */ /* ========================================================================== */ /* Y = X, where X and Y are both already allocated. The leading dimensions of * X and Y may differ, but both must be >= the # of rows in X and Y. * Entries in rows nrow to d-1 are not copied from X, since the space might not * be initialized. Y->nzmax is unchanged. X->nzmax is typically * (X->d)*(X->ncol), but a user might modify that condition outside of any * CHOLMOD routine. * * The two dense matrices X and Y must have the same numeric xtype. */ int CHOLMOD(copy_dense2) ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ /* ---- output --- */ cholmod_dense *Y, /* copy of matrix X */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (X, FALSE) ; RETURN_IF_NULL (Y, FALSE) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (Y, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; if (X->nrow != Y->nrow || X->ncol != Y->ncol || X->xtype != Y->xtype) { ERROR (CHOLMOD_INVALID, "X and Y must have same dimensions and xtype") ; return (FALSE) ; } if (X->d < X->nrow || Y->d < Y->nrow || (X->d * X->ncol) > X->nzmax || (Y->d * Y->ncol) > Y->nzmax) { ERROR (CHOLMOD_INVALID, "X and/or Y invalid") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* copy the matrix, using template routine */ /* ---------------------------------------------------------------------- */ switch (X->xtype) { case CHOLMOD_REAL: r_cholmod_copy_dense2 (X, Y) ; break ; case CHOLMOD_COMPLEX: c_cholmod_copy_dense2 (X, Y) ; break ; case CHOLMOD_ZOMPLEX: z_cholmod_copy_dense2 (X, Y) ; break ; } return (TRUE) ; } /* ========================================================================== */ /* === cholmod_copy_dense =================================================== */ /* ========================================================================== */ /* Y = X, copy a dense matrix */ cholmod_dense *CHOLMOD(copy_dense) ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *Y ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (X, NULL) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate result */ /* ---------------------------------------------------------------------- */ Y = CHOLMOD(allocate_dense) (X->nrow, X->ncol, X->d, X->xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory or X invalid */ } /* ---------------------------------------------------------------------- */ /* Y = X */ /* ---------------------------------------------------------------------- */ /* This cannot fail (X and Y are allocated, and have the same nrow, ncol * d, and xtype) */ CHOLMOD(copy_dense2) (X, Y, Common) ; /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ return (Y) ; } Matrix/src/CHOLMOD/Core/t_cholmod_change_factor.c0000644000175100001440000003751312271765436021305 0ustar hornikusers/* ========================================================================== */ /* === Core/t_cholmod_change_factor ========================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Template routine for cholmod_change_factor. All xtypes supported. */ #include "cholmod_template.h" /* ========================================================================== */ /* === t_change_simplicial_numeric ========================================== */ /* ========================================================================== */ static void TEMPLATE (change_simplicial_numeric) ( cholmod_factor *L, Int to_ll, Int to_packed, Int *newLi, double *newLx, double *newLz, Int lnz, Int grow, double grow1, Int grow2, Int make_ll, Int make_monotonic, Int make_ldl, cholmod_common *Common ) { double xlen, dj [1], ljj [1], lj2 [1] ; double *Lx, *Lz ; Int *Lp, *Li, *Lnz ; Int n, j, len, pnew, pold, k, p, pend ; n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ; Lz = L->z ; Lnz = L->nz ; if (make_ll) { L->minor = n ; } if (make_monotonic) { /* ------------------------------------------------------------------ */ /* reorder the columns to make them monotonic */ /* ------------------------------------------------------------------ */ pnew = 0 ; for (j = 0 ; j < n ; j++) { /* copy and pack column j */ len = Lnz [j] ; PRINT2 (("j: "ID" Lnz[j] "ID" len "ID" p "ID"\n", j, Lnz [j], len, pnew)) ; pold = Lp [j] ; ASSERT (Li [pold] == j) ; if (make_ll) { /* ---------------------------------------------------------- */ /* copy and convert LDL' to LL' */ /* ---------------------------------------------------------- */ /* dj = Lx [pold] ; */ ASSIGN_REAL (dj,0, Lx,pold) ; if (IS_LE_ZERO (dj [0])) { /* Conversion has failed; matrix is not positive definite. * Do not modify the column so that the LDL' factorization * can be restored if desired, by converting back to LDL'. * Continue the conversion, but flag the error. */ if (L->minor == (size_t) n) { ERROR (CHOLMOD_NOT_POSDEF, "L not positive definite") ; L->minor = j ; } for (k = 0 ; k < len ; k++) { newLi [pnew + k] = Li [pold + k] ; /* newLx [pnew + k] = Lx [pold + k] ; */ ASSIGN (newLx, newLz, pnew+k, Lx, Lz, pold+k) ; } } else { ljj [0] = sqrt (dj [0]) ; newLi [pnew] = j ; /* newLx [pnew] = ljj ; */ ASSIGN_REAL (newLx, pnew, ljj, 0) ; CLEAR_IMAG (newLx, newLz, pnew) ; for (k = 1 ; k < len ; k++) { newLi [pnew + k] = Li [pold + k] ; /* newLx [pnew + k] = Lx [pold + k] * ljj ; */ MULT_REAL (newLx, newLz, pnew+k, Lx, Lz, pold+k, ljj,0); } } } else if (make_ldl) { /* ---------------------------------------------------------- */ /* copy and convert LL' to LDL' */ /* ---------------------------------------------------------- */ /* ljj = Lx [pold] ; */ ASSIGN_REAL (ljj, 0, Lx, pold) ; if (ljj [0] <= 0) { /* matrix is not positive-definite; copy column as-is */ for (k = 0 ; k < len ; k++) { newLi [pnew + k] = Li [pold + k] ; /* newLx [pnew + k] = Lx [pold + k] ; */ ASSIGN (newLx, newLz, pnew+k, Lx, Lz, pold+k) ; } } else { newLi [pnew] = j ; /* newLx [pnew] = ljj*ljj ; */ lj2 [0] = ljj [0] * ljj [0] ; ASSIGN_REAL (newLx, pnew, lj2, 0) ; CLEAR_IMAG (newLx, newLz, pnew) ; for (k = 1 ; k < len ; k++) { newLi [pnew + k] = Li [pold + k] ; /* newLx [pnew + k] = Lx [pold + k] / ljj ; */ DIV_REAL (newLx, newLz, pnew+k, Lx, Lz, pold+k, ljj,0) ; } } } else { /* ---------------------------------------------------------- */ /* copy and leave LL' or LDL' as-is */ /* ---------------------------------------------------------- */ for (k = 0 ; k < len ; k++) { newLi [pnew + k] = Li [pold + k] ; /* newLx [pnew + k] = Lx [pold + k] ; */ ASSIGN (newLx, newLz, pnew+k, Lx, Lz, pold+k) ; } } Lp [j] = pnew ; /* compute len in double to avoid integer overflow */ if (grow) { xlen = (double) len ; xlen = grow1 * xlen + grow2 ; xlen = MIN (xlen, n-j) ; len = (Int) xlen ; } ASSERT (len >= Lnz [j] && len <= n-j) ; pnew += len ; ASSERT (pnew > 0) ; /* integer overflow case already covered */ } Lp [n] = pnew ; PRINT1 (("final pnew = "ID", lnz "ID" lnzmax %g\n", pnew, lnz, (double) L->nzmax)) ; ASSERT (pnew <= lnz) ; /* free the old L->i and L->x and replace with the new ones */ CHOLMOD(free) (L->nzmax, sizeof (Int), L->i, Common) ; #ifdef REAL CHOLMOD(free) (L->nzmax, sizeof (double), L->x, Common) ; #elif defined (COMPLEX) CHOLMOD(free) (L->nzmax, 2*sizeof (double), L->x, Common) ; #else CHOLMOD(free) (L->nzmax, sizeof (double), L->x, Common) ; CHOLMOD(free) (L->nzmax, sizeof (double), L->z, Common) ; #endif L->i = newLi ; L->x = newLx ; L->z = newLz ; L->nzmax = lnz ; /* reconstruct the link list */ natural_list (L) ; } else if (to_packed) { /* ------------------------------------------------------------------ */ /* already monotonic, just pack the columns of L */ /* ------------------------------------------------------------------ */ pnew = 0 ; if (make_ll) { /* -------------------------------------------------------------- */ /* pack and convert LDL' to LL' */ /* -------------------------------------------------------------- */ for (j = 0 ; j < n ; j++) { /* pack column j */ pold = Lp [j] ; len = Lnz [j] ; ASSERT (len > 0) ; ASSERT (Li [pold] == j) ; PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ; /* dj = Lx [pold] ; */ ASSIGN_REAL (dj,0, Lx,pold) ; if (IS_LE_ZERO (dj [0])) { /* Conversion has failed; matrix is not positive definite. * Do not modify the column so that the LDL' factorization * can be restored if desired, by converting back to LDL'. * Continue the conversion, but flag the error. */ if (L->minor == (size_t) n) { ERROR (CHOLMOD_NOT_POSDEF, "L not positive definite") ; L->minor = j ; } for (k = 0 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; /* Lx [pnew + k] = Lx [pold + k] ; */ ASSIGN (Lx, Lz, pnew+k, Lx, Lz, pold+k) ; } } else { ljj [0] = sqrt (dj [0]) ; Li [pnew] = j ; /* Lx [pnew] = ljj ; */ ASSIGN_REAL (Lx, pnew, ljj, 0) ; CLEAR_IMAG (Lx, Lz, pnew) ; for (k = 1 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; /* Lx [pnew + k] = Lx [pold + k] * ljj ; */ MULT_REAL (Lx, Lz, pnew+k, Lx, Lz, pold+k, ljj,0) ; } } Lp [j] = pnew ; pnew += len ; } } else if (make_ldl) { /* -------------------------------------------------------------- */ /* pack and convert LL' to LDL' */ /* -------------------------------------------------------------- */ for (j = 0 ; j < n ; j++) { /* pack column j */ pold = Lp [j] ; len = Lnz [j] ; /* ljj = Lx [pold] ; */ ASSIGN_REAL (ljj, 0, Lx, pold) ; ASSERT (len > 0) ; PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ; if (ljj [0] <= 0) { /* matrix is not positive-definite; pack column as-is */ for (k = 0 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; /* Lx [pnew + k] = Lx [pold + k] ; */ ASSIGN (Lx, Lz, pnew+k, Lx, Lz, pold+k) ; } } else { Li [pnew] = Li [pold] ; /* Lx [pnew] = ljj*ljj ; */ lj2 [0] = ljj [0] * ljj [0] ; ASSIGN_REAL (Lx, pnew, lj2, 0) ; CLEAR_IMAG (Lx, Lz, pnew) ; for (k = 1 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; /* Lx [pnew + k] = Lx [pold + k] / ljj ; */ DIV_REAL (Lx, Lz, pnew+k, Lx, Lz, pold+k, ljj,0) ; } } Lp [j] = pnew ; pnew += len ; } } else { /* ---------------------------------------------------------- */ /* pack and leave LL' or LDL' as-is */ /* ---------------------------------------------------------- */ for (j = 0 ; j < n ; j++) { /* pack column j */ pold = Lp [j] ; len = Lnz [j] ; ASSERT (len > 0) ; PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ; if (pnew < pold) { PRINT2 ((" pack this column\n")) ; for (k = 0 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; /* Lx [pnew + k] = Lx [pold + k] ; */ ASSIGN (Lx, Lz, pnew+k, Lx, Lz, pold+k) ; } Lp [j] = pnew ; } pnew += len ; } } Lp [n] = pnew ; PRINT2 (("Lp [n] = "ID"\n", pnew)) ; } else if (make_ll) { /* ------------------------------------------------------------------ */ /* convert LDL' to LL', but do so in-place */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < n ; j++) { p = Lp [j] ; pend = p + Lnz [j] ; /* dj = Lx [p] ; */ ASSIGN_REAL (dj,0, Lx,p) ; if (IS_LE_ZERO (dj [0])) { /* Conversion has failed; matrix is not positive definite. * Do not modify the column so that the LDL' factorization * can be restored if desired, by converting back to LDL'. * Continue the conversion, but flag the error. */ if (L->minor == (size_t) n) { ERROR (CHOLMOD_NOT_POSDEF, "L not positive definite") ; L->minor = j ; } } else { ljj [0] = sqrt (dj [0]) ; /* Lx [p] = ljj ; */ ASSIGN_REAL (Lx,p, ljj,0) ; CLEAR_IMAG (Lx, Lz, p) ; for (p++ ; p < pend ; p++) { /* Lx [p] *= ljj ; */ MULT_REAL (Lx,Lz,p, Lx,Lz,p, ljj,0) ; } } } } else if (make_ldl) { /* ------------------------------------------------------------------ */ /* convert LL' to LDL', but do so in-place */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < n ; j++) { p = Lp [j] ; pend = p + Lnz [j] ; /* ljj = Lx [p] ; */ ASSIGN_REAL (ljj, 0, Lx, p) ; if (ljj [0] > 0) { /* Lx [p] = ljj*ljj ; */ lj2 [0] = ljj [0] * ljj [0] ; ASSIGN_REAL (Lx, p, lj2, 0) ; CLEAR_IMAG (Lx, Lz, p) ; for (p++ ; p < pend ; p++) { /* Lx [p] /= ljj ; */ DIV_REAL (Lx,Lz,p, Lx,Lz,p, ljj,0) ; } } } } L->is_ll = to_ll ; DEBUG (CHOLMOD(dump_factor) (L, "done change simplicial numeric", Common)) ; } /* ========================================================================== */ /* === t_ll_super_to_simplicial_numeric ===================================== */ /* ========================================================================== */ /* A supernodal L can only be real or complex, not zomplex */ #ifndef ZOMPLEX static void TEMPLATE (ll_super_to_simplicial_numeric) ( cholmod_factor *L, Int to_packed, Int to_ll, cholmod_common *Common ) { double ljj [1], lj2 [1] ; double *Lx ; Int *Ls, *Lpi, *Lpx, *Super, *Lp, *Li, *Lnz ; Int n, lnz, s, nsuper, p, psi, psx, psend, nsrow, nscol, ii, jj, j, k1, k2, q ; L->is_ll = to_ll ; Lp = L->p ; Li = L->i ; Lx = L->x ; Lnz = L->nz ; lnz = L->nzmax ; n = L->n ; nsuper = L->nsuper ; Lpi = L->pi ; Lpx = L->px ; Ls = L->s ; Super = L->super ; p = 0 ; for (s = 0 ; s < nsuper ; s++) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; psx = Lpx [s] ; nsrow = psend - psi ; nscol = k2 - k1 ; for (jj = 0 ; jj < nscol ; jj++) { /* column j of L starts here */ j = jj + k1 ; if (to_ll) { if (to_packed) { /* ------------------------------------------------------ */ /* convert to LL' packed */ /* ------------------------------------------------------ */ Lp [j] = p ; PRINT2 (("Col j "ID" p "ID"\n", j, p)) ; for (ii = jj ; ii < nsrow ; ii++) { /* get L(i,j) from supernode and store in column j */ ASSERT (p < (Int) (L->xsize) && p <= psx+ii+jj*nsrow) ; Li [p] = Ls [psi + ii] ; /* Lx [p] = Lx [psx + ii + jj*nsrow] ; */ q = psx + ii + jj*nsrow ; ASSIGN (Lx,-,p, Lx,-,q) ; PRINT2 ((" i "ID" ", Li [p])) ; XPRINT2 (Lx,-,q) ; PRINT2 (("\n")) ; p++ ; } Lnz [j] = p - Lp [j] ; } else { /* ------------------------------------------------------ */ /* convert to LL' unpacked */ /* ------------------------------------------------------ */ p = psx + jj + jj*nsrow ; Lp [j] = p ; Li [p] = j ; Lnz [j] = nsrow - jj ; p++ ; for (ii = jj + 1 ; ii < nsrow ; ii++) { /* get L(i,j) from supernode and store in column j */ Li [psx + ii + jj*nsrow] = Ls [psi + ii] ; } } } else { if (to_packed) { /* ------------------------------------------------------ */ /* convert to LDL' packed */ /* ------------------------------------------------------ */ Lp [j] = p ; PRINT2 (("Col j "ID" p "ID"\n", Lp [j], p)) ; /* ljj = Lx [psx + jj + jj*nsrow] ; */ ASSIGN_REAL (ljj, 0, Lx, psx + jj + jj*nsrow) ; if (ljj [0] <= 0) { /* the matrix is not positive definite; do not divide */ /* Lx [p] = ljj ; */ ASSIGN_REAL (Lx, p, ljj, 0) ; CLEAR_IMAG (Lx, Lz, p) ; ljj [0] = 1 ; } else { lj2 [0] = ljj [0] * ljj [0] ; /* Lx [p] = ljj*ljj ; */ ASSIGN_REAL (Lx, p, lj2, 0) ; CLEAR_IMAG (Lx, Lz, p) ; } Li [p] = j ; p++ ; for (ii = jj + 1 ; ii < nsrow ; ii++) { /* get L(i,j) from supernode and store in column j */ ASSERT (p < (Int) (L->xsize) && p <= psx+ii+jj*nsrow) ; Li [p] = Ls [psi + ii] ; /* Lx [p] = Lx [psx + ii + jj*nsrow] / ljj ; */ q = psx + ii + jj*nsrow ; DIV_REAL (Lx, Lz, p, Lx, Lz, q, ljj,0) ; PRINT2 ((" i "ID" %g\n", Li [p], Lx [p])) ; p++ ; } Lnz [j] = p - Lp [j] ; } else { /* ------------------------------------------------------ */ /* convert to LDL' unpacked */ /* ------------------------------------------------------ */ p = psx + jj + jj*nsrow ; Lp [j] = p ; /* ljj = Lx [p] ; */ ASSIGN_REAL (ljj,0, Lx,p) ; if (ljj [0] <= 0) { /* the matrix is not positive definite; do not divide */ /* Lx [p] = ljj ; */ ASSIGN_REAL (Lx, p, ljj, 0) ; CLEAR_IMAG (Lx, Lz, p) ; ljj [0] = 1 ; } else { lj2 [0] = ljj [0] * ljj [0] ; /* Lx [p] = ljj*ljj ; */ ASSIGN_REAL (Lx, p, lj2, 0) ; CLEAR_IMAG (Lx, Lz, p) ; } Li [p] = j ; Lnz [j] = nsrow - jj ; p++ ; for (ii = jj + 1 ; ii < nsrow ; ii++) { /* get L(i,j) from supernode and store in column j */ Li [psx + ii + jj*nsrow] = Ls [psi + ii] ; /* Lx [psx + ii + jj*nsrow] /= ljj ; */ q = psx + ii + jj*nsrow ; DIV_REAL (Lx, Lz, q, Lx, Lz, q, ljj,0) ; } } } } } if (to_packed) { Lp [n] = p ; PRINT1 (("Final Lp "ID" n "ID" lnz "ID"\n", p, n, lnz)) ; ASSERT (Lp [n] == lnz) ; ASSERT (lnz <= (Int) (L->xsize)) ; /* reduce size of L->x to match L->i. This cannot fail. */ L->x = CHOLMOD(realloc) (lnz, #ifdef COMPLEX 2 * #endif sizeof (double), L->x, &(L->xsize), Common) ; ASSERT (lnz == (Int) (L->xsize)) ; Common->status = CHOLMOD_OK ; } else { Lp [n] = Lpx [nsuper] ; ASSERT (MAX (1,Lp [n]) == (Int) (L->xsize)) ; ASSERT (MAX (1,Lp [n]) == (Int) (L->nzmax)) ; } } #endif #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX Matrix/src/CHOLMOD/Core/t_cholmod_dense.c0000644000175100001440000001621112271765436017610 0ustar hornikusers/* ========================================================================== */ /* === Core/t_cholmod_dense ================================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Template routine for cholmod_dense. All xtypes supported, except that there * are no dense matrices with an xtype of pattern. */ #include "cholmod_template.h" /* ========================================================================== */ /* === t_cholmod_sparse_to_dense ============================================ */ /* ========================================================================== */ static cholmod_dense *TEMPLATE (cholmod_sparse_to_dense) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Xx, *Az, *Xz ; Int *Ap, *Ai, *Anz ; cholmod_dense *X ; Int i, j, p, pend, nrow, ncol, packed ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; ncol = A->ncol ; packed = A->packed ; Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; /* ---------------------------------------------------------------------- */ /* allocate result */ /* ---------------------------------------------------------------------- */ X = CHOLMOD(zeros) (nrow, ncol, XTYPE2, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } Xx = X->x ; Xz = X->z ; /* ---------------------------------------------------------------------- */ /* copy into dense matrix */ /* ---------------------------------------------------------------------- */ if (A->stype < 0) { /* A is symmetric with lower stored, but both parts of X are present */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= j) { ASSIGN2 (Xx, Xz, i+j*nrow, Ax, Az, p) ; ASSIGN2_CONJ (Xx, Xz, j+i*nrow, Ax, Az, p) ; } } } } else if (A->stype > 0) { /* A is symmetric with upper stored, but both parts of X are present */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i <= j) { ASSIGN2 (Xx, Xz, i+j*nrow, Ax, Az, p) ; ASSIGN2_CONJ (Xx, Xz, j+i*nrow, Ax, Az, p) ; } } } } else { /* both parts of A and X are present */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; ASSIGN2 (Xx, Xz, i+j*nrow, Ax, Az, p) ; } } } return (X) ; } #ifndef PATTERN /* There are no dense matrices of xtype CHOLMOD_PATTERN */ /* ========================================================================== */ /* === t_cholmod_dense_to_sparse ============================================ */ /* ========================================================================== */ static cholmod_sparse *TEMPLATE (cholmod_dense_to_sparse) ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ int values, /* TRUE if values to be copied, FALSE otherwise */ /* --------------- */ cholmod_common *Common ) { double *Xx, *Cx, *Xz, *Cz ; Int *Ci, *Cp ; cholmod_sparse *C ; Int i, j, p, d, nrow, ncol, nz ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = X->nrow ; ncol = X->ncol ; d = X->d ; Xx = X->x ; Xz = X->z ; /* ---------------------------------------------------------------------- */ /* count the number of nonzeros in the result */ /* ---------------------------------------------------------------------- */ nz = 0 ; for (j = 0 ; j < ncol ; j++) { for (i = 0 ; i < nrow ; i++) { if (ENTRY_IS_NONZERO (Xx, Xz, i+j*d)) { nz++ ; } } } /* ---------------------------------------------------------------------- */ /* allocate the result C */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_sparse) (nrow, ncol, nz, TRUE, TRUE, 0, values ? XTYPE : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } Cp = C->p ; Ci = C->i ; Cx = C->x ; Cz = C->z ; /* ---------------------------------------------------------------------- */ /* copy the dense matrix X into the sparse matrix C */ /* ---------------------------------------------------------------------- */ p = 0 ; for (j = 0 ; j < ncol ; j++) { Cp [j] = p ; for (i = 0 ; i < nrow ; i++) { if (ENTRY_IS_NONZERO (Xx, Xz, i+j*d)) { Ci [p] = i ; if (values) { ASSIGN (Cx, Cz, p, Xx, Xz, i+j*d) ; } p++ ; } } } ASSERT (p == nz) ; Cp [ncol] = nz ; /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (C, "C", Common) >= 0) ; return (C) ; } /* ========================================================================== */ /* === t_cholmod_copy_dense2 ================================================ */ /* ========================================================================== */ /* Y = X, where X and Y are both already allocated. */ static int TEMPLATE (cholmod_copy_dense2) ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ /* ---- output --- */ cholmod_dense *Y /* copy of matrix X */ ) { double *Xx, *Xz, *Yx, *Yz ; Int i, j, nrow, ncol, dy, dx ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Xx = X->x ; Xz = X->z ; Yx = Y->x ; Yz = Y->z ; dx = X->d ; dy = Y->d ; nrow = X->nrow ; ncol = X->ncol ; /* ---------------------------------------------------------------------- */ /* copy */ /* ---------------------------------------------------------------------- */ CLEAR (Yx, Yz, 0) ; for (j = 0 ; j < ncol ; j++) { for (i = 0 ; i < nrow ; i++) { ASSIGN (Yx, Yz, i+j*dy, Xx, Xz, i+j*dx) ; } } return (TRUE) ; } #endif #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX Matrix/src/CHOLMOD/Core/cholmod_common.c0000644000175100001440000005452012271765436017464 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_common ================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Core utility routines for the cholmod_common object: * * Primary routines: * ----------------- * cholmod_start the first call to CHOLMOD * cholmod_finish the last call to CHOLMOD * * Secondary routines: * ------------------- * cholmod_defaults restore (most) default control parameters * cholmod_allocate_work allocate (or reallocate) workspace in Common * cholmod_free_work free workspace in Common * cholmod_clear_flag clear Common->Flag in workspace * cholmod_maxrank column dimension of Common->Xwork workspace * * The Common object is unique. It cannot be allocated or deallocated by * CHOLMOD, since it contains the definition of the memory management routines * used (pointers to malloc, free, realloc, and calloc, or their equivalent). * The Common object contains workspace that is used between calls to * CHOLMOD routines. This workspace allocated by CHOLMOD as needed, by * cholmod_allocate_work and cholmod_free_work. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === cholmod_start ======================================================== */ /* ========================================================================== */ /* Initialize Common default parameters and statistics. Sets workspace * pointers to NULL. * * This routine must be called just once, prior to calling any other CHOLMOD * routine. Do not call this routine after any other CHOLMOD routine (except * cholmod_finish, to start a new CHOLMOD session), or a memory leak will * occur. * * workspace: none */ int CHOLMOD(start) ( cholmod_common *Common ) { int k ; if (Common == NULL) { return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* user error handling routine */ /* ---------------------------------------------------------------------- */ Common->error_handler = NULL ; /* ---------------------------------------------------------------------- */ /* integer and numerical types */ /* ---------------------------------------------------------------------- */ Common->itype = ITYPE ; Common->dtype = DTYPE ; /* ---------------------------------------------------------------------- */ /* default control parameters */ /* ---------------------------------------------------------------------- */ CHOLMOD(defaults) (Common) ; Common->try_catch = FALSE ; /* ---------------------------------------------------------------------- */ /* memory management routines */ /* ---------------------------------------------------------------------- */ /* The user can replace cholmod's memory management routines by redefining * these function pointers. */ #ifndef NMALLOC /* stand-alone ANSI C program */ Common->malloc_memory = malloc ; Common->free_memory = free ; Common->realloc_memory = realloc ; Common->calloc_memory = calloc ; #else /* no memory manager defined at compile-time; MUST define one at run-time */ Common->malloc_memory = NULL ; Common->free_memory = NULL ; Common->realloc_memory = NULL ; Common->calloc_memory = NULL ; #endif /* ---------------------------------------------------------------------- */ /* complex arithmetic routines */ /* ---------------------------------------------------------------------- */ Common->complex_divide = CHOLMOD(divcomplex) ; Common->hypotenuse = CHOLMOD(hypot) ; /* ---------------------------------------------------------------------- */ /* print routine */ /* ---------------------------------------------------------------------- */ #ifndef NPRINT /* stand-alone ANSI C program */ Common->print_function = printf ; #else /* printing disabled */ Common->print_function = NULL ; #endif /* ---------------------------------------------------------------------- */ /* workspace */ /* ---------------------------------------------------------------------- */ /* This code assumes the workspace held in Common is not initialized. If * it is, then a memory leak will occur because the pointers are * overwritten with NULL. */ Common->nrow = 0 ; Common->mark = EMPTY ; Common->xworksize = 0 ; Common->iworksize = 0 ; Common->Flag = NULL ; Common->Head = NULL ; Common->Iwork = NULL ; Common->Xwork = NULL ; Common->no_workspace_reallocate = FALSE ; /* ---------------------------------------------------------------------- */ /* statistics */ /* ---------------------------------------------------------------------- */ /* fl and lnz are computed in cholmod_analyze and cholmod_rowcolcounts */ Common->fl = EMPTY ; Common->lnz = EMPTY ; /* modfl is computed in cholmod_updown, cholmod_rowadd, and cholmod_rowdel*/ Common->modfl = EMPTY ; /* all routines use status as their error-report code */ Common->status = CHOLMOD_OK ; Common->malloc_count = 0 ; /* # calls to malloc minus # calls to free */ Common->memory_usage = 0 ; /* peak memory usage (in bytes) */ Common->memory_inuse = 0 ; /* current memory in use (in bytes) */ Common->nrealloc_col = 0 ; Common->nrealloc_factor = 0 ; Common->ndbounds_hit = 0 ; Common->rowfacfl = 0 ; Common->aatfl = EMPTY ; /* Common->called_nd is TRUE if cholmod_analyze called or NESDIS */ Common->called_nd = FALSE ; Common->blas_ok = TRUE ; /* false if BLAS int overflow occurs */ /* ---------------------------------------------------------------------- */ /* default SuiteSparseQR knobs and statististics */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < 4 ; k++) Common->SPQR_xstat [k] = 0 ; for (k = 0 ; k < 10 ; k++) Common->SPQR_istat [k] = 0 ; for (k = 0 ; k < 10 ; k++) Common->other1 [k] = 0 ; for (k = 0 ; k < 6 ; k++) Common->other2 [k] = 0 ; for (k = 0 ; k < 10 ; k++) Common->other3 [k] = 0 ; for (k = 0 ; k < 16 ; k++) Common->other4 [k] = 0 ; for (k = 0 ; k < 16 ; k++) Common->other5 [k] = (void *) NULL ; Common->SPQR_grain = 1 ; /* no Intel TBB multitasking, by default */ Common->SPQR_small = 1e6 ; /* target min task size for TBB */ Common->SPQR_shrink = 1 ; /* controls SPQR shrink realloc */ Common->SPQR_nthreads = 0 ; /* 0: let TBB decide how many threads to use */ /* ---------------------------------------------------------------------- */ /* GPU initializations */ /* ---------------------------------------------------------------------- */ #ifdef GPU_BLAS Common->cublasHandle = NULL ; Common->cudaStreamSyrk = NULL ; Common->cudaStreamGemm = NULL ; Common->cudaStreamTrsm = NULL ; Common->cudaStreamPotrf [0] = NULL ; Common->cudaStreamPotrf [1] = NULL ; Common->cudaStreamPotrf [2] = NULL ; Common->cublasEventPotrf [0] = NULL ; Common->cublasEventPotrf [1] = NULL ; Common->HostPinnedMemory = NULL ; Common->devPotrfWork = NULL ; Common->devSyrkGemmPtrLx = NULL ; Common->devSyrkGemmPtrC = NULL ; Common->GemmUsed = 0 ; Common->SyrkUsed = 0 ; Common->syrkStart = 0 ; #endif DEBUG_INIT ("cholmod start", Common) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_defaults ===================================================== */ /* ========================================================================== */ /* Set Common default parameters, except for the function pointers. * * workspace: none */ int CHOLMOD(defaults) ( cholmod_common *Common ) { Int i ; RETURN_IF_NULL_COMMON (FALSE) ; /* ---------------------------------------------------------------------- */ /* default control parameters */ /* ---------------------------------------------------------------------- */ Common->dbound = 0.0 ; Common->grow0 = 1.2 ; Common->grow1 = 1.2 ; Common->grow2 = 5 ; Common->maxrank = 8 ; Common->final_asis = TRUE ; Common->final_super = TRUE ; Common->final_ll = FALSE ; Common->final_pack = TRUE ; Common->final_monotonic = TRUE ; Common->final_resymbol = FALSE ; /* use simplicial factorization if flop/nnz(L) < 40, supernodal otherwise */ Common->supernodal = CHOLMOD_AUTO ; Common->supernodal_switch = 40 ; Common->nrelax [0] = 4 ; Common->nrelax [1] = 16 ; Common->nrelax [2] = 48 ; Common->zrelax [0] = 0.8 ; Common->zrelax [1] = 0.1 ; Common->zrelax [2] = 0.05 ; Common->prefer_zomplex = FALSE ; Common->prefer_upper = TRUE ; Common->prefer_binary = FALSE ; Common->quick_return_if_not_posdef = FALSE ; /* METIS workarounds */ Common->metis_memory = 0.0 ; /* > 0 for memory guard (2 is reasonable) */ Common->metis_nswitch = 3000 ; Common->metis_dswitch = 0.66 ; Common->print = 3 ; Common->precise = FALSE ; /* ---------------------------------------------------------------------- */ /* default ordering methods */ /* ---------------------------------------------------------------------- */ /* Note that if the Partition module is not installed, the CHOLMOD_METIS * and CHOLMOD_NESDIS methods will not be available. cholmod_analyze will * report the CHOLMOD_NOT_INSTALLED error, and safely skip over them. */ #if (CHOLMOD_MAXMETHODS < 9) #error "CHOLMOD_MAXMETHODS must be 9 or more (defined in cholmod_core.h)." #endif /* default strategy: try given, AMD, and then METIS if AMD reports high * fill-in. NESDIS can be used instead, if Common->default_nesdis is TRUE. */ Common->nmethods = 0 ; /* use default strategy */ Common->default_nesdis = FALSE ; /* use METIS in default strategy */ Common->current = 0 ; /* current method being tried */ Common->selected = 0 ; /* the best method selected */ /* first, fill each method with default parameters */ for (i = 0 ; i <= CHOLMOD_MAXMETHODS ; i++) { /* CHOLMOD's default method is AMD for A or AA' */ Common->method [i].ordering = CHOLMOD_AMD ; /* CHOLMOD nested dissection and minimum degree parameter */ Common->method [i].prune_dense = 10.0 ; /* dense row/col control */ /* min degree parameters (AMD, COLAMD, SYMAMD, CAMD, CCOLAMD, CSYMAMD)*/ Common->method [i].prune_dense2 = -1 ; /* COLAMD dense row control */ Common->method [i].aggressive = TRUE ; /* aggressive absorption */ Common->method [i].order_for_lu = FALSE ;/* order for Cholesky not LU */ /* CHOLMOD's nested dissection (METIS + constrained AMD) */ Common->method [i].nd_small = 200 ; /* small graphs aren't cut */ Common->method [i].nd_compress = TRUE ; /* compress graph & subgraphs */ Common->method [i].nd_camd = 1 ; /* use CAMD */ Common->method [i].nd_components = FALSE ; /* lump connected comp. */ Common->method [i].nd_oksep = 1.0 ; /* sep ok if < oksep*n */ /* statistics for each method are not yet computed */ Common->method [i].fl = EMPTY ; Common->method [i].lnz = EMPTY ; } Common->postorder = TRUE ; /* follow ordering with weighted postorder */ /* Next, define some methods. The first five use default parameters. */ Common->method [0].ordering = CHOLMOD_GIVEN ; /* skip if UserPerm NULL */ Common->method [1].ordering = CHOLMOD_AMD ; Common->method [2].ordering = CHOLMOD_METIS ; Common->method [3].ordering = CHOLMOD_NESDIS ; Common->method [4].ordering = CHOLMOD_NATURAL ; /* CHOLMOD's nested dissection with large leaves of separator tree */ Common->method [5].ordering = CHOLMOD_NESDIS ; Common->method [5].nd_small = 20000 ; /* CHOLMOD's nested dissection with tiny leaves, and no AMD ordering */ Common->method [6].ordering = CHOLMOD_NESDIS ; Common->method [6].nd_small = 4 ; Common->method [6].nd_camd = 0 ; /* no CSYMAMD or CAMD */ /* CHOLMOD's nested dissection with no dense node removal */ Common->method [7].ordering = CHOLMOD_NESDIS ; Common->method [7].prune_dense = -1. ; /* COLAMD for A*A', AMD for A */ Common->method [8].ordering = CHOLMOD_COLAMD ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_finish ======================================================= */ /* ========================================================================== */ /* The last call to CHOLMOD must be cholmod_finish. You may call this routine * more than once, and can safely call any other CHOLMOD routine after calling * it (including cholmod_start). * * The statistics and parameter settings in Common are preserved. The * workspace in Common is freed. This routine is just another name for * cholmod_free_work. */ int CHOLMOD(finish) ( cholmod_common *Common ) { return (CHOLMOD(free_work) (Common)) ; } /* ========================================================================== */ /* === cholmod_allocate_work ================================================ */ /* ========================================================================== */ /* Allocate and initialize workspace for CHOLMOD routines, or increase the size * of already-allocated workspace. If enough workspace is already allocated, * then nothing happens. * * workspace: Flag (nrow), Head (nrow+1), Iwork (iworksize), Xwork (xworksize) */ int CHOLMOD(allocate_work) ( /* ---- input ---- */ size_t nrow, /* # of rows in the matrix A */ size_t iworksize, /* size of Iwork */ size_t xworksize, /* size of Xwork */ /* --------------- */ cholmod_common *Common ) { double *W ; Int *Head ; Int i ; size_t nrow1 ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* Allocate Flag (nrow) and Head (nrow+1) */ /* ---------------------------------------------------------------------- */ nrow = MAX (1, nrow) ; /* nrow1 = nrow + 1 */ nrow1 = CHOLMOD(add_size_t) (nrow, 1, &ok) ; if (!ok) { /* nrow+1 causes size_t overflow ; problem is too large */ Common->status = CHOLMOD_TOO_LARGE ; CHOLMOD(free_work) (Common) ; return (FALSE) ; } if (nrow > Common->nrow) { if (Common->no_workspace_reallocate) { /* CHOLMOD is not allowed to change the workspace here */ Common->status = CHOLMOD_INVALID ; return (FALSE) ; } /* free the old workspace (if any) and allocate new space */ Common->Flag = CHOLMOD(free) (Common->nrow, sizeof (Int), Common->Flag, Common) ; Common->Head = CHOLMOD(free) (Common->nrow+1,sizeof (Int), Common->Head, Common) ; Common->Flag = CHOLMOD(malloc) (nrow, sizeof (Int), Common) ; Common->Head = CHOLMOD(malloc) (nrow1, sizeof (Int), Common) ; /* record the new size of Flag and Head */ Common->nrow = nrow ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_work) (Common) ; return (FALSE) ; } /* initialize Flag and Head */ Common->mark = EMPTY ; CHOLMOD(clear_flag) (Common) ; Head = Common->Head ; for (i = 0 ; i <= (Int) (nrow) ; i++) { Head [i] = EMPTY ; } } /* ---------------------------------------------------------------------- */ /* Allocate Iwork (iworksize) */ /* ---------------------------------------------------------------------- */ iworksize = MAX (1, iworksize) ; if (iworksize > Common->iworksize) { if (Common->no_workspace_reallocate) { /* CHOLMOD is not allowed to change the workspace here */ Common->status = CHOLMOD_INVALID ; return (FALSE) ; } /* free the old workspace (if any) and allocate new space. * integer overflow safely detected in cholmod_malloc */ CHOLMOD(free) (Common->iworksize, sizeof (Int), Common->Iwork, Common) ; Common->Iwork = CHOLMOD(malloc) (iworksize, sizeof (Int), Common) ; /* record the new size of Iwork */ Common->iworksize = iworksize ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_work) (Common) ; return (FALSE) ; } /* note that Iwork does not need to be initialized */ } /* ---------------------------------------------------------------------- */ /* Allocate Xwork (xworksize) and set it to ((double) 0.) */ /* ---------------------------------------------------------------------- */ /* make sure xworksize is >= 1 */ xworksize = MAX (1, xworksize) ; if (xworksize > Common->xworksize) { if (Common->no_workspace_reallocate) { /* CHOLMOD is not allowed to change the workspace here */ Common->status = CHOLMOD_INVALID ; return (FALSE) ; } /* free the old workspace (if any) and allocate new space */ CHOLMOD(free) (Common->xworksize, sizeof (double), Common->Xwork, Common) ; Common->Xwork = CHOLMOD(malloc) (xworksize, sizeof (double), Common) ; /* record the new size of Xwork */ Common->xworksize = xworksize ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_work) (Common) ; return (FALSE) ; } /* initialize Xwork */ W = Common->Xwork ; for (i = 0 ; i < (Int) xworksize ; i++) { W [i] = 0. ; } } return (TRUE) ; } /* ========================================================================== */ /* === cholmod_free_work ==================================================== */ /* ========================================================================== */ /* Deallocate the CHOLMOD workspace. * * workspace: deallocates all workspace in Common */ int CHOLMOD(free_work) ( cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->Flag = CHOLMOD(free) (Common->nrow, sizeof (Int), Common->Flag, Common) ; Common->Head = CHOLMOD(free) (Common->nrow+1, sizeof (Int), Common->Head, Common) ; Common->Iwork = CHOLMOD(free) (Common->iworksize, sizeof (Int), Common->Iwork, Common) ; Common->Xwork = CHOLMOD(free) (Common->xworksize, sizeof (double), Common->Xwork, Common) ; Common->nrow = 0 ; Common->iworksize = 0 ; Common->xworksize = 0 ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_clear_flag =================================================== */ /* ========================================================================== */ /* Increment mark to ensure Flag [0..nrow-1] < mark. If integer overflow * occurs, or mark was initially negative, reset the entire array. This is * not an error condition, but an intended function of the Flag workspace. * * workspace: Flag (nrow). Does not modify Flag if nrow is zero. */ SuiteSparse_long CHOLMOD(clear_flag) ( cholmod_common *Common ) { Int i, nrow, *Flag ; RETURN_IF_NULL_COMMON (-1) ; Common->mark++ ; if (Common->mark <= 0) { nrow = Common->nrow ; Flag = Common->Flag ; PRINT2 (("reset Flag: nrow "ID"\n", nrow)) ; PRINT2 (("reset Flag: mark %ld\n", Common->mark)) ; for (i = 0 ; i < nrow ; i++) { Flag [i] = EMPTY ; } Common->mark = 0 ; } return (Common->mark) ; } /* ========================================================================== */ /* ==== cholmod_maxrank ===================================================== */ /* ========================================================================== */ /* Find a valid value of Common->maxrank. Returns 0 if error, or 2, 4, or 8 * if successful. */ size_t CHOLMOD(maxrank) /* returns validated value of Common->maxrank */ ( /* ---- input ---- */ size_t n, /* A and L will have n rows */ /* --------------- */ cholmod_common *Common ) { size_t maxrank ; RETURN_IF_NULL_COMMON (0) ; maxrank = Common->maxrank ; if (n > 0) { /* Ensure maxrank*n*sizeof(double) does not result in integer overflow. * If n is so large that 2*n*sizeof(double) results in integer overflow * (n = 268,435,455 if an Int is 32 bits), then maxrank will be 0 or 1, * but maxrank will be set to 2 below. 2*n will not result in integer * overflow, and CHOLMOD will run out of memory or safely detect integer * overflow elsewhere. */ maxrank = MIN (maxrank, Size_max / (n * sizeof (double))) ; } if (maxrank <= 2) { maxrank = 2 ; } else if (maxrank <= 4) { maxrank = 4 ; } else { maxrank = 8 ; } return (maxrank) ; } /* ========================================================================== */ /* === cholmod_dbound ======================================================= */ /* ========================================================================== */ /* Ensure the absolute value of a diagonal entry, D (j,j), is greater than * Common->dbound. This routine is not meant for the user to call. It is used * by the various LDL' factorization and update/downdate routines. The * default value of Common->dbound is zero, and in that case this routine is not * called at all. No change is made if D (j,j) is NaN. CHOLMOD does not call * this routine if Common->dbound is NaN. */ double CHOLMOD(dbound) /* returns modified diagonal entry of D */ ( /* ---- input ---- */ double dj, /* diagonal entry of D, for LDL' factorization */ /* --------------- */ cholmod_common *Common ) { double dbound ; RETURN_IF_NULL_COMMON (0) ; if (!IS_NAN (dj)) { dbound = Common->dbound ; if (dj < 0) { if (dj > -dbound) { dj = -dbound ; Common->ndbounds_hit++ ; if (Common->status == CHOLMOD_OK) { ERROR (CHOLMOD_DSMALL, "diagonal below threshold") ; } } } else { if (dj < dbound) { dj = dbound ; Common->ndbounds_hit++ ; if (Common->status == CHOLMOD_OK) { ERROR (CHOLMOD_DSMALL, "diagonal below threshold") ; } } } } return (dj) ; } Matrix/src/CHOLMOD/Core/cholmod_triplet.c0000644000175100001440000005605112271765436017660 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_triplet ================================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Core utility routines for the cholmod_triplet object: * * A sparse matrix held in triplet form is the simplest one for a user to * create. It consists of a list of nz entries in arbitrary order, held in * three arrays: i, j, and x, each of length nk. The kth entry is in row i[k], * column j[k], with value x[k]. There may be duplicate values; if A(i,j) * appears more than once, its value is the sum of the entries with those row * and column indices. * * Primary routines: * ----------------- * cholmod_allocate_triplet allocate a triplet matrix * cholmod_free_triplet free a triplet matrix * * Secondary routines: * ------------------- * cholmod_reallocate_triplet reallocate a triplet matrix * cholmod_sparse_to_triplet create a triplet matrix copy of a sparse matrix * cholmod_triplet_to_sparse create a sparse matrix copy of a triplet matrix * cholmod_copy_triplet create a copy of a triplet matrix * * The relationship between an m-by-n cholmod_sparse matrix A and a * cholmod_triplet matrix (i, j, and x) is identical to how they are used in * the MATLAB "sparse" and "find" functions: * * [i j x] = find (A) * [m n] = size (A) * A = sparse (i,j,x,m,n) * * with the exception that the cholmod_sparse matrix may be "unpacked", may * have either sorted or unsorted columns (depending on the option selected), * and may be symmetric with just the upper or lower triangular part stored. * Likewise, the cholmod_triplet matrix may contain just the entries in the * upper or lower triangular part of a symmetric matrix. * * MATLAB sparse matrices are always "packed", always have sorted columns, * and always store both parts of a symmetric matrix. In some cases, MATLAB * behaves like CHOLMOD by ignoring entries in the upper or lower triangular * part of a matrix that is otherwise assumed to be symmetric (such as the * input to chol). In CHOLMOD, that option is a characteristic of the object. * In MATLAB, that option is based on how a matrix is used as the input to * a function. * * The triplet matrix is provided to give the user a simple way of constructing * a sparse matrix. There are very few operations supported for triplet * matrices. The assumption is that they will be converted to cholmod_sparse * matrix form first. * * Adding two triplet matrices simply involves concatenating the contents of * the three arrays (i, j, and x). To permute a triplet matrix, just replace * the row and column indices with their permuted values. For example, if * P is a permutation vector, then P [k] = j means row/column j is the kth * row/column in C=P*A*P'. In MATLAB notation, C=A(p,p). If Pinv is an array * of size n and T is the triplet form of A, then: * * Ti = T->i ; * Tj = T->j ; * for (k = 0 ; k < n ; k++) Pinv [P [k]] = k ; * for (k = 0 ; k < nz ; k++) Ti [k] = Pinv [Ti [k]] ; * for (k = 0 ; k < nz ; k++) Tj [k] = Pinv [Tj [k]] ; * * overwrites T with the triplet form of C=P*A*P'. The conversion * * C = cholmod_triplet_to_sparse (T, 0, &Common) ; * * will then return the matrix C = P*A*P'. * * Note that T->stype > 0 means that entries in the lower triangular part of * T are transposed into the upper triangular part when T is converted to * sparse matrix (cholmod_sparse) form with cholmod_triplet_to_sparse. The * opposite is true for T->stype < 0. * * Since the triplet matrix T is so simple to generate, it's quite easy * to remove entries that you do not want, prior to converting T to the * cholmod_sparse form. So if you include these entries in T, CHOLMOD * assumes that there must be a reason (such as the one above). Thus, * no entry in a triplet matrix is ever ignored. * * Other operations, such as extacting a submatrix, horizontal and vertical * concatenation, multiply a triplet matrix times a dense matrix, are also * simple. Multiplying two triplet matrices is not trivial; the simplest * method is to convert them to cholmod_sparse matrices first. * * Supports all xtypes (pattern, real, complex, and zomplex). */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define PATTERN #include "t_cholmod_triplet.c" #define REAL #include "t_cholmod_triplet.c" #define COMPLEX #include "t_cholmod_triplet.c" #define ZOMPLEX #include "t_cholmod_triplet.c" /* ========================================================================== */ /* === cholmod_allocate_triplet ============================================= */ /* ========================================================================== */ /* allocate space for a triplet matrix * * workspace: none */ cholmod_triplet *CHOLMOD(allocate_triplet) ( /* ---- input ---- */ size_t nrow, /* # of rows of T */ size_t ncol, /* # of columns of T */ size_t nzmax, /* max # of nonzeros of T */ int stype, /* stype of T */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { cholmod_triplet *T ; size_t nzmax0 ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; if (xtype < CHOLMOD_PATTERN || xtype > CHOLMOD_ZOMPLEX) { ERROR (CHOLMOD_INVALID, "xtype invalid") ; return (NULL) ; } /* ensure the dimensions do not cause integer overflow */ (void) CHOLMOD(add_size_t) (ncol, 2, &ok) ; if (!ok || nrow > Int_max || ncol > Int_max || nzmax > Int_max) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate header */ /* ---------------------------------------------------------------------- */ T = CHOLMOD(malloc) (sizeof (cholmod_triplet), 1, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } PRINT1 (("cholmod_allocate_triplet %d-by-%d nzmax %d xtype %d\n", nrow, ncol, nzmax, xtype)) ; nzmax = MAX (1, nzmax) ; T->nrow = nrow ; T->ncol = ncol ; T->nzmax = nzmax ; T->nnz = 0 ; T->stype = stype ; T->itype = ITYPE ; T->xtype = xtype ; T->dtype = DTYPE ; T->j = NULL ; T->i = NULL ; T->x = NULL ; T->z = NULL ; /* ---------------------------------------------------------------------- */ /* allocate the matrix itself */ /* ---------------------------------------------------------------------- */ nzmax0 = 0 ; CHOLMOD(realloc_multiple) (nzmax, 2, xtype, &(T->i), &(T->j), &(T->x), &(T->z), &nzmax0, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_triplet) (&T, Common) ; return (NULL) ; /* out of memory */ } return (T) ; } /* ========================================================================== */ /* === cholmod_free_triplet ================================================= */ /* ========================================================================== */ /* free a triplet matrix * * workspace: none */ int CHOLMOD(free_triplet) ( /* ---- in/out --- */ cholmod_triplet **THandle, /* matrix to deallocate, NULL on output */ /* --------------- */ cholmod_common *Common ) { Int nz ; cholmod_triplet *T ; RETURN_IF_NULL_COMMON (FALSE) ; if (THandle == NULL) { /* nothing to do */ return (TRUE) ; } T = *THandle ; if (T == NULL) { /* nothing to do */ return (TRUE) ; } nz = T->nzmax ; T->j = CHOLMOD(free) (nz, sizeof (Int), T->j, Common) ; T->i = CHOLMOD(free) (nz, sizeof (Int), T->i, Common) ; if (T->xtype == CHOLMOD_REAL) { T->x = CHOLMOD(free) (nz, sizeof (double), T->x, Common) ; } else if (T->xtype == CHOLMOD_COMPLEX) { T->x = CHOLMOD(free) (nz, 2*sizeof (double), T->x, Common) ; } else if (T->xtype == CHOLMOD_ZOMPLEX) { T->x = CHOLMOD(free) (nz, sizeof (double), T->x, Common) ; T->z = CHOLMOD(free) (nz, sizeof (double), T->z, Common) ; } *THandle = CHOLMOD(free) (1, sizeof (cholmod_triplet), (*THandle), Common) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_reallocate_triplet =========================================== */ /* ========================================================================== */ /* Change the size of T->i, T->j, and T->x, or allocate them if their current * size is zero. T->x is not modified if T->xtype is CHOLMOD_PATTERN. * * workspace: none */ int CHOLMOD(reallocate_triplet) ( /* ---- input ---- */ size_t nznew, /* new # of entries in T */ /* ---- in/out --- */ cholmod_triplet *T, /* triplet matrix to modify */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (T, FALSE) ; RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; PRINT1 (("realloc triplet %d to %d, xtype: %d\n", T->nzmax, nznew, T->xtype)) ; /* ---------------------------------------------------------------------- */ /* resize the matrix */ /* ---------------------------------------------------------------------- */ CHOLMOD(realloc_multiple) (MAX (1,nznew), 2, T->xtype, &(T->i), &(T->j), &(T->x), &(T->z), &(T->nzmax), Common) ; return (Common->status == CHOLMOD_OK) ; } /* ========================================================================== */ /* === cholmod_triplet_to_sparse ============================================ */ /* ========================================================================== */ /* Convert a set of triplets into a cholmod_sparse matrix. In MATLAB notation, * for unsymmetric matrices: * * A = sparse (Ti, Tj, Tx, nrow, ncol, nzmax) ; * * For the symmetric upper case: * * A = sparse (min(Ti,Tj), max(Ti,Tj), Tx, nrow, ncol, nzmax) ; * * For the symmetric lower case: * * A = sparse (max(Ti,Tj), min(Ti,Tj), Tx, nrow, ncol, nzmax) ; * * If Tx is NULL, then A->x is not allocated, and only the pattern of A is * computed. A is returned in packed form, and can be of any stype * (upper/lower/unsymmetric). It has enough space to hold the values in T, * or nzmax, whichever is larger. * * workspace: Iwork (max (nrow,ncol)) * allocates a temporary copy of its output matrix. * * The resulting sparse matrix has the same xtype as the input triplet matrix. */ cholmod_sparse *CHOLMOD(triplet_to_sparse) ( /* ---- input ---- */ cholmod_triplet *T, /* matrix to copy */ size_t nzmax, /* allocate at least this much space in output matrix */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *R, *A = NULL ; Int *Wj, *Rp, *Ri, *Rnz, *Ti, *Tj ; Int i, j, p, k, stype, nrow, ncol, nz, ok ; size_t anz = 0 ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (T, NULL) ; Ti = T->i ; Tj = T->j ; RETURN_IF_NULL (Ti, NULL) ; RETURN_IF_NULL (Tj, NULL) ; RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; stype = SIGN (T->stype) ; if (stype && T->nrow != T->ncol) { /* inputs invalid */ ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (NULL) ; } Common->status = CHOLMOD_OK ; DEBUG (CHOLMOD(dump_triplet) (T, "T", Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = T->nrow ; ncol = T->ncol ; nz = T->nnz ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ CHOLMOD(allocate_work) (0, MAX (nrow, ncol), 0, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* allocate temporary matrix R */ /* ---------------------------------------------------------------------- */ R = CHOLMOD(allocate_sparse) (ncol, nrow, nz, FALSE, FALSE, -stype, T->xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } Rp = R->p ; Ri = R->i ; Rnz = R->nz ; /* ---------------------------------------------------------------------- */ /* count the entries in each row of A (also counting duplicates) */ /* ---------------------------------------------------------------------- */ for (i = 0 ; i < nrow ; i++) { Rnz [i] = 0 ; } if (stype > 0) { for (k = 0 ; k < nz ; k++) { i = Ti [k] ; j = Tj [k] ; if (i < 0 || i >= nrow || j < 0 || j >= ncol) { ERROR (CHOLMOD_INVALID, "index out of range") ; break ; } /* A will be symmetric with just the upper triangular part stored. * Create a matrix R that is lower triangular. Entries in the * upper part of R are transposed to the lower part. */ Rnz [MIN (i,j)]++ ; } } else if (stype < 0) { for (k = 0 ; k < nz ; k++) { i = Ti [k] ; j = Tj [k] ; if (i < 0 || i >= nrow || j < 0 || j >= ncol) { ERROR (CHOLMOD_INVALID, "index out of range") ; break ; } /* A will be symmetric with just the lower triangular part stored. * Create a matrix R that is upper triangular. Entries in the * lower part of R are transposed to the upper part. */ Rnz [MAX (i,j)]++ ; } } else { for (k = 0 ; k < nz ; k++) { i = Ti [k] ; j = Tj [k] ; if (i < 0 || i >= nrow || j < 0 || j >= ncol) { ERROR (CHOLMOD_INVALID, "index out of range") ; break ; } /* constructing an unsymmetric matrix */ Rnz [i]++ ; } } if (Common->status < CHOLMOD_OK) { /* triplet matrix is invalid */ CHOLMOD(free_sparse) (&R, Common) ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* construct the row pointers */ /* ---------------------------------------------------------------------- */ p = 0 ; for (i = 0 ; i < nrow ; i++) { Rp [i] = p ; p += Rnz [i] ; } Rp [nrow] = p ; /* use Wj (i/l/l) as temporary row pointers */ Wj = Common->Iwork ; /* size MAX (nrow,ncol) FUTURE WORK: (i/l/l) */ for (i = 0 ; i < nrow ; i++) { Wj [i] = Rp [i] ; } /* ---------------------------------------------------------------------- */ /* construct triplet matrix, using template routine */ /* ---------------------------------------------------------------------- */ switch (T->xtype) { case CHOLMOD_PATTERN: anz = p_cholmod_triplet_to_sparse (T, R, Common) ; break ; case CHOLMOD_REAL: anz = r_cholmod_triplet_to_sparse (T, R, Common) ; break ; case CHOLMOD_COMPLEX: anz = c_cholmod_triplet_to_sparse (T, R, Common) ; break ; case CHOLMOD_ZOMPLEX: anz = z_cholmod_triplet_to_sparse (T, R, Common) ; break ; } /* ---------------------------------------------------------------------- */ /* A = R' (array transpose, not complex conjugate transpose) */ /* ---------------------------------------------------------------------- */ /* workspace: Iwork (R->nrow), which is A->ncol */ ASSERT (CHOLMOD(dump_sparse) (R, "R", Common) >= 0) ; A = CHOLMOD(allocate_sparse) (nrow, ncol, MAX (anz, nzmax), TRUE, TRUE, stype, T->xtype, Common) ; if (stype) { ok = CHOLMOD(transpose_sym) (R, 1, NULL, A, Common) ; } else { ok = CHOLMOD(transpose_unsym) (R, 1, NULL, NULL, 0, A, Common) ; } CHOLMOD(free_sparse) (&R, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&A, Common) ; } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (A, "A = triplet(T) result", Common) >= 0) ; return (A) ; } /* ========================================================================== */ /* === cholmod_sparse_to_triplet ============================================ */ /* ========================================================================== */ /* Converts a sparse column-oriented matrix to triplet form. * The resulting triplet matrix has the same xtype as the sparse matrix. * * workspace: none */ cholmod_triplet *CHOLMOD(sparse_to_triplet) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Az, *Tx, *Tz ; Int *Ap, *Ai, *Ti, *Tj, *Anz ; cholmod_triplet *T ; Int i, xtype, p, pend, k, j, nrow, ncol, nz, stype, packed, up, lo, both ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; stype = SIGN (A->stype) ; nrow = A->nrow ; ncol = A->ncol ; if (stype && nrow != ncol) { /* inputs invalid */ ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (NULL) ; } Ax = A->x ; Az = A->z ; xtype = A->xtype ; Common->status = CHOLMOD_OK ; ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* allocate triplet matrix */ /* ---------------------------------------------------------------------- */ nz = CHOLMOD(nnz) (A, Common) ; T = CHOLMOD(allocate_triplet) (nrow, ncol, nz, A->stype, A->xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* convert to a sparse matrix */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; Anz = A->nz ; packed = A->packed ; Ti = T->i ; Tj = T->j ; Tx = T->x ; Tz = T->z ; T->stype = A->stype ; both = (A->stype == 0) ; up = (A->stype > 0) ; lo = (A->stype < 0) ; k = 0 ; for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (both || (up && i <= j) || (lo && i >= j)) { Ti [k] = Ai [p] ; Tj [k] = j ; if (xtype == CHOLMOD_REAL) { Tx [k] = Ax [p] ; } else if (xtype == CHOLMOD_COMPLEX) { Tx [2*k ] = Ax [2*p ] ; Tx [2*k+1] = Ax [2*p+1] ; } else if (xtype == CHOLMOD_ZOMPLEX) { Tx [k] = Ax [p] ; Tz [k] = Az [p] ; } k++ ; ASSERT (k <= nz) ; } } } T->nnz = k ; /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_triplet) (T, "T", Common)) ; return (T) ; } /* ========================================================================== */ /* === cholmod_copy_triplet ================================================= */ /* ========================================================================== */ /* Create an exact copy of a triplet matrix, except that entries in unused * space are not copied (they might not be initialized, and copying them would * cause program checkers such as purify and valgrind to complain). * The output triplet matrix has the same xtype as the input triplet matrix. */ cholmod_triplet *CHOLMOD(copy_triplet) ( /* ---- input ---- */ cholmod_triplet *T, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) { double *Tx, *Tz, *Cx, *Cz ; Int *Ci, *Cj, *Ti, *Tj ; cholmod_triplet *C ; Int xtype, k, nz ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (T, NULL) ; RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; nz = T->nnz ; Ti = T->i ; Tj = T->j ; Tx = T->x ; Tz = T->z ; xtype = T->xtype ; RETURN_IF_NULL (Ti, NULL) ; RETURN_IF_NULL (Tj, NULL) ; Common->status = CHOLMOD_OK ; DEBUG (CHOLMOD(dump_triplet) (T, "T input", Common)) ; /* ---------------------------------------------------------------------- */ /* allocate copy */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_triplet) (T->nrow, T->ncol, T->nzmax, T->stype, xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* copy the triplet matrix */ /* ---------------------------------------------------------------------- */ Ci = C->i ; Cj = C->j ; Cx = C->x ; Cz = C->z ; C->nnz = nz ; for (k = 0 ; k < nz ; k++) { Ci [k] = Ti [k] ; } for (k = 0 ; k < nz ; k++) { Cj [k] = Tj [k] ; } if (xtype == CHOLMOD_REAL) { for (k = 0 ; k < nz ; k++) { Cx [k] = Tx [k] ; } } else if (xtype == CHOLMOD_COMPLEX) { for (k = 0 ; k < nz ; k++) { Cx [2*k ] = Tx [2*k ] ; Cx [2*k+1] = Tx [2*k+1] ; } } else if (xtype == CHOLMOD_ZOMPLEX) { for (k = 0 ; k < nz ; k++) { Cx [k] = Tx [k] ; Cz [k] = Tz [k] ; } } /* ---------------------------------------------------------------------- */ /* return the result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_triplet) (C, "C triplet copy", Common)) ; return (C) ; } Matrix/src/CHOLMOD/Core/cholmod_error.c0000644000175100001440000000531412271765436017322 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_error =================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* CHOLMOD error-handling routine. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* ==== cholmod_error ======================================================= */ /* ========================================================================== */ /* An error has occurred. Set the status, optionally print an error message, * and call the user error-handling routine (if it exists). If * Common->try_catch is TRUE, then CHOLMOD is inside a try/catch block. * The status is set, but no message is printed and the user error handler * is not called. This is not (yet) an error, since CHOLMOD may recover. * * In the current version, this try/catch mechanism is used internally only in * cholmod_analyze, which tries multiple ordering methods and picks the best * one. If one or more ordering method fails, it keeps going. Only one * ordering needs to succeed for cholmod_analyze to succeed. */ int CHOLMOD(error) ( /* ---- input ---- */ int status, /* error status */ const char *file, /* name of source code file where error occured */ int line, /* line number in source code file where error occured*/ const char *message, /* error message */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = status ; if (!(Common->try_catch)) { #ifndef NPRINT /* print a warning or error message */ if (Common->print_function != NULL) { if (status > 0 && Common->print > 1) { (Common->print_function) ("CHOLMOD warning: %s\n", message) ; fflush (stdout) ; fflush (stderr) ; } else if (Common->print > 0) { (Common->print_function) ("CHOLMOD error: %s\n", message) ; fflush (stdout) ; fflush (stderr) ; } } #endif /* call the user error handler, if it exists */ if (Common->error_handler != NULL) { Common->error_handler (status, file, line, message) ; } } return (TRUE) ; } Matrix/src/CHOLMOD/Core/cholmod_version.c0000644000175100001440000000262112271765436017654 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_version ================================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2013, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Return the current version of CHOLMOD. Unlike all other functions in CHOLMOD, this function does not require the CHOLMOD Common. */ #include "cholmod_internal.h" #include "cholmod_core.h" int CHOLMOD(version) /* returns CHOLMOD_VERSION */ ( /* output, contents not defined on input. Not used if NULL. version [0] = CHOLMOD_MAIN_VERSION ; version [1] = CHOLMOD_SUB_VERSION ; version [2] = CHOLMOD_SUBSUB_VERSION ; */ int version [3] ) { if (version != NULL) { version [0] = CHOLMOD_MAIN_VERSION ; version [1] = CHOLMOD_SUB_VERSION ; version [2] = CHOLMOD_SUBSUB_VERSION ; } return (CHOLMOD_VERSION) ; } Matrix/src/CHOLMOD/Core/cholmod_memory.c0000644000175100001440000004301112271765436017475 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_memory ================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2013, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Core memory management routines: * * Primary routines: * ----------------- * cholmod_malloc malloc wrapper * cholmod_free free wrapper * * Secondary routines: * ------------------- * cholmod_calloc calloc wrapper * cholmod_realloc realloc wrapper * cholmod_realloc_multiple realloc wrapper for multiple objects * * The user may make use of these, just like malloc and free. You can even * malloc an object and safely free it with cholmod_free, and visa versa * (except that the memory usage statistics will be corrupted). These routines * do differ from malloc and free. If cholmod_free is given a NULL pointer, * for example, it does nothing (unlike the ANSI free). cholmod_realloc does * not return NULL if given a non-NULL pointer and a nonzero size, even if it * fails (it sets an error code in Common->status instead). * * CHOLMOD keeps track of the amount of memory it has allocated, and so the * cholmod_free routine includes as a parameter the size of the object being * freed. This is only used for memory usage statistics, which are very useful * in finding memory leaks in your program. If you, the user of CHOLMOD, pass * the wrong size, the only consequence is that the memory usage statistics * will be invalid. This will causes assertions to fail if CHOLMOD is * compiled with debugging enabled, but otherwise it will cause no errors. * * The cholmod_free_* routines for each CHOLMOD object keep track of the size * of the blocks they free, so they do not require you to pass their sizes * as a parameter. * * If a block of size zero is requested, these routines allocate a block of * size one instead. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === cholmod_add_size_t =================================================== */ /* ========================================================================== */ /* Safely compute a+b, and check for integer overflow. If overflow occurs, * return 0 and set OK to FALSE. Also return 0 if OK is FALSE on input. */ size_t CHOLMOD(add_size_t) (size_t a, size_t b, int *ok) { size_t s = a + b ; (*ok) = (*ok) && (s >= a) ; return ((*ok) ? s : 0) ; } /* ========================================================================== */ /* === cholmod_mult_size_t ================================================== */ /* ========================================================================== */ /* Safely compute a*k, where k should be small, and check for integer overflow. * If overflow occurs, return 0 and set OK to FALSE. Also return 0 if OK is * FALSE on input. */ size_t CHOLMOD(mult_size_t) (size_t a, size_t k, int *ok) { size_t p = 0, s ; while (*ok) { if (k % 2) { p = p + a ; (*ok) = (*ok) && (p >= a) ; } k = k / 2 ; if (!k) return (p) ; s = a + a ; (*ok) = (*ok) && (s >= a) ; a = s ; } return (0) ; } /* ========================================================================== */ /* === cholmod_malloc ======================================================= */ /* ========================================================================== */ /* Wrapper around malloc routine. Allocates space of size MAX(1,n)*size, where * size is normally a sizeof (...). * * This routine, cholmod_calloc, and cholmod_realloc do not set Common->status * to CHOLMOD_OK on success, so that a sequence of cholmod_malloc's, _calloc's, * or _realloc's can be used. If any of them fails, the Common->status will * hold the most recent error status. * * Usage, for a pointer to int: * * p = cholmod_malloc (n, sizeof (int), Common) * * Uses a pointer to the malloc routine (or its equivalent) defined in Common. */ void *CHOLMOD(malloc) /* returns pointer to the newly malloc'd block */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* --------------- */ cholmod_common *Common ) { void *p ; size_t s ; int ok = TRUE ; RETURN_IF_NULL_COMMON (NULL) ; if (size == 0) { ERROR (CHOLMOD_INVALID, "sizeof(item) must be > 0") ; p = NULL ; } else if (n >= (Size_max / size) || n >= Int_max) { /* object is too big to allocate without causing integer overflow */ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; p = NULL ; } else { /* call malloc, or its equivalent */ s = CHOLMOD(mult_size_t) (MAX (1,n), size, &ok) ; p = ok ? ((Common->malloc_memory) (s)) : NULL ; if (p == NULL) { /* failure: out of memory */ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ; } else { /* success: increment the count of objects allocated */ Common->malloc_count++ ; Common->memory_inuse += (n * size) ; Common->memory_usage = MAX (Common->memory_usage, Common->memory_inuse) ; PRINTM (("cholmod_malloc %p %g cnt: %g inuse %g\n", p, (double) n*size, (double) Common->malloc_count, (double) Common->memory_inuse)) ; } } return (p) ; } /* ========================================================================== */ /* === cholmod_free ========================================================= */ /* ========================================================================== */ /* Wrapper around free routine. Returns NULL, which can be assigned to the * pointer being freed, as in: * * p = cholmod_free (n, sizeof (int), p, Common) ; * * In CHOLMOD, the syntax: * * cholmod_free (n, sizeof (int), p, Common) ; * * is used if p is a local pointer and the routine is returning shortly. * Uses a pointer to the free routine (or its equivalent) defined in Common. * Nothing is freed if the pointer is NULL. */ void *CHOLMOD(free) /* always returns NULL */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* ---- in/out --- */ void *p, /* block of memory to free */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (NULL) ; if (p != NULL) { /* only free the object if the pointer is not NULL */ /* call free, or its equivalent */ (Common->free_memory) (p) ; Common->malloc_count-- ; Common->memory_inuse -= (n * size) ; PRINTM (("cholmod_free %p %g cnt: %g inuse %g\n", p, (double) n*size, (double) Common->malloc_count, (double) Common->memory_inuse)) ; /* This assertion will fail if the user calls cholmod_malloc and * cholmod_free with mismatched memory sizes. It shouldn't fail * otherwise. */ ASSERT (IMPLIES (Common->malloc_count == 0, Common->memory_inuse == 0)); } /* return NULL, and the caller should assign this to p. This avoids * freeing the same pointer twice. */ return (NULL) ; } /* ========================================================================== */ /* === cholmod_calloc ======================================================= */ /* ========================================================================== */ /* Wrapper around calloc routine. * * Uses a pointer to the calloc routine (or its equivalent) defined in Common. * This routine is identical to malloc, except that it zeros the newly allocated * block to zero. */ void *CHOLMOD(calloc) /* returns pointer to the newly calloc'd block */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* --------------- */ cholmod_common *Common ) { void *p ; RETURN_IF_NULL_COMMON (NULL) ; if (size == 0) { ERROR (CHOLMOD_INVALID, "sizeof(item) must be > 0") ; p = NULL ; } else if (n >= (Size_max / size) || n >= Int_max) { /* object is too big to allocate without causing integer overflow */ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; p = NULL ; } else { /* call calloc, or its equivalent */ p = (Common->calloc_memory) (MAX (1,n), size) ; if (p == NULL) { /* failure: out of memory */ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ; } else { /* success: increment the count of objects allocated */ Common->malloc_count++ ; Common->memory_inuse += (n * size) ; Common->memory_usage = MAX (Common->memory_usage, Common->memory_inuse) ; PRINTM (("cholmod_malloc %p %g cnt: %g inuse %g\n", p, (double) n*size, (double) Common->malloc_count, (double) Common->memory_inuse)) ; } } return (p) ; } /* ========================================================================== */ /* === cholmod_realloc ====================================================== */ /* ========================================================================== */ /* Wrapper around realloc routine. Given a pointer p to a block of size * (*n)*size memory, it changes the size of the block pointed to by p to be * MAX(1,nnew)*size in size. It may return a pointer different than p. This * should be used as (for a pointer to int): * * p = cholmod_realloc (nnew, sizeof (int), p, *n, Common) ; * * If p is NULL, this is the same as p = cholmod_malloc (...). * A size of nnew=0 is treated as nnew=1. * * If the realloc fails, p is returned unchanged and Common->status is set * to CHOLMOD_OUT_OF_MEMORY. If successful, Common->status is not modified, * and p is returned (possibly changed) and pointing to a large block of memory. * * Uses a pointer to the realloc routine (or its equivalent) defined in Common. */ void *CHOLMOD(realloc) /* returns pointer to reallocated block */ ( /* ---- input ---- */ size_t nnew, /* requested # of items in reallocated block */ size_t size, /* size of each item */ /* ---- in/out --- */ void *p, /* block of memory to realloc */ size_t *n, /* current size on input, nnew on output if successful*/ /* --------------- */ cholmod_common *Common ) { size_t nold = (*n) ; void *pnew ; size_t s ; int ok = TRUE ; RETURN_IF_NULL_COMMON (NULL) ; if (size == 0) { ERROR (CHOLMOD_INVALID, "sizeof(item) must be > 0") ; p = NULL ; } else if (p == NULL) { /* A fresh object is being allocated. */ PRINT1 (("realloc fresh: %d %d\n", nnew, size)) ; p = CHOLMOD(malloc) (nnew, size, Common) ; *n = (p == NULL) ? 0 : nnew ; } else if (nold == nnew) { /* Nothing to do. Do not change p or n. */ PRINT1 (("realloc nothing: %d %d\n", nnew, size)) ; } else if (nnew >= (Size_max / size) || nnew >= Int_max) { /* failure: nnew is too big. Do not change p or n. */ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; } else { /* The object exists, and is changing to some other nonzero size. */ /* call realloc, or its equivalent */ PRINT1 (("realloc : %d to %d, %d\n", nold, nnew, size)) ; pnew = NULL ; s = CHOLMOD(mult_size_t) (MAX (1,nnew), size, &ok) ; pnew = ok ? ((Common->realloc_memory) (p, s)) : NULL ; if (pnew == NULL) { /* Do not change p, since it still points to allocated memory */ if (nnew <= nold) { /* The attempt to reduce the size of the block from n to * nnew has failed. The current block is not modified, so * pretend to succeed, but do not change p. Do change * CHOLMOD's notion of the size of the block, however. */ *n = nnew ; PRINTM (("nnew <= nold failed, pretend to succeed\n")) ; PRINTM (("cholmod_free %p %g cnt: %g inuse %g\n" "cholmod_malloc %p %g cnt: %g inuse %g\n", p, (double) nold*size, (double) Common->malloc_count-1, (double) (Common->memory_inuse - nold*size), p, (double) nnew*size, (double) Common->malloc_count, (double) (Common->memory_inuse + (nnew-nold)*size))) ; Common->memory_inuse += ((nnew-nold) * size) ; } else { /* Increasing the size of the block has failed. * Do not change n. */ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ; } } else { /* success: return revised p and change the size of the block */ PRINTM (("cholmod_free %p %g cnt: %g inuse %g\n" "cholmod_malloc %p %g cnt: %g inuse %g\n", p, (double) nold*size, (double) Common->malloc_count-1, (double) (Common->memory_inuse - nold*size), pnew, (double) nnew*size, (double) Common->malloc_count, (double) (Common->memory_inuse + (nnew-nold)*size))) ; p = pnew ; *n = nnew ; Common->memory_inuse += ((nnew-nold) * size) ; } Common->memory_usage = MAX (Common->memory_usage, Common->memory_inuse); } return (p) ; } /* ========================================================================== */ /* === cholmod_realloc_multiple ============================================= */ /* ========================================================================== */ /* reallocate multiple blocks of memory, all of the same size (up to two integer * and two real blocks). Either reallocations all succeed, or all are returned * in the original size (they are freed if the original size is zero). The nnew * blocks are of size 1 or more. */ int CHOLMOD(realloc_multiple) ( /* ---- input ---- */ size_t nnew, /* requested # of items in reallocated blocks */ int nint, /* number of int/SuiteSparse_long blocks */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* ---- in/out --- */ void **Iblock, /* int or SuiteSparse_long block */ void **Jblock, /* int or SuiteSparse_long block */ void **Xblock, /* complex or double block */ void **Zblock, /* zomplex case only: double block */ size_t *nold_p, /* current size of the I,J,X,Z blocks on input, * nnew on output if successful */ /* --------------- */ cholmod_common *Common ) { double *xx, *zz ; size_t i, j, x, z, nold ; RETURN_IF_NULL_COMMON (FALSE) ; if (xtype < CHOLMOD_PATTERN || xtype > CHOLMOD_ZOMPLEX) { ERROR (CHOLMOD_INVALID, "invalid xtype") ; return (FALSE) ; } nold = *nold_p ; if (nint < 1 && xtype == CHOLMOD_PATTERN) { /* nothing to do */ return (TRUE) ; } i = nold ; j = nold ; x = nold ; z = nold ; if (nint > 0) { *Iblock = CHOLMOD(realloc) (nnew, sizeof (Int), *Iblock, &i, Common) ; } if (nint > 1) { *Jblock = CHOLMOD(realloc) (nnew, sizeof (Int), *Jblock, &j, Common) ; } switch (xtype) { case CHOLMOD_REAL: *Xblock = CHOLMOD(realloc) (nnew, sizeof (double), *Xblock, &x, Common) ; break ; case CHOLMOD_COMPLEX: *Xblock = CHOLMOD(realloc) (nnew, 2*sizeof (double), *Xblock, &x, Common) ; break ; case CHOLMOD_ZOMPLEX: *Xblock = CHOLMOD(realloc) (nnew, sizeof (double), *Xblock, &x, Common) ; *Zblock = CHOLMOD(realloc) (nnew, sizeof (double), *Zblock, &z, Common) ; break ; } if (Common->status < CHOLMOD_OK) { /* one or more realloc's failed. Resize all back down to nold. */ if (nold == 0) { if (nint > 0) { *Iblock = CHOLMOD(free) (i, sizeof (Int), *Iblock, Common) ; } if (nint > 1) { *Jblock = CHOLMOD(free) (j, sizeof (Int), *Jblock, Common) ; } switch (xtype) { case CHOLMOD_REAL: *Xblock = CHOLMOD(free) (x, sizeof (double), *Xblock, Common) ; break ; case CHOLMOD_COMPLEX: *Xblock = CHOLMOD(free) (x, 2*sizeof (double), *Xblock, Common) ; break ; case CHOLMOD_ZOMPLEX: *Xblock = CHOLMOD(free) (x, sizeof (double), *Xblock, Common) ; *Zblock = CHOLMOD(free) (x, sizeof (double), *Zblock, Common) ; break ; } } else { if (nint > 0) { *Iblock = CHOLMOD(realloc) (nold, sizeof (Int), *Iblock, &i, Common) ; } if (nint > 1) { *Jblock = CHOLMOD(realloc) (nold, sizeof (Int), *Jblock, &j, Common) ; } switch (xtype) { case CHOLMOD_REAL: *Xblock = CHOLMOD(realloc) (nold, sizeof (double), *Xblock, &x, Common) ; break ; case CHOLMOD_COMPLEX: *Xblock = CHOLMOD(realloc) (nold, 2*sizeof (double), *Xblock, &x, Common) ; break ; case CHOLMOD_ZOMPLEX: *Xblock = CHOLMOD(realloc) (nold, sizeof (double), *Xblock, &x, Common) ; *Zblock = CHOLMOD(realloc) (nold, sizeof (double), *Zblock, &z, Common) ; break ; } } return (FALSE) ; } if (nold == 0) { /* New space was allocated. Clear the first entry so that valgrind * doesn't complain about its access in change_complexity * (Core/cholmod_complex.c). */ xx = *Xblock ; zz = *Zblock ; switch (xtype) { case CHOLMOD_REAL: xx [0] = 0 ; break ; case CHOLMOD_COMPLEX: xx [0] = 0 ; xx [1] = 0 ; break ; case CHOLMOD_ZOMPLEX: xx [0] = 0 ; zz [0] = 0 ; break ; } } /* all realloc's succeeded, change size to reflect realloc'ed size. */ *nold_p = nnew ; return (TRUE) ; } Matrix/src/CHOLMOD/Core/cholmod_complex.c0000644000175100001440000003775112271765436017652 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_complex ================================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* If you convert a matrix that contains uninitialized data, valgrind will * complain. This can occur in a factor L which has gaps (a partial * factorization, or after updates that change the nonzero pattern), an * unpacked sparse matrix, a dense matrix with leading dimension d > # of rows, * or any matrix (dense, sparse, triplet, or factor) with more space allocated * than is used. You can safely ignore any of these complaints by valgrind. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === cholmod_hypot ======================================================== */ /* ========================================================================== */ /* There is an equivalent routine called hypot in , which conforms * to ANSI C99. However, CHOLMOD does not assume that ANSI C99 is available. * You can use the ANSI C99 hypot routine with: * * #include * Common->hypotenuse = hypot ; * * Default value of the Common->hypotenuse pointer is cholmod_hypot. * * s = hypot (x,y) computes s = sqrt (x*x + y*y) but does so more accurately. * The NaN cases for the double relops x >= y and x+y == x are safely ignored. * * Source: Algorithm 312, "Absolute value and square root of a complex number," * P. Friedland, Comm. ACM, vol 10, no 10, October 1967, page 665. */ double CHOLMOD(hypot) (double x, double y) { double s, r ; x = fabs (x) ; y = fabs (y) ; if (x >= y) { if (x + y == x) { s = x ; } else { r = y / x ; s = x * sqrt (1.0 + r*r) ; } } else { if (y + x == y) { s = y ; } else { r = x / y ; s = y * sqrt (1.0 + r*r) ; } } return (s) ; } /* ========================================================================== */ /* === cholmod_divcomplex =================================================== */ /* ========================================================================== */ /* c = a/b where c, a, and b are complex. The real and imaginary parts are * passed as separate arguments to this routine. The NaN case is ignored * for the double relop br >= bi. Returns 1 if the denominator is zero, * 0 otherwise. Note that this return value is the single exception to the * rule that all CHOLMOD routines that return int return TRUE if successful * or FALSE otherise. * * This uses ACM Algo 116, by R. L. Smith, 1962, which tries to avoid * underflow and overflow. * * c can be the same variable as a or b. * * Default value of the Common->complex_divide pointer is cholmod_divcomplex. */ int CHOLMOD(divcomplex) ( double ar, double ai, /* real and imaginary parts of a */ double br, double bi, /* real and imaginary parts of b */ double *cr, double *ci /* real and imaginary parts of c */ ) { double tr, ti, r, den ; if (fabs (br) >= fabs (bi)) { r = bi / br ; den = br + r * bi ; tr = (ar + ai * r) / den ; ti = (ai - ar * r) / den ; } else { r = br / bi ; den = r * br + bi ; tr = (ar * r + ai) / den ; ti = (ai * r - ar) / den ; } *cr = tr ; *ci = ti ; return (IS_ZERO (den)) ; } /* ========================================================================== */ /* === change_complexity ==================================================== */ /* ========================================================================== */ /* X and Z represent an array of size nz, with numeric xtype given by xtype_in. * * If xtype_in is: * CHOLMOD_PATTERN: X and Z must be NULL. * CHOLMOD_REAL: X is of size nz, Z must be NULL. * CHOLMOD_COMPLEX: X is of size 2*nz, Z must be NULL. * CHOLMOD_ZOMPLEX: X is of size nz, Z is of size nz. * * The array is changed into the numeric xtype given by xtype_out, with the * same definitions of X and Z above. Note that the input conditions, above, * are not checked. These are checked in the caller routine. * * Returns TRUE if successful, FALSE otherwise. X and Z are not modified if * not successful. */ static int change_complexity ( /* ---- input ---- */ Int nz, /* size of X and/or Z */ int xtype_in, /* xtype of X and Z on input */ int xtype_out, /* requested xtype of X and Z on output */ int xtype1, /* xtype_out must be in the range [xtype1 .. xtype2] */ int xtype2, /* ---- in/out --- */ void **XX, /* old X on input, new X on output */ void **ZZ, /* old Z on input, new Z on output */ /* --------------- */ cholmod_common *Common ) { double *Xold, *Zold, *Xnew, *Znew ; Int k ; size_t nz2 ; if (xtype_out < xtype1 || xtype_out > xtype2) { ERROR (CHOLMOD_INVALID, "invalid xtype") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; Xold = *XX ; Zold = *ZZ ; switch (xtype_in) { /* ------------------------------------------------------------------ */ /* converting from pattern */ /* ------------------------------------------------------------------ */ case CHOLMOD_PATTERN: switch (xtype_out) { /* ---------------------------------------------------------- */ /* pattern -> real */ /* ---------------------------------------------------------- */ case CHOLMOD_REAL: /* allocate X and set to all ones */ Xnew = CHOLMOD(malloc) (nz, sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Xnew [k] = 1 ; } *XX = Xnew ; break ; /* ---------------------------------------------------------- */ /* pattern -> complex */ /* ---------------------------------------------------------- */ case CHOLMOD_COMPLEX: /* allocate X and set to all ones */ Xnew = CHOLMOD(malloc) (nz, 2*sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Xnew [2*k ] = 1 ; Xnew [2*k+1] = 0 ; } *XX = Xnew ; break ; /* ---------------------------------------------------------- */ /* pattern -> zomplex */ /* ---------------------------------------------------------- */ case CHOLMOD_ZOMPLEX: /* allocate X and Z and set to all ones */ Xnew = CHOLMOD(malloc) (nz, sizeof (double), Common) ; Znew = CHOLMOD(malloc) (nz, sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free) (nz, sizeof (double), Xnew, Common) ; CHOLMOD(free) (nz, sizeof (double), Znew, Common) ; return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Xnew [k] = 1 ; Znew [k] = 0 ; } *XX = Xnew ; *ZZ = Znew ; break ; } break ; /* ------------------------------------------------------------------ */ /* converting from real */ /* ------------------------------------------------------------------ */ case CHOLMOD_REAL: switch (xtype_out) { /* ---------------------------------------------------------- */ /* real -> pattern */ /* ---------------------------------------------------------- */ case CHOLMOD_PATTERN: /* free X */ *XX = CHOLMOD(free) (nz, sizeof (double), *XX, Common) ; break ; /* ---------------------------------------------------------- */ /* real -> complex */ /* ---------------------------------------------------------- */ case CHOLMOD_COMPLEX: /* allocate a new X and copy the old X */ Xnew = CHOLMOD(malloc) (nz, 2*sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Xnew [2*k ] = Xold [k] ; Xnew [2*k+1] = 0 ; } CHOLMOD(free) (nz, sizeof (double), *XX, Common) ; *XX = Xnew ; break ; /* ---------------------------------------------------------- */ /* real -> zomplex */ /* ---------------------------------------------------------- */ case CHOLMOD_ZOMPLEX: /* allocate a new Z and set it to zero */ Znew = CHOLMOD(malloc) (nz, sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Znew [k] = 0 ; } *ZZ = Znew ; break ; } break ; /* ------------------------------------------------------------------ */ /* converting from complex */ /* ------------------------------------------------------------------ */ case CHOLMOD_COMPLEX: switch (xtype_out) { /* ---------------------------------------------------------- */ /* complex -> pattern */ /* ---------------------------------------------------------- */ case CHOLMOD_PATTERN: /* free X */ *XX = CHOLMOD(free) (nz, 2*sizeof (double), *XX, Common) ; break ; /* ---------------------------------------------------------- */ /* complex -> real */ /* ---------------------------------------------------------- */ case CHOLMOD_REAL: /* pack the real part of X, discarding the imaginary part */ for (k = 0 ; k < nz ; k++) { Xold [k] = Xold [2*k] ; } /* shrink X in half (this cannot fail) */ nz2 = 2*nz ; *XX = CHOLMOD(realloc) (nz, sizeof (double), *XX, &nz2, Common) ; break ; /* ---------------------------------------------------------- */ /* complex -> zomplex */ /* ---------------------------------------------------------- */ case CHOLMOD_ZOMPLEX: /* allocate X and Z and copy the old X into them */ Xnew = CHOLMOD(malloc) (nz, sizeof (double), Common) ; Znew = CHOLMOD(malloc) (nz, sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free) (nz, sizeof (double), Xnew, Common) ; CHOLMOD(free) (nz, sizeof (double), Znew, Common) ; return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Xnew [k] = Xold [2*k ] ; Znew [k] = Xold [2*k+1] ; } CHOLMOD(free) (nz, 2*sizeof (double), *XX, Common) ; *XX = Xnew ; *ZZ = Znew ; break ; } break ; /* ------------------------------------------------------------------ */ /* converting from zomplex */ /* ------------------------------------------------------------------ */ case CHOLMOD_ZOMPLEX: switch (xtype_out) { /* ---------------------------------------------------------- */ /* zomplex -> pattern */ /* ---------------------------------------------------------- */ case CHOLMOD_PATTERN: /* free X and Z */ *XX = CHOLMOD(free) (nz, sizeof (double), *XX, Common) ; *ZZ = CHOLMOD(free) (nz, sizeof (double), *ZZ, Common) ; break ; /* ---------------------------------------------------------- */ /* zomplex -> real */ /* ---------------------------------------------------------- */ case CHOLMOD_REAL: /* free the imaginary part */ *ZZ = CHOLMOD(free) (nz, sizeof (double), *ZZ, Common) ; break ; /* ---------------------------------------------------------- */ /* zomplex -> complex */ /* ---------------------------------------------------------- */ case CHOLMOD_COMPLEX: Xnew = CHOLMOD(malloc) (nz, 2*sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Xnew [2*k ] = Xold [k] ; Xnew [2*k+1] = Zold [k] ; } CHOLMOD(free) (nz, sizeof (double), *XX, Common) ; CHOLMOD(free) (nz, sizeof (double), *ZZ, Common) ; *XX = Xnew ; *ZZ = NULL ; break ; } break ; } return (TRUE) ; } /* ========================================================================== */ /* === cholmod_sparse_xtype ================================================= */ /* ========================================================================== */ /* Change the numeric xtype of a sparse matrix. Supports any type on input * and output (pattern, real, complex, or zomplex). */ int CHOLMOD(sparse_xtype) ( /* ---- input ---- */ int to_xtype, /* requested xtype */ /* ---- in/out --- */ cholmod_sparse *A, /* sparse matrix to change */ /* --------------- */ cholmod_common *Common ) { Int ok ; RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; ok = change_complexity (A->nzmax, A->xtype, to_xtype, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, &(A->x), &(A->z), Common) ; if (ok) { A->xtype = to_xtype ; } return (ok) ; } /* ========================================================================== */ /* === cholmod_triplet_xtype ================================================ */ /* ========================================================================== */ /* Change the numeric xtype of a triplet matrix. Supports any type on input * and output (pattern, real, complex, or zomplex). */ int CHOLMOD(triplet_xtype) ( /* ---- input ---- */ int to_xtype, /* requested xtype */ /* ---- in/out --- */ cholmod_triplet *T, /* triplet matrix to change */ /* --------------- */ cholmod_common *Common ) { Int ok ; RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (T, FALSE) ; RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; ok = change_complexity (T->nzmax, T->xtype, to_xtype, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, &(T->x), &(T->z), Common) ; if (ok) { T->xtype = to_xtype ; } return (ok) ; } /* ========================================================================== */ /* === cholmod_dense_xtype ================================================= */ /* ========================================================================== */ /* Change the numeric xtype of a dense matrix. Supports real, complex or * zomplex on input and output */ int CHOLMOD(dense_xtype) ( /* ---- input ---- */ int to_xtype, /* requested xtype */ /* ---- in/out --- */ cholmod_dense *X, /* dense matrix to change */ /* --------------- */ cholmod_common *Common ) { Int ok ; RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (X, FALSE) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; ok = change_complexity (X->nzmax, X->xtype, to_xtype, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, &(X->x), &(X->z), Common) ; if (ok) { X->xtype = to_xtype ; } return (ok) ; } /* ========================================================================== */ /* === cholmod_factor_xtype ================================================= */ /* ========================================================================== */ /* Change the numeric xtype of a factor. Supports real, complex or zomplex on * input and output. Supernodal zomplex factors are not supported. */ int CHOLMOD(factor_xtype) ( /* ---- input ---- */ int to_xtype, /* requested xtype */ /* ---- in/out --- */ cholmod_factor *L, /* factor to change */ /* --------------- */ cholmod_common *Common ) { Int ok ; RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; if (L->is_super && (L->xtype == CHOLMOD_ZOMPLEX || to_xtype == CHOLMOD_ZOMPLEX)) { ERROR (CHOLMOD_INVALID, "invalid xtype for supernodal L") ; return (FALSE) ; } ok = change_complexity ((L->is_super ? L->xsize : L->nzmax), L->xtype, to_xtype, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, &(L->x), &(L->z), Common) ; if (ok) { L->xtype = to_xtype ; } return (ok) ; } Matrix/src/CHOLMOD/Core/t_cholmod_transpose.c0000644000175100001440000002124412271765436020532 0ustar hornikusers/* ========================================================================== */ /* === Core/t_cholmod_transpose ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Template routine for cholmod_transpose. All xtypes are supported. For * complex matrices, either the array tranpose or complex conjugate transpose * can be computed. */ #include "cholmod_template.h" /* ========================================================================== */ /* === t_cholmod_transpose_unsym ============================================ */ /* ========================================================================== */ /* Compute F = A', A (:,f)', or A (p,f)', where A is unsymmetric and F is * already allocated. The complex case performs either the array transpose * or complex conjugate transpose. * * workspace: * Iwork (MAX (nrow,ncol)) if fset is present * Iwork (nrow) if fset is NULL */ static int TEMPLATE (cholmod_transpose_unsym) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ Int *Perm, /* size nrow, if present (can be NULL) */ Int *fset, /* subset of 0:(A->ncol)-1 */ Int nf, /* size of fset */ /* ---- output --- */ cholmod_sparse *F, /* F = A', A(:,f)', or A(p,f)' */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Az, *Fx, *Fz ; Int *Ap, *Anz, *Ai, *Fp, *Fnz, *Fj, *Wi, *Iwork ; Int j, p, pend, nrow, ncol, Apacked, use_fset, fp, Fpacked, jj, permute ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ /* ensure the xtype of A and F match (ignored if this is pattern version) */ if (!XTYPE_OK (A->xtype)) { ERROR (CHOLMOD_INVALID, "real/complex mismatch") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ use_fset = (fset != NULL) ; nrow = A->nrow ; ncol = A->ncol ; Ap = A->p ; /* size A->ncol+1, column pointers of A */ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */ Ax = A->x ; /* size nz, real values of A */ Az = A->z ; /* size nz, imag values of A */ Anz = A->nz ; Apacked = A->packed ; ASSERT (IMPLIES (!Apacked, Anz != NULL)) ; permute = (Perm != NULL) ; Fp = F->p ; /* size A->nrow+1, row pointers of F */ Fj = F->i ; /* size nz, column indices of F */ Fx = F->x ; /* size nz, real values of F */ Fz = F->z ; /* size nz, imag values of F */ Fnz = F->nz ; Fpacked = F->packed ; ASSERT (IMPLIES (!Fpacked, Fnz != NULL)) ; nf = (use_fset) ? nf : ncol ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; Wi = Iwork ; /* size nrow (i/l/l) */ /* ---------------------------------------------------------------------- */ /* construct the transpose */ /* ---------------------------------------------------------------------- */ for (jj = 0 ; jj < nf ; jj++) { j = (use_fset) ? (fset [jj]) : jj ; p = Ap [j] ; pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { fp = Wi [Ai [p]]++ ; Fj [fp] = j ; #ifdef NCONJUGATE ASSIGN (Fx, Fz, fp, Ax, Az, p) ; #else ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ; #endif } } return (TRUE) ; } /* ========================================================================== */ /* === t_cholmod_transpose_sym ============================================== */ /* ========================================================================== */ /* Compute F = A' or A (p,p)', where A is symmetric and F is already allocated. * The complex case performs either the array transpose or complex conjugate * transpose. * * workspace: Iwork (nrow) if Perm NULL, Iwork (2*nrow) if Perm non-NULL. */ static int TEMPLATE (cholmod_transpose_sym) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ Int *Perm, /* size n, if present (can be NULL) */ /* ---- output --- */ cholmod_sparse *F, /* F = A' or A(p,p)' */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Az, *Fx, *Fz ; Int *Ap, *Anz, *Ai, *Fp, *Fj, *Wi, *Pinv, *Iwork ; Int p, pend, packed, fp, upper, permute, jold, n, i, j, iold ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ /* ensure the xtype of A and F match (ignored if this is pattern version) */ if (!XTYPE_OK (A->xtype)) { ERROR (CHOLMOD_INVALID, "real/complex mismatch") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ permute = (Perm != NULL) ; n = A->nrow ; Ap = A->p ; /* size A->ncol+1, column pointers of A */ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */ Ax = A->x ; /* size nz, real values of A */ Az = A->z ; /* size nz, imag values of A */ Anz = A->nz ; packed = A->packed ; ASSERT (IMPLIES (!packed, Anz != NULL)) ; upper = (A->stype > 0) ; Fp = F->p ; /* size A->nrow+1, row pointers of F */ Fj = F->i ; /* size nz, column indices of F */ Fx = F->x ; /* size nz, real values of F */ Fz = F->z ; /* size nz, imag values of F */ /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; Wi = Iwork ; /* size n (i/l/l) */ Pinv = Iwork + n ; /* size n (i/i/l) , unused if Perm NULL */ /* ---------------------------------------------------------------------- */ /* construct the transpose */ /* ---------------------------------------------------------------------- */ if (permute) { if (upper) { /* permuted, upper */ for (j = 0 ; j < n ; j++) { jold = Perm [j] ; p = Ap [jold] ; pend = (packed) ? Ap [jold+1] : p + Anz [jold] ; for ( ; p < pend ; p++) { iold = Ai [p] ; if (iold <= jold) { i = Pinv [iold] ; if (i < j) { fp = Wi [i]++ ; Fj [fp] = j ; #ifdef NCONJUGATE ASSIGN (Fx, Fz, fp, Ax, Az, p) ; #else ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ; #endif } else { fp = Wi [j]++ ; Fj [fp] = i ; ASSIGN (Fx, Fz, fp, Ax, Az, p) ; } } } } } else { /* permuted, lower */ for (j = 0 ; j < n ; j++) { jold = Perm [j] ; p = Ap [jold] ; pend = (packed) ? Ap [jold+1] : p + Anz [jold] ; for ( ; p < pend ; p++) { iold = Ai [p] ; if (iold >= jold) { i = Pinv [iold] ; if (i > j) { fp = Wi [i]++ ; Fj [fp] = j ; #ifdef NCONJUGATE ASSIGN (Fx, Fz, fp, Ax, Az, p) ; #else ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ; #endif } else { fp = Wi [j]++ ; Fj [fp] = i ; ASSIGN (Fx, Fz, fp, Ax, Az, p) ; } } } } } } else { if (upper) { /* unpermuted, upper */ for (j = 0 ; j < n ; j++) { p = Ap [j] ; pend = (packed) ? Ap [j+1] : p + Anz [j] ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i <= j) { fp = Wi [i]++ ; Fj [fp] = j ; #ifdef NCONJUGATE ASSIGN (Fx, Fz, fp, Ax, Az, p) ; #else ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ; #endif } } } } else { /* unpermuted, lower */ for (j = 0 ; j < n ; j++) { p = Ap [j] ; pend = (packed) ? Ap [j+1] : p + Anz [j] ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= j) { fp = Wi [i]++ ; Fj [fp] = j ; #ifdef NCONJUGATE ASSIGN (Fx, Fz, fp, Ax, Az, p) ; #else ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ; #endif } } } } } return (TRUE) ; } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX #undef NCONJUGATE Matrix/src/CHOLMOD/Core/cholmod_factor.c0000644000175100001440000006552112271765436017455 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_factor ================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2013, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Core utility routines for the cholmod_factor object: * * The data structure for an LL' or LDL' factorization is too complex to * describe in one sentence. This object can hold the symbolic analysis alone, * or in combination with a "simplicial" (similar to a sparse matrix) or * "supernodal" form of the numerical factorization. Only the routine to free * a factor is primary, since a factor object is created by the factorization * routine (cholmod_factorize). It must be freed with cholmod_free_factor. * * Primary routine: * ---------------- * cholmod_free_factor free a factor * * Secondary routines: * ------------------- * cholmod_allocate_factor allocate a symbolic factor (LL' or LDL') * cholmod_reallocate_factor change the # entries in a factor * cholmod_change_factor change the type of factor (e.g., LDL' to LL') * cholmod_pack_factor pack the columns of a factor * cholmod_reallocate_column resize a single column of a factor * cholmod_factor_to_sparse create a sparse matrix copy of a factor * cholmod_copy_factor create a copy of a factor * * Note that there is no cholmod_sparse_to_factor routine to create a factor * as a copy of a sparse matrix. It could be done, after a fashion, but a * lower triangular sparse matrix would not necessarily have a chordal graph, * which would break the many CHOLMOD routines that rely on this property. * * The cholmod_factor_to_sparse routine is provided so that matrix operations * in the MatrixOps module may be applied to L. Those operations operate on * cholmod_sparse objects, and they are not guaranteed to maintain the chordal * property of L. Such a modified L cannot be safely converted back to a * cholmod_factor object. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === cholmod_allocate_factor ============================================== */ /* ========================================================================== */ /* Allocate a simplicial symbolic factor, with L->Perm and L->ColCount allocated * and initialized to "empty" values (Perm [k] = k, and ColCount[k] = 1). * The integer and numerical parts of L are not allocated. L->xtype is returned * as CHOLMOD_PATTERN and L->is_super are returned as FALSE. L->is_ll is also * returned FALSE, but this may be modified when the matrix is factorized. * * This is sufficient (but far from ideal) for input to cholmod_factorize, * since the simplicial LL' or LDL' factorization (cholmod_rowfac) can * reallocate the columns of L as needed. The primary purpose of this routine * is to allocate space for a symbolic factorization, for the "expert" user to * do his or her own symbolic analysis. The typical user should use * cholmod_analyze instead of this routine. * * workspace: none */ cholmod_factor *CHOLMOD(allocate_factor) ( /* ---- input ---- */ size_t n, /* L is n-by-n */ /* --------------- */ cholmod_common *Common ) { Int j ; Int *Perm, *ColCount ; cholmod_factor *L ; int ok = TRUE ; RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; /* ensure the dimension does not cause integer overflow */ (void) CHOLMOD(add_size_t) (n, 2, &ok) ; if (!ok || n > Int_max) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } L = CHOLMOD(malloc) (sizeof (cholmod_factor), 1, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } L->n = n ; L->is_ll = FALSE ; L->is_super = FALSE ; L->is_monotonic = TRUE ; L->itype = ITYPE ; L->xtype = CHOLMOD_PATTERN ; L->dtype = DTYPE ; /* allocate the purely symbolic part of L */ L->ordering = CHOLMOD_NATURAL ; L->Perm = CHOLMOD(malloc) (n, sizeof (Int), Common) ; L->IPerm = NULL ; /* only created by cholmod_solve2 when needed */ L->ColCount = CHOLMOD(malloc) (n, sizeof (Int), Common) ; /* simplicial part of L is empty */ L->nzmax = 0 ; L->p = NULL ; L->i = NULL ; L->x = NULL ; L->z = NULL ; L->nz = NULL ; L->next = NULL ; L->prev = NULL ; /* supernodal part of L is also empty */ L->nsuper = 0 ; L->ssize = 0 ; L->xsize = 0 ; L->maxesize = 0 ; L->maxcsize = 0 ; L->super = NULL ; L->pi = NULL ; L->px = NULL ; L->s = NULL ; /* L has not been factorized */ L->minor = n ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_factor) (&L, Common) ; return (NULL) ; /* out of memory */ } /* initialize Perm and ColCount */ Perm = L->Perm ; for (j = 0 ; j < ((Int) n) ; j++) { Perm [j] = j ; } ColCount = L->ColCount ; for (j = 0 ; j < ((Int) n) ; j++) { ColCount [j] = 1 ; } return (L) ; } /* ========================================================================== */ /* === cholmod_free_factor ================================================== */ /* ========================================================================== */ /* Free a factor object. * * workspace: none */ int CHOLMOD(free_factor) ( /* ---- in/out --- */ cholmod_factor **LHandle, /* factor to free, NULL on output */ /* --------------- */ cholmod_common *Common ) { Int n, lnz, xs, ss, s ; cholmod_factor *L ; RETURN_IF_NULL_COMMON (FALSE) ; if (LHandle == NULL) { /* nothing to do */ return (TRUE) ; } L = *LHandle ; if (L == NULL) { /* nothing to do */ return (TRUE) ; } n = L->n ; lnz = L->nzmax ; s = L->nsuper + 1 ; xs = (L->is_super) ? ((Int) (L->xsize)) : (lnz) ; ss = L->ssize ; /* symbolic part of L */ CHOLMOD(free) (n, sizeof (Int), L->Perm, Common) ; CHOLMOD(free) (n, sizeof (Int), L->IPerm, Common) ; CHOLMOD(free) (n, sizeof (Int), L->ColCount, Common) ; /* simplicial form of L */ CHOLMOD(free) (n+1, sizeof (Int), L->p, Common) ; CHOLMOD(free) (lnz, sizeof (Int), L->i, Common) ; CHOLMOD(free) (n, sizeof (Int), L->nz, Common) ; CHOLMOD(free) (n+2, sizeof (Int), L->next, Common) ; CHOLMOD(free) (n+2, sizeof (Int), L->prev, Common) ; /* supernodal form of L */ CHOLMOD(free) (s, sizeof (Int), L->pi, Common) ; CHOLMOD(free) (s, sizeof (Int), L->px, Common) ; CHOLMOD(free) (s, sizeof (Int), L->super, Common) ; CHOLMOD(free) (ss, sizeof (Int), L->s, Common) ; /* numerical values for both simplicial and supernodal L */ if (L->xtype == CHOLMOD_REAL) { CHOLMOD(free) (xs, sizeof (double), L->x, Common) ; } else if (L->xtype == CHOLMOD_COMPLEX) { CHOLMOD(free) (xs, 2*sizeof (double), L->x, Common) ; } else if (L->xtype == CHOLMOD_ZOMPLEX) { CHOLMOD(free) (xs, sizeof (double), L->x, Common) ; CHOLMOD(free) (xs, sizeof (double), L->z, Common) ; } *LHandle = CHOLMOD(free) (1, sizeof (cholmod_factor), (*LHandle), Common) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_reallocate_factor ============================================ */ /* ========================================================================== */ /* Change the size of L->i and L->x, or allocate them if their current size * is zero. L must be simplicial. * * workspace: none */ int CHOLMOD(reallocate_factor) ( /* ---- input ---- */ size_t nznew, /* new # of entries in L */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; PRINT1 (("realloc factor: xtype %d\n", L->xtype)) ; if (L->is_super) { /* L must be simplicial, and not symbolic */ ERROR (CHOLMOD_INVALID, "L invalid") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; PRINT1 (("realloc factor %g to %g\n", (double) L->nzmax, (double) nznew)) ; /* ---------------------------------------------------------------------- */ /* resize (or allocate) the L->i and L->x components of the factor */ /* ---------------------------------------------------------------------- */ CHOLMOD(realloc_multiple) (nznew, 1, L->xtype, &(L->i), NULL, &(L->x), &(L->z), &(L->nzmax), Common) ; return (Common->status == CHOLMOD_OK) ; } /* ========================================================================== */ /* === cholmod_reallocate_column =========================================== */ /* ========================================================================== */ /* Column j needs more space, reallocate it at the end of L->i and L->x. * If the reallocation fails, the factor is converted to a simplicial * symbolic factor (no pattern, just L->Perm and L->ColCount). * * workspace: none */ int CHOLMOD(reallocate_column) ( /* ---- input ---- */ size_t j, /* the column to reallocate */ size_t need, /* required size of column j */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { double xneed ; double *Lx, *Lz ; Int *Lp, *Lprev, *Lnext, *Li, *Lnz ; Int n, pold, pnew, len, k, tail ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; if (L->is_super) { ERROR (CHOLMOD_INVALID, "L must be simplicial") ; return (FALSE) ; } n = L->n ; if (j >= L->n || need == 0) { ERROR (CHOLMOD_INVALID, "j invalid") ; return (FALSE) ; /* j out of range */ } Common->status = CHOLMOD_OK ; DEBUG (CHOLMOD(dump_factor) (L, "start colrealloc", Common)) ; /* ---------------------------------------------------------------------- */ /* increase the size of L if needed */ /* ---------------------------------------------------------------------- */ /* head = n+1 ; */ tail = n ; Lp = L->p ; Lnz = L->nz ; Lprev = L->prev ; Lnext = L->next ; ASSERT (Lnz != NULL) ; ASSERT (Lnext != NULL && Lprev != NULL) ; PRINT1 (("col %g need %g\n", (double) j, (double) need)) ; /* column j cannot have more than n-j entries if all entries are present */ need = MIN (need, n-j) ; /* compute need in double to avoid integer overflow */ if (Common->grow1 >= 1.0) { xneed = (double) need ; xneed = Common->grow1 * xneed + Common->grow2 ; xneed = MIN (xneed, n-j) ; need = (Int) xneed ; } PRINT1 (("really new need %g current %g\n", (double) need, (double) (Lp [Lnext [j]] - Lp [j]))) ; ASSERT (need >= 1 && need <= n-j) ; if (Lp [Lnext [j]] - Lp [j] >= (Int) need) { /* no need to reallocate the column, it's already big enough */ PRINT1 (("colrealloc: quick return %g %g\n", (double) (Lp [Lnext [j]] - Lp [j]), (double) need)) ; return (TRUE) ; } if (Lp [tail] + need > L->nzmax) { /* use double to avoid integer overflow */ xneed = (double) need ; if (Common->grow0 < 1.2) /* fl. pt. compare, false if NaN */ { /* if grow0 is less than 1.2 or NaN, don't use it */ xneed = 1.2 * (((double) L->nzmax) + xneed + 1) ; } else { xneed = Common->grow0 * (((double) L->nzmax) + xneed + 1) ; } if (xneed > Size_max || !CHOLMOD(reallocate_factor) ((Int) xneed, L, Common)) { /* out of memory, convert to simplicial symbolic */ CHOLMOD(change_factor) (CHOLMOD_PATTERN, L->is_ll, FALSE, TRUE, TRUE, L, Common) ; ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory; L now symbolic") ; return (FALSE) ; /* out of memory */ } PRINT1 (("\n=== GROW L from %g to %g\n", (double) L->nzmax, (double) xneed)) ; /* pack all columns so that each column has at most grow2 free space */ CHOLMOD(pack_factor) (L, Common) ; ASSERT (Common->status == CHOLMOD_OK) ; Common->nrealloc_factor++ ; } /* ---------------------------------------------------------------------- */ /* reallocate the column */ /* ---------------------------------------------------------------------- */ Common->nrealloc_col++ ; Li = L->i ; Lx = L->x ; Lz = L->z ; /* remove j from its current position in the list */ Lnext [Lprev [j]] = Lnext [j] ; Lprev [Lnext [j]] = Lprev [j] ; /* place j at the end of the list */ Lnext [Lprev [tail]] = j ; Lprev [j] = Lprev [tail] ; Lnext [j] = n ; Lprev [tail] = j ; /* L is no longer monotonic; columns are out-of-order */ L->is_monotonic = FALSE ; /* allocate space for column j */ pold = Lp [j] ; pnew = Lp [tail] ; Lp [j] = pnew ; Lp [tail] += need ; /* copy column j to the new space */ len = Lnz [j] ; for (k = 0 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; } if (L->xtype == CHOLMOD_REAL) { for (k = 0 ; k < len ; k++) { Lx [pnew + k] = Lx [pold + k] ; } } else if (L->xtype == CHOLMOD_COMPLEX) { for (k = 0 ; k < len ; k++) { Lx [2*(pnew + k) ] = Lx [2*(pold + k) ] ; Lx [2*(pnew + k)+1] = Lx [2*(pold + k)+1] ; } } else if (L->xtype == CHOLMOD_ZOMPLEX) { for (k = 0 ; k < len ; k++) { Lx [pnew + k] = Lx [pold + k] ; Lz [pnew + k] = Lz [pold + k] ; } } DEBUG (CHOLMOD(dump_factor) (L, "colrealloc done", Common)) ; /* successful reallocation of column j of L */ return (TRUE) ; } /* ========================================================================== */ /* === cholmod_pack_factor ================================================== */ /* ========================================================================== */ /* Pack the columns of a simplicial LDL' or LL' factor. This can be followed * by a call to cholmod_reallocate_factor to reduce the size of L to the exact * size required by the factor, if desired. Alternatively, you can leave the * size of L->i and L->x the same, to allow space for future updates/rowadds. * * Each column is reduced in size so that it has at most Common->grow2 free * space at the end of the column. * * Does nothing and returns silently if given any other type of factor. * * Does NOT force the columns of L to be monotonic. It thus differs from * cholmod_change_factor (xtype, -, FALSE, TRUE, TRUE, L, Common), which * packs the columns and ensures that they appear in monotonic order. */ int CHOLMOD(pack_factor) ( /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { double *Lx, *Lz ; Int *Lp, *Li, *Lnz, *Lnext ; Int pnew, j, k, pold, len, n, head, tail, grow2 ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; DEBUG (CHOLMOD(dump_factor) (L, "start pack", Common)) ; PRINT1 (("PACK factor %d\n", L->is_super)) ; if (L->xtype == CHOLMOD_PATTERN || L->is_super) { /* nothing to do unless L is simplicial numeric */ return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* pack */ /* ---------------------------------------------------------------------- */ grow2 = Common->grow2 ; PRINT1 (("\nPACK grow2 "ID"\n", grow2)) ; pnew = 0 ; n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ; Lz = L->z ; Lnz = L->nz ; Lnext = L->next ; head = n+1 ; tail = n ; for (j = Lnext [head] ; j != tail ; j = Lnext [j]) { /* pack column j */ pold = Lp [j] ; len = Lnz [j] ; ASSERT (len > 0) ; PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ; if (pnew < pold) { PRINT2 ((" pack this column\n")) ; for (k = 0 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; } if (L->xtype == CHOLMOD_REAL) { for (k = 0 ; k < len ; k++) { Lx [pnew + k] = Lx [pold + k] ; } } else if (L->xtype == CHOLMOD_COMPLEX) { for (k = 0 ; k < len ; k++) { Lx [2*(pnew + k) ] = Lx [2*(pold + k) ] ; Lx [2*(pnew + k)+1] = Lx [2*(pold + k)+1] ; } } else if (L->xtype == CHOLMOD_ZOMPLEX) { for (k = 0 ; k < len ; k++) { Lx [pnew + k] = Lx [pold + k] ; Lz [pnew + k] = Lz [pold + k] ; } } Lp [j] = pnew ; } len = MIN (len + grow2, n - j) ; pnew = MIN (Lp [j] + len, Lp [Lnext [j]]) ; } PRINT2 (("final pnew = "ID"\n", pnew)) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_factor_to_sparse ============================================= */ /* ========================================================================== */ /* Constructs a column-oriented sparse matrix containing the pattern and values * of a simplicial or supernodal numerical factor, and then converts the factor * into a simplicial symbolic factor. If L is already packed, monotonic, * and simplicial (which is the case when cholmod_factorize uses the simplicial * Cholesky factorization algorithm) then this routine requires only O(1) * memory and takes O(1) time. * * Only operates on numeric factors (real, complex, or zomplex). Does not * change the numeric L->xtype (the resulting sparse matrix has the same xtype * as L). If this routine fails, L is left unmodified. */ cholmod_sparse *CHOLMOD(factor_to_sparse) ( /* ---- in/out --- */ cholmod_factor *L, /* factor to copy, converted to symbolic on output */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *Lsparse ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (L, NULL) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ; Common->status = CHOLMOD_OK ; DEBUG (CHOLMOD(dump_factor) (L, "start convert to matrix", Common)) ; /* ---------------------------------------------------------------------- */ /* convert to packed, monotonic, simplicial, numeric */ /* ---------------------------------------------------------------------- */ /* leave as LL or LDL' */ if (!CHOLMOD(change_factor) (L->xtype, L->is_ll, FALSE, TRUE, TRUE, L, Common)) { ERROR (CHOLMOD_INVALID, "cannot convert L") ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* create Lsparse */ /* ---------------------------------------------------------------------- */ /* allocate the header for Lsparse, the sparse matrix version of L */ Lsparse = CHOLMOD(malloc) (sizeof (cholmod_sparse), 1, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* transfer the contents from L to Lsparse */ Lsparse->nrow = L->n ; Lsparse->ncol = L->n ; Lsparse->p = L->p ; Lsparse->i = L->i ; Lsparse->x = L->x ; Lsparse->z = L->z ; Lsparse->nz = NULL ; Lsparse->stype = 0 ; Lsparse->itype = L->itype ; Lsparse->xtype = L->xtype ; Lsparse->dtype = L->dtype ; Lsparse->sorted = TRUE ; Lsparse->packed = TRUE ; Lsparse->nzmax = L->nzmax ; ASSERT (CHOLMOD(dump_sparse) (Lsparse, "Lsparse", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* convert L to symbolic, but do not free contents transfered to Lsparse */ /* ---------------------------------------------------------------------- */ L->p = NULL ; L->i = NULL ; L->x = NULL ; L->z = NULL ; L->xtype = CHOLMOD_PATTERN ; CHOLMOD(change_factor) (CHOLMOD_PATTERN, FALSE, FALSE, TRUE, TRUE, L, Common) ; return (Lsparse) ; } /* ========================================================================== */ /* === cholmod_copy_factor ================================================== */ /* ========================================================================== */ /* Create an exact copy of a factor, with one exception: * * Entries in unused space are not copied (they might not be initialized, * and copying them would cause program checkers such as purify and * valgrind to complain). * * Note that a supernodal L cannot be zomplex. */ cholmod_factor *CHOLMOD(copy_factor) ( /* ---- input ---- */ cholmod_factor *L, /* factor to copy */ /* --------------- */ cholmod_common *Common ) { cholmod_factor *L2 ; double *Lx, *L2x, *Lz, *L2z ; Int *Perm, *ColCount, *Lp, *Li, *Lnz, *Lnext, *Lprev, *Lsuper, *Lpi, *Lpx, *Ls, *Perm2, *ColCount2, *L2p, *L2i, *L2nz, *L2next, *L2prev, *L2super, *L2pi, *L2px, *L2s ; Int n, j, p, pend, s, xsize, ssize, nsuper ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (L, NULL) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; Common->status = CHOLMOD_OK ; DEBUG (CHOLMOD(dump_factor) (L, "start copy", Common)) ; n = L->n ; /* ---------------------------------------------------------------------- */ /* allocate a simplicial symbolic factor */ /* ---------------------------------------------------------------------- */ /* allocates L2->Perm and L2->ColCount */ L2 = CHOLMOD(allocate_factor) (n, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } ASSERT (L2->xtype == CHOLMOD_PATTERN && !(L2->is_super)) ; Perm = L->Perm ; ColCount = L->ColCount ; Perm2 = L2->Perm ; ColCount2 = L2->ColCount ; L2->ordering = L->ordering ; for (j = 0 ; j < n ; j++) { Perm2 [j] = Perm [j] ; } for (j = 0 ; j < n ; j++) { ColCount2 [j] = ColCount [j] ; } L2->is_ll = L->is_ll ; /* ---------------------------------------------------------------------- */ /* copy the rest of the factor */ /* ---------------------------------------------------------------------- */ if (L->xtype != CHOLMOD_PATTERN && !(L->super)) { /* ------------------------------------------------------------------ */ /* allocate a simplicial numeric factor */ /* ------------------------------------------------------------------ */ /* allocate L2->p, L2->nz, L2->prev, L2->next, L2->i, and L2->x. * packed = -1 so that cholmod_change_factor allocates space of * size L2->nzmax */ L2->nzmax = L->nzmax ; if (!CHOLMOD(change_factor) (L->xtype, L->is_ll, FALSE, -1, TRUE, L2, Common)) { CHOLMOD(free_factor) (&L2, Common) ; return (NULL) ; /* out of memory */ } ASSERT (MAX (1, L->nzmax) == L2->nzmax) ; /* ------------------------------------------------------------------ */ /* copy the contents of a simplicial numeric factor */ /* ------------------------------------------------------------------ */ Lp = L->p ; Li = L->i ; Lx = L->x ; Lz = L->z ; Lnz = L->nz ; Lnext = L->next ; Lprev = L->prev ; L2p = L2->p ; L2i = L2->i ; L2x = L2->x ; L2z = L2->z ; L2nz = L2->nz ; L2next = L2->next ; L2prev = L2->prev ; L2->xtype = L->xtype ; L2->dtype = L->dtype ; for (j = 0 ; j <= n ; j++) { L2p [j] = Lp [j] ; } for (j = 0 ; j < n+2 ; j++) { L2prev [j] = Lprev [j] ; } for (j = 0 ; j < n+2 ; j++) { L2next [j] = Lnext [j] ; } for (j = 0 ; j < n ; j++) { L2nz [j] = Lnz [j] ; } for (j = 0 ; j < n ; j++) { p = Lp [j] ; pend = p + Lnz [j] ; for ( ; p < pend ; p++) { L2i [p] = Li [p] ; } p = Lp [j] ; if (L->xtype == CHOLMOD_REAL) { for ( ; p < pend ; p++) { L2x [p] = Lx [p] ; } } else if (L->xtype == CHOLMOD_COMPLEX) { for ( ; p < pend ; p++) { L2x [2*p ] = Lx [2*p ] ; L2x [2*p+1] = Lx [2*p+1] ; } } else if (L->xtype == CHOLMOD_ZOMPLEX) { for ( ; p < pend ; p++) { L2x [p] = Lx [p] ; L2z [p] = Lz [p] ; } } } } else if (L->is_super) { /* ------------------------------------------------------------------ */ /* copy a supernodal factor */ /* ------------------------------------------------------------------ */ xsize = L->xsize ; ssize = L->ssize ; nsuper = L->nsuper ; L2->xsize = xsize ; L2->ssize = ssize ; L2->nsuper = nsuper ; /* allocate L2->super, L2->pi, L2->px, and L2->s. Allocate L2->x if * L is numeric */ if (!CHOLMOD(change_factor) (L->xtype, TRUE, TRUE, TRUE, TRUE, L2, Common)) { CHOLMOD(free_factor) (&L2, Common) ; return (NULL) ; /* out of memory */ } ASSERT (L2->s != NULL) ; /* ------------------------------------------------------------------ */ /* copy the contents of a supernodal factor */ /* ------------------------------------------------------------------ */ Lsuper = L->super ; Lpi = L->pi ; Lpx = L->px ; Ls = L->s ; Lx = L->x ; L2super = L2->super ; L2pi = L2->pi ; L2px = L2->px ; L2s = L2->s ; L2x = L2->x ; L2->maxcsize = L->maxcsize ; L2->maxesize = L->maxesize ; for (s = 0 ; s <= nsuper ; s++) { L2super [s] = Lsuper [s] ; } for (s = 0 ; s <= nsuper ; s++) { L2pi [s] = Lpi [s] ; } for (s = 0 ; s <= nsuper ; s++) { L2px [s] = Lpx [s] ; } L2s [0] = 0 ; for (p = 0 ; p < ssize ; p++) { L2s [p] = Ls [p] ; } if (L->xtype == CHOLMOD_REAL) { for (p = 0 ; p < xsize ; p++) { L2x [p] = Lx [p] ; } } else if (L->xtype == CHOLMOD_COMPLEX) { for (p = 0 ; p < 2*xsize ; p++) { L2x [p] = Lx [p] ; } } } L2->minor = L->minor ; L2->is_monotonic = L->is_monotonic ; DEBUG (CHOLMOD(dump_factor) (L2, "L2 got copied", Common)) ; ASSERT (L2->xtype == L->xtype && L2->is_super == L->is_super) ; return (L2) ; } Matrix/src/CHOLMOD/Core/t_cholmod_triplet.c0000644000175100001440000001110312271765436020170 0ustar hornikusers/* ========================================================================== */ /* === Core/t_cholmod_triplet =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Template routine for cholmod_triplet. All xtypes supported */ #include "cholmod_template.h" /* ========================================================================== */ /* === t_cholmod_triplet_to_sparse ========================================== */ /* ========================================================================== */ static size_t TEMPLATE (cholmod_triplet_to_sparse) ( /* ---- input ---- */ cholmod_triplet *T, /* matrix to copy */ /* ---- in/out --- */ cholmod_sparse *R, /* output matrix */ /* --------------- */ cholmod_common *Common ) { double *Rx, *Rz, *Tx, *Tz ; Int *Wj, *Rp, *Ri, *Rnz, *Ti, *Tj ; Int i, j, p, p1, p2, pdest, pj, k, stype, nrow, ncol, nz ; size_t anz ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* Wj contains a copy of Rp on input [ */ Wj = Common->Iwork ; /* size MAX (nrow,ncol). (i/l/l) */ Rp = R->p ; Ri = R->i ; Rnz = R->nz ; Rx = R->x ; Rz = R->z ; Ti = T->i ; Tj = T->j ; Tx = T->x ; Tz = T->z ; nz = T->nnz ; nrow = T->nrow ; ncol = T->ncol ; stype = SIGN (T->stype) ; /* ---------------------------------------------------------------------- */ /* construct the row form */ /* ---------------------------------------------------------------------- */ /* if Ti is jumbled, this part dominates the run time */ if (stype > 0) { for (k = 0 ; k < nz ; k++) { i = Ti [k] ; j = Tj [k] ; if (i < j) { /* place triplet (j,i,x) in column i of R */ p = Wj [i]++ ; Ri [p] = j ; } else { /* place triplet (i,j,x) in column j of R */ p = Wj [j]++ ; Ri [p] = i ; } ASSIGN (Rx, Rz, p, Tx, Tz, k) ; } } else if (stype < 0) { for (k = 0 ; k < nz ; k++) { i = Ti [k] ; j = Tj [k] ; if (i > j) { /* place triplet (j,i,x) in column i of R */ p = Wj [i]++ ; Ri [p] = j ; } else { /* place triplet (i,j,x) in column j of R */ p = Wj [j]++ ; Ri [p] = i ; } ASSIGN (Rx, Rz, p, Tx, Tz, k) ; } } else { for (k = 0 ; k < nz ; k++) { /* place triplet (i,j,x) in column i of R */ p = Wj [Ti [k]]++ ; Ri [p] = Tj [k] ; ASSIGN (Rx, Rz, p, Tx, Tz, k) ; } } /* done using Wj (i/l/l) as temporary row pointers ] */ /* ---------------------------------------------------------------------- */ /* sum up duplicates */ /* ---------------------------------------------------------------------- */ /* use Wj (i/l/l) of size ncol to keep track of duplicates in each row [ */ for (j = 0 ; j < ncol ; j++) { Wj [j] = EMPTY ; } anz = 0 ; for (i = 0 ; i < nrow ; i++) { p1 = Rp [i] ; p2 = Rp [i+1] ; pdest = p1 ; /* at this point Wj [j] < p1 holds true for all columns j, because * Ri/Rx is stored in row oriented manner */ for (p = p1 ; p < p2 ; p++) { j = Ri [p] ; pj = Wj [j] ; if (pj >= p1) { /* this column index j is already in row i at position pj; * sum up the duplicate entry */ /* Rx [pj] += Rx [p] ; */ ASSEMBLE (Rx, Rz, pj, Rx, Rz, p) ; } else { /* keep the entry and keep track in Wj [j] for case above */ Wj [j] = pdest ; if (pdest != p) { Ri [pdest] = j ; ASSIGN (Rx, Rz, pdest, Rx, Rz, p) ; } pdest++ ; } } Rnz [i] = pdest - p1 ; anz += (pdest - p1) ; } /* done using Wj to keep track of duplicate entries in each row ] */ /* ---------------------------------------------------------------------- */ /* return number of entries after summing up duplicates */ /* ---------------------------------------------------------------------- */ return (anz) ; } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX Matrix/src/CHOLMOD/Core/cholmod_sparse.c0000644000175100001440000004277212271765436017477 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_sparse ================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Core utility routines for the cholmod_sparse object: * * A sparse matrix is held in compressed column form. In the basic type * ("packed", which corresponds to a MATLAB sparse matrix), an n-by-n matrix * with nz entries is held in three arrays: p of size n+1, i of size nz, and x * of size nz. Row indices of column j are held in i [p [j] ... p [j+1]-1] and * in the same locations in x. There may be no duplicate entries in a column. * Row indices in each column may be sorted or unsorted (CHOLMOD keeps track). * * Primary routines: * ----------------- * cholmod_allocate_sparse allocate a sparse matrix * cholmod_free_sparse free a sparse matrix * * Secondary routines: * ------------------- * cholmod_reallocate_sparse change the size (# entries) of sparse matrix * cholmod_nnz number of nonzeros in a sparse matrix * cholmod_speye sparse identity matrix * cholmod_spzeros sparse zero matrix * cholmod_copy_sparse create a copy of a sparse matrix * * All xtypes are supported (pattern, real, complex, and zomplex) */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === cholmod_allocate_sparse ============================================== */ /* ========================================================================== */ /* Allocate space for a matrix. A->i and A->x are not initialized. A->p * (and A->nz if A is not packed) are set to zero, so a matrix containing no * entries (all zero) is returned. See also cholmod_spzeros. * * workspace: none */ cholmod_sparse *CHOLMOD(allocate_sparse) ( /* ---- input ---- */ size_t nrow, /* # of rows of A */ size_t ncol, /* # of columns of A */ size_t nzmax, /* max # of nonzeros of A */ int sorted, /* TRUE if columns of A sorted, FALSE otherwise */ int packed, /* TRUE if A will be packed, FALSE otherwise */ int stype, /* stype of A */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *A ; Int *Ap, *Anz ; size_t nzmax0 ; Int j ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; if (stype != 0 && nrow != ncol) { ERROR (CHOLMOD_INVALID, "rectangular matrix with stype != 0 invalid") ; return (NULL) ; } if (xtype < CHOLMOD_PATTERN || xtype > CHOLMOD_ZOMPLEX) { ERROR (CHOLMOD_INVALID, "xtype invalid") ; return (NULL) ; } /* ensure the dimensions do not cause integer overflow */ (void) CHOLMOD(add_size_t) (ncol, 2, &ok) ; if (!ok || nrow > Int_max || ncol > Int_max || nzmax > Int_max) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate header */ /* ---------------------------------------------------------------------- */ A = CHOLMOD(malloc) (sizeof (cholmod_sparse), 1, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } PRINT1 (("cholmod_allocate_sparse %d-by-%d nzmax %d sorted %d packed %d" " xtype %d\n", nrow, ncol, nzmax, sorted, packed, xtype)) ; nzmax = MAX (1, nzmax) ; A->nrow = nrow ; A->ncol = ncol ; A->nzmax = nzmax ; A->packed = packed ; /* default is packed (A->nz not present) */ A->stype = stype ; A->itype = ITYPE ; A->xtype = xtype ; A->dtype = DTYPE ; A->nz = NULL ; A->p = NULL ; A->i = NULL ; A->x = NULL ; A->z = NULL ; /* A 1-by-m matrix always has sorted columns */ A->sorted = (nrow <= 1) ? TRUE : sorted ; /* ---------------------------------------------------------------------- */ /* allocate the matrix itself */ /* ---------------------------------------------------------------------- */ /* allocate O(ncol) space */ A->p = CHOLMOD(malloc) (((size_t) ncol)+1, sizeof (Int), Common) ; if (!packed) { A->nz = CHOLMOD(malloc) (ncol, sizeof (Int), Common) ; } /* allocate O(nz) space */ nzmax0 = 0 ; CHOLMOD(realloc_multiple) (nzmax, 1, xtype, &(A->i), NULL, &(A->x), &(A->z), &nzmax0, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&A, Common) ; return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* initialize A->p and A->nz so that A is an empty matrix */ /* ---------------------------------------------------------------------- */ Ap = A->p ; for (j = 0 ; j <= (Int) ncol ; j++) { Ap [j] = 0 ; } if (!packed) { Anz = A->nz ; for (j = 0 ; j < (Int) ncol ; j++) { Anz [j] = 0 ; } } return (A) ; } /* ========================================================================== */ /* === cholmod_free_sparse ================================================== */ /* ========================================================================== */ /* free a sparse matrix * * workspace: none */ int CHOLMOD(free_sparse) ( /* ---- in/out --- */ cholmod_sparse **AHandle, /* matrix to deallocate, NULL on output */ /* --------------- */ cholmod_common *Common ) { Int n, nz ; cholmod_sparse *A ; RETURN_IF_NULL_COMMON (FALSE) ; if (AHandle == NULL) { /* nothing to do */ return (TRUE) ; } A = *AHandle ; if (A == NULL) { /* nothing to do */ return (TRUE) ; } n = A->ncol ; nz = A->nzmax ; A->p = CHOLMOD(free) (n+1, sizeof (Int), A->p, Common) ; A->i = CHOLMOD(free) (nz, sizeof (Int), A->i, Common) ; A->nz = CHOLMOD(free) (n, sizeof (Int), A->nz, Common) ; switch (A->xtype) { case CHOLMOD_REAL: A->x = CHOLMOD(free) (nz, sizeof (double), A->x, Common) ; break ; case CHOLMOD_COMPLEX: A->x = CHOLMOD(free) (nz, 2*sizeof (double), A->x, Common) ; break ; case CHOLMOD_ZOMPLEX: A->x = CHOLMOD(free) (nz, sizeof (double), A->x, Common) ; A->z = CHOLMOD(free) (nz, sizeof (double), A->z, Common) ; break ; } *AHandle = CHOLMOD(free) (1, sizeof (cholmod_sparse), (*AHandle), Common) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_reallocate_sparse ============================================ */ /* ========================================================================== */ /* Change the size of A->i, A->x, and A->z, or allocate them if their current * size is zero. A->x and A->z are not modified if A->xtype is CHOLMOD_PATTERN. * A->z is not modified unless A->xtype is CHOLMOD_ZOMPLEX. * * workspace: none */ int CHOLMOD(reallocate_sparse) ( /* ---- input ---- */ size_t nznew, /* new # of entries in A */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix to reallocate */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; PRINT1 (("realloc matrix %d to %d, xtype: %d\n", A->nzmax, nznew, A->xtype)) ; /* ---------------------------------------------------------------------- */ /* resize the matrix */ /* ---------------------------------------------------------------------- */ CHOLMOD(realloc_multiple) (MAX (1,nznew), 1, A->xtype, &(A->i), NULL, &(A->x), &(A->z), &(A->nzmax), Common) ; return (Common->status == CHOLMOD_OK) ; } /* ========================================================================== */ /* === cholmod_speye ======================================================== */ /* ========================================================================== */ /* Return a sparse identity matrix. */ cholmod_sparse *CHOLMOD(speye) ( /* ---- input ---- */ size_t nrow, /* # of rows of A */ size_t ncol, /* # of columns of A */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Az ; cholmod_sparse *A ; Int *Ap, *Ai ; Int j, n ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate the matrix */ /* ---------------------------------------------------------------------- */ n = MIN (nrow, ncol) ; A = CHOLMOD(allocate_sparse) (nrow, ncol, n, TRUE, TRUE, 0, xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory or inputs invalid */ } /* ---------------------------------------------------------------------- */ /* create the identity matrix */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; for (j = 0 ; j < n ; j++) { Ap [j] = j ; } for (j = n ; j <= ((Int) ncol) ; j++) { Ap [j] = n ; } for (j = 0 ; j < n ; j++) { Ai [j] = j ; } switch (xtype) { case CHOLMOD_REAL: for (j = 0 ; j < n ; j++) { Ax [j] = 1 ; } break ; case CHOLMOD_COMPLEX: for (j = 0 ; j < n ; j++) { Ax [2*j ] = 1 ; Ax [2*j+1] = 0 ; } break ; case CHOLMOD_ZOMPLEX: for (j = 0 ; j < n ; j++) { Ax [j] = 1 ; } for (j = 0 ; j < n ; j++) { Az [j] = 0 ; } break ; } return (A) ; } /* ========================================================================== */ /* === cholmod_spzeros ====================================================== */ /* ========================================================================== */ /* Return a sparse zero matrix. */ cholmod_sparse *CHOLMOD(spzeros) ( /* ---- input ---- */ size_t nrow, /* # of rows of A */ size_t ncol, /* # of columns of A */ size_t nzmax, /* max # of nonzeros of A */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate the matrix */ /* ---------------------------------------------------------------------- */ return (CHOLMOD(allocate_sparse) (nrow, ncol, nzmax, TRUE, TRUE, 0, xtype, Common)) ; } /* ========================================================================== */ /* === cholmod_nnz ========================================================== */ /* ========================================================================== */ /* Return the number of entries in a sparse matrix. * * workspace: none * integer overflow cannot occur, since the matrix is already allocated. */ SuiteSparse_long CHOLMOD(nnz) ( /* ---- input ---- */ cholmod_sparse *A, /* --------------- */ cholmod_common *Common ) { Int *Ap, *Anz ; size_t nz ; Int j, ncol ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* return nnz (A) */ /* ---------------------------------------------------------------------- */ ncol = A->ncol ; if (A->packed) { Ap = A->p ; RETURN_IF_NULL (Ap, EMPTY) ; nz = Ap [ncol] ; } else { Anz = A->nz ; RETURN_IF_NULL (Anz, EMPTY) ; nz = 0 ; for (j = 0 ; j < ncol ; j++) { nz += MAX (0, Anz [j]) ; } } return (nz) ; } /* ========================================================================== */ /* === cholmod_copy_sparse ================================================== */ /* ========================================================================== */ /* C = A. Create an exact copy of a sparse matrix, with one exception. * Entries in unused space are not copied (they might not be initialized, * and copying them would cause program checkers such as purify and * valgrind to complain). The xtype of the resulting matrix C is the same as * the xtype of the input matrix A. * * See also Core/cholmod_copy, which copies a matrix with possible changes * in stype, presence of diagonal entries, pattern vs. numerical values, * real and/or imaginary parts, and so on. */ cholmod_sparse *CHOLMOD(copy_sparse) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Cx, *Az, *Cz ; Int *Ap, *Ai, *Anz, *Cp, *Ci, *Cnz ; cholmod_sparse *C ; Int p, pend, j, ncol, packed, nzmax, nz, xtype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; if (A->stype != 0 && A->nrow != A->ncol) { ERROR (CHOLMOD_INVALID, "rectangular matrix with stype != 0 invalid") ; return (NULL) ; } Common->status = CHOLMOD_OK ; ASSERT (CHOLMOD(dump_sparse) (A, "A original", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ncol = A->ncol ; nzmax = A->nzmax ; packed = A->packed ; Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; xtype = A->xtype ; /* ---------------------------------------------------------------------- */ /* allocate the copy */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_sparse) (A->nrow, A->ncol, A->nzmax, A->sorted, A->packed, A->stype, A->xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } Cp = C->p ; Ci = C->i ; Cx = C->x ; Cz = C->z ; Cnz = C->nz ; /* ---------------------------------------------------------------------- */ /* copy the matrix */ /* ---------------------------------------------------------------------- */ for (j = 0 ; j <= ncol ; j++) { Cp [j] = Ap [j] ; } if (packed) { nz = Ap [ncol] ; for (p = 0 ; p < nz ; p++) { Ci [p] = Ai [p] ; } switch (xtype) { case CHOLMOD_REAL: for (p = 0 ; p < nz ; p++) { Cx [p] = Ax [p] ; } break ; case CHOLMOD_COMPLEX: for (p = 0 ; p < 2*nz ; p++) { Cx [p] = Ax [p] ; } break ; case CHOLMOD_ZOMPLEX: for (p = 0 ; p < nz ; p++) { Cx [p] = Ax [p] ; Cz [p] = Az [p] ; } break ; } } else { for (j = 0 ; j < ncol ; j++) { Cnz [j] = Anz [j] ; } switch (xtype) { case CHOLMOD_PATTERN: for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = p + Anz [j] ; for ( ; p < pend ; p++) { Ci [p] = Ai [p] ; } } break ; case CHOLMOD_REAL: for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = p + Anz [j] ; for ( ; p < pend ; p++) { Ci [p] = Ai [p] ; Cx [p] = Ax [p] ; } } break ; case CHOLMOD_COMPLEX: for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = p + Anz [j] ; for ( ; p < pend ; p++) { Ci [p] = Ai [p] ; Cx [2*p ] = Ax [2*p ] ; Cx [2*p+1] = Ax [2*p+1] ; } } break ; case CHOLMOD_ZOMPLEX: for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = p + Anz [j] ; for ( ; p < pend ; p++) { Ci [p] = Ai [p] ; Cx [p] = Ax [p] ; Cz [p] = Az [p] ; } } break ; } } /* ---------------------------------------------------------------------- */ /* return the result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (C, "C copy", Common) >= 0) ; return (C) ; } Matrix/src/CHOLMOD/Core/cholmod_band.c0000644000175100001440000002332012271765436017072 0ustar hornikusers/* ========================================================================== */ /* === Core/cholmod_band ==================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* C = tril (triu (A,k1), k2) * * C is a matrix consisting of the diagonals of A from k1 to k2. * * k=0 is the main diagonal of A, k=1 is the superdiagonal, k=-1 is the * subdiagonal, and so on. If A is m-by-n, then: * * k1=-m C = tril (A,k2) * k2=n C = triu (A,k1) * k1=0 and k2=0 C = diag(A), except C is a matrix, not a vector * * Values of k1 and k2 less than -m are treated as -m, and values greater * than n are treated as n. * * A can be of any symmetry (upper, lower, or unsymmetric); C is returned in * the same form, and packed. If A->stype > 0, entries in the lower * triangular part of A are ignored, and the opposite is true if * A->stype < 0. If A has sorted columns, then so does C. * C has the same size as A. * * If inplace is TRUE, then the matrix A is modified in place. * Only packed matrices can be converted in place. * * C can be returned as a numerical valued matrix (if A has numerical values * and mode > 0), as a pattern-only (mode == 0), or as a pattern-only but with * the diagonal entries removed (mode < 0). * * workspace: none * * A can have an xtype of pattern or real. Complex and zomplex cases supported * only if mode <= 0 (in which case the numerical values are ignored). */ #include "cholmod_internal.h" #include "cholmod_core.h" static cholmod_sparse *band /* returns C, or NULL if failure */ ( /* ---- input or in/out if inplace is TRUE --- */ cholmod_sparse *A, /* ---- input ---- */ SuiteSparse_long k1, /* ignore entries below the k1-st diagonal */ SuiteSparse_long k2, /* ignore entries above the k2-nd diagonal */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diagonal) */ int inplace, /* if TRUE, then convert A in place */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Cx ; Int packed, nz, j, p, pend, i, ncol, nrow, jlo, jhi, ilo, ihi, sorted, values, diag ; Int *Ap, *Anz, *Ai, *Cp, *Ci ; cholmod_sparse *C ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; packed = A->packed ; diag = (mode >= 0) ; if (inplace && !packed) { /* cannot operate on an unpacked matrix in place */ ERROR (CHOLMOD_INVALID, "cannot operate on unpacked matrix in-place") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ PRINT1 (("k1 %ld k2 %ld\n", k1, k2)) ; Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; sorted = A->sorted ; if (A->stype > 0) { /* ignore any entries in strictly lower triangular part of A */ k1 = MAX (k1, 0) ; } if (A->stype < 0) { /* ignore any entries in strictly upper triangular part of A */ k2 = MIN (k2, 0) ; } ncol = A->ncol ; nrow = A->nrow ; /* ensure k1 and k2 are in the range -nrow to +ncol to * avoid possible integer overflow if k1 and k2 are huge */ k1 = MAX (-nrow, k1) ; k1 = MIN (k1, ncol) ; k2 = MAX (-nrow, k2) ; k2 = MIN (k2, ncol) ; /* consider columns jlo to jhi. columns outside this range are empty */ jlo = MAX (k1, 0) ; jhi = MIN (k2+nrow, ncol) ; if (k1 > k2) { /* nothing to do */ jlo = ncol ; jhi = ncol ; } /* ---------------------------------------------------------------------- */ /* allocate C, or operate on A in place */ /* ---------------------------------------------------------------------- */ if (inplace) { /* convert A in place */ C = A ; } else { /* count the number of entries in the result C */ nz = 0 ; if (sorted) { for (j = jlo ; j < jhi ; j++) { ilo = j-k2 ; ihi = j-k1 ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i > ihi) { break ; } if (i >= ilo && (diag || i != j)) { nz++ ; } } } } else { for (j = jlo ; j < jhi ; j++) { ilo = j-k2 ; ihi = j-k1 ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= ilo && i <= ihi && (diag || i != j)) { nz++ ; } } } } /* allocate C; A will not be modified. C is sorted if A is sorted */ C = CHOLMOD(allocate_sparse) (A->nrow, ncol, nz, sorted, TRUE, A->stype, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* construct C */ /* ---------------------------------------------------------------------- */ /* columns 0 to jlo-1 are empty */ for (j = 0 ; j < jlo ; j++) { Cp [j] = 0 ; } nz = 0 ; if (sorted) { if (values) { /* pattern and values */ ASSERT (diag) ; for (j = jlo ; j < jhi ; j++) { ilo = j-k2 ; ihi = j-k1 ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Cp [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i > ihi) { break ; } if (i >= ilo) { Ci [nz] = i ; Cx [nz] = Ax [p] ; nz++ ; } } } } else { /* pattern only, perhaps with no diagonal */ for (j = jlo ; j < jhi ; j++) { ilo = j-k2 ; ihi = j-k1 ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Cp [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i > ihi) { break ; } if (i >= ilo && (diag || i != j)) { Ci [nz++] = i ; } } } } } else { if (values) { /* pattern and values */ ASSERT (diag) ; for (j = jlo ; j < jhi ; j++) { ilo = j-k2 ; ihi = j-k1 ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Cp [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= ilo && i <= ihi) { Ci [nz] = i ; Cx [nz] = Ax [p] ; nz++ ; } } } } else { /* pattern only, perhaps with no diagonal */ for (j = jlo ; j < jhi ; j++) { ilo = j-k2 ; ihi = j-k1 ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Cp [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= ilo && i <= ihi && (diag || i != j)) { Ci [nz++] = i ; } } } } } /* columns jhi to ncol-1 are empty */ for (j = jhi ; j <= ncol ; j++) { Cp [j] = nz ; } /* ---------------------------------------------------------------------- */ /* reduce A in size if done in place */ /* ---------------------------------------------------------------------- */ if (inplace) { /* free the unused parts of A, and reduce A->i and A->x in size */ ASSERT (MAX (1,nz) <= A->nzmax) ; CHOLMOD(reallocate_sparse) (nz, A, Common) ; ASSERT (Common->status >= CHOLMOD_OK) ; } /* ---------------------------------------------------------------------- */ /* return the result C */ /* ---------------------------------------------------------------------- */ DEBUG (i = CHOLMOD(dump_sparse) (C, "band", Common)) ; ASSERT (IMPLIES (mode < 0, i == 0)) ; return (C) ; } /* ========================================================================== */ /* === cholmod_band ========================================================= */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(band) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to extract band matrix from */ SuiteSparse_long k1, /* ignore entries below the k1-st diagonal */ SuiteSparse_long k2, /* ignore entries above the k2-nd diagonal */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */ /* --------------- */ cholmod_common *Common ) { return (band (A, k1, k2, mode, FALSE, Common)) ; } /* ========================================================================== */ /* === cholmod_band_inplace ================================================= */ /* ========================================================================== */ int CHOLMOD(band_inplace) ( /* ---- input ---- */ SuiteSparse_long k1, /* ignore entries below the k1-st diagonal */ SuiteSparse_long k2, /* ignore entries above the k2-nd diagonal */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix from which entries not in band are removed */ /* --------------- */ cholmod_common *Common ) { return (band (A, k1, k2, mode, TRUE, Common) != NULL) ; } Matrix/src/CHOLMOD/MatrixOps/0000755000175100001440000000000012271765426015352 5ustar hornikusersMatrix/src/CHOLMOD/MatrixOps/cholmod_norm.c0000644000175100001440000002637512271765436020214 0ustar hornikusers/* ========================================================================== */ /* === MatrixOps/cholmod_norm =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* r = norm (A), compute the infinity-norm, 1-norm, or 2-norm of a sparse or * dense matrix. Can compute the 2-norm only for a dense column vector. * Returns -1 if an error occurs. * * Pattern, real, complex, and zomplex sparse matrices are supported. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === abs_value ============================================================ */ /* ========================================================================== */ /* Compute the absolute value of a real, complex, or zomplex value */ static double abs_value ( int xtype, double *Ax, double *Az, Int p, cholmod_common *Common ) { double s = 0 ; switch (xtype) { case CHOLMOD_PATTERN: s = 1 ; break ; case CHOLMOD_REAL: s = fabs (Ax [p]) ; break ; case CHOLMOD_COMPLEX: s = Common->hypotenuse (Ax [2*p], Ax [2*p+1]) ; break ; case CHOLMOD_ZOMPLEX: s = Common->hypotenuse (Ax [p], Az [p]) ; break ; } return (s) ; } /* ========================================================================== */ /* === cholmod_norm_dense =================================================== */ /* ========================================================================== */ double CHOLMOD(norm_dense) ( /* ---- input ---- */ cholmod_dense *X, /* matrix to compute the norm of */ int norm, /* type of norm: 0: inf. norm, 1: 1-norm, 2: 2-norm */ /* --------------- */ cholmod_common *Common ) { double xnorm, s, x, z ; double *Xx, *Xz, *W ; Int nrow, ncol, d, i, j, use_workspace, xtype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (X, EMPTY) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; ncol = X->ncol ; if (norm < 0 || norm > 2 || (norm == 2 && ncol > 1)) { ERROR (CHOLMOD_INVALID, "invalid norm") ; return (EMPTY) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = X->nrow ; d = X->d ; Xx = X->x ; Xz = X->z ; xtype = X->xtype ; /* ---------------------------------------------------------------------- */ /* allocate workspace, if needed */ /* ---------------------------------------------------------------------- */ W = NULL ; use_workspace = (norm == 0 && ncol > 4) ; if (use_workspace) { CHOLMOD(allocate_work) (0, 0, nrow, Common) ; W = Common->Xwork ; if (Common->status < CHOLMOD_OK) { /* oops, no workspace */ use_workspace = FALSE ; } } /* ---------------------------------------------------------------------- */ /* compute the norm */ /* ---------------------------------------------------------------------- */ xnorm = 0 ; if (use_workspace) { /* ------------------------------------------------------------------ */ /* infinity-norm = max row sum, using stride-1 access of X */ /* ------------------------------------------------------------------ */ DEBUG (for (i = 0 ; i < nrow ; i++) ASSERT (W [i] == 0)) ; /* this is faster than stride-d, but requires O(nrow) workspace */ for (j = 0 ; j < ncol ; j++) { for (i = 0 ; i < nrow ; i++) { W [i] += abs_value (xtype, Xx, Xz, i+j*d, Common) ; } } for (i = 0 ; i < nrow ; i++) { s = W [i] ; if ((IS_NAN (s) || s > xnorm) && !IS_NAN (xnorm)) { xnorm = s ; } W [i] = 0 ; } } else if (norm == 0) { /* ------------------------------------------------------------------ */ /* infinity-norm = max row sum, using stride-d access of X */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < nrow ; i++) { s = 0 ; for (j = 0 ; j < ncol ; j++) { s += abs_value (xtype, Xx, Xz, i+j*d, Common) ; } if ((IS_NAN (s) || s > xnorm) && !IS_NAN (xnorm)) { xnorm = s ; } } } else if (norm == 1) { /* ------------------------------------------------------------------ */ /* 1-norm = max column sum */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < ncol ; j++) { s = 0 ; for (i = 0 ; i < nrow ; i++) { s += abs_value (xtype, Xx, Xz, i+j*d, Common) ; } if ((IS_NAN (s) || s > xnorm) && !IS_NAN (xnorm)) { xnorm = s ; } } } else { /* ------------------------------------------------------------------ */ /* 2-norm = sqrt (sum (X.^2)) */ /* ------------------------------------------------------------------ */ switch (xtype) { case CHOLMOD_REAL: for (i = 0 ; i < nrow ; i++) { x = Xx [i] ; xnorm += x*x ; } break ; case CHOLMOD_COMPLEX: for (i = 0 ; i < nrow ; i++) { x = Xx [2*i ] ; z = Xx [2*i+1] ; xnorm += x*x + z*z ; } break ; case CHOLMOD_ZOMPLEX: for (i = 0 ; i < nrow ; i++) { x = Xx [i] ; z = Xz [i] ; xnorm += x*x + z*z ; } break ; } xnorm = sqrt (xnorm) ; } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ return (xnorm) ; } /* ========================================================================== */ /* === cholmod_norm_sparse ================================================== */ /* ========================================================================== */ double CHOLMOD(norm_sparse) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to compute the norm of */ int norm, /* type of norm: 0: inf. norm, 1: 1-norm */ /* --------------- */ cholmod_common *Common ) { double anorm, s ; double *Ax, *Az, *W ; Int *Ap, *Ai, *Anz ; Int i, j, p, pend, nrow, ncol, packed, xtype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; ncol = A->ncol ; nrow = A->nrow ; if (norm < 0 || norm > 1) { ERROR (CHOLMOD_INVALID, "invalid norm") ; return (EMPTY) ; } if (A->stype && nrow != ncol) { ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (EMPTY) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; packed = A->packed ; xtype = A->xtype ; /* ---------------------------------------------------------------------- */ /* allocate workspace, if needed */ /* ---------------------------------------------------------------------- */ W = NULL ; if (A->stype || norm == 0) { CHOLMOD(allocate_work) (0, 0, nrow, Common) ; W = Common->Xwork ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (EMPTY) ; } DEBUG (for (i = 0 ; i < nrow ; i++) ASSERT (W [i] == 0)) ; } /* ---------------------------------------------------------------------- */ /* compute the norm */ /* ---------------------------------------------------------------------- */ anorm = 0 ; if (A->stype > 0) { /* ------------------------------------------------------------------ */ /* A is symmetric with upper triangular part stored */ /* ------------------------------------------------------------------ */ /* infinity-norm = 1-norm = max row/col sum */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; s = abs_value (xtype, Ax, Az, p, Common) ; if (i == j) { W [i] += s ; } else if (i < j) { W [i] += s ; W [j] += s ; } } } } else if (A->stype < 0) { /* ------------------------------------------------------------------ */ /* A is symmetric with lower triangular part stored */ /* ------------------------------------------------------------------ */ /* infinity-norm = 1-norm = max row/col sum */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; s = abs_value (xtype, Ax, Az, p, Common) ; if (i == j) { W [i] += s ; } else if (i > j) { W [i] += s ; W [j] += s ; } } } } else if (norm == 0) { /* ------------------------------------------------------------------ */ /* A is unsymmetric, compute the infinity-norm */ /* ------------------------------------------------------------------ */ /* infinity-norm = max row sum */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { W [Ai [p]] += abs_value (xtype, Ax, Az, p, Common) ; } } } else { /* ------------------------------------------------------------------ */ /* A is unsymmetric, compute the 1-norm */ /* ------------------------------------------------------------------ */ /* 1-norm = max column sum */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; if (xtype == CHOLMOD_PATTERN) { s = pend - p ; } else { s = 0 ; for ( ; p < pend ; p++) { s += abs_value (xtype, Ax, Az, p, Common) ; } } if ((IS_NAN (s) || s > anorm) && !IS_NAN (anorm)) { anorm = s ; } } } /* ---------------------------------------------------------------------- */ /* compute the max row sum */ /* ---------------------------------------------------------------------- */ if (A->stype || norm == 0) { for (i = 0 ; i < nrow ; i++) { s = W [i] ; if ((IS_NAN (s) || s > anorm) && !IS_NAN (anorm)) { anorm = s ; } W [i] = 0 ; } } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ return (anorm) ; } #endif Matrix/src/CHOLMOD/MatrixOps/License.txt0000644000175100001440000000203011770402705017457 0ustar hornikusersCHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.suitesparse.com Note that this license is for the CHOLMOD/MatrixOps module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. Matrix/src/CHOLMOD/MatrixOps/t_cholmod_sdmult.c0000644000175100001440000004456312271765436021073 0ustar hornikusers/* ========================================================================== */ /* === MatrixOps/t_cholmod_sdmult =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Template routine for cholmod_sdmult */ #include "cholmod_template.h" #undef ADVANCE #ifdef REAL #define ADVANCE(x,z,d) x += d #elif defined (COMPLEX) #define ADVANCE(x,z,d) x += 2*d #else #define ADVANCE(x,z,d) x += d ; z += d #endif /* ========================================================================== */ /* === t_cholmod_sdmult ===================================================== */ /* ========================================================================== */ static void TEMPLATE (cholmod_sdmult) ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to multiply */ int transpose, /* use A if 0, or A' otherwise */ double alpha [2], /* scale factor for A */ double beta [2], /* scale factor for Y */ cholmod_dense *X, /* dense matrix to multiply */ /* ---- in/out --- */ cholmod_dense *Y, /* resulting dense matrix */ /* -- workspace -- */ double *W /* size 4*nx if needed, twice that for c/zomplex case */ ) { double yx [8], xx [8], ax [2] ; #ifdef ZOMPLEX double yz [4], xz [4], az [1] ; double betaz [1], alphaz [1] ; #endif double *Ax, *Az, *Xx, *Xz, *Yx, *Yz, *w, *Wz ; Int *Ap, *Ai, *Anz ; size_t nx, ny, dx, dy ; Int packed, nrow, ncol, j, k, p, pend, kcol, i ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ #ifdef ZOMPLEX betaz [0] = beta [1] ; alphaz [0] = alpha [1] ; #endif ny = transpose ? A->ncol : A->nrow ; /* required length of Y */ nx = transpose ? A->nrow : A->ncol ; /* required length of X */ nrow = A->nrow ; ncol = A->ncol ; Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; Az = A->z ; packed = A->packed ; Xx = X->x ; Xz = X->z ; Yx = Y->x ; Yz = Y->z ; kcol = X->ncol ; dy = Y->d ; dx = X->d ; w = W ; Wz = W + 4*nx ; /* ---------------------------------------------------------------------- */ /* Y = beta * Y */ /* ---------------------------------------------------------------------- */ if (ENTRY_IS_ZERO (beta, betaz, 0)) { for (k = 0 ; k < kcol ; k++) { for (i = 0 ; i < ((Int) ny) ; i++) { /* y [i] = 0. ; */ CLEAR (Yx, Yz, i) ; } /* y += dy ; */ ADVANCE (Yx,Yz,dy) ; } } else if (!ENTRY_IS_ONE (beta, betaz, 0)) { for (k = 0 ; k < kcol ; k++) { for (i = 0 ; i < ((Int) ny) ; i++) { /* y [i] *= beta [0] ; */ MULT (Yx,Yz,i, Yx,Yz,i, beta,betaz, 0) ; } /* y += dy ; */ ADVANCE (Yx,Yz,dy) ; } } if (ENTRY_IS_ZERO (alpha, alphaz, 0)) { /* nothing else to do */ return ; } /* ---------------------------------------------------------------------- */ /* Y += alpha * op(A) * X, where op(A)=A or A' */ /* ---------------------------------------------------------------------- */ Yx = Y->x ; Yz = Y->z ; k = 0 ; if (A->stype == 0) { if (transpose) { /* -------------------------------------------------------------- */ /* Y += alpha * A' * x, unsymmetric case */ /* -------------------------------------------------------------- */ if (kcol % 4 == 1) { for (j = 0 ; j < ncol ; j++) { /* yj = 0. ; */ CLEAR (yx, yz, 0) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { /* yj += conj(Ax [p]) * x [Ai [p]] ; */ i = Ai [p] ; ASSIGN_CONJ (ax,az,0, Ax,Az,p) ; MULTADD (yx,yz,0, ax,az,0, Xx,Xz,i) ; } /* y [j] += alpha [0] * yj ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; } /* y += dy ; */ /* x += dx ; */ ADVANCE (Yx,Yz,dy) ; ADVANCE (Xx,Xz,dx) ; k++ ; } else if (kcol % 4 == 2) { for (j = 0 ; j < ncol ; j++) { /* yj0 = 0. ; */ /* yj1 = 0. ; */ CLEAR (yx,yz,0) ; CLEAR (yx,yz,1) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* aij = conj (Ax [p]) ; */ ASSIGN_CONJ (ax,az,0, Ax,Az,p) ; /* yj0 += aij * x [i ] ; */ /* yj1 += aij * x [i+dx] ; */ MULTADD (yx,yz,0, ax,az,0, Xx,Xz,i) ; MULTADD (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ; } /* y [j ] += alpha [0] * yj0 ; */ /* y [j+dy] += alpha [0] * yj1 ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ; } /* y += 2*dy ; */ /* x += 2*dx ; */ ADVANCE (Yx,Yz,2*dy) ; ADVANCE (Xx,Xz,2*dx) ; k += 2 ; } else if (kcol % 4 == 3) { for (j = 0 ; j < ncol ; j++) { /* yj0 = 0. ; */ /* yj1 = 0. ; */ /* yj2 = 0. ; */ CLEAR (yx,yz,0) ; CLEAR (yx,yz,1) ; CLEAR (yx,yz,2) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* aij = conj (Ax [p]) ; */ ASSIGN_CONJ (ax,az,0, Ax,Az,p) ; /* yj0 += aij * x [i ] ; */ /* yj1 += aij * x [i+ dx] ; */ /* yj2 += aij * x [i+2*dx] ; */ MULTADD (yx,yz,0, ax,az,0, Xx,Xz,i) ; MULTADD (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ; MULTADD (yx,yz,2, ax,az,0, Xx,Xz,i+2*dx) ; } /* y [j ] += alpha [0] * yj0 ; */ /* y [j+ dy] += alpha [0] * yj1 ; */ /* y [j+2*dy] += alpha [0] * yj2 ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ; MULTADD (Yx,Yz,j+2*dy, alpha,alphaz,0, yx,yz,2) ; } /* y += 3*dy ; */ /* x += 3*dx ; */ ADVANCE (Yx,Yz,3*dy) ; ADVANCE (Xx,Xz,3*dx) ; k += 3 ; } for ( ; k < kcol ; k += 4) { for (j = 0 ; j < ncol ; j++) { /* yj0 = 0. ; */ /* yj1 = 0. ; */ /* yj2 = 0. ; */ /* yj3 = 0. ; */ CLEAR (yx,yz,0) ; CLEAR (yx,yz,1) ; CLEAR (yx,yz,2) ; CLEAR (yx,yz,3) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* aij = conj(Ax [p]) ; */ ASSIGN_CONJ (ax,az,0, Ax,Az,p) ; /* yj0 += aij * x [i ] ; */ /* yj1 += aij * x [i+ dx] ; */ /* yj2 += aij * x [i+2*dx] ; */ /* yj3 += aij * x [i+3*dx] ; */ MULTADD (yx,yz,0, ax,az,0, Xx,Xz,i) ; MULTADD (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ; MULTADD (yx,yz,2, ax,az,0, Xx,Xz,i+2*dx) ; MULTADD (yx,yz,3, ax,az,0, Xx,Xz,i+3*dx) ; } /* y [j ] += alpha [0] * yj0 ; */ /* y [j+ dy] += alpha [0] * yj1 ; */ /* y [j+2*dy] += alpha [0] * yj2 ; */ /* y [j+3*dy] += alpha [0] * yj3 ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ; MULTADD (Yx,Yz,j+2*dy, alpha,alphaz,0, yx,yz,2) ; MULTADD (Yx,Yz,j+3*dy, alpha,alphaz,0, yx,yz,3) ; } /* y += 4*dy ; */ /* x += 4*dx ; */ ADVANCE (Yx,Yz,4*dy) ; ADVANCE (Xx,Xz,4*dx) ; } } else { /* -------------------------------------------------------------- */ /* Y += alpha * A * x, unsymmetric case */ /* -------------------------------------------------------------- */ if (kcol % 4 == 1) { for (j = 0 ; j < ncol ; j++) { /* xj = alpha [0] * x [j] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { /* y [Ai [p]] += Ax [p] * xj ; */ i = Ai [p] ; MULTADD (Yx,Yz,i, Ax,Az,p, xx,xz,0) ; } } /* y += dy ; */ /* x += dx ; */ ADVANCE (Yx,Yz,dy) ; ADVANCE (Xx,Xz,dx) ; k++ ; } else if (kcol % 4 == 2) { for (j = 0 ; j < ncol ; j++) { /* xj0 = alpha [0] * x [j ] ; */ /* xj1 = alpha [0] * x [j+dx] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+dy] += aij * xj1 ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; } } /* y += 2*dy ; */ /* x += 2*dx ; */ ADVANCE (Yx,Yz,2*dy) ; ADVANCE (Xx,Xz,2*dx) ; k += 2 ; } else if (kcol % 4 == 3) { for (j = 0 ; j < ncol ; j++) { /* xj0 = alpha [0] * x [j ] ; */ /* xj1 = alpha [0] * x [j+ dx] ; */ /* xj2 = alpha [0] * x [j+2*dx] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ; MULT (xx,xz,2, alpha,alphaz,0, Xx,Xz,j+2*dx) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+ dy] += aij * xj1 ; */ /* y [i+2*dy] += aij * xj2 ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ; } } /* y += 3*dy ; */ /* x += 3*dx ; */ ADVANCE (Yx,Yz,3*dy) ; ADVANCE (Xx,Xz,3*dx) ; k += 3 ; } for ( ; k < kcol ; k += 4) { for (j = 0 ; j < ncol ; j++) { /* xj0 = alpha [0] * x [j ] ; */ /* xj1 = alpha [0] * x [j+ dx] ; */ /* xj2 = alpha [0] * x [j+2*dx] ; */ /* xj3 = alpha [0] * x [j+3*dx] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ; MULT (xx,xz,2, alpha,alphaz,0, Xx,Xz,j+2*dx) ; MULT (xx,xz,3, alpha,alphaz,0, Xx,Xz,j+3*dx) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+ dy] += aij * xj1 ; */ /* y [i+2*dy] += aij * xj2 ; */ /* y [i+3*dy] += aij * xj3 ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ; MULTADD (Yx,Yz,i+3*dy, ax,az,0, xx,xz,3) ; } } /* y += 4*dy ; */ /* x += 4*dx ; */ ADVANCE (Yx,Yz,4*dy) ; ADVANCE (Xx,Xz,4*dx) ; } } } else { /* ------------------------------------------------------------------ */ /* Y += alpha * (A or A') * x, symmetric case (upper/lower) */ /* ------------------------------------------------------------------ */ /* Only the upper/lower triangular part and the diagonal of A is used. * Since both x and y are written to in the innermost loop, this * code can experience cache bank conflicts if x is used directly. * Thus, a copy is made of x, four columns at a time, if x has * four or more columns. */ if (kcol % 4 == 1) { for (j = 0 ; j < ncol ; j++) { /* yj = 0. ; */ CLEAR (yx,yz,0) ; /* xj = alpha [0] * x [j] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i == j) { /* y [i] += Ax [p] * xj ; */ MULTADD (Yx,Yz,i, Ax,Az,p, xx,xz,0) ; } else if ((A->stype > 0 && i < j) || (A->stype < 0 && i > j)) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i] += aij * xj ; */ /* yj += aij * x [i] ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADDCONJ (yx,yz,0, ax,az,0, Xx,Xz,i) ; } } /* y [j] += alpha [0] * yj ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; } /* y += dy ; */ /* x += dx ; */ ADVANCE (Yx,Yz,dy) ; ADVANCE (Xx,Xz,dx) ; k++ ; } else if (kcol % 4 == 2) { for (j = 0 ; j < ncol ; j++) { /* yj0 = 0. ; */ /* yj1 = 0. ; */ CLEAR (yx,yz,0) ; CLEAR (yx,yz,1) ; /* xj0 = alpha [0] * x [j ] ; */ /* xj1 = alpha [0] * x [j+dx] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i == j) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+dy] += aij * xj1 ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; } else if ((A->stype > 0 && i < j) || (A->stype < 0 && i > j)) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+dy] += aij * xj1 ; */ /* yj0 += aij * x [i ] ; */ /* yj1 += aij * x [i+dx] ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; MULTADDCONJ (yx,yz,0, ax,az,0, Xx,Xz,i) ; MULTADDCONJ (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ; } } /* y [j ] += alpha [0] * yj0 ; */ /* y [j+dy] += alpha [0] * yj1 ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ; } /* y += 2*dy ; */ /* x += 2*dx ; */ ADVANCE (Yx,Yz,2*dy) ; ADVANCE (Xx,Xz,2*dx) ; k += 2 ; } else if (kcol % 4 == 3) { for (j = 0 ; j < ncol ; j++) { /* yj0 = 0. ; */ /* yj1 = 0. ; */ /* yj2 = 0. ; */ CLEAR (yx,yz,0) ; CLEAR (yx,yz,1) ; CLEAR (yx,yz,2) ; /* xj0 = alpha [0] * x [j ] ; */ /* xj1 = alpha [0] * x [j+ dx] ; */ /* xj2 = alpha [0] * x [j+2*dx] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ; MULT (xx,xz,2, alpha,alphaz,0, Xx,Xz,j+2*dx) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i == j) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+ dy] += aij * xj1 ; */ /* y [i+2*dy] += aij * xj2 ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ; } else if ((A->stype > 0 && i < j) || (A->stype < 0 && i > j)) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+ dy] += aij * xj1 ; */ /* y [i+2*dy] += aij * xj2 ; */ /* yj0 += aij * x [i ] ; */ /* yj1 += aij * x [i+ dx] ; */ /* yj2 += aij * x [i+2*dx] ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ; MULTADDCONJ (yx,yz,0, ax,az,0, Xx,Xz,i) ; MULTADDCONJ (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ; MULTADDCONJ (yx,yz,2, ax,az,0, Xx,Xz,i+2*dx) ; } } /* y [j ] += alpha [0] * yj0 ; */ /* y [j+ dy] += alpha [0] * yj1 ; */ /* y [j+2*dy] += alpha [0] * yj2 ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ; MULTADD (Yx,Yz,j+2*dy, alpha,alphaz,0, yx,yz,2) ; } /* y += 3*dy ; */ /* x += 3*dx ; */ ADVANCE (Yx,Yz,3*dy) ; ADVANCE (Xx,Xz,3*dx) ; k += 3 ; } /* copy four columns of X into W, and put in row form */ for ( ; k < kcol ; k += 4) { for (j = 0 ; j < ncol ; j++) { /* w [4*j ] = x [j ] ; */ /* w [4*j+1] = x [j+ dx] ; */ /* w [4*j+2] = x [j+2*dx] ; */ /* w [4*j+3] = x [j+3*dx] ; */ ASSIGN (w,Wz,4*j , Xx,Xz,j ) ; ASSIGN (w,Wz,4*j+1, Xx,Xz,j+dx ) ; ASSIGN (w,Wz,4*j+2, Xx,Xz,j+2*dx) ; ASSIGN (w,Wz,4*j+3, Xx,Xz,j+3*dx) ; } for (j = 0 ; j < ncol ; j++) { /* yj0 = 0. ; */ /* yj1 = 0. ; */ /* yj2 = 0. ; */ /* yj3 = 0. ; */ CLEAR (yx,yz,0) ; CLEAR (yx,yz,1) ; CLEAR (yx,yz,2) ; CLEAR (yx,yz,3) ; /* xj0 = alpha [0] * w [4*j ] ; */ /* xj1 = alpha [0] * w [4*j+1] ; */ /* xj2 = alpha [0] * w [4*j+2] ; */ /* xj3 = alpha [0] * w [4*j+3] ; */ MULT (xx,xz,0, alpha,alphaz,0, w,Wz,4*j) ; MULT (xx,xz,1, alpha,alphaz,0, w,Wz,4*j+1) ; MULT (xx,xz,2, alpha,alphaz,0, w,Wz,4*j+2) ; MULT (xx,xz,3, alpha,alphaz,0, w,Wz,4*j+3) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i == j) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+ dy] += aij * xj1 ; */ /* y [i+2*dy] += aij * xj2 ; */ /* y [i+3*dy] += aij * xj3 ; */ MULTADD (Yx,Yz,i , ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy , ax,az,0, xx,xz,1) ; MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ; MULTADD (Yx,Yz,i+3*dy, ax,az,0, xx,xz,3) ; } else if ((A->stype > 0 && i < j) || (A->stype < 0 && i > j)) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+ dy] += aij * xj1 ; */ /* y [i+2*dy] += aij * xj2 ; */ /* y [i+3*dy] += aij * xj3 ; */ /* yj0 += aij * w [4*i ] ; */ /* yj1 += aij * w [4*i+1] ; */ /* yj2 += aij * w [4*i+2] ; */ /* yj3 += aij * w [4*i+3] ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ; MULTADD (Yx,Yz,i+3*dy, ax,az,0, xx,xz,3) ; MULTADDCONJ (yx,yz,0, ax,az,0, w,Wz,4*i) ; MULTADDCONJ (yx,yz,1, ax,az,0, w,Wz,4*i+1) ; MULTADDCONJ (yx,yz,2, ax,az,0, w,Wz,4*i+2) ; MULTADDCONJ (yx,yz,3, ax,az,0, w,Wz,4*i+3) ; } } /* y [j ] += alpha [0] * yj0 ; */ /* y [j+ dy] += alpha [0] * yj1 ; */ /* y [j+2*dy] += alpha [0] * yj2 ; */ /* y [j+3*dy] += alpha [0] * yj3 ; */ MULTADD (Yx,Yz,j , alpha,alphaz,0, yx,yz,0) ; MULTADD (Yx,Yz,j+dy , alpha,alphaz,0, yx,yz,1) ; MULTADD (Yx,Yz,j+2*dy, alpha,alphaz,0, yx,yz,2) ; MULTADD (Yx,Yz,j+3*dy, alpha,alphaz,0, yx,yz,3) ; } /* y += 4*dy ; */ /* x += 4*dx ; */ ADVANCE (Yx,Yz,4*dy) ; ADVANCE (Xx,Xz,4*dx) ; } } } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX Matrix/src/CHOLMOD/MatrixOps/cholmod_submatrix.c0000644000175100001440000003164412271765436021252 0ustar hornikusers/* ========================================================================== */ /* === MatrixOps/cholmod_submatrix ========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* C = A (rset,cset), where C becomes length(rset)-by-length(cset) in dimension. * rset and cset can have duplicate entries. A and C must be unsymmetric. C * is packed. If the sorted flag is TRUE on input, or rset is sorted and A is * sorted, then C is sorted; otherwise C is unsorted. * * A NULL rset or cset means "[ ]" in MATLAB notation. * If the length of rset or cset is negative, it denotes ":" in MATLAB notation. * * For permuting a matrix, this routine is an alternative to cholmod_ptranspose * (which permutes and transposes a matrix and can work on symmetric matrices). * * The time taken by this routine is O(A->nrow) if the Common workspace needs * to be initialized, plus O(C->nrow + C->ncol + nnz (A (:,cset))). Thus, if C * is small and the workspace is not initialized, the time can be dominated by * the call to cholmod_allocate_work. However, once the workspace is * allocated, subsequent calls take less time. * * workspace: Iwork (max (A->nrow + length (rset), length (cset))). * allocates temporary copy of C if it is to be returned sorted. * * Future work: A common case occurs where A has sorted columns, and rset is in * the form lo:hi in MATLAB notation. This routine could exploit that case * to run even faster when the matrix is sorted, particularly when lo is small. * * Only pattern and real matrices are supported. Complex and zomplex matrices * are supported only when "values" is FALSE. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === check_subset ========================================================= */ /* ========================================================================== */ /* Check the rset or cset, and return TRUE if valid, FALSE if invalid */ static int check_subset (Int *set, Int len, Int n) { Int k ; if (set == NULL) { return (TRUE) ; } for (k = 0 ; k < len ; k++) { if (set [k] < 0 || set [k] >= n) { return (FALSE) ; } } return (TRUE) ; } /* ========================================================================== */ /* === cholmod_submatrix ==================================================== */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(submatrix) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to subreference */ Int *rset, /* set of row indices, duplicates OK */ SuiteSparse_long rsize, /* size of rset, or -1 for ":" */ Int *cset, /* set of column indices, duplicates OK */ SuiteSparse_long csize, /* size of cset, or -1 for ":" */ int values, /* if TRUE compute the numerical values of C */ int sorted, /* if TRUE then return C with sorted columns */ /* --------------- */ cholmod_common *Common ) { double aij = 0 ; double *Ax, *Cx ; Int *Ap, *Ai, *Anz, *Ci, *Cp, *Head, *Rlen, *Rnext, *Iwork ; cholmod_sparse *C ; Int packed, ancol, anrow, cnrow, cncol, nnz, i, j, csorted, ilast, p, pend, pdest, ci, cj, head, nr, nc ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; values = (values && (A->xtype != CHOLMOD_PATTERN)) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; if (A->stype != 0) { /* A must be unsymmetric */ ERROR (CHOLMOD_INVALID, "symmetric upper or lower case not supported") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ ancol = A->ncol ; anrow = A->nrow ; nr = rsize ; nc = csize ; if (rset == NULL) { /* nr = 0 denotes rset = [ ], nr < 0 denotes rset = 0:anrow-1 */ nr = (nr < 0) ? (-1) : 0 ; } if (cset == NULL) { /* nr = 0 denotes cset = [ ], nr < 0 denotes cset = 0:ancol-1 */ nc = (nc < 0) ? (-1) : 0 ; } cnrow = (nr < 0) ? anrow : nr ; /* negative rset means rset = 0:anrow-1 */ cncol = (nc < 0) ? ancol : nc ; /* negative cset means cset = 0:ancol-1 */ if (nr < 0 && nc < 0) { /* ------------------------------------------------------------------ */ /* C = A (:,:), use cholmod_copy instead */ /* ------------------------------------------------------------------ */ /* workspace: Iwork (max (C->nrow,C->ncol)) */ PRINT1 (("submatrix C = A (:,:)\n")) ; C = CHOLMOD(copy) (A, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } return (C) ; } PRINT1 (("submatrix nr "ID" nc "ID" Cnrow "ID" Cncol "ID"" " Anrow "ID" Ancol "ID"\n", nr, nc, cnrow, cncol, anrow, ancol)) ; /* s = MAX3 (anrow+MAX(0,nr), cncol, cnrow) ; */ s = CHOLMOD(add_size_t) (anrow, MAX (0,nr), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } s = MAX3 (s, ((size_t) cncol), ((size_t) cnrow)) ; CHOLMOD(allocate_work) (anrow, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; packed = A->packed ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Head = Common->Head ; /* size anrow */ Iwork = Common->Iwork ; Rlen = Iwork ; /* size anrow (i/i/l) */ Rnext = Iwork + anrow ; /* size nr (i/i/l), not used if nr < 0 */ /* ---------------------------------------------------------------------- */ /* construct inverse of rset and compute nnz (C) */ /* ---------------------------------------------------------------------- */ PRINT1 (("nr "ID" nc "ID"\n", nr, nc)) ; PRINT1 (("anrow "ID" ancol "ID"\n", anrow, ancol)) ; PRINT1 (("cnrow "ID" cncol "ID"\n", cnrow, cncol)) ; DEBUG (for (i = 0 ; i < nr ; i++) PRINT2 (("rset ["ID"] = "ID"\n", i, rset [i]))); DEBUG (for (i = 0 ; i < nc ; i++) PRINT2 (("cset ["ID"] = "ID"\n", i, cset [i]))); /* C is sorted if A and rset are sorted, or if C has one row or less */ csorted = A->sorted || (cnrow <= 1) ; if (!check_subset (rset, nr, anrow)) { ERROR (CHOLMOD_INVALID, "invalid rset") ; return (NULL) ; } if (!check_subset (cset, nc, ancol)) { ERROR (CHOLMOD_INVALID, "invalid cset") ; return (NULL) ; } nnz = 0 ; if (nr < 0) { /* C = A (:,cset) where cset = [ ] or cset is not empty */ ASSERT (IMPLIES (cncol > 0, cset != NULL)) ; for (cj = 0 ; cj < cncol ; cj++) { /* construct column cj of C, which is column j of A */ j = cset [cj] ; nnz += (packed) ? (Ap [j+1] - Ap [j]) : MAX (0, Anz [j]) ; } } else { /* C = A (rset,cset), where rset is not empty but cset might be empty */ /* create link lists in reverse order to preserve natural order */ ilast = anrow ; for (ci = nr-1 ; ci >= 0 ; ci--) { /* row i of A becomes row ci of C; add ci to ith link list */ i = rset [ci] ; head = Head [i] ; Rlen [i] = (head == EMPTY) ? 1 : (Rlen [i] + 1) ; Rnext [ci] = head ; Head [i] = ci ; if (i > ilast) { /* row indices in columns of C will not be sorted */ csorted = FALSE ; } ilast = i ; } #ifndef NDEBUG for (i = 0 ; i < anrow ; i++) { Int k = 0 ; Int rlen = (Head [i] != EMPTY) ? Rlen [i] : -1 ; PRINT1 (("Row "ID" Rlen "ID": ", i, rlen)) ; for (ci = Head [i] ; ci != EMPTY ; ci = Rnext [ci]) { k++ ; PRINT2 ((""ID" ", ci)) ; } PRINT1 (("\n")) ; ASSERT (IMPLIES (Head [i] != EMPTY, k == Rlen [i])) ; } #endif /* count nonzeros in C */ for (cj = 0 ; cj < cncol ; cj++) { /* count rows in column cj of C, which is column j of A */ j = (nc < 0) ? cj : (cset [cj]) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { /* row i of A becomes multiple rows (ci) of C */ i = Ai [p] ; ASSERT (i >= 0 && i < anrow) ; if (Head [i] != EMPTY) { nnz += Rlen [i] ; } } } } PRINT1 (("nnz (C) "ID"\n", nnz)) ; /* rset and cset are now valid */ DEBUG (CHOLMOD(dump_subset) (rset, rsize, anrow, "rset", Common)) ; DEBUG (CHOLMOD(dump_subset) (cset, csize, ancol, "cset", Common)) ; /* ---------------------------------------------------------------------- */ /* allocate C */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_sparse) (cnrow, cncol, nnz, csorted, TRUE, 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ for (i = 0 ; i < anrow ; i++) { Head [i] = EMPTY ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (NULL) ; } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* C = A (rset,cset) */ /* ---------------------------------------------------------------------- */ pdest = 0 ; if (nnz == 0) { /* C has no nonzeros */ for (cj = 0 ; cj <= cncol ; cj++) { Cp [cj] = 0 ; } } else if (nr < 0) { /* C = A (:,cset), where cset is not empty */ for (cj = 0 ; cj < cncol ; cj++) { /* construct column cj of C, which is column j of A */ PRINT1 (("construct cj = j = "ID"\n", cj)) ; j = cset [cj] ; Cp [cj] = pdest ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Ci [pdest] = Ai [p] ; if (values) { Cx [pdest] = Ax [p] ; } pdest++ ; ASSERT (pdest <= nnz) ; } } } else { /* C = A (rset,cset), where rset is not empty but cset might be empty */ for (cj = 0 ; cj < cncol ; cj++) { /* construct column cj of C, which is column j of A */ PRINT1 (("construct cj = "ID"\n", cj)) ; j = (nc < 0) ? cj : (cset [cj]) ; PRINT1 (("cj = "ID"\n", j)) ; Cp [cj] = pdest ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { /* row (Ai [p]) of A becomes multiple rows (ci) of C */ PRINT2 (("i: "ID" becomes: ", Ai [p])) ; if (values) { aij = Ax [p] ; } for (ci = Head [Ai [p]] ; ci != EMPTY ; ci = Rnext [ci]) { PRINT3 ((""ID" ", ci)) ; Ci [pdest] = ci ; if (values) { Cx [pdest] = aij ; } pdest++ ; ASSERT (pdest <= nnz) ; } PRINT2 (("\n")) ; } } } Cp [cncol] = pdest ; ASSERT (nnz == pdest) ; /* ---------------------------------------------------------------------- */ /* clear workspace */ /* ---------------------------------------------------------------------- */ for (ci = 0 ; ci < nr ; ci++) { Head [rset [ci]] = EMPTY ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* sort C, if requested */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (C , "C before sort", Common) >= 0) ; if (sorted && !csorted) { /* workspace: Iwork (max (C->nrow,C->ncol)) */ if (!CHOLMOD(sort) (C, Common)) { /* out of memory */ CHOLMOD(free_sparse) (&C, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (NULL) ; } } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (C , "Final C", Common) >= 0) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (C) ; } #endif Matrix/src/CHOLMOD/MatrixOps/cholmod_sdmult.c0000644000175100001440000001240212271765436020533 0ustar hornikusers/* ========================================================================== */ /* === MatrixOps/cholmod_sdmult ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Sparse matrix times dense matrix: * Y = alpha*(A*X) + beta*Y or Y = alpha*(A'*X) + beta*Y, * where A is sparse and X and Y are dense. * * when using A, X has A->ncol columns and Y has A->nrow rows * when using A', X has A->nrow columns and Y has A->ncol rows * * workspace: none in Common. Temporary workspace of size 4*(X->nrow) is used * if A is stored in symmetric form and X has four columns or more. If the * workspace is not available, a slower method is used instead that requires * no workspace. * * transpose = 0: use A * otherwise, use A' (complex conjugate transpose) * * transpose is ignored if the matrix is symmetric or Hermitian. * (the array transpose A.' is not supported). * * Supports real, complex, and zomplex matrices, but the xtypes of A, X, and Y * must all match. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define REAL #include "t_cholmod_sdmult.c" #define COMPLEX #include "t_cholmod_sdmult.c" #define ZOMPLEX #include "t_cholmod_sdmult.c" /* ========================================================================== */ /* === cholmod_sdmult ======================================================= */ /* ========================================================================== */ int CHOLMOD(sdmult) ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to multiply */ int transpose, /* use A if 0, otherwise use A' */ double alpha [2], /* scale factor for A */ double beta [2], /* scale factor for Y */ cholmod_dense *X, /* dense matrix to multiply */ /* ---- in/out --- */ cholmod_dense *Y, /* resulting dense matrix */ /* --------------- */ cholmod_common *Common ) { double *w ; size_t nx, ny ; Int e ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (X, FALSE) ; RETURN_IF_NULL (Y, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (Y, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; ny = transpose ? A->ncol : A->nrow ; /* required length of Y */ nx = transpose ? A->nrow : A->ncol ; /* required length of X */ if (X->nrow != nx || X->ncol != Y->ncol || Y->nrow != ny) { /* X and/or Y have the wrong dimension */ ERROR (CHOLMOD_INVALID, "X and/or Y have wrong dimensions") ; return (FALSE) ; } if (A->xtype != X->xtype || A->xtype != Y->xtype) { ERROR (CHOLMOD_INVALID, "A, X, and Y must have same xtype") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace, if required */ /* ---------------------------------------------------------------------- */ w = NULL ; e = (A->xtype == CHOLMOD_REAL ? 1:2) ; if (A->stype && X->ncol >= 4) { w = CHOLMOD(malloc) (nx, 4*e*sizeof (double), Common) ; } if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* Y = alpha*op(A)*X + beta*Y via template routine */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ; DEBUG (CHOLMOD(dump_dense) (X, "X", Common)) ; DEBUG (if (IS_NONZERO (beta [0]) || (IS_NONZERO (beta [1]) && A->xtype != CHOLMOD_REAL)) CHOLMOD(dump_dense) (Y, "Y", Common)) ; switch (A->xtype) { case CHOLMOD_REAL: r_cholmod_sdmult (A, transpose, alpha, beta, X, Y, w) ; break ; case CHOLMOD_COMPLEX: c_cholmod_sdmult (A, transpose, alpha, beta, X, Y, w) ; break ; case CHOLMOD_ZOMPLEX: z_cholmod_sdmult (A, transpose, alpha, beta, X, Y, w) ; break ; } /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ CHOLMOD(free) (4*nx, e*sizeof (double), w, Common) ; DEBUG (CHOLMOD(dump_dense) (Y, "Y", Common)) ; return (TRUE) ; } #endif Matrix/src/CHOLMOD/MatrixOps/cholmod_horzcat.c0000644000175100001440000001422212271765436020677 0ustar hornikusers/* ========================================================================== */ /* === MatrixOps/cholmod_horzcat ============================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Horizontal concatenation, C = [A , B] in MATLAB notation. * * A and B can be up/lo/unsym; C is unsymmetric and packed. * A and B must have the same number of rows. * C is sorted if both A and B are sorted. * * workspace: Iwork (max (A->nrow, A->ncol, B->nrow, B->ncol)). * allocates temporary copies of A and B if they are symmetric. * * A and B must have the same numeric xtype, unless values is FALSE. * A and B cannot be complex or zomplex, unless values is FALSE. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === cholmod_horzcat ====================================================== */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(horzcat) ( /* ---- input ---- */ cholmod_sparse *A, /* left matrix to concatenate */ cholmod_sparse *B, /* right matrix to concatenate */ int values, /* if TRUE compute the numerical values of C */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Bx, *Cx ; Int *Ap, *Ai, *Anz, *Bp, *Bi, *Bnz, *Cp, *Ci ; cholmod_sparse *C, *A2, *B2 ; Int apacked, bpacked, ancol, bncol, ncol, nrow, anz, bnz, nz, j, p, pend, pdest ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_NULL (B, NULL) ; values = values && (A->xtype != CHOLMOD_PATTERN) && (B->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; RETURN_IF_XTYPE_INVALID (B, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; if (A->nrow != B->nrow) { /* A and B must have the same number of rows */ ERROR (CHOLMOD_INVALID, "A and B must have same # rows") ; return (NULL) ; } /* A and B must have the same numerical type if values is TRUE (both must * be CHOLMOD_REAL, this is implicitly checked above) */ Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ ancol = A->ncol ; bncol = B->ncol ; nrow = A->nrow ; CHOLMOD(allocate_work) (0, MAX3 (nrow, ancol, bncol), 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* convert A to unsymmetric, if necessary */ A2 = NULL ; if (A->stype != 0) { /* workspace: Iwork (max (A->nrow,A->ncol)) */ A2 = CHOLMOD(copy) (A, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } A = A2 ; } /* convert B to unsymmetric, if necessary */ B2 = NULL ; if (B->stype != 0) { /* workspace: Iwork (max (B->nrow,B->ncol)) */ B2 = CHOLMOD(copy) (B, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; return (NULL) ; } B = B2 ; } Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; apacked = A->packed ; Bp = B->p ; Bnz = B->nz ; Bi = B->i ; Bx = B->x ; bpacked = B->packed ; /* ---------------------------------------------------------------------- */ /* allocate C */ /* ---------------------------------------------------------------------- */ anz = CHOLMOD(nnz) (A, Common) ; bnz = CHOLMOD(nnz) (B, Common) ; ncol = ancol + bncol ; nz = anz + bnz ; C = CHOLMOD(allocate_sparse) (nrow, ncol, nz, A->sorted && B->sorted, TRUE, 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; return (NULL) ; } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* C = [A , B] */ /* ---------------------------------------------------------------------- */ pdest = 0 ; /* copy A as the first A->ncol columns of C */ for (j = 0 ; j < ancol ; j++) { /* A(:,j) is the jth column of C */ p = Ap [j] ; pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ; Cp [j] = pdest ; for ( ; p < pend ; p++) { Ci [pdest] = Ai [p] ; if (values) Cx [pdest] = Ax [p] ; pdest++ ; } } /* copy B as the next B->ncol columns of C */ for (j = 0 ; j < bncol ; j++) { /* B(:,j) is the (ancol+j)th column of C */ p = Bp [j] ; pend = (bpacked) ? (Bp [j+1]) : (p + Bnz [j]) ; Cp [ancol + j] = pdest ; for ( ; p < pend ; p++) { Ci [pdest] = Bi [p] ; if (values) Cx [pdest] = Bx [p] ; pdest++ ; } } Cp [ncol] = pdest ; ASSERT (pdest == anz + bnz) ; /* ---------------------------------------------------------------------- */ /* free the unsymmetric copies of A and B, and return C */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; return (C) ; } #endif Matrix/src/CHOLMOD/MatrixOps/cholmod_symmetry.c0000644000175100001440000004020412271765436021115 0ustar hornikusers/* ========================================================================== */ /* === MatrixOps/cholmod_symmetry =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Determines if a sparse matrix is rectangular, unsymmetric, symmetric, * skew-symmetric, or Hermitian. It does so by looking at its numerical values * of both upper and lower triangular parts of a CHOLMOD "unsymmetric" * matrix, where A->stype == 0. The transpose of A is NOT constructed. * * If not unsymmetric, it also determines if the matrix has a diagonal whose * entries are all real and positive (and thus a candidate for sparse Cholesky * if A->stype is changed to a nonzero value). * * Note that a Matrix Market "general" matrix is either rectangular or * unsymmetric. * * The row indices in the column of each matrix MUST be sorted for this function * to work properly (A->sorted must be TRUE). This routine returns EMPTY if * A->stype is not zero, or if A->sorted is FALSE. The exception to this rule * is if A is rectangular. * * If option == 0, then this routine returns immediately when it finds a * non-positive diagonal entry (or one with nonzero imaginary part). If the * matrix is not a candidate for sparse Cholesky, it returns the value * CHOLMOD_MM_UNSYMMETRIC, even if the matrix might in fact be symmetric or * Hermitian. * * This routine is useful inside the MATLAB backslash, which must look at an * arbitrary matrix (A->stype == 0) and determine if it is a candidate for * sparse Cholesky. In that case, option should be 0. * * This routine is also useful when writing a MATLAB matrix to a file in * Rutherford/Boeing or Matrix Market format. Those formats require a * determination as to the symmetry of the matrix, and thus this routine should * not return upon encountering the first non-positive diagonal. In this case, * option should be 1. * * If option is 2, this function can be used to compute the numerical and * pattern symmetry, where 0 is a completely unsymmetric matrix, and 1 is a * perfectly symmetric matrix. This option is used when computing the following * statistics for the matrices in the UF Sparse Matrix Collection. * * numerical symmetry: number of matched offdiagonal nonzeros over * the total number of offdiagonal entries. A real entry A(i,j), i ~= j, * is matched if A (j,i) == A (i,j), but this is only counted if both * A(j,i) and A(i,j) are nonzero. This does not depend on Z. * (If A is complex, then the above test is modified; A (i,j) is matched * if conj (A (j,i)) == A (i,j)). * * Then numeric symmetry = xmatched / nzoffdiag, or 1 if nzoffdiag = 0. * * pattern symmetry: number of matched offdiagonal entries over the * total number of offdiagonal entries. An entry A(i,j), i ~= j, is * matched if A (j,i) is also an entry. * * Then pattern symmetry = pmatched / nzoffdiag, or 1 if nzoffdiag = 0. * * The symmetry of a matrix with no offdiagonal entries is equal to 1. * * A workspace of size ncol integers is allocated; EMPTY is returned if this * allocation fails. * * Summary of return values: * * EMPTY (-1) out of memory, stype not zero, A not sorted * CHOLMOD_MM_RECTANGULAR 1 A is rectangular * CHOLMOD_MM_UNSYMMETRIC 2 A is unsymmetric * CHOLMOD_MM_SYMMETRIC 3 A is symmetric, but with non-pos. diagonal * CHOLMOD_MM_HERMITIAN 4 A is Hermitian, but with non-pos. diagonal * CHOLMOD_MM_SKEW_SYMMETRIC 5 A is skew symmetric * CHOLMOD_MM_SYMMETRIC_POSDIAG 6 A is symmetric with positive diagonal * CHOLMOD_MM_HERMITIAN_POSDIAG 7 A is Hermitian with positive diagonal * * See also the spsym mexFunction, which is a MATLAB interface for this code. * * If the matrix is a candidate for sparse Cholesky, it will return a result * CHOLMOD_MM_SYMMETRIC_POSDIAG if real, or CHOLMOD_MM_HERMITIAN_POSDIAG if * complex. Otherwise, it will return a value less than this. This is true * regardless of the value of the option parameter. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === get_value ============================================================ */ /* ========================================================================== */ /* Get the pth value in the matrix. */ static void get_value ( double *Ax, /* real values, or real/imag. for CHOLMOD_COMPLEX type */ double *Az, /* imaginary values for CHOLMOD_ZOMPLEX type */ Int p, /* get the pth entry */ Int xtype, /* A->xtype: pattern, real, complex, or zomplex */ double *x, /* the real part */ double *z /* the imaginary part */ ) { switch (xtype) { case CHOLMOD_PATTERN: *x = 1 ; *z = 0 ; break ; case CHOLMOD_REAL: *x = Ax [p] ; *z = 0 ; break ; case CHOLMOD_COMPLEX: *x = Ax [2*p] ; *z = Ax [2*p+1] ; break ; case CHOLMOD_ZOMPLEX: *x = Ax [p] ; *z = Az [p] ; break ; } } /* ========================================================================== */ /* === cholmod_symmetry ===================================================== */ /* ========================================================================== */ /* Determine the symmetry of a matrix, and check its diagonal. * * option 0: Do not count # of matched pairs. Quick return if the * the matrix has a zero, negative, or imaginary diagonal entry. * * option 1: Do not count # of matched pairs. Do not return quickly if * the matrix has a zero, negative, or imaginary diagonal entry. * The result 1 to 7 is accurately computed: * * EMPTY (-1) out of memory, stype not zero, A not sorted * CHOLMOD_MM_RECTANGULAR 1 A is rectangular * CHOLMOD_MM_UNSYMMETRIC 2 A is unsymmetric * CHOLMOD_MM_SYMMETRIC 3 A is symmetric, with non-pos. diagonal * CHOLMOD_MM_HERMITIAN 4 A is Hermitian, with non-pos. diagonal * CHOLMOD_MM_SKEW_SYMMETRIC 5 A is skew symmetric * CHOLMOD_MM_SYMMETRIC_POSDIAG 6 is symmetric with positive diagonal * CHOLMOD_MM_HERMITIAN_POSDIAG 7 A is Hermitian with positive diagonal * * The routine returns as soon as the above is determined (that is, it * can return as soon as it determines the matrix is unsymmetric). * * option 2: All of the above, but also compute the number of matched off- * diagonal entries (of two types). xmatched is the number of * nonzero entries for which A(i,j) = conj(A(j,i)). pmatched is * the number of entries (i,j) for which A(i,j) and A(j,i) are both in * the pattern of A (the value doesn't matter). nzoffdiag is the total * number of off-diagonal entries in the pattern. nzdiag is the number of * diagonal entries in the pattern. * * With option 0 or 1, or if the matrix is rectangular, xmatched, pmatched, * nzoffdiag, and nzdiag are not computed. * * Note that a matched pair, A(i,j) and A(j,i) for i != j, is counted twice * (once per entry). */ int CHOLMOD(symmetry) ( /* ---- input ---- */ cholmod_sparse *A, int option, /* option 0, 1, or 2 (see above) */ /* ---- output --- */ /* outputs ignored if any are NULL */ Int *p_xmatched, /* # of matched numerical entries */ Int *p_pmatched, /* # of matched entries in pattern */ Int *p_nzoffdiag, /* # of off diagonal entries */ Int *p_nzdiag, /* # of diagonal entries */ /* --------------- */ cholmod_common *Common ) { double aij_real = 0, aij_imag = 0, aji_real = 0, aji_imag = 0 ; double *Ax, *Az ; Int *Ap, *Ai, *Anz, *munch ; Int packed, nrow, ncol, xtype, is_symmetric, is_skew, is_hermitian, posdiag, j, p, pend, i, piend, result, xmatched, pmatched, nzdiag, i2, found ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; ASSERT (CHOLMOD(dump_sparse) (A, "cholmod_symmetry", Common) >= 0) ; if (p_xmatched == NULL || p_pmatched == NULL || p_nzoffdiag == NULL || p_nzdiag == NULL) { /* option 2 is not performed if any output parameter is NULL */ option = MAX (option, 1) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; packed = A->packed ; ncol = A->ncol ; nrow = A->nrow ; xtype = A->xtype ; /* ---------------------------------------------------------------------- */ /* check if rectangular, unsorted, or stype is not zero */ /* ---------------------------------------------------------------------- */ if (nrow != ncol) { /* matrix is rectangular */ return (CHOLMOD_MM_RECTANGULAR) ; } if (!(A->sorted) || A->stype != 0) { /* this function cannot determine the type or symmetry */ return (EMPTY) ; } /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* this function requires uninitialized Int workspace of size ncol */ CHOLMOD(allocate_work) (0, ncol, 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (EMPTY) ; } munch = Common->Iwork ; /* the munch array is size ncol */ /* ---------------------------------------------------------------------- */ /* determine symmetry of a square matrix */ /* ---------------------------------------------------------------------- */ /* a complex or zomplex matrix is Hermitian until proven otherwise */ is_hermitian = (xtype >= CHOLMOD_COMPLEX) ; /* any matrix is symmetric until proven otherwise */ is_symmetric = TRUE ; /* a non-pattern matrix is skew-symmetric until proven otherwise */ is_skew = (xtype != CHOLMOD_PATTERN) ; /* a matrix has positive diagonal entries until proven otherwise */ posdiag = TRUE ; /* munch pointers start at the top of each column */ for (j = 0 ; j < ncol ; j++) { munch [j] = Ap [j] ; } xmatched = 0 ; pmatched = 0 ; nzdiag = 0 ; for (j = 0 ; j < ncol ; j++) /* examine each column of A */ { /* ------------------------------------------------------------------ */ /* look at the entire munch column j */ /* ------------------------------------------------------------------ */ /* start at the munch point of column j, and go to end of the column */ p = munch [j] ; pend = (packed) ? (Ap [j+1]) : (Ap [j] + Anz [j]) ; for ( ; p < pend ; p++) { /* get the row index of A(i,j) */ i = Ai [p] ; if (i < j) { /* ---------------------------------------------------------- */ /* A(i,j) in triu(A), but matching A(j,i) not in tril(A) */ /* ---------------------------------------------------------- */ /* entry A(i,j) is unmatched; it appears in the upper triangular * part, but not the lower triangular part. The matrix is * unsymmetric. */ is_hermitian = FALSE ; is_symmetric = FALSE ; is_skew = FALSE ; } else if (i == j) { /* ---------------------------------------------------------- */ /* the diagonal A(j,j) is present; check its value */ /* ---------------------------------------------------------- */ get_value (Ax, Az, p, xtype, &aij_real, &aij_imag) ; if (aij_real != 0. || aij_imag != 0.) { /* diagonal is nonzero; matrix is not skew-symmetric */ nzdiag++ ; is_skew = FALSE ; } if (aij_real <= 0. || aij_imag != 0.) { /* diagonal negative or imaginary; not chol candidate */ posdiag = FALSE ; } if (aij_imag != 0.) { /* imaginary part is present; not Hermitian */ is_hermitian = FALSE ; } } else /* i > j */ { /* ---------------------------------------------------------- */ /* consider column i, up to and including row j */ /* ---------------------------------------------------------- */ /* munch the entry at top of column i up to and incl row j */ piend = (packed) ? (Ap [i+1]) : (Ap [i] + Anz [i]) ; found = FALSE ; for ( ; munch [i] < piend ; munch [i]++) { i2 = Ai [munch [i]] ; if (i2 < j) { /* -------------------------------------------------- */ /* A(i2,i) in triu(A) but A(i,i2) not in tril(A) */ /* -------------------------------------------------- */ /* The matrix is unsymmetric. */ is_hermitian = FALSE ; is_symmetric = FALSE ; is_skew = FALSE ; } else if (i2 == j) { /* -------------------------------------------------- */ /* both A(i,j) and A(j,i) exist in the matrix */ /* -------------------------------------------------- */ /* this is one more matching entry in the pattern */ pmatched += 2 ; found = TRUE ; /* get the value of A(i,j) */ get_value (Ax, Az, p, xtype, &aij_real, &aij_imag) ; /* get the value of A(j,i) */ get_value (Ax, Az, munch [i], xtype, &aji_real, &aji_imag) ; /* compare A(i,j) with A(j,i) */ if (aij_real != aji_real || aij_imag != aji_imag) { /* the matrix cannot be symmetric */ is_symmetric = FALSE ; } if (aij_real != -aji_real || aij_imag != aji_imag) { /* the matrix cannot be skew-symmetric */ is_skew = FALSE ; } if (aij_real != aji_real || aij_imag != -aji_imag) { /* the matrix cannot be Hermitian */ is_hermitian = FALSE ; } else { /* A(i,j) and A(j,i) are numerically matched */ xmatched += 2 ; } } else /* i2 > j */ { /* -------------------------------------------------- */ /* entry A(i2,i) is not munched; consider it later */ /* -------------------------------------------------- */ break ; } } if (!found) { /* A(i,j) in tril(A) but A(j,i) not in triu(A). * The matrix is unsymmetric. */ is_hermitian = FALSE ; is_symmetric = FALSE ; is_skew = FALSE ; } } if (option < 2 && !(is_symmetric || is_skew || is_hermitian)) { /* matrix is unsymmetric; terminate the test */ return (CHOLMOD_MM_UNSYMMETRIC) ; } } /* ------------------------------------------------------------------ */ /* quick return if not Cholesky candidate */ /* ------------------------------------------------------------------ */ if (option < 1 && (!posdiag || nzdiag < ncol)) { /* Diagonal entry not present, or present but negative or with * nonzero imaginary part. Quick return for option 0. */ return (CHOLMOD_MM_UNSYMMETRIC) ; } } /* ---------------------------------------------------------------------- */ /* return the results */ /* ---------------------------------------------------------------------- */ if (nzdiag < ncol) { /* not all diagonal entries are present */ posdiag = FALSE ; } if (option >= 2) { *p_xmatched = xmatched ; *p_pmatched = pmatched ; *p_nzoffdiag = CHOLMOD(nnz) (A, Common) - nzdiag ; *p_nzdiag = nzdiag ; } result = CHOLMOD_MM_UNSYMMETRIC ; if (is_hermitian) { /* complex Hermitian matrix, with either pos. or non-pos. diagonal */ result = posdiag ? CHOLMOD_MM_HERMITIAN_POSDIAG : CHOLMOD_MM_HERMITIAN ; } else if (is_symmetric) { /* real or complex symmetric matrix, with pos. or non-pos. diagonal */ result = posdiag ? CHOLMOD_MM_SYMMETRIC_POSDIAG : CHOLMOD_MM_SYMMETRIC ; } else if (is_skew) { /* real or complex skew-symmetric matrix */ result = CHOLMOD_MM_SKEW_SYMMETRIC ; } return (result) ; } #endif Matrix/src/CHOLMOD/MatrixOps/cholmod_scale.c0000644000175100001440000001437512271765436020325 0ustar hornikusers/* ========================================================================== */ /* === MatrixOps/cholmod_scale ============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* scale a matrix: A = diag(s)*A, A*diag(s), s*A, or diag(s)*A*diag(s) * * A can be of any type (packed/unpacked, upper/lower/unsymmetric). * The symmetry of A is ignored; all entries in the matrix are modified. * * If A is m-by-n unsymmetric but scaled symmtrically, the result is * A = diag (s (1:m)) * A * diag (s (1:n)). * * Note: diag(s) should be interpretted as spdiags(s,0,n,n) where n=length(s). * * Row or column scaling of a symmetric matrix still results in a symmetric * matrix, since entries are still ignored by other routines. * For example, when row-scaling a symmetric matrix where just the upper * triangular part is stored (and lower triangular entries ignored) * A = diag(s)*triu(A) is performed, where the result A is also * symmetric-upper. This has the effect of modifying the implicit lower * triangular part. In MATLAB notation: * * U = diag(s)*triu(A) ; * L = tril (U',-1) * A = L + U ; * * The scale parameter determines the kind of scaling to perform: * * CHOLMOD_SCALAR: s[0]*A * CHOLMOD_ROW: diag(s)*A * CHOLMOD_COL: A*diag(s) * CHOLMOD_SYM: diag(s)*A*diag(s) * * The size of S depends on the scale parameter: * * CHOLMOD_SCALAR: size 1 * CHOLMOD_ROW: size nrow-by-1 or 1-by-nrow * CHOLMOD_COL: size ncol-by-1 or 1-by-ncol * CHOLMOD_SYM: size max(nrow,ncol)-by-1, or 1-by-max(nrow,ncol) * * workspace: none * * Only real matrices are supported. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === cholmod_scale ======================================================== */ /* ========================================================================== */ int CHOLMOD(scale) ( /* ---- input ---- */ cholmod_dense *S, /* scale factors (scalar or vector) */ int scale, /* type of scaling to compute */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix to scale */ /* --------------- */ cholmod_common *Common ) { double t ; double *Ax, *s ; Int *Ap, *Anz, *Ai ; Int packed, j, ncol, nrow, p, pend, sncol, snrow, nn, ok ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (S, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; RETURN_IF_XTYPE_INVALID (S, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; ncol = A->ncol ; nrow = A->nrow ; sncol = S->ncol ; snrow = S->nrow ; if (scale == CHOLMOD_SCALAR) { ok = (snrow == 1 && sncol == 1) ; } else if (scale == CHOLMOD_ROW) { ok = (snrow == nrow && sncol == 1) || (snrow == 1 && sncol == nrow) ; } else if (scale == CHOLMOD_COL) { ok = (snrow == ncol && sncol == 1) || (snrow == 1 && sncol == ncol) ; } else if (scale == CHOLMOD_SYM) { nn = MAX (nrow, ncol) ; ok = (snrow == nn && sncol == 1) || (snrow == 1 && sncol == nn) ; } else { /* scale invalid */ ERROR (CHOLMOD_INVALID, "invalid scaling option") ; return (FALSE) ; } if (!ok) { /* S is wrong size */ ERROR (CHOLMOD_INVALID, "invalid scale factors") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; packed = A->packed ; s = S->x ; /* ---------------------------------------------------------------------- */ /* scale the matrix */ /* ---------------------------------------------------------------------- */ if (scale == CHOLMOD_ROW) { /* ------------------------------------------------------------------ */ /* A = diag(s)*A, row scaling */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Ax [p] *= s [Ai [p]] ; } } } else if (scale == CHOLMOD_COL) { /* ------------------------------------------------------------------ */ /* A = A*diag(s), column scaling */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < ncol ; j++) { t = s [j] ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Ax [p] *= t ; } } } else if (scale == CHOLMOD_SYM) { /* ------------------------------------------------------------------ */ /* A = diag(s)*A*diag(s), symmetric scaling */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < ncol ; j++) { t = s [j] ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Ax [p] *= t * s [Ai [p]] ; } } } else if (scale == CHOLMOD_SCALAR) { /* ------------------------------------------------------------------ */ /* A = s[0] * A, scalar scaling */ /* ------------------------------------------------------------------ */ t = s [0] ; for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Ax [p] *= t ; } } } ASSERT (CHOLMOD(dump_sparse) (A, "A scaled", Common) >= 0) ; return (TRUE) ; } #endif Matrix/src/CHOLMOD/MatrixOps/cholmod_drop.c0000644000175100001440000001205512271765436020173 0ustar hornikusers/* ========================================================================== */ /* === MatrixOps/cholmod_drop =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Drop small entries from A, and entries in the ignored part of A if A * is symmetric. None of the matrix operations drop small numerical entries * from a matrix, except for this one. NaN's and Inf's are kept. * * workspace: none * * Supports pattern and real matrices, complex and zomplex not supported. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === cholmod_drop ========================================================= */ /* ========================================================================== */ int CHOLMOD(drop) ( /* ---- input ---- */ double tol, /* keep entries with absolute value > tol */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix to drop entries from */ /* --------------- */ cholmod_common *Common ) { double aij ; double *Ax ; Int *Ap, *Ai, *Anz ; Int packed, i, j, nrow, ncol, p, pend, nz, values ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_REAL, FALSE) ; Common->status = CHOLMOD_OK ; ASSERT (CHOLMOD(dump_sparse) (A, "A predrop", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; Ax = A->x ; Anz = A->nz ; packed = A->packed ; ncol = A->ncol ; nrow = A->nrow ; values = (A->xtype != CHOLMOD_PATTERN) ; nz = 0 ; if (values) { /* ------------------------------------------------------------------ */ /* drop small numerical entries from A, and entries in ignored part */ /* ------------------------------------------------------------------ */ if (A->stype > 0) { /* -------------------------------------------------------------- */ /* A is symmetric, with just upper triangular part stored */ /* -------------------------------------------------------------- */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Ap [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; aij = Ax [p] ; if (i <= j && (fabs (aij) > tol || IS_NAN (aij))) { Ai [nz] = i ; Ax [nz] = aij ; nz++ ; } } } } else if (A->stype < 0) { /* -------------------------------------------------------------- */ /* A is symmetric, with just lower triangular part stored */ /* -------------------------------------------------------------- */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Ap [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; aij = Ax [p] ; if (i >= j && (fabs (aij) > tol || IS_NAN (aij))) { Ai [nz] = i ; Ax [nz] = aij ; nz++ ; } } } } else { /* -------------------------------------------------------------- */ /* both parts of A present, just drop small entries */ /* -------------------------------------------------------------- */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Ap [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; aij = Ax [p] ; if (fabs (aij) > tol || IS_NAN (aij)) { Ai [nz] = i ; Ax [nz] = aij ; nz++ ; } } } } Ap [ncol] = nz ; /* reduce A->i and A->x in size */ ASSERT (MAX (1,nz) <= A->nzmax) ; CHOLMOD(reallocate_sparse) (nz, A, Common) ; ASSERT (Common->status >= CHOLMOD_OK) ; } else { /* ------------------------------------------------------------------ */ /* consider only the pattern of A */ /* ------------------------------------------------------------------ */ /* Note that cholmod_band_inplace calls cholmod_reallocate_sparse */ if (A->stype > 0) { CHOLMOD(band_inplace) (0, ncol, 0, A, Common) ; } else if (A->stype < 0) { CHOLMOD(band_inplace) (-nrow, 0, 0, A, Common) ; } } ASSERT (CHOLMOD(dump_sparse) (A, "A dropped", Common) >= 0) ; return (TRUE) ; } #endif Matrix/src/CHOLMOD/MatrixOps/cholmod_vertcat.c0000644000175100001440000001402312271765436020674 0ustar hornikusers/* ========================================================================== */ /* === MatrixOps/cholmod_vertcat ============================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Vertical concatenation, C = [A ; B] in MATLAB notation. * * A and B can be up/lo/unsym; C is unsymmetric and packed. * A and B must have the same number of columns. * C is sorted if both A and B are sorted. * * workspace: Iwork (max (A->nrow, A->ncol, B->nrow, B->ncol)). * allocates temporary copies of A and B if they are symmetric. * * Only pattern and real matrices are supported. Complex and zomplex matrices * are supported only if "values" is FALSE. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === cholmod_vertcat ====================================================== */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(vertcat) ( /* ---- input ---- */ cholmod_sparse *A, /* left matrix to concatenate */ cholmod_sparse *B, /* right matrix to concatenate */ int values, /* if TRUE compute the numerical values of C */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Bx, *Cx ; Int *Ap, *Ai, *Anz, *Bp, *Bi, *Bnz, *Cp, *Ci ; cholmod_sparse *C, *A2, *B2 ; Int apacked, bpacked, anrow, bnrow, ncol, nrow, anz, bnz, nz, j, p, pend, pdest ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_NULL (B, NULL) ; values = values && (A->xtype != CHOLMOD_PATTERN) && (B->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; RETURN_IF_XTYPE_INVALID (B, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; if (A->ncol != B->ncol) { /* A and B must have the same number of columns */ ERROR (CHOLMOD_INVALID, "A and B must have same # of columns") ; return (NULL) ; } /* A and B must have the same numerical type if values is TRUE (both must * be CHOLMOD_REAL, this is implicitly checked above) */ Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ anrow = A->nrow ; bnrow = B->nrow ; ncol = A->ncol ; CHOLMOD(allocate_work) (0, MAX3 (anrow, bnrow, ncol), 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* convert A to unsymmetric, if necessary */ A2 = NULL ; if (A->stype != 0) { /* workspace: Iwork (max (A->nrow,A->ncol)) */ A2 = CHOLMOD(copy) (A, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } A = A2 ; } /* convert B to unsymmetric, if necessary */ B2 = NULL ; if (B->stype != 0) { /* workspace: Iwork (max (B->nrow,B->ncol)) */ B2 = CHOLMOD(copy) (B, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; return (NULL) ; } B = B2 ; } Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; apacked = A->packed ; Bp = B->p ; Bnz = B->nz ; Bi = B->i ; Bx = B->x ; bpacked = B->packed ; /* ---------------------------------------------------------------------- */ /* allocate C */ /* ---------------------------------------------------------------------- */ anz = CHOLMOD(nnz) (A, Common) ; bnz = CHOLMOD(nnz) (B, Common) ; nrow = anrow + bnrow ; nz = anz + bnz ; C = CHOLMOD(allocate_sparse) (nrow, ncol, nz, A->sorted && B->sorted, TRUE, 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; return (NULL) ; } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* C = [A ; B] */ /* ---------------------------------------------------------------------- */ pdest = 0 ; for (j = 0 ; j < ncol ; j++) { /* attach A(:,j) as the first part of C(:,j) */ p = Ap [j] ; pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ; Cp [j] = pdest ; for ( ; p < pend ; p++) { Ci [pdest] = Ai [p] ; if (values) { Cx [pdest] = Ax [p] ; } pdest++ ; } /* attach B(:,j) as the second part of C(:,j) */ p = Bp [j] ; pend = (bpacked) ? (Bp [j+1]) : (p + Bnz [j]) ; for ( ; p < pend ; p++) { Ci [pdest] = Bi [p] + anrow ; if (values) { Cx [pdest] = Bx [p] ; } pdest++ ; } } Cp [ncol] = pdest ; ASSERT (pdest == nz) ; /* ---------------------------------------------------------------------- */ /* free the unsymmetric copies of A and B, and return C */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; return (C) ; } #endif Matrix/src/CHOLMOD/MatrixOps/cholmod_ssmult.c0000644000175100001440000003400012271765436020550 0ustar hornikusers/* ========================================================================== */ /* === MatrixOps/cholmod_ssmult ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* C = A*B. Multiply two sparse matrices. * * A and B can be packed or unpacked, sorted or unsorted, and of any stype. * If A or B are symmetric, an internal unsymmetric copy is made first, however. * C is computed as if A and B are unsymmetric, and then if the stype input * parameter requests a symmetric form (upper or lower) the matrix is converted * into that form. * * C is returned as packed, and either unsorted or sorted, depending on the * "sorted" input parameter. If C is returned sorted, then either C = (B'*A')' * or C = (A*B)'' is computed, depending on the number of nonzeros in A, B, and * C. * * workspace: * if C unsorted: Flag (A->nrow), W (A->nrow) if values * if C sorted: Flag (B->ncol), W (B->ncol) if values * Iwork (max (A->ncol, A->nrow, B->nrow, B->ncol)) * allocates temporary copies for A, B, and C, if required. * * Only pattern and real matrices are supported. Complex and zomplex matrices * are supported only when the numerical values are not computed ("values" * is FALSE). */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === cholmod_ssmult ======================================================= */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(ssmult) ( /* ---- input ---- */ cholmod_sparse *A, /* left matrix to multiply */ cholmod_sparse *B, /* right matrix to multiply */ int stype, /* requested stype of C */ int values, /* TRUE: do numerical values, FALSE: pattern only */ int sorted, /* if TRUE then return C with sorted columns */ /* --------------- */ cholmod_common *Common ) { double bjt ; double *Ax, *Bx, *Cx, *W ; Int *Ap, *Anz, *Ai, *Bp, *Bnz, *Bi, *Cp, *Ci, *Flag ; cholmod_sparse *C, *A2, *B2, *A3, *B3, *C2 ; Int apacked, bpacked, j, i, pa, paend, pb, pbend, ncol, mark, cnz, t, p, nrow, anz, bnz, do_swap_and_transpose, n1, n2 ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_NULL (B, NULL) ; values = values && (A->xtype != CHOLMOD_PATTERN) && (B->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; RETURN_IF_XTYPE_INVALID (B, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; if (A->ncol != B->nrow) { /* inner dimensions must agree */ ERROR (CHOLMOD_INVALID, "A and B inner dimensions must match") ; return (NULL) ; } /* A and B must have the same numerical type if values is TRUE (both must * be CHOLMOD_REAL, this is implicitly checked above) */ Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ if (A->nrow <= 1) { /* C will be implicitly sorted, so no need to sort it here */ sorted = FALSE ; } if (sorted) { n1 = MAX (A->nrow, B->ncol) ; } else { n1 = A->nrow ; } n2 = MAX4 (A->ncol, A->nrow, B->nrow, B->ncol) ; CHOLMOD(allocate_work) (n1, n2, values ? n1 : 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1 : 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* convert A to unsymmetric, if necessary */ A2 = NULL ; B2 = NULL ; if (A->stype) { /* workspace: Iwork (max (A->nrow,A->ncol)) */ A2 = CHOLMOD(copy) (A, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ; return (NULL) ; } A = A2 ; } /* convert B to unsymmetric, if necessary */ if (B->stype) { /* workspace: Iwork (max (B->nrow,B->ncol)) */ B2 = CHOLMOD(copy) (B, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ; return (NULL) ; } B = B2 ; } ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ; ASSERT (CHOLMOD(dump_sparse) (B, "B", Common) >= 0) ; /* get the A matrix */ Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; apacked = A->packed ; /* get the B matrix */ Bp = B->p ; Bnz = B->nz ; Bi = B->i ; Bx = B->x ; bpacked = B->packed ; /* get the size of C */ nrow = A->nrow ; ncol = B->ncol ; /* get workspace */ W = Common->Xwork ; /* size nrow, unused if values is FALSE */ Flag = Common->Flag ; /* size nrow, Flag [0..nrow-1] < mark on input*/ /* ---------------------------------------------------------------------- */ /* count the number of entries in the result C */ /* ---------------------------------------------------------------------- */ cnz = 0 ; for (j = 0 ; j < ncol ; j++) { /* clear the Flag array */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* for each nonzero B(t,j) in column j, do: */ pb = Bp [j] ; pbend = (bpacked) ? (Bp [j+1]) : (pb + Bnz [j]) ; for ( ; pb < pbend ; pb++) { /* B(t,j) is nonzero */ t = Bi [pb] ; /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */ pa = Ap [t] ; paend = (apacked) ? (Ap [t+1]) : (pa + Anz [t]) ; for ( ; pa < paend ; pa++) { i = Ai [pa] ; if (Flag [i] != mark) { Flag [i] = mark ; cnz++ ; } } } if (cnz < 0) { break ; /* integer overflow case */ } } /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* ---------------------------------------------------------------------- */ /* check for integer overflow */ /* ---------------------------------------------------------------------- */ if (cnz < 0) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* Determine how to return C sorted (if requested) */ /* ---------------------------------------------------------------------- */ do_swap_and_transpose = FALSE ; if (sorted) { /* Determine the best way to return C with sorted columns. Computing * C = (B'*A')' takes cnz + anz + bnz time (ignoring O(n) terms). * Sorting C when done, C = (A*B)'', takes 2*cnz time. Pick the one * with the least amount of work. */ anz = CHOLMOD(nnz) (A, Common) ; bnz = CHOLMOD(nnz) (B, Common) ; do_swap_and_transpose = (anz + bnz < cnz) ; if (do_swap_and_transpose) { /* -------------------------------------------------------------- */ /* C = (B'*A')' */ /* -------------------------------------------------------------- */ /* workspace: Iwork (A->nrow) */ A3 = CHOLMOD(ptranspose) (A, values, NULL, NULL, 0, Common) ; CHOLMOD(free_sparse) (&A2, Common) ; A2 = A3 ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)); return (NULL) ; } /* workspace: Iwork (B->nrow) */ B3 = CHOLMOD(ptranspose) (B, values, NULL, NULL, 0, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; B2 = B3 ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)); return (NULL) ; } A = B2 ; B = A2 ; /* get the new A matrix */ Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; apacked = A->packed ; /* get the new B matrix */ Bp = B->p ; Bnz = B->nz ; Bi = B->i ; Bx = B->x ; bpacked = B->packed ; /* get the size of C' */ nrow = A->nrow ; ncol = B->ncol ; } } /* ---------------------------------------------------------------------- */ /* allocate C */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_sparse) (nrow, ncol, cnz, FALSE, TRUE, 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ; return (NULL) ; } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* C = A*B */ /* ---------------------------------------------------------------------- */ cnz = 0 ; if (values) { /* pattern and values */ for (j = 0 ; j < ncol ; j++) { /* clear the Flag array */ /* mark = CHOLMOD(clear_flag (Common)) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* start column j of C */ Cp [j] = cnz ; /* for each nonzero B(t,j) in column j, do: */ pb = Bp [j] ; pbend = (bpacked) ? (Bp [j+1]) : (pb + Bnz [j]) ; for ( ; pb < pbend ; pb++) { /* B(t,j) is nonzero */ t = Bi [pb] ; bjt = Bx [pb] ; /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) * and scatter the values into W */ pa = Ap [t] ; paend = (apacked) ? (Ap [t+1]) : (pa + Anz [t]) ; for ( ; pa < paend ; pa++) { i = Ai [pa] ; if (Flag [i] != mark) { Flag [i] = mark ; Ci [cnz++] = i ; } W [i] += Ax [pa] * bjt ; } } /* gather the values into C(:,j) */ for (p = Cp [j] ; p < cnz ; p++) { i = Ci [p] ; Cx [p] = W [i] ; W [i] = 0 ; } } } else { /* pattern only */ for (j = 0 ; j < ncol ; j++) { /* clear the Flag array */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* start column j of C */ Cp [j] = cnz ; /* for each nonzero B(t,j) in column j, do: */ pb = Bp [j] ; pbend = (bpacked) ? (Bp [j+1]) : (pb + Bnz [j]) ; for ( ; pb < pbend ; pb++) { /* B(t,j) is nonzero */ t = Bi [pb] ; /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */ pa = Ap [t] ; paend = (apacked) ? (Ap [t+1]) : (pa + Anz [t]) ; for ( ; pa < paend ; pa++) { i = Ai [pa] ; if (Flag [i] != mark) { Flag [i] = mark ; Ci [cnz++] = i ; } } } } } Cp [ncol] = cnz ; ASSERT (MAX (1,cnz) == C->nzmax) ; /* ---------------------------------------------------------------------- */ /* clear workspace and free temporary matrices */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; /* CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ; /* ---------------------------------------------------------------------- */ /* convert C to a symmetric upper/lower matrix if requested */ /* ---------------------------------------------------------------------- */ /* convert C in place, which cannot fail since no memory is allocated */ if (stype > 0) { /* C = triu (C), in place */ (void) CHOLMOD(band_inplace) (0, ncol, values, C, Common) ; C->stype = 1 ; } else if (stype < 0) { /* C = tril (C), in place */ (void) CHOLMOD(band_inplace) (-nrow, 0, values, C, Common) ; C->stype = -1 ; } ASSERT (Common->status >= CHOLMOD_OK) ; /* ---------------------------------------------------------------------- */ /* sort C, if requested */ /* ---------------------------------------------------------------------- */ if (sorted) { if (do_swap_and_transpose) { /* workspace: Iwork (C->ncol), which is A->nrow since C=(B'*A') */ C2 = CHOLMOD(ptranspose) (C, values, NULL, NULL, 0, Common) ; CHOLMOD(free_sparse) (&C, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)); return (NULL) ; } C = C2 ; } else { /* workspace: Iwork (max (C->nrow,C->ncol)) */ if (!CHOLMOD(sort) (C, Common)) { /* out of memory */ CHOLMOD(free_sparse) (&C, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)); return (NULL) ; } } } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ DEBUG (CHOLMOD(dump_sparse) (C, "ssmult", Common) >= 0) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ; return (C) ; } #endif Matrix/src/CHOLMOD/Include/0000755000175100001440000000000012271765426015007 5ustar hornikusersMatrix/src/CHOLMOD/Include/cholmod.h0000644000175100001440000000746312271765436016620 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod.h ==================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod.h. * Copyright (C) 2005-2013, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * * Portions of CHOLMOD (the Core and Partition Modules) are copyrighted by the * University of Florida. The Modify Module is co-authored by William W. * Hager, Univ. of Florida. * * Acknowledgements: this work was supported in part by the National Science * Foundation (NFS CCR-0203270 and DMS-9803599), and a grant from Sandia * National Laboratories (Dept. of Energy) which supported the development of * CHOLMOD's Partition Module. * -------------------------------------------------------------------------- */ /* CHOLMOD include file, for inclusion user programs. * * The include files listed below include a short description of each user- * callable routine. Each routine in CHOLMOD has a consistent interface. * More details about the CHOLMOD data types is in the cholmod_core.h file. * * Naming convention: * ------------------ * * All routine names, data types, and CHOLMOD library files use the * cholmod_ prefix. All macros and other #define's use the CHOLMOD * prefix. * * Return value: * ------------- * * Most CHOLMOD routines return an int (TRUE (1) if successful, or FALSE * (0) otherwise. A SuiteSparse_long or double return value is >= 0 if * successful, or -1 otherwise. A size_t return value is > 0 if * successful, or 0 otherwise. * * If a routine returns a pointer, it is a pointer to a newly allocated * object or NULL if a failure occured, with one exception. cholmod_free * always returns NULL. * * "Common" parameter: * ------------------ * * The last parameter in all CHOLMOD routines is a pointer to the CHOLMOD * "Common" object. This contains control parameters, statistics, and * workspace used between calls to CHOLMOD. It is always an input/output * parameter. * * Input, Output, and Input/Output parameters: * ------------------------------------------- * * Input parameters are listed first. They are not modified by CHOLMOD. * * Input/output are listed next. They must be defined on input, and * are modified on output. * * Output parameters are listed next. If they are pointers, they must * point to allocated space on input, but their contents are not defined * on input. * * Workspace parameters appear next. They are used in only two routines * in the Supernodal module. * * The cholmod_common *Common parameter always appears as the last * parameter. It is always an input/output parameter. */ #ifndef CHOLMOD_H #define CHOLMOD_H /* make it easy for C++ programs to include CHOLMOD */ #ifdef __cplusplus extern "C" { #endif /* assume large file support. If problems occur, compile with -DNLARGEFILE */ #include "cholmod_io64.h" #include "SuiteSparse_config.h" #include "cholmod_config.h" /* CHOLMOD always includes the Core module. */ #include "cholmod_core.h" #ifndef NCHECK #include "cholmod_check.h" #endif #ifndef NCHOLESKY #include "cholmod_cholesky.h" #endif #ifndef NMATRIXOPS #include "cholmod_matrixops.h" #endif #ifndef NMODIFY #include "cholmod_modify.h" #endif #ifndef NCAMD #include "cholmod_camd.h" #endif #ifndef NPARTITION #include "cholmod_partition.h" #endif #ifndef NSUPERNODAL #include "cholmod_supernodal.h" #endif #ifdef __cplusplus } #endif #endif Matrix/src/CHOLMOD/Include/License.txt0000644000175100001440000000041211770402705017116 0ustar hornikusersCHOLMOD/Include/* files. Copyright (C) 2005-2006, either Univ. of Florida or T. Davis, depending on the file. Refer to each include file in this directory; each file is licensed separately, according to the Module for which it contains definitions and prototypes. Matrix/src/CHOLMOD/Include/cholmod_modify.h0000644000175100001440000003132112271765436020155 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_modify.h ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_modify.h. * Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager * CHOLMOD/Include/cholmod_modify.h is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* CHOLMOD Modify module. * * Sparse Cholesky modification routines: update / downdate / rowadd / rowdel. * Can also modify a corresponding solution to Lx=b when L is modified. This * module is most useful when applied on a Cholesky factorization computed by * the Cholesky module, but it does not actually require the Cholesky module. * The Core module can create an identity Cholesky factorization (LDL' where * L=D=I) that can then by modified by these routines. * * Primary routines: * ----------------- * * cholmod_updown multiple rank update/downdate * cholmod_rowadd add a row to an LDL' factorization * cholmod_rowdel delete a row from an LDL' factorization * * Secondary routines: * ------------------- * * cholmod_updown_solve update/downdate, and modify solution to Lx=b * cholmod_updown_mark update/downdate, and modify solution to partial Lx=b * cholmod_updown_mask update/downdate for LPDASA * cholmod_rowadd_solve add a row, and update solution to Lx=b * cholmod_rowadd_mark add a row, and update solution to partial Lx=b * cholmod_rowdel_solve delete a row, and downdate Lx=b * cholmod_rowdel_mark delete a row, and downdate solution to partial Lx=b * * Requires the Core module. Not required by any other CHOLMOD module. */ #ifndef CHOLMOD_MODIFY_H #define CHOLMOD_MODIFY_H #include "cholmod_core.h" /* -------------------------------------------------------------------------- */ /* cholmod_updown: multiple rank update/downdate */ /* -------------------------------------------------------------------------- */ /* Compute the new LDL' factorization of LDL'+CC' (an update) or LDL'-CC' * (a downdate). The factor object L need not be an LDL' factorization; it * is converted to one if it isn't. */ int cholmod_updown ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_updown (int, cholmod_sparse *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_updown_solve: update/downdate, and modify solution to Lx=b */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_updown, except that it also updates/downdates the * solution to Lx=b+DeltaB. x and b must be n-by-1 dense matrices. b is not * need as input to this routine, but a sparse change to b is (DeltaB). Only * entries in DeltaB corresponding to columns modified in L are accessed; the * rest must be zero. */ int cholmod_updown_solve ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_updown_solve (int, cholmod_sparse *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_updown_mark: update/downdate, and modify solution to partial Lx=b */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_updown_solve, except only part of L is used in * the update/downdate of the solution to Lx=b. This routine is an "expert" * routine. It is meant for use in LPDASA only. See cholmod_updown.c for * a description of colmark. */ int cholmod_updown_mark ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ int *colmark, /* int array of size n. See cholmod_updown.c */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_updown_mark (int, cholmod_sparse *, SuiteSparse_long *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_updown_mask: update/downdate, for LPDASA */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_updown_mark, except has an additional "mask" * argument. This routine is an "expert" routine. It is meant for use in * LPDASA only. See cholmod_updown.c for a description of mask. */ int cholmod_updown_mask ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ int *colmark, /* int array of size n. See cholmod_updown.c */ int *mask, /* size n */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_updown_mask (int, cholmod_sparse *, SuiteSparse_long *, SuiteSparse_long *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowadd: add a row to an LDL' factorization (a rank-2 update) */ /* -------------------------------------------------------------------------- */ /* cholmod_rowadd adds a row to the LDL' factorization. It computes the kth * row and kth column of L, and then updates the submatrix L (k+1:n,k+1:n) * accordingly. The kth row and column of L must originally be equal to the * kth row and column of the identity matrix. The kth row/column of L is * computed as the factorization of the kth row/column of the matrix to * factorize, which is provided as a single n-by-1 sparse matrix R. */ int cholmod_rowadd ( /* ---- input ---- */ size_t k, /* row/column index to add */ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowadd (size_t, cholmod_sparse *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowadd_solve: add a row, and update solution to Lx=b */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_rowadd, and also updates the solution to Lx=b * See cholmod_updown for a description of how Lx=b is updated. There is on * additional parameter: bk specifies the new kth entry of b. */ int cholmod_rowadd_solve ( /* ---- input ---- */ size_t k, /* row/column index to add */ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */ double bk [2], /* kth entry of the right-hand-side b */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowadd_solve (size_t, cholmod_sparse *, double *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowadd_mark: add a row, and update solution to partial Lx=b */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_rowadd_solve, except only part of L is used in * the update/downdate of the solution to Lx=b. This routine is an "expert" * routine. It is meant for use in LPDASA only. */ int cholmod_rowadd_mark ( /* ---- input ---- */ size_t k, /* row/column index to add */ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */ double bk [2], /* kth entry of the right hand side, b */ int *colmark, /* int array of size n. See cholmod_updown.c */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowadd_mark (size_t, cholmod_sparse *, double *, SuiteSparse_long *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowdel: delete a row from an LDL' factorization (a rank-2 update) */ /* -------------------------------------------------------------------------- */ /* Sets the kth row and column of L to be the kth row and column of the identity * matrix, and updates L(k+1:n,k+1:n) accordingly. To reduce the running time, * the caller can optionally provide the nonzero pattern (or an upper bound) of * kth row of L, as the sparse n-by-1 vector R. Provide R as NULL if you want * CHOLMOD to determine this itself, which is easier for the caller, but takes * a little more time. */ int cholmod_rowdel ( /* ---- input ---- */ size_t k, /* row/column index to delete */ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowdel (size_t, cholmod_sparse *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowdel_solve: delete a row, and downdate Lx=b */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_rowdel, but also downdates the solution to Lx=b. * When row/column k of A is "deleted" from the system A*y=b, this can induce * a change to x, in addition to changes arising when L and b are modified. * If this is the case, the kth entry of y is required as input (yk) */ int cholmod_rowdel_solve ( /* ---- input ---- */ size_t k, /* row/column index to delete */ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */ double yk [2], /* kth entry in the solution to A*y=b */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowdel_solve (size_t, cholmod_sparse *, double *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowdel_mark: delete a row, and downdate solution to partial Lx=b */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_rowdel_solve, except only part of L is used in * the update/downdate of the solution to Lx=b. This routine is an "expert" * routine. It is meant for use in LPDASA only. */ int cholmod_rowdel_mark ( /* ---- input ---- */ size_t k, /* row/column index to delete */ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */ double yk [2], /* kth entry in the solution to A*y=b */ int *colmark, /* int array of size n. See cholmod_updown.c */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowdel_mark (size_t, cholmod_sparse *, double *, SuiteSparse_long *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; #endif Matrix/src/CHOLMOD/Include/cholmod_complexity.h0000644000175100001440000002224412271765436021067 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_complexity.h ========================================= */ /* ========================================================================== */ /* Define operations on pattern, real, complex, and zomplex objects. * * The xtype of an object defines it numerical type. A qttern object has no * numerical values (A->x and A->z are NULL). A real object has no imaginary * qrt (A->x is used, A->z is NULL). A complex object has an imaginary qrt * that is stored interleaved with its real qrt (A->x is of size 2*nz, A->z * is NULL). A zomplex object has both real and imaginary qrts, which are * stored seqrately, as in MATLAB (A->x and A->z are both used). * * XTYPE is CHOLMOD_PATTERN, _REAL, _COMPLEX or _ZOMPLEX, and is the xtype of * the template routine under construction. XTYPE2 is equal to XTYPE, except * if XTYPE is CHOLMOD_PATTERN, in which case XTYPE is CHOLMOD_REAL. * XTYPE and XTYPE2 are defined in cholmod_template.h. */ /* -------------------------------------------------------------------------- */ /* pattern */ /* -------------------------------------------------------------------------- */ #define P_TEMPLATE(name) p_ ## name #define P_ASSIGN2(x,z,p,ax,az,q) x [p] = 1 #define P_PRINT(k,x,z,p) PRK(k, ("1")) /* -------------------------------------------------------------------------- */ /* real */ /* -------------------------------------------------------------------------- */ #define R_TEMPLATE(name) r_ ## name #define R_ASSEMBLE(x,z,p,ax,az,q) x [p] += ax [q] #define R_ASSIGN(x,z,p,ax,az,q) x [p] = ax [q] #define R_ASSIGN_CONJ(x,z,p,ax,az,q) x [p] = ax [q] #define R_ASSIGN_REAL(x,p,ax,q) x [p] = ax [q] #define R_XTYPE_OK(type) ((type) == CHOLMOD_REAL) #define R_IS_NONZERO(ax,az,q) IS_NONZERO (ax [q]) #define R_IS_ZERO(ax,az,q) IS_ZERO (ax [q]) #define R_IS_ONE(ax,az,q) (ax [q] == 1) #define R_MULT(x,z,p, ax,az,q, bx,bz,r) x [p] = ax [q] * bx [r] #define R_MULTADD(x,z,p, ax,az,q, bx,bz,r) x [p] += ax [q] * bx [r] #define R_MULTSUB(x,z,p, ax,az,q, bx,bz,r) x [p] -= ax [q] * bx [r] #define R_MULTADDCONJ(x,z,p, ax,az,q, bx,bz,r) x [p] += ax [q] * bx [r] #define R_MULTSUBCONJ(x,z,p, ax,az,q, bx,bz,r) x [p] -= ax [q] * bx [r] #define R_ADD(x,z,p, ax,az,q, bx,bz,r) x [p] = ax [q] + bx [r] #define R_ADD_REAL(x,p, ax,q, bx,r) x [p] = ax [q] + bx [r] #define R_CLEAR(x,z,p) x [p] = 0 #define R_CLEAR_IMAG(x,z,p) #define R_DIV(x,z,p,ax,az,q) x [p] /= ax [q] #define R_LLDOT(x,p, ax,az,q) x [p] -= ax [q] * ax [q] #define R_PRINT(k,x,z,p) PRK(k, ("%24.16e", x [p])) #define R_DIV_REAL(x,z,p, ax,az,q, bx,r) x [p] = ax [q] / bx [r] #define R_MULT_REAL(x,z,p, ax,az,q, bx,r) x [p] = ax [q] * bx [r] #define R_LDLDOT(x,p, ax,az,q, bx,r) x [p] -=(ax[q] * ax[q])/ bx[r] /* -------------------------------------------------------------------------- */ /* complex */ /* -------------------------------------------------------------------------- */ #define C_TEMPLATE(name) c_ ## name #define CT_TEMPLATE(name) ct_ ## name #define C_ASSEMBLE(x,z,p,ax,az,q) \ x [2*(p) ] += ax [2*(q) ] ; \ x [2*(p)+1] += ax [2*(q)+1] #define C_ASSIGN(x,z,p,ax,az,q) \ x [2*(p) ] = ax [2*(q) ] ; \ x [2*(p)+1] = ax [2*(q)+1] #define C_ASSIGN_REAL(x,p,ax,q) x [2*(p)] = ax [2*(q)] #define C_ASSIGN_CONJ(x,z,p,ax,az,q) \ x [2*(p) ] = ax [2*(q) ] ; \ x [2*(p)+1] = -ax [2*(q)+1] #define C_XTYPE_OK(type) ((type) == CHOLMOD_COMPLEX) #define C_IS_NONZERO(ax,az,q) \ (IS_NONZERO (ax [2*(q)]) || IS_NONZERO (ax [2*(q)+1])) #define C_IS_ZERO(ax,az,q) \ (IS_ZERO (ax [2*(q)]) && IS_ZERO (ax [2*(q)+1])) #define C_IS_ONE(ax,az,q) \ ((ax [2*(q)] == 1) && IS_ZERO (ax [2*(q)+1])) #define C_IMAG_IS_NONZERO(ax,az,q) (IS_NONZERO (ax [2*(q)+1])) #define C_MULT(x,z,p, ax,az,q, bx,bz,r) \ x [2*(p) ] = ax [2*(q) ] * bx [2*(r)] - ax [2*(q)+1] * bx [2*(r)+1] ; \ x [2*(p)+1] = ax [2*(q)+1] * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1] #define C_MULTADD(x,z,p, ax,az,q, bx,bz,r) \ x [2*(p) ] += ax [2*(q) ] * bx [2*(r)] - ax [2*(q)+1] * bx [2*(r)+1] ; \ x [2*(p)+1] += ax [2*(q)+1] * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1] #define C_MULTSUB(x,z,p, ax,az,q, bx,bz,r) \ x [2*(p) ] -= ax [2*(q) ] * bx [2*(r)] - ax [2*(q)+1] * bx [2*(r)+1] ; \ x [2*(p)+1] -= ax [2*(q)+1] * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1] /* s += conj(a)*b */ #define C_MULTADDCONJ(x,z,p, ax,az,q, bx,bz,r) \ x [2*(p) ] += ax [2*(q) ] * bx [2*(r)] + ax [2*(q)+1] * bx [2*(r)+1] ; \ x [2*(p)+1] += (-ax [2*(q)+1]) * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1] /* s -= conj(a)*b */ #define C_MULTSUBCONJ(x,z,p, ax,az,q, bx,bz,r) \ x [2*(p) ] -= ax [2*(q) ] * bx [2*(r)] + ax [2*(q)+1] * bx [2*(r)+1] ; \ x [2*(p)+1] -= (-ax [2*(q)+1]) * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1] #define C_ADD(x,z,p, ax,az,q, bx,bz,r) \ x [2*(p) ] = ax [2*(q) ] + bx [2*(r) ] ; \ x [2*(p)+1] = ax [2*(q)+1] + bx [2*(r)+1] #define C_ADD_REAL(x,p, ax,q, bx,r) \ x [2*(p)] = ax [2*(q)] + bx [2*(r)] #define C_CLEAR(x,z,p) \ x [2*(p) ] = 0 ; \ x [2*(p)+1] = 0 #define C_CLEAR_IMAG(x,z,p) \ x [2*(p)+1] = 0 /* s = s / a */ #define C_DIV(x,z,p,ax,az,q) \ Common->complex_divide ( \ x [2*(p)], x [2*(p)+1], \ ax [2*(q)], ax [2*(q)+1], \ &x [2*(p)], &x [2*(p)+1]) /* s -= conj(a)*a ; note that the result of conj(a)*a is real */ #define C_LLDOT(x,p, ax,az,q) \ x [2*(p)] -= ax [2*(q)] * ax [2*(q)] + ax [2*(q)+1] * ax [2*(q)+1] #define C_PRINT(k,x,z,p) PRK(k, ("(%24.16e,%24.16e)", x [2*(p)], x [2*(p)+1])) #define C_DIV_REAL(x,z,p, ax,az,q, bx,r) \ x [2*(p) ] = ax [2*(q) ] / bx [2*(r)] ; \ x [2*(p)+1] = ax [2*(q)+1] / bx [2*(r)] #define C_MULT_REAL(x,z,p, ax,az,q, bx,r) \ x [2*(p) ] = ax [2*(q) ] * bx [2*(r)] ; \ x [2*(p)+1] = ax [2*(q)+1] * bx [2*(r)] /* s -= conj(a)*a/t */ #define C_LDLDOT(x,p, ax,az,q, bx,r) \ x [2*(p)] -= (ax [2*(q)] * ax [2*(q)] + ax [2*(q)+1] * ax [2*(q)+1]) / bx[r] /* -------------------------------------------------------------------------- */ /* zomplex */ /* -------------------------------------------------------------------------- */ #define Z_TEMPLATE(name) z_ ## name #define ZT_TEMPLATE(name) zt_ ## name #define Z_ASSEMBLE(x,z,p,ax,az,q) \ x [p] += ax [q] ; \ z [p] += az [q] #define Z_ASSIGN(x,z,p,ax,az,q) \ x [p] = ax [q] ; \ z [p] = az [q] #define Z_ASSIGN_REAL(x,p,ax,q) x [p] = ax [q] #define Z_ASSIGN_CONJ(x,z,p,ax,az,q) \ x [p] = ax [q] ; \ z [p] = -az [q] #define Z_XTYPE_OK(type) ((type) == CHOLMOD_ZOMPLEX) #define Z_IS_NONZERO(ax,az,q) \ (IS_NONZERO (ax [q]) || IS_NONZERO (az [q])) #define Z_IS_ZERO(ax,az,q) \ (IS_ZERO (ax [q]) && IS_ZERO (az [q])) #define Z_IS_ONE(ax,az,q) \ ((ax [q] == 1) && IS_ZERO (az [q])) #define Z_IMAG_IS_NONZERO(ax,az,q) (IS_NONZERO (az [q])) #define Z_MULT(x,z,p, ax,az,q, bx,bz,r) \ x [p] = ax [q] * bx [r] - az [q] * bz [r] ; \ z [p] = az [q] * bx [r] + ax [q] * bz [r] #define Z_MULTADD(x,z,p, ax,az,q, bx,bz,r) \ x [p] += ax [q] * bx [r] - az [q] * bz [r] ; \ z [p] += az [q] * bx [r] + ax [q] * bz [r] #define Z_MULTSUB(x,z,p, ax,az,q, bx,bz,r) \ x [p] -= ax [q] * bx [r] - az [q] * bz [r] ; \ z [p] -= az [q] * bx [r] + ax [q] * bz [r] #define Z_MULTADDCONJ(x,z,p, ax,az,q, bx,bz,r) \ x [p] += ax [q] * bx [r] + az [q] * bz [r] ; \ z [p] += (-az [q]) * bx [r] + ax [q] * bz [r] #define Z_MULTSUBCONJ(x,z,p, ax,az,q, bx,bz,r) \ x [p] -= ax [q] * bx [r] + az [q] * bz [r] ; \ z [p] -= (-az [q]) * bx [r] + ax [q] * bz [r] #define Z_ADD(x,z,p, ax,az,q, bx,bz,r) \ x [p] = ax [q] + bx [r] ; \ z [p] = az [q] + bz [r] #define Z_ADD_REAL(x,p, ax,q, bx,r) \ x [p] = ax [q] + bx [r] #define Z_CLEAR(x,z,p) \ x [p] = 0 ; \ z [p] = 0 #define Z_CLEAR_IMAG(x,z,p) \ z [p] = 0 /* s = s/a */ #define Z_DIV(x,z,p,ax,az,q) \ Common->complex_divide (x [p], z [p], ax [q], az [q], &x [p], &z [p]) /* s -= conj(a)*a ; note that the result of conj(a)*a is real */ #define Z_LLDOT(x,p, ax,az,q) \ x [p] -= ax [q] * ax [q] + az [q] * az [q] #define Z_PRINT(k,x,z,p) PRK(k, ("(%24.16e,%24.16e)", x [p], z [p])) #define Z_DIV_REAL(x,z,p, ax,az,q, bx,r) \ x [p] = ax [q] / bx [r] ; \ z [p] = az [q] / bx [r] #define Z_MULT_REAL(x,z,p, ax,az,q, bx,r) \ x [p] = ax [q] * bx [r] ; \ z [p] = az [q] * bx [r] /* s -= conj(a)*a/t */ #define Z_LDLDOT(x,p, ax,az,q, bx,r) \ x [p] -= (ax [q] * ax [q] + az [q] * az [q]) / bx[r] /* -------------------------------------------------------------------------- */ /* all classes */ /* -------------------------------------------------------------------------- */ /* Check if A->xtype and the two arrays A->x and A->z are valid. Set status to * invalid, unless status is already "out of memory". A can be a sparse matrix, * dense matrix, factor, or triplet. */ #define RETURN_IF_XTYPE_INVALID(A,xtype1,xtype2,result) \ { \ if ((A)->xtype < (xtype1) || (A)->xtype > (xtype2) || \ ((A)->xtype != CHOLMOD_PATTERN && ((A)->x) == NULL) || \ ((A)->xtype == CHOLMOD_ZOMPLEX && ((A)->z) == NULL)) \ { \ if (Common->status != CHOLMOD_OUT_OF_MEMORY) \ { \ ERROR (CHOLMOD_INVALID, "invalid xtype") ; \ } \ return (result) ; \ } \ } Matrix/src/CHOLMOD/Include/cholmod_io64.h0000644000175100001440000000320212271765436017444 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_io64 ================================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_io64.h. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_io64.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* Definitions required for large file I/O, which must come before any other * #includes. These are not used if -DNLARGEFILE is defined at compile time. * Large file support may not be portable across all platforms and compilers; * if you encounter an error here, compile your code with -DNLARGEFILE. In * particular, you must use -DNLARGEFILE for MATLAB 6.5 or earlier (which does * not have the io64.h include file). */ #ifndef CHOLMOD_IO_H #define CHOLMOD_IO_H /* skip all of this if NLARGEFILE is defined at the compiler command line */ #ifndef NLARGEFILE #if defined(MATLAB_MEX_FILE) || defined(MATHWORKS) /* CHOLMOD is being compiled as a MATLAB mexFunction, or for use in MATLAB */ #include "io64.h" #else /* CHOLMOD is being compiled in a stand-alone library */ #undef _LARGEFILE64_SOURCE #define _LARGEFILE64_SOURCE #undef _FILE_OFFSET_BITS #define _FILE_OFFSET_BITS 64 #endif #endif #endif Matrix/src/CHOLMOD/Include/cholmod_camd.h0000644000175100001440000000717712271765436017606 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_camd.h =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_camd.h. * Copyright (C) 2005-2013, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_partition.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* CHOLMOD Partition module, interface to CAMD, CCOLAMD, and CSYMAMD * * An interface to CCOLAMD and CSYMAMD, constrained minimum degree ordering * methods which order a matrix following constraints determined via nested * dissection. * * These functions do not require METIS. They are installed unless NCAMD * is defined: * cholmod_ccolamd interface to CCOLAMD ordering * cholmod_csymamd interface to CSYMAMD ordering * cholmod_camd interface to CAMD ordering * * Requires the Core and Cholesky modules, and two packages: CAMD, * and CCOLAMD. Used by functions in the Partition Module. */ #ifndef CHOLMOD_CAMD_H #define CHOLMOD_CAMD_H #include "cholmod_core.h" /* -------------------------------------------------------------------------- */ /* cholmod_ccolamd */ /* -------------------------------------------------------------------------- */ /* Order AA' or A(:,f)*A(:,f)' using CCOLAMD. */ int cholmod_ccolamd ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int *Cmember, /* size A->nrow. Cmember [i] = c if row i is in the * constraint set c. c must be >= 0. The # of * constraint sets is max (Cmember) + 1. If Cmember is * NULL, then it is interpretted as Cmember [i] = 0 for * all i */ /* ---- output --- */ int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_ccolamd (cholmod_sparse *, SuiteSparse_long *, size_t, SuiteSparse_long *, SuiteSparse_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_csymamd */ /* -------------------------------------------------------------------------- */ /* Order A using CSYMAMD. */ int cholmod_csymamd ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ /* ---- output --- */ int *Cmember, /* size nrow. see cholmod_ccolamd above */ int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_csymamd (cholmod_sparse *, SuiteSparse_long *, SuiteSparse_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_camd */ /* -------------------------------------------------------------------------- */ /* Order A using CAMD. */ int cholmod_camd ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ int *Cmember, /* size nrow. see cholmod_ccolamd above */ int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_camd (cholmod_sparse *, SuiteSparse_long *, size_t, SuiteSparse_long *, SuiteSparse_long *, cholmod_common *) ; #endif Matrix/src/CHOLMOD/Include/cholmod_blas.h0000644000175100001440000003320412271765436017611 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_blas.h =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_blas.h. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_blas.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* This does not need to be included in the user's program. */ #ifndef CHOLMOD_BLAS_H #define CHOLMOD_BLAS_H /* ========================================================================== */ /* === Architecture ========================================================= */ /* ========================================================================== */ #if defined (__sun) || defined (MSOL2) || defined (ARCH_SOL2) #define CHOLMOD_SOL2 #define CHOLMOD_ARCHITECTURE "Sun Solaris" #elif defined (__sgi) || defined (MSGI) || defined (ARCH_SGI) #define CHOLMOD_SGI #define CHOLMOD_ARCHITECTURE "SGI Irix" #elif defined (__linux) || defined (MGLNX86) || defined (ARCH_GLNX86) #define CHOLMOD_LINUX #define CHOLMOD_ARCHITECTURE "Linux" #elif defined (__APPLE__) #define CHOLMOD_MAC #define CHOLMOD_ARCHITECTURE "Mac" #elif defined (_AIX) || defined (MIBM_RS) || defined (ARCH_IBM_RS) #define CHOLMOD_AIX #define CHOLMOD_ARCHITECTURE "IBM AIX" /* recent reports from IBM AIX seem to indicate that this is not needed: */ /* #define BLAS_NO_UNDERSCORE */ #elif defined (__alpha) || defined (MALPHA) || defined (ARCH_ALPHA) #define CHOLMOD_ALPHA #define CHOLMOD_ARCHITECTURE "Compaq Alpha" #elif defined (_WIN32) || defined (WIN32) || defined (_WIN64) || defined (WIN64) #if defined (__MINGW32__) || defined (__MINGW32__) #define CHOLMOD_MINGW #elif defined (__CYGWIN32__) || defined (__CYGWIN32__) #define CHOLMOD_CYGWIN #else #define CHOLMOD_WINDOWS #define BLAS_NO_UNDERSCORE #endif #define CHOLMOD_ARCHITECTURE "Microsoft Windows" #elif defined (__hppa) || defined (__hpux) || defined (MHPUX) || defined (ARCH_HPUX) #define CHOLMOD_HP #define CHOLMOD_ARCHITECTURE "HP Unix" #define BLAS_NO_UNDERSCORE #elif defined (__hp700) || defined (MHP700) || defined (ARCH_HP700) #define CHOLMOD_HP #define CHOLMOD_ARCHITECTURE "HP 700 Unix" #define BLAS_NO_UNDERSCORE #else /* If the architecture is unknown, and you call the BLAS, you may need to */ /* define BLAS_BY_VALUE, BLAS_NO_UNDERSCORE, and/or BLAS_CHAR_ARG yourself. */ #define CHOLMOD_ARCHITECTURE "unknown" #endif /* ========================================================================== */ /* === BLAS and LAPACK names ================================================ */ /* ========================================================================== */ /* Prototypes for the various versions of the BLAS. */ /* Determine if the 64-bit Sun Performance BLAS is to be used */ #if defined(CHOLMOD_SOL2) && !defined(NSUNPERF) && defined(BLAS64) #define SUN64 #endif #ifdef SUN64 #define BLAS_DTRSV dtrsv_64_ #define BLAS_DGEMV dgemv_64_ #define BLAS_DTRSM dtrsm_64_ #define BLAS_DGEMM dgemm_64_ #define BLAS_DSYRK dsyrk_64_ #define BLAS_DGER dger_64_ #define BLAS_DSCAL dscal_64_ #define LAPACK_DPOTRF dpotrf_64_ #define BLAS_ZTRSV ztrsv_64_ #define BLAS_ZGEMV zgemv_64_ #define BLAS_ZTRSM ztrsm_64_ #define BLAS_ZGEMM zgemm_64_ #define BLAS_ZHERK zherk_64_ #define BLAS_ZGER zgeru_64_ #define BLAS_ZSCAL zscal_64_ #define LAPACK_ZPOTRF zpotrf_64_ #elif defined (BLAS_NO_UNDERSCORE) #define BLAS_DTRSV dtrsv #define BLAS_DGEMV dgemv #define BLAS_DTRSM dtrsm #define BLAS_DGEMM dgemm #define BLAS_DSYRK dsyrk #define BLAS_DGER dger #define BLAS_DSCAL dscal #define LAPACK_DPOTRF dpotrf #define BLAS_ZTRSV ztrsv #define BLAS_ZGEMV zgemv #define BLAS_ZTRSM ztrsm #define BLAS_ZGEMM zgemm #define BLAS_ZHERK zherk #define BLAS_ZGER zgeru #define BLAS_ZSCAL zscal #define LAPACK_ZPOTRF zpotrf #else #define BLAS_DTRSV dtrsv_ #define BLAS_DGEMV dgemv_ #define BLAS_DTRSM dtrsm_ #define BLAS_DGEMM dgemm_ #define BLAS_DSYRK dsyrk_ #define BLAS_DGER dger_ #define BLAS_DSCAL dscal_ #define LAPACK_DPOTRF dpotrf_ #define BLAS_ZTRSV ztrsv_ #define BLAS_ZGEMV zgemv_ #define BLAS_ZTRSM ztrsm_ #define BLAS_ZGEMM zgemm_ #define BLAS_ZHERK zherk_ #define BLAS_ZGER zgeru_ #define BLAS_ZSCAL zscal_ #define LAPACK_ZPOTRF zpotrf_ #endif /* ========================================================================== */ /* === BLAS and LAPACK integer arguments ==================================== */ /* ========================================================================== */ /* Compile CHOLMOD, UMFPACK, and SPQR with -DBLAS64 if you have a BLAS that * uses 64-bit integers */ #if defined (LONGBLAS) || defined (BLAS64) #define BLAS_INT SuiteSparse_long #else #define BLAS_INT int #endif /* If the BLAS integer is smaller than the basic CHOLMOD integer, then we need * to check for integer overflow when converting from Int to BLAS_INT. If * any integer overflows, the externally-defined BLAS_OK variable is * set to FALSE. BLAS_OK should be set to TRUE before calling any * BLAS_* macro. */ #define CHECK_BLAS_INT (sizeof (BLAS_INT) < sizeof (Int)) #define EQ(K,k) (((BLAS_INT) K) == ((Int) k)) /* ========================================================================== */ /* === BLAS and LAPACK prototypes and macros ================================ */ /* ========================================================================== */ void BLAS_DGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta, double *Y, BLAS_INT *incy) ; #define BLAS_dgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \ { \ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \ if (CHECK_BLAS_INT && !(EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && \ EQ (INCX,incx) && EQ (INCY,incy))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_DGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \ } \ } void BLAS_ZGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta, double *Y, BLAS_INT *incy) ; #define BLAS_zgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \ { \ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \ if (CHECK_BLAS_INT && !(EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && \ EQ (INCX,incx) && EQ (INCY,incy))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_ZGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \ } \ } void BLAS_DTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A, BLAS_INT *lda, double *X, BLAS_INT *incx) ; #define BLAS_dtrsv(uplo,trans,diag,n,A,lda,X,incx) \ { \ BLAS_INT N = n, LDA = lda, INCX = incx ; \ if (CHECK_BLAS_INT && !(EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_DTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \ } \ } void BLAS_ZTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A, BLAS_INT *lda, double *X, BLAS_INT *incx) ; #define BLAS_ztrsv(uplo,trans,diag,n,A,lda,X,incx) \ { \ BLAS_INT N = n, LDA = lda, INCX = incx ; \ if (CHECK_BLAS_INT && !(EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_ZTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \ } \ } void BLAS_DTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m, BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B, BLAS_INT *ldb) ; #define BLAS_dtrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \ { \ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \ if (CHECK_BLAS_INT && !(EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && \ EQ (LDB,ldb))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_DTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\ } \ } void BLAS_ZTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m, BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B, BLAS_INT *ldb) ; #define BLAS_ztrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \ { \ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \ if (CHECK_BLAS_INT && !(EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && \ EQ (LDB,ldb))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_ZTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\ } \ } void BLAS_DGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n, BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B, BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ; #define BLAS_dgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \ { \ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \ if (CHECK_BLAS_INT && !(EQ (M,m) && EQ (N,n) && EQ (K,k) && \ EQ (LDA,lda) && EQ (LDB,ldb) && EQ (LDC,ldc))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_DGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \ C, &LDC) ; \ } \ } void BLAS_ZGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n, BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B, BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ; #define BLAS_zgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \ { \ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \ if (CHECK_BLAS_INT && !(EQ (M,m) && EQ (N,n) && EQ (K,k) && \ EQ (LDA,lda) && EQ (LDB,ldb) && EQ (LDC,ldc))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_ZGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \ C, &LDC) ; \ } \ } void BLAS_DSYRK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *beta, double *C, BLAS_INT *ldc) ; #define BLAS_dsyrk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \ { \ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \ if (CHECK_BLAS_INT && !(EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && \ EQ (LDC,ldc))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_DSYRK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \ } \ } \ void BLAS_ZHERK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *beta, double *C, BLAS_INT *ldc) ; #define BLAS_zherk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \ { \ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \ if (CHECK_BLAS_INT && !(EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && \ EQ (LDC,ldc))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_ZHERK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \ } \ } \ void LAPACK_DPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda, BLAS_INT *info) ; #define LAPACK_dpotrf(uplo,n,A,lda,info) \ { \ BLAS_INT N = n, LDA = lda, INFO = 1 ; \ if (CHECK_BLAS_INT && !(EQ (N,n) && EQ (LDA,lda))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ LAPACK_DPOTRF (uplo, &N, A, &LDA, &INFO) ; \ } \ info = INFO ; \ } void LAPACK_ZPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda, BLAS_INT *info) ; #define LAPACK_zpotrf(uplo,n,A,lda,info) \ { \ BLAS_INT N = n, LDA = lda, INFO = 1 ; \ if (CHECK_BLAS_INT && !(EQ (N,n) && EQ (LDA,lda))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ LAPACK_ZPOTRF (uplo, &N, A, &LDA, &INFO) ; \ } \ info = INFO ; \ } /* ========================================================================== */ void BLAS_DSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ; #define BLAS_dscal(n,alpha,Y,incy) \ { \ BLAS_INT N = n, INCY = incy ; \ if (CHECK_BLAS_INT && !(EQ (N,n) && EQ (INCY,incy))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_DSCAL (&N, alpha, Y, &INCY) ; \ } \ } void BLAS_ZSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ; #define BLAS_zscal(n,alpha,Y,incy) \ { \ BLAS_INT N = n, INCY = incy ; \ if (CHECK_BLAS_INT && !(EQ (N,n) && EQ (INCY,incy))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_ZSCAL (&N, alpha, Y, &INCY) ; \ } \ } void BLAS_DGER (BLAS_INT *m, BLAS_INT *n, double *alpha, double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy, double *A, BLAS_INT *lda) ; #define BLAS_dger(m,n,alpha,X,incx,Y,incy,A,lda) \ { \ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \ if (CHECK_BLAS_INT && !(EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && \ EQ (INCX,incx) && EQ (INCY,incy))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_DGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \ } \ } void BLAS_ZGER (BLAS_INT *m, BLAS_INT *n, double *alpha, double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy, double *A, BLAS_INT *lda) ; #define BLAS_zgeru(m,n,alpha,X,incx,Y,incy,A,lda) \ { \ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \ if (CHECK_BLAS_INT && !(EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && \ EQ (INCX,incx) && EQ (INCY,incy))) \ { \ BLAS_OK = FALSE ; \ } \ if (!CHECK_BLAS_INT || BLAS_OK) \ { \ BLAS_ZGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \ } \ } #endif Matrix/src/CHOLMOD/Include/cholmod_matrixops.h0000644000175100001440000002076312271765436020724 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_matrixops.h ========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_matrixops.h. * Copyright (C) 2005-2006, Timothy A. Davis * CHOLMOD/Include/cholmod_matrixops.h is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* CHOLMOD MatrixOps module. * * Basic operations on sparse and dense matrices. * * cholmod_drop A = entries in A with abs. value >= tol * cholmod_norm_dense s = norm (X), 1-norm, inf-norm, or 2-norm * cholmod_norm_sparse s = norm (A), 1-norm or inf-norm * cholmod_horzcat C = [A,B] * cholmod_scale A = diag(s)*A, A*diag(s), s*A or diag(s)*A*diag(s) * cholmod_sdmult Y = alpha*(A*X) + beta*Y or alpha*(A'*X) + beta*Y * cholmod_ssmult C = A*B * cholmod_submatrix C = A (i,j), where i and j are arbitrary vectors * cholmod_vertcat C = [A ; B] * * A, B, C: sparse matrices (cholmod_sparse) * X, Y: dense matrices (cholmod_dense) * s: scalar or vector * * Requires the Core module. Not required by any other CHOLMOD module. */ #ifndef CHOLMOD_MATRIXOPS_H #define CHOLMOD_MATRIXOPS_H #include "cholmod_core.h" /* -------------------------------------------------------------------------- */ /* cholmod_drop: drop entries with small absolute value */ /* -------------------------------------------------------------------------- */ int cholmod_drop ( /* ---- input ---- */ double tol, /* keep entries with absolute value > tol */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix to drop entries from */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_drop (double, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_norm_dense: s = norm (X), 1-norm, inf-norm, or 2-norm */ /* -------------------------------------------------------------------------- */ double cholmod_norm_dense ( /* ---- input ---- */ cholmod_dense *X, /* matrix to compute the norm of */ int norm, /* type of norm: 0: inf. norm, 1: 1-norm, 2: 2-norm */ /* --------------- */ cholmod_common *Common ) ; double cholmod_l_norm_dense (cholmod_dense *, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_norm_sparse: s = norm (A), 1-norm or inf-norm */ /* -------------------------------------------------------------------------- */ double cholmod_norm_sparse ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to compute the norm of */ int norm, /* type of norm: 0: inf. norm, 1: 1-norm */ /* --------------- */ cholmod_common *Common ) ; double cholmod_l_norm_sparse (cholmod_sparse *, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_horzcat: C = [A,B] */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_horzcat ( /* ---- input ---- */ cholmod_sparse *A, /* left matrix to concatenate */ cholmod_sparse *B, /* right matrix to concatenate */ int values, /* if TRUE compute the numerical values of C */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_horzcat (cholmod_sparse *, cholmod_sparse *, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_scale: A = diag(s)*A, A*diag(s), s*A or diag(s)*A*diag(s) */ /* -------------------------------------------------------------------------- */ /* scaling modes, selected by the scale input parameter: */ #define CHOLMOD_SCALAR 0 /* A = s*A */ #define CHOLMOD_ROW 1 /* A = diag(s)*A */ #define CHOLMOD_COL 2 /* A = A*diag(s) */ #define CHOLMOD_SYM 3 /* A = diag(s)*A*diag(s) */ int cholmod_scale ( /* ---- input ---- */ cholmod_dense *S, /* scale factors (scalar or vector) */ int scale, /* type of scaling to compute */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix to scale */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_scale (cholmod_dense *, int, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_sdmult: Y = alpha*(A*X) + beta*Y or alpha*(A'*X) + beta*Y */ /* -------------------------------------------------------------------------- */ /* Sparse matrix times dense matrix */ int cholmod_sdmult ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to multiply */ int transpose, /* use A if 0, or A' otherwise */ double alpha [2], /* scale factor for A */ double beta [2], /* scale factor for Y */ cholmod_dense *X, /* dense matrix to multiply */ /* ---- in/out --- */ cholmod_dense *Y, /* resulting dense matrix */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_sdmult (cholmod_sparse *, int, double *, double *, cholmod_dense *, cholmod_dense *Y, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_ssmult: C = A*B */ /* -------------------------------------------------------------------------- */ /* Sparse matrix times sparse matrix */ cholmod_sparse *cholmod_ssmult ( /* ---- input ---- */ cholmod_sparse *A, /* left matrix to multiply */ cholmod_sparse *B, /* right matrix to multiply */ int stype, /* requested stype of C */ int values, /* TRUE: do numerical values, FALSE: pattern only */ int sorted, /* if TRUE then return C with sorted columns */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_ssmult (cholmod_sparse *, cholmod_sparse *, int, int, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_submatrix: C = A (r,c), where i and j are arbitrary vectors */ /* -------------------------------------------------------------------------- */ /* rsize < 0 denotes ":" in MATLAB notation, or more precisely 0:(A->nrow)-1. * In this case, r can be NULL. An rsize of zero, or r = NULL and rsize >= 0, * denotes "[ ]" in MATLAB notation (the empty set). * Similar rules hold for csize. */ cholmod_sparse *cholmod_submatrix ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to subreference */ int *rset, /* set of row indices, duplicates OK */ SuiteSparse_long rsize, /* size of r; rsize < 0 denotes ":" */ int *cset, /* set of column indices, duplicates OK */ SuiteSparse_long csize, /* size of c; csize < 0 denotes ":" */ int values, /* if TRUE compute the numerical values of C */ int sorted, /* if TRUE then return C with sorted columns */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_submatrix (cholmod_sparse *, SuiteSparse_long *, SuiteSparse_long, SuiteSparse_long *, SuiteSparse_long, int, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_vertcat: C = [A ; B] */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_vertcat ( /* ---- input ---- */ cholmod_sparse *A, /* left matrix to concatenate */ cholmod_sparse *B, /* right matrix to concatenate */ int values, /* if TRUE compute the numerical values of C */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_vertcat (cholmod_sparse *, cholmod_sparse *, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_symmetry: determine if a sparse matrix is symmetric */ /* -------------------------------------------------------------------------- */ int cholmod_symmetry ( /* ---- input ---- */ cholmod_sparse *A, int option, /* ---- output ---- */ int *xmatched, int *pmatched, int *nzoffdiag, int *nzdiag, /* --------------- */ cholmod_common *Common ) ; int cholmod_l_symmetry (cholmod_sparse *, int, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, cholmod_common *) ; #endif Matrix/src/CHOLMOD/Include/cholmod_internal.h0000644000175100001440000003531712271765436020513 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_internal.h =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_internal.h. * Copyright (C) 2005-2013, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_internal.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* CHOLMOD internal include file. * * This file contains internal definitions for CHOLMOD, not meant to be included * in user code. They define macros that are not prefixed with CHOLMOD_. This * file can safely #include'd in user code if you want to make use of the * macros defined here, and don't mind the possible name conflicts with your * code, however. * * Required by all CHOLMOD routines. Not required by any user routine that * uses CHOLMOMD. Unless debugging is enabled, this file does not require any * CHOLMOD module (not even the Core module). * * If debugging is enabled, all CHOLMOD modules require the Check module. * Enabling debugging requires that this file be editted. Debugging cannot be * enabled with a compiler flag. This is because CHOLMOD is exceedingly slow * when debugging is enabled. Debugging is meant for development of CHOLMOD * itself, not by users of CHOLMOD. */ #ifndef CHOLMOD_INTERNAL_H #define CHOLMOD_INTERNAL_H /* ========================================================================== */ /* === large file I/O ======================================================= */ /* ========================================================================== */ /* Definitions for large file I/O must come before any other #includes. If * this causes problems (may not be portable to all platforms), then compile * CHOLMOD with -DNLARGEFILE. You must do this for MATLAB 6.5 and earlier, * for example. */ #include "cholmod_io64.h" /* ========================================================================== */ /* === debugging and basic includes ========================================= */ /* ========================================================================== */ /* turn off debugging */ #ifndef NDEBUG #define NDEBUG #endif /* Uncomment this line to enable debugging. CHOLMOD will be very slow. #undef NDEBUG */ #ifdef MATLAB_MEX_FILE #include "mex.h" #endif #if !defined(NPRINT) || !defined(NDEBUG) #include #endif #include #include #include #include #include /* ========================================================================== */ /* === basic definitions ==================================================== */ /* ========================================================================== */ /* Some non-conforming compilers insist on defining TRUE and FALSE. */ #undef TRUE #undef FALSE #define TRUE 1 #define FALSE 0 #define BOOLEAN(x) ((x) ? TRUE : FALSE) /* NULL should already be defined, but ensure it is here. */ #ifndef NULL #define NULL ((void *) 0) #endif /* FLIP is a "negation about -1", and is used to mark an integer i that is * normally non-negative. FLIP (EMPTY) is EMPTY. FLIP of a number > EMPTY * is negative, and FLIP of a number < EMTPY is positive. FLIP (FLIP (i)) = i * for all integers i. UNFLIP (i) is >= EMPTY. */ #define EMPTY (-1) #define FLIP(i) (-(i)-2) #define UNFLIP(i) (((i) < EMPTY) ? FLIP (i) : (i)) /* MAX and MIN are not safe to use for NaN's */ #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define MAX3(a,b,c) (((a) > (b)) ? (MAX (a,c)) : (MAX (b,c))) #define MAX4(a,b,c,d) (((a) > (b)) ? (MAX3 (a,c,d)) : (MAX3 (b,c,d))) #define MIN(a,b) (((a) < (b)) ? (a) : (b)) #define IMPLIES(p,q) (!(p) || (q)) /* find the sign: -1 if x < 0, 1 if x > 0, zero otherwise. * Not safe for NaN's */ #define SIGN(x) (((x) < 0) ? (-1) : (((x) > 0) ? 1 : 0)) /* round up an integer x to a multiple of s */ #define ROUNDUP(x,s) ((s) * (((x) + ((s) - 1)) / (s))) #define ERROR(status,msg) \ CHOLMOD(error) (status, __FILE__, __LINE__, msg, Common) /* Check a pointer and return if null. Set status to invalid, unless the * status is already "out of memory" */ #define RETURN_IF_NULL(A,result) \ { \ if ((A) == NULL) \ { \ if (Common->status != CHOLMOD_OUT_OF_MEMORY) \ { \ ERROR (CHOLMOD_INVALID, "argument missing") ; \ } \ return (result) ; \ } \ } /* Return if Common is NULL or invalid */ #define RETURN_IF_NULL_COMMON(result) \ { \ if (Common == NULL) \ { \ return (result) ; \ } \ if (Common->itype != ITYPE || Common->dtype != DTYPE) \ { \ Common->status = CHOLMOD_INVALID ; \ return (result) ; \ } \ } #define IS_NAN(x) CHOLMOD_IS_NAN(x) #define IS_ZERO(x) CHOLMOD_IS_ZERO(x) #define IS_NONZERO(x) CHOLMOD_IS_NONZERO(x) #define IS_LT_ZERO(x) CHOLMOD_IS_LT_ZERO(x) #define IS_GT_ZERO(x) CHOLMOD_IS_GT_ZERO(x) #define IS_LE_ZERO(x) CHOLMOD_IS_LE_ZERO(x) /* 1e308 is a huge number that doesn't take many characters to print in a * file, in CHOLMOD/Check/cholmod_read and _write. Numbers larger than this * are interpretted as Inf, since sscanf doesn't read in Inf's properly. * This assumes IEEE double precision arithmetic. DBL_MAX would be a little * better, except that it takes too many digits to print in a file. */ #define HUGE_DOUBLE 1e308 /* ========================================================================== */ /* === int/long and double/float definitions ================================ */ /* ========================================================================== */ /* CHOLMOD is designed for 3 types of integer variables: * * (1) all integers are int * (2) most integers are int, some are SuiteSparse_long * (3) all integers are SuiteSparse_long * * and two kinds of floating-point values: * * (1) double * (2) float * * the complex types (ANSI-compatible complex, and MATLAB-compatable zomplex) * are based on the double or float type, and are not selected here. They * are typically selected via template routines. * * This gives 6 different modes in which CHOLMOD can be compiled (only the * first two are currently supported): * * DINT double, int prefix: cholmod_ * DLONG double, SuiteSparse_long prefix: cholmod_l_ * DMIX double, mixed int/SuiteSparse_long prefix: cholmod_m_ * SINT float, int prefix: cholmod_si_ * SLONG float, SuiteSparse_long prefix: cholmod_sl_ * SMIX float, mixed int/log prefix: cholmod_sm_ * * These are selected with compile time flags (-DDLONG, for example). If no * flag is selected, the default is DINT. * * All six versions use the same include files. The user-visible include files * are completely independent of which int/long/double/float version is being * used. The integer / real types in all data structures (sparse, triplet, * dense, common, and triplet) are defined at run-time, not compile-time, so * there is only one "cholmod_sparse" data type. Void pointers are used inside * that data structure to point to arrays of the proper type. Each data * structure has an itype and dtype field which determines the kind of basic * types used. These are defined in Include/cholmod_core.h. * * FUTURE WORK: support all six types (float, and mixed int/long) * * SuiteSparse_long is normally defined as long. However, for WIN64 it is * __int64. It can also be redefined for other platforms, by modifying * SuiteSparse_config.h. */ #include "SuiteSparse_config.h" /* -------------------------------------------------------------------------- */ /* Size_max: the largest value of size_t */ /* -------------------------------------------------------------------------- */ #define Size_max ((size_t) (-1)) /* routines for doing arithmetic on size_t, and checking for overflow */ size_t cholmod_add_size_t (size_t a, size_t b, int *ok) ; size_t cholmod_mult_size_t (size_t a, size_t k, int *ok) ; size_t cholmod_l_add_size_t (size_t a, size_t b, int *ok) ; size_t cholmod_l_mult_size_t (size_t a, size_t k, int *ok) ; /* -------------------------------------------------------------------------- */ /* double (also complex double), SuiteSparse_long */ /* -------------------------------------------------------------------------- */ #ifdef DLONG #define Real double #define Int SuiteSparse_long #define Int_max SuiteSparse_long_max #define CHOLMOD(name) cholmod_l_ ## name #define LONG #define DOUBLE #define ITYPE CHOLMOD_LONG #define DTYPE CHOLMOD_DOUBLE #define ID SuiteSparse_long_id /* -------------------------------------------------------------------------- */ /* double, int/SuiteSparse_long */ /* -------------------------------------------------------------------------- */ #elif defined (DMIX) #error "mixed int/SuiteSparse_long not yet supported" /* -------------------------------------------------------------------------- */ /* single, int */ /* -------------------------------------------------------------------------- */ #elif defined (SINT) #error "single-precision not yet supported" /* -------------------------------------------------------------------------- */ /* single, SuiteSparse_long */ /* -------------------------------------------------------------------------- */ #elif defined (SLONG) #error "single-precision not yet supported" /* -------------------------------------------------------------------------- */ /* single, int/SuiteSparse_long */ /* -------------------------------------------------------------------------- */ #elif defined (SMIX) #error "single-precision not yet supported" /* -------------------------------------------------------------------------- */ /* double (also complex double), int: this is the default */ /* -------------------------------------------------------------------------- */ #else #ifndef DINT #define DINT #endif #define INT #define DOUBLE #define Real double #define Int int #define Int_max INT_MAX #define CHOLMOD(name) cholmod_ ## name #define ITYPE CHOLMOD_INT #define DTYPE CHOLMOD_DOUBLE #define ID "%d" #endif /* ========================================================================== */ /* === real/complex arithmetic ============================================== */ /* ========================================================================== */ #include "cholmod_complexity.h" /* ========================================================================== */ /* === Architecture and BLAS ================================================ */ /* ========================================================================== */ #define BLAS_OK Common->blas_ok #include "cholmod_blas.h" /* ========================================================================== */ /* === debugging definitions ================================================ */ /* ========================================================================== */ #ifndef NDEBUG #include #include "cholmod.h" /* The cholmod_dump routines are in the Check module. No CHOLMOD routine * calls the cholmod_check_* or cholmod_print_* routines in the Check module, * since they use Common workspace that may already be in use. Instead, they * use the cholmod_dump_* routines defined there, which allocate their own * workspace if they need it. */ #ifndef EXTERN #define EXTERN extern #endif /* double, int */ EXTERN int cholmod_dump ; EXTERN int cholmod_dump_malloc ; SuiteSparse_long cholmod_dump_sparse (cholmod_sparse *, const char *, cholmod_common *) ; int cholmod_dump_factor (cholmod_factor *, const char *, cholmod_common *) ; int cholmod_dump_triplet (cholmod_triplet *, const char *, cholmod_common *) ; int cholmod_dump_dense (cholmod_dense *, const char *, cholmod_common *) ; int cholmod_dump_subset (int *, size_t, size_t, const char *, cholmod_common *) ; int cholmod_dump_perm (int *, size_t, size_t, const char *, cholmod_common *) ; int cholmod_dump_parent (int *, size_t, const char *, cholmod_common *) ; void cholmod_dump_init (const char *, cholmod_common *) ; int cholmod_dump_mem (const char *, SuiteSparse_long, cholmod_common *) ; void cholmod_dump_real (const char *, Real *, SuiteSparse_long, SuiteSparse_long, int, int, cholmod_common *) ; void cholmod_dump_super (SuiteSparse_long, int *, int *, int *, int *, double *, int, cholmod_common *) ; int cholmod_dump_partition (SuiteSparse_long, int *, int *, int *, int *, SuiteSparse_long, cholmod_common *) ; int cholmod_dump_work(int, int, SuiteSparse_long, cholmod_common *) ; /* double, SuiteSparse_long */ EXTERN int cholmod_l_dump ; EXTERN int cholmod_l_dump_malloc ; SuiteSparse_long cholmod_l_dump_sparse (cholmod_sparse *, const char *, cholmod_common *) ; int cholmod_l_dump_factor (cholmod_factor *, const char *, cholmod_common *) ; int cholmod_l_dump_triplet (cholmod_triplet *, const char *, cholmod_common *); int cholmod_l_dump_dense (cholmod_dense *, const char *, cholmod_common *) ; int cholmod_l_dump_subset (SuiteSparse_long *, size_t, size_t, const char *, cholmod_common *) ; int cholmod_l_dump_perm (SuiteSparse_long *, size_t, size_t, const char *, cholmod_common *) ; int cholmod_l_dump_parent (SuiteSparse_long *, size_t, const char *, cholmod_common *) ; void cholmod_l_dump_init (const char *, cholmod_common *) ; int cholmod_l_dump_mem (const char *, SuiteSparse_long, cholmod_common *) ; void cholmod_l_dump_real (const char *, Real *, SuiteSparse_long, SuiteSparse_long, int, int, cholmod_common *) ; void cholmod_l_dump_super (SuiteSparse_long, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, double *, int, cholmod_common *) ; int cholmod_l_dump_partition (SuiteSparse_long, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long, cholmod_common *) ; int cholmod_l_dump_work(int, int, SuiteSparse_long, cholmod_common *) ; #define DEBUG_INIT(s,Common) { CHOLMOD(dump_init)(s, Common) ; } #define ASSERT(expression) (assert (expression)) #define PRK(k,params) \ { \ if (CHOLMOD(dump) >= (k) && Common->print_function != NULL) \ { \ (Common->print_function) params ; \ } \ } #define PRINT0(params) PRK (0, params) #define PRINT1(params) PRK (1, params) #define PRINT2(params) PRK (2, params) #define PRINT3(params) PRK (3, params) #define PRINTM(params) \ { \ if (CHOLMOD(dump_malloc) > 0) \ { \ printf params ; \ } \ } #define DEBUG(statement) statement #else /* Debugging disabled (the normal case) */ #define PRK(k,params) #define DEBUG_INIT(s,Common) #define PRINT0(params) #define PRINT1(params) #define PRINT2(params) #define PRINT3(params) #define PRINTM(params) #define ASSERT(expression) #define DEBUG(statement) #endif #endif Matrix/src/CHOLMOD/Include/cholmod_config.h0000644000175100001440000000630612271765436020140 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_config.h ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_config.h. * Copyright (C) 2005-2013, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_config.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* CHOLMOD configuration file, for inclusion in user programs. * * You do not have to edit any CHOLMOD files to compile and install CHOLMOD. * However, if you do not use all of CHOLMOD's modules, you need to compile * with the appropriate flag, or edit this file to add the appropriate #define. * * If you wish to use CHOLMOD under the GNU LGPL license only, then you must * compile CHOLMOD with -DNMATRIXOPS -DNSUPERNODAL and -DNMODIFY. This can * be done using just -DNGPL. * * Compiler flags for CHOLMOD: * * -DNCHECK do not include the Check module. License: GNU LGPL * -DNCHOLESKY do not include the Cholesky module. License: GNU LGPL * -DNPARTITION do not include the Partition module. License: GNU LGPL * -DNCAMD do not include the interfaces to CAMD, * CCOLAMD, CSYMAND in Partition module. License: GNU LGPL * * -DNGPL do not include any GNU GPL Modules in the CHOLMOD library. * -DNMATRIXOPS do not include the MatrixOps module. License: GNU GPL * -DNMODIFY do not include the Modify module. License: GNU GPL * -DNSUPERNODAL do not include the Supernodal module. License: GNU GPL * * -DNPRINT do not print anything * * -D'LONGBLAS=long' or -DLONGBLAS='long long' defines the integers used by * LAPACK and the BLAS. Use LONGBLAS=long on Solaris to use * the 64-bit Sun Performance BLAS in cholmod_l_* routines. * You may need to use -D'LONGBLAS=long long' on the SGI * (this is not tested). * * -DNSUNPERF for Solaris only. If defined, do not use the Sun * Performance Library. The default is to use SunPerf. * You must compile CHOLMOD with -xlic_lib=sunperf. * * The Core Module (License GNU LGPL) is always included in the CHOLMOD library. */ #ifndef CHOLMOD_CONFIG_H #define CHOLMOD_CONFIG_H /* Use the compiler flag, or uncomment the definition(s), if you want to use * one or more non-default installation options: */ /* #define NCHECK #define NCHOLESKY #define NCAMD #define NPARTITION #define NGPL #define NMATRIXOPS #define NMODIFY #define NSUPERNODAL #define NPRINT #define LONGBLAS long #define LONGBLAS long long #define NSUNPERF */ /* -------------------------------------------------------------------------- */ /* if NGPL is defined, disable all GNU GPL Modules */ /* -------------------------------------------------------------------------- */ #ifdef NGPL #define NMATRIXOPS #define NMODIFY #define NSUPERNODAL #endif #endif Matrix/src/CHOLMOD/Include/cholmod_template.h0000644000175100001440000002200112271765436020474 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_template.h =========================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* undefine current xtype macros, and then define macros for current type */ /* -------------------------------------------------------------------------- */ #undef TEMPLATE #undef XTYPE #undef XTYPE2 #undef XTYPE_OK #undef ENTRY_IS_NONZERO #undef ENTRY_IS_ZERO #undef ENTRY_IS_ONE #undef IMAG_IS_NONZERO #undef ASSEMBLE #undef ASSIGN #undef ASSIGN_CONJ #undef ASSIGN2 #undef ASSIGN2_CONJ #undef ASSIGN_REAL #undef MULT #undef MULTADD #undef ADD #undef ADD_REAL #undef MULTSUB #undef MULTADDCONJ #undef MULTSUBCONJ #undef LLDOT #undef CLEAR #undef DIV #undef DIV_REAL #undef MULT_REAL #undef CLEAR_IMAG #undef LDLDOT #undef PREFIX #undef ENTRY_SIZE #undef XPRINT0 #undef XPRINT1 #undef XPRINT2 #undef XPRINT3 /* -------------------------------------------------------------------------- */ /* pattern */ /* -------------------------------------------------------------------------- */ #ifdef PATTERN #define PREFIX p_ #define TEMPLATE(name) P_TEMPLATE(name) #define XTYPE CHOLMOD_PATTERN #define XTYPE2 CHOLMOD_REAL #define XTYPE_OK(type) (TRUE) #define ENTRY_IS_NONZERO(ax,az,q) (TRUE) #define ENTRY_IS_ZERO(ax,az,q) (FALSE) #define ENTRY_IS_ONE(ax,az,q) (TRUE) #define IMAG_IS_NONZERO(ax,az,q) (FALSE) #define ENTRY_SIZE 0 #define ASSEMBLE(x,z,p,ax,az,q) #define ASSIGN(x,z,p,ax,az,q) #define ASSIGN_CONJ(x,z,p,ax,az,q) #define ASSIGN2(x,z,p,ax,az,q) P_ASSIGN2(x,z,p,ax,az,q) #define ASSIGN2_CONJ(x,z,p,ax,az,q) P_ASSIGN2(x,z,p,ax,az,q) #define ASSIGN_REAL(x,p,ax,q) #define MULT(x,z,p,ax,az,q,bx,bz,pb) #define MULTADD(x,z,p,ax,az,q,bx,bz,pb) #define ADD(x,z,p,ax,az,q,bx,bz,pb) #define ADD_REAL(x,p, ax,q, bx,r) #define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) #define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) #define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) #define LLDOT(x,p,ax,az,q) #define CLEAR(x,z,p) #define CLEAR_IMAG(x,z,p) #define DIV(x,z,p,ax,az,q) #define DIV_REAL(x,z,p, ax,az,q, bx,r) #define MULT_REAL(x,z,p, ax,az,q, bx,r) #define LDLDOT(x,p, ax,az,q, bx,r) #define XPRINT0(x,z,p) P_PRINT(0,x,z,p) #define XPRINT1(x,z,p) P_PRINT(1,x,z,p) #define XPRINT2(x,z,p) P_PRINT(2,x,z,p) #define XPRINT3(x,z,p) P_PRINT(3,x,z,p) /* -------------------------------------------------------------------------- */ /* real */ /* -------------------------------------------------------------------------- */ #elif defined (REAL) #define PREFIX r_ #define TEMPLATE(name) R_TEMPLATE(name) #define XTYPE CHOLMOD_REAL #define XTYPE2 CHOLMOD_REAL #define XTYPE_OK(type) R_XTYPE_OK(type) #define ENTRY_IS_NONZERO(ax,az,q) R_IS_NONZERO(ax,az,q) #define ENTRY_IS_ZERO(ax,az,q) R_IS_ZERO(ax,az,q) #define ENTRY_IS_ONE(ax,az,q) R_IS_ONE(ax,az,q) #define IMAG_IS_NONZERO(ax,az,q) (FALSE) #define ENTRY_SIZE 1 #define ASSEMBLE(x,z,p,ax,az,q) R_ASSEMBLE(x,z,p,ax,az,q) #define ASSIGN(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q) #define ASSIGN_CONJ(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q) #define ASSIGN2(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q) #define ASSIGN2_CONJ(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q) #define ASSIGN_REAL(x,p,ax,q) R_ASSIGN_REAL(x,p,ax,q) #define MULT(x,z,p,ax,az,q,bx,bz,pb) R_MULT(x,z,p,ax,az,q,bx,bz,pb) #define MULTADD(x,z,p,ax,az,q,bx,bz,pb) R_MULTADD(x,z,p,ax,az,q,bx,bz,pb) #define ADD(x,z,p,ax,az,q,bx,bz,pb) R_ADD(x,z,p,ax,az,q,bx,bz,pb) #define ADD_REAL(x,p, ax,q, bx,r) R_ADD_REAL(x,p, ax,q, bx,r) #define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) R_MULTSUB(x,z,p,ax,az,q,bx,bz,pb) #define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) \ R_MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) #define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) \ R_MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) #define LLDOT(x,p,ax,az,q) R_LLDOT(x,p,ax,az,q) #define CLEAR(x,z,p) R_CLEAR(x,z,p) #define CLEAR_IMAG(x,z,p) R_CLEAR_IMAG(x,z,p) #define DIV(x,z,p,ax,az,q) R_DIV(x,z,p,ax,az,q) #define DIV_REAL(x,z,p, ax,az,q, bx,r) R_DIV_REAL(x,z,p, ax,az,q, bx,r) #define MULT_REAL(x,z,p, ax,az,q, bx,r) R_MULT_REAL(x,z,p, ax,az,q, bx,r) #define LDLDOT(x,p, ax,az,q, bx,r) R_LDLDOT(x,p, ax,az,q, bx,r) #define XPRINT0(x,z,p) R_PRINT(0,x,z,p) #define XPRINT1(x,z,p) R_PRINT(1,x,z,p) #define XPRINT2(x,z,p) R_PRINT(2,x,z,p) #define XPRINT3(x,z,p) R_PRINT(3,x,z,p) /* -------------------------------------------------------------------------- */ /* complex */ /* -------------------------------------------------------------------------- */ #elif defined (COMPLEX) #define PREFIX c_ #ifdef NCONJUGATE #define TEMPLATE(name) CT_TEMPLATE(name) #else #define TEMPLATE(name) C_TEMPLATE(name) #endif #define ASSEMBLE(x,z,p,ax,az,q) C_ASSEMBLE(x,z,p,ax,az,q) #define ASSIGN(x,z,p,ax,az,q) C_ASSIGN(x,z,p,ax,az,q) #define ASSIGN_CONJ(x,z,p,ax,az,q) C_ASSIGN_CONJ(x,z,p,ax,az,q) #define ASSIGN2(x,z,p,ax,az,q) C_ASSIGN(x,z,p,ax,az,q) #define ASSIGN2_CONJ(x,z,p,ax,az,q) C_ASSIGN_CONJ(x,z,p,ax,az,q) #define ASSIGN_REAL(x,p,ax,q) C_ASSIGN_REAL(x,p,ax,q) #define XTYPE CHOLMOD_COMPLEX #define XTYPE2 CHOLMOD_COMPLEX #define XTYPE_OK(type) C_XTYPE_OK(type) #define ENTRY_IS_NONZERO(ax,az,q) C_IS_NONZERO(ax,az,q) #define ENTRY_IS_ZERO(ax,az,q) C_IS_ZERO(ax,az,q) #define ENTRY_IS_ONE(ax,az,q) C_IS_ONE(ax,az,q) #define IMAG_IS_NONZERO(ax,az,q) C_IMAG_IS_NONZERO(ax,az,q) #define ENTRY_SIZE 2 #define MULTADD(x,z,p,ax,az,q,bx,bz,pb) C_MULTADD(x,z,p,ax,az,q,bx,bz,pb) #define MULT(x,z,p,ax,az,q,bx,bz,pb) C_MULT(x,z,p,ax,az,q,bx,bz,pb) #define ADD(x,z,p,ax,az,q,bx,bz,pb) C_ADD(x,z,p,ax,az,q,bx,bz,pb) #define ADD_REAL(x,p, ax,q, bx,r) C_ADD_REAL(x,p, ax,q, bx,r) #define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) C_MULTSUB(x,z,p,ax,az,q,bx,bz,pb) #define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) \ C_MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) #define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) \ C_MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) #define LLDOT(x,p,ax,az,q) C_LLDOT(x,p,ax,az,q) #define CLEAR(x,z,p) C_CLEAR(x,z,p) #define CLEAR_IMAG(x,z,p) C_CLEAR_IMAG(x,z,p) #define DIV(x,z,p,ax,az,q) C_DIV(x,z,p,ax,az,q) #define DIV_REAL(x,z,p, ax,az,q, bx,r) C_DIV_REAL(x,z,p, ax,az,q, bx,r) #define MULT_REAL(x,z,p, ax,az,q, bx,r) C_MULT_REAL(x,z,p, ax,az,q, bx,r) #define LDLDOT(x,p, ax,az,q, bx,r) C_LDLDOT(x,p, ax,az,q, bx,r) #define XPRINT0(x,z,p) C_PRINT(0,x,z,p) #define XPRINT1(x,z,p) C_PRINT(1,x,z,p) #define XPRINT2(x,z,p) C_PRINT(2,x,z,p) #define XPRINT3(x,z,p) C_PRINT(3,x,z,p) /* -------------------------------------------------------------------------- */ /* zomplex */ /* -------------------------------------------------------------------------- */ #elif defined (ZOMPLEX) #define PREFIX z_ #ifdef NCONJUGATE #define TEMPLATE(name) ZT_TEMPLATE(name) #else #define TEMPLATE(name) Z_TEMPLATE(name) #endif #define ASSEMBLE(x,z,p,ax,az,q) Z_ASSEMBLE(x,z,p,ax,az,q) #define ASSIGN(x,z,p,ax,az,q) Z_ASSIGN(x,z,p,ax,az,q) #define ASSIGN_CONJ(x,z,p,ax,az,q) Z_ASSIGN_CONJ(x,z,p,ax,az,q) #define ASSIGN2(x,z,p,ax,az,q) Z_ASSIGN(x,z,p,ax,az,q) #define ASSIGN2_CONJ(x,z,p,ax,az,q) Z_ASSIGN_CONJ(x,z,p,ax,az,q) #define ASSIGN_REAL(x,p,ax,q) Z_ASSIGN_REAL(x,p,ax,q) #define XTYPE CHOLMOD_ZOMPLEX #define XTYPE2 CHOLMOD_ZOMPLEX #define XTYPE_OK(type) Z_XTYPE_OK(type) #define ENTRY_IS_NONZERO(ax,az,q) Z_IS_NONZERO(ax,az,q) #define ENTRY_IS_ZERO(ax,az,q) Z_IS_ZERO(ax,az,q) #define ENTRY_IS_ONE(ax,az,q) Z_IS_ONE(ax,az,q) #define IMAG_IS_NONZERO(ax,az,q) Z_IMAG_IS_NONZERO(ax,az,q) #define ENTRY_SIZE 1 #define MULTADD(x,z,p,ax,az,q,bx,bz,pb) Z_MULTADD(x,z,p,ax,az,q,bx,bz,pb) #define MULT(x,z,p,ax,az,q,bx,bz,pb) Z_MULT(x,z,p,ax,az,q,bx,bz,pb) #define ADD(x,z,p,ax,az,q,bx,bz,pb) Z_ADD(x,z,p,ax,az,q,bx,bz,pb) #define ADD_REAL(x,p, ax,q, bx,r) Z_ADD_REAL(x,p, ax,q, bx,r) #define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) Z_MULTSUB(x,z,p,ax,az,q,bx,bz,pb) #define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) \ Z_MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) #define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) \ Z_MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) #define LLDOT(x,p,ax,az,q) Z_LLDOT(x,p,ax,az,q) #define CLEAR(x,z,p) Z_CLEAR(x,z,p) #define CLEAR_IMAG(x,z,p) Z_CLEAR_IMAG(x,z,p) #define DIV(x,z,p,ax,az,q) Z_DIV(x,z,p,ax,az,q) #define DIV_REAL(x,z,p, ax,az,q, bx,r) Z_DIV_REAL(x,z,p, ax,az,q, bx,r) #define MULT_REAL(x,z,p, ax,az,q, bx,r) Z_MULT_REAL(x,z,p, ax,az,q, bx,r) #define LDLDOT(x,p, ax,az,q, bx,r) Z_LDLDOT(x,p, ax,az,q, bx,r) #define XPRINT0(x,z,p) Z_PRINT(0,x,z,p) #define XPRINT1(x,z,p) Z_PRINT(1,x,z,p) #define XPRINT2(x,z,p) Z_PRINT(2,x,z,p) #define XPRINT3(x,z,p) Z_PRINT(3,x,z,p) #endif Matrix/src/CHOLMOD/Include/cholmod_core.h0000644000175100001440000030506712271765436017631 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_core.h =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_core.h. * Copyright (C) 2005-2013, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_core.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* CHOLMOD Core module: basic CHOLMOD objects and routines. * Required by all CHOLMOD modules. Requires no other module or package. * * The CHOLMOD modules are: * * Core basic data structures and definitions * Check check/print the 5 CHOLMOD objects, & 3 types of integer vectors * Cholesky sparse Cholesky factorization * Modify sparse Cholesky update/downdate/row-add/row-delete * MatrixOps sparse matrix functions (add, multiply, norm, ...) * Supernodal supernodal sparse Cholesky factorization * Partition graph-partitioning based orderings * * The CHOLMOD objects: * -------------------- * * cholmod_common parameters, statistics, and workspace * cholmod_sparse a sparse matrix in compressed column form * cholmod_factor an LL' or LDL' factorization * cholmod_dense a dense matrix * cholmod_triplet a sparse matrix in "triplet" form * * The Core module described here defines the CHOLMOD data structures, and * basic operations on them. To create and solve a sparse linear system Ax=b, * the user must create A and b, populate them with values, and then pass them * to the routines in the CHOLMOD Cholesky module. There are two primary * methods for creating A: (1) allocate space for a column-oriented sparse * matrix and fill it with pattern and values, or (2) create a triplet form * matrix and convert it to a sparse matrix. The latter option is simpler. * * The matrices b and x are typically dense matrices, but can also be sparse. * You can allocate and free them as dense matrices with the * cholmod_allocate_dense and cholmod_free_dense routines. * * The cholmod_factor object contains the symbolic and numeric LL' or LDL' * factorization of sparse symmetric matrix. The matrix must be positive * definite for an LL' factorization. It need only be symmetric and have well- * conditioned leading submatrices for it to have an LDL' factorization * (CHOLMOD does not pivot for numerical stability). It is typically created * with the cholmod_factorize routine in the Cholesky module, but can also * be initialized to L=D=I in the Core module and then modified by the Modify * module. It must be freed with cholmod_free_factor, defined below. * * The Core routines for each object are described below. Each list is split * into two parts: the primary routines and secondary routines. * * ============================================================================ * === cholmod_common ========================================================= * ============================================================================ * * The Common object contains control parameters, statistics, and * You must call cholmod_start before calling any other CHOLMOD routine, and * must call cholmod_finish as your last call to CHOLMOD, with two exceptions: * you may call cholmod_print_common and cholmod_check_common in the Check * module after calling cholmod_finish. * * cholmod_start first call to CHOLMOD * cholmod_finish last call to CHOLMOD * ----------------------------- * cholmod_defaults restore default parameters * cholmod_maxrank maximum rank for update/downdate * cholmod_allocate_work allocate workspace in Common * cholmod_free_work free workspace in Common * cholmod_clear_flag clear Flag workspace in Common * cholmod_error called when CHOLMOD encounters an error * cholmod_dbound for internal use in CHOLMOD only * cholmod_hypot compute sqrt (x*x + y*y) accurately * cholmod_divcomplex complex division, c = a/b * * ============================================================================ * === cholmod_sparse ========================================================= * ============================================================================ * * A sparse matrix is held in compressed column form. In the basic type * ("packed", which corresponds to a MATLAB sparse matrix), an n-by-n matrix * with nz entries is held in three arrays: p of size n+1, i of size nz, and x * of size nz. Row indices of column j are held in i [p [j] ... p [j+1]-1] and * in the same locations in x. There may be no duplicate entries in a column. * Row indices in each column may be sorted or unsorted (CHOLMOD keeps track). * A->stype determines the storage mode: 0 if both upper/lower parts are stored, * -1 if A is symmetric and just tril(A) is stored, +1 if symmetric and triu(A) * is stored. * * cholmod_allocate_sparse allocate a sparse matrix * cholmod_free_sparse free a sparse matrix * ----------------------------- * cholmod_reallocate_sparse change the size (# entries) of sparse matrix * cholmod_nnz number of nonzeros in a sparse matrix * cholmod_speye sparse identity matrix * cholmod_spzeros sparse zero matrix * cholmod_transpose transpose a sparse matrix * cholmod_ptranspose transpose/permute a sparse matrix * cholmod_transpose_unsym transpose/permute an unsymmetric sparse matrix * cholmod_transpose_sym transpose/permute a symmetric sparse matrix * cholmod_sort sort row indices in each column of sparse matrix * cholmod_band C = tril (triu (A,k1), k2) * cholmod_band_inplace A = tril (triu (A,k1), k2) * cholmod_aat C = A*A' * cholmod_copy_sparse C = A, create an exact copy of a sparse matrix * cholmod_copy C = A, with possible change of stype * cholmod_add C = alpha*A + beta*B * cholmod_sparse_xtype change the xtype of a sparse matrix * * ============================================================================ * === cholmod_factor ========================================================= * ============================================================================ * * The data structure for an LL' or LDL' factorization is too complex to * describe in one sentence. This object can hold the symbolic analysis alone, * or in combination with a "simplicial" (similar to a sparse matrix) or * "supernodal" form of the numerical factorization. Only the routine to free * a factor is primary, since a factor object is created by the factorization * routine (cholmod_factorize). It must be freed with cholmod_free_factor. * * cholmod_free_factor free a factor * ----------------------------- * cholmod_allocate_factor allocate a factor (LL' or LDL') * cholmod_reallocate_factor change the # entries in a factor * cholmod_change_factor change the type of factor (e.g., LDL' to LL') * cholmod_pack_factor pack the columns of a factor * cholmod_reallocate_column resize a single column of a factor * cholmod_factor_to_sparse create a sparse matrix copy of a factor * cholmod_copy_factor create a copy of a factor * cholmod_factor_xtype change the xtype of a factor * * Note that there is no cholmod_sparse_to_factor routine to create a factor * as a copy of a sparse matrix. It could be done, after a fashion, but a * lower triangular sparse matrix would not necessarily have a chordal graph, * which would break the many CHOLMOD routines that rely on this property. * * ============================================================================ * === cholmod_dense ========================================================== * ============================================================================ * * The solve routines and some of the MatrixOps and Modify routines use dense * matrices as inputs. These are held in column-major order. With a leading * dimension of d, the entry in row i and column j is held in x [i+j*d]. * * cholmod_allocate_dense allocate a dense matrix * cholmod_free_dense free a dense matrix * ----------------------------- * cholmod_zeros allocate a dense matrix of all zeros * cholmod_ones allocate a dense matrix of all ones * cholmod_eye allocate a dense identity matrix * cholmod_sparse_to_dense create a dense matrix copy of a sparse matrix * cholmod_dense_to_sparse create a sparse matrix copy of a dense matrix * cholmod_copy_dense create a copy of a dense matrix * cholmod_copy_dense2 copy a dense matrix (pre-allocated) * cholmod_dense_xtype change the xtype of a dense matrix * cholmod_ensure_dense ensure a dense matrix has a given size and type * * ============================================================================ * === cholmod_triplet ======================================================== * ============================================================================ * * A sparse matrix held in triplet form is the simplest one for a user to * create. It consists of a list of nz entries in arbitrary order, held in * three arrays: i, j, and x, each of length nk. The kth entry is in row i[k], * column j[k], with value x[k]. There may be duplicate values; if A(i,j) * appears more than once, its value is the sum of the entries with those row * and column indices. * * cholmod_allocate_triplet allocate a triplet matrix * cholmod_triplet_to_sparse create a sparse matrix copy of a triplet matrix * cholmod_free_triplet free a triplet matrix * ----------------------------- * cholmod_reallocate_triplet change the # of entries in a triplet matrix * cholmod_sparse_to_triplet create a triplet matrix copy of a sparse matrix * cholmod_copy_triplet create a copy of a triplet matrix * cholmod_triplet_xtype change the xtype of a triplet matrix * * ============================================================================ * === memory management ====================================================== * ============================================================================ * * cholmod_malloc malloc wrapper * cholmod_calloc calloc wrapper * cholmod_free free wrapper * cholmod_realloc realloc wrapper * cholmod_realloc_multiple realloc wrapper for multiple objects * * ============================================================================ * === Core CHOLMOD prototypes ================================================ * ============================================================================ * * All CHOLMOD routines (in all modules) use the following protocol for return * values, with one exception: * * int TRUE (1) if successful, or FALSE (0) otherwise. * (exception: cholmod_divcomplex) * SuiteSparse_long a value >= 0 if successful, or -1 otherwise. * double a value >= 0 if successful, or -1 otherwise. * size_t a value > 0 if successful, or 0 otherwise. * void * a non-NULL pointer to newly allocated memory if * successful, or NULL otherwise. * cholmod_sparse * a non-NULL pointer to a newly allocated matrix * if successful, or NULL otherwise. * cholmod_factor * a non-NULL pointer to a newly allocated factor * if successful, or NULL otherwise. * cholmod_triplet * a non-NULL pointer to a newly allocated triplet * matrix if successful, or NULL otherwise. * cholmod_dense * a non-NULL pointer to a newly allocated triplet * matrix if successful, or NULL otherwise. * * The last parameter to all routines is always a pointer to the CHOLMOD * Common object. * * TRUE and FALSE are not defined here, since they may conflict with the user * program. A routine that described here returning TRUE or FALSE returns 1 * or 0, respectively. Any TRUE/FALSE parameter is true if nonzero, false if * zero. */ #ifndef CHOLMOD_CORE_H #define CHOLMOD_CORE_H /* ========================================================================== */ /* === CHOLMOD version ====================================================== */ /* ========================================================================== */ /* All versions of CHOLMOD will include the following definitions. * As an example, to test if the version you are using is 1.3 or later: * * if (CHOLMOD_VERSION >= CHOLMOD_VER_CODE (1,3)) ... * * This also works during compile-time: * * #if CHOLMOD_VERSION >= CHOLMOD_VER_CODE (1,3) * printf ("This is version 1.3 or later\n") ; * #else * printf ("This is version is earlier than 1.3\n") ; * #endif */ #define CHOLMOD_HAS_VERSION_FUNCTION #define CHOLMOD_DATE "April 25, 2013" #define CHOLMOD_VER_CODE(main,sub) ((main) * 1000 + (sub)) #define CHOLMOD_MAIN_VERSION 2 #define CHOLMOD_SUB_VERSION 1 #define CHOLMOD_SUBSUB_VERSION 2 #define CHOLMOD_VERSION \ CHOLMOD_VER_CODE(CHOLMOD_MAIN_VERSION,CHOLMOD_SUB_VERSION) /* ========================================================================== */ /* === non-CHOLMOD include files ============================================ */ /* ========================================================================== */ /* This is the only non-CHOLMOD include file imposed on the user program. * It required for size_t definition used here. CHOLMOD itself includes other * ANSI C89 standard #include files, but does not expose them to the user. * * CHOLMOD assumes that your C compiler is ANSI C89 compliant. It does not make * use of ANSI C99 features. */ #include #include /* ========================================================================== */ /* === CUDA BLAS for the GPU ================================================ */ /* ========================================================================== */ #ifdef GPU_BLAS #include #include #endif /* ========================================================================== */ /* === CHOLMOD objects ====================================================== */ /* ========================================================================== */ /* Each CHOLMOD object has its own type code. */ #define CHOLMOD_COMMON 0 #define CHOLMOD_SPARSE 1 #define CHOLMOD_FACTOR 2 #define CHOLMOD_DENSE 3 #define CHOLMOD_TRIPLET 4 /* ========================================================================== */ /* === CHOLMOD Common ======================================================= */ /* ========================================================================== */ /* itype defines the types of integer used: */ #define CHOLMOD_INT 0 /* all integer arrays are int */ #define CHOLMOD_INTLONG 1 /* most are int, some are SuiteSparse_long */ #define CHOLMOD_LONG 2 /* all integer arrays are SuiteSparse_long */ /* The itype of all parameters for all CHOLMOD routines must match. * FUTURE WORK: CHOLMOD_INTLONG is not yet supported. */ /* dtype defines what the numerical type is (double or float): */ #define CHOLMOD_DOUBLE 0 /* all numerical values are double */ #define CHOLMOD_SINGLE 1 /* all numerical values are float */ /* The dtype of all parameters for all CHOLMOD routines must match. * * Scalar floating-point values are always passed as double arrays of size 2 * (for the real and imaginary parts). They are typecast to float as needed. * FUTURE WORK: the float case is not supported yet. */ /* xtype defines the kind of numerical values used: */ #define CHOLMOD_PATTERN 0 /* pattern only, no numerical values */ #define CHOLMOD_REAL 1 /* a real matrix */ #define CHOLMOD_COMPLEX 2 /* a complex matrix (ANSI C99 compatible) */ #define CHOLMOD_ZOMPLEX 3 /* a complex matrix (MATLAB compatible) */ /* The xtype of all parameters for all CHOLMOD routines must match. * * CHOLMOD_PATTERN: x and z are ignored. * CHOLMOD_DOUBLE: x is non-null of size nzmax, z is ignored. * CHOLMOD_COMPLEX: x is non-null of size 2*nzmax doubles, z is ignored. * CHOLMOD_ZOMPLEX: x and z are non-null of size nzmax * * In the real case, z is ignored. The kth entry in the matrix is x [k]. * There are two methods for the complex case. In the ANSI C99-compatible * CHOLMOD_COMPLEX case, the real and imaginary parts of the kth entry * are in x [2*k] and x [2*k+1], respectively. z is ignored. In the * MATLAB-compatible CHOLMOD_ZOMPLEX case, the real and imaginary * parts of the kth entry are in x [k] and z [k]. * * Scalar floating-point values are always passed as double arrays of size 2 * (real and imaginary parts). The imaginary part of a scalar is ignored if * the routine operates on a real matrix. * * These Modules support complex and zomplex matrices, with a few exceptions: * * Check all routines * Cholesky all routines * Core all except cholmod_aat, add, band, copy * Demo all routines * Partition all routines * Supernodal all routines support any real, complex, or zomplex input. * There will never be a supernodal zomplex L; a complex * supernodal L is created if A is zomplex. * Tcov all routines * Valgrind all routines * * These Modules provide partial support for complex and zomplex matrices: * * MATLAB all routines support real and zomplex only, not complex, * with the exception of ldlupdate, which supports * real matrices only. This is a minor constraint since * MATLAB's matrices are all real or zomplex. * MatrixOps only norm_dense, norm_sparse, and sdmult support complex * and zomplex * * These Modules do not support complex and zomplex matrices at all: * * Modify all routines support real matrices only */ /* Definitions for cholmod_common: */ #define CHOLMOD_MAXMETHODS 9 /* maximum number of different methods that */ /* cholmod_analyze can try. Must be >= 9. */ /* Common->status values. zero means success, negative means a fatal error, * positive is a warning. */ #define CHOLMOD_OK 0 /* success */ #define CHOLMOD_NOT_INSTALLED (-1) /* failure: method not installed */ #define CHOLMOD_OUT_OF_MEMORY (-2) /* failure: out of memory */ #define CHOLMOD_TOO_LARGE (-3) /* failure: integer overflow occured */ #define CHOLMOD_INVALID (-4) /* failure: invalid input */ #define CHOLMOD_GPU_PROBLEM (-5) /* failure: GPU fatal error */ #define CHOLMOD_NOT_POSDEF (1) /* warning: matrix not pos. def. */ #define CHOLMOD_DSMALL (2) /* warning: D for LDL' or diag(L) or */ /* LL' has tiny absolute value */ /* ordering method (also used for L->ordering) */ #define CHOLMOD_NATURAL 0 /* use natural ordering */ #define CHOLMOD_GIVEN 1 /* use given permutation */ #define CHOLMOD_AMD 2 /* use minimum degree (AMD) */ #define CHOLMOD_METIS 3 /* use METIS' nested dissection */ #define CHOLMOD_NESDIS 4 /* use CHOLMOD's version of nested dissection:*/ /* node bisector applied recursively, followed * by constrained minimum degree (CSYMAMD or * CCOLAMD) */ #define CHOLMOD_COLAMD 5 /* use AMD for A, COLAMD for A*A' */ /* POSTORDERED is not a method, but a result of natural ordering followed by a * weighted postorder. It is used for L->ordering, not method [ ].ordering. */ #define CHOLMOD_POSTORDERED 6 /* natural ordering, postordered. */ /* supernodal strategy (for Common->supernodal) */ #define CHOLMOD_SIMPLICIAL 0 /* always do simplicial */ #define CHOLMOD_AUTO 1 /* select simpl/super depending on matrix */ #define CHOLMOD_SUPERNODAL 2 /* always do supernodal */ typedef struct cholmod_common_struct { /* ---------------------------------------------------------------------- */ /* parameters for symbolic/numeric factorization and update/downdate */ /* ---------------------------------------------------------------------- */ double dbound ; /* Smallest absolute value of diagonal entries of D * for LDL' factorization and update/downdate/rowadd/ * rowdel, or the diagonal of L for an LL' factorization. * Entries in the range 0 to dbound are replaced with dbound. * Entries in the range -dbound to 0 are replaced with -dbound. No * changes are made to the diagonal if dbound <= 0. Default: zero */ double grow0 ; /* For a simplicial factorization, L->i and L->x can * grow if necessary. grow0 is the factor by which * it grows. For the initial space, L is of size MAX (1,grow0) times * the required space. If L runs out of space, the new size of L is * MAX(1.2,grow0) times the new required space. If you do not plan on * modifying the LDL' factorization in the Modify module, set grow0 to * zero (or set grow2 to 0, see below). Default: 1.2 */ double grow1 ; size_t grow2 ; /* For a simplicial factorization, each column j of L * is initialized with space equal to * grow1*L->ColCount[j] + grow2. If grow0 < 1, grow1 < 1, or grow2 == 0, * then the space allocated is exactly equal to L->ColCount[j]. If the * column j runs out of space, it increases to grow1*need + grow2 in * size, where need is the total # of nonzeros in that column. If you do * not plan on modifying the factorization in the Modify module, set * grow2 to zero. Default: grow1 = 1.2, grow2 = 5. */ size_t maxrank ; /* rank of maximum update/downdate. Valid values: * 2, 4, or 8. A value < 2 is set to 2, and a * value > 8 is set to 8. It is then rounded up to the next highest * power of 2, if not already a power of 2. Workspace (Xwork, below) of * size nrow-by-maxrank double's is allocated for the update/downdate. * If an update/downdate of rank-k is requested, with k > maxrank, * it is done in steps of maxrank. Default: 8, which is fastest. * Memory usage can be reduced by setting maxrank to 2 or 4. */ double supernodal_switch ; /* supernodal vs simplicial factorization */ int supernodal ; /* If Common->supernodal <= CHOLMOD_SIMPLICIAL * (0) then cholmod_analyze performs a * simplicial analysis. If >= CHOLMOD_SUPERNODAL (2), then a supernodal * analysis is performed. If == CHOLMOD_AUTO (1) and * flop/nnz(L) < Common->supernodal_switch, then a simplicial analysis * is done. A supernodal analysis done otherwise. * Default: CHOLMOD_AUTO. Default supernodal_switch = 40 */ int final_asis ; /* If TRUE, then ignore the other final_* parameters * (except for final_pack). * The factor is left as-is when done. Default: TRUE.*/ int final_super ; /* If TRUE, leave a factor in supernodal form when * supernodal factorization is finished. If FALSE, * then convert to a simplicial factor when done. * Default: TRUE */ int final_ll ; /* If TRUE, leave factor in LL' form when done. * Otherwise, leave in LDL' form. Default: FALSE */ int final_pack ; /* If TRUE, pack the columns when done. If TRUE, and * cholmod_factorize is called with a symbolic L, L is * allocated with exactly the space required, using L->ColCount. If you * plan on modifying the factorization, set Common->final_pack to FALSE, * and each column will be given a little extra slack space for future * growth in fill-in due to updates. Default: TRUE */ int final_monotonic ; /* If TRUE, ensure columns are monotonic when done. * Default: TRUE */ int final_resymbol ;/* if cholmod_factorize performed a supernodal * factorization, final_resymbol is true, and * final_super is FALSE (convert a simplicial numeric factorization), * then numerically zero entries that resulted from relaxed supernodal * amalgamation are removed. This does not remove entries that are zero * due to exact numeric cancellation, since doing so would break the * update/downdate rowadd/rowdel routines. Default: FALSE. */ /* supernodal relaxed amalgamation parameters: */ double zrelax [3] ; size_t nrelax [3] ; /* Let ns be the total number of columns in two adjacent supernodes. * Let z be the fraction of zero entries in the two supernodes if they * are merged (z includes zero entries from prior amalgamations). The * two supernodes are merged if: * (ns <= nrelax [0]) || (no new zero entries added) || * (ns <= nrelax [1] && z < zrelax [0]) || * (ns <= nrelax [2] && z < zrelax [1]) || (z < zrelax [2]) * * Default parameters result in the following rule: * (ns <= 4) || (no new zero entries added) || * (ns <= 16 && z < 0.8) || (ns <= 48 && z < 0.1) || (z < 0.05) */ int prefer_zomplex ; /* X = cholmod_solve (sys, L, B, Common) computes * x=A\b or solves a related system. If L and B are * both real, then X is real. Otherwise, X is returned as * CHOLMOD_COMPLEX if Common->prefer_zomplex is FALSE, or * CHOLMOD_ZOMPLEX if Common->prefer_zomplex is TRUE. This parameter * is needed because there is no supernodal zomplex L. Suppose the * caller wants all complex matrices to be stored in zomplex form * (MATLAB, for example). A supernodal L is returned in complex form * if A is zomplex. B can be real, and thus X = cholmod_solve (L,B) * should return X as zomplex. This cannot be inferred from the input * arguments L and B. Default: FALSE, since all data types are * supported in CHOLMOD_COMPLEX form and since this is the native type * of LAPACK and the BLAS. Note that the MATLAB/cholmod.c mexFunction * sets this parameter to TRUE, since MATLAB matrices are in * CHOLMOD_ZOMPLEX form. */ int prefer_upper ; /* cholmod_analyze and cholmod_factorize work * fastest when a symmetric matrix is stored in * upper triangular form when a fill-reducing ordering is used. In * MATLAB, this corresponds to how x=A\b works. When the matrix is * ordered as-is, they work fastest when a symmetric matrix is in lower * triangular form. In MATLAB, R=chol(A) does the opposite. This * parameter affects only how cholmod_read returns a symmetric matrix. * If TRUE (the default case), a symmetric matrix is always returned in * upper-triangular form (A->stype = 1). */ int quick_return_if_not_posdef ; /* if TRUE, the supernodal numeric * factorization will return quickly if * the matrix is not positive definite. Default: FALSE. */ /* ---------------------------------------------------------------------- */ /* printing and error handling options */ /* ---------------------------------------------------------------------- */ int print ; /* print level. Default: 3 */ int precise ; /* if TRUE, print 16 digits. Otherwise print 5 */ int (*print_function) (const char *, ...) ; /* pointer to printf */ int try_catch ; /* if TRUE, then ignore errors; CHOLMOD is in the middle * of a try/catch block. No error message is printed * and the Common->error_handler function is not called. */ void (*error_handler) (int status, const char *file, int line, const char *message) ; /* Common->error_handler is the user's error handling routine. If not * NULL, this routine is called if an error occurs in CHOLMOD. status * can be CHOLMOD_OK (0), negative for a fatal error, and positive for * a warning. file is a string containing the name of the source code * file where the error occured, and line is the line number in that * file. message is a string describing the error in more detail. */ /* ---------------------------------------------------------------------- */ /* ordering options */ /* ---------------------------------------------------------------------- */ /* The cholmod_analyze routine can try many different orderings and select * the best one. It can also try one ordering method multiple times, with * different parameter settings. The default is to use three orderings, * the user's permutation (if provided), AMD which is the fastest ordering * and generally gives good fill-in, and METIS. CHOLMOD's nested dissection * (METIS with a constrained AMD) usually gives a better ordering than METIS * alone (by about 5% to 10%) but it takes more time. * * If you know the method that is best for your matrix, set Common->nmethods * to 1 and set Common->method [0] to the set of parameters for that method. * If you set it to 1 and do not provide a permutation, then only AMD will * be called. * * If METIS is not available, the default # of methods tried is 2 (the user * permutation, if any, and AMD). * * To try other methods, set Common->nmethods to the number of methods you * want to try. The suite of default methods and their parameters is * described in the cholmod_defaults routine, and summarized here: * * Common->method [i]: * i = 0: user-provided ordering (cholmod_analyze_p only) * i = 1: AMD (for both A and A*A') * i = 2: METIS * i = 3: CHOLMOD's nested dissection (NESDIS), default parameters * i = 4: natural * i = 5: NESDIS with nd_small = 20000 * i = 6: NESDIS with nd_small = 4, no constrained minimum degree * i = 7: NESDIS with no dense node removal * i = 8: AMD for A, COLAMD for A*A' * * You can modify the suite of methods you wish to try by modifying * Common.method [...] after calling cholmod_start or cholmod_defaults. * * For example, to use AMD, followed by a weighted postordering: * * Common->nmethods = 1 ; * Common->method [0].ordering = CHOLMOD_AMD ; * Common->postorder = TRUE ; * * To use the natural ordering (with no postordering): * * Common->nmethods = 1 ; * Common->method [0].ordering = CHOLMOD_NATURAL ; * Common->postorder = FALSE ; * * If you are going to factorize hundreds or more matrices with the same * nonzero pattern, you may wish to spend a great deal of time finding a * good permutation. In this case, try setting Common->nmethods to 9. * The time spent in cholmod_analysis will be very high, but you need to * call it only once. * * cholmod_analyze sets Common->current to a value between 0 and nmethods-1. * Each ordering method uses the set of options defined by this parameter. */ int nmethods ; /* The number of ordering methods to try. Default: 0. * nmethods = 0 is a special case. cholmod_analyze * will try the user-provided ordering (if given) and AMD. Let fl and * lnz be the flop count and nonzeros in L from AMD's ordering. Let * anz be the number of nonzeros in the upper or lower triangular part * of the symmetric matrix A. If fl/lnz < 500 or lnz/anz < 5, then this * is a good ordering, and METIS is not attempted. Otherwise, METIS is * tried. The best ordering found is used. If nmethods > 0, the * methods used are given in the method[ ] array, below. The first * three methods in the default suite of orderings is (1) use the given * permutation (if provided), (2) use AMD, and (3) use METIS. Maximum * allowed value is CHOLMOD_MAXMETHODS. */ int current ; /* The current method being tried. Default: 0. Valid * range is 0 to nmethods-1. */ int selected ; /* The best method found. */ /* The suite of ordering methods and parameters: */ struct cholmod_method_struct { /* statistics for this method */ double lnz ; /* nnz(L) excl. zeros from supernodal amalgamation, * for a "pure" L */ double fl ; /* flop count for a "pure", real simplicial LL' * factorization, with no extra work due to * amalgamation. Subtract n to get the LDL' flop count. Multiply * by about 4 if the matrix is complex or zomplex. */ /* ordering method parameters */ double prune_dense ;/* dense row/col control for AMD, SYMAMD, CSYMAMD, * and NESDIS (cholmod_nested_dissection). For a * symmetric n-by-n matrix, rows/columns with more than * MAX (16, prune_dense * sqrt (n)) entries are removed prior to * ordering. They appear at the end of the re-ordered matrix. * * If prune_dense < 0, only completely dense rows/cols are removed. * * This paramater is also the dense column control for COLAMD and * CCOLAMD. For an m-by-n matrix, columns with more than * MAX (16, prune_dense * sqrt (MIN (m,n))) entries are removed prior * to ordering. They appear at the end of the re-ordered matrix. * CHOLMOD factorizes A*A', so it calls COLAMD and CCOLAMD with A', * not A. Thus, this parameter affects the dense *row* control for * CHOLMOD's matrix, and the dense *column* control for COLAMD and * CCOLAMD. * * Removing dense rows and columns improves the run-time of the * ordering methods. It has some impact on ordering quality * (usually minimal, sometimes good, sometimes bad). * * Default: 10. */ double prune_dense2 ;/* dense row control for COLAMD and CCOLAMD. * Rows with more than MAX (16, dense2 * sqrt (n)) * for an m-by-n matrix are removed prior to ordering. CHOLMOD's * matrix is transposed before ordering it with COLAMD or CCOLAMD, * so this controls the dense *columns* of CHOLMOD's matrix, and * the dense *rows* of COLAMD's or CCOLAMD's matrix. * * If prune_dense2 < 0, only completely dense rows/cols are removed. * * Default: -1. Note that this is not the default for COLAMD and * CCOLAMD. -1 is best for Cholesky. 10 is best for LU. */ double nd_oksep ; /* in NESDIS, when a node separator is computed, it * discarded if nsep >= nd_oksep*n, where nsep is * the number of nodes in the separator, and n is the size of the * graph being cut. Valid range is 0 to 1. If 1 or greater, the * separator is discarded if it consists of the entire graph. * Default: 1 */ double other_1 [4] ; /* future expansion */ size_t nd_small ; /* do not partition graphs with fewer nodes than * nd_small, in NESDIS. Default: 200 (same as * METIS) */ size_t other_2 [4] ; /* future expansion */ int aggressive ; /* Aggresive absorption in AMD, COLAMD, SYMAMD, * CCOLAMD, and CSYMAMD. Default: TRUE */ int order_for_lu ; /* CCOLAMD can be optimized to produce an ordering * for LU or Cholesky factorization. CHOLMOD only * performs a Cholesky factorization. However, you may wish to use * CHOLMOD as an interface for CCOLAMD but use it for your own LU * factorization. In this case, order_for_lu should be set to FALSE. * When factorizing in CHOLMOD itself, you should *** NEVER *** set * this parameter FALSE. Default: TRUE. */ int nd_compress ; /* If TRUE, compress the graph and subgraphs before * partitioning them in NESDIS. Default: TRUE */ int nd_camd ; /* If 1, follow the nested dissection ordering * with a constrained minimum degree ordering that * respects the partitioning just found (using CAMD). If 2, use * CSYMAMD instead. If you set nd_small very small, you may not need * this ordering, and can save time by setting it to zero (no * constrained minimum degree ordering). Default: 1. */ int nd_components ; /* The nested dissection ordering finds a node * separator that splits the graph into two parts, * which may be unconnected. If nd_components is TRUE, each of * these connected components is split independently. If FALSE, * each part is split as a whole, even if it consists of more than * one connected component. Default: FALSE */ /* fill-reducing ordering to use */ int ordering ; size_t other_3 [4] ; /* future expansion */ } method [CHOLMOD_MAXMETHODS + 1] ; int postorder ; /* If TRUE, cholmod_analyze follows the ordering with a * weighted postorder of the elimination tree. Improves * supernode amalgamation. Does not affect fundamental nnz(L) and * flop count. Default: TRUE. */ /* ---------------------------------------------------------------------- */ /* memory management routines */ /* ---------------------------------------------------------------------- */ void *(*malloc_memory) (size_t) ; /* pointer to malloc */ void *(*realloc_memory) (void *, size_t) ; /* pointer to realloc */ void (*free_memory) (void *) ; /* pointer to free */ void *(*calloc_memory) (size_t, size_t) ; /* pointer to calloc */ /* ---------------------------------------------------------------------- */ /* routines for complex arithmetic */ /* ---------------------------------------------------------------------- */ int (*complex_divide) (double ax, double az, double bx, double bz, double *cx, double *cz) ; /* flag = complex_divide (ax, az, bx, bz, &cx, &cz) computes the complex * division c = a/b, where ax and az hold the real and imaginary part * of a, and b and c are stored similarly. flag is returned as 1 if * a divide-by-zero occurs, or 0 otherwise. By default, the function * pointer Common->complex_divide is set equal to cholmod_divcomplex. */ double (*hypotenuse) (double x, double y) ; /* s = hypotenuse (x,y) computes s = sqrt (x*x + y*y), but does so more * accurately. By default, the function pointer Common->hypotenuse is * set equal to cholmod_hypot. See also the hypot function in the C99 * standard, which has an identical syntax and function. If you have * a C99-compliant compiler, you can set Common->hypotenuse = hypot. */ /* ---------------------------------------------------------------------- */ /* METIS workarounds */ /* ---------------------------------------------------------------------- */ double metis_memory ; /* This is a parameter for CHOLMOD's interface to * METIS, not a parameter to METIS itself. METIS * uses an amount of memory that is difficult to estimate precisely * beforehand. If it runs out of memory, it terminates your program. * All routines in CHOLMOD except for CHOLMOD's interface to METIS * return an error status and safely return to your program if they run * out of memory. To mitigate this problem, the CHOLMOD interface * can allocate a single block of memory equal in size to an empirical * upper bound of METIS's memory usage times the Common->metis_memory * parameter, and then immediately free it. It then calls METIS. If * this pre-allocation fails, it is possible that METIS will fail as * well, and so CHOLMOD returns with an out-of-memory condition without * calling METIS. * * METIS_NodeND (used in the CHOLMOD_METIS ordering option) with its * default parameter settings typically uses about (4*nz+40n+4096) * times sizeof(int) memory, where nz is equal to the number of entries * in A for the symmetric case or AA' if an unsymmetric matrix is * being ordered (where nz includes both the upper and lower parts * of A or AA'). The observed "upper bound" (with 2 exceptions), * measured in an instrumented copy of METIS 4.0.1 on thousands of * matrices, is (10*nz+50*n+4096) * sizeof(int). Two large matrices * exceeded this bound, one by almost a factor of 2 (Gupta/gupta2). * * If your program is terminated by METIS, try setting metis_memory to * 2.0, or even higher if needed. By default, CHOLMOD assumes that METIS * does not have this problem (so that CHOLMOD will work correctly when * this issue is fixed in METIS). Thus, the default value is zero. * This work-around is not guaranteed anyway. * * If a matrix exceeds this predicted memory usage, AMD is attempted * instead. It, too, may run out of memory, but if it does so it will * not terminate your program. */ double metis_dswitch ; /* METIS_NodeND in METIS 4.0.1 gives a seg */ size_t metis_nswitch ; /* fault with one matrix of order n = 3005 and * nz = 6,036,025. This is a very dense graph. * The workaround is to use AMD instead of METIS for matrices of dimension * greater than Common->metis_nswitch (default 3000) or more and with * density of Common->metis_dswitch (default 0.66) or more. * cholmod_nested_dissection has no problems with the same matrix, even * though it uses METIS_NodeComputeSeparator on this matrix. If this * seg fault does not affect you, set metis_nswitch to zero or less, * and CHOLMOD will not switch to AMD based just on the density of the * matrix (it will still switch to AMD if the metis_memory parameter * causes the switch). */ /* ---------------------------------------------------------------------- */ /* workspace */ /* ---------------------------------------------------------------------- */ /* CHOLMOD has several routines that take less time than the size of * workspace they require. Allocating and initializing the workspace would * dominate the run time, unless workspace is allocated and initialized * just once. CHOLMOD allocates this space when needed, and holds it here * between calls to CHOLMOD. cholmod_start sets these pointers to NULL * (which is why it must be the first routine called in CHOLMOD). * cholmod_finish frees the workspace (which is why it must be the last * call to CHOLMOD). */ size_t nrow ; /* size of Flag and Head */ SuiteSparse_long mark ; /* mark value for Flag array */ size_t iworksize ; /* size of Iwork. Upper bound: 6*nrow+ncol */ size_t xworksize ; /* size of Xwork, in bytes. * maxrank*nrow*sizeof(double) for update/downdate. * 2*nrow*sizeof(double) otherwise */ /* initialized workspace: contents needed between calls to CHOLMOD */ void *Flag ; /* size nrow, an integer array. Kept cleared between * calls to cholmod rouines (Flag [i] < mark) */ void *Head ; /* size nrow+1, an integer array. Kept cleared between * calls to cholmod routines (Head [i] = EMPTY) */ void *Xwork ; /* a double array. Its size varies. It is nrow for * most routines (cholmod_rowfac, cholmod_add, * cholmod_aat, cholmod_norm, cholmod_ssmult) for the real case, twice * that when the input matrices are complex or zomplex. It is of size * 2*nrow for cholmod_rowadd and cholmod_rowdel. For cholmod_updown, * its size is maxrank*nrow where maxrank is 2, 4, or 8. Kept cleared * between calls to cholmod (set to zero). */ /* uninitialized workspace, contents not needed between calls to CHOLMOD */ void *Iwork ; /* size iworksize, 2*nrow+ncol for most routines, * up to 6*nrow+ncol for cholmod_analyze. */ int itype ; /* If CHOLMOD_LONG, Flag, Head, and Iwork are * SuiteSparse_long. Otherwise all three are int. */ int dtype ; /* double or float */ /* Common->itype and Common->dtype are used to define the types of all * sparse matrices, triplet matrices, dense matrices, and factors * created using this Common struct. The itypes and dtypes of all * parameters to all CHOLMOD routines must match. */ int no_workspace_reallocate ; /* this is an internal flag, used as a * precaution by cholmod_analyze. It is normally false. If true, * cholmod_allocate_work is not allowed to reallocate any workspace; * they must use the existing workspace in Common (Iwork, Flag, Head, * and Xwork). Added for CHOLMOD v1.1 */ /* ---------------------------------------------------------------------- */ /* statistics */ /* ---------------------------------------------------------------------- */ /* fl and lnz are set only in cholmod_analyze and cholmod_rowcolcounts, * in the Cholesky modudle. modfl is set only in the Modify module. */ int status ; /* error code */ double fl ; /* LL' flop count from most recent analysis */ double lnz ; /* fundamental nz in L */ double anz ; /* nonzeros in tril(A) if A is symmetric/lower, * triu(A) if symmetric/upper, or tril(A*A') if * unsymmetric, in last call to cholmod_analyze. */ double modfl ; /* flop count from most recent update/downdate/ * rowadd/rowdel (excluding flops to modify the * solution to Lx=b, if computed) */ size_t malloc_count ; /* # of objects malloc'ed minus the # free'd*/ size_t memory_usage ; /* peak memory usage in bytes */ size_t memory_inuse ; /* current memory usage in bytes */ double nrealloc_col ; /* # of column reallocations */ double nrealloc_factor ;/* # of factor reallocations due to col. reallocs */ double ndbounds_hit ; /* # of times diagonal modified by dbound */ double rowfacfl ; /* # of flops in last call to cholmod_rowfac */ double aatfl ; /* # of flops to compute A(:,f)*A(:,f)' */ /* ---------------------------------------------------------------------- */ /* statistics, parameters, and future expansion */ /* ---------------------------------------------------------------------- */ /* The goal for future expansion is to keep sizeof(Common) unchanged. */ double other1 [10] ; /* [0..9] for CHOLMOD GPU/CPU numerical factorization statistics, and [0..3] used by SuiteSparseQR statistics */ double SPQR_xstat [4] ; /* for SuiteSparseQR statistics */ /* SuiteSparseQR control parameters: */ double SPQR_grain ; /* task size is >= max (total flops / grain) */ double SPQR_small ; /* task size is >= small */ /* ---------------------------------------------------------------------- */ SuiteSparse_long SPQR_istat [10] ; /* for SuiteSparseQR statistics */ SuiteSparse_long other2 [6] ; /* unused (for future expansion) */ /* ---------------------------------------------------------------------- */ int other3 [10] ; /* unused (for future expansion) */ int prefer_binary ; /* cholmod_read_triplet converts a symmetric * pattern-only matrix into a real matrix. If * prefer_binary is FALSE, the diagonal entries are set to 1 + the degree * of the row/column, and off-diagonal entries are set to -1 (resulting * in a positive definite matrix if the diagonal is zero-free). Most * symmetric patterns are the pattern a positive definite matrix. If * this parameter is TRUE, then the matrix is returned with a 1 in each * entry, instead. Default: FALSE. Added in v1.3. */ /* control parameter (added for v1.2): */ int default_nesdis ; /* Default: FALSE. If FALSE, then the default * ordering strategy (when Common->nmethods == 0) * is to try the given ordering (if present), AMD, and then METIS if AMD * reports high fill-in. If Common->default_nesdis is TRUE then NESDIS * is used instead in the default strategy. */ /* statistic (added for v1.2): */ int called_nd ; /* TRUE if the last call to * cholmod_analyze called NESDIS or METIS. */ int blas_ok ; /* FALSE if BLAS int overflow; TRUE otherwise */ /* SuiteSparseQR control parameters: */ int SPQR_shrink ; /* controls stack realloc method */ int SPQR_nthreads ; /* number of TBB threads, 0 = auto */ /* ---------------------------------------------------------------------- */ size_t other4 [16] ; /* [0..7] for CHOLMOD GPU/CPU numerical factorization statistics, remainder unused (for future expansion) */ /* ---------------------------------------------------------------------- */ void *other5 [16] ; /* unused (for future expansion) */ /* ---------------------------------------------------------------------- */ /* GPU configuration */ /* ---------------------------------------------------------------------- */ #ifdef GPU_BLAS /* gpuConfig_t gpuConfig ; */ cublasHandle_t cublasHandle ; cudaStream_t cudaStreamSyrk ; cudaStream_t cudaStreamGemm ; cudaStream_t cudaStreamTrsm ; cudaStream_t cudaStreamPotrf [3] ; cudaEvent_t cublasEventPotrf [2] ; void *HostPinnedMemory ; void *devPotrfWork ; void *devSyrkGemmPtrLx ; void *devSyrkGemmPtrC ; int GemmUsed ; /* TRUE if cuda dgemm used, false otherwise */ int SyrkUsed ; /* TRUE if cuda dsyrk used, false otherwise */ double syrkStart ; /* time syrk started */ #endif } cholmod_common ; /* size_t BLAS statistcs in Common: */ #define CHOLMOD_CPU_GEMM_CALLS other4 [0] #define CHOLMOD_CPU_SYRK_CALLS other4 [1] #define CHOLMOD_CPU_TRSM_CALLS other4 [2] #define CHOLMOD_CPU_POTRF_CALLS other4 [3] #define CHOLMOD_GPU_GEMM_CALLS other4 [4] #define CHOLMOD_GPU_SYRK_CALLS other4 [5] #define CHOLMOD_GPU_TRSM_CALLS other4 [6] #define CHOLMOD_GPU_POTRF_CALLS other4 [7] /* double BLAS statistics in Common: */ #define CHOLMOD_CPU_GEMM_TIME other1 [0] #define CHOLMOD_CPU_SYRK_TIME other1 [1] #define CHOLMOD_CPU_TRSM_TIME other1 [2] #define CHOLMOD_CPU_POTRF_TIME other1 [3] #define CHOLMOD_GPU_GEMM_TIME other1 [4] #define CHOLMOD_GPU_SYRK_TIME other1 [5] #define CHOLMOD_GPU_TRSM_TIME other1 [6] #define CHOLMOD_GPU_POTRF_TIME other1 [7] #define CHOLMOD_ASSEMBLE_TIME other1 [8] #define CHOLMOD_ASSEMBLE_TIME2 other1 [9] /* -------------------------------------------------------------------------- */ /* cholmod_start: first call to CHOLMOD */ /* -------------------------------------------------------------------------- */ int cholmod_start ( cholmod_common *Common ) ; int cholmod_l_start (cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_finish: last call to CHOLMOD */ /* -------------------------------------------------------------------------- */ int cholmod_finish ( cholmod_common *Common ) ; int cholmod_l_finish (cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_defaults: restore default parameters */ /* -------------------------------------------------------------------------- */ int cholmod_defaults ( cholmod_common *Common ) ; int cholmod_l_defaults (cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_maxrank: return valid maximum rank for update/downdate */ /* -------------------------------------------------------------------------- */ size_t cholmod_maxrank /* returns validated value of Common->maxrank */ ( /* ---- input ---- */ size_t n, /* A and L will have n rows */ /* --------------- */ cholmod_common *Common ) ; size_t cholmod_l_maxrank (size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_allocate_work: allocate workspace in Common */ /* -------------------------------------------------------------------------- */ int cholmod_allocate_work ( /* ---- input ---- */ size_t nrow, /* size: Common->Flag (nrow), Common->Head (nrow+1) */ size_t iworksize, /* size of Common->Iwork */ size_t xworksize, /* size of Common->Xwork */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_allocate_work (size_t, size_t, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_free_work: free workspace in Common */ /* -------------------------------------------------------------------------- */ int cholmod_free_work ( cholmod_common *Common ) ; int cholmod_l_free_work (cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_clear_flag: clear Flag workspace in Common */ /* -------------------------------------------------------------------------- */ /* use a macro for speed */ #define CHOLMOD_CLEAR_FLAG(Common) \ { \ Common->mark++ ; \ if (Common->mark <= 0) \ { \ Common->mark = EMPTY ; \ CHOLMOD (clear_flag) (Common) ; \ } \ } SuiteSparse_long cholmod_clear_flag ( cholmod_common *Common ) ; SuiteSparse_long cholmod_l_clear_flag (cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_error: called when CHOLMOD encounters an error */ /* -------------------------------------------------------------------------- */ int cholmod_error ( /* ---- input ---- */ int status, /* error status */ const char *file, /* name of source code file where error occured */ int line, /* line number in source code file where error occured*/ const char *message,/* error message */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_error (int, const char *, int, const char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_dbound: for internal use in CHOLMOD only */ /* -------------------------------------------------------------------------- */ double cholmod_dbound /* returns modified diagonal entry of D or L */ ( /* ---- input ---- */ double dj, /* diagonal entry of D for LDL' or L for LL' */ /* --------------- */ cholmod_common *Common ) ; double cholmod_l_dbound (double, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_hypot: compute sqrt (x*x + y*y) accurately */ /* -------------------------------------------------------------------------- */ double cholmod_hypot ( /* ---- input ---- */ double x, double y ) ; double cholmod_l_hypot (double, double) ; /* -------------------------------------------------------------------------- */ /* cholmod_divcomplex: complex division, c = a/b */ /* -------------------------------------------------------------------------- */ int cholmod_divcomplex /* return 1 if divide-by-zero, 0 otherise */ ( /* ---- input ---- */ double ar, double ai, /* real and imaginary parts of a */ double br, double bi, /* real and imaginary parts of b */ /* ---- output --- */ double *cr, double *ci /* real and imaginary parts of c */ ) ; int cholmod_l_divcomplex (double, double, double, double, double *, double *) ; /* ========================================================================== */ /* === Core/cholmod_sparse ================================================== */ /* ========================================================================== */ /* A sparse matrix stored in compressed-column form. */ typedef struct cholmod_sparse_struct { size_t nrow ; /* the matrix is nrow-by-ncol */ size_t ncol ; size_t nzmax ; /* maximum number of entries in the matrix */ /* pointers to int or SuiteSparse_long: */ void *p ; /* p [0..ncol], the column pointers */ void *i ; /* i [0..nzmax-1], the row indices */ /* for unpacked matrices only: */ void *nz ; /* nz [0..ncol-1], the # of nonzeros in each col. In * packed form, the nonzero pattern of column j is in * A->i [A->p [j] ... A->p [j+1]-1]. In unpacked form, column j is in * A->i [A->p [j] ... A->p [j]+A->nz[j]-1] instead. In both cases, the * numerical values (if present) are in the corresponding locations in * the array x (or z if A->xtype is CHOLMOD_ZOMPLEX). */ /* pointers to double or float: */ void *x ; /* size nzmax or 2*nzmax, if present */ void *z ; /* size nzmax, if present */ int stype ; /* Describes what parts of the matrix are considered: * * 0: matrix is "unsymmetric": use both upper and lower triangular parts * (the matrix may actually be symmetric in pattern and value, but * both parts are explicitly stored and used). May be square or * rectangular. * >0: matrix is square and symmetric, use upper triangular part. * Entries in the lower triangular part are ignored. * <0: matrix is square and symmetric, use lower triangular part. * Entries in the upper triangular part are ignored. * * Note that stype>0 and stype<0 are different for cholmod_sparse and * cholmod_triplet. See the cholmod_triplet data structure for more * details. */ int itype ; /* CHOLMOD_INT: p, i, and nz are int. * CHOLMOD_INTLONG: p is SuiteSparse_long, * i and nz are int. * CHOLMOD_LONG: p, i, and nz are SuiteSparse_long */ int xtype ; /* pattern, real, complex, or zomplex */ int dtype ; /* x and z are double or float */ int sorted ; /* TRUE if columns are sorted, FALSE otherwise */ int packed ; /* TRUE if packed (nz ignored), FALSE if unpacked * (nz is required) */ } cholmod_sparse ; /* -------------------------------------------------------------------------- */ /* cholmod_allocate_sparse: allocate a sparse matrix */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_allocate_sparse ( /* ---- input ---- */ size_t nrow, /* # of rows of A */ size_t ncol, /* # of columns of A */ size_t nzmax, /* max # of nonzeros of A */ int sorted, /* TRUE if columns of A sorted, FALSE otherwise */ int packed, /* TRUE if A will be packed, FALSE otherwise */ int stype, /* stype of A */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_allocate_sparse (size_t, size_t, size_t, int, int, int, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_free_sparse: free a sparse matrix */ /* -------------------------------------------------------------------------- */ int cholmod_free_sparse ( /* ---- in/out --- */ cholmod_sparse **A, /* matrix to deallocate, NULL on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_free_sparse (cholmod_sparse **, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_reallocate_sparse: change the size (# entries) of sparse matrix */ /* -------------------------------------------------------------------------- */ int cholmod_reallocate_sparse ( /* ---- input ---- */ size_t nznew, /* new # of entries in A */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix to reallocate */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_reallocate_sparse ( size_t, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_nnz: return number of nonzeros in a sparse matrix */ /* -------------------------------------------------------------------------- */ SuiteSparse_long cholmod_nnz ( /* ---- input ---- */ cholmod_sparse *A, /* --------------- */ cholmod_common *Common ) ; SuiteSparse_long cholmod_l_nnz (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_speye: sparse identity matrix */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_speye ( /* ---- input ---- */ size_t nrow, /* # of rows of A */ size_t ncol, /* # of columns of A */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_speye (size_t, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_spzeros: sparse zero matrix */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_spzeros ( /* ---- input ---- */ size_t nrow, /* # of rows of A */ size_t ncol, /* # of columns of A */ size_t nzmax, /* max # of nonzeros of A */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_spzeros (size_t, size_t, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_transpose: transpose a sparse matrix */ /* -------------------------------------------------------------------------- */ /* Return A' or A.' The "values" parameter is 0, 1, or 2 to denote the pattern * transpose, the array transpose (A.'), and the complex conjugate transpose * (A'). */ cholmod_sparse *cholmod_transpose ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_transpose (cholmod_sparse *, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_transpose_unsym: transpose an unsymmetric sparse matrix */ /* -------------------------------------------------------------------------- */ /* Compute F = A', A (:,f)', or A (p,f)', where A is unsymmetric and F is * already allocated. See cholmod_transpose for a simpler routine. */ int cholmod_transpose_unsym ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */ int *Perm, /* size nrow, if present (can be NULL) */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ cholmod_sparse *F, /* F = A', A(:,f)', or A(p,f)' */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_transpose_unsym (cholmod_sparse *, int, SuiteSparse_long *, SuiteSparse_long *, size_t, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_transpose_sym: transpose a symmetric sparse matrix */ /* -------------------------------------------------------------------------- */ /* Compute F = A' or A (p,p)', where A is symmetric and F is already allocated. * See cholmod_transpose for a simpler routine. */ int cholmod_transpose_sym ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */ int *Perm, /* size nrow, if present (can be NULL) */ /* ---- output --- */ cholmod_sparse *F, /* F = A' or A(p,p)' */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_transpose_sym (cholmod_sparse *, int, SuiteSparse_long *, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_ptranspose: transpose a sparse matrix */ /* -------------------------------------------------------------------------- */ /* Return A' or A(p,p)' if A is symmetric. Return A', A(:,f)', or A(p,f)' if * A is unsymmetric. */ cholmod_sparse *cholmod_ptranspose ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */ int *Perm, /* if non-NULL, F = A(p,f) or A(p,p) */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_ptranspose (cholmod_sparse *, int, SuiteSparse_long *, SuiteSparse_long *, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_sort: sort row indices in each column of sparse matrix */ /* -------------------------------------------------------------------------- */ int cholmod_sort ( /* ---- in/out --- */ cholmod_sparse *A, /* matrix to sort */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_sort (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_band: C = tril (triu (A,k1), k2) */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_band ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to extract band matrix from */ SuiteSparse_long k1, /* ignore entries below the k1-st diagonal */ SuiteSparse_long k2, /* ignore entries above the k2-nd diagonal */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_band (cholmod_sparse *, SuiteSparse_long, SuiteSparse_long, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_band_inplace: A = tril (triu (A,k1), k2) */ /* -------------------------------------------------------------------------- */ int cholmod_band_inplace ( /* ---- input ---- */ SuiteSparse_long k1, /* ignore entries below the k1-st diagonal */ SuiteSparse_long k2, /* ignore entries above the k2-nd diagonal */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix from which entries not in band are removed */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_band_inplace (SuiteSparse_long, SuiteSparse_long, int, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_aat: C = A*A' or A(:,f)*A(:,f)' */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_aat ( /* ---- input ---- */ cholmod_sparse *A, /* input matrix; C=A*A' is constructed */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag), * -2: pattern only, no diagonal, add 50%+n extra * space to C */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_aat (cholmod_sparse *, SuiteSparse_long *, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_copy_sparse: C = A, create an exact copy of a sparse matrix */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_copy_sparse ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_copy_sparse (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_copy: C = A, with possible change of stype */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_copy ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ int stype, /* requested stype of C */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_copy (cholmod_sparse *, int, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_add: C = alpha*A + beta*B */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_add ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to add */ cholmod_sparse *B, /* matrix to add */ double alpha [2], /* scale factor for A */ double beta [2], /* scale factor for B */ int values, /* if TRUE compute the numerical values of C */ int sorted, /* if TRUE, sort columns of C */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_add (cholmod_sparse *, cholmod_sparse *, double *, double *, int, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_sparse_xtype: change the xtype of a sparse matrix */ /* -------------------------------------------------------------------------- */ int cholmod_sparse_xtype ( /* ---- input ---- */ int to_xtype, /* requested xtype (pattern, real, complex, zomplex) */ /* ---- in/out --- */ cholmod_sparse *A, /* sparse matrix to change */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_sparse_xtype (int, cholmod_sparse *, cholmod_common *) ; /* ========================================================================== */ /* === Core/cholmod_factor ================================================== */ /* ========================================================================== */ /* A symbolic and numeric factorization, either simplicial or supernodal. * In all cases, the row indices in the columns of L are kept sorted. */ typedef struct cholmod_factor_struct { /* ---------------------------------------------------------------------- */ /* for both simplicial and supernodal factorizations */ /* ---------------------------------------------------------------------- */ size_t n ; /* L is n-by-n */ size_t minor ; /* If the factorization failed, L->minor is the column * at which it failed (in the range 0 to n-1). A value * of n means the factorization was successful or * the matrix has not yet been factorized. */ /* ---------------------------------------------------------------------- */ /* symbolic ordering and analysis */ /* ---------------------------------------------------------------------- */ void *Perm ; /* size n, permutation used */ void *ColCount ; /* size n, column counts for simplicial L */ void *IPerm ; /* size n, inverse permutation. Only created by * cholmod_solve2 if Bset is used. */ /* ---------------------------------------------------------------------- */ /* simplicial factorization */ /* ---------------------------------------------------------------------- */ size_t nzmax ; /* size of i and x */ void *p ; /* p [0..ncol], the column pointers */ void *i ; /* i [0..nzmax-1], the row indices */ void *x ; /* x [0..nzmax-1], the numerical values */ void *z ; void *nz ; /* nz [0..ncol-1], the # of nonzeros in each column. * i [p [j] ... p [j]+nz[j]-1] contains the row indices, * and the numerical values are in the same locatins * in x. The value of i [p [k]] is always k. */ void *next ; /* size ncol+2. next [j] is the next column in i/x */ void *prev ; /* size ncol+2. prev [j] is the prior column in i/x. * head of the list is ncol+1, and the tail is ncol. */ /* ---------------------------------------------------------------------- */ /* supernodal factorization */ /* ---------------------------------------------------------------------- */ /* Note that L->x is shared with the simplicial data structure. L->x has * size L->nzmax for a simplicial factor, and size L->xsize for a supernodal * factor. */ size_t nsuper ; /* number of supernodes */ size_t ssize ; /* size of s, integer part of supernodes */ size_t xsize ; /* size of x, real part of supernodes */ size_t maxcsize ; /* size of largest update matrix */ size_t maxesize ; /* max # of rows in supernodes, excl. triangular part */ void *super ; /* size nsuper+1, first col in each supernode */ void *pi ; /* size nsuper+1, pointers to integer patterns */ void *px ; /* size nsuper+1, pointers to real parts */ void *s ; /* size ssize, integer part of supernodes */ /* ---------------------------------------------------------------------- */ /* factorization type */ /* ---------------------------------------------------------------------- */ int ordering ; /* ordering method used */ int is_ll ; /* TRUE if LL', FALSE if LDL' */ int is_super ; /* TRUE if supernodal, FALSE if simplicial */ int is_monotonic ; /* TRUE if columns of L appear in order 0..n-1. * Only applicable to simplicial numeric types. */ /* There are 8 types of factor objects that cholmod_factor can represent * (only 6 are used): * * Numeric types (xtype is not CHOLMOD_PATTERN) * -------------------------------------------- * * simplicial LDL': (is_ll FALSE, is_super FALSE). Stored in compressed * column form, using the simplicial components above (nzmax, p, i, * x, z, nz, next, and prev). The unit diagonal of L is not stored, * and D is stored in its place. There are no supernodes. * * simplicial LL': (is_ll TRUE, is_super FALSE). Uses the same storage * scheme as the simplicial LDL', except that D does not appear. * The first entry of each column of L is the diagonal entry of * that column of L. * * supernodal LDL': (is_ll FALSE, is_super TRUE). Not used. * FUTURE WORK: add support for supernodal LDL' * * supernodal LL': (is_ll TRUE, is_super TRUE). A supernodal factor, * using the supernodal components described above (nsuper, ssize, * xsize, maxcsize, maxesize, super, pi, px, s, x, and z). * * * Symbolic types (xtype is CHOLMOD_PATTERN) * ----------------------------------------- * * simplicial LDL': (is_ll FALSE, is_super FALSE). Nothing is present * except Perm and ColCount. * * simplicial LL': (is_ll TRUE, is_super FALSE). Identical to the * simplicial LDL', except for the is_ll flag. * * supernodal LDL': (is_ll FALSE, is_super TRUE). Not used. * FUTURE WORK: add support for supernodal LDL' * * supernodal LL': (is_ll TRUE, is_super TRUE). A supernodal symbolic * factorization. The simplicial symbolic information is present * (Perm and ColCount), as is all of the supernodal factorization * except for the numerical values (x and z). */ int itype ; /* The integer arrays are Perm, ColCount, p, i, nz, * next, prev, super, pi, px, and s. If itype is * CHOLMOD_INT, all of these are int arrays. * CHOLMOD_INTLONG: p, pi, px are SuiteSparse_long, others int. * CHOLMOD_LONG: all integer arrays are SuiteSparse_long. */ int xtype ; /* pattern, real, complex, or zomplex */ int dtype ; /* x and z double or float */ } cholmod_factor ; /* -------------------------------------------------------------------------- */ /* cholmod_allocate_factor: allocate a factor (symbolic LL' or LDL') */ /* -------------------------------------------------------------------------- */ cholmod_factor *cholmod_allocate_factor ( /* ---- input ---- */ size_t n, /* L is n-by-n */ /* --------------- */ cholmod_common *Common ) ; cholmod_factor *cholmod_l_allocate_factor (size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_free_factor: free a factor */ /* -------------------------------------------------------------------------- */ int cholmod_free_factor ( /* ---- in/out --- */ cholmod_factor **L, /* factor to free, NULL on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_free_factor (cholmod_factor **, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_reallocate_factor: change the # entries in a factor */ /* -------------------------------------------------------------------------- */ int cholmod_reallocate_factor ( /* ---- input ---- */ size_t nznew, /* new # of entries in L */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_reallocate_factor (size_t, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_change_factor: change the type of factor (e.g., LDL' to LL') */ /* -------------------------------------------------------------------------- */ int cholmod_change_factor ( /* ---- input ---- */ int to_xtype, /* to CHOLMOD_PATTERN, _REAL, _COMPLEX, _ZOMPLEX */ int to_ll, /* TRUE: convert to LL', FALSE: LDL' */ int to_super, /* TRUE: convert to supernodal, FALSE: simplicial */ int to_packed, /* TRUE: pack simplicial columns, FALSE: do not pack */ int to_monotonic, /* TRUE: put simplicial columns in order, FALSE: not */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_change_factor ( int, int, int, int, int, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_pack_factor: pack the columns of a factor */ /* -------------------------------------------------------------------------- */ /* Pack the columns of a simplicial factor. Unlike cholmod_change_factor, * it can pack the columns of a factor even if they are not stored in their * natural order (non-monotonic). */ int cholmod_pack_factor ( /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_pack_factor (cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_reallocate_column: resize a single column of a factor */ /* -------------------------------------------------------------------------- */ int cholmod_reallocate_column ( /* ---- input ---- */ size_t j, /* the column to reallocate */ size_t need, /* required size of column j */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_reallocate_column (size_t, size_t, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_factor_to_sparse: create a sparse matrix copy of a factor */ /* -------------------------------------------------------------------------- */ /* Only operates on numeric factors, not symbolic ones */ cholmod_sparse *cholmod_factor_to_sparse ( /* ---- in/out --- */ cholmod_factor *L, /* factor to copy, converted to symbolic on output */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_factor_to_sparse (cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_copy_factor: create a copy of a factor */ /* -------------------------------------------------------------------------- */ cholmod_factor *cholmod_copy_factor ( /* ---- input ---- */ cholmod_factor *L, /* factor to copy */ /* --------------- */ cholmod_common *Common ) ; cholmod_factor *cholmod_l_copy_factor (cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_factor_xtype: change the xtype of a factor */ /* -------------------------------------------------------------------------- */ int cholmod_factor_xtype ( /* ---- input ---- */ int to_xtype, /* requested xtype (real, complex, or zomplex) */ /* ---- in/out --- */ cholmod_factor *L, /* factor to change */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_factor_xtype (int, cholmod_factor *, cholmod_common *) ; /* ========================================================================== */ /* === Core/cholmod_dense =================================================== */ /* ========================================================================== */ /* A dense matrix in column-oriented form. It has no itype since it contains * no integers. Entry in row i and column j is located in x [i+j*d]. */ typedef struct cholmod_dense_struct { size_t nrow ; /* the matrix is nrow-by-ncol */ size_t ncol ; size_t nzmax ; /* maximum number of entries in the matrix */ size_t d ; /* leading dimension (d >= nrow must hold) */ void *x ; /* size nzmax or 2*nzmax, if present */ void *z ; /* size nzmax, if present */ int xtype ; /* pattern, real, complex, or zomplex */ int dtype ; /* x and z double or float */ } cholmod_dense ; /* -------------------------------------------------------------------------- */ /* cholmod_allocate_dense: allocate a dense matrix (contents uninitialized) */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_allocate_dense ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ size_t d, /* leading dimension */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_allocate_dense (size_t, size_t, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_zeros: allocate a dense matrix and set it to zero */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_zeros ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_zeros (size_t, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_ones: allocate a dense matrix and set it to all ones */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_ones ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_ones (size_t, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_eye: allocate a dense matrix and set it to the identity matrix */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_eye ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_eye (size_t, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_free_dense: free a dense matrix */ /* -------------------------------------------------------------------------- */ int cholmod_free_dense ( /* ---- in/out --- */ cholmod_dense **X, /* dense matrix to deallocate, NULL on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_free_dense (cholmod_dense **, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_ensure_dense: ensure a dense matrix has a given size and type */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_ensure_dense ( /* ---- input/output ---- */ cholmod_dense **XHandle, /* matrix handle to check */ /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ size_t d, /* leading dimension */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_ensure_dense (cholmod_dense **, size_t, size_t, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_sparse_to_dense: create a dense matrix copy of a sparse matrix */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_sparse_to_dense ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_sparse_to_dense (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_dense_to_sparse: create a sparse matrix copy of a dense matrix */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_dense_to_sparse ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ int values, /* TRUE if values to be copied, FALSE otherwise */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_dense_to_sparse (cholmod_dense *, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_copy_dense: create a copy of a dense matrix */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_copy_dense ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_copy_dense (cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_copy_dense2: copy a dense matrix (pre-allocated) */ /* -------------------------------------------------------------------------- */ int cholmod_copy_dense2 ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ /* ---- output --- */ cholmod_dense *Y, /* copy of matrix X */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_copy_dense2 (cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_dense_xtype: change the xtype of a dense matrix */ /* -------------------------------------------------------------------------- */ int cholmod_dense_xtype ( /* ---- input ---- */ int to_xtype, /* requested xtype (real, complex,or zomplex) */ /* ---- in/out --- */ cholmod_dense *X, /* dense matrix to change */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_dense_xtype (int, cholmod_dense *, cholmod_common *) ; /* ========================================================================== */ /* === Core/cholmod_triplet ================================================= */ /* ========================================================================== */ /* A sparse matrix stored in triplet form. */ typedef struct cholmod_triplet_struct { size_t nrow ; /* the matrix is nrow-by-ncol */ size_t ncol ; size_t nzmax ; /* maximum number of entries in the matrix */ size_t nnz ; /* number of nonzeros in the matrix */ void *i ; /* i [0..nzmax-1], the row indices */ void *j ; /* j [0..nzmax-1], the column indices */ void *x ; /* size nzmax or 2*nzmax, if present */ void *z ; /* size nzmax, if present */ int stype ; /* Describes what parts of the matrix are considered: * * 0: matrix is "unsymmetric": use both upper and lower triangular parts * (the matrix may actually be symmetric in pattern and value, but * both parts are explicitly stored and used). May be square or * rectangular. * >0: matrix is square and symmetric. Entries in the lower triangular * part are transposed and added to the upper triangular part when * the matrix is converted to cholmod_sparse form. * <0: matrix is square and symmetric. Entries in the upper triangular * part are transposed and added to the lower triangular part when * the matrix is converted to cholmod_sparse form. * * Note that stype>0 and stype<0 are different for cholmod_sparse and * cholmod_triplet. The reason is simple. You can permute a symmetric * triplet matrix by simply replacing a row and column index with their * new row and column indices, via an inverse permutation. Suppose * P = L->Perm is your permutation, and Pinv is an array of size n. * Suppose a symmetric matrix A is represent by a triplet matrix T, with * entries only in the upper triangular part. Then the following code: * * Ti = T->i ; * Tj = T->j ; * for (k = 0 ; k < n ; k++) Pinv [P [k]] = k ; * for (k = 0 ; k < nz ; k++) Ti [k] = Pinv [Ti [k]] ; * for (k = 0 ; k < nz ; k++) Tj [k] = Pinv [Tj [k]] ; * * creates the triplet form of C=P*A*P'. However, if T initially * contains just the upper triangular entries (T->stype = 1), after * permutation it has entries in both the upper and lower triangular * parts. These entries should be transposed when constructing the * cholmod_sparse form of A, which is what cholmod_triplet_to_sparse * does. Thus: * * C = cholmod_triplet_to_sparse (T, 0, &Common) ; * * will return the matrix C = P*A*P'. * * Since the triplet matrix T is so simple to generate, it's quite easy * to remove entries that you do not want, prior to converting T to the * cholmod_sparse form. So if you include these entries in T, CHOLMOD * assumes that there must be a reason (such as the one above). Thus, * no entry in a triplet matrix is ever ignored. */ int itype ; /* CHOLMOD_LONG: i and j are SuiteSparse_long. Otherwise int */ int xtype ; /* pattern, real, complex, or zomplex */ int dtype ; /* x and z are double or float */ } cholmod_triplet ; /* -------------------------------------------------------------------------- */ /* cholmod_allocate_triplet: allocate a triplet matrix */ /* -------------------------------------------------------------------------- */ cholmod_triplet *cholmod_allocate_triplet ( /* ---- input ---- */ size_t nrow, /* # of rows of T */ size_t ncol, /* # of columns of T */ size_t nzmax, /* max # of nonzeros of T */ int stype, /* stype of T */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_triplet *cholmod_l_allocate_triplet (size_t, size_t, size_t, int, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_free_triplet: free a triplet matrix */ /* -------------------------------------------------------------------------- */ int cholmod_free_triplet ( /* ---- in/out --- */ cholmod_triplet **T, /* triplet matrix to deallocate, NULL on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_free_triplet (cholmod_triplet **, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_reallocate_triplet: change the # of entries in a triplet matrix */ /* -------------------------------------------------------------------------- */ int cholmod_reallocate_triplet ( /* ---- input ---- */ size_t nznew, /* new # of entries in T */ /* ---- in/out --- */ cholmod_triplet *T, /* triplet matrix to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_reallocate_triplet (size_t, cholmod_triplet *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_sparse_to_triplet: create a triplet matrix copy of a sparse matrix*/ /* -------------------------------------------------------------------------- */ cholmod_triplet *cholmod_sparse_to_triplet ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) ; cholmod_triplet *cholmod_l_sparse_to_triplet (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_triplet_to_sparse: create a sparse matrix copy of a triplet matrix*/ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_triplet_to_sparse ( /* ---- input ---- */ cholmod_triplet *T, /* matrix to copy */ size_t nzmax, /* allocate at least this much space in output matrix */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_triplet_to_sparse (cholmod_triplet *, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_copy_triplet: create a copy of a triplet matrix */ /* -------------------------------------------------------------------------- */ cholmod_triplet *cholmod_copy_triplet ( /* ---- input ---- */ cholmod_triplet *T, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) ; cholmod_triplet *cholmod_l_copy_triplet (cholmod_triplet *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_triplet_xtype: change the xtype of a triplet matrix */ /* -------------------------------------------------------------------------- */ int cholmod_triplet_xtype ( /* ---- input ---- */ int to_xtype, /* requested xtype (pattern, real, complex,or zomplex)*/ /* ---- in/out --- */ cholmod_triplet *T, /* triplet matrix to change */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_triplet_xtype (int, cholmod_triplet *, cholmod_common *) ; /* ========================================================================== */ /* === Core/cholmod_memory ================================================== */ /* ========================================================================== */ /* The user may make use of these, just like malloc and free. You can even * malloc an object and safely free it with cholmod_free, and visa versa * (except that the memory usage statistics will be corrupted). These routines * do differ from malloc and free. If cholmod_free is given a NULL pointer, * for example, it does nothing (unlike the ANSI free). cholmod_realloc does * not return NULL if given a non-NULL pointer and a nonzero size, even if it * fails (it returns the original pointer and sets an error code in * Common->status instead). * * CHOLMOD keeps track of the amount of memory it has allocated, and so the * cholmod_free routine also takes the size of the object being freed. This * is only used for statistics. If you, the user of CHOLMOD, pass the wrong * size, the only consequence is that the memory usage statistics will be * corrupted. */ void *cholmod_malloc /* returns pointer to the newly malloc'd block */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* --------------- */ cholmod_common *Common ) ; void *cholmod_l_malloc (size_t, size_t, cholmod_common *) ; void *cholmod_calloc /* returns pointer to the newly calloc'd block */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* --------------- */ cholmod_common *Common ) ; void *cholmod_l_calloc (size_t, size_t, cholmod_common *) ; void *cholmod_free /* always returns NULL */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* ---- in/out --- */ void *p, /* block of memory to free */ /* --------------- */ cholmod_common *Common ) ; void *cholmod_l_free (size_t, size_t, void *, cholmod_common *) ; void *cholmod_realloc /* returns pointer to reallocated block */ ( /* ---- input ---- */ size_t nnew, /* requested # of items in reallocated block */ size_t size, /* size of each item */ /* ---- in/out --- */ void *p, /* block of memory to realloc */ size_t *n, /* current size on input, nnew on output if successful*/ /* --------------- */ cholmod_common *Common ) ; void *cholmod_l_realloc (size_t, size_t, void *, size_t *, cholmod_common *) ; int cholmod_realloc_multiple ( /* ---- input ---- */ size_t nnew, /* requested # of items in reallocated blocks */ int nint, /* number of int/SuiteSparse_long blocks */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* ---- in/out --- */ void **Iblock, /* int or SuiteSparse_long block */ void **Jblock, /* int or SuiteSparse_long block */ void **Xblock, /* complex, double, or float block */ void **Zblock, /* zomplex case only: double or float block */ size_t *n, /* current size of the I,J,X,Z blocks on input, * nnew on output if successful */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_realloc_multiple (size_t, int, int, void **, void **, void **, void **, size_t *, cholmod_common *) ; /* ========================================================================== */ /* === version control ====================================================== */ /* ========================================================================== */ int cholmod_version /* returns CHOLMOD_VERSION */ ( /* output, contents not defined on input. Not used if NULL. version [0] = CHOLMOD_MAIN_VERSION version [1] = CHOLMOD_SUB_VERSION version [2] = CHOLMOD_SUBSUB_VERSION */ int version [3] ) ; int cholmod_l_version (int version [3]) ; /* Versions prior to 2.1.1 do not have the above function. The following code fragment will work with any version of CHOLMOD: #ifdef CHOLMOD_HAS_VERSION_FUNCTION v = cholmod_version (NULL) ; #else v = CHOLMOD_VERSION ; #endif */ /* ========================================================================== */ /* === symmetry types ======================================================= */ /* ========================================================================== */ #define CHOLMOD_MM_RECTANGULAR 1 #define CHOLMOD_MM_UNSYMMETRIC 2 #define CHOLMOD_MM_SYMMETRIC 3 #define CHOLMOD_MM_HERMITIAN 4 #define CHOLMOD_MM_SKEW_SYMMETRIC 5 #define CHOLMOD_MM_SYMMETRIC_POSDIAG 6 #define CHOLMOD_MM_HERMITIAN_POSDIAG 7 /* ========================================================================== */ /* === Numerical relop macros =============================================== */ /* ========================================================================== */ /* These macros correctly handle the NaN case. * * CHOLMOD_IS_NAN(x): * True if x is NaN. False otherwise. The commonly-existing isnan(x) * function could be used, but it's not in Kernighan & Ritchie 2nd edition * (ANSI C89). It may appear in , but I'm not certain about * portability. The expression x != x is true if and only if x is NaN, * according to the IEEE 754 floating-point standard. * * CHOLMOD_IS_ZERO(x): * True if x is zero. False if x is nonzero, NaN, or +/- Inf. * This is (x == 0) if the compiler is IEEE 754 compliant. * * CHOLMOD_IS_NONZERO(x): * True if x is nonzero, NaN, or +/- Inf. False if x zero. * This is (x != 0) if the compiler is IEEE 754 compliant. * * CHOLMOD_IS_LT_ZERO(x): * True if x is < zero or -Inf. False if x is >= 0, NaN, or +Inf. * This is (x < 0) if the compiler is IEEE 754 compliant. * * CHOLMOD_IS_GT_ZERO(x): * True if x is > zero or +Inf. False if x is <= 0, NaN, or -Inf. * This is (x > 0) if the compiler is IEEE 754 compliant. * * CHOLMOD_IS_LE_ZERO(x): * True if x is <= zero or -Inf. False if x is > 0, NaN, or +Inf. * This is (x <= 0) if the compiler is IEEE 754 compliant. */ #ifdef CHOLMOD_WINDOWS /* Yes, this is exceedingly ugly. Blame Microsoft, which hopelessly */ /* violates the IEEE 754 floating-point standard in a bizarre way. */ /* If you're using an IEEE 754-compliant compiler, then x != x is true */ /* iff x is NaN. For Microsoft, (x < x) is true iff x is NaN. */ /* So either way, this macro safely detects a NaN. */ #define CHOLMOD_IS_NAN(x) (((x) != (x)) || (((x) < (x)))) #define CHOLMOD_IS_ZERO(x) (((x) == 0.) && !CHOLMOD_IS_NAN(x)) #define CHOLMOD_IS_NONZERO(x) (((x) != 0.) || CHOLMOD_IS_NAN(x)) #define CHOLMOD_IS_LT_ZERO(x) (((x) < 0.) && !CHOLMOD_IS_NAN(x)) #define CHOLMOD_IS_GT_ZERO(x) (((x) > 0.) && !CHOLMOD_IS_NAN(x)) #define CHOLMOD_IS_LE_ZERO(x) (((x) <= 0.) && !CHOLMOD_IS_NAN(x)) #else /* These all work properly, according to the IEEE 754 standard ... except on */ /* a PC with windows. Works fine in Linux on the same PC... */ #define CHOLMOD_IS_NAN(x) ((x) != (x)) #define CHOLMOD_IS_ZERO(x) ((x) == 0.) #define CHOLMOD_IS_NONZERO(x) ((x) != 0.) #define CHOLMOD_IS_LT_ZERO(x) ((x) < 0.) #define CHOLMOD_IS_GT_ZERO(x) ((x) > 0.) #define CHOLMOD_IS_LE_ZERO(x) ((x) <= 0.) #endif #endif Matrix/src/CHOLMOD/Include/cholmod_supernodal.h0000644000175100001440000001445012271765436021046 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_supernodal.h ========================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_supernodal.h. * Copyright (C) 2005-2006, Timothy A. Davis * CHOLMOD/Include/cholmod_supernodal.h is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* CHOLMOD Supernodal module. * * Supernodal analysis, factorization, and solve. The simplest way to use * these routines is via the Cholesky module. It does not provide any * fill-reducing orderings, but does accept the orderings computed by the * Cholesky module. It does not require the Cholesky module itself, however. * * Primary routines: * ----------------- * cholmod_super_symbolic supernodal symbolic analysis * cholmod_super_numeric supernodal numeric factorization * cholmod_super_lsolve supernodal Lx=b solve * cholmod_super_ltsolve supernodal L'x=b solve * * Prototypes for the BLAS and LAPACK routines that CHOLMOD uses are listed * below, including how they are used in CHOLMOD. * * BLAS routines: * -------------- * dtrsv solve Lx=b or L'x=b, L non-unit diagonal, x and b stride-1 * dtrsm solve LX=B or L'X=b, L non-unit diagonal * dgemv y=y-A*x or y=y-A'*x (x and y stride-1) * dgemm C=A*B', C=C-A*B, or C=C-A'*B * dsyrk C=tril(A*A') * * LAPACK routines: * ---------------- * dpotrf LAPACK: A=chol(tril(A)) * * Requires the Core module, and two external packages: LAPACK and the BLAS. * Optionally used by the Cholesky module. */ #ifndef CHOLMOD_SUPERNODAL_H #define CHOLMOD_SUPERNODAL_H #include "cholmod_core.h" /* -------------------------------------------------------------------------- */ /* cholmod_super_symbolic */ /* -------------------------------------------------------------------------- */ /* Analyzes A, AA', or A(:,f)*A(:,f)' in preparation for a supernodal numeric * factorization. The user need not call this directly; cholmod_analyze is * a "simple" wrapper for this routine. */ int cholmod_super_symbolic ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ cholmod_sparse *F, /* F = A' or A(:,f)' */ int *Parent, /* elimination tree */ /* ---- in/out --- */ cholmod_factor *L, /* simplicial symbolic on input, * supernodal symbolic on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_super_symbolic (cholmod_sparse *, cholmod_sparse *, SuiteSparse_long *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_super_symbolic2 */ /* -------------------------------------------------------------------------- */ /* Analyze for supernodal Cholesky or multifrontal QR. CHOLMOD itself always * analyzes for supernodal Cholesky, of course. This "for_cholesky = TRUE" * option is used by SuiteSparseQR only. Added for V1.7 */ int cholmod_super_symbolic2 ( /* ---- input ---- */ int for_cholesky, /* Cholesky if TRUE, QR if FALSE */ cholmod_sparse *A, /* matrix to analyze */ cholmod_sparse *F, /* F = A' or A(:,f)' */ int *Parent, /* elimination tree */ /* ---- in/out --- */ cholmod_factor *L, /* simplicial symbolic on input, * supernodal symbolic on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_super_symbolic2 (int, cholmod_sparse *, cholmod_sparse *, SuiteSparse_long *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_super_numeric */ /* -------------------------------------------------------------------------- */ /* Computes the numeric LL' factorization of A, AA', or A(:,f)*A(:,f)' using * a BLAS-based supernodal method. The user need not call this directly; * cholmod_factorize is a "simple" wrapper for this routine. */ int cholmod_super_numeric ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* F = A' or A(:,f)' */ double beta [2], /* beta*I is added to diagonal of matrix to factorize */ /* ---- in/out --- */ cholmod_factor *L, /* factorization */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_super_numeric (cholmod_sparse *, cholmod_sparse *, double *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_super_lsolve */ /* -------------------------------------------------------------------------- */ /* Solve Lx=b where L is from a supernodal numeric factorization. The user * need not call this routine directly. cholmod_solve is a "simple" wrapper * for this routine. */ int cholmod_super_lsolve ( /* ---- input ---- */ cholmod_factor *L, /* factor to use for the forward solve */ /* ---- output ---- */ cholmod_dense *X, /* b on input, solution to Lx=b on output */ /* ---- workspace */ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_super_lsolve (cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_super_ltsolve */ /* -------------------------------------------------------------------------- */ /* Solve L'x=b where L is from a supernodal numeric factorization. The user * need not call this routine directly. cholmod_solve is a "simple" wrapper * for this routine. */ int cholmod_super_ltsolve ( /* ---- input ---- */ cholmod_factor *L, /* factor to use for the backsolve */ /* ---- output ---- */ cholmod_dense *X, /* b on input, solution to L'x=b on output */ /* ---- workspace */ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_super_ltsolve (cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; #endif Matrix/src/CHOLMOD/Include/cholmod_cholesky.h0000644000175100001440000005330712271765436020517 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_cholesky.h =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_cholesky.h. Copyright (C) 2005-2013, Timothy A. Davis * CHOLMOD/Include/cholmod_cholesky.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* CHOLMOD Cholesky module. * * Sparse Cholesky routines: analysis, factorization, and solve. * * The primary routines are all that a user requires to order, analyze, and * factorize a sparse symmetric positive definite matrix A (or A*A'), and * to solve Ax=b (or A*A'x=b). The primary routines rely on the secondary * routines, the CHOLMOD Core module, and the AMD and COLAMD packages. They * make optional use of the CHOLMOD Supernodal and Partition modules, the * METIS package, and the CCOLAMD package. * * Primary routines: * ----------------- * * cholmod_analyze order and analyze (simplicial or supernodal) * cholmod_factorize simplicial or supernodal Cholesky factorization * cholmod_solve solve a linear system (simplicial or supernodal) * cholmod_solve2 like cholmod_solve, but reuse workspace * cholmod_spsolve solve a linear system (sparse x and b) * * Secondary routines: * ------------------ * * cholmod_analyze_p analyze, with user-provided permutation or f set * cholmod_factorize_p factorize, with user-provided permutation or f * cholmod_analyze_ordering analyze a fill-reducing ordering * cholmod_etree find the elimination tree * cholmod_rowcolcounts compute the row/column counts of L * cholmod_amd order using AMD * cholmod_colamd order using COLAMD * cholmod_rowfac incremental simplicial factorization * cholmod_rowfac_mask rowfac, specific to LPDASA * cholmod_row_subtree find the nonzero pattern of a row of L * cholmod_resymbol recompute the symbolic pattern of L * cholmod_resymbol_noperm recompute the symbolic pattern of L, no L->Perm * cholmod_postorder postorder a tree * * Requires the Core module, and two packages: AMD and COLAMD. * Optionally uses the Supernodal and Partition modules. * Required by the Partition module. */ #ifndef CHOLMOD_CHOLESKY_H #define CHOLMOD_CHOLESKY_H #include "cholmod_config.h" #include "cholmod_core.h" #ifndef NPARTITION #include "cholmod_partition.h" #endif #ifndef NSUPERNODAL #include "cholmod_supernodal.h" #endif /* -------------------------------------------------------------------------- */ /* cholmod_analyze: order and analyze (simplicial or supernodal) */ /* -------------------------------------------------------------------------- */ /* Orders and analyzes A, AA', PAP', or PAA'P' and returns a symbolic factor * that can later be passed to cholmod_factorize. */ cholmod_factor *cholmod_analyze ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order and analyze */ /* --------------- */ cholmod_common *Common ) ; cholmod_factor *cholmod_l_analyze (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_analyze_p: analyze, with user-provided permutation or f set */ /* -------------------------------------------------------------------------- */ /* Orders and analyzes A, AA', PAP', PAA'P', FF', or PFF'P and returns a * symbolic factor that can later be passed to cholmod_factorize, where * F = A(:,fset) if fset is not NULL and A->stype is zero. * UserPerm is tried if non-NULL. */ cholmod_factor *cholmod_analyze_p ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order and analyze */ int *UserPerm, /* user-provided permutation, size A->nrow */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* --------------- */ cholmod_common *Common ) ; cholmod_factor *cholmod_l_analyze_p (cholmod_sparse *, SuiteSparse_long *, SuiteSparse_long *, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_analyze_p2: analyze for sparse Cholesky or sparse QR */ /* -------------------------------------------------------------------------- */ cholmod_factor *cholmod_analyze_p2 ( /* ---- input ---- */ int for_cholesky, /* if TRUE, then analyze for Cholesky; else for QR */ cholmod_sparse *A, /* matrix to order and analyze */ int *UserPerm, /* user-provided permutation, size A->nrow */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* --------------- */ cholmod_common *Common ) ; cholmod_factor *cholmod_l_analyze_p2 (int, cholmod_sparse *, SuiteSparse_long *, SuiteSparse_long *, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_factorize: simplicial or supernodal Cholesky factorization */ /* -------------------------------------------------------------------------- */ /* Factorizes PAP' (or PAA'P' if A->stype is 0), using a factor obtained * from cholmod_analyze. The analysis can be re-used simply by calling this * routine a second time with another matrix. A must have the same nonzero * pattern as that passed to cholmod_analyze. */ int cholmod_factorize ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ /* ---- in/out --- */ cholmod_factor *L, /* resulting factorization */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_factorize (cholmod_sparse *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_factorize_p: factorize, with user-provided permutation or fset */ /* -------------------------------------------------------------------------- */ /* Same as cholmod_factorize, but with more options. */ int cholmod_factorize_p ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ double beta [2], /* factorize beta*I+A or beta*I+A'*A */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- in/out --- */ cholmod_factor *L, /* resulting factorization */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_factorize_p (cholmod_sparse *, double *, SuiteSparse_long *, size_t, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_solve: solve a linear system (simplicial or supernodal) */ /* -------------------------------------------------------------------------- */ /* Solves one of many linear systems with a dense right-hand-side, using the * factorization from cholmod_factorize (or as modified by any other CHOLMOD * routine). D is identity for LL' factorizations. */ #define CHOLMOD_A 0 /* solve Ax=b */ #define CHOLMOD_LDLt 1 /* solve LDL'x=b */ #define CHOLMOD_LD 2 /* solve LDx=b */ #define CHOLMOD_DLt 3 /* solve DL'x=b */ #define CHOLMOD_L 4 /* solve Lx=b */ #define CHOLMOD_Lt 5 /* solve L'x=b */ #define CHOLMOD_D 6 /* solve Dx=b */ #define CHOLMOD_P 7 /* permute x=Px */ #define CHOLMOD_Pt 8 /* permute x=P'x */ cholmod_dense *cholmod_solve /* returns the solution X */ ( /* ---- input ---- */ int sys, /* system to solve */ cholmod_factor *L, /* factorization to use */ cholmod_dense *B, /* right-hand-side */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_solve (int, cholmod_factor *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_solve2: like cholmod_solve, but with reusable workspace */ /* -------------------------------------------------------------------------- */ int cholmod_solve2 /* returns TRUE on success, FALSE on failure */ ( /* ---- input ---- */ int sys, /* system to solve */ cholmod_factor *L, /* factorization to use */ cholmod_dense *B, /* right-hand-side */ cholmod_sparse *Bset, /* ---- output --- */ cholmod_dense **X_Handle, /* solution, allocated if need be */ cholmod_sparse **Xset_Handle, /* ---- workspace */ cholmod_dense **Y_Handle, /* workspace, or NULL */ cholmod_dense **E_Handle, /* workspace, or NULL */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_solve2 (int, cholmod_factor *, cholmod_dense *, cholmod_sparse *, cholmod_dense **, cholmod_sparse **, cholmod_dense **, cholmod_dense **, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_spsolve: solve a linear system with a sparse right-hand-side */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_spsolve ( /* ---- input ---- */ int sys, /* system to solve */ cholmod_factor *L, /* factorization to use */ cholmod_sparse *B, /* right-hand-side */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_spsolve (int, cholmod_factor *, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_etree: find the elimination tree of A or A'*A */ /* -------------------------------------------------------------------------- */ int cholmod_etree ( /* ---- input ---- */ cholmod_sparse *A, /* ---- output --- */ int *Parent, /* size ncol. Parent [j] = p if p is the parent of j */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_etree (cholmod_sparse *, SuiteSparse_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowcolcounts: compute the row/column counts of L */ /* -------------------------------------------------------------------------- */ int cholmod_rowcolcounts ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int *Parent, /* size nrow. Parent [i] = p if p is the parent of i */ int *Post, /* size nrow. Post [k] = i if i is the kth node in * the postordered etree. */ /* ---- output --- */ int *RowCount, /* size nrow. RowCount [i] = # entries in the ith row of * L, including the diagonal. */ int *ColCount, /* size nrow. ColCount [i] = # entries in the ith * column of L, including the diagonal. */ int *First, /* size nrow. First [i] = k is the least postordering * of any descendant of i. */ int *Level, /* size nrow. Level [i] is the length of the path from * i to the root, with Level [root] = 0. */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowcolcounts (cholmod_sparse *, SuiteSparse_long *, size_t, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_analyze_ordering: analyze a fill-reducing ordering */ /* -------------------------------------------------------------------------- */ int cholmod_analyze_ordering ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ int ordering, /* ordering method used */ int *Perm, /* size n, fill-reducing permutation to analyze */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ int *Parent, /* size n, elimination tree */ int *Post, /* size n, postordering of elimination tree */ int *ColCount, /* size n, nnz in each column of L */ /* ---- workspace */ int *First, /* size nworkspace for cholmod_postorder */ int *Level, /* size n workspace for cholmod_postorder */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_analyze_ordering (cholmod_sparse *, int, SuiteSparse_long *, SuiteSparse_long *, size_t, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_amd: order using AMD */ /* -------------------------------------------------------------------------- */ /* Finds a permutation P to reduce fill-in in the factorization of P*A*P' * or P*A*A'P' */ int cholmod_amd ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_amd (cholmod_sparse *, SuiteSparse_long *, size_t, SuiteSparse_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_colamd: order using COLAMD */ /* -------------------------------------------------------------------------- */ /* Finds a permutation P to reduce fill-in in the factorization of P*A*A'*P'. * Orders F*F' where F = A (:,fset) if fset is not NULL */ int cholmod_colamd ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int postorder, /* if TRUE, follow with a coletree postorder */ /* ---- output --- */ int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_colamd (cholmod_sparse *, SuiteSparse_long *, size_t, int, SuiteSparse_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowfac: incremental simplicial factorization */ /* -------------------------------------------------------------------------- */ /* Partial or complete simplicial factorization. Rows and columns kstart:kend-1 * of L and D must be initially equal to rows/columns kstart:kend-1 of the * identity matrix. Row k can only be factorized if all descendants of node * k in the elimination tree have been factorized. */ int cholmod_rowfac ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,fset)' */ double beta [2], /* factorize beta*I+A or beta*I+A'*A */ size_t kstart, /* first row to factorize */ size_t kend, /* last row to factorize is kend-1 */ /* ---- in/out --- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowfac (cholmod_sparse *, cholmod_sparse *, double *, size_t, size_t, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowfac_mask: incremental simplicial factorization */ /* -------------------------------------------------------------------------- */ /* cholmod_rowfac_mask is a version of cholmod_rowfac that is specific to * LPDASA. It is unlikely to be needed by any other application. */ int cholmod_rowfac_mask ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,fset)' */ double beta [2], /* factorize beta*I+A or beta*I+A'*A */ size_t kstart, /* first row to factorize */ size_t kend, /* last row to factorize is kend-1 */ int *mask, /* if mask[i] >= 0, then set row i to zero */ int *RLinkUp, /* link list of rows to compute */ /* ---- in/out --- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowfac_mask (cholmod_sparse *, cholmod_sparse *, double *, size_t, size_t, SuiteSparse_long *, SuiteSparse_long *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_row_subtree: find the nonzero pattern of a row of L */ /* -------------------------------------------------------------------------- */ /* Find the nonzero pattern of x for the system Lx=b where L = (0:k-1,0:k-1) * and b = kth column of A or A*A' (rows 0 to k-1 only) */ int cholmod_row_subtree ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,fset)' */ size_t k, /* row k of L */ int *Parent, /* elimination tree */ /* ---- output --- */ cholmod_sparse *R, /* pattern of L(k,:), n-by-1 with R->nzmax >= n */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_row_subtree (cholmod_sparse *, cholmod_sparse *, size_t, SuiteSparse_long *, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_lsolve_pattern: find the nonzero pattern of x=L\b */ /* -------------------------------------------------------------------------- */ int cholmod_lsolve_pattern ( /* ---- input ---- */ cholmod_sparse *B, /* sparse right-hand-side (a single sparse column) */ cholmod_factor *L, /* the factor L from which parent(i) is derived */ /* ---- output --- */ cholmod_sparse *X, /* pattern of X=L\B, n-by-1 with X->nzmax >= n */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_lsolve_pattern (cholmod_sparse *, cholmod_factor *, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_row_lsubtree: find the nonzero pattern of a row of L */ /* -------------------------------------------------------------------------- */ /* Identical to cholmod_row_subtree, except that it finds the elimination tree * from L itself. */ int cholmod_row_lsubtree ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ int *Fi, size_t fnz, /* nonzero pattern of kth row of A', not required * for the symmetric case. Need not be sorted. */ size_t k, /* row k of L */ cholmod_factor *L, /* the factor L from which parent(i) is derived */ /* ---- output --- */ cholmod_sparse *R, /* pattern of L(k,:), n-by-1 with R->nzmax >= n */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_row_lsubtree (cholmod_sparse *, SuiteSparse_long *, size_t, size_t, cholmod_factor *, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_resymbol: recompute the symbolic pattern of L */ /* -------------------------------------------------------------------------- */ /* Remove entries from L that are not in the factorization of P*A*P', P*A*A'*P', * or P*F*F'*P' (depending on A->stype and whether fset is NULL or not). * * cholmod_resymbol is the same as cholmod_resymbol_noperm, except that it * first permutes A according to L->Perm. A can be upper/lower/unsymmetric, * in contrast to cholmod_resymbol_noperm (which can be lower or unsym). */ int cholmod_resymbol ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int pack, /* if TRUE, pack the columns of L */ /* ---- in/out --- */ cholmod_factor *L, /* factorization, entries pruned on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_resymbol (cholmod_sparse *, SuiteSparse_long *, size_t, int, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_resymbol_noperm: recompute the symbolic pattern of L, no L->Perm */ /* -------------------------------------------------------------------------- */ /* Remove entries from L that are not in the factorization of A, A*A', * or F*F' (depending on A->stype and whether fset is NULL or not). */ int cholmod_resymbol_noperm ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int pack, /* if TRUE, pack the columns of L */ /* ---- in/out --- */ cholmod_factor *L, /* factorization, entries pruned on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_resymbol_noperm (cholmod_sparse *, SuiteSparse_long *, size_t, int, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rcond: compute rough estimate of reciprocal of condition number */ /* -------------------------------------------------------------------------- */ double cholmod_rcond /* return min(diag(L)) / max(diag(L)) */ ( /* ---- input ---- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) ; double cholmod_l_rcond (cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_postorder: Compute the postorder of a tree */ /* -------------------------------------------------------------------------- */ SuiteSparse_long cholmod_postorder /* return # of nodes postordered */ ( /* ---- input ---- */ int *Parent, /* size n. Parent [j] = p if p is the parent of j */ size_t n, int *Weight_p, /* size n, optional. Weight [j] is weight of node j */ /* ---- output --- */ int *Post, /* size n. Post [k] = j is kth in postordered tree */ /* --------------- */ cholmod_common *Common ) ; SuiteSparse_long cholmod_l_postorder (SuiteSparse_long *, size_t, SuiteSparse_long *, SuiteSparse_long *, cholmod_common *) ; #endif Matrix/src/CHOLMOD/Include/README.txt0000644000175100001440000000240511770402705016475 0ustar hornikusersCHOLMOD: a sparse Cholesky factorization package. http://www.suitesparse.com The Include/*.h files in this directory provide a basic documentation of all user-callable routines and user-visible data structures in the CHOLMOD package. Start with cholmod.h, which describes the general structure of the parameter lists of CHOLMOD routines. cholmod_core.h describes the data structures and basic operations on them (creating and deleting them). cholmod.h single include file for all user programs cholmod_config.h CHOLMOD compile-time configuration cholmod_core.h Core module: data structures and basic support routines cholmod_check.h Check module: check/print CHOLMOD data structures cholmod_cholesky.h Cholesky module: LL' and LDL' factorization cholmod_matrixops.h MatrixOps module: sparse matrix operators (add, mult,..) cholmod_modify.h Modify module: update/downdate/... cholmod_partition.h Partition module: nested dissection ordering cholmod_supernodal.h Supernodal module: supernodal Cholesky These include files are not used in user programs, but in CHOLMOD only: cholmod_blas.h BLAS definitions cholmod_complexity.h complex arithmetic cholmod_template.h complex arithmetic for template routines cholmod_internal.h internal definitions, not visible to user program Matrix/src/CHOLMOD/Include/cholmod_check.h0000644000175100001440000003535412271765436017755 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_check.h ============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_check.h. Copyright (C) 2005-2006, Timothy A. Davis * CHOLMOD/Include/cholmod_check.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* CHOLMOD Check module. * * Routines that check and print the 5 basic data types in CHOLMOD, and 3 kinds * of integer vectors (subset, perm, and parent), and read in matrices from a * file: * * cholmod_check_common check/print the Common object * cholmod_print_common * * cholmod_check_sparse check/print a sparse matrix in column-oriented form * cholmod_print_sparse * * cholmod_check_dense check/print a dense matrix * cholmod_print_dense * * cholmod_check_factor check/print a Cholesky factorization * cholmod_print_factor * * cholmod_check_triplet check/print a sparse matrix in triplet form * cholmod_print_triplet * * cholmod_check_subset check/print a subset (integer vector in given range) * cholmod_print_subset * * cholmod_check_perm check/print a permutation (an integer vector) * cholmod_print_perm * * cholmod_check_parent check/print an elimination tree (an integer vector) * cholmod_print_parent * * cholmod_read_triplet read a matrix in triplet form (any Matrix Market * "coordinate" format, or a generic triplet format). * * cholmod_read_sparse read a matrix in sparse form (same file format as * cholmod_read_triplet). * * cholmod_read_dense read a dense matrix (any Matrix Market "array" * format, or a generic dense format). * * cholmod_write_sparse write a sparse matrix to a Matrix Market file. * * cholmod_write_dense write a dense matrix to a Matrix Market file. * * cholmod_print_common and cholmod_check_common are the only two routines that * you may call after calling cholmod_finish. * * Requires the Core module. Not required by any CHOLMOD module, except when * debugging is enabled (in which case all modules require the Check module). * * See cholmod_read.c for a description of the file formats supported by the * cholmod_read_* routines. */ #ifndef CHOLMOD_CHECK_H #define CHOLMOD_CHECK_H #include "cholmod_core.h" #include /* -------------------------------------------------------------------------- */ /* cholmod_check_common: check the Common object */ /* -------------------------------------------------------------------------- */ int cholmod_check_common ( cholmod_common *Common ) ; int cholmod_l_check_common (cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_common: print the Common object */ /* -------------------------------------------------------------------------- */ int cholmod_print_common ( /* ---- input ---- */ const char *name, /* printed name of Common object */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_common (const char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_gpu_stats: print the GPU / CPU statistics */ /* -------------------------------------------------------------------------- */ int cholmod_gpu_stats (cholmod_common *) ; int cholmod_l_gpu_stats (cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_check_sparse: check a sparse matrix */ /* -------------------------------------------------------------------------- */ int cholmod_check_sparse ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to check */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_sparse (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_sparse */ /* -------------------------------------------------------------------------- */ int cholmod_print_sparse ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to print */ const char *name, /* printed name of sparse matrix */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_sparse (cholmod_sparse *, const char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_check_dense: check a dense matrix */ /* -------------------------------------------------------------------------- */ int cholmod_check_dense ( /* ---- input ---- */ cholmod_dense *X, /* dense matrix to check */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_dense (cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_dense: print a dense matrix */ /* -------------------------------------------------------------------------- */ int cholmod_print_dense ( /* ---- input ---- */ cholmod_dense *X, /* dense matrix to print */ const char *name, /* printed name of dense matrix */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_dense (cholmod_dense *, const char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_check_factor: check a factor */ /* -------------------------------------------------------------------------- */ int cholmod_check_factor ( /* ---- input ---- */ cholmod_factor *L, /* factor to check */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_factor (cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_factor: print a factor */ /* -------------------------------------------------------------------------- */ int cholmod_print_factor ( /* ---- input ---- */ cholmod_factor *L, /* factor to print */ const char *name, /* printed name of factor */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_factor (cholmod_factor *, const char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_check_triplet: check a sparse matrix in triplet form */ /* -------------------------------------------------------------------------- */ int cholmod_check_triplet ( /* ---- input ---- */ cholmod_triplet *T, /* triplet matrix to check */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_triplet (cholmod_triplet *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_triplet: print a triplet matrix */ /* -------------------------------------------------------------------------- */ int cholmod_print_triplet ( /* ---- input ---- */ cholmod_triplet *T, /* triplet matrix to print */ const char *name, /* printed name of triplet matrix */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_triplet (cholmod_triplet *, const char *, cholmod_common *); /* -------------------------------------------------------------------------- */ /* cholmod_check_subset: check a subset */ /* -------------------------------------------------------------------------- */ int cholmod_check_subset ( /* ---- input ---- */ int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */ SuiteSparse_long len, /* size of Set (an integer array) */ size_t n, /* 0:n-1 is valid range */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_subset (SuiteSparse_long *, SuiteSparse_long, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_subset: print a subset */ /* -------------------------------------------------------------------------- */ int cholmod_print_subset ( /* ---- input ---- */ int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */ SuiteSparse_long len, /* size of Set (an integer array) */ size_t n, /* 0:n-1 is valid range */ const char *name, /* printed name of Set */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_subset (SuiteSparse_long *, SuiteSparse_long, size_t, const char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_check_perm: check a permutation */ /* -------------------------------------------------------------------------- */ int cholmod_check_perm ( /* ---- input ---- */ int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */ size_t len, /* size of Perm (an integer array) */ size_t n, /* 0:n-1 is valid range */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_perm (SuiteSparse_long *, size_t, size_t, cholmod_common *); /* -------------------------------------------------------------------------- */ /* cholmod_print_perm: print a permutation vector */ /* -------------------------------------------------------------------------- */ int cholmod_print_perm ( /* ---- input ---- */ int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */ size_t len, /* size of Perm (an integer array) */ size_t n, /* 0:n-1 is valid range */ const char *name, /* printed name of Perm */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_perm (SuiteSparse_long *, size_t, size_t, const char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_check_parent: check an elimination tree */ /* -------------------------------------------------------------------------- */ int cholmod_check_parent ( /* ---- input ---- */ int *Parent, /* Parent [0:n-1] is an elimination tree */ size_t n, /* size of Parent */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_parent (SuiteSparse_long *, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_parent */ /* -------------------------------------------------------------------------- */ int cholmod_print_parent ( /* ---- input ---- */ int *Parent, /* Parent [0:n-1] is an elimination tree */ size_t n, /* size of Parent */ const char *name, /* printed name of Parent */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_parent (SuiteSparse_long *, size_t, const char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_read_sparse: read a sparse matrix from a file */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_read_sparse ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_read_sparse (FILE *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_read_triplet: read a triplet matrix from a file */ /* -------------------------------------------------------------------------- */ cholmod_triplet *cholmod_read_triplet ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ /* --------------- */ cholmod_common *Common ) ; cholmod_triplet *cholmod_l_read_triplet (FILE *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_read_dense: read a dense matrix from a file */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_read_dense ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_read_dense (FILE *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_read_matrix: read a sparse or dense matrix from a file */ /* -------------------------------------------------------------------------- */ void *cholmod_read_matrix ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ int prefer, /* If 0, a sparse matrix is always return as a * cholmod_triplet form. It can have any stype * (symmetric-lower, unsymmetric, or * symmetric-upper). * If 1, a sparse matrix is returned as an unsymmetric * cholmod_sparse form (A->stype == 0), with both * upper and lower triangular parts present. * This is what the MATLAB mread mexFunction does, * since MATLAB does not have an stype. * If 2, a sparse matrix is returned with an stype of 0 * or 1 (unsymmetric, or symmetric with upper part * stored). * This argument has no effect for dense matrices. */ /* ---- output---- */ int *mtype, /* CHOLMOD_TRIPLET, CHOLMOD_SPARSE or CHOLMOD_DENSE */ /* --------------- */ cholmod_common *Common ) ; void *cholmod_l_read_matrix (FILE *, int, int *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_write_sparse: write a sparse matrix to a file */ /* -------------------------------------------------------------------------- */ int cholmod_write_sparse ( /* ---- input ---- */ FILE *f, /* file to write to, must already be open */ cholmod_sparse *A, /* matrix to print */ cholmod_sparse *Z, /* optional matrix with pattern of explicit zeros */ const char *comments, /* optional filename of comments to include */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_write_sparse (FILE *, cholmod_sparse *, cholmod_sparse *, const char *c, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_write_dense: write a dense matrix to a file */ /* -------------------------------------------------------------------------- */ int cholmod_write_dense ( /* ---- input ---- */ FILE *f, /* file to write to, must already be open */ cholmod_dense *X, /* matrix to print */ const char *comments, /* optional filename of comments to include */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_write_dense (FILE *, cholmod_dense *, const char *, cholmod_common *) ; #endif Matrix/src/CHOLMOD/Include/cholmod_partition.h0000644000175100001440000001512712271765436020705 0ustar hornikusers/* ========================================================================== */ /* === Include/cholmod_partition.h ========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_partition.h. * Copyright (C) 2005-2013, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_partition.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * -------------------------------------------------------------------------- */ /* CHOLMOD Partition module. * * Graph partitioning and graph-partition-based orderings. Includes an * interface to CCOLAMD and CSYMAMD, constrained minimum degree ordering * methods which order a matrix following constraints determined via nested * dissection. * * These functions require METIS: * cholmod_nested_dissection CHOLMOD nested dissection ordering * cholmod_metis METIS nested dissection ordering (METIS_NodeND) * cholmod_bisect graph partitioner (currently based on METIS) * cholmod_metis_bisector direct interface to METIS_NodeComputeSeparator * * Requires the Core and Cholesky modules, and three packages: METIS, CAMD, * and CCOLAMD. Optionally used by the Cholesky module. * * Note that METIS does not have a version that uses SuiteSparse_long integers. * If you try to use cholmod_nested_dissection, cholmod_metis, cholmod_bisect, * or cholmod_metis_bisector on a matrix that is too large, an error code will * be returned. METIS does have an "idxtype", which could be redefined as * SuiteSparse_long, if you wish to edit METIS or use compile-time flags to * redefine idxtype. */ #ifndef CHOLMOD_PARTITION_H #define CHOLMOD_PARTITION_H #include "cholmod_core.h" #include "cholmod_camd.h" /* -------------------------------------------------------------------------- */ /* cholmod_nested_dissection */ /* -------------------------------------------------------------------------- */ /* Order A, AA', or A(:,f)*A(:,f)' using CHOLMOD's nested dissection method * (METIS's node bisector applied recursively to compute the separator tree * and constraint sets, followed by CCOLAMD using the constraints). Usually * finds better orderings than METIS_NodeND, but takes longer. */ SuiteSparse_long cholmod_nested_dissection /* returns # of components */ ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ int *Perm, /* size A->nrow, output permutation */ int *CParent, /* size A->nrow. On output, CParent [c] is the parent * of component c, or EMPTY if c is a root, and where * c is in the range 0 to # of components minus 1 */ int *Cmember, /* size A->nrow. Cmember [j] = c if node j of A is * in component c */ /* --------------- */ cholmod_common *Common ) ; SuiteSparse_long cholmod_l_nested_dissection (cholmod_sparse *, SuiteSparse_long *, size_t, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_metis */ /* -------------------------------------------------------------------------- */ /* Order A, AA', or A(:,f)*A(:,f)' using METIS_NodeND. */ int cholmod_metis ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int postorder, /* if TRUE, follow with etree or coletree postorder */ /* ---- output --- */ int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_metis (cholmod_sparse *, SuiteSparse_long *, size_t, int, SuiteSparse_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_bisect */ /* -------------------------------------------------------------------------- */ /* Finds a node bisector of A, A*A', A(:,f)*A(:,f)'. */ SuiteSparse_long cholmod_bisect /* returns # of nodes in separator */ ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to bisect */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int compress, /* if TRUE, compress the graph first */ /* ---- output --- */ int *Partition, /* size A->nrow. Node i is in the left graph if * Partition [i] = 0, the right graph if 1, and in the * separator if 2. */ /* --------------- */ cholmod_common *Common ) ; SuiteSparse_long cholmod_l_bisect (cholmod_sparse *, SuiteSparse_long *, size_t, int, SuiteSparse_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_metis_bisector */ /* -------------------------------------------------------------------------- */ /* Find a set of nodes that bisects the graph of A or AA' (direct interface * to METIS_NodeComputeSeparator). */ SuiteSparse_long cholmod_metis_bisector /* returns separator size */ ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to bisect */ int *Anw, /* size A->nrow, node weights */ int *Aew, /* size nz, edge weights */ /* ---- output --- */ int *Partition, /* size A->nrow. see cholmod_bisect above. */ /* --------------- */ cholmod_common *Common ) ; SuiteSparse_long cholmod_l_metis_bisector (cholmod_sparse *, SuiteSparse_long *, SuiteSparse_long *, SuiteSparse_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_collapse_septree */ /* -------------------------------------------------------------------------- */ /* Collapse nodes in a separator tree. */ SuiteSparse_long cholmod_collapse_septree ( /* ---- input ---- */ size_t n, /* # of nodes in the graph */ size_t ncomponents, /* # of nodes in the separator tree (must be <= n) */ double nd_oksep, /* collapse if #sep >= nd_oksep * #nodes in subtree */ size_t nd_small, /* collapse if #nodes in subtree < nd_small */ /* ---- in/out --- */ int *CParent, /* size ncomponents; from cholmod_nested_dissection */ int *Cmember, /* size n; from cholmod_nested_dissection */ /* --------------- */ cholmod_common *Common ) ; SuiteSparse_long cholmod_l_collapse_septree (size_t, size_t, double, size_t, SuiteSparse_long *, SuiteSparse_long *, cholmod_common *) ; #endif Matrix/src/dtCMatrix.h0000644000175100001440000000110312271765436014403 0ustar hornikusers#ifndef MATRIX_TSC_H #define MATRIX_TSC_H #include "Mutils.h" #include "dgCMatrix.h" extern SEXP Csparse_diagU2N(SEXP x); /* SEXP Parent_inverse(SEXP par, SEXP unitdiag); */ /* int parent_inv_ap(int n, int countDiag, const int pr[], int ap[]); */ /* void parent_inv_ai(int n, int countDiag, const int pr[], int ai[]); */ SEXP tCMatrix_validate(SEXP x); SEXP tRMatrix_validate(SEXP x); /* SEXP dtCMatrix_solve(SEXP a); */ SEXP dtCMatrix_matrix_solve(SEXP a, SEXP b, SEXP classed); SEXP dtCMatrix_sparse_solve(SEXP a, SEXP b); /* SEXP dtCMatrix_upper_solve(SEXP a); */ #endif Matrix/src/factorizations.h0000644000175100001440000000046312271765436015553 0ustar hornikusers#ifndef MATRIX_FACTORS_H #define MATRIX_FACTORS_H #include "Mutils.h" SEXP LU_validate(SEXP obj); SEXP BunchKaufman_validate(SEXP obj); SEXP pBunchKaufman_validate(SEXP obj); SEXP Cholesky_validate(SEXP obj); SEXP pCholesky_validate(SEXP obj); SEXP SVD_validate(SEXP obj); SEXP LU_expand(SEXP x); #endif Matrix/src/dsyMatrix.h0000644000175100001440000000102112271765436014467 0ustar hornikusers#ifndef MATRIX_SYMATRIX_H #define MATRIX_SYMATRIX_H #include "Mutils.h" #include "R_ext/Lapack.h" SEXP dsyMatrix_as_dspMatrix(SEXP from); SEXP dsyMatrix_as_matrix(SEXP from, SEXP keep_dimnames); SEXP dsyMatrix_matrix_mm(SEXP a, SEXP b, SEXP rt); SEXP dsyMatrix_matrix_solve(SEXP a, SEXP b); SEXP dsyMatrix_norm(SEXP obj, SEXP type); SEXP dsyMatrix_rcond(SEXP obj, SEXP type); SEXP dsyMatrix_solve(SEXP a); SEXP dsyMatrix_trf(SEXP x); SEXP dsyMatrix_validate(SEXP obj); double get_norm_sy(SEXP obj, const char *typstr); #endif Matrix/src/dtrMatrix.c0000644000175100001440000002274112271765436014470 0ustar hornikusers/* double (precision) TRiangular Matrices */ #include "dtrMatrix.h" SEXP triangularMatrix_validate(SEXP obj) { SEXP val = GET_SLOT(obj, Matrix_DimSym); if (LENGTH(val) < 2) return mkString(_("'Dim' slot has length less than two")); if (INTEGER(val)[0] != INTEGER(val)[1]) return mkString(_("Matrix is not square")); if (isString(val = check_scalar_string(GET_SLOT(obj, Matrix_uploSym), "LU", "uplo"))) return val; if (isString(val = check_scalar_string(GET_SLOT(obj, Matrix_diagSym), "NU", "diag"))) return val; return ScalarLogical(1); } SEXP dtrMatrix_validate(SEXP obj) { /* since "dtr" inherits from "triangular", and "dMatrix", only need this:*/ return dense_nonpacked_validate(obj); } static double get_norm(SEXP obj, const char *typstr) { char typnm[] = {'\0', '\0'}; int *dims = INTEGER(GET_SLOT(obj, Matrix_DimSym)); double *work = (double *) NULL; typnm[0] = La_norm_type(typstr); if (*typnm == 'I') { work = (double *) R_alloc(dims[0], sizeof(double)); } return F77_CALL(dlantr)(typnm, uplo_P(obj), diag_P(obj), dims, dims+1, REAL(GET_SLOT(obj, Matrix_xSym)), dims, work); } SEXP dtrMatrix_norm(SEXP obj, SEXP type) { return ScalarReal(get_norm(obj, CHAR(asChar(type)))); } SEXP dtrMatrix_rcond(SEXP obj, SEXP type) { char typnm[] = {'\0', '\0'}; int *dims = INTEGER(GET_SLOT(obj, Matrix_DimSym)), info; double rcond; typnm[0] = La_rcond_type(CHAR(asChar(type))); F77_CALL(dtrcon)(typnm, uplo_P(obj), diag_P(obj), dims, REAL(GET_SLOT(obj, Matrix_xSym)), dims, &rcond, (double *) R_alloc(3*dims[0], sizeof(double)), (int *) R_alloc(dims[0], sizeof(int)), &info); return ScalarReal(rcond); } SEXP dtrMatrix_solve(SEXP a) { SEXP val = PROTECT(duplicate(a)); int info, *Dim = INTEGER(GET_SLOT(val, Matrix_DimSym)); F77_CALL(dtrtri)(uplo_P(val), diag_P(val), Dim, REAL(GET_SLOT(val, Matrix_xSym)), Dim, &info); UNPROTECT(1); return val; } SEXP dtrMatrix_chol2inv(SEXP a) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dpoMatrix"))); int info, n; slot_dup(val, a, Matrix_DimSym); slot_dup(val, a, Matrix_uploSym); slot_dup(val, a, Matrix_diagSym); slot_dup(val, a, Matrix_DimNamesSym); slot_dup(val, a, Matrix_xSym); n = *INTEGER(GET_SLOT(val, Matrix_DimSym)); F77_CALL(dpotri)(uplo_P(val), &n, REAL(GET_SLOT(val, Matrix_xSym)), &n, &info); UNPROTECT(1); return val; } SEXP dtrMatrix_matrix_solve(SEXP a, SEXP b) { SEXP ans = PROTECT(dup_mMatrix_as_dgeMatrix(b)); int *adims = INTEGER(GET_SLOT(a, Matrix_DimSym)), *bdims = INTEGER(GET_SLOT(ans, Matrix_DimSym)); int n = bdims[0], nrhs = bdims[1]; double one = 1.0; if (*adims != *bdims || bdims[1] < 1 || *adims < 1 || *adims != adims[1]) error(_("Dimensions of system to be solved are inconsistent")); F77_CALL(dtrsm)("L", uplo_P(a), "N", diag_P(a), &n, &nrhs, &one, REAL(GET_SLOT(a, Matrix_xSym)), &n, REAL(GET_SLOT(ans, Matrix_xSym)), &n); UNPROTECT(1); return ans; } /* to bu used for all three: '%*%', crossprod() and tcrossprod() */ SEXP dtrMatrix_matrix_mm(SEXP a, SEXP b, SEXP right, SEXP trans) { /* Because a must be square, the size of the answer, val, * is the same as the size of b */ SEXP val = PROTECT(dup_mMatrix_as_dgeMatrix(b)); int rt = asLogical(right); /* if(rt), compute b %*% op(a), else op(a) %*% b */ int tr = asLogical(trans);/* if true, use t(a) */ int *adims = INTEGER(GET_SLOT(a, Matrix_DimSym)), *bdims = INTEGER(GET_SLOT(val, Matrix_DimSym)); int m = bdims[0], n = bdims[1]; double one = 1.; if (adims[0] != adims[1]) error(_("dtrMatrix must be square")); if ((rt && adims[0] != n) || (!rt && adims[1] != m)) error(_("Matrices are not conformable for multiplication")); if (m < 1 || n < 1) { /* error(_("Matrices with zero extents cannot be multiplied")); */ } else /* BLAS */ F77_CALL(dtrmm)(rt ? "R" : "L", uplo_P(a), /*trans_A = */ tr ? "T" : "N", diag_P(a), &m, &n, &one, REAL(GET_SLOT(a, Matrix_xSym)), adims, REAL(GET_SLOT(val, Matrix_xSym)), &m); UNPROTECT(1); return val; } SEXP dtrMatrix_dtrMatrix_mm(SEXP a, SEXP b, SEXP right, SEXP trans) { /* to be called from "%*%" and crossprod(), tcrossprod(), * from ../R/products.R * * TWO cases : (1) result is triangular <=> uplo are equal * === (2) result is "general" */ SEXP val,/* = in case (2): PROTECT(dup_mMatrix_as_dgeMatrix(b)); */ d_a = GET_SLOT(a, Matrix_DimSym), uplo_a = GET_SLOT(a, Matrix_uploSym), diag_a = GET_SLOT(a, Matrix_diagSym); /* if(rt), compute b %*% a, else a %*% b */ int rt = asLogical(right); int tr = asLogical(trans);/* if true, use t(a) */ int *adims = INTEGER(d_a), n = adims[0]; double *valx = (double *) NULL /*Wall*/; const char *uplo_a_ch = CHAR(STRING_ELT(uplo_a, 0)), /* = uplo_P(a) */ *diag_a_ch = CHAR(STRING_ELT(diag_a, 0)); /* = diag_P(a) */ Rboolean same_uplo = (*uplo_a_ch == *uplo_P(b)), uDiag_b = /* -Wall: */ FALSE; if (INTEGER(GET_SLOT(b, Matrix_DimSym))[0] != n) /* validity checking already "assures" square matrices ... */ error(_("dtrMatrices in %*% must have matching (square) dim.")); if(same_uplo) { /* ==> result is triangular -- "dtrMatrix" ! * val := dup_mMatrix_as_dtrMatrix(b) : */ int sz = n * n; val = PROTECT(NEW_OBJECT(MAKE_CLASS("dtrMatrix"))); SET_SLOT(val, Matrix_uploSym, duplicate(uplo_a)); SET_SLOT(val, Matrix_DimSym, duplicate(d_a)); SET_DimNames(val, b); valx = REAL(ALLOC_SLOT(val, Matrix_xSym, REALSXP, sz)); Memcpy(valx, REAL(GET_SLOT(b, Matrix_xSym)), sz); if((uDiag_b = *diag_P(b) == 'U')) { /* unit-diagonal b - may contain garbage in diagonal */ for (int i = 0; i < n; i++) valx[i * (n+1)] = 1.; } } else { /* different "uplo" ==> result is "dgeMatrix" ! */ val = PROTECT(dup_mMatrix_as_dgeMatrix(b)); } if (n >= 1) { double alpha = 1.; /* Level 3 BLAS - DTRMM(): Compute one of the matrix multiplication operations * B := alpha*op( A )*B ["L"], or B := alpha*B*op( A ) ["R"], * where trans_A determines op(A):= A "N"one or * op(A):= t(A) "T"ransposed */ F77_CALL(dtrmm)(rt ? "R" : "L", uplo_a_ch, /*trans_A = */ tr ? "T" : "N", diag_a_ch, &n, &n, &alpha, REAL(GET_SLOT(a, Matrix_xSym)), adims, REAL(GET_SLOT(val, Matrix_xSym)), &n); } if(same_uplo) { make_d_matrix_triangular(valx, a); /* set "other triangle" to 0 */ if(*diag_a_ch == 'U' && uDiag_b) /* result remains uni-diagonal */ SET_SLOT(val, Matrix_diagSym, duplicate(diag_a)); } UNPROTECT(1); return val; } SEXP dtrMatrix_as_matrix(SEXP from, SEXP keep_dimnames) { int *Dim = INTEGER(GET_SLOT(from, Matrix_DimSym)); int m = Dim[0], n = Dim[1]; SEXP val = PROTECT(allocMatrix(REALSXP, m, n)); make_d_matrix_triangular(Memcpy(REAL(val), REAL(GET_SLOT(from, Matrix_xSym)), m * n), from); if(asLogical(keep_dimnames)) setAttrib(val, R_DimNamesSymbol, GET_SLOT(from, Matrix_DimNamesSym)); UNPROTECT(1); return val; } #define GET_trMatrix_Diag(_C_TYPE_, _SEXPTYPE_, _SEXP_, _ONE_) \ int i, n = INTEGER(GET_SLOT(x, Matrix_DimSym))[0]; \ SEXP x_x = GET_SLOT(x, Matrix_xSym); \ \ SEXP ret = PROTECT(allocVector(_SEXPTYPE_, n)); \ _C_TYPE_ *rv = _SEXP_(ret), \ *xv = _SEXP_(x_x); \ \ if ('U' == diag_P(x)[0]) { \ for (i = 0; i < n; i++) rv[i] = _ONE_; \ } else { \ for (i = 0; i < n; i++) rv[i] = xv[i * (n + 1)]; \ } \ UNPROTECT(1); \ return ret SEXP dtrMatrix_getDiag(SEXP x) { GET_trMatrix_Diag(double, REALSXP, REAL, 1.); } SEXP ltrMatrix_getDiag(SEXP x) { GET_trMatrix_Diag( int, LGLSXP, LOGICAL, 1); } #define SET_trMatrix_Diag(_C_TYPE_, _SEXP_) \ int n = INTEGER(GET_SLOT(x, Matrix_DimSym))[0]; \ SEXP ret = PROTECT(duplicate(x)); \ SEXP r_x = GET_SLOT(ret, Matrix_xSym); \ _C_TYPE_ *dv = _SEXP_(d), \ *rv = _SEXP_(r_x); \ \ if ('U' == diag_P(x)[0]) \ error(_("cannot set diag() as long as 'diag = \"U\"'")); \ for (int i = 0; i < n; i++) rv[i * (n + 1)] = dv[i]; \ \ UNPROTECT(1); \ return ret SEXP dtrMatrix_setDiag(SEXP x, SEXP d) { SET_trMatrix_Diag(double, REAL); } SEXP ltrMatrix_setDiag(SEXP x, SEXP d) { SET_trMatrix_Diag( int, LOGICAL); } SEXP dtrMatrix_addDiag(SEXP x, SEXP d) { int n = INTEGER(GET_SLOT(x, Matrix_DimSym))[0]; SEXP ret = PROTECT(duplicate(x)), r_x = GET_SLOT(ret, Matrix_xSym); double *dv = REAL(d), *rv = REAL(r_x); if ('U' == diag_P(x)[0]) error(_("cannot add diag() as long as 'diag = \"U\"'")); for (int i = 0; i < n; i++) rv[i * (n + 1)] += dv[i]; UNPROTECT(1); return ret; } SEXP dtrMatrix_as_dtpMatrix(SEXP from) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dtpMatrix"))), uplo = GET_SLOT(from, Matrix_uploSym), diag = GET_SLOT(from, Matrix_diagSym), dimP = GET_SLOT(from, Matrix_DimSym); int n = *INTEGER(dimP); SET_SLOT(val, Matrix_DimSym, duplicate(dimP)); SET_SLOT(val, Matrix_diagSym, duplicate(diag)); SET_SLOT(val, Matrix_uploSym, duplicate(uplo)); full_to_packed_double( REAL(ALLOC_SLOT(val, Matrix_xSym, REALSXP, (n*(n+1))/2)), REAL(GET_SLOT(from, Matrix_xSym)), n, *CHAR(STRING_ELT(uplo, 0)) == 'U' ? UPP : LOW, *CHAR(STRING_ELT(diag, 0)) == 'U' ? UNT : NUN); SET_SLOT(val, Matrix_DimNamesSym, duplicate(GET_SLOT(from, Matrix_DimNamesSym))); UNPROTECT(1); return val; } Matrix/src/factorizations.c0000644000175100001440000000774412271765436015557 0ustar hornikusers#include "factorizations.h" SEXP LU_validate(SEXP obj) { return ScalarLogical(1); } SEXP BunchKaufman_validate(SEXP obj) { return ScalarLogical(1); } SEXP pBunchKaufman_validate(SEXP obj) { return ScalarLogical(1); } SEXP Cholesky_validate(SEXP obj) { return ScalarLogical(1); } SEXP pCholesky_validate(SEXP obj) { return ScalarLogical(1); } SEXP SVD_validate(SEXP obj) { return ScalarLogical(1); } SEXP LU_expand(SEXP x) { const char *nms[] = {"L", "U", "P", ""}; // x[,] is m x n (using LAPACK dgetrf notation) SEXP L, U, P, val = PROTECT(Rf_mkNamed(VECSXP, nms)), lux = GET_SLOT(x, Matrix_xSym), dd = GET_SLOT(x, Matrix_DimSym); int *iperm, *perm, *pivot = INTEGER(GET_SLOT(x, Matrix_permSym)), *dim = INTEGER(dd), m = dim[0], n = dim[1], nn = m, i; Rboolean is_sq = (n == m), L_is_tri = TRUE, U_is_tri = TRUE; // nn := min(n,m) == length(pivot[]) if(!is_sq) { if(n < m) { // "long" nn = n; L_is_tri = FALSE; } else { // m < n : "wide" U_is_tri = FALSE; } } SET_VECTOR_ELT(val, 0, NEW_OBJECT(MAKE_CLASS(L_is_tri ? "dtrMatrix":"dgeMatrix"))); SET_VECTOR_ELT(val, 1, NEW_OBJECT(MAKE_CLASS(U_is_tri ? "dtrMatrix":"dgeMatrix"))); SET_VECTOR_ELT(val, 2, NEW_OBJECT(MAKE_CLASS("pMatrix"))); L = VECTOR_ELT(val, 0); U = VECTOR_ELT(val, 1); P = VECTOR_ELT(val, 2); if(is_sq || !L_is_tri) { SET_SLOT(L, Matrix_xSym, duplicate(lux)); SET_SLOT(L, Matrix_DimSym, duplicate(dd)); } else { // !is_sq && L_is_tri -- m < n -- "wide" -- L is m x m double *Lx = REAL(ALLOC_SLOT(L, Matrix_xSym, REALSXP, m * m)); int *dL = INTEGER(ALLOC_SLOT(L, Matrix_DimSym, INTSXP, 2)); dL[0] = dL[1] = m; // fill lower-diagonal (non-{0,1}) part -- remainder by make_d_matrix*() below: Memcpy(Lx, REAL(lux), m * m); } if(is_sq || !U_is_tri) { SET_SLOT(U, Matrix_xSym, duplicate(lux)); SET_SLOT(U, Matrix_DimSym, duplicate(dd)); } else { // !is_sq && U_is_tri -- m > n -- "long" -- U is n x n double *Ux = REAL(ALLOC_SLOT(U, Matrix_xSym, REALSXP, n * n)), *xx = REAL(lux); int *dU = INTEGER(ALLOC_SLOT(U, Matrix_DimSym, INTSXP, 2)); dU[0] = dU[1] = n; /* fill upper-diagonal (non-0) part -- remainder by make_d_matrix*() below: * this is more complicated than in the L case, as the x / lux part we need * is *not* continguous: Memcpy(Ux, REAL(lux), n * n); -- is WRONG */ for (int j = 0; j < n; j++) { Memcpy(Ux+j*n, xx+j*m, j+1); // for (i = 0; i <= j; i++) // Ux[i + j*n] = xx[i + j*m]; } } if(L_is_tri) { SET_SLOT(L, Matrix_uploSym, mkString("L")); SET_SLOT(L, Matrix_diagSym, mkString("U")); make_d_matrix_triangular(REAL(GET_SLOT(L, Matrix_xSym)), L); } else { // L is "unit-diagonal" trapezoidal -- m > n -- "long" // fill the upper right part with 0 *and* the diagonal with 1 double *Lx = REAL(GET_SLOT(L, Matrix_xSym)); int ii; for (i = 0, ii = 0; i < n; i++, ii+=(m+1)) { // ii = i*(m+1) Lx[ii] = 1.; for (int j = i*m; j < ii; j++) Lx[j] = 0.; } } if(U_is_tri) { SET_SLOT(U, Matrix_uploSym, mkString("U")); SET_SLOT(U, Matrix_diagSym, mkString("N")); make_d_matrix_triangular(REAL(GET_SLOT(U, Matrix_xSym)), U); } else { // U is trapezoidal -- m < n // fill the lower left part with 0 double *Ux = REAL(GET_SLOT(U, Matrix_xSym)); for (i = 0; i < m; i++) for (int j = i*(m+1)+1; j < (i+1)*m; j++) Ux[j] = 0.; } SET_SLOT(P, Matrix_DimSym, duplicate(dd)); if(!is_sq) // m != n -- P is m x m INTEGER(GET_SLOT(P, Matrix_DimSym))[1] = m; perm = INTEGER(ALLOC_SLOT(P, Matrix_permSym, INTSXP, m)); iperm = Alloca(m, int); R_CheckStack(); for (i = 0; i < m; i++) iperm[i] = i + 1; /* initialize permutation*/ for (i = 0; i < nn; i++) { /* generate inverse permutation */ int newp = pivot[i] - 1; if (newp != i) { // swap int tmp = iperm[i]; iperm[i] = iperm[newp]; iperm[newp] = tmp; } } // invert the inverse for (i = 0; i < m; i++) perm[iperm[i] - 1] = i + 1; UNPROTECT(1); return val; } Matrix/src/sparseQR.h0000644000175100001440000000045612271765436014256 0ustar hornikusers#ifndef MATRIX_SPARSEQR_H #define MATRIX_SPARSEQR_H #include "Mutils.h" #include "cs_utils.h" #include "chm_common.h" SEXP sparseQR_validate(SEXP x); SEXP sparseQR_qty(SEXP qr, SEXP y, SEXP trans); SEXP sparseQR_coef(SEXP qr, SEXP y); SEXP sparseQR_resid_fitted(SEXP qr, SEXP y, SEXP resid); #endif Matrix/src/dsCMatrix.c0000644000175100001440000001743412271765436014413 0ustar hornikusers#include "dsCMatrix.h" static int chk_nm(const char *nm, int perm, int LDL, int super) { if (strlen(nm) != 11) return 0; if (strcmp(nm + 3, "Cholesky")) return 0; if (super > 0 && nm[0] != 'S') return 0; if (super == 0 && nm[0] != 's') return 0; if (perm > 0 && nm[1] != 'P') return 0; if (perm == 0 && nm[1] != 'p') return 0; if (LDL > 0 && nm[2] != 'D') return 0; if (LDL == 0 && nm[2] != 'd') return 0; return 1; } SEXP R_chkName_Cholesky(SEXP nm, SEXP perm, SEXP LDL, SEXP super) { return ScalarLogical(chk_nm(CHAR(asChar(nm)), asLogical(perm), asLogical(LDL), asLogical(super))); } // must be called with 'nm' a string of length 11 static void chm_factor_name(char* nm, int perm, int LDL, int super) { if (strlen(nm) != 11) { error(_("chm_factor_name(): did not get string of length 11")); return; } nm[0] = (super > 0) ? 'S' : 's'; nm[1] = (perm == 0) ? 'p' : 'P'; nm[2] = (LDL == 0) ? 'd' : 'D'; return; } // must be called with 'nm' a string of length 11 SEXP R_chm_factor_name(SEXP perm, SEXP LDL, SEXP super) { char nm[12] = "...Cholesky";// 11 + final \0 chm_factor_name(nm, asLogical(perm), asLogical(LDL), asLogical(super)); return mkString(nm); } /** * Return a CHOLMOD copy of the cached Cholesky decomposition with the * required perm, LDL and super attributes. If Imult is nonzero, * update the numeric values before returning. * * If no cached copy is available then evaluate one, cache it (for * zero Imult), and return a copy. * * @param Ap dsCMatrix object * @param perm integer indicating if permutation is required (!= 0), * forbidden (0) [not yet: or optional (<0)] * @param LDL integer indicating if the LDL' form is required (>0), * forbidden (0) or optional (<0) * @param super integer indicating if the supernodal form is required (>0), * forbidden (0) or optional (<0) * @param Imult numeric multiplier of I in |A + Imult * I| */ static CHM_FR internal_chm_factor(SEXP Ap, int perm, int LDL, int super, double Imult) { SEXP facs = GET_SLOT(Ap, Matrix_factorSym); SEXP nms = getAttrib(facs, R_NamesSymbol); CHM_FR L; CHM_SP A = AS_CHM_SP__(Ap); R_CheckStack(); CHM_store_common(); /* save settings from c */ if (LENGTH(facs)) { for (int i = 0; i < LENGTH(nms); i++) { /* look for a match in cache */ if (chk_nm(CHAR(STRING_ELT(nms, i)), perm, LDL, super)) { L = AS_CHM_FR(VECTOR_ELT(facs, i)); R_CheckStack(); /* copy the factor so later it can safely be cholmod_free'd */ L = cholmod_copy_factor(L, &c); if (Imult) cholmod_factorize_p(A, &Imult, (int*)NULL, 0, L, &c); return L; } } } /* Else: No cached factor - create one */ c.final_ll = (LDL == 0) ? 1 : 0; c.supernodal = (super > 0) ? CHOLMOD_SUPERNODAL : ((super < 0) ? CHOLMOD_AUTO : /* super == 0 */ CHOLMOD_SIMPLICIAL); if (perm) { /* obtain fill-reducing permutation */ L = cholmod_analyze(A, &c); } else { /* require identity permutation */ c.nmethods = 1; c.method[0].ordering = CHOLMOD_NATURAL; c.postorder = FALSE; // *_restore_*() below or in R_cholmod_error() will restore c. L = cholmod_analyze(A, &c); } if (!cholmod_factorize_p(A, &Imult, (int*)NULL, 0 /*fsize*/, L, &c)) // have never seen this, rather R_cholmod_error(status, ..) is called : error(_("Cholesky factorization failed; unusually, please report to Matrix-authors")); if (!Imult) { /* cache the factor */ if(!chm_factor_ok(L)) { cholmod_free_factor(&L, &c);// <- do not leak! CHM_restore_common(); error(_("internal_chm_factor: Cholesky factorization failed")); } /* now that we allow (super, LDL) to be "< 0", be careful :*/ if(super < 0) super = L->is_super ? 1 : 0; if(LDL < 0) LDL = L->is_ll ? 0 : 1; char fnm[12] = "...Cholesky";// 11 + final \0 chm_factor_name(fnm, perm, LDL, super); set_factors(Ap, chm_factor_to_SEXP(L, 0), fnm); } CHM_restore_common(); return L; } SEXP dsCMatrix_chol(SEXP x, SEXP pivot) { int pivP = asLogical(pivot); CHM_FR L = internal_chm_factor(x, pivP, /*LDL = */ 0, /* super = */ 0, /* Imult = */ 0.); CHM_SP R, Rt; SEXP ans; Rt = cholmod_factor_to_sparse(L, &c); R = cholmod_transpose(Rt, /*values*/ 1, &c); cholmod_free_sparse(&Rt, &c); ans = PROTECT(chm_sparse_to_SEXP(R, 1/*do_free*/, 1/*uploT*/, 0/*Rkind*/, "N"/*diag*/, GET_SLOT(x, Matrix_DimNamesSym))); if (pivP) { SEXP piv = PROTECT(allocVector(INTSXP, L->n)); int *dest = INTEGER(piv), *src = (int*)L->Perm; for (int i = 0; i < L->n; i++) dest[i] = src[i] + 1; setAttrib(ans, install("pivot"), piv); setAttrib(ans, install("rank"), ScalarInteger((size_t) L->minor)); UNPROTECT(1); } cholmod_free_factor(&L, &c); UNPROTECT(1); return ans; } SEXP dsCMatrix_Cholesky(SEXP Ap, SEXP perm, SEXP LDL, SEXP super, SEXP Imult) { int iSuper = asLogical(super), iPerm = asLogical(perm), iLDL = asLogical(LDL); /* When parameter is set to NA in R, let CHOLMOD choose */ if(iSuper == NA_LOGICAL) iSuper = -1; /* if(iPerm == NA_LOGICAL) iPerm = -1; */ if(iLDL == NA_LOGICAL) iLDL = -1; SEXP r = chm_factor_to_SEXP(internal_chm_factor(Ap, iPerm, iLDL, iSuper, asReal(Imult)), 1 /* dofree */); return r; } /** * Fast version of getting at the diagonal matrix D of the * (generalized) simplicial Cholesky LDL' decomposition of a * (sparse symmetric) dsCMatrix. * * @param Ap symmetric CsparseMatrix * @param permP logical indicating if permutation is allowed * @param resultKind an (SEXP) string indicating which kind of result * is desired. * * @return SEXP containing either the vector diagonal entries of D, * or just sum_i D[i], prod_i D[i] or sum_i log(D[i]). */ SEXP dsCMatrix_LDL_D(SEXP Ap, SEXP permP, SEXP resultKind) { CHM_FR L; SEXP ans; L = internal_chm_factor(Ap, asLogical(permP), /*LDL*/ 1, /*super*/0, /*Imult*/0.); // ./Csparse.c : ans = PROTECT(diag_tC_ptr(L->n, L->p, L->x, L->Perm, resultKind)); cholmod_free_factor(&L, &c); UNPROTECT(1); return(ans); } // using cholmod_spsolve() --> sparse result SEXP dsCMatrix_Csparse_solve(SEXP a, SEXP b) { CHM_FR L = internal_chm_factor(a, /*perm*/-1, /*LDL*/-1, /*super*/-1, /*Imult*/0.); CHM_SP cx, cb; if(!chm_factor_ok(L)) return R_NilValue;// == "CHOLMOD factorization failed" cb = AS_CHM_SP(b); R_CheckStack(); cx = cholmod_spsolve(CHOLMOD_A, L, cb, &c); cholmod_free_factor(&L, &c); return chm_sparse_to_SEXP(cx, /*do_free*/ 1, /*uploT*/ 0, /*Rkind*/ 0, /*diag*/ "N", /*dimnames = */ R_NilValue); } // using cholmod_solve() --> dense result SEXP dsCMatrix_matrix_solve(SEXP a, SEXP b) { CHM_FR L = internal_chm_factor(a, -1, -1, -1, 0.); CHM_DN cx, cb; if(!chm_factor_ok(L)) return R_NilValue;// == "CHOLMOD factorization failed" cb = AS_CHM_DN(PROTECT(mMatrix_as_dgeMatrix(b))); R_CheckStack(); cx = cholmod_solve(CHOLMOD_A, L, cb, &c); cholmod_free_factor(&L, &c); UNPROTECT(1); return chm_dense_to_SEXP(cx, 1, 0, /*dimnames = */ R_NilValue); } /* Needed for printing dsCMatrix objects */ /* FIXME: Create a more general version of this operation: also for lsC, (dsR?),.. * e.g. make compressed_to_dgTMatrix() in ./dgCMatrix.c work for dsC */ SEXP dsCMatrix_to_dgTMatrix(SEXP x) { CHM_SP A = AS_CHM_SP__(x); CHM_SP Afull = cholmod_copy(A, /*stype*/ 0, /*mode*/ 1, &c); CHM_TR At = cholmod_sparse_to_triplet(Afull, &c); R_CheckStack(); if (!A->stype) error(_("Non-symmetric matrix passed to dsCMatrix_to_dgTMatrix")); cholmod_free_sparse(&Afull, &c); return chm_triplet_to_SEXP(At, 1, /*uploT*/ 0, /*Rkind*/ 0, "", GET_SLOT(x, Matrix_DimNamesSym)); } Matrix/src/dspMatrix.c0000644000175100001440000001300112271765436014452 0ustar hornikusers#include "dspMatrix.h" /* Note: also used for lspMatrix */ SEXP dspMatrix_validate(SEXP obj) { SEXP val = symmetricMatrix_validate(obj); if(isString(val)) return(val); else { /* identical to the test in dtpMatrix_validate() : */ int d = INTEGER(GET_SLOT(obj, Matrix_DimSym))[0], lx = length(GET_SLOT(obj, Matrix_xSym)); if(lx * 2 != d*(d+1)) return(mkString(_("Incorrect length of 'x' slot"))); return ScalarLogical(1); } } double get_norm_sp(SEXP obj, const char *typstr) { char typnm[] = {'\0', '\0'}; int *dims = INTEGER(GET_SLOT(obj, Matrix_DimSym)); double *work = (double *) NULL; typnm[0] = La_norm_type(typstr); if (*typnm == 'I' || *typnm == 'O') { work = (double *) R_alloc(dims[0], sizeof(double)); } return F77_CALL(dlansp)(typnm, uplo_P(obj), dims, REAL(GET_SLOT(obj, Matrix_xSym)), work); } SEXP dspMatrix_norm(SEXP obj, SEXP type) { return ScalarReal(get_norm_sp(obj, CHAR(asChar(type)))); } SEXP dspMatrix_rcond(SEXP obj, SEXP type) { SEXP trf = dspMatrix_trf(obj); int *dims = INTEGER(GET_SLOT(obj, Matrix_DimSym)), info; double anorm = get_norm_sp(obj, "O"), rcond; F77_CALL(dspcon)(uplo_P(trf), dims, REAL (GET_SLOT(trf, Matrix_xSym)), INTEGER(GET_SLOT(trf, Matrix_permSym)), &anorm, &rcond, (double *) R_alloc(2*dims[0], sizeof(double)), (int *) R_alloc(dims[0], sizeof(int)), &info); return ScalarReal(rcond); } SEXP dspMatrix_solve(SEXP a) { SEXP trf = dspMatrix_trf(a); SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dspMatrix"))); int *dims = INTEGER(GET_SLOT(trf, Matrix_DimSym)), info; slot_dup(val, trf, Matrix_uploSym); slot_dup(val, trf, Matrix_xSym); slot_dup(val, trf, Matrix_DimSym); F77_CALL(dsptri)(uplo_P(val), dims, REAL(GET_SLOT(val, Matrix_xSym)), INTEGER(GET_SLOT(trf, Matrix_permSym)), (double *) R_alloc((long) dims[0], sizeof(double)), &info); UNPROTECT(1); return val; } SEXP dspMatrix_matrix_solve(SEXP a, SEXP b) { SEXP trf = dspMatrix_trf(a), val = PROTECT(dup_mMatrix_as_dgeMatrix(b)); int *adims = INTEGER(GET_SLOT(a, Matrix_DimSym)), *bdims = INTEGER(GET_SLOT(val, Matrix_DimSym)); int n = bdims[0], nrhs = bdims[1], info; if (adims[0] != n || nrhs < 1 || n < 1) error(_("Dimensions of system to be solved are inconsistent")); F77_CALL(dsptrs)(uplo_P(trf), &n, &nrhs, REAL(GET_SLOT(trf, Matrix_xSym)), INTEGER(GET_SLOT(trf, Matrix_permSym)), REAL(GET_SLOT(val, Matrix_xSym)), &n, &info); UNPROTECT(1); return val; } SEXP dspMatrix_getDiag(SEXP x) { int n = *INTEGER(GET_SLOT(x, Matrix_DimSym)); SEXP val = PROTECT(allocVector(REALSXP, n)); d_packed_getDiag(REAL(val), x, n); UNPROTECT(1); return val; } SEXP lspMatrix_getDiag(SEXP x) { int n = *INTEGER(GET_SLOT(x, Matrix_DimSym)); SEXP val = PROTECT(allocVector(LGLSXP, n)); l_packed_getDiag(LOGICAL(val), x, n); UNPROTECT(1); return val; } SEXP dspMatrix_setDiag(SEXP x, SEXP d) { int n = INTEGER(GET_SLOT(x, Matrix_DimSym))[0]; return d_packed_setDiag(REAL(d), LENGTH(d), x, n); } SEXP lspMatrix_setDiag(SEXP x, SEXP d) { int n = INTEGER(GET_SLOT(x, Matrix_DimSym))[0]; return l_packed_setDiag(INTEGER(d), LENGTH(d), x, n); } SEXP dspMatrix_as_dsyMatrix(SEXP from) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dsyMatrix"))), uplo = GET_SLOT(from, Matrix_uploSym), dimP = GET_SLOT(from, Matrix_DimSym), dmnP = GET_SLOT(from, Matrix_DimNamesSym); int n = *INTEGER(dimP); SET_SLOT(val, Matrix_DimSym, duplicate(dimP)); SET_SLOT(val, Matrix_DimNamesSym, duplicate(dmnP)); SET_SLOT(val, Matrix_uploSym, duplicate(uplo)); packed_to_full_double(REAL(ALLOC_SLOT(val, Matrix_xSym, REALSXP, n*n)), REAL(GET_SLOT(from, Matrix_xSym)), n, *CHAR(STRING_ELT(uplo, 0)) == 'U' ? UPP : LOW); UNPROTECT(1); return val; } SEXP dspMatrix_matrix_mm(SEXP a, SEXP b) { SEXP val = PROTECT(dup_mMatrix_as_dgeMatrix(b)); int *bdims = INTEGER(GET_SLOT(val, Matrix_DimSym)); int i, ione = 1, n = bdims[0], nrhs = bdims[1]; const char *uplo = uplo_P(a); double *ax = REAL(GET_SLOT(a, Matrix_xSym)), one = 1., zero = 0., *vx = REAL(GET_SLOT(val, Matrix_xSym)); double *bx = Alloca(n * nrhs, double); R_CheckStack(); Memcpy(bx, vx, n * nrhs); if (bdims[0] != n) error(_("Matrices are not conformable for multiplication")); if (nrhs < 1 || n < 1) { /* error(_("Matrices with zero extents cannot be multiplied")); */ } else for (i = 0; i < nrhs; i++) F77_CALL(dspmv)(uplo, &n, &one, ax, bx + i * n, &ione, &zero, vx + i * n, &ione); UNPROTECT(1); return val; } SEXP dspMatrix_trf(SEXP x) { SEXP val = get_factors(x, "pBunchKaufman"), dimP = GET_SLOT(x, Matrix_DimSym), uploP = GET_SLOT(x, Matrix_uploSym); int *dims = INTEGER(dimP), *perm, info; int n = dims[0]; const char *uplo = CHAR(STRING_ELT(uploP, 0)); if (val != R_NilValue) return val; dims = INTEGER(dimP); val = PROTECT(NEW_OBJECT(MAKE_CLASS("pBunchKaufman"))); SET_SLOT(val, Matrix_uploSym, duplicate(uploP)); SET_SLOT(val, Matrix_diagSym, mkString("N")); SET_SLOT(val, Matrix_DimSym, duplicate(dimP)); slot_dup(val, x, Matrix_xSym); perm = INTEGER(ALLOC_SLOT(val, Matrix_permSym, INTSXP, n)); F77_CALL(dsptrf)(uplo, dims, REAL(GET_SLOT(val, Matrix_xSym)), perm, &info); if (info) error(_("Lapack routine %s returned error code %d"), "dsptrf", info); UNPROTECT(1); return set_factors(x, val, "pBunchKaufman"); } Matrix/src/lgCMatrix.c0000644000175100001440000000344412271765436014403 0ustar hornikusers#include "lgCMatrix.h" #include "dgCMatrix.h" /* validate: -> xCMatrix_validate() in ./dgCMatrix.c */ SEXP lgC_to_matrix(SEXP x) { SEXP ans, pslot = GET_SLOT(x, Matrix_pSym), dn = GET_SLOT(x, Matrix_DimNamesSym); int j, ncol = length(pslot) - 1, nrow = INTEGER(GET_SLOT(x, Matrix_DimSym))[0], *xp = INTEGER(pslot), *xi = INTEGER(GET_SLOT(x, Matrix_iSym)); int *xx = LOGICAL(GET_SLOT(x, Matrix_xSym)), *ax; ax = LOGICAL(ans = PROTECT(allocMatrix(LGLSXP, nrow, ncol))); for (j = 0; j < (nrow * ncol); j++) ax[j] = 0; for (j = 0; j < ncol; j++) { int ind; for (ind = xp[j]; ind < xp[j+1]; ind++) ax[j * nrow + xi[ind]] = xx[ind]; } if (!(isNull(VECTOR_ELT(dn,0)) && isNull(VECTOR_ELT(dn,1)))) setAttrib(ans, R_DimNamesSymbol, duplicate(dn)); UNPROTECT(1); return ans; } /* as above, '1' instead of 'x' slot: */ SEXP ngC_to_matrix(SEXP x) { SEXP ans, pslot = GET_SLOT(x, Matrix_pSym), dn = GET_SLOT(x, Matrix_DimNamesSym); int j, ncol = length(pslot) - 1, nrow = INTEGER(GET_SLOT(x, Matrix_DimSym))[0], *xp = INTEGER(pslot), *xi = INTEGER(GET_SLOT(x, Matrix_iSym)); int *ax; ax = LOGICAL(ans = PROTECT(allocMatrix(LGLSXP, nrow, ncol))); for (j = 0; j < (nrow * ncol); j++) ax[j] = 0; for (j = 0; j < ncol; j++) { int ind; for (ind = xp[j]; ind < xp[j+1]; ind++) ax[j * nrow + xi[ind]] = 1; } if (!(isNull(VECTOR_ELT(dn,0)) && isNull(VECTOR_ELT(dn,1)))) setAttrib(ans, R_DimNamesSymbol, duplicate(dn)); UNPROTECT(1); return ans; } #ifdef _NEED_logical_to_csc_FIRST_ /* very parallel to matrix_to_csc() in ./dgCMatrix.c */ SEXP matrix_to_lcsc(SEXP A) { if (!(isMatrix(A) && isLogical(A))) error(_("A must be a logical matrix")); return logical_to_csc(LOGICAL(A), INTEGER(getAttrib(A, R_DimSymbol))); } #endif Matrix/src/SuiteSparse_config/0000755000175100001440000000000012271765426016133 5ustar hornikusersMatrix/src/SuiteSparse_config/Makefile0000644000175100001440000000067512271765436017604 0ustar hornikusers#------------------------------------------------------------------------------- # SuiteSparse_config Makefile #------------------------------------------------------------------------------- VERSION = 4.2.1 PKG_CPPFLAGS = -DNTIMER include $(MkInclude) LIB = ../SuiteSparse_config.a library: $(LIB) $(LIB): SuiteSparse_config.o $(AR) -rucs $(LIB) SuiteSparse_config.o mostlyclean: clean clean: @-rm -rf .libs _libs $(LIB) @-rm -f *.o Matrix/src/SuiteSparse_config/SuiteSparse_config.c0000644000175100001440000001354512271765436022104 0ustar hornikusers/* ========================================================================== */ /* === SuiteSparse_config =================================================== */ /* ========================================================================== */ /* Copyright (c) 2012, Timothy A. Davis. No licensing restrictions * apply to this file or to the SuiteSparse_config directory. * Author: Timothy A. Davis. */ #include "SuiteSparse_config.h" /* -------------------------------------------------------------------------- */ /* SuiteSparse_malloc: malloc wrapper */ /* -------------------------------------------------------------------------- */ void *SuiteSparse_malloc /* pointer to allocated block of memory */ ( size_t nitems, /* number of items to malloc (>=1 is enforced) */ size_t size_of_item, /* sizeof each item */ int *ok, /* TRUE if successful, FALSE otherwise */ SuiteSparse_config *config /* SuiteSparse-wide configuration */ ) { void *p ; if (nitems < 1) nitems = 1 ; if (nitems * size_of_item != ((double) nitems) * size_of_item) { /* Int overflow */ *ok = 0 ; return (NULL) ; } if (!config || config->malloc_memory == NULL) { /* use malloc by default */ p = (void *) malloc (nitems * size_of_item) ; } else { /* use the pointer to malloc in the config */ p = (void *) (config->malloc_memory) (nitems * size_of_item) ; } *ok = (p != NULL) ; return (p) ; } /* -------------------------------------------------------------------------- */ /* SuiteSparse_free: free wrapper */ /* -------------------------------------------------------------------------- */ void *SuiteSparse_free /* always returns NULL */ ( void *p, /* block to free */ SuiteSparse_config *config /* SuiteSparse-wide configuration */ ) { if (p) { if (!config || config->free_memory == NULL) { /* use free by default */ free (p) ; } else { /* use the pointer to free in the config */ (config->free_memory) (p) ; } } return (NULL) ; } /* -------------------------------------------------------------------------- */ /* SuiteSparse_tic: return current wall clock time */ /* -------------------------------------------------------------------------- */ /* Returns the number of seconds (tic [0]) and nanoseconds (tic [1]) since some * unspecified but fixed time in the past. If no timer is installed, zero is * returned. A scalar double precision value for 'tic' could be used, but this * might cause loss of precision because clock_getttime returns the time from * some distant time in the past. Thus, an array of size 2 is used. * * The timer is enabled by default. To disable the timer, compile with * -DNTIMER. If enabled on a POSIX C 1993 system, the timer requires linking * with the -lrt library. * * example: * * double tic [2], r, s, t ; * SuiteSparse_tic (tic) ; // start the timer * // do some work A * t = SuiteSparse_toc (tic) ; // t is time for work A, in seconds * // do some work B * s = SuiteSparse_toc (tic) ; // s is time for work A and B, in seconds * SuiteSparse_tic (tic) ; // restart the timer * // do some work C * r = SuiteSparse_toc (tic) ; // s is time for work C, in seconds * * A double array of size 2 is used so that this routine can be more easily * ported to non-POSIX systems. The caller does not rely on the POSIX * include file. */ #ifdef SUITESPARSE_TIMER_ENABLED #include void SuiteSparse_tic ( double tic [2] /* output, contents undefined on input */ ) { /* POSIX C 1993 timer, requires -librt */ struct timespec t ; clock_gettime (CLOCK_MONOTONIC, &t) ; tic [0] = (double) (t.tv_sec) ; tic [1] = (double) (t.tv_nsec) ; } #else void SuiteSparse_tic ( double tic [2] /* output, contents undefined on input */ ) { /* no timer installed */ tic [0] = 0 ; tic [1] = 0 ; } #endif /* -------------------------------------------------------------------------- */ /* SuiteSparse_toc: return time since last tic */ /* -------------------------------------------------------------------------- */ /* Assuming SuiteSparse_tic is accurate to the nanosecond, this function is * accurate down to the nanosecond for 2^53 nanoseconds since the last call to * SuiteSparse_tic, which is sufficient for SuiteSparse (about 104 days). If * additional accuracy is required, the caller can use two calls to * SuiteSparse_tic and do the calculations differently. */ double SuiteSparse_toc /* returns time in seconds since last tic */ ( double tic [2] /* input, not modified from last call to SuiteSparse_tic */ ) { double toc [2] ; SuiteSparse_tic (toc) ; return ((toc [0] - tic [0]) + 1e-9 * (toc [1] - tic [1])) ; } /* -------------------------------------------------------------------------- */ /* SuiteSparse_time: return current wallclock time in seconds */ /* -------------------------------------------------------------------------- */ /* This function might not be accurate down to the nanosecond. */ double SuiteSparse_time /* returns current wall clock time in seconds */ ( void ) { double toc [2] ; SuiteSparse_tic (toc) ; return (toc [0] + 1e-9 * toc [1]) ; } /* -------------------------------------------------------------------------- */ /* SuiteSparse_version: return the current version of SuiteSparse */ /* -------------------------------------------------------------------------- */ int SuiteSparse_version ( int version [3] ) { if (version != NULL) { version [0] = SUITESPARSE_MAIN_VERSION ; version [1] = SUITESPARSE_SUB_VERSION ; version [2] = SUITESPARSE_SUBSUB_VERSION ; } return (SUITESPARSE_VERSION) ; } Matrix/src/SuiteSparse_config/SuiteSparse_config.h0000644000175100001440000001576312271765436022115 0ustar hornikusers/* ========================================================================== */ /* === SuiteSparse_config =================================================== */ /* ========================================================================== */ /* Configuration file for SuiteSparse: a Suite of Sparse matrix packages * (AMD, COLAMD, CCOLAMD, CAMD, CHOLMOD, UMFPACK, CXSparse, and others). * * SuiteSparse_config.h provides the definition of the long integer. On most * systems, a C program can be compiled in LP64 mode, in which long's and * pointers are both 64-bits, and int's are 32-bits. Windows 64, however, uses * the LLP64 model, in which int's and long's are 32-bits, and long long's and * pointers are 64-bits. * * SuiteSparse packages that include long integer versions are * intended for the LP64 mode. However, as a workaround for Windows 64 * (and perhaps other systems), the long integer can be redefined. * * If _WIN64 is defined, then the __int64 type is used instead of long. * * The long integer can also be defined at compile time. For example, this * could be added to SuiteSparse_config.mk: * * CFLAGS = -O -D'SuiteSparse_long=long long' \ * -D'SuiteSparse_long_max=9223372036854775801' -D'SuiteSparse_long_idd="lld"' * * This file defines SuiteSparse_long as either long (on all but _WIN64) or * __int64 on Windows 64. The intent is that a SuiteSparse_long is always a * 64-bit integer in a 64-bit code. ptrdiff_t might be a better choice than * long; it is always the same size as a pointer. * * This file also defines the SUITESPARSE_VERSION and related definitions. * * Copyright (c) 2012, Timothy A. Davis. No licensing restrictions apply * to this file or to the SuiteSparse_config directory. * Author: Timothy A. Davis. */ #ifndef _SUITESPARSECONFIG_H #define _SUITESPARSECONFIG_H #ifdef __cplusplus extern "C" { #endif #include #include /* ========================================================================== */ /* === SuiteSparse_long ===================================================== */ /* ========================================================================== */ #ifndef SuiteSparse_long #ifdef _WIN64 #define SuiteSparse_long __int64 #define SuiteSparse_long_max _I64_MAX #define SuiteSparse_long_idd "I64d" #else #define SuiteSparse_long long #define SuiteSparse_long_max LONG_MAX #define SuiteSparse_long_idd "ld" #endif #define SuiteSparse_long_id "%" SuiteSparse_long_idd #endif /* For backward compatibility with prior versions of SuiteSparse. The UF_* * macros are deprecated and will be removed in a future version. */ #ifndef UF_long #define UF_long SuiteSparse_long #define UF_long_max SuiteSparse_long_max #define UF_long_idd SuiteSparse_long_idd #define UF_long_id SuiteSparse_long_id #endif /* ========================================================================== */ /* === SuiteSparse_config parameters and functions ========================== */ /* ========================================================================== */ /* SuiteSparse-wide parameters will be placed in this struct. */ typedef struct SuiteSparse_config_struct { void *(*malloc_memory) (size_t) ; /* pointer to malloc */ void *(*realloc_memory) (void *, size_t) ; /* pointer to realloc */ void (*free_memory) (void *) ; /* pointer to free */ void *(*calloc_memory) (size_t, size_t) ; /* pointer to calloc */ } SuiteSparse_config ; void *SuiteSparse_malloc /* pointer to allocated block of memory */ ( size_t nitems, /* number of items to malloc (>=1 is enforced) */ size_t size_of_item, /* sizeof each item */ int *ok, /* TRUE if successful, FALSE otherwise */ SuiteSparse_config *config /* SuiteSparse-wide configuration */ ) ; void *SuiteSparse_free /* always returns NULL */ ( void *p, /* block to free */ SuiteSparse_config *config /* SuiteSparse-wide configuration */ ) ; void SuiteSparse_tic /* start the timer */ ( double tic [2] /* output, contents undefined on input */ ) ; double SuiteSparse_toc /* return time in seconds since last tic */ ( double tic [2] /* input: from last call to SuiteSparse_tic */ ) ; double SuiteSparse_time /* returns current wall clock time in seconds */ ( void ) ; /* determine which timer to use, if any */ #ifndef NTIMER #ifdef _POSIX_C_SOURCE #if _POSIX_C_SOURCE >= 199309L #define SUITESPARSE_TIMER_ENABLED #endif #endif #endif /* ========================================================================== */ /* === SuiteSparse version ================================================== */ /* ========================================================================== */ /* SuiteSparse is not a package itself, but a collection of packages, some of * which must be used together (UMFPACK requires AMD, CHOLMOD requires AMD, * COLAMD, CAMD, and CCOLAMD, etc). A version number is provided here for the * collection itself. The versions of packages within each version of * SuiteSparse are meant to work together. Combining one packge from one * version of SuiteSparse, with another package from another version of * SuiteSparse, may or may not work. * * SuiteSparse contains the following packages: * * SuiteSparse_config version 4.2.1 (version always the same as SuiteSparse) * AMD version 2.3.1 * BTF version 1.2.0 * CAMD version 2.3.1 * CCOLAMD version 2.8.0 * CHOLMOD version 2.1.2 * COLAMD version 2.8.0 * CSparse version 3.1.2 * CXSparse version 3.1.2 * KLU version 1.2.1 * LDL version 2.1.0 * RBio version 2.1.1 * SPQR version 1.3.1 (full name is SuiteSparseQR) * UMFPACK version 5.6.2 * MATLAB_Tools various packages & M-files * * Other package dependencies: * BLAS required by CHOLMOD and UMFPACK * LAPACK required by CHOLMOD * METIS 4.0.1 required by CHOLMOD (optional) and KLU (optional) */ int SuiteSparse_version /* returns SUITESPARSE_VERSION */ ( /* output, not defined on input. Not used if NULL. Returns the three version codes in version [0..2]: version [0] is SUITESPARSE_MAIN_VERSION version [1] is SUITESPARSE_SUB_VERSION version [2] is SUITESPARSE_SUBSUB_VERSION */ int version [3] ) ; /* Versions prior to 4.2.0 do not have the above function. The following code fragment will work with any version of SuiteSparse: #ifdef SUITESPARSE_HAS_VERSION_FUNCTION v = SuiteSparse_version (NULL) ; #else v = SUITESPARSE_VERSION ; #endif */ #define SUITESPARSE_HAS_VERSION_FUNCTION #define SUITESPARSE_DATE "April 25, 2013" #define SUITESPARSE_VER_CODE(main,sub) ((main) * 1000 + (sub)) #define SUITESPARSE_MAIN_VERSION 4 #define SUITESPARSE_SUB_VERSION 2 #define SUITESPARSE_SUBSUB_VERSION 1 #define SUITESPARSE_VERSION \ SUITESPARSE_VER_CODE(SUITESPARSE_MAIN_VERSION,SUITESPARSE_SUB_VERSION) #ifdef __cplusplus } #endif #endif Matrix/src/SuiteSparse_config/SuiteSparse_config.mk0000644000175100001440000000000011770402705022235 0ustar hornikusersMatrix/src/cs.h0000644000175100001440000001435412271765436013125 0ustar hornikusers#ifndef _CS_H #define _CS_H #include #include #include // needed for FILE: #include #include // For use with R package 'Matrix' # include # define printf Rprintf #ifdef MATLAB_MEX_FILE #include "mex.h" #endif #define CS_VER 3 /* CSparse Version */ #define CS_SUBVER 1 #define CS_SUBSUB 2 #define CS_DATE "April 16, 2013" /* CSparse release date */ #define CS_COPYRIGHT "Copyright (c) Timothy A. Davis, 2006-2013" #ifdef MATLAB_MEX_FILE #undef csi #define csi mwSignedIndex #endif #ifndef csi #define csi int #endif /* --- primary CSparse routines and data structures ------------------------- */ typedef struct cs_sparse /* matrix in compressed-column or triplet form */ { csi nzmax ; /* maximum number of entries */ csi m ; /* number of rows */ csi n ; /* number of columns */ csi *p ; /* column pointers (size n+1) or col indices (size nzmax) */ csi *i ; /* row indices, size nzmax */ double *x ; /* numerical values, size nzmax */ csi nz ; /* # of entries in triplet matrix, -1 for compressed-col */ } cs ; cs *cs_add (const cs *A, const cs *B, double alpha, double beta) ; csi cs_cholsol (csi order, const cs *A, double *b) ; cs *cs_compress (const cs *T) ; csi cs_dupl (cs *A) ; csi cs_entry (cs *T, csi i, csi j, double x) ; csi cs_gaxpy (const cs *A, const double *x, double *y) ; cs *cs_load (FILE *f) ; csi cs_lusol (csi order, const cs *A, double *b, double tol) ; cs *cs_multiply (const cs *A, const cs *B) ; double cs_norm (const cs *A) ; csi cs_print (const cs *A, csi brief) ; csi cs_qrsol (csi order, const cs *A, double *b) ; cs *cs_transpose (const cs *A, csi values) ; /* utilities */ void *cs_calloc (csi n, size_t size) ; void *cs_free (void *p) ; void *cs_realloc (void *p, csi n, size_t size, csi *ok) ; cs *cs_spalloc (csi m, csi n, csi nzmax, csi values, csi triplet) ; cs *cs_spfree (cs *A) ; csi cs_sprealloc (cs *A, csi nzmax) ; void *cs_malloc (csi n, size_t size) ; /* --- secondary CSparse routines and data structures ----------------------- */ typedef struct cs_symbolic /* symbolic Cholesky, LU, or QR analysis */ { csi *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */ csi *q ; /* fill-reducing column permutation for LU and QR */ csi *parent ; /* elimination tree for Cholesky and QR */ csi *cp ; /* column pointers for Cholesky, row counts for QR */ csi *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */ csi m2 ; /* # of rows for QR, after adding fictitious rows */ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */ double unz ; /* # entries in U for LU; in R for QR */ } css ; typedef struct cs_numeric /* numeric Cholesky, LU, or QR factorization */ { cs *L ; /* L for LU and Cholesky, V for QR */ cs *U ; /* U for LU, R for QR, not used for Cholesky */ csi *pinv ; /* partial pivoting for LU */ double *B ; /* beta [0..n-1] for QR */ } csn ; typedef struct cs_dmperm_results /* cs_dmperm or cs_scc output */ { csi *p ; /* size m, row permutation */ csi *q ; /* size n, column permutation */ csi *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */ csi *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */ csi nb ; /* # of blocks in fine dmperm decomposition */ csi rr [5] ; /* coarse row decomposition */ csi cc [5] ; /* coarse column decomposition */ } csd ; csi *cs_amd (csi order, const cs *A) ; csn *cs_chol (const cs *A, const css *S) ; csd *cs_dmperm (const cs *A, csi seed) ; csi cs_droptol (cs *A, double tol) ; csi cs_dropzeros (cs *A) ; csi cs_happly (const cs *V, csi i, double beta, double *x) ; csi cs_ipvec (const csi *p, const double *b, double *x, csi n) ; csi cs_lsolve (const cs *L, double *x) ; csi cs_ltsolve (const cs *L, double *x) ; csn *cs_lu (const cs *A, const css *S, double tol) ; cs *cs_permute (const cs *A, const csi *pinv, const csi *q, csi values) ; csi *cs_pinv (const csi *p, csi n) ; csi cs_pvec (const csi *p, const double *b, double *x, csi n) ; csn *cs_qr (const cs *A, const css *S) ; css *cs_schol (csi order, const cs *A) ; css *cs_sqr (csi order, const cs *A, csi qr) ; cs *cs_symperm (const cs *A, const csi *pinv, csi values) ; csi cs_updown (cs *L, csi sigma, const cs *C, const csi *parent) ; csi cs_usolve (const cs *U, double *x) ; csi cs_utsolve (const cs *U, double *x) ; /* utilities */ css *cs_sfree (css *S) ; csn *cs_nfree (csn *N) ; csd *cs_dfree (csd *D) ; /* --- tertiary CSparse routines -------------------------------------------- */ csi *cs_counts (const cs *A, const csi *parent, const csi *post, csi ata) ; double cs_cumsum (csi *p, csi *c, csi n) ; csi cs_dfs (csi j, cs *G, csi top, csi *xi, csi *pstack, const csi *pinv) ; csi cs_ereach (const cs *A, csi k, const csi *parent, csi *s, csi *w) ; csi *cs_etree (const cs *A, csi ata) ; csi cs_fkeep (cs *A, csi (*fkeep) (csi, csi, double, void *), void *other) ; double cs_house (double *x, double *beta, csi n) ; csi cs_leaf (csi i, csi j, const csi *first, csi *maxfirst, csi *prevleaf, csi *ancestor, csi *jleaf) ; csi *cs_maxtrans (const cs *A, csi seed) ; csi *cs_post (const csi *parent, csi n) ; csi *cs_randperm (csi n, csi seed) ; csi cs_reach (cs *G, const cs *B, csi k, csi *xi, const csi *pinv) ; csi cs_scatter (const cs *A, csi j, double beta, csi *w, double *x, csi mark, cs *C, csi nz) ; csd *cs_scc (cs *A) ; csi cs_spsolve (cs *G, const cs *B, csi k, csi *xi, double *x, const csi *pinv, csi lo) ; csi cs_tdfs (csi j, csi k, csi *head, const csi *next, csi *post, csi *stack) ; /* utilities */ csd *cs_dalloc (csi m, csi n) ; csd *cs_ddone (csd *D, cs *C, void *w, csi ok) ; cs *cs_done (cs *C, void *w, void *x, csi ok) ; csi *cs_idone (csi *p, cs *C, void *w, csi ok) ; csn *cs_ndone (csn *N, cs *C, void *w, void *x, csi ok) ; #define CS_MAX(a,b) (((a) > (b)) ? (a) : (b)) #define CS_MIN(a,b) (((a) < (b)) ? (a) : (b)) #define CS_FLIP(i) (-(i)-2) #define CS_UNFLIP(i) (((i) < 0) ? CS_FLIP(i) : (i)) #define CS_MARKED(w,j) (w [j] < 0) #define CS_MARK(w,j) { w [j] = CS_FLIP (w [j]) ; } #define CS_CSC(A) (A && (A->nz == -1)) #define CS_TRIPLET(A) (A && (A->nz >= 0)) #endif Matrix/src/TMatrix_as.c0000644000175100001440000001175512271765436014570 0ustar hornikusers /* Sparse symmetric matrices in triplet format */ #include "TMatrix_as.h" #define MAYBE_DECLARE_AND_GET_X_SLOT(__T__, __S__) \ DECLARE_AND_GET_X_SLOT(__T__, __S__) #define Matrix_T_as_DENSE(_C_TYPE_, _SEXP_, _SEXPTYPE_) \ SEXP dimP = GET_SLOT(x, Matrix_DimSym), \ xiP = GET_SLOT(x, Matrix_iSym); \ int k, n = INTEGER(dimP)[0], nnz = length(xiP); \ int *xi = INTEGER(xiP), *xj = INTEGER(GET_SLOT(x, Matrix_jSym)), \ sz = n * n; \ _C_TYPE_ *tx = _SEXP_(ALLOC_SLOT(val, Matrix_xSym, _SEXPTYPE_, sz)); \ MAYBE_DECLARE_AND_GET_X_SLOT(_C_TYPE_, _SEXP_); \ \ SET_SLOT(val, Matrix_DimSym, duplicate(dimP)); \ SET_DimNames(val, x); \ slot_dup(val, x, Matrix_uploSym) #define Matrix_T_as_DENSE_FINISH(_X_k_) \ AZERO(tx, sz); \ for (k = 0; k < nnz; k++) \ tx[xi[k] + xj[k] * n] = _X_k_; \ UNPROTECT(1); \ return val SEXP dsTMatrix_as_dsyMatrix(SEXP x) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dsyMatrix"))); Matrix_T_as_DENSE(double, REAL, REALSXP); Matrix_T_as_DENSE_FINISH(xx[k]); } SEXP lsTMatrix_as_lsyMatrix(SEXP x) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("lsyMatrix"))); Matrix_T_as_DENSE(int, LOGICAL, LGLSXP); Matrix_T_as_DENSE_FINISH(xx[k]); } /* ---- Now the triangular ones -- have an extra 'diag' slot : ------ */ SEXP dtTMatrix_as_dtrMatrix(SEXP x) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dtrMatrix"))); Matrix_T_as_DENSE(double, REAL, REALSXP); slot_dup(val, x, Matrix_diagSym); Matrix_T_as_DENSE_FINISH(xx[k]); } SEXP ltTMatrix_as_ltrMatrix(SEXP x) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("ltrMatrix"))); Matrix_T_as_DENSE(int, LOGICAL, LGLSXP); slot_dup(val, x, Matrix_diagSym); Matrix_T_as_DENSE_FINISH(xx[k]); } /*===================== Coercion to gTMatrix ================================*/ #undef MAYBE_DECLARE_AND_GET_X_SLOT #define MAYBE_DECLARE_AND_GET_X_SLOT(__T__, __S__) \ DECLARE_AND_GET_X_SLOT(__T__, __S__), *vx #define ALLOC_val_x_SLOT(__SEXP__, __S_TYPE__) \ vx = __SEXP__(ALLOC_SLOT(val, Matrix_xSym,__S_TYPE__, nv)) #define MAYBE_ALLOC_val_x_SLOT(_S1_, _S2_) \ ALLOC_val_x_SLOT(_S1_, _S2_) #define MEMCPY_x_SLOT Memcpy(&vx[nv], xx, nnz) #define MAYBE_MEMCPY_x_SLOT MEMCPY_x_SLOT #define SET_x_SLOT vx[nv] = xx[i] #define MAYBE_SET_x_SLOT SET_x_SLOT #define Matrix_T_as_GENERAL(_C_TYPE_, _SEXP_, _SEXPTYPE_) \ SEXP xiP = GET_SLOT(x, Matrix_iSym); \ /* , uplo = GET_SLOT(x, Matrix_uploSym); */ \ int i, nnz = length(xiP), n0d, nv, \ *xi = INTEGER(xiP), \ *xj = INTEGER(GET_SLOT(x, Matrix_jSym)), \ *vi, *vj; \ MAYBE_DECLARE_AND_GET_X_SLOT(_C_TYPE_, _SEXP_); \ \ /* Find *length* of result slots: */ \ /* = 2 * nnz - n0d; n0d := #{non-0 diagonals} :*/ \ for(i = 0, n0d = 0; i < nnz; i++) \ if(xi[i] == xj[i]) n0d++ ; \ nv = 2 * nnz - n0d; \ \ vi = INTEGER(ALLOC_SLOT(val, Matrix_iSym, INTSXP, nv)); \ vj = INTEGER(ALLOC_SLOT(val, Matrix_jSym, INTSXP, nv)); \ MAYBE_ALLOC_val_x_SLOT(_SEXP_, _SEXPTYPE_); \ \ slot_dup(val, x, Matrix_DimSym); \ SET_DimNames(val, x); \ /* copy the upper/lower triangle (including the diagonal)*/ \ /* "at end" ([nv]): */ \ nv = nnz - n0d; \ Memcpy(&vi[nv], xi, nnz); \ Memcpy(&vj[nv], xj, nnz); \ MAYBE_MEMCPY_x_SLOT; \ \ for(i = 0, nv = 0; i < nnz; i++) { /* copy the other triangle */ \ if(xi[i] != xj[i]) { /* but not the diagonal */ \ vi[nv] = xj[i]; \ vj[nv] = xi[i]; \ MAYBE_SET_x_SLOT; \ nv++; \ } \ } \ \ UNPROTECT(1); \ return val /* this corresponds to changing 'stype' of a cholmod_triplet; * seems not available there */ SEXP dsTMatrix_as_dgTMatrix(SEXP x) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dgTMatrix"))); Matrix_T_as_GENERAL(double, REAL, REALSXP); } SEXP lsTMatrix_as_lgTMatrix(SEXP x) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("lgTMatrix"))); Matrix_T_as_GENERAL(int, LOGICAL, LGLSXP); } /* Now the 'nsparseMatrix' ones where input has no 'x' slot : ---------------*/ #undef MAYBE_DECLARE_AND_GET_X_SLOT #define MAYBE_DECLARE_AND_GET_X_SLOT(__T__, __S__) #undef MAYBE_ALLOC_val_x_SLOT #define MAYBE_ALLOC_val_x_SLOT(_S1_, _S2_) #undef MAYBE_MEMCPY_x_SLOT #define MAYBE_MEMCPY_x_SLOT #undef MAYBE_SET_x_SLOT #define MAYBE_SET_x_SLOT SEXP nsTMatrix_as_nsyMatrix(SEXP x) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("nsyMatrix"))); Matrix_T_as_DENSE(int, LOGICAL, LGLSXP); Matrix_T_as_DENSE_FINISH(1); } SEXP ntTMatrix_as_ntrMatrix(SEXP x) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("ntrMatrix"))); Matrix_T_as_DENSE(int, LOGICAL, LGLSXP); slot_dup(val, x, Matrix_diagSym); Matrix_T_as_DENSE_FINISH(1); } SEXP nsTMatrix_as_ngTMatrix(SEXP x) { SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("ngTMatrix"))); Matrix_T_as_GENERAL(int, LOGICAL, LGLSXP); } Matrix/src/dgeMatrix.c0000644000175100001440000005764112271765436014445 0ustar hornikusers#include "dgeMatrix.h" SEXP dMatrix_validate(SEXP obj) { SEXP x = GET_SLOT(obj, Matrix_xSym), Dim = GET_SLOT(obj, Matrix_DimSym); int m, n; if (length(Dim) != 2) return mkString(_("Dim slot must have length 2")); m = INTEGER(Dim)[0]; n = INTEGER(Dim)[1]; if (m < 0 || n < 0) return mkString(dngettext("Matrix", "Negative value in Dim", "Negative values in Dim", (m*n > 0) ? 2 : 1)); if (!isReal(x)) return mkString(_("x slot must be numeric \"double\"")); return ScalarLogical(1); } SEXP dgeMatrix_validate(SEXP obj) { SEXP val, fact = GET_SLOT(obj, Matrix_factorSym); if (isString(val = dense_nonpacked_validate(obj))) return(val); if (length(fact) > 0 && getAttrib(fact, R_NamesSymbol) == R_NilValue) return mkString(_("factors slot must be named list")); return ScalarLogical(1); } static double get_norm(SEXP obj, const char *typstr) { if(any_NA_in_x(obj)) return NA_REAL; else { char typnm[] = {'\0', '\0'}; int *dims = INTEGER(GET_SLOT(obj, Matrix_DimSym)); double *work = (double *) NULL; typnm[0] = La_norm_type(typstr); if (*typnm == 'I') { work = (double *) R_alloc(dims[0], sizeof(double)); } return F77_CALL(dlange)(typstr, dims, dims+1, REAL(GET_SLOT(obj, Matrix_xSym)), dims, work); } } SEXP dgeMatrix_norm(SEXP obj, SEXP type) { return ScalarReal(get_norm(obj, CHAR(asChar(type)))); } SEXP dgeMatrix_rcond(SEXP obj, SEXP type) { SEXP LU = PROTECT(dgeMatrix_LU_(obj, FALSE));/* <- not warning about singularity */ char typnm[] = {'\0', '\0'}; int *dims = INTEGER(GET_SLOT(LU, Matrix_DimSym)), info; double anorm, rcond; if (dims[0] != dims[1] || dims[0] < 1) { UNPROTECT(1); error(_("rcond requires a square, non-empty matrix")); } typnm[0] = La_rcond_type(CHAR(asChar(type))); anorm = get_norm(obj, typnm); F77_CALL(dgecon)(typnm, dims, REAL(GET_SLOT(LU, Matrix_xSym)), dims, &anorm, &rcond, (double *) R_alloc(4*dims[0], sizeof(double)), (int *) R_alloc(dims[0], sizeof(int)), &info); UNPROTECT(1); return ScalarReal(rcond); } SEXP dgeMatrix_crossprod(SEXP x, SEXP trans) { int tr = asLogical(trans);/* trans=TRUE: tcrossprod(x) */ SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dpoMatrix"))), nms = VECTOR_ELT(GET_SLOT(x, Matrix_DimNamesSym), tr ? 0 : 1), vDnms = ALLOC_SLOT(val, Matrix_DimNamesSym, VECSXP, 2); int *Dims = INTEGER(GET_SLOT(x, Matrix_DimSym)), *vDims = INTEGER(ALLOC_SLOT(val, Matrix_DimSym, INTSXP, 2)); int k = tr ? Dims[1] : Dims[0], n = tr ? Dims[0] : Dims[1]; double *vx = REAL(ALLOC_SLOT(val, Matrix_xSym, REALSXP, n * n)), one = 1.0, zero = 0.0; AZERO(vx, n * n); SET_SLOT(val, Matrix_uploSym, mkString("U")); ALLOC_SLOT(val, Matrix_factorSym, VECSXP, 0); vDims[0] = vDims[1] = n; SET_VECTOR_ELT(vDnms, 0, duplicate(nms)); SET_VECTOR_ELT(vDnms, 1, duplicate(nms)); if(n) F77_CALL(dsyrk)("U", tr ? "N" : "T", &n, &k, &one, REAL(GET_SLOT(x, Matrix_xSym)), Dims, &zero, vx, &n); SET_SLOT(val, Matrix_factorSym, allocVector(VECSXP, 0)); UNPROTECT(1); return val; } SEXP dgeMatrix_dgeMatrix_crossprod(SEXP x, SEXP y, SEXP trans) { int tr = asLogical(trans);/* trans=TRUE: tcrossprod(x,y) */ SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dgeMatrix"))), dn = PROTECT(allocVector(VECSXP, 2)); int *xDims = INTEGER(GET_SLOT(x, Matrix_DimSym)), *yDims = INTEGER(GET_SLOT(y, Matrix_DimSym)), *vDims; int m = xDims[!tr], n = yDims[!tr];/* -> result dim */ int xd = xDims[ tr], yd = yDims[ tr];/* the conformable dims */ double one = 1.0, zero = 0.0; SET_SLOT(val, Matrix_factorSym, allocVector(VECSXP, 0)); SET_SLOT(val, Matrix_DimSym, allocVector(INTSXP, 2)); vDims = INTEGER(GET_SLOT(val, Matrix_DimSym)); if (xd > 0 && yd > 0 && n > 0 && m > 0) { if (xd != yd) error(_("Dimensions of x and y are not compatible for %s"), tr ? "tcrossprod" : "crossprod"); vDims[0] = m; vDims[1] = n; SET_SLOT(val, Matrix_xSym, allocVector(REALSXP, m * n)); F77_CALL(dgemm)(tr ? "N" : "T", tr ? "T" : "N", &m, &n, &xd, &one, REAL(GET_SLOT(x, Matrix_xSym)), xDims, REAL(GET_SLOT(y, Matrix_xSym)), yDims, &zero, REAL(GET_SLOT(val, Matrix_xSym)), &m); /* establish dimnames */ SET_VECTOR_ELT(dn, 0, duplicate(VECTOR_ELT(GET_SLOT(x, Matrix_DimNamesSym), tr ? 0 : 1))); SET_VECTOR_ELT(dn, 1, duplicate(VECTOR_ELT(GET_SLOT(y, Matrix_DimNamesSym), tr ? 0 : 1))); SET_SLOT(val, Matrix_DimNamesSym, dn); } UNPROTECT(2); return val; } SEXP dgeMatrix_matrix_crossprod(SEXP x, SEXP y, SEXP trans) { int tr = asLogical(trans);/* trans=TRUE: tcrossprod(x,y) */ SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dgeMatrix"))), dn = PROTECT(allocVector(VECSXP, 2)), yDnms = R_NilValue, yD; int *xDims = INTEGER(GET_SLOT(x, Matrix_DimSym)), *yDims, *vDims, nprot = 2; int m = xDims[!tr], xd = xDims[ tr]; double one = 1.0, zero = 0.0; Rboolean y_has_dimNames; if (isInteger(y)) { y = PROTECT(coerceVector(y, REALSXP)); nprot++; } if (!isReal(y)) error(_("Argument y must be numeric or integer")); if(isMatrix(y)) { yDims = INTEGER(getAttrib(y, R_DimSymbol)); yDnms = getAttrib(y, R_DimNamesSymbol); y_has_dimNames = yDnms != R_NilValue; } else { // ! matrix yDims = INTEGER(yD = PROTECT(allocVector(INTSXP, 2))); nprot++; yDims[0] = LENGTH(y); yDims[1] = 1; y_has_dimNames = FALSE; } int n = yDims[!tr],/* (m,n) -> result dim */ yd = yDims[ tr];/* (xd,yd): the conformable dims */ SET_SLOT(val, Matrix_factorSym, allocVector(VECSXP, 0)); SET_SLOT(val, Matrix_DimSym, allocVector(INTSXP, 2)); vDims = INTEGER(GET_SLOT(val, Matrix_DimSym)); if (xd > 0 && yd > 0 && n > 0 && m > 0) { if (xd != yd) error(_("Dimensions of x and y are not compatible for %s"), tr ? "tcrossprod" : "crossprod"); vDims[0] = m; vDims[1] = n; SET_SLOT(val, Matrix_xSym, allocVector(REALSXP, m * n)); F77_CALL(dgemm)(tr ? "N" : "T", tr ? "T" : "N", &m, &n, &xd, &one, REAL(GET_SLOT(x, Matrix_xSym)), xDims, REAL(y), yDims, &zero, REAL(GET_SLOT(val, Matrix_xSym)), &m); /* establish dimnames */ SET_VECTOR_ELT(dn, 0, duplicate(VECTOR_ELT(GET_SLOT(x, Matrix_DimNamesSym), tr ? 0 : 1))); if(y_has_dimNames) SET_VECTOR_ELT(dn, 1, duplicate(VECTOR_ELT(yDnms, tr ? 0 : 1))); SET_SLOT(val, Matrix_DimNamesSym, dn); } UNPROTECT(nprot); return val; } SEXP dgeMatrix_getDiag(SEXP x) { #define geMatrix_getDiag_1 \ int *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)); \ int i, m = dims[0], nret = (m < dims[1]) ? m : dims[1]; \ SEXP x_x = GET_SLOT(x, Matrix_xSym) geMatrix_getDiag_1; SEXP ret = PROTECT(allocVector(REALSXP, nret)); double *rv = REAL(ret), *xv = REAL(x_x); #define geMatrix_getDiag_2 \ for (i = 0; i < nret; i++) { \ rv[i] = xv[i * (m + 1)]; \ } \ UNPROTECT(1); \ return ret geMatrix_getDiag_2; } SEXP lgeMatrix_getDiag(SEXP x) { geMatrix_getDiag_1; SEXP ret = PROTECT(allocVector(LGLSXP, nret)); int *rv = LOGICAL(ret), *xv = LOGICAL(x_x); geMatrix_getDiag_2; } #undef geMatrix_getDiag_1 #undef geMatrix_getDiag_2 SEXP dgeMatrix_setDiag(SEXP x, SEXP d) { #define geMatrix_setDiag_1 \ int *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)); \ int m = dims[0], nret = (m < dims[1]) ? m : dims[1]; \ SEXP ret = PROTECT(duplicate(x)); \ SEXP r_x = GET_SLOT(ret, Matrix_xSym); \ int l_d = LENGTH(d); Rboolean d_full = (l_d == nret); \ if (!d_full && l_d != 1) \ error("replacement diagonal has wrong length") geMatrix_setDiag_1; double *dv = REAL(d), *rv = REAL(r_x); #define geMatrix_setDiag_2 \ if(d_full) for (int i = 0; i < nret; i++) \ rv[i * (m + 1)] = dv[i]; \ else for (int i = 0; i < nret; i++) \ rv[i * (m + 1)] = *dv; \ UNPROTECT(1); \ return ret geMatrix_setDiag_2; } SEXP lgeMatrix_setDiag(SEXP x, SEXP d) { geMatrix_setDiag_1; int *dv = INTEGER(d), *rv = INTEGER(r_x); geMatrix_setDiag_2; } #undef geMatrix_setDiag_1 #undef geMatrix_setDiag_2 SEXP dgeMatrix_addDiag(SEXP x, SEXP d) { int *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)), m = dims[0], nret = (m < dims[1]) ? m : dims[1]; SEXP ret = PROTECT(duplicate(x)), r_x = GET_SLOT(ret, Matrix_xSym); double *dv = REAL(d), *rv = REAL(r_x); int l_d = LENGTH(d); Rboolean d_full = (l_d == nret); if (!d_full && l_d != 1) error("diagonal to be added has wrong length"); if(d_full) for (int i = 0; i < nret; i++) rv[i * (m + 1)] += dv[i]; else for (int i = 0; i < nret; i++) rv[i * (m + 1)] += *dv; UNPROTECT(1); return ret; } SEXP dgeMatrix_LU_(SEXP x, Rboolean warn_sing) { SEXP val = get_factors(x, "LU"); int *dims, npiv, info; if (val != R_NilValue) /* nothing to do if it's there in 'factors' slot */ return val; dims = INTEGER(GET_SLOT(x, Matrix_DimSym)); if (dims[0] < 1 || dims[1] < 1) error(_("Cannot factor a matrix with zero extents")); npiv = (dims[0] < dims[1]) ? dims[0] : dims[1]; val = PROTECT(NEW_OBJECT(MAKE_CLASS("denseLU"))); slot_dup(val, x, Matrix_xSym); slot_dup(val, x, Matrix_DimSym); F77_CALL(dgetrf)(dims, dims + 1, REAL(GET_SLOT(val, Matrix_xSym)), dims, INTEGER(ALLOC_SLOT(val, Matrix_permSym, INTSXP, npiv)), &info); if (info < 0) error(_("Lapack routine %s returned error code %d"), "dgetrf", info); else if (info > 0 && warn_sing) warning(_("Exact singularity detected during LU decomposition: %s, i=%d."), "U[i,i]=0", info); UNPROTECT(1); return set_factors(x, val, "LU"); } // FIXME: also allow an interface to LAPACK's dgesvx() which uses LU fact. // and then optionally does "equilibration" (row and column scaling) // maybe also allow low-level interface to dgeEQU() ... SEXP dgeMatrix_LU(SEXP x, SEXP warn_singularity) { return dgeMatrix_LU_(x, asLogical(warn_singularity)); } SEXP dgeMatrix_determinant(SEXP x, SEXP logarithm) { int lg = asLogical(logarithm); int *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)), n = dims[0], sign = 1; double modulus = lg ? 0. : 1; /* initialize; = result for n == 0 */ if (n != dims[1]) error(_("Determinant requires a square matrix")); if (n > 0) { SEXP lu = dgeMatrix_LU_(x, /* do not warn about singular LU: */ FALSE); int i, *jpvt = INTEGER(GET_SLOT(lu, Matrix_permSym)); double *luvals = REAL(GET_SLOT(lu, Matrix_xSym)); for (i = 0; i < n; i++) if (jpvt[i] != (i + 1)) sign = -sign; if (lg) { for (i = 0; i < n; i++) { double dii = luvals[i*(n + 1)]; /* ith diagonal element */ modulus += log(dii < 0 ? -dii : dii); if (dii < 0) sign = -sign; } } else { for (i = 0; i < n; i++) modulus *= luvals[i*(n + 1)]; if (modulus < 0) { modulus = -modulus; sign = -sign; } } } return as_det_obj(modulus, lg, sign); } SEXP dgeMatrix_solve(SEXP a) { /* compute the 1-norm of the matrix, which is needed later for the computation of the reciprocal condition number. */ double aNorm = get_norm(a, "1"); /* the LU decomposition : */ SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dgeMatrix"))), lu = dgeMatrix_LU_(a, TRUE); int *dims = INTEGER(GET_SLOT(lu, Matrix_DimSym)), *pivot = INTEGER(GET_SLOT(lu, Matrix_permSym)); /* prepare variables for the dgetri calls */ double *x, tmp; int info, lwork = -1; if (dims[0] != dims[1]) error(_("Solve requires a square matrix")); slot_dup(val, lu, Matrix_xSym); x = REAL(GET_SLOT(val, Matrix_xSym)); slot_dup(val, lu, Matrix_DimSym); if(dims[0]) /* the dimension is not zero */ { /* is the matrix is *computationally* singular ? */ double rcond; F77_CALL(dgecon)("1", dims, x, dims, &aNorm, &rcond, (double *) R_alloc(4*dims[0], sizeof(double)), (int *) R_alloc(dims[0], sizeof(int)), &info); if (info) error(_("error [%d] from Lapack 'dgecon()'"), info); if(rcond < DOUBLE_EPS) error(_("Lapack dgecon(): system computationally singular, reciprocal condition number = %g"), rcond); /* only now try the inversion and check if the matrix is *exactly* singular: */ F77_CALL(dgetri)(dims, x, dims, pivot, &tmp, &lwork, &info); lwork = (int) tmp; F77_CALL(dgetri)(dims, x, dims, pivot, (double *) R_alloc((size_t) lwork, sizeof(double)), &lwork, &info); if (info) error(_("Lapack routine dgetri: system is exactly singular")); } UNPROTECT(1); return val; } SEXP dgeMatrix_matrix_solve(SEXP a, SEXP b) { SEXP val = PROTECT(dup_mMatrix_as_dgeMatrix(b)), lu = PROTECT(dgeMatrix_LU_(a, TRUE)); int *adims = INTEGER(GET_SLOT(lu, Matrix_DimSym)), *bdims = INTEGER(GET_SLOT(val, Matrix_DimSym)); int info, n = bdims[0], nrhs = bdims[1]; if (*adims != *bdims || bdims[1] < 1 || *adims < 1 || *adims != adims[1]) error(_("Dimensions of system to be solved are inconsistent")); F77_CALL(dgetrs)("N", &n, &nrhs, REAL(GET_SLOT(lu, Matrix_xSym)), &n, INTEGER(GET_SLOT(lu, Matrix_permSym)), REAL(GET_SLOT(val, Matrix_xSym)), &n, &info); if (info) error(_("Lapack routine dgetrs: system is exactly singular")); UNPROTECT(2); return val; } // right = TRUE: %*% is called as *(y, x, right=TRUE) SEXP dgeMatrix_matrix_mm(SEXP a, SEXP bP, SEXP right) { SEXP b = PROTECT(mMatrix_as_dgeMatrix(bP)), val= PROTECT(NEW_OBJECT(MAKE_CLASS("dgeMatrix"))), dn = PROTECT(allocVector(VECSXP, 2)); int *adims = INTEGER(GET_SLOT(a, Matrix_DimSym)), *bdims = INTEGER(GET_SLOT(b, Matrix_DimSym)), *cdims = INTEGER(ALLOC_SLOT(val, Matrix_DimSym, INTSXP, 2)); double one = 1., zero = 0.; if (asLogical(right)) { // b %*% a int m = bdims[0], n = adims[1], k = bdims[1]; if (adims[0] != k) error(_("Matrices are not conformable for multiplication")); cdims[0] = m; cdims[1] = n; if (m < 1 || n < 1 || k < 1) { /* error(_("Matrices with zero extents cannot be multiplied")); */ ALLOC_SLOT(val, Matrix_xSym, REALSXP, m * n); } else { F77_CALL(dgemm) ("N", "N", &m, &n, &k, &one, REAL(GET_SLOT(b, Matrix_xSym)), &m, REAL(GET_SLOT(a, Matrix_xSym)), &k, &zero, REAL(ALLOC_SLOT(val, Matrix_xSym, REALSXP, m * n)), &m); SET_VECTOR_ELT(dn, 0, duplicate(VECTOR_ELT(GET_SLOT(b, Matrix_DimNamesSym), 0))); SET_VECTOR_ELT(dn, 1, duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), 1))); } } else { // a %*% b int m = adims[0], n = bdims[1], k = adims[1]; if (bdims[0] != k) error(_("Matrices are not conformable for multiplication")); cdims[0] = m; cdims[1] = n; if (m < 1 || n < 1 || k < 1) { /* error(_("Matrices with zero extents cannot be multiplied")); */ ALLOC_SLOT(val, Matrix_xSym, REALSXP, m * n); } else { F77_CALL(dgemm) ("N", "N", &m, &n, &k, &one, REAL(GET_SLOT(a, Matrix_xSym)), &m, REAL(GET_SLOT(b, Matrix_xSym)), &k, &zero, REAL(ALLOC_SLOT(val, Matrix_xSym, REALSXP, m * n)), &m); SET_VECTOR_ELT(dn, 0, duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), 0))); SET_VECTOR_ELT(dn, 1, duplicate(VECTOR_ELT(GET_SLOT(b, Matrix_DimNamesSym), 1))); } } /* establish dimnames */ SET_SLOT(val, Matrix_DimNamesSym, dn); UNPROTECT(3); return val; } SEXP dgeMatrix_svd(SEXP x, SEXP nnu, SEXP nnv) { int /* nu = asInteger(nnu), nv = asInteger(nnv), */ *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)); double *xx = REAL(GET_SLOT(x, Matrix_xSym)); SEXP val = PROTECT(allocVector(VECSXP, 3)); if (dims[0] && dims[1]) { int m = dims[0], n = dims[1], mm = (m < n)?m:n, lwork = -1, info; double tmp, *work; int *iwork = Alloca(8 * mm, int); R_CheckStack(); SET_VECTOR_ELT(val, 0, allocVector(REALSXP, mm)); SET_VECTOR_ELT(val, 1, allocMatrix(REALSXP, m, mm)); SET_VECTOR_ELT(val, 2, allocMatrix(REALSXP, mm, n)); F77_CALL(dgesdd)("S", &m, &n, xx, &m, REAL(VECTOR_ELT(val, 0)), REAL(VECTOR_ELT(val, 1)), &m, REAL(VECTOR_ELT(val, 2)), &mm, &tmp, &lwork, iwork, &info); lwork = (int) tmp; work = Alloca(lwork, double); R_CheckStack(); F77_CALL(dgesdd)("S", &m, &n, xx, &m, REAL(VECTOR_ELT(val, 0)), REAL(VECTOR_ELT(val, 1)), &m, REAL(VECTOR_ELT(val, 2)), &mm, work, &lwork, iwork, &info); } UNPROTECT(1); return val; } const static double padec [] = /* for matrix exponential calculation. */ { 5.0000000000000000e-1, 1.1666666666666667e-1, 1.6666666666666667e-2, 1.6025641025641026e-3, 1.0683760683760684e-4, 4.8562548562548563e-6, 1.3875013875013875e-7, 1.9270852604185938e-9, }; /** * Matrix exponential - based on the _corrected_ code for Octave's expm function. * * @param x real square matrix to exponentiate * * @return matrix exponential of x */ SEXP dgeMatrix_exp(SEXP x) { const double one = 1.0, zero = 0.0; const int i1 = 1; int *Dims = INTEGER(GET_SLOT(x, Matrix_DimSym)); const int n = Dims[1], nsqr = n * n, np1 = n + 1; SEXP val = PROTECT(duplicate(x)); int i, ilo, ilos, ihi, ihis, j, sqpow; int *pivot = Calloc(n, int); double *dpp = Calloc(nsqr, double), /* denominator power Pade' */ *npp = Calloc(nsqr, double), /* numerator power Pade' */ *perm = Calloc(n, double), *scale = Calloc(n, double), *v = REAL(GET_SLOT(val, Matrix_xSym)), *work = Calloc(nsqr, double), inf_norm, m1_j/*= (-1)^j */, trshift; R_CheckStack(); if (n < 1 || Dims[0] != n) error(_("Matrix exponential requires square, non-null matrix")); if(n == 1) { v[0] = exp(v[0]); UNPROTECT(1); return val; } /* Preconditioning 1. Shift diagonal by average diagonal if positive. */ trshift = 0; /* determine average diagonal element */ for (i = 0; i < n; i++) trshift += v[i * np1]; trshift /= n; if (trshift > 0.) { /* shift diagonal by -trshift */ for (i = 0; i < n; i++) v[i * np1] -= trshift; } /* Preconditioning 2. Balancing with dgebal. */ F77_CALL(dgebal)("P", &n, v, &n, &ilo, &ihi, perm, &j); if (j) error(_("dgeMatrix_exp: LAPACK routine dgebal returned %d"), j); F77_CALL(dgebal)("S", &n, v, &n, &ilos, &ihis, scale, &j); if (j) error(_("dgeMatrix_exp: LAPACK routine dgebal returned %d"), j); /* Preconditioning 3. Scaling according to infinity norm */ inf_norm = F77_CALL(dlange)("I", &n, &n, v, &n, work); sqpow = (inf_norm > 0) ? (int) (1 + log(inf_norm)/log(2.)) : 0; if (sqpow < 0) sqpow = 0; if (sqpow > 0) { double scale_factor = 1.0; for (i = 0; i < sqpow; i++) scale_factor *= 2.; for (i = 0; i < nsqr; i++) v[i] /= scale_factor; } /* Pade' approximation. Powers v^8, v^7, ..., v^1 */ AZERO(npp, nsqr); AZERO(dpp, nsqr); m1_j = -1; for (j = 7; j >=0; j--) { double mult = padec[j]; /* npp = m * npp + padec[j] *m */ F77_CALL(dgemm)("N", "N", &n, &n, &n, &one, v, &n, npp, &n, &zero, work, &n); for (i = 0; i < nsqr; i++) npp[i] = work[i] + mult * v[i]; /* dpp = m * dpp + (m1_j * padec[j]) * m */ mult *= m1_j; F77_CALL(dgemm)("N", "N", &n, &n, &n, &one, v, &n, dpp, &n, &zero, work, &n); for (i = 0; i < nsqr; i++) dpp[i] = work[i] + mult * v[i]; m1_j *= -1; } /* Zero power */ for (i = 0; i < nsqr; i++) dpp[i] *= -1.; for (j = 0; j < n; j++) { npp[j * np1] += 1.; dpp[j * np1] += 1.; } /* Pade' approximation is solve(dpp, npp) */ F77_CALL(dgetrf)(&n, &n, dpp, &n, pivot, &j); if (j) error(_("dgeMatrix_exp: dgetrf returned error code %d"), j); F77_CALL(dgetrs)("N", &n, &n, dpp, &n, pivot, npp, &n, &j); if (j) error(_("dgeMatrix_exp: dgetrs returned error code %d"), j); Memcpy(v, npp, nsqr); /* Now undo all of the preconditioning */ /* Preconditioning 3: square the result for every power of 2 */ while (sqpow--) { F77_CALL(dgemm)("N", "N", &n, &n, &n, &one, v, &n, v, &n, &zero, work, &n); Memcpy(v, work, nsqr); } /* Preconditioning 2: apply inverse scaling */ for (j = 0; j < n; j++) for (i = 0; i < n; i++) v[i + j * n] *= scale[i]/scale[j]; /* 2 b) Inverse permutation (if not the identity permutation) */ if (ilo != 1 || ihi != n) { /* Martin Maechler's code */ #define SWAP_ROW(I,J) F77_CALL(dswap)(&n, &v[(I)], &n, &v[(J)], &n) #define SWAP_COL(I,J) F77_CALL(dswap)(&n, &v[(I)*n], &i1, &v[(J)*n], &i1) #define RE_PERMUTE(I) \ int p_I = (int) (perm[I]) - 1; \ SWAP_COL(I, p_I); \ SWAP_ROW(I, p_I) /* reversion of "leading permutations" : in reverse order */ for (i = (ilo - 1) - 1; i >= 0; i--) { RE_PERMUTE(i); } /* reversion of "trailing permutations" : applied in forward order */ for (i = (ihi + 1) - 1; i < n; i++) { RE_PERMUTE(i); } } /* Preconditioning 1: Trace normalization */ if (trshift > 0.) { double mult = exp(trshift); for (i = 0; i < nsqr; i++) v[i] *= mult; } /* Clean up */ Free(work); Free(scale); Free(perm); Free(npp); Free(dpp); Free(pivot); UNPROTECT(1); return val; } SEXP dgeMatrix_Schur(SEXP x, SEXP vectors, SEXP isDGE) { // 'x' is either a traditional matrix or a dgeMatrix, as indicated by isDGE. int *dims, n, vecs = asLogical(vectors), is_dge = asLogical(isDGE), info, izero = 0, lwork = -1, nprot = 1; if(is_dge) { dims = INTEGER(GET_SLOT(x, Matrix_DimSym)); } else { // traditional matrix dims = INTEGER(getAttrib(x, R_DimSymbol)); if(!isReal(x)) { // may not be "numeric" .. x = PROTECT(coerceVector(x, REALSXP)); // -> maybe error nprot++; } } double *work, tmp; const char *nms[] = {"WR", "WI", "T", "Z", ""}; SEXP val = PROTECT(Rf_mkNamed(VECSXP, nms)); n = dims[0]; if (n != dims[1] || n < 1) error(_("dgeMatrix_Schur: argument x must be a non-null square matrix")); SET_VECTOR_ELT(val, 0, allocVector(REALSXP, n)); SET_VECTOR_ELT(val, 1, allocVector(REALSXP, n)); SET_VECTOR_ELT(val, 2, allocMatrix(REALSXP, n, n)); Memcpy(REAL(VECTOR_ELT(val, 2)), REAL(is_dge ? GET_SLOT(x, Matrix_xSym) : x), n * n); SET_VECTOR_ELT(val, 3, allocMatrix(REALSXP, vecs ? n : 0, vecs ? n : 0)); F77_CALL(dgees)(vecs ? "V" : "N", "N", NULL, dims, (double *) NULL, dims, &izero, (double *) NULL, (double *) NULL, (double *) NULL, dims, &tmp, &lwork, (int *) NULL, &info); if (info) error(_("dgeMatrix_Schur: first call to dgees failed")); lwork = (int) tmp; work = Alloca(lwork, double); R_CheckStack(); F77_CALL(dgees)(vecs ? "V" : "N", "N", NULL, dims, REAL(VECTOR_ELT(val, 2)), dims, &izero, REAL(VECTOR_ELT(val, 0)), REAL(VECTOR_ELT(val, 1)), REAL(VECTOR_ELT(val, 3)), dims, work, &lwork, (int *) NULL, &info); if (info) error(_("dgeMatrix_Schur: dgees returned code %d"), info); UNPROTECT(nprot); return val; } // dgeMatrix_Schur SEXP dgeMatrix_colsums(SEXP x, SEXP naRmP, SEXP cols, SEXP mean) { int keepNA = !asLogical(naRmP); int doMean = asLogical(mean); int useCols = asLogical(cols); int *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)); int i, j, m = dims[0], n = dims[1]; SEXP ans = PROTECT(allocVector(REALSXP, (useCols) ? n : m)); double *aa = REAL(ans), *xx = REAL(GET_SLOT(x, Matrix_xSym)); if (useCols) { /* col(Sums|Means) : */ int cnt = m; for (j = 0; j < n; j++) { double *rx = xx + m * j; aa[j] = 0; if (keepNA) for (i = 0; i < m; i++) aa[j] += rx[i]; else { cnt = 0; for (i = 0; i < m; i++) if (!ISNAN(rx[i])) {cnt++; aa[j] += rx[i];} } if (doMean) { if (cnt > 0) aa[j] /= cnt; else aa[j] = NA_REAL; } } } else { /* row(Sums|Means) : */ double *Count = ((!keepNA) && doMean) ? Alloca(m, double) : (double*)NULL ; R_CheckStack(); for (i = 0; i < m; i++) aa[i] = 0.0; for (j = 0; j < n; j++) { if (keepNA) for (i = 0; i < m; i++) aa[i] += xx[i + j * m]; else for (i = 0; i < m; i++) { double el = xx[i + j * m]; if (!ISNAN(el)) { aa[i] += el; if (doMean) Count[i]++; } } } if (doMean) { if (keepNA) for (i = 0; i < m; i++) aa[i] /= n; else for (i = 0; i < m; i++) aa[i] = (Count[i]>0)? aa[i]/Count[i]: NA_REAL; } } UNPROTECT(1); return ans; } Matrix/src/t_Matrix_rle.c0000644000175100001440000000467712271765436015153 0ustar hornikusers/*------ Definition of a template for Matrix_rle_[di](...) : * * -------- ~~~~~~~~~~~~~~~~~~~~~~ * i.e., included several times from ./abIndex.c * ~~~~~~~~~~~ */ /* for all cases with an 'x' slot -- i.e. almost all cases ; * just redefine this in the other cases: */ #ifdef _rle_d_ # define Matrix_RLE_ Matrix_rle_d # define Type_x_ double # define STYP_x_ REAL # define SXP_ans REALSXP #elif defined _rle_i_ # define Matrix_RLE_ Matrix_rle_i # define Type_x_ int # define STYP_x_ INTEGER # define SXP_ans INTSXP #else # error "invalid _rle_ macro logic" #endif /** * RLE (Run Length Encoding) -- only when it's worth * * @param x_ R vector which can be coerced to "double" / "integer" * @param force_ R logical indicating if the result must be "RLE" even when inefficient * * @return NULL or a valid R object of class "rle" */ SEXP Matrix_RLE_(SEXP x_, SEXP force_) { int n = LENGTH(PROTECT(x_ = coerceVector(x_, SXP_ans))); Rboolean no_force = !asLogical(force_); if (no_force && n < 3) { UNPROTECT(1); return R_NilValue; } else { register Type_x_ lv; register int ln, i, c = 0; int n2 = (no_force) ? n / 3 : n; /* upper bound: ==> max RAM requirement 2 x n2, (= 2/3 n); * using 2 instead of 3 would need 50% more time, have max * RAM requirement 2.5x for savings of any size */ Type_x_ *x = STYP_x_(x_), *val; int *len; const char *res_nms[] = {"lengths", "values", ""}; SEXP ans; if(n > 0) { /* needed for force=TRUE */ len = Calloc(n2, int); val = Calloc(n2, Type_x_); lv = x[0]; ln = 1; for(i = 1; i < n; i++) { if (x[i] == lv) { ln++; } else { val[c] = lv; len[c] = ln; c++; if (no_force && c == n2) { /* reached the "efficiency bound" */ Free(len); Free(val); UNPROTECT(1); return R_NilValue; } lv = x[i]; ln = 1; } } val[c] = lv; len[c] = ln; c++; } ans = PROTECT(Rf_mkNamed(VECSXP, res_nms)); SET_VECTOR_ELT(ans, 0, allocVector(INTSXP, c)); /* lengths */ SET_VECTOR_ELT(ans, 1, allocVector(SXP_ans, c)); /* values */ if(n > 0) { Memcpy(INTEGER(VECTOR_ELT(ans, 0)), len, c); Memcpy(STYP_x_(VECTOR_ELT(ans, 1)), val, c); } setAttrib(ans, R_ClassSymbol, mkString("rle")); if(n > 0) { Free(len); Free(val); } UNPROTECT(2); return ans; } } /* Matrix_RLE_() template */ #undef Matrix_RLE_ #undef Type_x_ #undef STYP_x_ #undef SXP_ans Matrix/src/dense.c0000644000175100001440000004026012271765436013604 0ustar hornikusers#include "dense.h" #include "Mutils.h" #include "chm_common.h" /** * Perform a left cyclic shift of columns j to k in the upper triangular * matrix x, then restore it to upper triangular form with Givens rotations. * The algorithm is based on the Fortran routine DCHEX from Linpack. * * The lower triangle of x is not modified. * * @param x Matrix stored in column-major order * @param ldx leading dimension of x * @param j column number (0-based) that will be shifted to position k * @param k last column number (0-based) to be shifted * @param cosines cosines of the Givens rotations * @param sines sines of the Givens rotations * * @return 0 for success */ static int left_cyclic(double x[], int ldx, int j, int k, double cosines[], double sines[]) { double *lastcol; int i, jj; if (j >= k) error(_("incorrect left cyclic shift, j (%d) >= k (%d)"), j, k); if (j < 0) error(_("incorrect left cyclic shift, j (%d) < 0"), j, k); if (ldx < k) error(_("incorrect left cyclic shift, k (%d) > ldx (%d)"), k, ldx); lastcol = (double*) R_alloc(k+1, sizeof(double)); /* keep a copy of column j */ for(i = 0; i <= j; i++) lastcol[i] = x[i + j*ldx]; /* For safety, zero the rest */ for(i = j+1; i <= k; i++) lastcol[i] = 0.; for(jj = j+1; jj <= k; jj++) { /* columns to be shifted */ int diagind = jj*(ldx+1), ind = (jj-j) - 1; double tmp = x[diagind], cc, ss; /* Calculate the Givens rotation. */ /* This modified the super-diagonal element */ F77_CALL(drotg)(x + diagind-1, &tmp, cosines + ind, sines + ind); cc = cosines[ind]; ss = sines[ind]; /* Copy column jj+1 to column jj. */ for(i = 0; i < jj; i++) x[i + (jj-1)*ldx] = x[i+jj*ldx]; /* Apply rotation to columns up to k */ for(i = jj; i < k; i++) { tmp = cc*x[(jj-1)+i*ldx] + ss*x[jj+i*ldx]; x[jj+i*ldx] = cc*x[jj+i*ldx] - ss*x[(jj-1)+i*ldx]; x[(jj-1)+i*ldx] = tmp; } /* Apply rotation to lastcol */ lastcol[jj] = -ss*lastcol[jj-1]; lastcol[jj-1] *= cc; } /* Copy lastcol to column k */ for(i = 0; i <= k; i++) x[i+k*ldx] = lastcol[i]; return 0; } static SEXP getGivens(double x[], int ldx, int jmin, int rank) { int shiftlen = (rank - jmin) - 1; SEXP ans = PROTECT(allocVector(VECSXP, 4)), nms, cosines, sines; SET_VECTOR_ELT(ans, 0, ScalarInteger(jmin)); SET_VECTOR_ELT(ans, 1, ScalarInteger(rank)); SET_VECTOR_ELT(ans, 2, cosines = allocVector(REALSXP, shiftlen)); SET_VECTOR_ELT(ans, 3, sines = allocVector(REALSXP, shiftlen)); setAttrib(ans, R_NamesSymbol, nms = allocVector(STRSXP, 4)); SET_STRING_ELT(nms, 0, mkChar("jmin")); SET_STRING_ELT(nms, 1, mkChar("rank")); SET_STRING_ELT(nms, 2, mkChar("cosines")); SET_STRING_ELT(nms, 3, mkChar("sines")); if (left_cyclic(x, ldx, jmin, rank - 1, REAL(cosines), REAL(sines))) error(_("Unknown error in getGivens")); UNPROTECT(1); return ans; } SEXP checkGivens(SEXP X, SEXP jmin, SEXP rank) { SEXP ans = PROTECT(allocVector(VECSXP, 2)), Xcp = PROTECT(duplicate(X)); int *Xdims; if (!(isReal(X) & isMatrix(X))) error(_("X must be a numeric (double precision) matrix")); Xdims = INTEGER(coerceVector(getAttrib(X, R_DimSymbol), INTSXP)); SET_VECTOR_ELT(ans, 1, getGivens(REAL(Xcp), Xdims[0], asInteger(jmin), asInteger(rank))); SET_VECTOR_ELT(ans, 0, Xcp); UNPROTECT(2); return ans; } SEXP lsq_dense_Chol(SEXP X, SEXP y) { SEXP ans; int info, n, p, k, *Xdims, *ydims; double *xpx, d_one = 1., d_zero = 0.; if (!(isReal(X) & isMatrix(X))) error(_("X must be a numeric (double precision) matrix")); Xdims = INTEGER(coerceVector(getAttrib(X, R_DimSymbol), INTSXP)); n = Xdims[0]; p = Xdims[1]; if (!(isReal(y) & isMatrix(y))) error(_("y must be a numeric (double precision) matrix")); ydims = INTEGER(coerceVector(getAttrib(y, R_DimSymbol), INTSXP)); if (ydims[0] != n) error(_( "number of rows in y (%d) does not match number of rows in X (%d)"), ydims[0], n); k = ydims[1]; if (k < 1 || p < 1) return allocMatrix(REALSXP, p, k); ans = PROTECT(allocMatrix(REALSXP, p, k)); F77_CALL(dgemm)("T", "N", &p, &k, &n, &d_one, REAL(X), &n, REAL(y), &n, &d_zero, REAL(ans), &p); xpx = (double *) R_alloc(p * p, sizeof(double)); F77_CALL(dsyrk)("U", "T", &p, &n, &d_one, REAL(X), &n, &d_zero, xpx, &p); F77_CALL(dposv)("U", &p, &k, xpx, &p, REAL(ans), &p, &info); if (info) error(_("Lapack routine dposv returned error code %d"), info); UNPROTECT(1); return ans; } SEXP lsq_dense_QR(SEXP X, SEXP y) { SEXP ans; int info, n, p, k, *Xdims, *ydims, lwork; double *work, tmp, *xvals; if (!(isReal(X) & isMatrix(X))) error(_("X must be a numeric (double precision) matrix")); Xdims = INTEGER(coerceVector(getAttrib(X, R_DimSymbol), INTSXP)); n = Xdims[0]; p = Xdims[1]; if (!(isReal(y) & isMatrix(y))) error(_("y must be a numeric (double precision) matrix")); ydims = INTEGER(coerceVector(getAttrib(y, R_DimSymbol), INTSXP)); if (ydims[0] != n) error(_( "number of rows in y (%d) does not match number of rows in X (%d)"), ydims[0], n); k = ydims[1]; if (k < 1 || p < 1) return allocMatrix(REALSXP, p, k); xvals = (double *) R_alloc(n * p, sizeof(double)); Memcpy(xvals, REAL(X), n * p); ans = PROTECT(duplicate(y)); lwork = -1; F77_CALL(dgels)("N", &n, &p, &k, xvals, &n, REAL(ans), &n, &tmp, &lwork, &info); if (info) error(_("First call to Lapack routine dgels returned error code %d"), info); lwork = (int) tmp; work = (double *) R_alloc(lwork, sizeof(double)); F77_CALL(dgels)("N", &n, &p, &k, xvals, &n, REAL(ans), &n, work, &lwork, &info); if (info) error(_("Second call to Lapack routine dgels returned error code %d"), info); UNPROTECT(1); return ans; } SEXP lapack_qr(SEXP Xin, SEXP tl) { SEXP ans, Givens, Gcpy, nms, pivot, qraux, X; int i, n, nGivens = 0, p, trsz, *Xdims, rank; double rcond = 0., tol = asReal(tl), *work; if (!(isReal(Xin) & isMatrix(Xin))) error(_("X must be a real (numeric) matrix")); if (tol < 0.) error(_("tol, given as %g, must be non-negative"), tol); if (tol > 1.) error(_("tol, given as %g, must be <= 1"), tol); ans = PROTECT(allocVector(VECSXP,5)); SET_VECTOR_ELT(ans, 0, X = duplicate(Xin)); Xdims = INTEGER(coerceVector(getAttrib(X, R_DimSymbol), INTSXP)); n = Xdims[0]; p = Xdims[1]; SET_VECTOR_ELT(ans, 2, qraux = allocVector(REALSXP, (n < p) ? n : p)); SET_VECTOR_ELT(ans, 3, pivot = allocVector(INTSXP, p)); for (i = 0; i < p; i++) INTEGER(pivot)[i] = i + 1; trsz = (n < p) ? n : p; /* size of triangular part of decomposition */ rank = trsz; Givens = PROTECT(allocVector(VECSXP, rank - 1)); setAttrib(ans, R_NamesSymbol, nms = allocVector(STRSXP, 5)); SET_STRING_ELT(nms, 0, mkChar("qr")); SET_STRING_ELT(nms, 1, mkChar("rank")); SET_STRING_ELT(nms, 2, mkChar("qraux")); SET_STRING_ELT(nms, 3, mkChar("pivot")); SET_STRING_ELT(nms, 4, mkChar("Givens")); if (n > 0 && p > 0) { int info, *iwork, lwork; double *xpt = REAL(X), tmp; lwork = -1; F77_CALL(dgeqrf)(&n, &p, xpt, &n, REAL(qraux), &tmp, &lwork, &info); if (info) error(_("First call to dgeqrf returned error code %d"), info); lwork = (int) tmp; work = (double *) R_alloc((lwork < 3*trsz) ? 3*trsz : lwork, sizeof(double)); F77_CALL(dgeqrf)(&n, &p, xpt, &n, REAL(qraux), work, &lwork, &info); if (info) error(_("Second call to dgeqrf returned error code %d"), info); iwork = (int *) R_alloc(trsz, sizeof(int)); F77_CALL(dtrcon)("1", "U", "N", &rank, xpt, &n, &rcond, work, iwork, &info); if (info) error(_("Lapack routine dtrcon returned error code %d"), info); while (rcond < tol) { /* check diagonal elements */ double minabs = (xpt[0] < 0.) ? -xpt[0]: xpt[0]; int jmin = 0; for (i = 1; i < rank; i++) { double el = xpt[i*(n+1)]; el = (el < 0.) ? -el: el; if (el < minabs) { jmin = i; minabs = el; } } if (jmin < (rank - 1)) { SET_VECTOR_ELT(Givens, nGivens, getGivens(xpt, n, jmin, rank)); nGivens++; } rank--; F77_CALL(dtrcon)("1", "U", "N", &rank, xpt, &n, &rcond, work, iwork, &info); if (info) error(_("Lapack routine dtrcon returned error code %d"), info); } } SET_VECTOR_ELT(ans, 4, Gcpy = allocVector(VECSXP, nGivens)); for (i = 0; i < nGivens; i++) SET_VECTOR_ELT(Gcpy, i, VECTOR_ELT(Givens, i)); SET_VECTOR_ELT(ans, 1, ScalarInteger(rank)); setAttrib(ans, install("useLAPACK"), ScalarLogical(1)); setAttrib(ans, install("rcond"), ScalarReal(rcond)); UNPROTECT(2); return ans; } SEXP dense_to_Csparse(SEXP x) { CHM_DN chxd = AS_CHM_DN(PROTECT(mMatrix_as_geMatrix(x))); /* cholmod_dense_to_sparse() in CHOLMOD/Core/ below does only work for "REAL" 'xtypes', i.e. *not* for "nMatrix". ===> need "_x" in above call. Also it cannot keep symmetric / triangular, hence the as_geMatrix() above. Note that this is already a *waste* for symmetric matrices; However, we could conceivably use an enhanced cholmod_dense_to_sparse(), with an extra boolean argument for symmetry. */ CHM_SP chxs = cholmod_dense_to_sparse(chxd, 1, &c); int Rkind = (chxd->xtype == CHOLMOD_REAL) ? Real_KIND2(x) : 0; /* Note: when 'x' was integer Matrix, Real_KIND(x) = -1, but *_KIND2(.) = 0 */ R_CheckStack(); UNPROTECT(1); /* chm_sparse_to_SEXP() *could* deal with symmetric * if chxs had such an stype; and we should be able to use uplo below */ return chm_sparse_to_SEXP(chxs, 1, 0/*TODO: uplo_P(x) if x has an uplo slot*/, Rkind, "", isMatrix(x) ? getAttrib(x, R_DimNamesSymbol) : GET_SLOT(x, Matrix_DimNamesSym)); } SEXP dense_band(SEXP x, SEXP k1P, SEXP k2P) /* Always returns a full matrix with entries outside the band zeroed * Class of the value can be [dln]trMatrix or [dln]geMatrix */ { int k1 = asInteger(k1P), k2 = asInteger(k2P); if (k1 > k2) { error(_("Lower band %d > upper band %d"), k1, k2); return R_NilValue; /* -Wall */ } else { SEXP ans = PROTECT(dup_mMatrix_as_geMatrix(x)); int *adims = INTEGER(GET_SLOT(ans, Matrix_DimSym)), j, m = adims[0], n = adims[1], sqr = (adims[0] == adims[1]), tru = (k1 >= 0), trl = (k2 <= 0); const char *cl = class_P(ans); enum dense_enum { ddense, ldense, ndense } M_type = ( (cl[0] == 'd') ? ddense : ((cl[0] == 'l') ? ldense : ndense)); #define SET_ZERO_OUTSIDE \ for (j = 0; j < n; j++) { \ int i, i1 = j - k2, i2 = j + 1 - k1; \ if(i1 > m) i1 = m; \ if(i2 < 0) i2 = 0; \ for (i = 0; i < i1; i++) xx[i + j * m] = 0; \ for (i = i2; i < m; i++) xx[i + j * m] = 0; \ } if(M_type == ddense) { double *xx = REAL(GET_SLOT(ans, Matrix_xSym)); SET_ZERO_OUTSIDE } else { /* (M_type == ldense || M_type == ndense) */ int *xx = LOGICAL(GET_SLOT(ans, Matrix_xSym)); SET_ZERO_OUTSIDE } if (!sqr || (!tru && !trl)) { /* return the *geMatrix */ UNPROTECT(1); return ans; } else { /* Copy ans to a *trMatrix object (must be square) */ SEXP aa= PROTECT(NEW_OBJECT(MAKE_CLASS(M_type == ddense? "dtrMatrix": (M_type== ldense? "ltrMatrix" : "ntrMatrix")))); /* Because slots of ans are freshly allocated and ans will not be * used, we use the slots themselves and don't duplicate */ SET_SLOT(aa, Matrix_xSym, GET_SLOT(ans, Matrix_xSym)); SET_SLOT(aa, Matrix_DimSym, GET_SLOT(ans, Matrix_DimSym)); SET_SLOT(aa, Matrix_DimNamesSym,GET_SLOT(ans, Matrix_DimNamesSym)); SET_SLOT(aa, Matrix_diagSym, mkString("N")); SET_SLOT(aa, Matrix_uploSym, mkString(tru ? "U" : "L")); UNPROTECT(2); return aa; } } } SEXP dense_to_symmetric(SEXP x, SEXP uplo, SEXP symm_test) /* Class of result will be [dln]syMatrix */ { int symm_tst = asLogical(symm_test); SEXP dx = PROTECT(dup_mMatrix_as_geMatrix(x)); SEXP ans, dns; const char *cl = class_P(dx); /* same as in ..._geMatrix() above:*/ enum dense_enum { ddense, ldense, ndense } M_type = ( (cl[0] == 'd') ? ddense : ((cl[0] == 'l') ? ldense : ndense)); int *adims = INTEGER(GET_SLOT(dx, Matrix_DimSym)), n = adims[0]; if(n != adims[1]) { UNPROTECT(1); error(_("ddense_to_symmetric(): matrix is not square!")); return R_NilValue; /* -Wall */ } if(symm_tst) { int i,j; #define CHECK_SYMMETRIC \ for (j = 0; j < n; j++) \ for (i = 0; i < j; i++) \ if(xx[j * n + i] != xx[i * n + j]) { \ UNPROTECT(1); \ error(_("matrix is not symmetric [%d,%d]"), i+1, j+1); \ return R_NilValue; /* -Wall */ \ } if(M_type == ddense) { double *xx = REAL(GET_SLOT(dx, Matrix_xSym)); CHECK_SYMMETRIC } else { /* (M_type == ldense || M_type == ndense) */ int *xx = LOGICAL(GET_SLOT(dx, Matrix_xSym)); CHECK_SYMMETRIC } } dns = GET_SLOT(dx, Matrix_DimNamesSym); if(!equal_string_vectors(VECTOR_ELT(dns,0), VECTOR_ELT(dns,1))) { /* need _symmetric_ dimnames */ if(*CHAR(asChar(uplo)) == 'U') SET_VECTOR_ELT(dns,0, VECTOR_ELT(dns,1)); else SET_VECTOR_ELT(dns,1, VECTOR_ELT(dns,0)); } /* Copy dx to ans; * Because slots of dx are freshly allocated and dx will not be * used, we use the slots themselves and don't duplicate */ ans = PROTECT(NEW_OBJECT(MAKE_CLASS( M_type == ddense ? "dsyMatrix" : (M_type == ldense ? "lsyMatrix" : "nsyMatrix")))); SET_SLOT(ans, Matrix_xSym, GET_SLOT(dx, Matrix_xSym)); SET_SLOT(ans, Matrix_DimSym, GET_SLOT(dx, Matrix_DimSym)); SET_SLOT(ans, Matrix_DimNamesSym, dns); SET_SLOT(ans, Matrix_uploSym, ScalarString(asChar(uplo))); UNPROTECT(2); return ans; } SEXP ddense_symmpart(SEXP x) /* Class of the value will be dsyMatrix */ { SEXP dx = PROTECT(dup_mMatrix_as_dgeMatrix(x)); int *adims = INTEGER(GET_SLOT(dx, Matrix_DimSym)), n = adims[0]; if(n != adims[1]) { UNPROTECT(1); error(_("matrix is not square! (symmetric part)")); return R_NilValue; /* -Wall */ } else { SEXP ans = PROTECT(NEW_OBJECT(MAKE_CLASS("dsyMatrix"))), dns; double *xx = REAL(GET_SLOT(dx, Matrix_xSym)); int i,j; /* only need to assign the *upper* triangle (uplo = "U"); * noting that diagonal remains unchanged */ for (j = 0; j < n; j++) { for (i = 0; i < j; i++) { xx[j * n + i] = (xx[j * n + i] + xx[i * n + j]) / 2.; } } dns = GET_SLOT(dx, Matrix_DimNamesSym); if(!equal_string_vectors(VECTOR_ELT(dns,0), VECTOR_ELT(dns,1))) { /* need _symmetric_ dimnames */ SET_VECTOR_ELT(dns,0, VECTOR_ELT(dns,1));/* ==> uplo = "U" */ } /* Copy dx to ans; * Because slots of dx are freshly allocated and dx will not be * used, we use the slots themselves and don't duplicate */ SET_SLOT(ans, Matrix_xSym, GET_SLOT(dx, Matrix_xSym)); SET_SLOT(ans, Matrix_DimSym, GET_SLOT(dx, Matrix_DimSym)); SET_SLOT(ans, Matrix_DimNamesSym, dns); SET_SLOT(ans, Matrix_uploSym, mkString("U")); UNPROTECT(2); return ans; } } SEXP ddense_skewpart(SEXP x) /* Class of the value will be dgeMatrix */ { SEXP dx = PROTECT(dup_mMatrix_as_dgeMatrix(x)); int *adims = INTEGER(GET_SLOT(dx, Matrix_DimSym)), n = adims[0]; if(n != adims[1]) { UNPROTECT(1); error(_("matrix is not square! (skew-symmetric part)")); return R_NilValue; /* -Wall */ } else { SEXP ans = PROTECT(NEW_OBJECT(MAKE_CLASS("dgeMatrix"))), dns; double *xx = REAL(GET_SLOT(dx, Matrix_xSym)); int i,j; for (j = 0; j < n; j++) { xx[j * n + j] = 0.; for (i = 0; i < j; i++) { double s = (xx[j * n + i] - xx[i * n + j]) / 2.; xx[j * n + i] = s; xx[i * n + j] = -s; } } dns = GET_SLOT(dx, Matrix_DimNamesSym); if(!equal_string_vectors(VECTOR_ELT(dns,0), VECTOR_ELT(dns,1))) { /* need _symmetric_ dimnames */ SET_VECTOR_ELT(dns,0, VECTOR_ELT(dns,1));/* uplo = "U" */ } /* Copy dx to ans; * Because slots of dx are freshly allocated and dx will not be * used, we use the slots themselves and don't duplicate */ SET_SLOT(ans, Matrix_xSym, GET_SLOT(dx, Matrix_xSym)); SET_SLOT(ans, Matrix_DimSym, GET_SLOT(dx, Matrix_DimSym)); SET_SLOT(ans, Matrix_DimNamesSym, dns); SET_SLOT(ans, Matrix_uploSym, mkString("U")); UNPROTECT(2); return ans; } } Matrix/src/chm_common.c0000644000175100001440000011367712271765436014642 0ustar hornikusers#include "chm_common.h" #include "Mutils.h" Rboolean isValid_Csparse(SEXP x); /* -> Csparse.c */ SEXP get_SuiteSparse_version() { SEXP ans = allocVector(INTSXP, 3); int* version = INTEGER(ans); SuiteSparse_version(version); return ans; } cholmod_common c; cholmod_common cl; SEXP chm_common_env; static SEXP dboundSym, grow0Sym, grow1Sym, grow2Sym, maxrankSym, supernodal_switchSym, supernodalSym, final_asisSym, final_superSym, final_llSym, final_packSym, final_monotonicSym, final_resymbolSym, prefer_zomplexSym, prefer_upperSym, quick_return_if_not_posdefSym, nmethodsSym, m0_ordSym, postorderSym; void CHM_store_common() { SEXP rho = chm_common_env; defineVar(dboundSym, ScalarReal(c.dbound), rho); defineVar(grow0Sym, ScalarReal(c.grow0), rho); defineVar(grow1Sym, ScalarReal(c.grow1), rho); defineVar(grow2Sym, ScalarInteger(c.grow2), rho); defineVar(maxrankSym, ScalarInteger(c.maxrank), rho); defineVar(supernodal_switchSym, ScalarReal(c.supernodal_switch), rho); defineVar(supernodalSym, ScalarInteger(c.supernodal), rho); defineVar(final_asisSym, ScalarLogical(c.final_asis), rho); defineVar(final_superSym, ScalarLogical(c.final_super), rho); defineVar(final_llSym, ScalarLogical(c.final_ll), rho); defineVar(final_packSym, ScalarLogical(c.final_pack), rho); defineVar(final_monotonicSym, ScalarLogical(c.final_monotonic), rho); defineVar(final_resymbolSym, ScalarLogical(c.final_resymbol), rho); defineVar(prefer_zomplexSym, ScalarLogical(c.prefer_zomplex), rho); defineVar(prefer_upperSym, ScalarLogical(c.prefer_upper), rho); defineVar(quick_return_if_not_posdefSym, ScalarLogical(c.quick_return_if_not_posdef), rho); defineVar(nmethodsSym, ScalarInteger(c.nmethods), rho); defineVar(m0_ordSym, ScalarInteger(c.method[0].ordering), rho); defineVar(postorderSym, ScalarLogical(c.postorder), rho); } void CHM_restore_common() { SEXP rho = chm_common_env; c.dbound = asReal(findVarInFrame(rho, dboundSym)); c.grow0 = asReal(findVarInFrame(rho, grow0Sym)); c.grow1 = asReal(findVarInFrame(rho, grow1Sym)); c.grow2 = asInteger(findVarInFrame(rho, grow2Sym)); c.maxrank = asInteger(findVarInFrame(rho, maxrankSym)); c.supernodal_switch = asReal(findVarInFrame(rho, supernodal_switchSym)); c.supernodal = asLogical(findVarInFrame(rho, supernodalSym)); c.final_asis = asLogical(findVarInFrame(rho, final_asisSym)); c.final_super = asLogical(findVarInFrame(rho, final_superSym)); c.final_ll = asLogical(findVarInFrame(rho, final_llSym)); c.final_pack = asLogical(findVarInFrame(rho, final_packSym)); c.final_monotonic = asLogical(findVarInFrame(rho, final_monotonicSym)); c.final_resymbol = asLogical(findVarInFrame(rho, final_resymbolSym)); c.prefer_zomplex = asLogical(findVarInFrame(rho, prefer_zomplexSym)); c.prefer_upper = asLogical(findVarInFrame(rho, prefer_upperSym)); c.quick_return_if_not_posdef = asLogical(findVarInFrame(rho, quick_return_if_not_posdefSym)); c.nmethods = asInteger(findVarInFrame(rho, nmethodsSym)); c.method[0].ordering = asInteger(findVarInFrame(rho, m0_ordSym)); c.postorder = asLogical(findVarInFrame(rho, postorderSym)); } SEXP CHM_set_common_env(SEXP rho) { if (!isEnvironment(rho)) error(_("Argument rho must be an environment")); chm_common_env = rho; dboundSym = install("dbound"); grow0Sym = install("grow0"); grow1Sym = install("grow1"); grow2Sym = install("grow2"); maxrankSym = install("maxrank"); supernodal_switchSym = install("supernodal_switch"); supernodalSym = install("supernodal"); final_asisSym = install("final_asis"); final_superSym = install("final_super"); final_llSym = install("final_ll"); final_packSym = install("final_pack"); final_monotonicSym = install("final_monotonic"); final_resymbolSym = install("final_resymbol"); prefer_zomplexSym = install("final_zomplex"); prefer_upperSym = install("final_upper"); quick_return_if_not_posdefSym = install("quick_return_if_not_posdef"); nmethodsSym = install("nmethods"); m0_ordSym = install("m0.ord"); postorderSym = install("postorder"); CHM_store_common(); return R_NilValue; } static int stype(int ctype, SEXP x) { if ((ctype % 3) == 1) return (*uplo_P(x) == 'U') ? 1 : -1; return 0; } static int xtype(int ctype) { switch(ctype / 3) { case 0: /* "d" */ case 1: /* "l" */ return CHOLMOD_REAL; case 2: /* "n" */ return CHOLMOD_PATTERN; case 3: /* "z" */ return CHOLMOD_COMPLEX; } return -1; } /* coerce a vector to REAL and copy the result to freshly R_alloc'd memory */ static void *RallocedREAL(SEXP x) { SEXP rx = PROTECT(coerceVector(x, REALSXP)); int lx = LENGTH(rx); /* We over-allocate the memory chunk so that it is never NULL. */ /* The CHOLMOD code checks for a NULL pointer even in the length-0 case. */ double *ans = Memcpy((double*)R_alloc(lx + 1, sizeof(double)), REAL(rx), lx); UNPROTECT(1); return (void*)ans; } static void *xpt(int ctype, SEXP x) { switch(ctype / 3) { case 0: /* "d" */ return (void *) REAL(GET_SLOT(x, Matrix_xSym)); case 1: /* "l" */ return RallocedREAL(GET_SLOT(x, Matrix_xSym)); case 2: /* "n" */ return (void *) NULL; case 3: /* "z" */ return (void *) COMPLEX(GET_SLOT(x, Matrix_xSym)); } return (void *) NULL; /* -Wall */ } Rboolean check_sorted_chm(CHM_SP A) { int *Ai = (int*)(A->i), *Ap = (int*)(A->p); int j, p; for (j = 0; j < A->ncol; j++) { int p1 = Ap[j], p2 = Ap[j + 1] - 1; for (p = p1; p < p2; p++) if (Ai[p] >= Ai[p + 1]) return FALSE; } return TRUE; } /** Copy cholmod_sparse, to an R_alloc()ed version of it */ static void chm2Ralloc(CHM_SP dest, CHM_SP src) { int np1, nnz; /* copy all the characteristics of src to dest */ memcpy(dest, src, sizeof(cholmod_sparse)); /* R_alloc the vector storage for dest and copy the contents from src */ np1 = src->ncol + 1; nnz = (int) cholmod_nnz(src, &c); dest->p = (void*) Memcpy((int*)R_alloc(sizeof(int), np1), (int*)(src->p), np1); dest->i = (void*) Memcpy((int*)R_alloc(sizeof(int), nnz), (int*)(src->i), nnz); if(src->xtype) dest->x = (void*) Memcpy((double*)R_alloc(sizeof(double), nnz), (double*)(src->x), nnz); } /** Copy cholmod_triplet to an R_alloc()ed version of it */ static void chTr2Ralloc(CHM_TR dest, CHM_TR src) { int nnz; /* copy all the (non-pointer) characteristics of src to dest */ memcpy(dest, src, sizeof(cholmod_triplet)); /* R_alloc the vector storage for dest and copy the contents from src */ nnz = src->nnz; dest->i = (void*) Memcpy((int*)R_alloc(sizeof(int), nnz), (int*)(src->i), nnz); dest->j = (void*) Memcpy((int*)R_alloc(sizeof(int), nnz), (int*)(src->j), nnz); if(src->xtype) dest->x = (void*) Memcpy((double*)R_alloc(sizeof(double), nnz), (double*)(src->x), nnz); } /** * Populate ans with the pointers from x and modify its scalar * elements accordingly. Note that later changes to the contents of * ans will change the contents of the SEXP. * * In most cases this function is called through the macros * AS_CHM_SP() or AS_CHM_SP__(). It is unusual to call it directly. * * @param ans a CHM_SP pointer * @param x pointer to an object that inherits from CsparseMatrix * @param check_Udiag boolean - should a check for (and consequent * expansion of) a unit diagonal be performed. * @param sort_in_place boolean - if the i and x slots are to be sorted * should they be sorted in place? If the i and x slots are pointers * to an input SEXP they should not be modified. * * @return ans containing pointers to the slots of x, *unless* * check_Udiag and x is unitriangular. */ CHM_SP as_cholmod_sparse(CHM_SP ans, SEXP x, Rboolean check_Udiag, Rboolean sort_in_place) { static const char *valid[] = { MATRIX_VALID_Csparse, ""}; int *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)), ctype = Matrix_check_class_etc(x, valid); SEXP islot = GET_SLOT(x, Matrix_iSym); if (ctype < 0) error(_("invalid class of object to as_cholmod_sparse")); if (!isValid_Csparse(x)) error(_("invalid object passed to as_cholmod_sparse")); memset(ans, 0, sizeof(cholmod_sparse)); /* zero the struct */ ans->itype = CHOLMOD_INT; /* characteristics of the system */ ans->dtype = CHOLMOD_DOUBLE; ans->packed = TRUE; /* slots always present */ ans->i = INTEGER(islot); ans->p = INTEGER(GET_SLOT(x, Matrix_pSym)); /* dimensions and nzmax */ ans->nrow = dims[0]; ans->ncol = dims[1]; /* Allow for over-allocation of the i and x slots. Needed for * sparse X form in lme4. Right now it looks too difficult to * check for the length of the x slot, because of the xpt * utility, but the lengths of x and i should agree. */ ans->nzmax = LENGTH(islot); /* values depending on ctype */ ans->x = xpt(ctype, x); ans->stype = stype(ctype, x); ans->xtype = xtype(ctype); /* are the columns sorted (increasing row numbers) ?*/ ans->sorted = check_sorted_chm(ans); if (!(ans->sorted)) { /* sort columns */ if(sort_in_place) { if (!cholmod_sort(ans, &c)) error(_("in_place cholmod_sort returned an error code")); ans->sorted = 1; } else { CHM_SP tmp = cholmod_copy_sparse(ans, &c); if (!cholmod_sort(tmp, &c)) error(_("cholmod_sort returned an error code")); #ifdef DEBUG_Matrix /* This "triggers" exactly for return values of dtCMatrix_sparse_solve():*/ /* Don't want to translate this: want it report */ Rprintf("Note: as_cholmod_sparse() needed cholmod_sort()ing\n"); #endif chm2Ralloc(ans, tmp); cholmod_free_sparse(&tmp, &c); } } if (check_Udiag && ctype % 3 == 2 // triangular && (*diag_P(x) == 'U')) { /* diagU2N(.) "in place" : */ double one[] = {1, 0}; CHM_SP eye = cholmod_speye(ans->nrow, ans->ncol, ans->xtype, &c); CHM_SP tmp = cholmod_add(ans, eye, one, one, TRUE, TRUE, &c); #ifdef DEBUG_Matrix_verbose /* quite often, e.g. in ../tests/indexing.R */ Rprintf("Note: as_cholmod_sparse() - diagU2N\n", ctype); #endif chm2Ralloc(ans, tmp); cholmod_free_sparse(&tmp, &c); cholmod_free_sparse(&eye, &c); } /* else : * NOTE: if(*diag_P(x) == 'U'), the diagonal is lost (!); * ---- that may be ok, e.g. if we are just converting from/to Tsparse, * but is *not* at all ok, e.g. when used before matrix products */ return ans; } /** * Copy the contents of a to an appropriate CsparseMatrix object and, * optionally, free a or free both a and its the pointers to its contents. * * @param a (cholmod_sparse) matrix to be converted * @param dofree 0 - don't free a; > 0 cholmod_free a; < 0 Free a * @param uploT 0 - not triangular; > 0 upper triangular; < 0 lower * @param Rkind - vector type to store for a->xtype == CHOLMOD_REAL, * 0 - REAL; 1 - LOGICAL * @param diag character string suitable for the diag slot of a * triangular matrix (not accessed if uploT == 0). * @param dn either R_NilValue or an SEXP suitable for the Dimnames slot. * * @return SEXP containing a copy of a */ SEXP chm_sparse_to_SEXP(CHM_SP a, int dofree, int uploT, int Rkind, const char* diag, SEXP dn) { SEXP ans; char *cls = "";/* -Wall */ int *dims, nnz, *ansp, *ansi, *aii = (int*)(a->i), *api = (int*)(a->p), longi = (a->itype) == CHOLMOD_LONG; UF_long *ail = (UF_long*)(a->i), *apl = (UF_long*)(a->p); PROTECT(dn); /* dn is usually UNPROTECTed before the call */ /* ensure a is sorted and packed */ if (!a->sorted || !a->packed) longi ? cholmod_l_sort(a, &cl) : cholmod_sort(a, &c); /* determine the class of the result */ #define DOFREE_MAYBE \ if (dofree > 0) \ longi ? cholmod_l_free_sparse(&a, &cl) : cholmod_free_sparse(&a, &c); \ else if (dofree < 0) Free(a) switch(a->xtype){ case CHOLMOD_PATTERN: cls = uploT ? "ntCMatrix": ((a->stype) ? "nsCMatrix" : "ngCMatrix"); break; case CHOLMOD_REAL: switch(Rkind) { case 0: cls = uploT ? "dtCMatrix": ((a->stype) ? "dsCMatrix" : "dgCMatrix"); break; case 1: cls = uploT ? "ltCMatrix": ((a->stype) ? "lsCMatrix" : "lgCMatrix"); break; default: DOFREE_MAYBE; error(_("chm_sparse_to_SEXP(, *): invalid 'Rkind' (real kind code)")); } break; case CHOLMOD_COMPLEX: cls = uploT ? "ztCMatrix": ((a->stype) ? "zsCMatrix" : "zgCMatrix"); break; default: DOFREE_MAYBE; error(_("unknown xtype in cholmod_sparse object")); } ans = PROTECT(NEW_OBJECT(MAKE_CLASS(cls))); /* allocate and copy common slots */ nnz = longi ? cholmod_l_nnz(a, &cl) : cholmod_nnz(a, &c); dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2)); dims[0] = a->nrow; dims[1] = a->ncol; ansp = INTEGER(ALLOC_SLOT(ans, Matrix_pSym, INTSXP, a->ncol + 1)); ansi = INTEGER(ALLOC_SLOT(ans, Matrix_iSym, INTSXP, nnz)); for (int j = 0; j <= a->ncol; j++) ansp[j] = longi ? (int)(apl[j]) : api[j]; for (int p = 0; p < nnz; p++) ansi[p] = longi ? (int)(ail[p]) : aii[p]; /* copy data slot if present */ if (a->xtype == CHOLMOD_REAL) { int i, *m_x; double *a_x = (double *) a->x; switch(Rkind) { case 0: Memcpy(REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, nnz)), a_x, nnz); break; case 1: m_x = LOGICAL(ALLOC_SLOT(ans, Matrix_xSym, LGLSXP, nnz)); for (i=0; i < nnz; i++) m_x[i] = ISNAN(a_x[i]) ? NA_LOGICAL : (a_x[i] != 0); break; } } else if (a->xtype == CHOLMOD_COMPLEX) { DOFREE_MAYBE; error(_("complex sparse matrix code not yet written")); /* Memcpy(COMPLEX(ALLOC_SLOT(ans, Matrix_xSym, CPLXSXP, nnz)), */ /* (complex *) a->x, nnz); */ } if (uploT) { /* slots for triangularMatrix */ if (a->stype) error(_("Symmetric and triangular both set")); SET_SLOT(ans, Matrix_uploSym, mkString((uploT > 0) ? "U" : "L")); SET_SLOT(ans, Matrix_diagSym, mkString(diag)); } if (a->stype) /* slot for symmetricMatrix */ SET_SLOT(ans, Matrix_uploSym, mkString((a->stype > 0) ? "U" : "L")); DOFREE_MAYBE; if (dn != R_NilValue) SET_SLOT(ans, Matrix_DimNamesSym, duplicate(dn)); UNPROTECT(2); return ans; } #undef DOFREE_MAYBE /** * Populate ans with the pointers from x and modify its scalar * elements accordingly. Note that later changes to the contents of * ans will change the contents of the SEXP. * * In most cases this function is called through the macros * AS_CHM_TR() or AS_CHM_TR__(). It is unusual to call it directly. * * @param ans a CHM_TR pointer * @param x pointer to an object that inherits from TsparseMatrix * @param check_Udiag boolean - should a check for (and consequent * expansion of) a unit diagonal be performed. * * @return ans containing pointers to the slots of x, *unless* * check_Udiag and x is unitriangular. */ CHM_TR as_cholmod_triplet(CHM_TR ans, SEXP x, Rboolean check_Udiag) { static const char *valid[] = { MATRIX_VALID_Tsparse, ""}; int *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)), ctype = Matrix_check_class_etc(x, valid); SEXP islot = GET_SLOT(x, Matrix_iSym); int m = LENGTH(islot); Rboolean do_Udiag = (check_Udiag && ctype % 3 == 2 && (*diag_P(x) == 'U')); if (ctype < 0) error(_("invalid class of object to as_cholmod_triplet")); memset(ans, 0, sizeof(cholmod_triplet)); /* zero the struct */ ans->itype = CHOLMOD_INT; /* characteristics of the system */ ans->dtype = CHOLMOD_DOUBLE; /* nzmax, dimensions, types and slots : */ ans->nnz = ans->nzmax = m; ans->nrow = dims[0]; ans->ncol = dims[1]; ans->stype = stype(ctype, x); ans->xtype = xtype(ctype); ans->i = (void *) INTEGER(islot); ans->j = (void *) INTEGER(GET_SLOT(x, Matrix_jSym)); ans->x = xpt(ctype, x); if(do_Udiag) { /* diagU2N(.) "in place", similarly to Tsparse_diagU2N [./Tsparse.c] (but without new SEXP): */ int k = m + dims[0]; CHM_TR tmp = cholmod_l_copy_triplet(ans, &c); int *a_i, *a_j; if(!cholmod_reallocate_triplet((size_t) k, tmp, &c)) error(_("as_cholmod_triplet(): could not reallocate for internal diagU2N()" )); /* TODO? instead of copy_triplet() & reallocate_triplet() * ---- allocate to correct length + Memcpy() here, as in * Tsparse_diagU2N() & chTr2Ralloc() below */ a_i = tmp->i; a_j = tmp->j; /* add (@i, @j)[k+m] = k, @x[k+m] = 1. for k = 0,..,(n-1) */ for(k=0; k < dims[0]; k++) { a_i[k+m] = k; a_j[k+m] = k; switch(ctype / 3) { case 0: { /* "d" */ double *a_x = tmp->x; a_x[k+m] = 1.; break; } case 1: { /* "l" */ int *a_x = tmp->x; a_x[k+m] = 1; break; } case 2: /* "n" */ break; case 3: { /* "z" */ double *a_x = tmp->x; a_x[2*(k+m) ] = 1.; a_x[2*(k+m)+1] = 0.; break; } } } /* for(k) */ chTr2Ralloc(ans, tmp); cholmod_l_free_triplet(&tmp, &c); } /* else : * NOTE: if(*diag_P(x) == 'U'), the diagonal is lost (!); * ---- that may be ok, e.g. if we are just converting from/to Tsparse, * but is *not* at all ok, e.g. when used before matrix products */ return ans; } /** * Copy the contents of a to an appropriate TsparseMatrix object and, * optionally, free a or free both a and its the pointers to its contents. * * @param a matrix to be converted * @param dofree 0 - don't free a; > 0 cholmod_free a; < 0 Free a * @param uploT 0 - not triangular; > 0 upper triangular; < 0 lower * @param Rkind - vector type to store for a->xtype == CHOLMOD_REAL, * 0 - REAL; 1 - LOGICAL * @param diag character string suitable for the diag slot of a * triangular matrix (not accessed if uploT == 0). * @param dn either R_NilValue or an SEXP suitable for the Dimnames slot. * * @return SEXP containing a copy of a */ SEXP chm_triplet_to_SEXP(CHM_TR a, int dofree, int uploT, int Rkind, const char* diag, SEXP dn) { SEXP ans; char *cl = ""; /* -Wall */ int *dims; PROTECT(dn); /* dn is usually UNPROTECTed before the call */ /* determine the class of the result */ #define DOFREE_MAYBE \ if (dofree > 0) cholmod_free_triplet(&a, &c); \ else if (dofree < 0) Free(a) switch(a->xtype) { case CHOLMOD_PATTERN: cl = uploT ? "ntTMatrix" : ((a->stype) ? "nsTMatrix" : "ngTMatrix"); break; case CHOLMOD_REAL: switch(Rkind) { case 0: cl = uploT ? "dtTMatrix" : ((a->stype) ? "dsTMatrix" : "dgTMatrix"); break; case 1: cl = uploT ? "ltTMatrix" : ((a->stype) ? "lsTMatrix" : "lgTMatrix"); break; } break; case CHOLMOD_COMPLEX: cl = uploT ? "ztTMatrix" : ((a->stype) ? "zsTMatrix" : "zgTMatrix"); break; default: DOFREE_MAYBE; error(_("unknown xtype in cholmod_triplet object")); } ans = PROTECT(NEW_OBJECT(MAKE_CLASS(cl))); /* allocate and copy common slots */ dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2)); dims[0] = a->nrow; dims[1] = a->ncol; Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_iSym, INTSXP, a->nnz)), (int *) a->i, a->nnz); Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_jSym, INTSXP, a->nnz)), (int *) a->j, a->nnz); /* copy data slot if present */ if (a->xtype == CHOLMOD_REAL) { int i, *m_x; double *a_x = (double *) a->x; switch(Rkind) { case 0: Memcpy(REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, a->nnz)), a_x, a->nnz); break; case 1: m_x = LOGICAL(ALLOC_SLOT(ans, Matrix_xSym, LGLSXP, a->nnz)); for (i=0; i < a->nnz; i++) m_x[i] = ISNAN(a_x[i]) ? NA_LOGICAL : (a_x[i] != 0); break; } } else if (a->xtype == CHOLMOD_COMPLEX) { DOFREE_MAYBE; error(_("complex sparse matrix code not yet written")); /* Memcpy(COMPLEX(ALLOC_SLOT(ans, Matrix_xSym, CPLXSXP, a->nnz)), */ /* (complex *) a->x, a->nz); */ } if (uploT) { /* slots for triangularMatrix */ if (a->stype) error(_("Symmetric and triangular both set")); SET_SLOT(ans, Matrix_uploSym, mkString((uploT > 0) ? "U" : "L")); SET_SLOT(ans, Matrix_diagSym, mkString(diag)); } /* set symmetry attributes */ if (a->stype) SET_SLOT(ans, Matrix_uploSym, mkString((a->stype > 0) ? "U" : "L")); DOFREE_MAYBE; if (dn != R_NilValue) SET_SLOT(ans, Matrix_DimNamesSym, duplicate(dn)); UNPROTECT(2); return ans; } #undef DOFREE_MAYBE /** * Populate ans with the pointers from x and modify its scalar * elements accordingly. Note that later changes to the contents of * ans will change the contents of the SEXP. * * In most cases this function is called through the macro AS_CHM_DN. * It is unusual to call it directly. * * @param ans a CHM_DN pointer. * @param x pointer to an object that inherits from (denseMatrix ^ generalMatrix) * * @return ans containing pointers to the slots of x. */ CHM_DN as_cholmod_dense(CHM_DN ans, SEXP x) { #define _AS_cholmod_dense_1 \ static const char *valid[] = { MATRIX_VALID_dense, ""}; \ int dims[2], ctype = Matrix_check_class_etc(x, valid), nprot = 0; \ \ if (ctype < 0) { /* not a classed matrix */ \ if (isMatrix(x)) Memcpy(dims, INTEGER(getAttrib(x, R_DimSymbol)), 2); \ else {dims[0] = LENGTH(x); dims[1] = 1;} \ if (isInteger(x)) { \ x = PROTECT(coerceVector(x, REALSXP)); \ nprot++; \ } \ ctype = (isReal(x) ? 0 : \ (isLogical(x) ? 2 : /* logical -> default to "l", not "n" */ \ (isComplex(x) ? 6 : -1))); \ } else Memcpy(dims, INTEGER(GET_SLOT(x, Matrix_DimSym)), 2); \ if (ctype < 0) error(_("invalid class of object to as_cholmod_dense")); \ memset(ans, 0, sizeof(cholmod_dense)); /* zero the struct */ \ \ ans->dtype = CHOLMOD_DOUBLE; /* characteristics of the system */ \ ans->x = ans->z = (void *) NULL; \ /* dimensions and nzmax */ \ ans->d = ans->nrow = dims[0]; \ ans->ncol = dims[1]; \ ans->nzmax = dims[0] * dims[1]; \ /* set the xtype and any elements */ \ switch(ctype / 2) { \ case 0: /* "d" */ \ ans->xtype = CHOLMOD_REAL; \ ans->x = (void *) REAL((ctype % 2) ? GET_SLOT(x, Matrix_xSym) : x); \ break _AS_cholmod_dense_1; case 1: /* "l" */ ans->xtype = CHOLMOD_REAL; ans->x = RallocedREAL((ctype % 2) ? GET_SLOT(x, Matrix_xSym) : x); break; case 2: /* "n" */ ans->xtype = CHOLMOD_PATTERN; ans->x = (void *) LOGICAL((ctype % 2) ? GET_SLOT(x, Matrix_xSym) : x); break; #define _AS_cholmod_dense_2 \ case 3: /* "z" */ \ ans->xtype = CHOLMOD_COMPLEX; \ ans->x = (void *) COMPLEX((ctype % 2) ? GET_SLOT(x, Matrix_xSym) : x); \ break; \ } \ UNPROTECT(nprot); \ return ans _AS_cholmod_dense_2; } /* version of as_cholmod_dense() that produces a cholmod_dense matrix * with REAL 'x' slot -- i.e. treats "nMatrix" as "lMatrix" -- as only difference; * Not just via a flag in as_cholmod_dense() since that has fixed API */ CHM_DN as_cholmod_x_dense(cholmod_dense *ans, SEXP x) { _AS_cholmod_dense_1; case 1: /* "l" */ case 2: /* "n" (no NA in 'x', but *has* 'x' slot => treat as "l" */ ans->xtype = CHOLMOD_REAL; ans->x = RallocedREAL((ctype % 2) ? GET_SLOT(x, Matrix_xSym) : x); break; _AS_cholmod_dense_2; } #undef _AS_cholmod_dense_1 #undef _AS_cholmod_dense_2 void R_cholmod_error(int status, const char *file, int line, const char *message) { CHM_restore_common(); /* restore any setting that may have been changed */ /* NB: keep in sync with M_R_cholmod_error(), ../inst/include/Matrix_stubs.c */ /* From CHOLMOD/Include/cholmod_core.h : ...status values. zero means success, negative means a fatal error, positive is a warning. */ #ifndef R_CHOLMOD_ALWAYS_ERROR if(status < 0) { #endif error(_("Cholmod error '%s' at file %s, line %d"), message, file, line); #ifndef R_CHOLMOD_ALWAYS_ERROR } else warning(_("Cholmod warning '%s' at file %s, line %d"), message, file, line); #endif } /* just to get 'int' instead of 'void' as required by CHOLMOD's print_function */ static int R_cholmod_printf(const char* fmt, ...) { va_list(ap); va_start(ap, fmt); Rprintf((char *)fmt, ap); va_end(ap); return 0; } /** * Initialize the CHOLMOD library and replace the print and error functions * by R-specific versions. * * @param c pointer to a cholmod_common structure to be initialized * * @return TRUE if successful */ int R_cholmod_start(CHM_CM c) { int res; if (!(res = cholmod_start(c))) error(_("Unable to initialize cholmod: error code %d"), res); c->print_function = R_cholmod_printf; /* Rprintf gives warning */ /* Since we provide an error handler, it may not be a good idea to allow CHOLMOD printing, * because that's not easily suppressed on the R level : * Hence consider, at least temporarily * c->print_function = NULL; */ c->error_handler = R_cholmod_error; return TRUE; } /** * Copy the contents of a to an appropriate denseMatrix object and, * optionally, free a or free both a and its pointer to its contents. * * @param a matrix to be converted * @param dofree 0 - don't free a; > 0 cholmod_free a; < 0 Free a * @param Rkind type of R matrix to be generated (special to this function) * @param dn -- dimnames [list(.,.) or NULL] * * @return SEXP containing a copy of a */ /* FIXME: should also have args (int uploST, char *diag) */ SEXP chm_dense_to_SEXP(CHM_DN a, int dofree, int Rkind, SEXP dn) { SEXP ans; char *cl = ""; /* -Wall */ int *dims, ntot; PROTECT(dn); /* << (why? -- just cut&paste from chm_dense_to_mat.. below*/ #define DOFREE_de_MAYBE \ if (dofree > 0) cholmod_free_dense(&a, &c); \ else if (dofree < 0) Free(a); switch(a->xtype) { /* determine the class of the result */ /* CHOLMOD_PATTERN never happens because cholmod_dense can't : * case CHOLMOD_PATTERN: * cl = "ngeMatrix"; break; */ case CHOLMOD_REAL: switch(Rkind) { /* -1: special for this function! */ case -1: cl = "ngeMatrix"; break; case 0: cl = "dgeMatrix"; break; case 1: cl = "lgeMatrix"; break; default: DOFREE_de_MAYBE; error(_("unknown 'Rkind'")); } break; case CHOLMOD_COMPLEX: cl = "zgeMatrix"; break; default: DOFREE_de_MAYBE; error(_("unknown xtype")); } ans = PROTECT(NEW_OBJECT(MAKE_CLASS(cl))); /* allocate and copy common slots */ dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2)); dims[0] = a->nrow; dims[1] = a->ncol; ntot = dims[0] * dims[1]; if (a->d == a->nrow) { /* copy data slot -- always present in dense(!) */ if (a->xtype == CHOLMOD_REAL) { int i, *m_x; double *a_x = (double *) a->x; switch(Rkind) { case 0: Memcpy(REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, ntot)), a_x, ntot); break; case -1: /* nge*/ case 1: /* lge*/ m_x = LOGICAL(ALLOC_SLOT(ans, Matrix_xSym, LGLSXP, ntot)); for (i=0; i < ntot; i++) m_x[i] = ISNAN(a_x[i]) ? NA_LOGICAL : (a_x[i] != 0); break; } } else if (a->xtype == CHOLMOD_COMPLEX) { DOFREE_de_MAYBE; error(_("complex sparse matrix code not yet written")); /* Memcpy(COMPLEX(ALLOC_SLOT(ans, Matrix_xSym, CPLXSXP, ntot)), */ /* (complex *) a->x, ntot); */ } } else { DOFREE_de_MAYBE; error(_("code for cholmod_dense with holes not yet written")); } DOFREE_de_MAYBE; if (dn != R_NilValue) SET_SLOT(ans, Matrix_DimNamesSym, duplicate(dn)); UNPROTECT(2); return ans; } /** * Copy the contents of a to a matrix object and, optionally, free a * or free both a and its pointer to its contents. * * @param a cholmod_dense structure to be converted {already REAL for original l..CMatrix} * @param dofree 0 - don't free a; > 0 cholmod_free a; < 0 Free a * @param dn either R_NilValue or an SEXP suitable for the Dimnames slot. * * @return SEXP containing a copy of a as a matrix object */ SEXP chm_dense_to_matrix(CHM_DN a, int dofree, SEXP dn) { #define CHM_DENSE_TYPE \ SEXPTYPE typ; \ /* determine the class of the result */ \ typ = (a->xtype == CHOLMOD_PATTERN) ? LGLSXP : \ ((a->xtype == CHOLMOD_REAL) ? REALSXP : \ ((a->xtype == CHOLMOD_COMPLEX) ? CPLXSXP : NILSXP)); \ if (typ == NILSXP) { \ DOFREE_de_MAYBE; \ error(_("unknown xtype")); \ } PROTECT(dn); CHM_DENSE_TYPE; SEXP ans = PROTECT(allocMatrix(typ, a->nrow, a->ncol)); #define CHM_DENSE_COPY_DATA \ if (a->d == a->nrow) { /* copy data slot if present */ \ if (a->xtype == CHOLMOD_REAL) \ Memcpy(REAL(ans), (double *) a->x, a->nrow * a->ncol); \ else if (a->xtype == CHOLMOD_COMPLEX) { \ DOFREE_de_MAYBE; \ error(_("complex sparse matrix code not yet written")); \ /* Memcpy(COMPLEX(ALLOC_SLOT(ans, Matrix_xSym, CPLXSXP, a->nnz)), */ \ /* (complex *) a->x, a->nz); */ \ } else if (a->xtype == CHOLMOD_PATTERN) { \ DOFREE_de_MAYBE; \ error(_("don't know if a dense pattern matrix makes sense")); \ } \ } else { \ DOFREE_de_MAYBE; \ error(_("code for cholmod_dense with holes not yet written")); \ } CHM_DENSE_COPY_DATA; DOFREE_de_MAYBE; if (dn != R_NilValue) setAttrib(ans, R_DimNamesSymbol, duplicate(dn)); UNPROTECT(2); return ans; } /** * Copy the contents of a to a numeric R object and, optionally, free a * or free both a and its pointer to its contents. * * @param a cholmod_dense structure to be converted * @param dofree 0 - don't free a; > 0 cholmod_free a; < 0 Free a * * @return SEXP containing a copy of a in the sense of as.vector(a) */ SEXP chm_dense_to_vector(CHM_DN a, int dofree) { CHM_DENSE_TYPE; SEXP ans = PROTECT(allocVector(typ, a->nrow * a->ncol)); CHM_DENSE_COPY_DATA; DOFREE_de_MAYBE; UNPROTECT(1); return ans; } CHM_DN numeric_as_chm_dense(CHM_DN ans, double *v, int nr, int nc) { ans->d = ans->nrow = nr; ans->ncol = nc; ans->nzmax = nr * nc; ans->x = (void *) v; ans->xtype = CHOLMOD_REAL; ans->dtype = CHOLMOD_DOUBLE; return ans; } /** * Populate ans with the pointers from x and modify its scalar * elements accordingly. Note that later changes to the contents of * ans will change the contents of the SEXP. * * In most cases this function is called through the macro AS_CHM_FR. * It is unusual to call it directly. * * @param ans an CHM_FR object * @param x pointer to an object that inherits from CHMfactor * * @return ans containing pointers to the slots of x. */ CHM_FR as_cholmod_factor(CHM_FR ans, SEXP x) { static const char *valid[] = { MATRIX_VALID_CHMfactor, ""}; int *type = INTEGER(GET_SLOT(x, install("type"))), ctype = Matrix_check_class_etc(x, valid); SEXP tmp; if (ctype < 0) error(_("invalid class of object to as_cholmod_factor")); memset(ans, 0, sizeof(cholmod_factor)); /* zero the struct */ ans->itype = CHOLMOD_INT; /* characteristics of the system */ ans->dtype = CHOLMOD_DOUBLE; ans->z = (void *) NULL; ans->xtype = (ctype < 2) ? CHOLMOD_REAL : CHOLMOD_PATTERN; ans->ordering = type[0]; /* unravel the type */ ans->is_ll = (type[1] ? 1 : 0); ans->is_super = (type[2] ? 1 : 0); ans->is_monotonic = (type[3] ? 1 : 0); /* check for consistency */ if ((!(ans->is_ll)) && ans->is_super) error(_("Supernodal LDL' decomposition not available")); if ((!type[2]) ^ (ctype % 2)) error(_("Supernodal/simplicial class inconsistent with type flags")); /* slots always present */ tmp = GET_SLOT(x, Matrix_permSym); ans->minor = ans->n = LENGTH(tmp); ans->Perm = INTEGER(tmp); ans->ColCount = INTEGER(GET_SLOT(x, install("colcount"))); ans->z = ans->x = (void *) NULL; if (ctype < 2) { tmp = GET_SLOT(x, Matrix_xSym); ans->x = REAL(tmp); } if (ans->is_super) { /* supernodal factorization */ ans->xsize = LENGTH(tmp); ans->maxcsize = type[4]; ans->maxesize = type[5]; ans->i = (int*)NULL; tmp = GET_SLOT(x, install("super")); ans->nsuper = LENGTH(tmp) - 1; ans->super = INTEGER(tmp); /* Move these checks to the CHMfactor_validate function */ if (ans->nsuper < 1) error(_("Number of supernodes must be positive when is_super is TRUE")); tmp = GET_SLOT(x, install("pi")); if (LENGTH(tmp) != ans->nsuper + 1) error(_("Lengths of super and pi must be equal")); ans->pi = INTEGER(tmp); tmp = GET_SLOT(x, install("px")); if (LENGTH(tmp) != ans->nsuper + 1) error(_("Lengths of super and px must be equal")); ans->px = INTEGER(tmp); tmp = GET_SLOT(x, install("s")); ans->ssize = LENGTH(tmp); ans->s = INTEGER(tmp); } else { ans->nzmax = LENGTH(tmp); ans->p = INTEGER(GET_SLOT(x, Matrix_pSym)); ans->i = INTEGER(GET_SLOT(x, Matrix_iSym)); ans->nz = INTEGER(GET_SLOT(x, install("nz"))); ans->next = INTEGER(GET_SLOT(x, install("nxt"))); ans->prev = INTEGER(GET_SLOT(x, install("prv"))); } if (!cholmod_check_factor(ans, &c)) error(_("failure in as_cholmod_factor")); return ans; } /** * Copy the contents of f to an appropriate CHMfactor object and, * optionally, free f or free both f and its pointer to its contents. * * @param f cholmod_factor object to be converted * @param dofree 0 - don't free a; > 0 cholmod_free a; < 0 Free a * * @return SEXP containing a copy of a */ SEXP chm_factor_to_SEXP(CHM_FR f, int dofree) { SEXP ans; int *dims, *type; char *class = (char*) NULL; /* -Wall */ #define DOFREE_MAYBE \ if(dofree) { \ if (dofree > 0) cholmod_free_factor(&f, &c); \ else /* dofree < 0 */ Free(f); \ } if(!chm_factor_ok(f)) { DOFREE_MAYBE; error(_("CHOLMOD factorization was unsuccessful")); // error(_("previous CHOLMOD factorization was unsuccessful")); } switch(f->xtype) { case CHOLMOD_REAL: class = f->is_super ? "dCHMsuper" : "dCHMsimpl"; break; case CHOLMOD_PATTERN: class = f->is_super ? "nCHMsuper" : "nCHMsimpl"; break; default: DOFREE_MAYBE; error(_("f->xtype of %d not recognized"), f->xtype); } ans = PROTECT(NEW_OBJECT(MAKE_CLASS(class))); dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2)); dims[0] = dims[1] = f->n; /* copy component of known length */ Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_permSym, INTSXP, f->n)), (int*)f->Perm, f->n); Memcpy(INTEGER(ALLOC_SLOT(ans, install("colcount"), INTSXP, f->n)), (int*)f->ColCount, f->n); type = INTEGER(ALLOC_SLOT(ans, install("type"), INTSXP, f->is_super ? 6 : 4)); type[0] = f->ordering; type[1] = f->is_ll; type[2] = f->is_super; type[3] = f->is_monotonic; if (f->is_super) { type[4] = f->maxcsize; type[5] = f->maxesize; Memcpy(INTEGER(ALLOC_SLOT(ans, install("super"), INTSXP, f->nsuper + 1)), (int*)f->super, f->nsuper+1); Memcpy(INTEGER(ALLOC_SLOT(ans, install("pi"), INTSXP, f->nsuper + 1)), (int*)f->pi, f->nsuper + 1); Memcpy(INTEGER(ALLOC_SLOT(ans, install("px"), INTSXP, f->nsuper + 1)), (int*)f->px, f->nsuper + 1); Memcpy(INTEGER(ALLOC_SLOT(ans, install("s"), INTSXP, f->ssize)), (int*)f->s, f->ssize); Memcpy(REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, f->xsize)), (double*)f->x, f->xsize); } else { Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_iSym, INTSXP, f->nzmax)), (int*)f->i, f->nzmax); Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_pSym, INTSXP, f->n + 1)), (int*)f->p, f->n + 1); Memcpy(REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, f->nzmax)), (double*)f->x, f->nzmax); Memcpy(INTEGER(ALLOC_SLOT(ans, install("nz"), INTSXP, f->n)), (int*)f->nz, f->n); Memcpy(INTEGER(ALLOC_SLOT(ans, install("nxt"), INTSXP, f->n + 2)), (int*)f->next, f->n + 2); Memcpy(INTEGER(ALLOC_SLOT(ans, install("prv"), INTSXP, f->n + 2)), (int*)f->prev, f->n + 2); } DOFREE_MAYBE; UNPROTECT(1); return ans; } #undef DOFREE_MAYBE /** * Drop the (unit) diagonal entries from a cholmod_sparse matrix * * @param chx cholmod_sparse matrix. * Note that the matrix "slots" are modified _in place_ * @param uploT integer code (= +/- 1) indicating if chx is * upper (+1) or lower (-1) triangular * @param do_realloc Rboolean indicating, if a cholmod_sprealloc() should * finalize the procedure; not needed, e.g. when the * result is converted to a SEXP immediately afterwards. */ void chm_diagN2U(CHM_SP chx, int uploT, Rboolean do_realloc) { int i, n = chx->nrow, nnz = (int)cholmod_nnz(chx, &c), n_nnz = nnz - n, /* the new nnz : we will have removed n entries */ i_to = 0, i_from = 0; if(chx->ncol != n) error(_("chm_diagN2U(): nrow=%d, ncol=%d"), n, chx->ncol); if (!chx->sorted || !chx->packed) cholmod_sort(chx, &c); /* dimensions and nzmax */ #define _i(I) ( (int*) chx->i)[I] #define _x(I) ((double*) chx->x)[I] #define _p(I) ( (int*) chx->p)[I] /* work by copying from i_from to i_to ==> MUST i_to <= i_from */ if(uploT == 1) { /* "U" : upper triangular */ for(i = 0; i < n; i++) { /* looking at i-th column */ int j, n_i = _p(i+1) - _p(i); /* = #{entries} in this column */ /* 1) copy all but the last _above-diagonal_ column-entries: */ for(j = 1; j < n_i; j++, i_to++, i_from++) { _i(i_to) = _i(i_from); _x(i_to) = _x(i_from); } /* 2) drop the last column-entry == diagonal entry */ i_from++; } } else if(uploT == -1) { /* "L" : lower triangular */ for(i = 0; i < n; i++) { /* looking at i-th column */ int j, n_i = _p(i+1) - _p(i); /* = #{entries} in this column */ /* 1) drop the first column-entry == diagonal entry */ i_from++; /* 2) copy the other _below-diagonal_ column-entries: */ for(j = 1; j < n_i; j++, i_to++, i_from++) { _i(i_to) = _i(i_from); _x(i_to) = _x(i_from); } } } else { error(_("chm_diagN2U(x, uploT = %d): uploT should be +- 1"), uploT); } /* the column pointers are modified the same in both cases :*/ for(i=1; i <= n; i++) _p(i) -= i; #undef _i #undef _x #undef _p if(do_realloc) /* shorten (i- and x-slots from nnz to n_nnz */ cholmod_reallocate_sparse(n_nnz, chx, &c); return; } /* Placeholders; TODO: use checks above (search "CHMfactor_validate"): */ SEXP CHMfactor_validate(SEXP obj) /* placeholder */ { return ScalarLogical(1); } SEXP CHMsimpl_validate(SEXP obj) /* placeholder */ { return ScalarLogical(1); } SEXP CHMsuper_validate(SEXP obj) /* placeholder */ { return ScalarLogical(1); } Matrix/src/abIndex.h0000644000175100001440000000025112271765436014061 0ustar hornikusers#ifndef MATRIX_AbstrINDEX_H #define MATRIX_AbstrINDEX_H #include "Mutils.h" SEXP Matrix_rle_i(SEXP x_, SEXP force_); SEXP Matrix_rle_d(SEXP x_, SEXP force_); #endif Matrix/src/AMD/0000755000175100001440000000000012271765426012740 5ustar hornikusersMatrix/src/AMD/Source/0000755000175100001440000000000012271765426014200 5ustar hornikusersMatrix/src/AMD/Source/amd_global.c0000644000175100001440000000625412271765436016435 0ustar hornikusers/* ========================================================================= */ /* === amd_global ========================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ #include #ifdef MATLAB_MEX_FILE #include "mex.h" #include "matrix.h" #endif #ifndef NULL #define NULL 0 #endif /* ========================================================================= */ /* === Default AMD memory manager ========================================== */ /* ========================================================================= */ /* The user can redefine these global pointers at run-time to change the memory * manager used by AMD. AMD only uses malloc and free; realloc and calloc are * include for completeness, in case another package wants to use the same * memory manager as AMD. * * If compiling as a MATLAB mexFunction, the default memory manager is mxMalloc. * You can also compile AMD as a standard ANSI-C library and link a mexFunction * against it, and then redefine these pointers at run-time, in your * mexFunction. * * If -DNMALLOC is defined at compile-time, no memory manager is specified at * compile-time. You must then define these functions at run-time, before * calling AMD, for AMD to work properly. */ #ifndef NMALLOC #ifdef MATLAB_MEX_FILE /* MATLAB mexFunction: */ void *(*amd_malloc) (size_t) = mxMalloc ; void (*amd_free) (void *) = mxFree ; void *(*amd_realloc) (void *, size_t) = mxRealloc ; void *(*amd_calloc) (size_t, size_t) = mxCalloc ; #else /* standard ANSI-C: */ void *(*amd_malloc) (size_t) = malloc ; void (*amd_free) (void *) = free ; void *(*amd_realloc) (void *, size_t) = realloc ; void *(*amd_calloc) (size_t, size_t) = calloc ; #endif #else /* no memory manager defined at compile-time; you MUST define one at run-time */ void *(*amd_malloc) (size_t) = NULL ; void (*amd_free) (void *) = NULL ; void *(*amd_realloc) (void *, size_t) = NULL ; void *(*amd_calloc) (size_t, size_t) = NULL ; #endif /* ========================================================================= */ /* === Default AMD printf routine ========================================== */ /* ========================================================================= */ /* The user can redefine this global pointer at run-time to change the printf * routine used by AMD. If NULL, no printing occurs. * * If -DNPRINT is defined at compile-time, stdio.h is not included. Printing * can then be enabled at run-time by setting amd_printf to a non-NULL function. */ #ifndef NPRINT #ifdef MATLAB_MEX_FILE int (*amd_printf) (const char *, ...) = mexPrintf ; #else #include // For use with R package 'Matrix': #include void (*amd_printf) (const char *, ...) = Rprintf ; #endif #else int (*amd_printf) (const char *, ...) = NULL ; #endif Matrix/src/AMD/Source/Makefile0000644000175100001440000000036312271765436015643 0ustar hornikusersinclude $(MkInclude) PKG_CPPFLAGS = -I../Include -I../../SuiteSparse_config LIB = ../../AMD.a lib: $(LIB) include make_o.mk $(LIB): $(OBJS) $(AR) -rucs $(LIB) $(OBJS) mostlyclean: clean clean: @-rm -rf .libs _libs $(LIB) @-rm -f *.o Matrix/src/AMD/Source/amd_aat.c0000644000175100001440000001135712271765436015742 0ustar hornikusers/* ========================================================================= */ /* === AMD_aat ============================================================= */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* AMD_aat: compute the symmetry of the pattern of A, and count the number of * nonzeros each column of A+A' (excluding the diagonal). Assumes the input * matrix has no errors, with sorted columns and no duplicates * (AMD_valid (n, n, Ap, Ai) must be AMD_OK, but this condition is not * checked). */ #include "amd_internal.h" GLOBAL size_t AMD_aat /* returns nz in A+A' */ ( Int n, const Int Ap [ ], const Int Ai [ ], Int Len [ ], /* Len [j]: length of column j of A+A', excl diagonal*/ Int Tp [ ], /* workspace of size n */ double Info [ ] ) { Int p1, p2, p, i, j, pj, pj2, k, nzdiag, nzboth, nz ; double sym ; size_t nzaat ; #ifndef NDEBUG AMD_debug_init ("AMD AAT") ; for (k = 0 ; k < n ; k++) Tp [k] = EMPTY ; ASSERT (AMD_valid (n, n, Ap, Ai) == AMD_OK) ; #endif if (Info != (double *) NULL) { /* clear the Info array, if it exists */ for (i = 0 ; i < AMD_INFO ; i++) { Info [i] = EMPTY ; } Info [AMD_STATUS] = AMD_OK ; } for (k = 0 ; k < n ; k++) { Len [k] = 0 ; } nzdiag = 0 ; nzboth = 0 ; nz = Ap [n] ; for (k = 0 ; k < n ; k++) { p1 = Ap [k] ; p2 = Ap [k+1] ; AMD_DEBUG2 (("\nAAT Column: "ID" p1: "ID" p2: "ID"\n", k, p1, p2)) ; /* construct A+A' */ for (p = p1 ; p < p2 ; ) { /* scan the upper triangular part of A */ j = Ai [p] ; if (j < k) { /* entry A (j,k) is in the strictly upper triangular part, * add both A (j,k) and A (k,j) to the matrix A+A' */ Len [j]++ ; Len [k]++ ; AMD_DEBUG3 ((" upper ("ID","ID") ("ID","ID")\n", j,k, k,j)); p++ ; } else if (j == k) { /* skip the diagonal */ p++ ; nzdiag++ ; break ; } else /* j > k */ { /* first entry below the diagonal */ break ; } /* scan lower triangular part of A, in column j until reaching * row k. Start where last scan left off. */ ASSERT (Tp [j] != EMPTY) ; ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ; pj2 = Ap [j+1] ; for (pj = Tp [j] ; pj < pj2 ; ) { i = Ai [pj] ; if (i < k) { /* A (i,j) is only in the lower part, not in upper. * add both A (i,j) and A (j,i) to the matrix A+A' */ Len [i]++ ; Len [j]++ ; AMD_DEBUG3 ((" lower ("ID","ID") ("ID","ID")\n", i,j, j,i)) ; pj++ ; } else if (i == k) { /* entry A (k,j) in lower part and A (j,k) in upper */ pj++ ; nzboth++ ; break ; } else /* i > k */ { /* consider this entry later, when k advances to i */ break ; } } Tp [j] = pj ; } /* Tp [k] points to the entry just below the diagonal in column k */ Tp [k] = p ; } /* clean up, for remaining mismatched entries */ for (j = 0 ; j < n ; j++) { for (pj = Tp [j] ; pj < Ap [j+1] ; pj++) { i = Ai [pj] ; /* A (i,j) is only in the lower part, not in upper. * add both A (i,j) and A (j,i) to the matrix A+A' */ Len [i]++ ; Len [j]++ ; AMD_DEBUG3 ((" lower cleanup ("ID","ID") ("ID","ID")\n", i,j, j,i)) ; } } /* --------------------------------------------------------------------- */ /* compute the symmetry of the nonzero pattern of A */ /* --------------------------------------------------------------------- */ /* Given a matrix A, the symmetry of A is: * B = tril (spones (A), -1) + triu (spones (A), 1) ; * sym = nnz (B & B') / nnz (B) ; * or 1 if nnz (B) is zero. */ if (nz == nzdiag) { sym = 1 ; } else { sym = (2 * (double) nzboth) / ((double) (nz - nzdiag)) ; } nzaat = 0 ; for (k = 0 ; k < n ; k++) { nzaat += Len [k] ; } AMD_DEBUG1 (("AMD nz in A+A', excluding diagonal (nzaat) = %g\n", (double) nzaat)) ; AMD_DEBUG1 ((" nzboth: "ID" nz: "ID" nzdiag: "ID" symmetry: %g\n", nzboth, nz, nzdiag, sym)) ; if (Info != (double *) NULL) { Info [AMD_STATUS] = AMD_OK ; Info [AMD_N] = n ; Info [AMD_NZ] = nz ; Info [AMD_SYMMETRY] = sym ; /* symmetry of pattern of A */ Info [AMD_NZDIAG] = nzdiag ; /* nonzeros on diagonal of A */ Info [AMD_NZ_A_PLUS_AT] = nzaat ; /* nonzeros in A+A' */ } return (nzaat) ; } Matrix/src/AMD/Source/amd_info.c0000644000175100001440000001011512271765436016117 0ustar hornikusers/* ========================================================================= */ /* === AMD_info ============================================================ */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* User-callable. Prints the output statistics for AMD. See amd.h * for details. If the Info array is not present, nothing is printed. */ #include "amd_internal.h" #define PRI(format,x) { if (x >= 0) { PRINTF ((format, x)) ; }} GLOBAL void AMD_info ( double Info [ ] ) { double n, ndiv, nmultsubs_ldl, nmultsubs_lu, lnz, lnzd ; PRINTF (("\nAMD version %d.%d.%d, %s, results:\n", AMD_MAIN_VERSION, AMD_SUB_VERSION, AMD_SUBSUB_VERSION, AMD_DATE)) ; if (!Info) { return ; } n = Info [AMD_N] ; ndiv = Info [AMD_NDIV] ; nmultsubs_ldl = Info [AMD_NMULTSUBS_LDL] ; nmultsubs_lu = Info [AMD_NMULTSUBS_LU] ; lnz = Info [AMD_LNZ] ; lnzd = (n >= 0 && lnz >= 0) ? (n + lnz) : (-1) ; /* AMD return status */ PRINTF ((" status: ")) ; if (Info [AMD_STATUS] == AMD_OK) { PRINTF (("OK\n")) ; } else if (Info [AMD_STATUS] == AMD_OUT_OF_MEMORY) { PRINTF (("out of memory\n")) ; } else if (Info [AMD_STATUS] == AMD_INVALID) { PRINTF (("invalid matrix\n")) ; } else if (Info [AMD_STATUS] == AMD_OK_BUT_JUMBLED) { PRINTF (("OK, but jumbled\n")) ; } else { PRINTF (("unknown\n")) ; } /* statistics about the input matrix */ PRI (" n, dimension of A: %.20g\n", n); PRI (" nz, number of nonzeros in A: %.20g\n", Info [AMD_NZ]) ; PRI (" symmetry of A: %.4f\n", Info [AMD_SYMMETRY]) ; PRI (" number of nonzeros on diagonal: %.20g\n", Info [AMD_NZDIAG]) ; PRI (" nonzeros in pattern of A+A' (excl. diagonal): %.20g\n", Info [AMD_NZ_A_PLUS_AT]) ; PRI (" # dense rows/columns of A+A': %.20g\n", Info [AMD_NDENSE]) ; /* statistics about AMD's behavior */ PRI (" memory used, in bytes: %.20g\n", Info [AMD_MEMORY]) ; PRI (" # of memory compactions: %.20g\n", Info [AMD_NCMPA]) ; /* statistics about the ordering quality */ PRINTF (("\n" " The following approximate statistics are for a subsequent\n" " factorization of A(P,P) + A(P,P)'. They are slight upper\n" " bounds if there are no dense rows/columns in A+A', and become\n" " looser if dense rows/columns exist.\n\n")) ; PRI (" nonzeros in L (excluding diagonal): %.20g\n", lnz) ; PRI (" nonzeros in L (including diagonal): %.20g\n", lnzd) ; PRI (" # divide operations for LDL' or LU: %.20g\n", ndiv) ; PRI (" # multiply-subtract operations for LDL': %.20g\n", nmultsubs_ldl) ; PRI (" # multiply-subtract operations for LU: %.20g\n", nmultsubs_lu) ; PRI (" max nz. in any column of L (incl. diagonal): %.20g\n", Info [AMD_DMAX]) ; /* total flop counts for various factorizations */ if (n >= 0 && ndiv >= 0 && nmultsubs_ldl >= 0 && nmultsubs_lu >= 0) { PRINTF (("\n" " chol flop count for real A, sqrt counted as 1 flop: %.20g\n" " LDL' flop count for real A: %.20g\n" " LDL' flop count for complex A: %.20g\n" " LU flop count for real A (with no pivoting): %.20g\n" " LU flop count for complex A (with no pivoting): %.20g\n\n", n + ndiv + 2*nmultsubs_ldl, ndiv + 2*nmultsubs_ldl, 9*ndiv + 8*nmultsubs_ldl, ndiv + 2*nmultsubs_lu, 9*ndiv + 8*nmultsubs_lu)) ; } } Matrix/src/AMD/Source/amd_preprocess.c0000644000175100001440000000734012271765436017357 0ustar hornikusers/* ========================================================================= */ /* === AMD_preprocess ====================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* Sorts, removes duplicate entries, and transposes from the nonzero pattern of * a column-form matrix A, to obtain the matrix R. The input matrix can have * duplicate entries and/or unsorted columns (AMD_valid (n,Ap,Ai) must not be * AMD_INVALID). * * This input condition is NOT checked. This routine is not user-callable. */ #include "amd_internal.h" /* ========================================================================= */ /* === AMD_preprocess ====================================================== */ /* ========================================================================= */ /* AMD_preprocess does not check its input for errors or allocate workspace. * On input, the condition (AMD_valid (n,n,Ap,Ai) != AMD_INVALID) must hold. */ GLOBAL void AMD_preprocess ( Int n, /* input matrix: A is n-by-n */ const Int Ap [ ], /* size n+1 */ const Int Ai [ ], /* size nz = Ap [n] */ /* output matrix R: */ Int Rp [ ], /* size n+1 */ Int Ri [ ], /* size nz (or less, if duplicates present) */ Int W [ ], /* workspace of size n */ Int Flag [ ] /* workspace of size n */ ) { /* --------------------------------------------------------------------- */ /* local variables */ /* --------------------------------------------------------------------- */ Int i, j, p, p2 ; ASSERT (AMD_valid (n, n, Ap, Ai) != AMD_INVALID) ; /* --------------------------------------------------------------------- */ /* count the entries in each row of A (excluding duplicates) */ /* --------------------------------------------------------------------- */ for (i = 0 ; i < n ; i++) { W [i] = 0 ; /* # of nonzeros in row i (excl duplicates) */ Flag [i] = EMPTY ; /* Flag [i] = j if i appears in column j */ } for (j = 0 ; j < n ; j++) { p2 = Ap [j+1] ; for (p = Ap [j] ; p < p2 ; p++) { i = Ai [p] ; if (Flag [i] != j) { /* row index i has not yet appeared in column j */ W [i]++ ; /* one more entry in row i */ Flag [i] = j ; /* flag row index i as appearing in col j*/ } } } /* --------------------------------------------------------------------- */ /* compute the row pointers for R */ /* --------------------------------------------------------------------- */ Rp [0] = 0 ; for (i = 0 ; i < n ; i++) { Rp [i+1] = Rp [i] + W [i] ; } for (i = 0 ; i < n ; i++) { W [i] = Rp [i] ; Flag [i] = EMPTY ; } /* --------------------------------------------------------------------- */ /* construct the row form matrix R */ /* --------------------------------------------------------------------- */ /* R = row form of pattern of A */ for (j = 0 ; j < n ; j++) { p2 = Ap [j+1] ; for (p = Ap [j] ; p < p2 ; p++) { i = Ai [p] ; if (Flag [i] != j) { /* row index i has not yet appeared in column j */ Ri [W [i]++] = j ; /* put col j in row i */ Flag [i] = j ; /* flag row index i as appearing in col j*/ } } } #ifndef NDEBUG ASSERT (AMD_valid (n, n, Rp, Ri) == AMD_OK) ; for (j = 0 ; j < n ; j++) { ASSERT (W [j] == Rp [j+1]) ; } #endif } Matrix/src/AMD/Source/amd_postorder.c0000644000175100001440000001260512271765436017213 0ustar hornikusers/* ========================================================================= */ /* === AMD_postorder ======================================================= */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* Perform a postordering (via depth-first search) of an assembly tree. */ #include "amd_internal.h" GLOBAL void AMD_postorder ( /* inputs, not modified on output: */ Int nn, /* nodes are in the range 0..nn-1 */ Int Parent [ ], /* Parent [j] is the parent of j, or EMPTY if root */ Int Nv [ ], /* Nv [j] > 0 number of pivots represented by node j, * or zero if j is not a node. */ Int Fsize [ ], /* Fsize [j]: size of node j */ /* output, not defined on input: */ Int Order [ ], /* output post-order */ /* workspaces of size nn: */ Int Child [ ], Int Sibling [ ], Int Stack [ ] ) { Int i, j, k, parent, frsize, f, fprev, maxfrsize, bigfprev, bigf, fnext ; for (j = 0 ; j < nn ; j++) { Child [j] = EMPTY ; Sibling [j] = EMPTY ; } /* --------------------------------------------------------------------- */ /* place the children in link lists - bigger elements tend to be last */ /* --------------------------------------------------------------------- */ for (j = nn-1 ; j >= 0 ; j--) { if (Nv [j] > 0) { /* this is an element */ parent = Parent [j] ; if (parent != EMPTY) { /* place the element in link list of the children its parent */ /* bigger elements will tend to be at the end of the list */ Sibling [j] = Child [parent] ; Child [parent] = j ; } } } #ifndef NDEBUG { Int nels, ff, nchild ; AMD_DEBUG1 (("\n\n================================ AMD_postorder:\n")); nels = 0 ; for (j = 0 ; j < nn ; j++) { if (Nv [j] > 0) { AMD_DEBUG1 (( ""ID" : nels "ID" npiv "ID" size "ID " parent "ID" maxfr "ID"\n", j, nels, Nv [j], Fsize [j], Parent [j], Fsize [j])) ; /* this is an element */ /* dump the link list of children */ nchild = 0 ; AMD_DEBUG1 ((" Children: ")) ; for (ff = Child [j] ; ff != EMPTY ; ff = Sibling [ff]) { AMD_DEBUG1 ((ID" ", ff)) ; ASSERT (Parent [ff] == j) ; nchild++ ; ASSERT (nchild < nn) ; } AMD_DEBUG1 (("\n")) ; parent = Parent [j] ; if (parent != EMPTY) { ASSERT (Nv [parent] > 0) ; } nels++ ; } } } AMD_DEBUG1 (("\n\nGo through the children of each node, and put\n" "the biggest child last in each list:\n")) ; #endif /* --------------------------------------------------------------------- */ /* place the largest child last in the list of children for each node */ /* --------------------------------------------------------------------- */ for (i = 0 ; i < nn ; i++) { if (Nv [i] > 0 && Child [i] != EMPTY) { #ifndef NDEBUG Int nchild ; AMD_DEBUG1 (("Before partial sort, element "ID"\n", i)) ; nchild = 0 ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { ASSERT (f >= 0 && f < nn) ; AMD_DEBUG1 ((" f: "ID" size: "ID"\n", f, Fsize [f])) ; nchild++ ; ASSERT (nchild <= nn) ; } #endif /* find the biggest element in the child list */ fprev = EMPTY ; maxfrsize = EMPTY ; bigfprev = EMPTY ; bigf = EMPTY ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { ASSERT (f >= 0 && f < nn) ; frsize = Fsize [f] ; if (frsize >= maxfrsize) { /* this is the biggest seen so far */ maxfrsize = frsize ; bigfprev = fprev ; bigf = f ; } fprev = f ; } ASSERT (bigf != EMPTY) ; fnext = Sibling [bigf] ; AMD_DEBUG1 (("bigf "ID" maxfrsize "ID" bigfprev "ID" fnext "ID " fprev " ID"\n", bigf, maxfrsize, bigfprev, fnext, fprev)) ; if (fnext != EMPTY) { /* if fnext is EMPTY then bigf is already at the end of list */ if (bigfprev == EMPTY) { /* delete bigf from the element of the list */ Child [i] = fnext ; } else { /* delete bigf from the middle of the list */ Sibling [bigfprev] = fnext ; } /* put bigf at the end of the list */ Sibling [bigf] = EMPTY ; ASSERT (Child [i] != EMPTY) ; ASSERT (fprev != bigf) ; ASSERT (fprev != EMPTY) ; Sibling [fprev] = bigf ; } #ifndef NDEBUG AMD_DEBUG1 (("After partial sort, element "ID"\n", i)) ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { ASSERT (f >= 0 && f < nn) ; AMD_DEBUG1 ((" "ID" "ID"\n", f, Fsize [f])) ; ASSERT (Nv [f] > 0) ; nchild-- ; } ASSERT (nchild == 0) ; #endif } } /* --------------------------------------------------------------------- */ /* postorder the assembly tree */ /* --------------------------------------------------------------------- */ for (i = 0 ; i < nn ; i++) { Order [i] = EMPTY ; } k = 0 ; for (i = 0 ; i < nn ; i++) { if (Parent [i] == EMPTY && Nv [i] > 0) { AMD_DEBUG1 (("Root of assembly tree "ID"\n", i)) ; k = AMD_post_tree (i, k, Child, Sibling, Order, Stack #ifndef NDEBUG , nn #endif ) ; } } } Matrix/src/AMD/Source/make-Make.R0000644000175100001440000000143311772413724016110 0ustar hornikusers## From: Prof Brian Ripley ## To: Martin Maechler ## cc: Doug and Martin ## Subject: Re: [Rd] Package Matrix does not compile in R-devel_2009-01-10 (fwd) ## Date: Thu, 15 Jan 2009 14:22:17 +0000 (GMT) AMD <- c("aat", "1", "2", "postorder", "post_tree", "defaults", "order", "control", "info", "valid", "preprocess", "dump", "global") cat("OBJS = ") for (i in AMD) cat(sprintf("amd_i_%s.o amd_l_%s.o ", i, i)) cat("\n\n") CC1 <- "\t$(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include" for (i in AMD) cat(sprintf("amd_i_%s.o: amd_%s.c $(INC)", i, i), sprintf(paste(CC1, "-DDINT -c amd_%s.c -o $@"), i), sep="\n") cat("\n") for (i in AMD) cat(sprintf("amd_l_%s.o: amd_%s.c $(INC)", i,i), sprintf(paste(CC1, "-DDLONG -c amd_%s.c -o $@"), i), sep="\n") Matrix/src/AMD/Source/amd_control.c0000644000175100001440000000337212271765436016653 0ustar hornikusers/* ========================================================================= */ /* === AMD_control ========================================================= */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* User-callable. Prints the control parameters for AMD. See amd.h * for details. If the Control array is not present, the defaults are * printed instead. */ #include "amd_internal.h" GLOBAL void AMD_control ( double Control [ ] ) { double alpha ; Int aggressive ; if (Control != (double *) NULL) { alpha = Control [AMD_DENSE] ; aggressive = Control [AMD_AGGRESSIVE] != 0 ; } else { alpha = AMD_DEFAULT_DENSE ; aggressive = AMD_DEFAULT_AGGRESSIVE ; } PRINTF (("\nAMD version %d.%d.%d, %s: approximate minimum degree ordering\n" " dense row parameter: %g\n", AMD_MAIN_VERSION, AMD_SUB_VERSION, AMD_SUBSUB_VERSION, AMD_DATE, alpha)) ; if (alpha < 0) { PRINTF ((" no rows treated as dense\n")) ; } else { PRINTF (( " (rows with more than max (%g * sqrt (n), 16) entries are\n" " considered \"dense\", and placed last in output permutation)\n", alpha)) ; } if (aggressive) { PRINTF ((" aggressive absorption: yes\n")) ; } else { PRINTF ((" aggressive absorption: no\n")) ; } PRINTF ((" size of AMD integer: %d\n\n", sizeof (Int))) ; } Matrix/src/AMD/Source/make_o.mk0000644000175100001440000000643311772413724015766 0ustar hornikusersOBJS = amd_i_aat.o amd_l_aat.o amd_i_1.o amd_l_1.o amd_i_2.o amd_l_2.o amd_i_postorder.o amd_l_postorder.o amd_i_post_tree.o amd_l_post_tree.o amd_i_defaults.o amd_l_defaults.o amd_i_order.o amd_l_order.o amd_i_control.o amd_l_control.o amd_i_info.o amd_l_info.o amd_i_valid.o amd_l_valid.o amd_i_preprocess.o amd_l_preprocess.o amd_i_dump.o amd_l_dump.o amd_i_global.o amd_l_global.o amd_i_aat.o: amd_aat.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDINT -c amd_aat.c -o $@ amd_i_1.o: amd_1.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDINT -c amd_1.c -o $@ amd_i_2.o: amd_2.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDINT -c amd_2.c -o $@ amd_i_postorder.o: amd_postorder.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDINT -c amd_postorder.c -o $@ amd_i_post_tree.o: amd_post_tree.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDINT -c amd_post_tree.c -o $@ amd_i_defaults.o: amd_defaults.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDINT -c amd_defaults.c -o $@ amd_i_order.o: amd_order.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDINT -c amd_order.c -o $@ amd_i_control.o: amd_control.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDINT -c amd_control.c -o $@ amd_i_info.o: amd_info.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDINT -c amd_info.c -o $@ amd_i_valid.o: amd_valid.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDINT -c amd_valid.c -o $@ amd_i_preprocess.o: amd_preprocess.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDINT -c amd_preprocess.c -o $@ amd_i_dump.o: amd_dump.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDINT -c amd_dump.c -o $@ amd_i_global.o: amd_global.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDINT -c amd_global.c -o $@ amd_l_aat.o: amd_aat.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c amd_aat.c -o $@ amd_l_1.o: amd_1.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c amd_1.c -o $@ amd_l_2.o: amd_2.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c amd_2.c -o $@ amd_l_postorder.o: amd_postorder.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c amd_postorder.c -o $@ amd_l_post_tree.o: amd_post_tree.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c amd_post_tree.c -o $@ amd_l_defaults.o: amd_defaults.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c amd_defaults.c -o $@ amd_l_order.o: amd_order.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c amd_order.c -o $@ amd_l_control.o: amd_control.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c amd_control.c -o $@ amd_l_info.o: amd_info.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c amd_info.c -o $@ amd_l_valid.o: amd_valid.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c amd_valid.c -o $@ amd_l_preprocess.o: amd_preprocess.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c amd_preprocess.c -o $@ amd_l_dump.o: amd_dump.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c amd_dump.c -o $@ amd_l_global.o: amd_global.c $(INC) $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c amd_global.c -o $@ Matrix/src/AMD/Source/amd_order.c0000644000175100001440000001337412271765436016311 0ustar hornikusers/* ========================================================================= */ /* === AMD_order =========================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* User-callable AMD minimum degree ordering routine. See amd.h for * documentation. */ #include "amd_internal.h" /* ========================================================================= */ /* === AMD_order =========================================================== */ /* ========================================================================= */ GLOBAL Int AMD_order ( Int n, const Int Ap [ ], const Int Ai [ ], Int P [ ], double Control [ ], double Info [ ] ) { Int *Len, *S, nz, i, *Pinv, info, status, *Rp, *Ri, *Cp, *Ci, ok ; size_t nzaat, slen ; double mem = 0 ; #ifndef NDEBUG AMD_debug_init ("amd") ; #endif /* clear the Info array, if it exists */ info = Info != (double *) NULL ; if (info) { for (i = 0 ; i < AMD_INFO ; i++) { Info [i] = EMPTY ; } Info [AMD_N] = n ; Info [AMD_STATUS] = AMD_OK ; } /* make sure inputs exist and n is >= 0 */ if (Ai == (Int *) NULL || Ap == (Int *) NULL || P == (Int *) NULL || n < 0) { if (info) Info [AMD_STATUS] = AMD_INVALID ; return (AMD_INVALID) ; /* arguments are invalid */ } if (n == 0) { return (AMD_OK) ; /* n is 0 so there's nothing to do */ } nz = Ap [n] ; if (info) { Info [AMD_NZ] = nz ; } if (nz < 0) { if (info) Info [AMD_STATUS] = AMD_INVALID ; return (AMD_INVALID) ; } /* check if n or nz will cause size_t overflow */ if (((size_t) n) >= SIZE_T_MAX / sizeof (Int) || ((size_t) nz) >= SIZE_T_MAX / sizeof (Int)) { if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; return (AMD_OUT_OF_MEMORY) ; /* problem too large */ } /* check the input matrix: AMD_OK, AMD_INVALID, or AMD_OK_BUT_JUMBLED */ status = AMD_valid (n, n, Ap, Ai) ; if (status == AMD_INVALID) { if (info) Info [AMD_STATUS] = AMD_INVALID ; return (AMD_INVALID) ; /* matrix is invalid */ } /* allocate two size-n integer workspaces */ Len = amd_malloc (n * sizeof (Int)) ; Pinv = amd_malloc (n * sizeof (Int)) ; mem += n ; mem += n ; if (!Len || !Pinv) { /* :: out of memory :: */ amd_free (Len) ; amd_free (Pinv) ; if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; return (AMD_OUT_OF_MEMORY) ; } if (status == AMD_OK_BUT_JUMBLED) { /* sort the input matrix and remove duplicate entries */ AMD_DEBUG1 (("Matrix is jumbled\n")) ; Rp = amd_malloc ((n+1) * sizeof (Int)) ; Ri = amd_malloc (MAX (nz,1) * sizeof (Int)) ; mem += (n+1) ; mem += MAX (nz,1) ; if (!Rp || !Ri) { /* :: out of memory :: */ amd_free (Rp) ; amd_free (Ri) ; amd_free (Len) ; amd_free (Pinv) ; if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; return (AMD_OUT_OF_MEMORY) ; } /* use Len and Pinv as workspace to create R = A' */ AMD_preprocess (n, Ap, Ai, Rp, Ri, Len, Pinv) ; Cp = Rp ; Ci = Ri ; } else { /* order the input matrix as-is. No need to compute R = A' first */ Rp = NULL ; Ri = NULL ; Cp = (Int *) Ap ; Ci = (Int *) Ai ; } /* --------------------------------------------------------------------- */ /* determine the symmetry and count off-diagonal nonzeros in A+A' */ /* --------------------------------------------------------------------- */ nzaat = AMD_aat (n, Cp, Ci, Len, P, Info) ; AMD_DEBUG1 (("nzaat: %g\n", (double) nzaat)) ; ASSERT ((MAX (nz-n, 0) <= nzaat) && (nzaat <= 2 * (size_t) nz)) ; /* --------------------------------------------------------------------- */ /* allocate workspace for matrix, elbow room, and 6 size-n vectors */ /* --------------------------------------------------------------------- */ S = NULL ; slen = nzaat ; /* space for matrix */ ok = ((slen + nzaat/5) >= slen) ; /* check for size_t overflow */ slen += nzaat/5 ; /* add elbow room */ for (i = 0 ; ok && i < 7 ; i++) { ok = ((slen + n) > slen) ; /* check for size_t overflow */ slen += n ; /* size-n elbow room, 6 size-n work */ } mem += slen ; ok = ok && (slen < SIZE_T_MAX / sizeof (Int)) ; /* check for overflow */ ok = ok && (slen < Int_MAX) ; /* S[i] for Int i must be OK */ if (ok) { S = amd_malloc (slen * sizeof (Int)) ; } AMD_DEBUG1 (("slen %g\n", (double) slen)) ; if (!S) { /* :: out of memory :: (or problem too large) */ amd_free (Rp) ; amd_free (Ri) ; amd_free (Len) ; amd_free (Pinv) ; if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; return (AMD_OUT_OF_MEMORY) ; } if (info) { /* memory usage, in bytes. */ Info [AMD_MEMORY] = mem * sizeof (Int) ; } /* --------------------------------------------------------------------- */ /* order the matrix */ /* --------------------------------------------------------------------- */ AMD_1 (n, Cp, Ci, P, Pinv, Len, slen, S, Control, Info) ; /* --------------------------------------------------------------------- */ /* free the workspace */ /* --------------------------------------------------------------------- */ amd_free (Rp) ; amd_free (Ri) ; amd_free (Len) ; amd_free (Pinv) ; amd_free (S) ; if (info) Info [AMD_STATUS] = status ; return (status) ; /* successful ordering */ } Matrix/src/AMD/Source/amd_dump.c0000644000175100001440000001162412271765436016137 0ustar hornikusers/* ========================================================================= */ /* === AMD_dump ============================================================ */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* Debugging routines for AMD. Not used if NDEBUG is not defined at compile- * time (the default). See comments in amd_internal.h on how to enable * debugging. Not user-callable. */ #include "amd_internal.h" #ifndef NDEBUG /* This global variable is present only when debugging */ GLOBAL Int AMD_debug = -999 ; /* default is no debug printing */ /* ========================================================================= */ /* === AMD_debug_init ====================================================== */ /* ========================================================================= */ /* Sets the debug print level, by reading the file debug.amd (if it exists) */ GLOBAL void AMD_debug_init ( char *s ) { FILE *f ; f = fopen ("debug.amd", "r") ; if (f == (FILE *) NULL) { AMD_debug = -999 ; } else { fscanf (f, ID, &AMD_debug) ; fclose (f) ; } if (AMD_debug >= 0) { printf ("%s: AMD_debug_init, D= "ID"\n", s, AMD_debug) ; } } /* ========================================================================= */ /* === AMD_dump ============================================================ */ /* ========================================================================= */ /* Dump AMD's data structure, except for the hash buckets. This routine * cannot be called when the hash buckets are non-empty. */ GLOBAL void AMD_dump ( Int n, /* A is n-by-n */ Int Pe [ ], /* pe [0..n-1]: index in iw of start of row i */ Int Iw [ ], /* workspace of size iwlen, iwlen [0..pfree-1] * holds the matrix on input */ Int Len [ ], /* len [0..n-1]: length for row i */ Int iwlen, /* length of iw */ Int pfree, /* iw [pfree ... iwlen-1] is empty on input */ Int Nv [ ], /* nv [0..n-1] */ Int Next [ ], /* next [0..n-1] */ Int Last [ ], /* last [0..n-1] */ Int Head [ ], /* head [0..n-1] */ Int Elen [ ], /* size n */ Int Degree [ ], /* size n */ Int W [ ], /* size n */ Int nel ) { Int i, pe, elen, nv, len, e, p, k, j, deg, w, cnt, ilast ; if (AMD_debug < 0) return ; ASSERT (pfree <= iwlen) ; AMD_DEBUG3 (("\nAMD dump, pfree: "ID"\n", pfree)) ; for (i = 0 ; i < n ; i++) { pe = Pe [i] ; elen = Elen [i] ; nv = Nv [i] ; len = Len [i] ; w = W [i] ; if (elen >= EMPTY) { if (nv == 0) { AMD_DEBUG3 (("\nI "ID": nonprincipal: ", i)) ; ASSERT (elen == EMPTY) ; if (pe == EMPTY) { AMD_DEBUG3 ((" dense node\n")) ; ASSERT (w == 1) ; } else { ASSERT (pe < EMPTY) ; AMD_DEBUG3 ((" i "ID" -> parent "ID"\n", i, FLIP (Pe[i]))); } } else { AMD_DEBUG3 (("\nI "ID": active principal supervariable:\n",i)); AMD_DEBUG3 ((" nv(i): "ID" Flag: %d\n", nv, (nv < 0))) ; ASSERT (elen >= 0) ; ASSERT (nv > 0 && pe >= 0) ; p = pe ; AMD_DEBUG3 ((" e/s: ")) ; if (elen == 0) AMD_DEBUG3 ((" : ")) ; ASSERT (pe + len <= pfree) ; for (k = 0 ; k < len ; k++) { j = Iw [p] ; AMD_DEBUG3 ((" "ID"", j)) ; ASSERT (j >= 0 && j < n) ; if (k == elen-1) AMD_DEBUG3 ((" : ")) ; p++ ; } AMD_DEBUG3 (("\n")) ; } } else { e = i ; if (w == 0) { AMD_DEBUG3 (("\nE "ID": absorbed element: w "ID"\n", e, w)) ; ASSERT (nv > 0 && pe < 0) ; AMD_DEBUG3 ((" e "ID" -> parent "ID"\n", e, FLIP (Pe [e]))) ; } else { AMD_DEBUG3 (("\nE "ID": unabsorbed element: w "ID"\n", e, w)) ; ASSERT (nv > 0 && pe >= 0) ; p = pe ; AMD_DEBUG3 ((" : ")) ; ASSERT (pe + len <= pfree) ; for (k = 0 ; k < len ; k++) { j = Iw [p] ; AMD_DEBUG3 ((" "ID"", j)) ; ASSERT (j >= 0 && j < n) ; p++ ; } AMD_DEBUG3 (("\n")) ; } } } /* this routine cannot be called when the hash buckets are non-empty */ AMD_DEBUG3 (("\nDegree lists:\n")) ; if (nel >= 0) { cnt = 0 ; for (deg = 0 ; deg < n ; deg++) { if (Head [deg] == EMPTY) continue ; ilast = EMPTY ; AMD_DEBUG3 ((ID": \n", deg)) ; for (i = Head [deg] ; i != EMPTY ; i = Next [i]) { AMD_DEBUG3 ((" "ID" : next "ID" last "ID" deg "ID"\n", i, Next [i], Last [i], Degree [i])) ; ASSERT (i >= 0 && i < n && ilast == Last [i] && deg == Degree [i]) ; cnt += Nv [i] ; ilast = i ; } AMD_DEBUG3 (("\n")) ; } ASSERT (cnt == n - nel) ; } } #endif Matrix/src/AMD/Source/amd_defaults.c0000644000175100001440000000234512271765436017001 0ustar hornikusers/* ========================================================================= */ /* === AMD_defaults ======================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* User-callable. Sets default control parameters for AMD. See amd.h * for details. */ #include "amd_internal.h" /* ========================================================================= */ /* === AMD defaults ======================================================== */ /* ========================================================================= */ GLOBAL void AMD_defaults ( double Control [ ] ) { Int i ; if (Control != (double *) NULL) { for (i = 0 ; i < AMD_CONTROL ; i++) { Control [i] = 0 ; } Control [AMD_DENSE] = AMD_DEFAULT_DENSE ; Control [AMD_AGGRESSIVE] = AMD_DEFAULT_AGGRESSIVE ; } } Matrix/src/AMD/Source/amd_valid.c0000644000175100001440000000564412271765436016276 0ustar hornikusers/* ========================================================================= */ /* === AMD_valid =========================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* Check if a column-form matrix is valid or not. The matrix A is * n_row-by-n_col. The row indices of entries in column j are in * Ai [Ap [j] ... Ap [j+1]-1]. Required conditions are: * * n_row >= 0 * n_col >= 0 * nz = Ap [n_col] >= 0 number of entries in the matrix * Ap [0] == 0 * Ap [j] <= Ap [j+1] for all j in the range 0 to n_col. * Ai [0 ... nz-1] must be in the range 0 to n_row-1. * * If any of the above conditions hold, AMD_INVALID is returned. If the * following condition holds, AMD_OK_BUT_JUMBLED is returned (a warning, * not an error): * * row indices in Ai [Ap [j] ... Ap [j+1]-1] are not sorted in ascending * order, and/or duplicate entries exist. * * Otherwise, AMD_OK is returned. * * In v1.2 and earlier, this function returned TRUE if the matrix was valid * (now returns AMD_OK), or FALSE otherwise (now returns AMD_INVALID or * AMD_OK_BUT_JUMBLED). */ #include "amd_internal.h" GLOBAL Int AMD_valid ( /* inputs, not modified on output: */ Int n_row, /* A is n_row-by-n_col */ Int n_col, const Int Ap [ ], /* column pointers of A, of size n_col+1 */ const Int Ai [ ] /* row indices of A, of size nz = Ap [n_col] */ ) { Int nz, j, p1, p2, ilast, i, p, result = AMD_OK ; if (n_row < 0 || n_col < 0 || Ap == NULL || Ai == NULL) { return (AMD_INVALID) ; } nz = Ap [n_col] ; if (Ap [0] != 0 || nz < 0) { /* column pointers must start at Ap [0] = 0, and Ap [n] must be >= 0 */ AMD_DEBUG0 (("column 0 pointer bad or nz < 0\n")) ; return (AMD_INVALID) ; } for (j = 0 ; j < n_col ; j++) { p1 = Ap [j] ; p2 = Ap [j+1] ; AMD_DEBUG2 (("\nColumn: "ID" p1: "ID" p2: "ID"\n", j, p1, p2)) ; if (p1 > p2) { /* column pointers must be ascending */ AMD_DEBUG0 (("column "ID" pointer bad\n", j)) ; return (AMD_INVALID) ; } ilast = EMPTY ; for (p = p1 ; p < p2 ; p++) { i = Ai [p] ; AMD_DEBUG3 (("row: "ID"\n", i)) ; if (i < 0 || i >= n_row) { /* row index out of range */ AMD_DEBUG0 (("index out of range, col "ID" row "ID"\n", j, i)); return (AMD_INVALID) ; } if (i <= ilast) { /* row index unsorted, or duplicate entry present */ AMD_DEBUG1 (("index unsorted/dupl col "ID" row "ID"\n", j, i)); result = AMD_OK_BUT_JUMBLED ; } ilast = i ; } } return (result) ; } Matrix/src/AMD/Source/amd_1.c0000644000175100001440000001311612271765436015330 0ustar hornikusers/* ========================================================================= */ /* === AMD_1 =============================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* AMD_1: Construct A+A' for a sparse matrix A and perform the AMD ordering. * * The n-by-n sparse matrix A can be unsymmetric. It is stored in MATLAB-style * compressed-column form, with sorted row indices in each column, and no * duplicate entries. Diagonal entries may be present, but they are ignored. * Row indices of column j of A are stored in Ai [Ap [j] ... Ap [j+1]-1]. * Ap [0] must be zero, and nz = Ap [n] is the number of entries in A. The * size of the matrix, n, must be greater than or equal to zero. * * This routine must be preceded by a call to AMD_aat, which computes the * number of entries in each row/column in A+A', excluding the diagonal. * Len [j], on input, is the number of entries in row/column j of A+A'. This * routine constructs the matrix A+A' and then calls AMD_2. No error checking * is performed (this was done in AMD_valid). */ #include "amd_internal.h" GLOBAL void AMD_1 ( Int n, /* n > 0 */ const Int Ap [ ], /* input of size n+1, not modified */ const Int Ai [ ], /* input of size nz = Ap [n], not modified */ Int P [ ], /* size n output permutation */ Int Pinv [ ], /* size n output inverse permutation */ Int Len [ ], /* size n input, undefined on output */ Int slen, /* slen >= sum (Len [0..n-1]) + 7n, * ideally slen = 1.2 * sum (Len) + 8n */ Int S [ ], /* size slen workspace */ double Control [ ], /* input array of size AMD_CONTROL */ double Info [ ] /* output array of size AMD_INFO */ ) { Int i, j, k, p, pfree, iwlen, pj, p1, p2, pj2, *Iw, *Pe, *Nv, *Head, *Elen, *Degree, *s, *W, *Sp, *Tp ; /* --------------------------------------------------------------------- */ /* construct the matrix for AMD_2 */ /* --------------------------------------------------------------------- */ ASSERT (n > 0) ; iwlen = slen - 6*n ; s = S ; Pe = s ; s += n ; Nv = s ; s += n ; Head = s ; s += n ; Elen = s ; s += n ; Degree = s ; s += n ; W = s ; s += n ; Iw = s ; s += iwlen ; ASSERT (AMD_valid (n, n, Ap, Ai) == AMD_OK) ; /* construct the pointers for A+A' */ Sp = Nv ; /* use Nv and W as workspace for Sp and Tp [ */ Tp = W ; pfree = 0 ; for (j = 0 ; j < n ; j++) { Pe [j] = pfree ; Sp [j] = pfree ; pfree += Len [j] ; } /* Note that this restriction on iwlen is slightly more restrictive than * what is strictly required in AMD_2. AMD_2 can operate with no elbow * room at all, but it will be very slow. For better performance, at * least size-n elbow room is enforced. */ ASSERT (iwlen >= pfree + n) ; #ifndef NDEBUG for (p = 0 ; p < iwlen ; p++) Iw [p] = EMPTY ; #endif for (k = 0 ; k < n ; k++) { AMD_DEBUG1 (("Construct row/column k= "ID" of A+A'\n", k)) ; p1 = Ap [k] ; p2 = Ap [k+1] ; /* construct A+A' */ for (p = p1 ; p < p2 ; ) { /* scan the upper triangular part of A */ j = Ai [p] ; ASSERT (j >= 0 && j < n) ; if (j < k) { /* entry A (j,k) in the strictly upper triangular part */ ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ; ASSERT (Sp [k] < (k == n-1 ? pfree : Pe [k+1])) ; Iw [Sp [j]++] = k ; Iw [Sp [k]++] = j ; p++ ; } else if (j == k) { /* skip the diagonal */ p++ ; break ; } else /* j > k */ { /* first entry below the diagonal */ break ; } /* scan lower triangular part of A, in column j until reaching * row k. Start where last scan left off. */ ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ; pj2 = Ap [j+1] ; for (pj = Tp [j] ; pj < pj2 ; ) { i = Ai [pj] ; ASSERT (i >= 0 && i < n) ; if (i < k) { /* A (i,j) is only in the lower part, not in upper */ ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ; ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ; Iw [Sp [i]++] = j ; Iw [Sp [j]++] = i ; pj++ ; } else if (i == k) { /* entry A (k,j) in lower part and A (j,k) in upper */ pj++ ; break ; } else /* i > k */ { /* consider this entry later, when k advances to i */ break ; } } Tp [j] = pj ; } Tp [k] = p ; } /* clean up, for remaining mismatched entries */ for (j = 0 ; j < n ; j++) { for (pj = Tp [j] ; pj < Ap [j+1] ; pj++) { i = Ai [pj] ; ASSERT (i >= 0 && i < n) ; /* A (i,j) is only in the lower part, not in upper */ ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ; ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ; Iw [Sp [i]++] = j ; Iw [Sp [j]++] = i ; } } #ifndef NDEBUG for (j = 0 ; j < n-1 ; j++) ASSERT (Sp [j] == Pe [j+1]) ; ASSERT (Sp [n-1] == pfree) ; #endif /* Tp and Sp no longer needed ] */ /* --------------------------------------------------------------------- */ /* order the matrix */ /* --------------------------------------------------------------------- */ AMD_2 (n, Pe, Iw, Len, iwlen, pfree, Nv, Pinv, P, Head, Elen, Degree, W, Control, Info) ; } Matrix/src/AMD/Source/amd_2.c0000644000175100001440000017647112271765436015347 0ustar hornikusers/* ========================================================================= */ /* === AMD_2 =============================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* AMD_2: performs the AMD ordering on a symmetric sparse matrix A, followed * by a postordering (via depth-first search) of the assembly tree using the * AMD_postorder routine. */ #include "amd_internal.h" /* ========================================================================= */ /* === clear_flag ========================================================== */ /* ========================================================================= */ static Int clear_flag (Int wflg, Int wbig, Int W [ ], Int n) { Int x ; if (wflg < 2 || wflg >= wbig) { for (x = 0 ; x < n ; x++) { if (W [x] != 0) W [x] = 1 ; } wflg = 2 ; } /* at this point, W [0..n-1] < wflg holds */ return (wflg) ; } /* ========================================================================= */ /* === AMD_2 =============================================================== */ /* ========================================================================= */ GLOBAL void AMD_2 ( Int n, /* A is n-by-n, where n > 0 */ Int Pe [ ], /* Pe [0..n-1]: index in Iw of row i on input */ Int Iw [ ], /* workspace of size iwlen. Iw [0..pfree-1] * holds the matrix on input */ Int Len [ ], /* Len [0..n-1]: length for row/column i on input */ Int iwlen, /* length of Iw. iwlen >= pfree + n */ Int pfree, /* Iw [pfree ... iwlen-1] is empty on input */ /* 7 size-n workspaces, not defined on input: */ Int Nv [ ], /* the size of each supernode on output */ Int Next [ ], /* the output inverse permutation */ Int Last [ ], /* the output permutation */ Int Head [ ], Int Elen [ ], /* the size columns of L for each supernode */ Int Degree [ ], Int W [ ], /* control parameters and output statistics */ double Control [ ], /* array of size AMD_CONTROL */ double Info [ ] /* array of size AMD_INFO */ ) { /* * Given a representation of the nonzero pattern of a symmetric matrix, A, * (excluding the diagonal) perform an approximate minimum (UMFPACK/MA38-style) * degree ordering to compute a pivot order such that the introduction of * nonzeros (fill-in) in the Cholesky factors A = LL' is kept low. At each * step, the pivot selected is the one with the minimum UMFAPACK/MA38-style * upper-bound on the external degree. This routine can optionally perform * aggresive absorption (as done by MC47B in the Harwell Subroutine * Library). * * The approximate degree algorithm implemented here is the symmetric analog of * the degree update algorithm in MA38 and UMFPACK (the Unsymmetric-pattern * MultiFrontal PACKage, both by Davis and Duff). The routine is based on the * MA27 minimum degree ordering algorithm by Iain Duff and John Reid. * * This routine is a translation of the original AMDBAR and MC47B routines, * in Fortran, with the following modifications: * * (1) dense rows/columns are removed prior to ordering the matrix, and placed * last in the output order. The presence of a dense row/column can * increase the ordering time by up to O(n^2), unless they are removed * prior to ordering. * * (2) the minimum degree ordering is followed by a postordering (depth-first * search) of the assembly tree. Note that mass elimination (discussed * below) combined with the approximate degree update can lead to the mass * elimination of nodes with lower exact degree than the current pivot * element. No additional fill-in is caused in the representation of the * Schur complement. The mass-eliminated nodes merge with the current * pivot element. They are ordered prior to the current pivot element. * Because they can have lower exact degree than the current element, the * merger of two or more of these nodes in the current pivot element can * lead to a single element that is not a "fundamental supernode". The * diagonal block can have zeros in it. Thus, the assembly tree used here * is not guaranteed to be the precise supernodal elemination tree (with * "funadmental" supernodes), and the postordering performed by this * routine is not guaranteed to be a precise postordering of the * elimination tree. * * (3) input parameters are added, to control aggressive absorption and the * detection of "dense" rows/columns of A. * * (4) additional statistical information is returned, such as the number of * nonzeros in L, and the flop counts for subsequent LDL' and LU * factorizations. These are slight upper bounds, because of the mass * elimination issue discussed above. * * (5) additional routines are added to interface this routine to MATLAB * to provide a simple C-callable user-interface, to check inputs for * errors, compute the symmetry of the pattern of A and the number of * nonzeros in each row/column of A+A', to compute the pattern of A+A', * to perform the assembly tree postordering, and to provide debugging * ouput. Many of these functions are also provided by the Fortran * Harwell Subroutine Library routine MC47A. * * (6) both int and SuiteSparse_long versions are provided. In the * descriptions below and integer is and int or SuiteSparse_long depending * on which version is being used. ********************************************************************** ***** CAUTION: ARGUMENTS ARE NOT CHECKED FOR ERRORS ON INPUT. ****** ********************************************************************** ** If you want error checking, a more versatile input format, and a ** ** simpler user interface, use amd_order or amd_l_order instead. ** ** This routine is not meant to be user-callable. ** ********************************************************************** * ---------------------------------------------------------------------------- * References: * ---------------------------------------------------------------------------- * * [1] Timothy A. Davis and Iain Duff, "An unsymmetric-pattern multifrontal * method for sparse LU factorization", SIAM J. Matrix Analysis and * Applications, vol. 18, no. 1, pp. 140-158. Discusses UMFPACK / MA38, * which first introduced the approximate minimum degree used by this * routine. * * [2] Patrick Amestoy, Timothy A. Davis, and Iain S. Duff, "An approximate * minimum degree ordering algorithm," SIAM J. Matrix Analysis and * Applications, vol. 17, no. 4, pp. 886-905, 1996. Discusses AMDBAR and * MC47B, which are the Fortran versions of this routine. * * [3] Alan George and Joseph Liu, "The evolution of the minimum degree * ordering algorithm," SIAM Review, vol. 31, no. 1, pp. 1-19, 1989. * We list below the features mentioned in that paper that this code * includes: * * mass elimination: * Yes. MA27 relied on supervariable detection for mass elimination. * * indistinguishable nodes: * Yes (we call these "supervariables"). This was also in the MA27 * code - although we modified the method of detecting them (the * previous hash was the true degree, which we no longer keep track * of). A supervariable is a set of rows with identical nonzero * pattern. All variables in a supervariable are eliminated together. * Each supervariable has as its numerical name that of one of its * variables (its principal variable). * * quotient graph representation: * Yes. We use the term "element" for the cliques formed during * elimination. This was also in the MA27 code. The algorithm can * operate in place, but it will work more efficiently if given some * "elbow room." * * element absorption: * Yes. This was also in the MA27 code. * * external degree: * Yes. The MA27 code was based on the true degree. * * incomplete degree update and multiple elimination: * No. This was not in MA27, either. Our method of degree update * within MC47B is element-based, not variable-based. It is thus * not well-suited for use with incomplete degree update or multiple * elimination. * * Authors, and Copyright (C) 2004 by: * Timothy A. Davis, Patrick Amestoy, Iain S. Duff, John K. Reid. * * Acknowledgements: This work (and the UMFPACK package) was supported by the * National Science Foundation (ASC-9111263, DMS-9223088, and CCR-0203270). * The UMFPACK/MA38 approximate degree update algorithm, the unsymmetric analog * which forms the basis of AMD, was developed while Tim Davis was supported by * CERFACS (Toulouse, France) in a post-doctoral position. This C version, and * the etree postorder, were written while Tim Davis was on sabbatical at * Stanford University and Lawrence Berkeley National Laboratory. * ---------------------------------------------------------------------------- * INPUT ARGUMENTS (unaltered): * ---------------------------------------------------------------------------- * n: The matrix order. Restriction: n >= 1. * * iwlen: The size of the Iw array. On input, the matrix is stored in * Iw [0..pfree-1]. However, Iw [0..iwlen-1] should be slightly larger * than what is required to hold the matrix, at least iwlen >= pfree + n. * Otherwise, excessive compressions will take place. The recommended * value of iwlen is 1.2 * pfree + n, which is the value used in the * user-callable interface to this routine (amd_order.c). The algorithm * will not run at all if iwlen < pfree. Restriction: iwlen >= pfree + n. * Note that this is slightly more restrictive than the actual minimum * (iwlen >= pfree), but AMD_2 will be very slow with no elbow room. * Thus, this routine enforces a bare minimum elbow room of size n. * * pfree: On input the tail end of the array, Iw [pfree..iwlen-1], is empty, * and the matrix is stored in Iw [0..pfree-1]. During execution, * additional data is placed in Iw, and pfree is modified so that * Iw [pfree..iwlen-1] is always the unused part of Iw. * * Control: A double array of size AMD_CONTROL containing input parameters * that affect how the ordering is computed. If NULL, then default * settings are used. * * Control [AMD_DENSE] is used to determine whether or not a given input * row is "dense". A row is "dense" if the number of entries in the row * exceeds Control [AMD_DENSE] times sqrt (n), except that rows with 16 or * fewer entries are never considered "dense". To turn off the detection * of dense rows, set Control [AMD_DENSE] to a negative number, or to a * number larger than sqrt (n). The default value of Control [AMD_DENSE] * is AMD_DEFAULT_DENSE, which is defined in amd.h as 10. * * Control [AMD_AGGRESSIVE] is used to determine whether or not aggressive * absorption is to be performed. If nonzero, then aggressive absorption * is performed (this is the default). * ---------------------------------------------------------------------------- * INPUT/OUPUT ARGUMENTS: * ---------------------------------------------------------------------------- * * Pe: An integer array of size n. On input, Pe [i] is the index in Iw of * the start of row i. Pe [i] is ignored if row i has no off-diagonal * entries. Thus Pe [i] must be in the range 0 to pfree-1 for non-empty * rows. * * During execution, it is used for both supervariables and elements: * * Principal supervariable i: index into Iw of the description of * supervariable i. A supervariable represents one or more rows of * the matrix with identical nonzero pattern. In this case, * Pe [i] >= 0. * * Non-principal supervariable i: if i has been absorbed into another * supervariable j, then Pe [i] = FLIP (j), where FLIP (j) is defined * as (-(j)-2). Row j has the same pattern as row i. Note that j * might later be absorbed into another supervariable j2, in which * case Pe [i] is still FLIP (j), and Pe [j] = FLIP (j2) which is * < EMPTY, where EMPTY is defined as (-1) in amd_internal.h. * * Unabsorbed element e: the index into Iw of the description of element * e, if e has not yet been absorbed by a subsequent element. Element * e is created when the supervariable of the same name is selected as * the pivot. In this case, Pe [i] >= 0. * * Absorbed element e: if element e is absorbed into element e2, then * Pe [e] = FLIP (e2). This occurs when the pattern of e (which we * refer to as Le) is found to be a subset of the pattern of e2 (that * is, Le2). In this case, Pe [i] < EMPTY. If element e is "null" * (it has no nonzeros outside its pivot block), then Pe [e] = EMPTY, * and e is the root of an assembly subtree (or the whole tree if * there is just one such root). * * Dense variable i: if i is "dense", then Pe [i] = EMPTY. * * On output, Pe holds the assembly tree/forest, which implicitly * represents a pivot order with identical fill-in as the actual order * (via a depth-first search of the tree), as follows. If Nv [i] > 0, * then i represents a node in the assembly tree, and the parent of i is * Pe [i], or EMPTY if i is a root. If Nv [i] = 0, then (i, Pe [i]) * represents an edge in a subtree, the root of which is a node in the * assembly tree. Note that i refers to a row/column in the original * matrix, not the permuted matrix. * * Info: A double array of size AMD_INFO. If present, (that is, not NULL), * then statistics about the ordering are returned in the Info array. * See amd.h for a description. * ---------------------------------------------------------------------------- * INPUT/MODIFIED (undefined on output): * ---------------------------------------------------------------------------- * * Len: An integer array of size n. On input, Len [i] holds the number of * entries in row i of the matrix, excluding the diagonal. The contents * of Len are undefined on output. * * Iw: An integer array of size iwlen. On input, Iw [0..pfree-1] holds the * description of each row i in the matrix. The matrix must be symmetric, * and both upper and lower triangular parts must be present. The * diagonal must not be present. Row i is held as follows: * * Len [i]: the length of the row i data structure in the Iw array. * Iw [Pe [i] ... Pe [i] + Len [i] - 1]: * the list of column indices for nonzeros in row i (simple * supervariables), excluding the diagonal. All supervariables * start with one row/column each (supervariable i is just row i). * If Len [i] is zero on input, then Pe [i] is ignored on input. * * Note that the rows need not be in any particular order, and there * may be empty space between the rows. * * During execution, the supervariable i experiences fill-in. This is * represented by placing in i a list of the elements that cause fill-in * in supervariable i: * * Len [i]: the length of supervariable i in the Iw array. * Iw [Pe [i] ... Pe [i] + Elen [i] - 1]: * the list of elements that contain i. This list is kept short * by removing absorbed elements. * Iw [Pe [i] + Elen [i] ... Pe [i] + Len [i] - 1]: * the list of supervariables in i. This list is kept short by * removing nonprincipal variables, and any entry j that is also * contained in at least one of the elements (j in Le) in the list * for i (e in row i). * * When supervariable i is selected as pivot, we create an element e of * the same name (e=i): * * Len [e]: the length of element e in the Iw array. * Iw [Pe [e] ... Pe [e] + Len [e] - 1]: * the list of supervariables in element e. * * An element represents the fill-in that occurs when supervariable i is * selected as pivot (which represents the selection of row i and all * non-principal variables whose principal variable is i). We use the * term Le to denote the set of all supervariables in element e. Absorbed * supervariables and elements are pruned from these lists when * computationally convenient. * * CAUTION: THE INPUT MATRIX IS OVERWRITTEN DURING COMPUTATION. * The contents of Iw are undefined on output. * ---------------------------------------------------------------------------- * OUTPUT (need not be set on input): * ---------------------------------------------------------------------------- * * Nv: An integer array of size n. During execution, ABS (Nv [i]) is equal to * the number of rows that are represented by the principal supervariable * i. If i is a nonprincipal or dense variable, then Nv [i] = 0. * Initially, Nv [i] = 1 for all i. Nv [i] < 0 signifies that i is a * principal variable in the pattern Lme of the current pivot element me. * After element me is constructed, Nv [i] is set back to a positive * value. * * On output, Nv [i] holds the number of pivots represented by super * row/column i of the original matrix, or Nv [i] = 0 for non-principal * rows/columns. Note that i refers to a row/column in the original * matrix, not the permuted matrix. * * Elen: An integer array of size n. See the description of Iw above. At the * start of execution, Elen [i] is set to zero for all rows i. During * execution, Elen [i] is the number of elements in the list for * supervariable i. When e becomes an element, Elen [e] = FLIP (esize) is * set, where esize is the size of the element (the number of pivots, plus * the number of nonpivotal entries). Thus Elen [e] < EMPTY. * Elen (i) = EMPTY set when variable i becomes nonprincipal. * * For variables, Elen (i) >= EMPTY holds until just before the * postordering and permutation vectors are computed. For elements, * Elen [e] < EMPTY holds. * * On output, Elen [i] is the degree of the row/column in the Cholesky * factorization of the permuted matrix, corresponding to the original row * i, if i is a super row/column. It is equal to EMPTY if i is * non-principal. Note that i refers to a row/column in the original * matrix, not the permuted matrix. * * Note that the contents of Elen on output differ from the Fortran * version (Elen holds the inverse permutation in the Fortran version, * which is instead returned in the Next array in this C version, * described below). * * Last: In a degree list, Last [i] is the supervariable preceding i, or EMPTY * if i is the head of the list. In a hash bucket, Last [i] is the hash * key for i. * * Last [Head [hash]] is also used as the head of a hash bucket if * Head [hash] contains a degree list (see the description of Head, * below). * * On output, Last [0..n-1] holds the permutation. That is, if * i = Last [k], then row i is the kth pivot row (where k ranges from 0 to * n-1). Row Last [k] of A is the kth row in the permuted matrix, PAP'. * * Next: Next [i] is the supervariable following i in a link list, or EMPTY if * i is the last in the list. Used for two kinds of lists: degree lists * and hash buckets (a supervariable can be in only one kind of list at a * time). * * On output Next [0..n-1] holds the inverse permutation. That is, if * k = Next [i], then row i is the kth pivot row. Row i of A appears as * the (Next[i])-th row in the permuted matrix, PAP'. * * Note that the contents of Next on output differ from the Fortran * version (Next is undefined on output in the Fortran version). * ---------------------------------------------------------------------------- * LOCAL WORKSPACE (not input or output - used only during execution): * ---------------------------------------------------------------------------- * * Degree: An integer array of size n. If i is a supervariable, then * Degree [i] holds the current approximation of the external degree of * row i (an upper bound). The external degree is the number of nonzeros * in row i, minus ABS (Nv [i]), the diagonal part. The bound is equal to * the exact external degree if Elen [i] is less than or equal to two. * * We also use the term "external degree" for elements e to refer to * |Le \ Lme|. If e is an element, then Degree [e] is |Le|, which is the * degree of the off-diagonal part of the element e (not including the * diagonal part). * * Head: An integer array of size n. Head is used for degree lists. * Head [deg] is the first supervariable in a degree list. All * supervariables i in a degree list Head [deg] have the same approximate * degree, namely, deg = Degree [i]. If the list Head [deg] is empty then * Head [deg] = EMPTY. * * During supervariable detection Head [hash] also serves as a pointer to * a hash bucket. If Head [hash] >= 0, there is a degree list of degree * hash. The hash bucket head pointer is Last [Head [hash]]. If * Head [hash] = EMPTY, then the degree list and hash bucket are both * empty. If Head [hash] < EMPTY, then the degree list is empty, and * FLIP (Head [hash]) is the head of the hash bucket. After supervariable * detection is complete, all hash buckets are empty, and the * (Last [Head [hash]] = EMPTY) condition is restored for the non-empty * degree lists. * * W: An integer array of size n. The flag array W determines the status of * elements and variables, and the external degree of elements. * * for elements: * if W [e] = 0, then the element e is absorbed. * if W [e] >= wflg, then W [e] - wflg is the size of the set * |Le \ Lme|, in terms of nonzeros (the sum of ABS (Nv [i]) for * each principal variable i that is both in the pattern of * element e and NOT in the pattern of the current pivot element, * me). * if wflg > W [e] > 0, then e is not absorbed and has not yet been * seen in the scan of the element lists in the computation of * |Le\Lme| in Scan 1 below. * * for variables: * during supervariable detection, if W [j] != wflg then j is * not in the pattern of variable i. * * The W array is initialized by setting W [i] = 1 for all i, and by * setting wflg = 2. It is reinitialized if wflg becomes too large (to * ensure that wflg+n does not cause integer overflow). * ---------------------------------------------------------------------------- * LOCAL INTEGERS: * ---------------------------------------------------------------------------- */ Int deg, degme, dext, lemax, e, elenme, eln, i, ilast, inext, j, jlast, jnext, k, knt1, knt2, knt3, lenj, ln, me, mindeg, nel, nleft, nvi, nvj, nvpiv, slenme, wbig, we, wflg, wnvi, ok, ndense, ncmpa, dense, aggressive ; unsigned Int hash ; /* unsigned, so that hash % n is well defined.*/ /* * deg: the degree of a variable or element * degme: size, |Lme|, of the current element, me (= Degree [me]) * dext: external degree, |Le \ Lme|, of some element e * lemax: largest |Le| seen so far (called dmax in Fortran version) * e: an element * elenme: the length, Elen [me], of element list of pivotal variable * eln: the length, Elen [...], of an element list * hash: the computed value of the hash function * i: a supervariable * ilast: the entry in a link list preceding i * inext: the entry in a link list following i * j: a supervariable * jlast: the entry in a link list preceding j * jnext: the entry in a link list, or path, following j * k: the pivot order of an element or variable * knt1: loop counter used during element construction * knt2: loop counter used during element construction * knt3: loop counter used during compression * lenj: Len [j] * ln: length of a supervariable list * me: current supervariable being eliminated, and the current * element created by eliminating that supervariable * mindeg: current minimum degree * nel: number of pivots selected so far * nleft: n - nel, the number of nonpivotal rows/columns remaining * nvi: the number of variables in a supervariable i (= Nv [i]) * nvj: the number of variables in a supervariable j (= Nv [j]) * nvpiv: number of pivots in current element * slenme: number of variables in variable list of pivotal variable * wbig: = (INT_MAX - n) for the int version, (SuiteSparse_long_max - n) * for the SuiteSparse_long version. wflg is not allowed to * be >= wbig. * we: W [e] * wflg: used for flagging the W array. See description of Iw. * wnvi: wflg - Nv [i] * x: either a supervariable or an element * * ok: true if supervariable j can be absorbed into i * ndense: number of "dense" rows/columns * dense: rows/columns with initial degree > dense are considered "dense" * aggressive: true if aggressive absorption is being performed * ncmpa: number of garbage collections * ---------------------------------------------------------------------------- * LOCAL DOUBLES, used for statistical output only (except for alpha): * ---------------------------------------------------------------------------- */ double f, r, ndiv, s, nms_lu, nms_ldl, dmax, alpha, lnz, lnzme ; /* * f: nvpiv * r: degme + nvpiv * ndiv: number of divisions for LU or LDL' factorizations * s: number of multiply-subtract pairs for LU factorization, for the * current element me * nms_lu number of multiply-subtract pairs for LU factorization * nms_ldl number of multiply-subtract pairs for LDL' factorization * dmax: the largest number of entries in any column of L, including the * diagonal * alpha: "dense" degree ratio * lnz: the number of nonzeros in L (excluding the diagonal) * lnzme: the number of nonzeros in L (excl. the diagonal) for the * current element me * ---------------------------------------------------------------------------- * LOCAL "POINTERS" (indices into the Iw array) * ---------------------------------------------------------------------------- */ Int p, p1, p2, p3, p4, pdst, pend, pj, pme, pme1, pme2, pn, psrc ; /* * Any parameter (Pe [...] or pfree) or local variable starting with "p" (for * Pointer) is an index into Iw, and all indices into Iw use variables starting * with "p." The only exception to this rule is the iwlen input argument. * * p: pointer into lots of things * p1: Pe [i] for some variable i (start of element list) * p2: Pe [i] + Elen [i] - 1 for some variable i * p3: index of first supervariable in clean list * p4: * pdst: destination pointer, for compression * pend: end of memory to compress * pj: pointer into an element or variable * pme: pointer into the current element (pme1...pme2) * pme1: the current element, me, is stored in Iw [pme1...pme2] * pme2: the end of the current element * pn: pointer into a "clean" variable, also used to compress * psrc: source pointer, for compression */ /* ========================================================================= */ /* INITIALIZATIONS */ /* ========================================================================= */ /* Note that this restriction on iwlen is slightly more restrictive than * what is actually required in AMD_2. AMD_2 can operate with no elbow * room at all, but it will be slow. For better performance, at least * size-n elbow room is enforced. */ ASSERT (iwlen >= pfree + n) ; ASSERT (n > 0) ; /* initialize output statistics */ lnz = 0 ; ndiv = 0 ; nms_lu = 0 ; nms_ldl = 0 ; dmax = 1 ; me = EMPTY ; mindeg = 0 ; ncmpa = 0 ; nel = 0 ; lemax = 0 ; /* get control parameters */ if (Control != (double *) NULL) { alpha = Control [AMD_DENSE] ; aggressive = (Control [AMD_AGGRESSIVE] != 0) ; } else { alpha = AMD_DEFAULT_DENSE ; aggressive = AMD_DEFAULT_AGGRESSIVE ; } /* Note: if alpha is NaN, this is undefined: */ if (alpha < 0) { /* only remove completely dense rows/columns */ dense = n-2 ; } else { dense = alpha * sqrt ((double) n) ; } dense = MAX (16, dense) ; dense = MIN (n, dense) ; AMD_DEBUG1 (("\n\nAMD (debug), alpha %g, aggr. "ID"\n", alpha, aggressive)) ; for (i = 0 ; i < n ; i++) { Last [i] = EMPTY ; Head [i] = EMPTY ; Next [i] = EMPTY ; /* if separate Hhead array is used for hash buckets: * Hhead [i] = EMPTY ; */ Nv [i] = 1 ; W [i] = 1 ; Elen [i] = 0 ; Degree [i] = Len [i] ; } #ifndef NDEBUG AMD_DEBUG1 (("\n======Nel "ID" initial\n", nel)) ; AMD_dump (n, Pe, Iw, Len, iwlen, pfree, Nv, Next, Last, Head, Elen, Degree, W, -1) ; #endif /* initialize wflg */ wbig = Int_MAX - n ; wflg = clear_flag (0, wbig, W, n) ; /* --------------------------------------------------------------------- */ /* initialize degree lists and eliminate dense and empty rows */ /* --------------------------------------------------------------------- */ ndense = 0 ; for (i = 0 ; i < n ; i++) { deg = Degree [i] ; ASSERT (deg >= 0 && deg < n) ; if (deg == 0) { /* ------------------------------------------------------------- * we have a variable that can be eliminated at once because * there is no off-diagonal non-zero in its row. Note that * Nv [i] = 1 for an empty variable i. It is treated just * the same as an eliminated element i. * ------------------------------------------------------------- */ Elen [i] = FLIP (1) ; nel++ ; Pe [i] = EMPTY ; W [i] = 0 ; } else if (deg > dense) { /* ------------------------------------------------------------- * Dense variables are not treated as elements, but as unordered, * non-principal variables that have no parent. They do not take * part in the postorder, since Nv [i] = 0. Note that the Fortran * version does not have this option. * ------------------------------------------------------------- */ AMD_DEBUG1 (("Dense node "ID" degree "ID"\n", i, deg)) ; ndense++ ; Nv [i] = 0 ; /* do not postorder this node */ Elen [i] = EMPTY ; nel++ ; Pe [i] = EMPTY ; } else { /* ------------------------------------------------------------- * place i in the degree list corresponding to its degree * ------------------------------------------------------------- */ inext = Head [deg] ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = i ; Next [i] = inext ; Head [deg] = i ; } } /* ========================================================================= */ /* WHILE (selecting pivots) DO */ /* ========================================================================= */ while (nel < n) { #ifndef NDEBUG AMD_DEBUG1 (("\n======Nel "ID"\n", nel)) ; if (AMD_debug >= 2) { AMD_dump (n, Pe, Iw, Len, iwlen, pfree, Nv, Next, Last, Head, Elen, Degree, W, nel) ; } #endif /* ========================================================================= */ /* GET PIVOT OF MINIMUM DEGREE */ /* ========================================================================= */ /* ----------------------------------------------------------------- */ /* find next supervariable for elimination */ /* ----------------------------------------------------------------- */ ASSERT (mindeg >= 0 && mindeg < n) ; for (deg = mindeg ; deg < n ; deg++) { me = Head [deg] ; if (me != EMPTY) break ; } mindeg = deg ; ASSERT (me >= 0 && me < n) ; AMD_DEBUG1 (("=================me: "ID"\n", me)) ; /* ----------------------------------------------------------------- */ /* remove chosen variable from link list */ /* ----------------------------------------------------------------- */ inext = Next [me] ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = EMPTY ; Head [deg] = inext ; /* ----------------------------------------------------------------- */ /* me represents the elimination of pivots nel to nel+Nv[me]-1. */ /* place me itself as the first in this set. */ /* ----------------------------------------------------------------- */ elenme = Elen [me] ; nvpiv = Nv [me] ; ASSERT (nvpiv > 0) ; nel += nvpiv ; /* ========================================================================= */ /* CONSTRUCT NEW ELEMENT */ /* ========================================================================= */ /* ----------------------------------------------------------------- * At this point, me is the pivotal supervariable. It will be * converted into the current element. Scan list of the pivotal * supervariable, me, setting tree pointers and constructing new list * of supervariables for the new element, me. p is a pointer to the * current position in the old list. * ----------------------------------------------------------------- */ /* flag the variable "me" as being in Lme by negating Nv [me] */ Nv [me] = -nvpiv ; degme = 0 ; ASSERT (Pe [me] >= 0 && Pe [me] < iwlen) ; if (elenme == 0) { /* ------------------------------------------------------------- */ /* construct the new element in place */ /* ------------------------------------------------------------- */ pme1 = Pe [me] ; pme2 = pme1 - 1 ; for (p = pme1 ; p <= pme1 + Len [me] - 1 ; p++) { i = Iw [p] ; ASSERT (i >= 0 && i < n && Nv [i] >= 0) ; nvi = Nv [i] ; if (nvi > 0) { /* ----------------------------------------------------- */ /* i is a principal variable not yet placed in Lme. */ /* store i in new list */ /* ----------------------------------------------------- */ /* flag i as being in Lme by negating Nv [i] */ degme += nvi ; Nv [i] = -nvi ; Iw [++pme2] = i ; /* ----------------------------------------------------- */ /* remove variable i from degree list. */ /* ----------------------------------------------------- */ ilast = Last [i] ; inext = Next [i] ; ASSERT (ilast >= EMPTY && ilast < n) ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = ilast ; if (ilast != EMPTY) { Next [ilast] = inext ; } else { /* i is at the head of the degree list */ ASSERT (Degree [i] >= 0 && Degree [i] < n) ; Head [Degree [i]] = inext ; } } } } else { /* ------------------------------------------------------------- */ /* construct the new element in empty space, Iw [pfree ...] */ /* ------------------------------------------------------------- */ p = Pe [me] ; pme1 = pfree ; slenme = Len [me] - elenme ; for (knt1 = 1 ; knt1 <= elenme + 1 ; knt1++) { if (knt1 > elenme) { /* search the supervariables in me. */ e = me ; pj = p ; ln = slenme ; AMD_DEBUG2 (("Search sv: "ID" "ID" "ID"\n", me,pj,ln)) ; } else { /* search the elements in me. */ e = Iw [p++] ; ASSERT (e >= 0 && e < n) ; pj = Pe [e] ; ln = Len [e] ; AMD_DEBUG2 (("Search element e "ID" in me "ID"\n", e,me)) ; ASSERT (Elen [e] < EMPTY && W [e] > 0 && pj >= 0) ; } ASSERT (ln >= 0 && (ln == 0 || (pj >= 0 && pj < iwlen))) ; /* --------------------------------------------------------- * search for different supervariables and add them to the * new list, compressing when necessary. this loop is * executed once for each element in the list and once for * all the supervariables in the list. * --------------------------------------------------------- */ for (knt2 = 1 ; knt2 <= ln ; knt2++) { i = Iw [pj++] ; ASSERT (i >= 0 && i < n && (i == me || Elen [i] >= EMPTY)); nvi = Nv [i] ; AMD_DEBUG2 ((": "ID" "ID" "ID" "ID"\n", i, Elen [i], Nv [i], wflg)) ; if (nvi > 0) { /* ------------------------------------------------- */ /* compress Iw, if necessary */ /* ------------------------------------------------- */ if (pfree >= iwlen) { AMD_DEBUG1 (("GARBAGE COLLECTION\n")) ; /* prepare for compressing Iw by adjusting pointers * and lengths so that the lists being searched in * the inner and outer loops contain only the * remaining entries. */ Pe [me] = p ; Len [me] -= knt1 ; /* check if nothing left of supervariable me */ if (Len [me] == 0) Pe [me] = EMPTY ; Pe [e] = pj ; Len [e] = ln - knt2 ; /* nothing left of element e */ if (Len [e] == 0) Pe [e] = EMPTY ; ncmpa++ ; /* one more garbage collection */ /* store first entry of each object in Pe */ /* FLIP the first entry in each object */ for (j = 0 ; j < n ; j++) { pn = Pe [j] ; if (pn >= 0) { ASSERT (pn >= 0 && pn < iwlen) ; Pe [j] = Iw [pn] ; Iw [pn] = FLIP (j) ; } } /* psrc/pdst point to source/destination */ psrc = 0 ; pdst = 0 ; pend = pme1 - 1 ; while (psrc <= pend) { /* search for next FLIP'd entry */ j = FLIP (Iw [psrc++]) ; if (j >= 0) { AMD_DEBUG2 (("Got object j: "ID"\n", j)) ; Iw [pdst] = Pe [j] ; Pe [j] = pdst++ ; lenj = Len [j] ; /* copy from source to destination */ for (knt3 = 0 ; knt3 <= lenj - 2 ; knt3++) { Iw [pdst++] = Iw [psrc++] ; } } } /* move the new partially-constructed element */ p1 = pdst ; for (psrc = pme1 ; psrc <= pfree-1 ; psrc++) { Iw [pdst++] = Iw [psrc] ; } pme1 = p1 ; pfree = pdst ; pj = Pe [e] ; p = Pe [me] ; } /* ------------------------------------------------- */ /* i is a principal variable not yet placed in Lme */ /* store i in new list */ /* ------------------------------------------------- */ /* flag i as being in Lme by negating Nv [i] */ degme += nvi ; Nv [i] = -nvi ; Iw [pfree++] = i ; AMD_DEBUG2 ((" s: "ID" nv "ID"\n", i, Nv [i])); /* ------------------------------------------------- */ /* remove variable i from degree link list */ /* ------------------------------------------------- */ ilast = Last [i] ; inext = Next [i] ; ASSERT (ilast >= EMPTY && ilast < n) ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = ilast ; if (ilast != EMPTY) { Next [ilast] = inext ; } else { /* i is at the head of the degree list */ ASSERT (Degree [i] >= 0 && Degree [i] < n) ; Head [Degree [i]] = inext ; } } } if (e != me) { /* set tree pointer and flag to indicate element e is * absorbed into new element me (the parent of e is me) */ AMD_DEBUG1 ((" Element "ID" => "ID"\n", e, me)) ; Pe [e] = FLIP (me) ; W [e] = 0 ; } } pme2 = pfree - 1 ; } /* ----------------------------------------------------------------- */ /* me has now been converted into an element in Iw [pme1..pme2] */ /* ----------------------------------------------------------------- */ /* degme holds the external degree of new element */ Degree [me] = degme ; Pe [me] = pme1 ; Len [me] = pme2 - pme1 + 1 ; ASSERT (Pe [me] >= 0 && Pe [me] < iwlen) ; Elen [me] = FLIP (nvpiv + degme) ; /* FLIP (Elen (me)) is now the degree of pivot (including * diagonal part). */ #ifndef NDEBUG AMD_DEBUG2 (("New element structure: length= "ID"\n", pme2-pme1+1)) ; for (pme = pme1 ; pme <= pme2 ; pme++) AMD_DEBUG3 ((" "ID"", Iw[pme])); AMD_DEBUG3 (("\n")) ; #endif /* ----------------------------------------------------------------- */ /* make sure that wflg is not too large. */ /* ----------------------------------------------------------------- */ /* With the current value of wflg, wflg+n must not cause integer * overflow */ wflg = clear_flag (wflg, wbig, W, n) ; /* ========================================================================= */ /* COMPUTE (W [e] - wflg) = |Le\Lme| FOR ALL ELEMENTS */ /* ========================================================================= */ /* ----------------------------------------------------------------- * Scan 1: compute the external degrees of previous elements with * respect to the current element. That is: * (W [e] - wflg) = |Le \ Lme| * for each element e that appears in any supervariable in Lme. The * notation Le refers to the pattern (list of supervariables) of a * previous element e, where e is not yet absorbed, stored in * Iw [Pe [e] + 1 ... Pe [e] + Len [e]]. The notation Lme * refers to the pattern of the current element (stored in * Iw [pme1..pme2]). If aggressive absorption is enabled, and * (W [e] - wflg) becomes zero, then the element e will be absorbed * in Scan 2. * ----------------------------------------------------------------- */ AMD_DEBUG2 (("me: ")) ; for (pme = pme1 ; pme <= pme2 ; pme++) { i = Iw [pme] ; ASSERT (i >= 0 && i < n) ; eln = Elen [i] ; AMD_DEBUG3 ((""ID" Elen "ID": \n", i, eln)) ; if (eln > 0) { /* note that Nv [i] has been negated to denote i in Lme: */ nvi = -Nv [i] ; ASSERT (nvi > 0 && Pe [i] >= 0 && Pe [i] < iwlen) ; wnvi = wflg - nvi ; for (p = Pe [i] ; p <= Pe [i] + eln - 1 ; p++) { e = Iw [p] ; ASSERT (e >= 0 && e < n) ; we = W [e] ; AMD_DEBUG4 ((" e "ID" we "ID" ", e, we)) ; if (we >= wflg) { /* unabsorbed element e has been seen in this loop */ AMD_DEBUG4 ((" unabsorbed, first time seen")) ; we -= nvi ; } else if (we != 0) { /* e is an unabsorbed element */ /* this is the first we have seen e in all of Scan 1 */ AMD_DEBUG4 ((" unabsorbed")) ; we = Degree [e] + wnvi ; } AMD_DEBUG4 (("\n")) ; W [e] = we ; } } } AMD_DEBUG2 (("\n")) ; /* ========================================================================= */ /* DEGREE UPDATE AND ELEMENT ABSORPTION */ /* ========================================================================= */ /* ----------------------------------------------------------------- * Scan 2: for each i in Lme, sum up the degree of Lme (which is * degme), plus the sum of the external degrees of each Le for the * elements e appearing within i, plus the supervariables in i. * Place i in hash list. * ----------------------------------------------------------------- */ for (pme = pme1 ; pme <= pme2 ; pme++) { i = Iw [pme] ; ASSERT (i >= 0 && i < n && Nv [i] < 0 && Elen [i] >= 0) ; AMD_DEBUG2 (("Updating: i "ID" "ID" "ID"\n", i, Elen[i], Len [i])); p1 = Pe [i] ; p2 = p1 + Elen [i] - 1 ; pn = p1 ; hash = 0 ; deg = 0 ; ASSERT (p1 >= 0 && p1 < iwlen && p2 >= -1 && p2 < iwlen) ; /* ------------------------------------------------------------- */ /* scan the element list associated with supervariable i */ /* ------------------------------------------------------------- */ /* UMFPACK/MA38-style approximate degree: */ if (aggressive) { for (p = p1 ; p <= p2 ; p++) { e = Iw [p] ; ASSERT (e >= 0 && e < n) ; we = W [e] ; if (we != 0) { /* e is an unabsorbed element */ /* dext = | Le \ Lme | */ dext = we - wflg ; if (dext > 0) { deg += dext ; Iw [pn++] = e ; hash += e ; AMD_DEBUG4 ((" e: "ID" hash = "ID"\n",e,hash)) ; } else { /* external degree of e is zero, absorb e into me*/ AMD_DEBUG1 ((" Element "ID" =>"ID" (aggressive)\n", e, me)) ; ASSERT (dext == 0) ; Pe [e] = FLIP (me) ; W [e] = 0 ; } } } } else { for (p = p1 ; p <= p2 ; p++) { e = Iw [p] ; ASSERT (e >= 0 && e < n) ; we = W [e] ; if (we != 0) { /* e is an unabsorbed element */ dext = we - wflg ; ASSERT (dext >= 0) ; deg += dext ; Iw [pn++] = e ; hash += e ; AMD_DEBUG4 ((" e: "ID" hash = "ID"\n",e,hash)) ; } } } /* count the number of elements in i (including me): */ Elen [i] = pn - p1 + 1 ; /* ------------------------------------------------------------- */ /* scan the supervariables in the list associated with i */ /* ------------------------------------------------------------- */ /* The bulk of the AMD run time is typically spent in this loop, * particularly if the matrix has many dense rows that are not * removed prior to ordering. */ p3 = pn ; p4 = p1 + Len [i] ; for (p = p2 + 1 ; p < p4 ; p++) { j = Iw [p] ; ASSERT (j >= 0 && j < n) ; nvj = Nv [j] ; if (nvj > 0) { /* j is unabsorbed, and not in Lme. */ /* add to degree and add to new list */ deg += nvj ; Iw [pn++] = j ; hash += j ; AMD_DEBUG4 ((" s: "ID" hash "ID" Nv[j]= "ID"\n", j, hash, nvj)) ; } } /* ------------------------------------------------------------- */ /* update the degree and check for mass elimination */ /* ------------------------------------------------------------- */ /* with aggressive absorption, deg==0 is identical to the * Elen [i] == 1 && p3 == pn test, below. */ ASSERT (IMPLIES (aggressive, (deg==0) == (Elen[i]==1 && p3==pn))) ; if (Elen [i] == 1 && p3 == pn) { /* --------------------------------------------------------- */ /* mass elimination */ /* --------------------------------------------------------- */ /* There is nothing left of this node except for an edge to * the current pivot element. Elen [i] is 1, and there are * no variables adjacent to node i. Absorb i into the * current pivot element, me. Note that if there are two or * more mass eliminations, fillin due to mass elimination is * possible within the nvpiv-by-nvpiv pivot block. It is this * step that causes AMD's analysis to be an upper bound. * * The reason is that the selected pivot has a lower * approximate degree than the true degree of the two mass * eliminated nodes. There is no edge between the two mass * eliminated nodes. They are merged with the current pivot * anyway. * * No fillin occurs in the Schur complement, in any case, * and this effect does not decrease the quality of the * ordering itself, just the quality of the nonzero and * flop count analysis. It also means that the post-ordering * is not an exact elimination tree post-ordering. */ AMD_DEBUG1 ((" MASS i "ID" => parent e "ID"\n", i, me)) ; Pe [i] = FLIP (me) ; nvi = -Nv [i] ; degme -= nvi ; nvpiv += nvi ; nel += nvi ; Nv [i] = 0 ; Elen [i] = EMPTY ; } else { /* --------------------------------------------------------- */ /* update the upper-bound degree of i */ /* --------------------------------------------------------- */ /* the following degree does not yet include the size * of the current element, which is added later: */ Degree [i] = MIN (Degree [i], deg) ; /* --------------------------------------------------------- */ /* add me to the list for i */ /* --------------------------------------------------------- */ /* move first supervariable to end of list */ Iw [pn] = Iw [p3] ; /* move first element to end of element part of list */ Iw [p3] = Iw [p1] ; /* add new element, me, to front of list. */ Iw [p1] = me ; /* store the new length of the list in Len [i] */ Len [i] = pn - p1 + 1 ; /* --------------------------------------------------------- */ /* place in hash bucket. Save hash key of i in Last [i]. */ /* --------------------------------------------------------- */ /* NOTE: this can fail if hash is negative, because the ANSI C * standard does not define a % b when a and/or b are negative. * That's why hash is defined as an unsigned Int, to avoid this * problem. */ hash = hash % n ; ASSERT (((Int) hash) >= 0 && ((Int) hash) < n) ; /* if the Hhead array is not used: */ j = Head [hash] ; if (j <= EMPTY) { /* degree list is empty, hash head is FLIP (j) */ Next [i] = FLIP (j) ; Head [hash] = FLIP (i) ; } else { /* degree list is not empty, use Last [Head [hash]] as * hash head. */ Next [i] = Last [j] ; Last [j] = i ; } /* if a separate Hhead array is used: * Next [i] = Hhead [hash] ; Hhead [hash] = i ; */ Last [i] = hash ; } } Degree [me] = degme ; /* ----------------------------------------------------------------- */ /* Clear the counter array, W [...], by incrementing wflg. */ /* ----------------------------------------------------------------- */ /* make sure that wflg+n does not cause integer overflow */ lemax = MAX (lemax, degme) ; wflg += lemax ; wflg = clear_flag (wflg, wbig, W, n) ; /* at this point, W [0..n-1] < wflg holds */ /* ========================================================================= */ /* SUPERVARIABLE DETECTION */ /* ========================================================================= */ AMD_DEBUG1 (("Detecting supervariables:\n")) ; for (pme = pme1 ; pme <= pme2 ; pme++) { i = Iw [pme] ; ASSERT (i >= 0 && i < n) ; AMD_DEBUG2 (("Consider i "ID" nv "ID"\n", i, Nv [i])) ; if (Nv [i] < 0) { /* i is a principal variable in Lme */ /* --------------------------------------------------------- * examine all hash buckets with 2 or more variables. We do * this by examing all unique hash keys for supervariables in * the pattern Lme of the current element, me * --------------------------------------------------------- */ /* let i = head of hash bucket, and empty the hash bucket */ ASSERT (Last [i] >= 0 && Last [i] < n) ; hash = Last [i] ; /* if Hhead array is not used: */ j = Head [hash] ; if (j == EMPTY) { /* hash bucket and degree list are both empty */ i = EMPTY ; } else if (j < EMPTY) { /* degree list is empty */ i = FLIP (j) ; Head [hash] = EMPTY ; } else { /* degree list is not empty, restore Last [j] of head j */ i = Last [j] ; Last [j] = EMPTY ; } /* if separate Hhead array is used: * i = Hhead [hash] ; Hhead [hash] = EMPTY ; */ ASSERT (i >= EMPTY && i < n) ; AMD_DEBUG2 (("----i "ID" hash "ID"\n", i, hash)) ; while (i != EMPTY && Next [i] != EMPTY) { /* ----------------------------------------------------- * this bucket has one or more variables following i. * scan all of them to see if i can absorb any entries * that follow i in hash bucket. Scatter i into w. * ----------------------------------------------------- */ ln = Len [i] ; eln = Elen [i] ; ASSERT (ln >= 0 && eln >= 0) ; ASSERT (Pe [i] >= 0 && Pe [i] < iwlen) ; /* do not flag the first element in the list (me) */ for (p = Pe [i] + 1 ; p <= Pe [i] + ln - 1 ; p++) { ASSERT (Iw [p] >= 0 && Iw [p] < n) ; W [Iw [p]] = wflg ; } /* ----------------------------------------------------- */ /* scan every other entry j following i in bucket */ /* ----------------------------------------------------- */ jlast = i ; j = Next [i] ; ASSERT (j >= EMPTY && j < n) ; while (j != EMPTY) { /* ------------------------------------------------- */ /* check if j and i have identical nonzero pattern */ /* ------------------------------------------------- */ AMD_DEBUG3 (("compare i "ID" and j "ID"\n", i,j)) ; /* check if i and j have the same Len and Elen */ ASSERT (Len [j] >= 0 && Elen [j] >= 0) ; ASSERT (Pe [j] >= 0 && Pe [j] < iwlen) ; ok = (Len [j] == ln) && (Elen [j] == eln) ; /* skip the first element in the list (me) */ for (p = Pe [j] + 1 ; ok && p <= Pe [j] + ln - 1 ; p++) { ASSERT (Iw [p] >= 0 && Iw [p] < n) ; if (W [Iw [p]] != wflg) ok = 0 ; } if (ok) { /* --------------------------------------------- */ /* found it! j can be absorbed into i */ /* --------------------------------------------- */ AMD_DEBUG1 (("found it! j "ID" => i "ID"\n", j,i)); Pe [j] = FLIP (i) ; /* both Nv [i] and Nv [j] are negated since they */ /* are in Lme, and the absolute values of each */ /* are the number of variables in i and j: */ Nv [i] += Nv [j] ; Nv [j] = 0 ; Elen [j] = EMPTY ; /* delete j from hash bucket */ ASSERT (j != Next [j]) ; j = Next [j] ; Next [jlast] = j ; } else { /* j cannot be absorbed into i */ jlast = j ; ASSERT (j != Next [j]) ; j = Next [j] ; } ASSERT (j >= EMPTY && j < n) ; } /* ----------------------------------------------------- * no more variables can be absorbed into i * go to next i in bucket and clear flag array * ----------------------------------------------------- */ wflg++ ; i = Next [i] ; ASSERT (i >= EMPTY && i < n) ; } } } AMD_DEBUG2 (("detect done\n")) ; /* ========================================================================= */ /* RESTORE DEGREE LISTS AND REMOVE NONPRINCIPAL SUPERVARIABLES FROM ELEMENT */ /* ========================================================================= */ p = pme1 ; nleft = n - nel ; for (pme = pme1 ; pme <= pme2 ; pme++) { i = Iw [pme] ; ASSERT (i >= 0 && i < n) ; nvi = -Nv [i] ; AMD_DEBUG3 (("Restore i "ID" "ID"\n", i, nvi)) ; if (nvi > 0) { /* i is a principal variable in Lme */ /* restore Nv [i] to signify that i is principal */ Nv [i] = nvi ; /* --------------------------------------------------------- */ /* compute the external degree (add size of current element) */ /* --------------------------------------------------------- */ deg = Degree [i] + degme - nvi ; deg = MIN (deg, nleft - nvi) ; ASSERT (IMPLIES (aggressive, deg > 0) && deg >= 0 && deg < n) ; /* --------------------------------------------------------- */ /* place the supervariable at the head of the degree list */ /* --------------------------------------------------------- */ inext = Head [deg] ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = i ; Next [i] = inext ; Last [i] = EMPTY ; Head [deg] = i ; /* --------------------------------------------------------- */ /* save the new degree, and find the minimum degree */ /* --------------------------------------------------------- */ mindeg = MIN (mindeg, deg) ; Degree [i] = deg ; /* --------------------------------------------------------- */ /* place the supervariable in the element pattern */ /* --------------------------------------------------------- */ Iw [p++] = i ; } } AMD_DEBUG2 (("restore done\n")) ; /* ========================================================================= */ /* FINALIZE THE NEW ELEMENT */ /* ========================================================================= */ AMD_DEBUG2 (("ME = "ID" DONE\n", me)) ; Nv [me] = nvpiv ; /* save the length of the list for the new element me */ Len [me] = p - pme1 ; if (Len [me] == 0) { /* there is nothing left of the current pivot element */ /* it is a root of the assembly tree */ Pe [me] = EMPTY ; W [me] = 0 ; } if (elenme != 0) { /* element was not constructed in place: deallocate part of */ /* it since newly nonprincipal variables may have been removed */ pfree = p ; } /* The new element has nvpiv pivots and the size of the contribution * block for a multifrontal method is degme-by-degme, not including * the "dense" rows/columns. If the "dense" rows/columns are included, * the frontal matrix is no larger than * (degme+ndense)-by-(degme+ndense). */ if (Info != (double *) NULL) { f = nvpiv ; r = degme + ndense ; dmax = MAX (dmax, f + r) ; /* number of nonzeros in L (excluding the diagonal) */ lnzme = f*r + (f-1)*f/2 ; lnz += lnzme ; /* number of divide operations for LDL' and for LU */ ndiv += lnzme ; /* number of multiply-subtract pairs for LU */ s = f*r*r + r*(f-1)*f + (f-1)*f*(2*f-1)/6 ; nms_lu += s ; /* number of multiply-subtract pairs for LDL' */ nms_ldl += (s + lnzme)/2 ; } #ifndef NDEBUG AMD_DEBUG2 (("finalize done nel "ID" n "ID"\n ::::\n", nel, n)) ; for (pme = Pe [me] ; pme <= Pe [me] + Len [me] - 1 ; pme++) { AMD_DEBUG3 ((" "ID"", Iw [pme])) ; } AMD_DEBUG3 (("\n")) ; #endif } /* ========================================================================= */ /* DONE SELECTING PIVOTS */ /* ========================================================================= */ if (Info != (double *) NULL) { /* count the work to factorize the ndense-by-ndense submatrix */ f = ndense ; dmax = MAX (dmax, (double) ndense) ; /* number of nonzeros in L (excluding the diagonal) */ lnzme = (f-1)*f/2 ; lnz += lnzme ; /* number of divide operations for LDL' and for LU */ ndiv += lnzme ; /* number of multiply-subtract pairs for LU */ s = (f-1)*f*(2*f-1)/6 ; nms_lu += s ; /* number of multiply-subtract pairs for LDL' */ nms_ldl += (s + lnzme)/2 ; /* number of nz's in L (excl. diagonal) */ Info [AMD_LNZ] = lnz ; /* number of divide ops for LU and LDL' */ Info [AMD_NDIV] = ndiv ; /* number of multiply-subtract pairs for LDL' */ Info [AMD_NMULTSUBS_LDL] = nms_ldl ; /* number of multiply-subtract pairs for LU */ Info [AMD_NMULTSUBS_LU] = nms_lu ; /* number of "dense" rows/columns */ Info [AMD_NDENSE] = ndense ; /* largest front is dmax-by-dmax */ Info [AMD_DMAX] = dmax ; /* number of garbage collections in AMD */ Info [AMD_NCMPA] = ncmpa ; /* successful ordering */ Info [AMD_STATUS] = AMD_OK ; } /* ========================================================================= */ /* POST-ORDERING */ /* ========================================================================= */ /* ------------------------------------------------------------------------- * Variables at this point: * * Pe: holds the elimination tree. The parent of j is FLIP (Pe [j]), * or EMPTY if j is a root. The tree holds both elements and * non-principal (unordered) variables absorbed into them. * Dense variables are non-principal and unordered. * * Elen: holds the size of each element, including the diagonal part. * FLIP (Elen [e]) > 0 if e is an element. For unordered * variables i, Elen [i] is EMPTY. * * Nv: Nv [e] > 0 is the number of pivots represented by the element e. * For unordered variables i, Nv [i] is zero. * * Contents no longer needed: * W, Iw, Len, Degree, Head, Next, Last. * * The matrix itself has been destroyed. * * n: the size of the matrix. * No other scalars needed (pfree, iwlen, etc.) * ------------------------------------------------------------------------- */ /* restore Pe */ for (i = 0 ; i < n ; i++) { Pe [i] = FLIP (Pe [i]) ; } /* restore Elen, for output information, and for postordering */ for (i = 0 ; i < n ; i++) { Elen [i] = FLIP (Elen [i]) ; } /* Now the parent of j is Pe [j], or EMPTY if j is a root. Elen [e] > 0 * is the size of element e. Elen [i] is EMPTY for unordered variable i. */ #ifndef NDEBUG AMD_DEBUG2 (("\nTree:\n")) ; for (i = 0 ; i < n ; i++) { AMD_DEBUG2 ((" "ID" parent: "ID" ", i, Pe [i])) ; ASSERT (Pe [i] >= EMPTY && Pe [i] < n) ; if (Nv [i] > 0) { /* this is an element */ e = i ; AMD_DEBUG2 ((" element, size is "ID"\n", Elen [i])) ; ASSERT (Elen [e] > 0) ; } AMD_DEBUG2 (("\n")) ; } AMD_DEBUG2 (("\nelements:\n")) ; for (e = 0 ; e < n ; e++) { if (Nv [e] > 0) { AMD_DEBUG3 (("Element e= "ID" size "ID" nv "ID" \n", e, Elen [e], Nv [e])) ; } } AMD_DEBUG2 (("\nvariables:\n")) ; for (i = 0 ; i < n ; i++) { Int cnt ; if (Nv [i] == 0) { AMD_DEBUG3 (("i unordered: "ID"\n", i)) ; j = Pe [i] ; cnt = 0 ; AMD_DEBUG3 ((" j: "ID"\n", j)) ; if (j == EMPTY) { AMD_DEBUG3 ((" i is a dense variable\n")) ; } else { ASSERT (j >= 0 && j < n) ; while (Nv [j] == 0) { AMD_DEBUG3 ((" j : "ID"\n", j)) ; j = Pe [j] ; AMD_DEBUG3 ((" j:: "ID"\n", j)) ; cnt++ ; if (cnt > n) break ; } e = j ; AMD_DEBUG3 ((" got to e: "ID"\n", e)) ; } } } #endif /* ========================================================================= */ /* compress the paths of the variables */ /* ========================================================================= */ for (i = 0 ; i < n ; i++) { if (Nv [i] == 0) { /* ------------------------------------------------------------- * i is an un-ordered row. Traverse the tree from i until * reaching an element, e. The element, e, was the principal * supervariable of i and all nodes in the path from i to when e * was selected as pivot. * ------------------------------------------------------------- */ AMD_DEBUG1 (("Path compression, i unordered: "ID"\n", i)) ; j = Pe [i] ; ASSERT (j >= EMPTY && j < n) ; AMD_DEBUG3 ((" j: "ID"\n", j)) ; if (j == EMPTY) { /* Skip a dense variable. It has no parent. */ AMD_DEBUG3 ((" i is a dense variable\n")) ; continue ; } /* while (j is a variable) */ while (Nv [j] == 0) { AMD_DEBUG3 ((" j : "ID"\n", j)) ; j = Pe [j] ; AMD_DEBUG3 ((" j:: "ID"\n", j)) ; ASSERT (j >= 0 && j < n) ; } /* got to an element e */ e = j ; AMD_DEBUG3 (("got to e: "ID"\n", e)) ; /* ------------------------------------------------------------- * traverse the path again from i to e, and compress the path * (all nodes point to e). Path compression allows this code to * compute in O(n) time. * ------------------------------------------------------------- */ j = i ; /* while (j is a variable) */ while (Nv [j] == 0) { jnext = Pe [j] ; AMD_DEBUG3 (("j "ID" jnext "ID"\n", j, jnext)) ; Pe [j] = e ; j = jnext ; ASSERT (j >= 0 && j < n) ; } } } /* ========================================================================= */ /* postorder the assembly tree */ /* ========================================================================= */ AMD_postorder (n, Pe, Nv, Elen, W, /* output order */ Head, Next, Last) ; /* workspace */ /* ========================================================================= */ /* compute output permutation and inverse permutation */ /* ========================================================================= */ /* W [e] = k means that element e is the kth element in the new * order. e is in the range 0 to n-1, and k is in the range 0 to * the number of elements. Use Head for inverse order. */ for (k = 0 ; k < n ; k++) { Head [k] = EMPTY ; Next [k] = EMPTY ; } for (e = 0 ; e < n ; e++) { k = W [e] ; ASSERT ((k == EMPTY) == (Nv [e] == 0)) ; if (k != EMPTY) { ASSERT (k >= 0 && k < n) ; Head [k] = e ; } } /* construct output inverse permutation in Next, * and permutation in Last */ nel = 0 ; for (k = 0 ; k < n ; k++) { e = Head [k] ; if (e == EMPTY) break ; ASSERT (e >= 0 && e < n && Nv [e] > 0) ; Next [e] = nel ; nel += Nv [e] ; } ASSERT (nel == n - ndense) ; /* order non-principal variables (dense, & those merged into supervar's) */ for (i = 0 ; i < n ; i++) { if (Nv [i] == 0) { e = Pe [i] ; ASSERT (e >= EMPTY && e < n) ; if (e != EMPTY) { /* This is an unordered variable that was merged * into element e via supernode detection or mass * elimination of i when e became the pivot element. * Place i in order just before e. */ ASSERT (Next [i] == EMPTY && Nv [e] > 0) ; Next [i] = Next [e] ; Next [e]++ ; } else { /* This is a dense unordered variable, with no parent. * Place it last in the output order. */ Next [i] = nel++ ; } } } ASSERT (nel == n) ; AMD_DEBUG2 (("\n\nPerm:\n")) ; for (i = 0 ; i < n ; i++) { k = Next [i] ; ASSERT (k >= 0 && k < n) ; Last [k] = i ; AMD_DEBUG2 ((" perm ["ID"] = "ID"\n", k, i)) ; } } Matrix/src/AMD/Source/amd_post_tree.c0000644000175100001440000000716712271765436017205 0ustar hornikusers/* ========================================================================= */ /* === AMD_post_tree ======================================================= */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* Post-ordering of a supernodal elimination tree. */ #include "amd_internal.h" GLOBAL Int AMD_post_tree ( Int root, /* root of the tree */ Int k, /* start numbering at k */ Int Child [ ], /* input argument of size nn, undefined on * output. Child [i] is the head of a link * list of all nodes that are children of node * i in the tree. */ const Int Sibling [ ], /* input argument of size nn, not modified. * If f is a node in the link list of the * children of node i, then Sibling [f] is the * next child of node i. */ Int Order [ ], /* output order, of size nn. Order [i] = k * if node i is the kth node of the reordered * tree. */ Int Stack [ ] /* workspace of size nn */ #ifndef NDEBUG , Int nn /* nodes are in the range 0..nn-1. */ #endif ) { Int f, head, h, i ; #if 0 /* --------------------------------------------------------------------- */ /* recursive version (Stack [ ] is not used): */ /* --------------------------------------------------------------------- */ /* this is simple, but can caouse stack overflow if nn is large */ i = root ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { k = AMD_post_tree (f, k, Child, Sibling, Order, Stack, nn) ; } Order [i] = k++ ; return (k) ; #endif /* --------------------------------------------------------------------- */ /* non-recursive version, using an explicit stack */ /* --------------------------------------------------------------------- */ /* push root on the stack */ head = 0 ; Stack [0] = root ; while (head >= 0) { /* get head of stack */ ASSERT (head < nn) ; i = Stack [head] ; AMD_DEBUG1 (("head of stack "ID" \n", i)) ; ASSERT (i >= 0 && i < nn) ; if (Child [i] != EMPTY) { /* the children of i are not yet ordered */ /* push each child onto the stack in reverse order */ /* so that small ones at the head of the list get popped first */ /* and the biggest one at the end of the list gets popped last */ for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { head++ ; ASSERT (head < nn) ; ASSERT (f >= 0 && f < nn) ; } h = head ; ASSERT (head < nn) ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { ASSERT (h > 0) ; Stack [h--] = f ; AMD_DEBUG1 (("push "ID" on stack\n", f)) ; ASSERT (f >= 0 && f < nn) ; } ASSERT (Stack [h] == i) ; /* delete child list so that i gets ordered next time we see it */ Child [i] = EMPTY ; } else { /* the children of i (if there were any) are already ordered */ /* remove i from the stack and order it. Front i is kth front */ head-- ; AMD_DEBUG1 (("pop "ID" order "ID"\n", i, k)) ; Order [i] = k++ ; ASSERT (k <= nn) ; } #ifndef NDEBUG AMD_DEBUG1 (("\nStack:")) ; for (h = head ; h >= 0 ; h--) { Int j = Stack [h] ; AMD_DEBUG1 ((" "ID, j)) ; ASSERT (j >= 0 && j < nn) ; } AMD_DEBUG1 (("\n\n")) ; ASSERT (head < nn) ; #endif } return (k) ; } Matrix/src/AMD/Makefile0000644000175100001440000000027612271765436014406 0ustar hornikusers# compile just the C-callable library library: ( cd Source ; $(MAKE) lib ) # remove object files, but keep the compiled programs and library archives clean: ( cd Source ; $(MAKE) clean ) Matrix/src/AMD/Include/0000755000175100001440000000000012271765426014323 5ustar hornikusersMatrix/src/AMD/Include/amd.h0000644000175100001440000004363012271765436015244 0ustar hornikusers/* ========================================================================= */ /* === AMD: approximate minimum degree ordering =========================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD Version 2.2, Copyright (c) 2007 by Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* AMD finds a symmetric ordering P of a matrix A so that the Cholesky * factorization of P*A*P' has fewer nonzeros and takes less work than the * Cholesky factorization of A. If A is not symmetric, then it performs its * ordering on the matrix A+A'. Two sets of user-callable routines are * provided, one for int integers and the other for SuiteSparse_long integers. * * The method is based on the approximate minimum degree algorithm, discussed * in Amestoy, Davis, and Duff, "An approximate degree ordering algorithm", * SIAM Journal of Matrix Analysis and Applications, vol. 17, no. 4, pp. * 886-905, 1996. This package can perform both the AMD ordering (with * aggressive absorption), and the AMDBAR ordering (without aggressive * absorption) discussed in the above paper. This package differs from the * Fortran codes discussed in the paper: * * (1) it can ignore "dense" rows and columns, leading to faster run times * (2) it computes the ordering of A+A' if A is not symmetric * (3) it is followed by a depth-first post-ordering of the assembly tree * (or supernodal elimination tree) * * For historical reasons, the Fortran versions, amd.f and amdbar.f, have * been left (nearly) unchanged. They compute the identical ordering as * described in the above paper. */ #ifndef AMD_H #define AMD_H /* make it easy for C++ programs to include AMD */ #ifdef __cplusplus extern "C" { #endif /* get the definition of size_t: */ #include #include "SuiteSparse_config.h" int amd_order /* returns AMD_OK, AMD_OK_BUT_JUMBLED, * AMD_INVALID, or AMD_OUT_OF_MEMORY */ ( int n, /* A is n-by-n. n must be >= 0. */ const int Ap [ ], /* column pointers for A, of size n+1 */ const int Ai [ ], /* row indices of A, of size nz = Ap [n] */ int P [ ], /* output permutation, of size n */ double Control [ ], /* input Control settings, of size AMD_CONTROL */ double Info [ ] /* output Info statistics, of size AMD_INFO */ ) ; SuiteSparse_long amd_l_order /* see above for description of arguments */ ( SuiteSparse_long n, const SuiteSparse_long Ap [ ], const SuiteSparse_long Ai [ ], SuiteSparse_long P [ ], double Control [ ], double Info [ ] ) ; /* Input arguments (not modified): * * n: the matrix A is n-by-n. * Ap: an int/SuiteSparse_long array of size n+1, containing column * pointers of A. * Ai: an int/SuiteSparse_long array of size nz, containing the row * indices of A, where nz = Ap [n]. * Control: a double array of size AMD_CONTROL, containing control * parameters. Defaults are used if Control is NULL. * * Output arguments (not defined on input): * * P: an int/SuiteSparse_long array of size n, containing the output * permutation. If row i is the kth pivot row, then P [k] = i. In * MATLAB notation, the reordered matrix is A (P,P). * Info: a double array of size AMD_INFO, containing statistical * information. Ignored if Info is NULL. * * On input, the matrix A is stored in column-oriented form. The row indices * of nonzero entries in column j are stored in Ai [Ap [j] ... Ap [j+1]-1]. * * If the row indices appear in ascending order in each column, and there * are no duplicate entries, then amd_order is slightly more efficient in * terms of time and memory usage. If this condition does not hold, a copy * of the matrix is created (where these conditions do hold), and the copy is * ordered. This feature is new to v2.0 (v1.2 and earlier required this * condition to hold for the input matrix). * * Row indices must be in the range 0 to * n-1. Ap [0] must be zero, and thus nz = Ap [n] is the number of nonzeros * in A. The array Ap is of size n+1, and the array Ai is of size nz = Ap [n]. * The matrix does not need to be symmetric, and the diagonal does not need to * be present (if diagonal entries are present, they are ignored except for * the output statistic Info [AMD_NZDIAG]). The arrays Ai and Ap are not * modified. This form of the Ap and Ai arrays to represent the nonzero * pattern of the matrix A is the same as that used internally by MATLAB. * If you wish to use a more flexible input structure, please see the * umfpack_*_triplet_to_col routines in the UMFPACK package, at * http://www.suitesparse.com. * * Restrictions: n >= 0. Ap [0] = 0. Ap [j] <= Ap [j+1] for all j in the * range 0 to n-1. nz = Ap [n] >= 0. Ai [0..nz-1] must be in the range 0 * to n-1. Finally, Ai, Ap, and P must not be NULL. If any of these * restrictions are not met, AMD returns AMD_INVALID. * * AMD returns: * * AMD_OK if the matrix is valid and sufficient memory can be allocated to * perform the ordering. * * AMD_OUT_OF_MEMORY if not enough memory can be allocated. * * AMD_INVALID if the input arguments n, Ap, Ai are invalid, or if P is * NULL. * * AMD_OK_BUT_JUMBLED if the matrix had unsorted columns, and/or duplicate * entries, but was otherwise valid. * * The AMD routine first forms the pattern of the matrix A+A', and then * computes a fill-reducing ordering, P. If P [k] = i, then row/column i of * the original is the kth pivotal row. In MATLAB notation, the permuted * matrix is A (P,P), except that 0-based indexing is used instead of the * 1-based indexing in MATLAB. * * The Control array is used to set various parameters for AMD. If a NULL * pointer is passed, default values are used. The Control array is not * modified. * * Control [AMD_DENSE]: controls the threshold for "dense" rows/columns. * A dense row/column in A+A' can cause AMD to spend a lot of time in * ordering the matrix. If Control [AMD_DENSE] >= 0, rows/columns * with more than Control [AMD_DENSE] * sqrt (n) entries are ignored * during the ordering, and placed last in the output order. The * default value of Control [AMD_DENSE] is 10. If negative, no * rows/columns are treated as "dense". Rows/columns with 16 or * fewer off-diagonal entries are never considered "dense". * * Control [AMD_AGGRESSIVE]: controls whether or not to use aggressive * absorption, in which a prior element is absorbed into the current * element if is a subset of the current element, even if it is not * adjacent to the current pivot element (refer to Amestoy, Davis, * & Duff, 1996, for more details). The default value is nonzero, * which means to perform aggressive absorption. This nearly always * leads to a better ordering (because the approximate degrees are * more accurate) and a lower execution time. There are cases where * it can lead to a slightly worse ordering, however. To turn it off, * set Control [AMD_AGGRESSIVE] to 0. * * Control [2..4] are not used in the current version, but may be used in * future versions. * * The Info array provides statistics about the ordering on output. If it is * not present, the statistics are not returned. This is not an error * condition. * * Info [AMD_STATUS]: the return value of AMD, either AMD_OK, * AMD_OK_BUT_JUMBLED, AMD_OUT_OF_MEMORY, or AMD_INVALID. * * Info [AMD_N]: n, the size of the input matrix * * Info [AMD_NZ]: the number of nonzeros in A, nz = Ap [n] * * Info [AMD_SYMMETRY]: the symmetry of the matrix A. It is the number * of "matched" off-diagonal entries divided by the total number of * off-diagonal entries. An entry A(i,j) is matched if A(j,i) is also * an entry, for any pair (i,j) for which i != j. In MATLAB notation, * S = spones (A) ; * B = tril (S, -1) + triu (S, 1) ; * symmetry = nnz (B & B') / nnz (B) ; * * Info [AMD_NZDIAG]: the number of entries on the diagonal of A. * * Info [AMD_NZ_A_PLUS_AT]: the number of nonzeros in A+A', excluding the * diagonal. If A is perfectly symmetric (Info [AMD_SYMMETRY] = 1) * with a fully nonzero diagonal, then Info [AMD_NZ_A_PLUS_AT] = nz-n * (the smallest possible value). If A is perfectly unsymmetric * (Info [AMD_SYMMETRY] = 0, for an upper triangular matrix, for * example) with no diagonal, then Info [AMD_NZ_A_PLUS_AT] = 2*nz * (the largest possible value). * * Info [AMD_NDENSE]: the number of "dense" rows/columns of A+A' that were * removed from A prior to ordering. These are placed last in the * output order P. * * Info [AMD_MEMORY]: the amount of memory used by AMD, in bytes. In the * current version, this is 1.2 * Info [AMD_NZ_A_PLUS_AT] + 9*n * times the size of an integer. This is at most 2.4nz + 9n. This * excludes the size of the input arguments Ai, Ap, and P, which have * a total size of nz + 2*n + 1 integers. * * Info [AMD_NCMPA]: the number of garbage collections performed. * * Info [AMD_LNZ]: the number of nonzeros in L (excluding the diagonal). * This is a slight upper bound because mass elimination is combined * with the approximate degree update. It is a rough upper bound if * there are many "dense" rows/columns. The rest of the statistics, * below, are also slight or rough upper bounds, for the same reasons. * The post-ordering of the assembly tree might also not exactly * correspond to a true elimination tree postordering. * * Info [AMD_NDIV]: the number of divide operations for a subsequent LDL' * or LU factorization of the permuted matrix A (P,P). * * Info [AMD_NMULTSUBS_LDL]: the number of multiply-subtract pairs for a * subsequent LDL' factorization of A (P,P). * * Info [AMD_NMULTSUBS_LU]: the number of multiply-subtract pairs for a * subsequent LU factorization of A (P,P), assuming that no numerical * pivoting is required. * * Info [AMD_DMAX]: the maximum number of nonzeros in any column of L, * including the diagonal. * * Info [14..19] are not used in the current version, but may be used in * future versions. */ /* ------------------------------------------------------------------------- */ /* direct interface to AMD */ /* ------------------------------------------------------------------------- */ /* amd_2 is the primary AMD ordering routine. It is not meant to be * user-callable because of its restrictive inputs and because it destroys * the user's input matrix. It does not check its inputs for errors, either. * However, if you can work with these restrictions it can be faster than * amd_order and use less memory (assuming that you can create your own copy * of the matrix for AMD to destroy). Refer to AMD/Source/amd_2.c for a * description of each parameter. */ void amd_2 ( int n, int Pe [ ], int Iw [ ], int Len [ ], int iwlen, int pfree, int Nv [ ], int Next [ ], int Last [ ], int Head [ ], int Elen [ ], int Degree [ ], int W [ ], double Control [ ], double Info [ ] ) ; void amd_l2 ( SuiteSparse_long n, SuiteSparse_long Pe [ ], SuiteSparse_long Iw [ ], SuiteSparse_long Len [ ], SuiteSparse_long iwlen, SuiteSparse_long pfree, SuiteSparse_long Nv [ ], SuiteSparse_long Next [ ], SuiteSparse_long Last [ ], SuiteSparse_long Head [ ], SuiteSparse_long Elen [ ], SuiteSparse_long Degree [ ], SuiteSparse_long W [ ], double Control [ ], double Info [ ] ) ; /* ------------------------------------------------------------------------- */ /* amd_valid */ /* ------------------------------------------------------------------------- */ /* Returns AMD_OK or AMD_OK_BUT_JUMBLED if the matrix is valid as input to * amd_order; the latter is returned if the matrix has unsorted and/or * duplicate row indices in one or more columns. Returns AMD_INVALID if the * matrix cannot be passed to amd_order. For amd_order, the matrix must also * be square. The first two arguments are the number of rows and the number * of columns of the matrix. For its use in AMD, these must both equal n. * * NOTE: this routine returned TRUE/FALSE in v1.2 and earlier. */ int amd_valid ( int n_row, /* # of rows */ int n_col, /* # of columns */ const int Ap [ ], /* column pointers, of size n_col+1 */ const int Ai [ ] /* row indices, of size Ap [n_col] */ ) ; SuiteSparse_long amd_l_valid ( SuiteSparse_long n_row, SuiteSparse_long n_col, const SuiteSparse_long Ap [ ], const SuiteSparse_long Ai [ ] ) ; /* ------------------------------------------------------------------------- */ /* AMD memory manager and printf routines */ /* ------------------------------------------------------------------------- */ /* The user can redefine these to change the malloc, free, and printf routines * that AMD uses. */ #ifndef EXTERN #define EXTERN extern #endif EXTERN void *(*amd_malloc) (size_t) ; /* pointer to malloc */ EXTERN void (*amd_free) (void *) ; /* pointer to free */ EXTERN void *(*amd_realloc) (void *, size_t) ; /* pointer to realloc */ EXTERN void *(*amd_calloc) (size_t, size_t) ; /* pointer to calloc */ EXTERN int (*amd_printf) (const char *, ...) ; /* pointer to printf */ /* ------------------------------------------------------------------------- */ /* AMD Control and Info arrays */ /* ------------------------------------------------------------------------- */ /* amd_defaults: sets the default control settings */ void amd_defaults (double Control [ ]) ; void amd_l_defaults (double Control [ ]) ; /* amd_control: prints the control settings */ void amd_control (double Control [ ]) ; void amd_l_control (double Control [ ]) ; /* amd_info: prints the statistics */ void amd_info (double Info [ ]) ; void amd_l_info (double Info [ ]) ; #define AMD_CONTROL 5 /* size of Control array */ #define AMD_INFO 20 /* size of Info array */ /* contents of Control */ #define AMD_DENSE 0 /* "dense" if degree > Control [0] * sqrt (n) */ #define AMD_AGGRESSIVE 1 /* do aggressive absorption if Control [1] != 0 */ /* default Control settings */ #define AMD_DEFAULT_DENSE 10.0 /* default "dense" degree 10*sqrt(n) */ #define AMD_DEFAULT_AGGRESSIVE 1 /* do aggressive absorption by default */ /* contents of Info */ #define AMD_STATUS 0 /* return value of amd_order and amd_l_order */ #define AMD_N 1 /* A is n-by-n */ #define AMD_NZ 2 /* number of nonzeros in A */ #define AMD_SYMMETRY 3 /* symmetry of pattern (1 is sym., 0 is unsym.) */ #define AMD_NZDIAG 4 /* # of entries on diagonal */ #define AMD_NZ_A_PLUS_AT 5 /* nz in A+A' */ #define AMD_NDENSE 6 /* number of "dense" rows/columns in A */ #define AMD_MEMORY 7 /* amount of memory used by AMD */ #define AMD_NCMPA 8 /* number of garbage collections in AMD */ #define AMD_LNZ 9 /* approx. nz in L, excluding the diagonal */ #define AMD_NDIV 10 /* number of fl. point divides for LU and LDL' */ #define AMD_NMULTSUBS_LDL 11 /* number of fl. point (*,-) pairs for LDL' */ #define AMD_NMULTSUBS_LU 12 /* number of fl. point (*,-) pairs for LU */ #define AMD_DMAX 13 /* max nz. in any column of L, incl. diagonal */ /* ------------------------------------------------------------------------- */ /* return values of AMD */ /* ------------------------------------------------------------------------- */ #define AMD_OK 0 /* success */ #define AMD_OUT_OF_MEMORY -1 /* malloc failed, or problem too large */ #define AMD_INVALID -2 /* input arguments are not valid */ #define AMD_OK_BUT_JUMBLED 1 /* input matrix is OK for amd_order, but * columns were not sorted, and/or duplicate entries were present. AMD had * to do extra work before ordering the matrix. This is a warning, not an * error. */ /* ========================================================================== */ /* === AMD version ========================================================== */ /* ========================================================================== */ /* AMD Version 1.2 and later include the following definitions. * As an example, to test if the version you are using is 1.2 or later: * * #ifdef AMD_VERSION * if (AMD_VERSION >= AMD_VERSION_CODE (1,2)) ... * #endif * * This also works during compile-time: * * #if defined(AMD_VERSION) && (AMD_VERSION >= AMD_VERSION_CODE (1,2)) * printf ("This is version 1.2 or later\n") ; * #else * printf ("This is an early version\n") ; * #endif * * Versions 1.1 and earlier of AMD do not include a #define'd version number. */ #define AMD_DATE "Jun 20, 2012" #define AMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub)) #define AMD_MAIN_VERSION 2 #define AMD_SUB_VERSION 3 #define AMD_SUBSUB_VERSION 1 #define AMD_VERSION AMD_VERSION_CODE(AMD_MAIN_VERSION,AMD_SUB_VERSION) #ifdef __cplusplus } #endif #endif Matrix/src/AMD/Include/amd_internal.h0000644000175100001440000002167512271765436017145 0ustar hornikusers/* ========================================================================= */ /* === amd_internal.h ====================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: DrTimothyAldenDavis@gmail.com */ /* ------------------------------------------------------------------------- */ /* This file is for internal use in AMD itself, and does not normally need to * be included in user code (it is included in UMFPACK, however). All others * should use amd.h instead. * * The following compile-time definitions affect how AMD is compiled. * * -DNPRINT * * Disable all printing. stdio.h will not be included. Printing can * be re-enabled at run-time by setting the global pointer amd_printf * to printf (or mexPrintf for a MATLAB mexFunction). * * -DNMALLOC * * No memory manager is defined at compile-time. You MUST define the * function pointers amd_malloc, amd_free, amd_realloc, and * amd_calloc at run-time for AMD to work properly. */ // For use with R package 'Matrix': #define NPRINT /* ========================================================================= */ /* === NDEBUG ============================================================== */ /* ========================================================================= */ /* * Turning on debugging takes some work (see below). If you do not edit this * file, then debugging is always turned off, regardless of whether or not * -DNDEBUG is specified in your compiler options. * * If AMD is being compiled as a mexFunction, then MATLAB_MEX_FILE is defined, * and mxAssert is used instead of assert. If debugging is not enabled, no * MATLAB include files or functions are used. Thus, the AMD library libamd.a * can be safely used in either a stand-alone C program or in another * mexFunction, without any change. */ /* AMD will be exceedingly slow when running in debug mode. The next three lines ensure that debugging is turned off. */ #ifndef NDEBUG #define NDEBUG #endif /* To enable debugging, uncomment the following line: #undef NDEBUG */ /* ------------------------------------------------------------------------- */ /* ANSI include files */ /* ------------------------------------------------------------------------- */ /* from stdlib.h: size_t, malloc, free, realloc, and calloc */ #include #if !defined(NPRINT) || !defined(NDEBUG) /* from stdio.h: printf. Not included if NPRINT is defined at compile time. * fopen and fscanf are used when debugging. */ #include #endif /* from limits.h: INT_MAX and LONG_MAX */ #include /* from math.h: sqrt */ #include /* ------------------------------------------------------------------------- */ /* MATLAB include files (only if being used in or via MATLAB) */ /* ------------------------------------------------------------------------- */ #ifdef MATLAB_MEX_FILE #include "matrix.h" #include "mex.h" #endif /* ------------------------------------------------------------------------- */ /* basic definitions */ /* ------------------------------------------------------------------------- */ #ifdef FLIP #undef FLIP #endif #ifdef MAX #undef MAX #endif #ifdef MIN #undef MIN #endif #ifdef EMPTY #undef EMPTY #endif #ifdef GLOBAL #undef GLOBAL #endif #ifdef PRIVATE #undef PRIVATE #endif /* FLIP is a "negation about -1", and is used to mark an integer i that is * normally non-negative. FLIP (EMPTY) is EMPTY. FLIP of a number > EMPTY * is negative, and FLIP of a number < EMTPY is positive. FLIP (FLIP (i)) = i * for all integers i. UNFLIP (i) is >= EMPTY. */ #define EMPTY (-1) #define FLIP(i) (-(i)-2) #define UNFLIP(i) ((i < EMPTY) ? FLIP (i) : (i)) /* for integer MAX/MIN, or for doubles when we don't care how NaN's behave: */ #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define MIN(a,b) (((a) < (b)) ? (a) : (b)) /* logical expression of p implies q: */ #define IMPLIES(p,q) (!(p) || (q)) /* Note that the IBM RS 6000 xlc predefines TRUE and FALSE in . */ /* The Compaq Alpha also predefines TRUE and FALSE. */ #ifdef TRUE #undef TRUE #endif #ifdef FALSE #undef FALSE #endif #define TRUE (1) #define FALSE (0) #define PRIVATE static #define GLOBAL #define EMPTY (-1) /* Note that Linux's gcc 2.96 defines NULL as ((void *) 0), but other */ /* compilers (even gcc 2.95.2 on Solaris) define NULL as 0 or (0). We */ /* need to use the ANSI standard value of 0. */ #ifdef NULL #undef NULL #endif #define NULL 0 /* largest value of size_t */ #ifndef SIZE_T_MAX #ifdef SIZE_MAX /* C99 only */ #define SIZE_T_MAX SIZE_MAX #else #define SIZE_T_MAX ((size_t) (-1)) #endif #endif /* ------------------------------------------------------------------------- */ /* integer type for AMD: int or SuiteSparse_long */ /* ------------------------------------------------------------------------- */ #include "amd.h" #if defined (DLONG) || defined (ZLONG) #define Int SuiteSparse_long #define ID SuiteSparse_long_id #define Int_MAX SuiteSparse_long_max #define AMD_order amd_l_order #define AMD_defaults amd_l_defaults #define AMD_control amd_l_control #define AMD_info amd_l_info #define AMD_1 amd_l1 #define AMD_2 amd_l2 #define AMD_valid amd_l_valid #define AMD_aat amd_l_aat #define AMD_postorder amd_l_postorder #define AMD_post_tree amd_l_post_tree #define AMD_dump amd_l_dump #define AMD_debug amd_l_debug #define AMD_debug_init amd_l_debug_init #define AMD_preprocess amd_l_preprocess #else #define Int int #define ID "%d" #define Int_MAX INT_MAX #define AMD_order amd_order #define AMD_defaults amd_defaults #define AMD_control amd_control #define AMD_info amd_info #define AMD_1 amd_1 #define AMD_2 amd_2 #define AMD_valid amd_valid #define AMD_aat amd_aat #define AMD_postorder amd_postorder #define AMD_post_tree amd_post_tree #define AMD_dump amd_dump #define AMD_debug amd_debug #define AMD_debug_init amd_debug_init #define AMD_preprocess amd_preprocess #endif /* ========================================================================= */ /* === PRINTF macro ======================================================== */ /* ========================================================================= */ /* All output goes through the PRINTF macro. */ #define PRINTF(params) { if (amd_printf != NULL) (void) amd_printf params ; } /* ------------------------------------------------------------------------- */ /* AMD routine definitions (not user-callable) */ /* ------------------------------------------------------------------------- */ GLOBAL size_t AMD_aat ( Int n, const Int Ap [ ], const Int Ai [ ], Int Len [ ], Int Tp [ ], double Info [ ] ) ; GLOBAL void AMD_1 ( Int n, const Int Ap [ ], const Int Ai [ ], Int P [ ], Int Pinv [ ], Int Len [ ], Int slen, Int S [ ], double Control [ ], double Info [ ] ) ; GLOBAL void AMD_postorder ( Int nn, Int Parent [ ], Int Npiv [ ], Int Fsize [ ], Int Order [ ], Int Child [ ], Int Sibling [ ], Int Stack [ ] ) ; GLOBAL Int AMD_post_tree ( Int root, Int k, Int Child [ ], const Int Sibling [ ], Int Order [ ], Int Stack [ ] #ifndef NDEBUG , Int nn #endif ) ; GLOBAL void AMD_preprocess ( Int n, const Int Ap [ ], const Int Ai [ ], Int Rp [ ], Int Ri [ ], Int W [ ], Int Flag [ ] ) ; /* ------------------------------------------------------------------------- */ /* debugging definitions */ /* ------------------------------------------------------------------------- */ #ifndef NDEBUG /* from assert.h: assert macro */ #include #ifndef EXTERN #define EXTERN extern #endif EXTERN Int AMD_debug ; GLOBAL void AMD_debug_init ( char *s ) ; GLOBAL void AMD_dump ( Int n, Int Pe [ ], Int Iw [ ], Int Len [ ], Int iwlen, Int pfree, Int Nv [ ], Int Next [ ], Int Last [ ], Int Head [ ], Int Elen [ ], Int Degree [ ], Int W [ ], Int nel ) ; #ifdef ASSERT #undef ASSERT #endif /* Use mxAssert if AMD is compiled into a mexFunction */ #ifdef MATLAB_MEX_FILE #define ASSERT(expression) (mxAssert ((expression), "")) #else #define ASSERT(expression) (assert (expression)) #endif #define AMD_DEBUG0(params) { PRINTF (params) ; } #define AMD_DEBUG1(params) { if (AMD_debug >= 1) PRINTF (params) ; } #define AMD_DEBUG2(params) { if (AMD_debug >= 2) PRINTF (params) ; } #define AMD_DEBUG3(params) { if (AMD_debug >= 3) PRINTF (params) ; } #define AMD_DEBUG4(params) { if (AMD_debug >= 4) PRINTF (params) ; } #else /* no debugging */ #define ASSERT(expression) #define AMD_DEBUG0(params) #define AMD_DEBUG1(params) #define AMD_DEBUG2(params) #define AMD_DEBUG3(params) #define AMD_DEBUG4(params) #endif Matrix/src/Syms.h0000644000175100001440000000043112271765436013442 0ustar hornikusersSEXP Matrix_DimNamesSym, Matrix_DimSym, Matrix_diagSym, Matrix_factorSym, Matrix_iSym, Matrix_jSym, Matrix_lengthSym, Matrix_pSym, Matrix_permSym, Matrix_uploSym, Matrix_xSym, Matrix_NS;/* the Matrix Namespace ('environment') */ Matrix/src/init.c0000644000175100001440000002660312271765436013456 0ustar hornikusers#include "Mutils.h" #include "abIndex.h" #include "chm_common.h" #include "CHMfactor.h" #include "Csparse.h" #include "Tsparse.h" #include "dense.h" #include "dgCMatrix.h" #include "dgTMatrix.h" #include "dgeMatrix.h" #include "dpoMatrix.h" #include "dppMatrix.h" #include "dsCMatrix.h" #include "TMatrix_as.h" #include "dspMatrix.h" #include "dsyMatrix.h" #include "dtCMatrix.h" #include "dtTMatrix.h" #include "dtrMatrix.h" #include "dtpMatrix.h" #include "factorizations.h" #include "ldense.h" #include "lgCMatrix.h" #include "sparseQR.h" #include #include "Syms.h" #define CALLDEF(name, n) {#name, (DL_FUNC) &name, n} #define EXTDEF(name, n) {#name, (DL_FUNC) &name, n} static R_CallMethodDef CallEntries[] = { CALLDEF(BunchKaufman_validate, 1), CALLDEF(pBunchKaufman_validate, 1), CALLDEF(CHMfactor_to_sparse, 1), CALLDEF(CHMfactor_solve, 3), CALLDEF(CHMfactor_spsolve, 3), CALLDEF(CHMfactor_ldetL2, 1), CALLDEF(CHMfactor_ldetL2up, 3), CALLDEF(CHMfactor_update, 3), CALLDEF(CHMfactor_updown,3), CALLDEF(destructive_CHM_update, 3), CALLDEF(Cholesky_validate, 1), CALLDEF(Csparse_Csparse_prod, 2), CALLDEF(Csparse_Csparse_crossprod, 3), CALLDEF(Csparse_MatrixMarket, 2), CALLDEF(Csparse_band, 3), CALLDEF(Csparse_crossprod, 3), CALLDEF(Csparse_dense_crossprod, 2), CALLDEF(Csparse_dense_prod, 2), CALLDEF(Csparse_diagN2U, 1), CALLDEF(Csparse_diagU2N, 1), CALLDEF(Csparse_drop, 2), CALLDEF(Csparse_horzcat, 2), CALLDEF(Csparse_sort, 1), CALLDEF(Csparse_to_Tsparse, 2), CALLDEF(Csparse_to_dense, 1), CALLDEF(Csparse_to_nz_pattern, 2), CALLDEF(Csparse_to_matrix, 2), CALLDEF(Csparse_to_vector, 1), CALLDEF(Csparse_submatrix, 3), CALLDEF(dCsparse_subassign, 4), CALLDEF(lCsparse_subassign, 4), CALLDEF(iCsparse_subassign, 4), CALLDEF(nCsparse_subassign, 4), CALLDEF(zCsparse_subassign, 4), CALLDEF(Csparse_general_to_symmetric, 2), CALLDEF(Csparse_symmetric_to_general, 1), CALLDEF(Csparse_transpose, 2), CALLDEF(Csparse_validate, 1), CALLDEF(Csparse_validate2, 2), CALLDEF(Csparse_vertcat, 2), CALLDEF(pCholesky_validate, 1), CALLDEF(Rsparse_validate, 1), CALLDEF(diag_tC, 4), #ifdef _valid_only_for_old_graph_package CALLDEF(graphNEL_as_dgTMatrix, 2), #endif CALLDEF(LU_expand, 1), CALLDEF(LU_validate, 1), CALLDEF(Matrix_expand_pointers, 1), CALLDEF(R_all0, 1), CALLDEF(R_any0, 1), CALLDEF(R_to_CMatrix, 1), CALLDEF(SVD_validate, 1), CALLDEF(Tsparse_validate, 1), CALLDEF(Tsparse_diagU2N, 1), CALLDEF(Tsparse_to_Csparse, 2), CALLDEF(Tsparse_to_tCsparse, 3), CALLDEF(compressed_to_TMatrix, 2), CALLDEF(compressed_non_0_ij, 2), CALLDEF(dense_to_Csparse, 1), CALLDEF(nz_pattern_to_Csparse, 2), CALLDEF(dense_nonpacked_validate, 1), CALLDEF(dense_band, 3), CALLDEF(dense_to_symmetric, 3), CALLDEF(ddense_symmpart, 1), CALLDEF(ddense_skewpart, 1), CALLDEF(dMatrix_validate, 1), CALLDEF(dgCMatrix_LU, 4), CALLDEF(dgCMatrix_QR, 2), #ifdef Matrix_with_SPQR CALLDEF(dgCMatrix_SPQR, 4), #endif CALLDEF(dgCMatrix_colSums, 5), CALLDEF(igCMatrix_colSums, 5), CALLDEF(lgCMatrix_colSums, 5), CALLDEF(ngCMatrix_colSums, 5), CALLDEF(dgCMatrix_cholsol, 2), /* CALLDEF(dgCMatrix_lusol, 2), */ CALLDEF(dgCMatrix_matrix_solve, 3), CALLDEF(dgCMatrix_qrsol, 3), CALLDEF(dgTMatrix_to_dgeMatrix, 1), CALLDEF(lgTMatrix_to_lgeMatrix, 1), CALLDEF(dgTMatrix_to_matrix, 1), CALLDEF(lgTMatrix_to_matrix, 1), CALLDEF(dgeMatrix_LU, 2), CALLDEF(dgeMatrix_Schur, 3), CALLDEF(dgeMatrix_colsums, 4), CALLDEF(dgeMatrix_crossprod, 2), CALLDEF(dgeMatrix_determinant, 2), CALLDEF(dgeMatrix_dgeMatrix_crossprod, 3), CALLDEF(dgeMatrix_matrix_mm, 3), CALLDEF(dgeMatrix_matrix_solve, 2), CALLDEF(dgeMatrix_dtpMatrix_mm, 2), CALLDEF(dgeMatrix_exp, 1), CALLDEF(dgeMatrix_addDiag, 2), CALLDEF(dgeMatrix_getDiag, 1), CALLDEF(lgeMatrix_getDiag, 1), CALLDEF(dgeMatrix_setDiag, 2), CALLDEF(lgeMatrix_setDiag, 2), CALLDEF(dgeMatrix_matrix_crossprod, 3), CALLDEF(dgeMatrix_norm, 2), CALLDEF(dgeMatrix_rcond, 2), CALLDEF(dgeMatrix_solve, 1), CALLDEF(dgeMatrix_validate, 1), CALLDEF(dpoMatrix_chol, 1), CALLDEF(dpoMatrix_dgeMatrix_solve, 2), CALLDEF(dpoMatrix_matrix_solve, 2), CALLDEF(dpoMatrix_rcond, 2), CALLDEF(dpoMatrix_solve, 1), CALLDEF(dpoMatrix_validate, 1), CALLDEF(dppMatrix_chol, 1), CALLDEF(dppMatrix_matrix_solve, 2), CALLDEF(dppMatrix_rcond, 2), CALLDEF(dppMatrix_solve, 1), CALLDEF(dppMatrix_validate, 1), CALLDEF(R_chkName_Cholesky, 4), CALLDEF(R_chm_factor_name, 3), CALLDEF(dsCMatrix_Cholesky, 5), CALLDEF(dsCMatrix_LDL_D, 3), CALLDEF(dsCMatrix_chol, 2), CALLDEF(dsCMatrix_Csparse_solve, 2), CALLDEF(dsCMatrix_matrix_solve, 2), CALLDEF(dsCMatrix_to_dgTMatrix, 1), CALLDEF(dsTMatrix_as_dgTMatrix, 1), CALLDEF(lsTMatrix_as_lgTMatrix, 1), CALLDEF(nsTMatrix_as_ngTMatrix, 1), CALLDEF(dsTMatrix_as_dsyMatrix, 1), CALLDEF(lsTMatrix_as_lsyMatrix, 1), CALLDEF(nsTMatrix_as_nsyMatrix, 1), CALLDEF(dsyMatrix_as_dspMatrix, 1), CALLDEF(dsyMatrix_as_matrix, 2), CALLDEF(dsyMatrix_matrix_mm, 3), CALLDEF(dsyMatrix_matrix_solve, 2), CALLDEF(dsyMatrix_norm, 2), CALLDEF(dsyMatrix_rcond, 2), CALLDEF(dsyMatrix_solve, 1), CALLDEF(dsyMatrix_trf, 1), CALLDEF(dsyMatrix_validate, 1), CALLDEF(dspMatrix_as_dsyMatrix, 1), CALLDEF(dspMatrix_matrix_mm, 2), CALLDEF(dspMatrix_matrix_solve, 2), CALLDEF(dspMatrix_norm, 2), CALLDEF(dspMatrix_rcond, 2), CALLDEF(dspMatrix_solve, 1), CALLDEF(dspMatrix_trf, 1), CALLDEF(dspMatrix_validate, 1), CALLDEF(dspMatrix_getDiag, 1), CALLDEF(lspMatrix_getDiag, 1), CALLDEF(dspMatrix_setDiag, 2), CALLDEF(lspMatrix_setDiag, 2), /* CALLDEF(dtCMatrix_solve, 1), */ CALLDEF(dtCMatrix_matrix_solve, 3), CALLDEF(dtCMatrix_sparse_solve, 2), CALLDEF(dtTMatrix_as_dtrMatrix, 1), CALLDEF(ltTMatrix_as_ltrMatrix, 1), CALLDEF(ntTMatrix_as_ntrMatrix, 1), CALLDEF(dtpMatrix_as_dtrMatrix, 1), CALLDEF(dtpMatrix_addDiag, 2), CALLDEF(dtpMatrix_getDiag, 1), CALLDEF(ltpMatrix_getDiag, 1), CALLDEF(dtpMatrix_setDiag, 2), CALLDEF(ltpMatrix_setDiag, 2), CALLDEF(dtpMatrix_matrix_mm, 4), CALLDEF(dtpMatrix_matrix_solve, 2), CALLDEF(dtpMatrix_norm, 2), CALLDEF(dtpMatrix_rcond, 2), CALLDEF(dtpMatrix_solve, 1), CALLDEF(dtpMatrix_validate, 1), CALLDEF(dtrMatrix_as_dtpMatrix, 1), CALLDEF(dtrMatrix_as_matrix, 2), CALLDEF(dtrMatrix_matrix_mm, 4), CALLDEF(dtrMatrix_dtrMatrix_mm, 4), CALLDEF(dtrMatrix_chol2inv, 1), CALLDEF(dtrMatrix_addDiag, 2), CALLDEF(dtrMatrix_getDiag, 1), CALLDEF(ltrMatrix_getDiag, 1), CALLDEF(dtrMatrix_setDiag, 2), CALLDEF(ltrMatrix_setDiag, 2), CALLDEF(dtrMatrix_matrix_solve, 2), CALLDEF(dtrMatrix_norm, 2), CALLDEF(dtrMatrix_rcond, 2), CALLDEF(dtrMatrix_solve, 1), CALLDEF(dtrMatrix_validate, 1), CALLDEF(dup_mMatrix_as_dgeMatrix, 1), CALLDEF(dup_mMatrix_as_geMatrix, 1), /* for dgC* _and_ lgC* : */ CALLDEF(xCMatrix_validate, 1), CALLDEF(xRMatrix_validate, 1), CALLDEF(xTMatrix_validate, 1), CALLDEF(tCMatrix_validate, 1), CALLDEF(tRMatrix_validate, 1), CALLDEF(tTMatrix_validate, 1), CALLDEF(lapack_qr, 2), CALLDEF(lgC_to_matrix, 1), CALLDEF(ngC_to_matrix, 1), CALLDEF(lspMatrix_as_lsyMatrix, 2), CALLDEF(lsyMatrix_as_lspMatrix, 2), CALLDEF(lsyMatrix_as_lgeMatrix, 2), CALLDEF(ltpMatrix_as_ltrMatrix, 2), CALLDEF(ltrMatrix_as_lgeMatrix, 2), CALLDEF(ltrMatrix_as_ltpMatrix, 2), CALLDEF(lsq_dense_Chol, 2), CALLDEF(lsq_dense_QR, 2), CALLDEF(sparseQR_validate, 1), CALLDEF(sparseQR_qty, 3), CALLDEF(sparseQR_coef, 2), CALLDEF(sparseQR_resid_fitted, 3), CALLDEF(triangularMatrix_validate, 1), CALLDEF(symmetricMatrix_validate, 1), /* still simple placeholders, but already used in ../R/AllClass.R : */ CALLDEF(CHMfactor_validate, 1), CALLDEF(CHMsimpl_validate, 1), CALLDEF(CHMsuper_validate, 1), CALLDEF(CHM_set_common_env, 1), CALLDEF(inv_permutation, 3), CALLDEF(m_encodeInd, 3), CALLDEF(m_encodeInd2, 4), CALLDEF(Matrix_rle_i, 2), CALLDEF(Matrix_rle_d, 2), CALLDEF(R_set_factors, 3), CALLDEF(get_SuiteSparse_version, 0), {NULL, NULL, 0} }; static const R_ExternalMethodDef ExtEntries[] = { EXTDEF(Mmatrix, 7), {NULL, NULL, 0} }; void #ifdef HAVE_VISIBILITY_ATTRIBUTE __attribute__ ((visibility ("default"))) #endif R_init_Matrix(DllInfo *dll) { R_registerRoutines(dll, NULL, CallEntries, NULL, ExtEntries); R_useDynamicSymbols(dll, FALSE); /* These are callable from other packages' C code: */ #define RREGDEF(name) R_RegisterCCallable("Matrix", #name, (DL_FUNC) name) RREGDEF(Csparse_diagU2N); RREGDEF(as_cholmod_dense); RREGDEF(as_cholmod_factor); RREGDEF(as_cholmod_sparse); RREGDEF(as_cholmod_triplet); RREGDEF(chm_factor_to_SEXP); RREGDEF(chm_factor_ldetL2); RREGDEF(chm_factor_update); RREGDEF(chm_sparse_to_SEXP); RREGDEF(chm_triplet_to_SEXP); RREGDEF(cholmod_aat); RREGDEF(cholmod_add); RREGDEF(cholmod_allocate_dense); RREGDEF(cholmod_allocate_sparse); RREGDEF(cholmod_allocate_triplet); RREGDEF(cholmod_analyze); RREGDEF(cholmod_analyze_p); RREGDEF(cholmod_band_inplace); RREGDEF(cholmod_change_factor); RREGDEF(cholmod_copy); RREGDEF(cholmod_copy_dense); RREGDEF(cholmod_copy_factor); RREGDEF(cholmod_copy_sparse); RREGDEF(cholmod_dense_to_sparse); RREGDEF(cholmod_factor_to_sparse); RREGDEF(cholmod_factorize); RREGDEF(cholmod_factorize_p); RREGDEF(cholmod_finish); RREGDEF(cholmod_free_dense); RREGDEF(cholmod_free_factor); RREGDEF(cholmod_free_sparse); RREGDEF(cholmod_free_triplet); RREGDEF(cholmod_nnz); RREGDEF(cholmod_scale); RREGDEF(cholmod_sdmult); RREGDEF(cholmod_solve); RREGDEF(cholmod_sort); RREGDEF(cholmod_sparse_to_dense); RREGDEF(cholmod_sparse_to_triplet); RREGDEF(cholmod_speye); RREGDEF(cholmod_spsolve); RREGDEF(cholmod_ssmult); RREGDEF(cholmod_start); RREGDEF(cholmod_submatrix); RREGDEF(cholmod_transpose); RREGDEF(cholmod_triplet_to_sparse); RREGDEF(cholmod_vertcat); RREGDEF(cholmod_updown); RREGDEF(dpoMatrix_chol); RREGDEF(numeric_as_chm_dense); R_cholmod_start(&c); // R_cholmod_l_start(&cl); Matrix_DimNamesSym = install("Dimnames"); Matrix_DimSym = install("Dim"); Matrix_diagSym = install("diag"); Matrix_factorSym = install("factors"); Matrix_iSym = install("i"); Matrix_jSym = install("j"); Matrix_lengthSym = install("length"); Matrix_pSym = install("p"); Matrix_permSym = install("perm"); Matrix_uploSym = install("uplo"); Matrix_xSym = install("x"); Matrix_NS = R_FindNamespace(mkString("Matrix")); if(Matrix_NS == R_UnboundValue) error(_("missing 'Matrix' namespace: should never happen")); #ifdef DEBUG_Matrix if(isEnvironment(Matrix_NS)) Rprintf("Matrix_NS: %s\n", CHAR(asChar(eval(lang2(install("format"),Matrix_NS), R_GlobalEnv)))); else #else if(!isEnvironment(Matrix_NS)) #endif error(_("Matrix namespace not determined correctly")); } void R_unload_Matrix(DllInfo *dll) { cholmod_finish(&c); } Matrix/src/COLAMD/0000755000175100001440000000000012271765436013277 5ustar hornikusersMatrix/src/COLAMD/Source/0000755000175100001440000000000012271765426014536 5ustar hornikusersMatrix/src/COLAMD/Source/colamd.c0000644000175100001440000032302412271765436016146 0ustar hornikusers/* ========================================================================== */ /* === colamd/symamd - a sparse matrix column ordering algorithm ============ */ /* ========================================================================== */ /* COLAMD / SYMAMD colamd: an approximate minimum degree column ordering algorithm, for LU factorization of symmetric or unsymmetric matrices, QR factorization, least squares, interior point methods for linear programming problems, and other related problems. symamd: an approximate minimum degree ordering algorithm for Cholesky factorization of symmetric matrices. Purpose: Colamd computes a permutation Q such that the Cholesky factorization of (AQ)'(AQ) has less fill-in and requires fewer floating point operations than A'A. This also provides a good ordering for sparse partial pivoting methods, P(AQ) = LU, where Q is computed prior to numerical factorization, and P is computed during numerical factorization via conventional partial pivoting with row interchanges. Colamd is the column ordering method used in SuperLU, part of the ScaLAPACK library. It is also available as built-in function in MATLAB Version 6, available from MathWorks, Inc. (http://www.mathworks.com). This routine can be used in place of colmmd in MATLAB. Symamd computes a permutation P of a symmetric matrix A such that the Cholesky factorization of PAP' has less fill-in and requires fewer floating point operations than A. Symamd constructs a matrix M such that M'M has the same nonzero pattern of A, and then orders the columns of M using colmmd. The column ordering of M is then returned as the row and column ordering P of A. Authors: The authors of the code itself are Stefan I. Larimore and Timothy A. Davis (DrTimothyAldenDavis@gmail.com). The algorithm was developed in collaboration with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974 and DMS-9803599. Copyright and License: Copyright (c) 1998-2007, Timothy A. Davis, All Rights Reserved. COLAMD is also available under alternate licenses, contact T. Davis for details. This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU LGPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. Availability: The colamd/symamd library is available at http://www.suitesparse.com Appears as ACM Algorithm 836. See the ChangeLog file for changes since Version 1.0. References: T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, An approximate column minimum degree ordering algorithm, ACM Transactions on Mathematical Software, vol. 30, no. 3., pp. 353-376, 2004. T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836: COLAMD, an approximate column minimum degree ordering algorithm, ACM Transactions on Mathematical Software, vol. 30, no. 3., pp. 377-380, 2004. */ /* ========================================================================== */ /* === Description of user-callable routines ================================ */ /* ========================================================================== */ /* COLAMD includes both int and SuiteSparse_long versions of all its routines. The description below is for the int version. For SuiteSparse_long, all int arguments become SuiteSparse_long. SuiteSparse_long is normally defined as long, except for WIN64. ---------------------------------------------------------------------------- colamd_recommended: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" size_t colamd_recommended (int nnz, int n_row, int n_col) ; size_t colamd_l_recommended (SuiteSparse_long nnz, SuiteSparse_long n_row, SuiteSparse_long n_col) ; Purpose: Returns recommended value of Alen for use by colamd. Returns 0 if any input argument is negative. The use of this routine is optional. Not needed for symamd, which dynamically allocates its own memory. Note that in v2.4 and earlier, these routines returned int or long. They now return a value of type size_t. Arguments (all input arguments): int nnz ; Number of nonzeros in the matrix A. This must be the same value as p [n_col] in the call to colamd - otherwise you will get a wrong value of the recommended memory to use. int n_row ; Number of rows in the matrix A. int n_col ; Number of columns in the matrix A. ---------------------------------------------------------------------------- colamd_set_defaults: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" colamd_set_defaults (double knobs [COLAMD_KNOBS]) ; colamd_l_set_defaults (double knobs [COLAMD_KNOBS]) ; Purpose: Sets the default parameters. The use of this routine is optional. Arguments: double knobs [COLAMD_KNOBS] ; Output only. NOTE: the meaning of the dense row/col knobs has changed in v2.4 knobs [0] and knobs [1] control dense row and col detection: Colamd: rows with more than max (16, knobs [COLAMD_DENSE_ROW] * sqrt (n_col)) entries are removed prior to ordering. Columns with more than max (16, knobs [COLAMD_DENSE_COL] * sqrt (MIN (n_row,n_col))) entries are removed prior to ordering, and placed last in the output column ordering. Symamd: uses only knobs [COLAMD_DENSE_ROW], which is knobs [0]. Rows and columns with more than max (16, knobs [COLAMD_DENSE_ROW] * sqrt (n)) entries are removed prior to ordering, and placed last in the output ordering. COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1, respectively, in colamd.h. Default values of these two knobs are both 10. Currently, only knobs [0] and knobs [1] are used, but future versions may use more knobs. If so, they will be properly set to their defaults by the future version of colamd_set_defaults, so that the code that calls colamd will not need to change, assuming that you either use colamd_set_defaults, or pass a (double *) NULL pointer as the knobs array to colamd or symamd. knobs [2]: aggressive absorption knobs [COLAMD_AGGRESSIVE] controls whether or not to do aggressive absorption during the ordering. Default is TRUE. ---------------------------------------------------------------------------- colamd: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" int colamd (int n_row, int n_col, int Alen, int *A, int *p, double knobs [COLAMD_KNOBS], int stats [COLAMD_STATS]) ; SuiteSparse_long colamd_l (SuiteSparse_long n_row, SuiteSparse_long n_col, SuiteSparse_long Alen, SuiteSparse_long *A, SuiteSparse_long *p, double knobs [COLAMD_KNOBS], SuiteSparse_long stats [COLAMD_STATS]) ; Purpose: Computes a column ordering (Q) of A such that P(AQ)=LU or (AQ)'AQ=LL' have less fill-in and require fewer floating point operations than factorizing the unpermuted matrix A or A'A, respectively. Returns: TRUE (1) if successful, FALSE (0) otherwise. Arguments: int n_row ; Input argument. Number of rows in the matrix A. Restriction: n_row >= 0. Colamd returns FALSE if n_row is negative. int n_col ; Input argument. Number of columns in the matrix A. Restriction: n_col >= 0. Colamd returns FALSE if n_col is negative. int Alen ; Input argument. Restriction (see note): Alen >= 2*nnz + 6*(n_col+1) + 4*(n_row+1) + n_col Colamd returns FALSE if these conditions are not met. Note: this restriction makes an modest assumption regarding the size of the two typedef's structures in colamd.h. We do, however, guarantee that Alen >= colamd_recommended (nnz, n_row, n_col) will be sufficient. Note: the macro version does not check for integer overflow, and thus is not recommended. Use the colamd_recommended routine instead. int A [Alen] ; Input argument, undefined on output. A is an integer array of size Alen. Alen must be at least as large as the bare minimum value given above, but this is very low, and can result in excessive run time. For best performance, we recommend that Alen be greater than or equal to colamd_recommended (nnz, n_row, n_col), which adds nnz/5 to the bare minimum value given above. On input, the row indices of the entries in column c of the matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices in a given column c need not be in ascending order, and duplicate row indices may be be present. However, colamd will work a little faster if both of these conditions are met (Colamd puts the matrix into this format, if it finds that the the conditions are not met). The matrix is 0-based. That is, rows are in the range 0 to n_row-1, and columns are in the range 0 to n_col-1. Colamd returns FALSE if any row index is out of range. The contents of A are modified during ordering, and are undefined on output. int p [n_col+1] ; Both input and output argument. p is an integer array of size n_col+1. On input, it holds the "pointers" for the column form of the matrix A. Column c of the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first entry, p [0], must be zero, and p [c] <= p [c+1] must hold for all c in the range 0 to n_col-1. The value p [n_col] is thus the total number of entries in the pattern of the matrix A. Colamd returns FALSE if these conditions are not met. On output, if colamd returns TRUE, the array p holds the column permutation (Q, for P(AQ)=LU or (AQ)'(AQ)=LL'), where p [0] is the first column index in the new ordering, and p [n_col-1] is the last. That is, p [k] = j means that column j of A is the kth pivot column, in AQ, where k is in the range 0 to n_col-1 (p [0] = j means that column j of A is the first column in AQ). If colamd returns FALSE, then no permutation is returned, and p is undefined on output. double knobs [COLAMD_KNOBS] ; Input argument. See colamd_set_defaults for a description. int stats [COLAMD_STATS] ; Output argument. Statistics on the ordering, and error status. See colamd.h for related definitions. Colamd returns FALSE if stats is not present. stats [0]: number of dense or empty rows ignored. stats [1]: number of dense or empty columns ignored (and ordered last in the output permutation p) Note that a row can become "empty" if it contains only "dense" and/or "empty" columns, and similarly a column can become "empty" if it only contains "dense" and/or "empty" rows. stats [2]: number of garbage collections performed. This can be excessively high if Alen is close to the minimum required value. stats [3]: status code. < 0 is an error code. > 1 is a warning or notice. 0 OK. Each column of the input matrix contained row indices in increasing order, with no duplicates. 1 OK, but columns of input matrix were jumbled (unsorted columns or duplicate entries). Colamd had to do some extra work to sort the matrix first and remove duplicate entries, but it still was able to return a valid permutation (return value of colamd was TRUE). stats [4]: highest numbered column that is unsorted or has duplicate entries. stats [5]: last seen duplicate or unsorted row index. stats [6]: number of duplicate or unsorted row indices. -1 A is a null pointer -2 p is a null pointer -3 n_row is negative stats [4]: n_row -4 n_col is negative stats [4]: n_col -5 number of nonzeros in matrix is negative stats [4]: number of nonzeros, p [n_col] -6 p [0] is nonzero stats [4]: p [0] -7 A is too small stats [4]: required size stats [5]: actual size (Alen) -8 a column has a negative number of entries stats [4]: column with < 0 entries stats [5]: number of entries in col -9 a row index is out of bounds stats [4]: column with bad row index stats [5]: bad row index stats [6]: n_row, # of rows of matrx -10 (unused; see symamd.c) -999 (unused; see symamd.c) Future versions may return more statistics in the stats array. Example: See colamd_example.c for a complete example. To order the columns of a 5-by-4 matrix with 11 nonzero entries in the following nonzero pattern x 0 x 0 x 0 x x 0 x x 0 0 0 x x x x 0 0 with default knobs and no output statistics, do the following: #include "colamd.h" #define ALEN 100 int A [ALEN] = {0, 1, 4, 2, 4, 0, 1, 2, 3, 1, 3} ; int p [ ] = {0, 3, 5, 9, 11} ; int stats [COLAMD_STATS] ; colamd (5, 4, ALEN, A, p, (double *) NULL, stats) ; The permutation is returned in the array p, and A is destroyed. ---------------------------------------------------------------------------- symamd: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" int symamd (int n, int *A, int *p, int *perm, double knobs [COLAMD_KNOBS], int stats [COLAMD_STATS], void (*allocate) (size_t, size_t), void (*release) (void *)) ; SuiteSparse_long symamd_l (SuiteSparse_long n, SuiteSparse_long *A, SuiteSparse_long *p, SuiteSparse_long *perm, double knobs [COLAMD_KNOBS], SuiteSparse_long stats [COLAMD_STATS], void (*allocate) (size_t, size_t), void (*release) (void *)) ; Purpose: The symamd routine computes an ordering P of a symmetric sparse matrix A such that the Cholesky factorization PAP' = LL' remains sparse. It is based on a column ordering of a matrix M constructed so that the nonzero pattern of M'M is the same as A. The matrix A is assumed to be symmetric; only the strictly lower triangular part is accessed. You must pass your selected memory allocator (usually calloc/free or mxCalloc/mxFree) to symamd, for it to allocate memory for the temporary matrix M. Returns: TRUE (1) if successful, FALSE (0) otherwise. Arguments: int n ; Input argument. Number of rows and columns in the symmetrix matrix A. Restriction: n >= 0. Symamd returns FALSE if n is negative. int A [nnz] ; Input argument. A is an integer array of size nnz, where nnz = p [n]. The row indices of the entries in column c of the matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices in a given column c need not be in ascending order, and duplicate row indices may be present. However, symamd will run faster if the columns are in sorted order with no duplicate entries. The matrix is 0-based. That is, rows are in the range 0 to n-1, and columns are in the range 0 to n-1. Symamd returns FALSE if any row index is out of range. The contents of A are not modified. int p [n+1] ; Input argument. p is an integer array of size n+1. On input, it holds the "pointers" for the column form of the matrix A. Column c of the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first entry, p [0], must be zero, and p [c] <= p [c+1] must hold for all c in the range 0 to n-1. The value p [n] is thus the total number of entries in the pattern of the matrix A. Symamd returns FALSE if these conditions are not met. The contents of p are not modified. int perm [n+1] ; Output argument. On output, if symamd returns TRUE, the array perm holds the permutation P, where perm [0] is the first index in the new ordering, and perm [n-1] is the last. That is, perm [k] = j means that row and column j of A is the kth column in PAP', where k is in the range 0 to n-1 (perm [0] = j means that row and column j of A are the first row and column in PAP'). The array is used as a workspace during the ordering, which is why it must be of length n+1, not just n. double knobs [COLAMD_KNOBS] ; Input argument. See colamd_set_defaults for a description. int stats [COLAMD_STATS] ; Output argument. Statistics on the ordering, and error status. See colamd.h for related definitions. Symamd returns FALSE if stats is not present. stats [0]: number of dense or empty row and columns ignored (and ordered last in the output permutation perm). Note that a row/column can become "empty" if it contains only "dense" and/or "empty" columns/rows. stats [1]: (same as stats [0]) stats [2]: number of garbage collections performed. stats [3]: status code. < 0 is an error code. > 1 is a warning or notice. 0 OK. Each column of the input matrix contained row indices in increasing order, with no duplicates. 1 OK, but columns of input matrix were jumbled (unsorted columns or duplicate entries). Symamd had to do some extra work to sort the matrix first and remove duplicate entries, but it still was able to return a valid permutation (return value of symamd was TRUE). stats [4]: highest numbered column that is unsorted or has duplicate entries. stats [5]: last seen duplicate or unsorted row index. stats [6]: number of duplicate or unsorted row indices. -1 A is a null pointer -2 p is a null pointer -3 (unused, see colamd.c) -4 n is negative stats [4]: n -5 number of nonzeros in matrix is negative stats [4]: # of nonzeros (p [n]). -6 p [0] is nonzero stats [4]: p [0] -7 (unused) -8 a column has a negative number of entries stats [4]: column with < 0 entries stats [5]: number of entries in col -9 a row index is out of bounds stats [4]: column with bad row index stats [5]: bad row index stats [6]: n_row, # of rows of matrx -10 out of memory (unable to allocate temporary workspace for M or count arrays using the "allocate" routine passed into symamd). Future versions may return more statistics in the stats array. void * (*allocate) (size_t, size_t) A pointer to a function providing memory allocation. The allocated memory must be returned initialized to zero. For a C application, this argument should normally be a pointer to calloc. For a MATLAB mexFunction, the routine mxCalloc is passed instead. void (*release) (size_t, size_t) A pointer to a function that frees memory allocated by the memory allocation routine above. For a C application, this argument should normally be a pointer to free. For a MATLAB mexFunction, the routine mxFree is passed instead. ---------------------------------------------------------------------------- colamd_report: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" colamd_report (int stats [COLAMD_STATS]) ; colamd_l_report (SuiteSparse_long stats [COLAMD_STATS]) ; Purpose: Prints the error status and statistics recorded in the stats array on the standard error output (for a standard C routine) or on the MATLAB output (for a mexFunction). Arguments: int stats [COLAMD_STATS] ; Input only. Statistics from colamd. ---------------------------------------------------------------------------- symamd_report: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" symamd_report (int stats [COLAMD_STATS]) ; symamd_l_report (SuiteSparse_long stats [COLAMD_STATS]) ; Purpose: Prints the error status and statistics recorded in the stats array on the standard error output (for a standard C routine) or on the MATLAB output (for a mexFunction). Arguments: int stats [COLAMD_STATS] ; Input only. Statistics from symamd. */ /* ========================================================================== */ /* === Scaffolding code definitions ======================================== */ /* ========================================================================== */ /* Ensure that debugging is turned off: */ #ifndef NDEBUG #define NDEBUG #endif /* turn on debugging by uncommenting the following line #undef NDEBUG */ /* Our "scaffolding code" philosophy: In our opinion, well-written library code should keep its "debugging" code, and just normally have it turned off by the compiler so as not to interfere with performance. This serves several purposes: (1) assertions act as comments to the reader, telling you what the code expects at that point. All assertions will always be true (unless there really is a bug, of course). (2) leaving in the scaffolding code assists anyone who would like to modify the code, or understand the algorithm (by reading the debugging output, one can get a glimpse into what the code is doing). (3) (gasp!) for actually finding bugs. This code has been heavily tested and "should" be fully functional and bug-free ... but you never know... The code will become outrageously slow when debugging is enabled. To control the level of debugging output, set an environment variable D to 0 (little), 1 (some), 2, 3, or 4 (lots). When debugging, you should see the following message on the standard output: colamd: debug version, D = 1 (THIS WILL BE SLOW!) or a similar message for symamd. If you don't, then debugging has not been enabled. */ /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include "colamd.h" #include #include #ifdef MATLAB_MEX_FILE #include "mex.h" #include "matrix.h" #endif /* MATLAB_MEX_FILE */ #if !defined (NPRINT) || !defined (NDEBUG) #include #endif #ifndef NULL #define NULL ((void *) 0) #endif /* ========================================================================== */ /* === int or SuiteSparse_long ============================================== */ /* ========================================================================== */ #ifdef DLONG #define Int SuiteSparse_long #define ID SuiteSparse_long_id #define Int_MAX SuiteSparse_long_max #define COLAMD_recommended colamd_l_recommended #define COLAMD_set_defaults colamd_l_set_defaults #define COLAMD_MAIN colamd_l #define SYMAMD_MAIN symamd_l #define COLAMD_report colamd_l_report #define SYMAMD_report symamd_l_report #else #define Int int #define ID "%d" #define Int_MAX INT_MAX #define COLAMD_recommended colamd_recommended #define COLAMD_set_defaults colamd_set_defaults #define COLAMD_MAIN colamd #define SYMAMD_MAIN symamd #define COLAMD_report colamd_report #define SYMAMD_report symamd_report #endif /* ========================================================================== */ /* === Row and Column structures ============================================ */ /* ========================================================================== */ /* User code that makes use of the colamd/symamd routines need not directly */ /* reference these structures. They are used only for colamd_recommended. */ typedef struct Colamd_Col_struct { Int start ; /* index for A of first row in this column, or DEAD */ /* if column is dead */ Int length ; /* number of rows in this column */ union { Int thickness ; /* number of original columns represented by this */ /* col, if the column is alive */ Int parent ; /* parent in parent tree super-column structure, if */ /* the column is dead */ } shared1 ; union { Int score ; /* the score used to maintain heap, if col is alive */ Int order ; /* pivot ordering of this column, if col is dead */ } shared2 ; union { Int headhash ; /* head of a hash bucket, if col is at the head of */ /* a degree list */ Int hash ; /* hash value, if col is not in a degree list */ Int prev ; /* previous column in degree list, if col is in a */ /* degree list (but not at the head of a degree list) */ } shared3 ; union { Int degree_next ; /* next column, if col is in a degree list */ Int hash_next ; /* next column, if col is in a hash list */ } shared4 ; } Colamd_Col ; typedef struct Colamd_Row_struct { Int start ; /* index for A of first col in this row */ Int length ; /* number of principal columns in this row */ union { Int degree ; /* number of principal & non-principal columns in row */ Int p ; /* used as a row pointer in init_rows_cols () */ } shared1 ; union { Int mark ; /* for computing set differences and marking dead rows*/ Int first_column ;/* first column in row (used in garbage collection) */ } shared2 ; } Colamd_Row ; /* ========================================================================== */ /* === Definitions ========================================================== */ /* ========================================================================== */ /* Routines are either PUBLIC (user-callable) or PRIVATE (not user-callable) */ #define PUBLIC #define PRIVATE static #define DENSE_DEGREE(alpha,n) \ ((Int) MAX (16.0, (alpha) * sqrt ((double) (n)))) #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define MIN(a,b) (((a) < (b)) ? (a) : (b)) #define ONES_COMPLEMENT(r) (-(r)-1) /* -------------------------------------------------------------------------- */ /* Change for version 2.1: define TRUE and FALSE only if not yet defined */ /* -------------------------------------------------------------------------- */ #ifndef TRUE #define TRUE (1) #endif #ifndef FALSE #define FALSE (0) #endif /* -------------------------------------------------------------------------- */ #define EMPTY (-1) /* Row and column status */ #define ALIVE (0) #define DEAD (-1) /* Column status */ #define DEAD_PRINCIPAL (-1) #define DEAD_NON_PRINCIPAL (-2) /* Macros for row and column status update and checking. */ #define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark) #define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE) #define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE) #define COL_IS_DEAD(c) (Col [c].start < ALIVE) #define COL_IS_ALIVE(c) (Col [c].start >= ALIVE) #define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL) #define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; } #define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; } #define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; } /* ========================================================================== */ /* === Colamd reporting mechanism =========================================== */ /* ========================================================================== */ #if defined (MATLAB_MEX_FILE) || defined (MATHWORKS) /* In MATLAB, matrices are 1-based to the user, but 0-based internally */ #define INDEX(i) ((i)+1) #else /* In C, matrices are 0-based and indices are reported as such in *_report */ #define INDEX(i) (i) #endif /* All output goes through the PRINTF macro. */ #define PRINTF(params) { if (colamd_printf != NULL) (void) colamd_printf params ; } /* ========================================================================== */ /* === Prototypes of PRIVATE routines ======================================= */ /* ========================================================================== */ PRIVATE Int init_rows_cols ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int p [], Int stats [COLAMD_STATS] ) ; PRIVATE void init_scoring ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int head [], double knobs [COLAMD_KNOBS], Int *p_n_row2, Int *p_n_col2, Int *p_max_deg ) ; PRIVATE Int find_ordering ( Int n_row, Int n_col, Int Alen, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int head [], Int n_col2, Int max_deg, Int pfree, Int aggressive ) ; PRIVATE void order_children ( Int n_col, Colamd_Col Col [], Int p [] ) ; PRIVATE void detect_super_cols ( #ifndef NDEBUG Int n_col, Colamd_Row Row [], #endif /* NDEBUG */ Colamd_Col Col [], Int A [], Int head [], Int row_start, Int row_length ) ; PRIVATE Int garbage_collection ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int *pfree ) ; PRIVATE Int clear_mark ( Int tag_mark, Int max_mark, Int n_row, Colamd_Row Row [] ) ; PRIVATE void print_report ( char *method, Int stats [COLAMD_STATS] ) ; /* ========================================================================== */ /* === Debugging prototypes and definitions ================================= */ /* ========================================================================== */ #ifndef NDEBUG #include /* colamd_debug is the *ONLY* global variable, and is only */ /* present when debugging */ PRIVATE Int colamd_debug = 0 ; /* debug print level */ #define DEBUG0(params) { PRINTF (params) ; } #define DEBUG1(params) { if (colamd_debug >= 1) PRINTF (params) ; } #define DEBUG2(params) { if (colamd_debug >= 2) PRINTF (params) ; } #define DEBUG3(params) { if (colamd_debug >= 3) PRINTF (params) ; } #define DEBUG4(params) { if (colamd_debug >= 4) PRINTF (params) ; } #ifdef MATLAB_MEX_FILE #define ASSERT(expression) (mxAssert ((expression), "")) #else #define ASSERT(expression) (assert (expression)) #endif /* MATLAB_MEX_FILE */ PRIVATE void colamd_get_debug /* gets the debug print level from getenv */ ( char *method ) ; PRIVATE void debug_deg_lists ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int head [], Int min_score, Int should, Int max_deg ) ; PRIVATE void debug_mark ( Int n_row, Colamd_Row Row [], Int tag_mark, Int max_mark ) ; PRIVATE void debug_matrix ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [] ) ; PRIVATE void debug_structures ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int n_col2 ) ; #else /* NDEBUG */ /* === No debugging ========================================================= */ #define DEBUG0(params) ; #define DEBUG1(params) ; #define DEBUG2(params) ; #define DEBUG3(params) ; #define DEBUG4(params) ; #define ASSERT(expression) #endif /* NDEBUG */ /* ========================================================================== */ /* === USER-CALLABLE ROUTINES: ============================================== */ /* ========================================================================== */ /* ========================================================================== */ /* === colamd_recommended =================================================== */ /* ========================================================================== */ /* The colamd_recommended routine returns the suggested size for Alen. This value has been determined to provide good balance between the number of garbage collections and the memory requirements for colamd. If any argument is negative, or if integer overflow occurs, a 0 is returned as an error condition. 2*nnz space is required for the row and column indices of the matrix. COLAMD_C (n_col) + COLAMD_R (n_row) space is required for the Col and Row arrays, respectively, which are internal to colamd (roughly 6*n_col + 4*n_row). An additional n_col space is the minimal amount of "elbow room", and nnz/5 more space is recommended for run time efficiency. Alen is approximately 2.2*nnz + 7*n_col + 4*n_row + 10. This function is not needed when using symamd. */ /* add two values of type size_t, and check for integer overflow */ static size_t t_add (size_t a, size_t b, int *ok) { (*ok) = (*ok) && ((a + b) >= MAX (a,b)) ; return ((*ok) ? (a + b) : 0) ; } /* compute a*k where k is a small integer, and check for integer overflow */ static size_t t_mult (size_t a, size_t k, int *ok) { size_t i, s = 0 ; for (i = 0 ; i < k ; i++) { s = t_add (s, a, ok) ; } return (s) ; } /* size of the Col and Row structures */ #define COLAMD_C(n_col,ok) \ ((t_mult (t_add (n_col, 1, ok), sizeof (Colamd_Col), ok) / sizeof (Int))) #define COLAMD_R(n_row,ok) \ ((t_mult (t_add (n_row, 1, ok), sizeof (Colamd_Row), ok) / sizeof (Int))) PUBLIC size_t COLAMD_recommended /* returns recommended value of Alen. */ ( /* === Parameters ======================================================= */ Int nnz, /* number of nonzeros in A */ Int n_row, /* number of rows in A */ Int n_col /* number of columns in A */ ) { size_t s, c, r ; int ok = TRUE ; if (nnz < 0 || n_row < 0 || n_col < 0) { return (0) ; } s = t_mult (nnz, 2, &ok) ; /* 2*nnz */ c = COLAMD_C (n_col, &ok) ; /* size of column structures */ r = COLAMD_R (n_row, &ok) ; /* size of row structures */ s = t_add (s, c, &ok) ; s = t_add (s, r, &ok) ; s = t_add (s, n_col, &ok) ; /* elbow room */ s = t_add (s, nnz/5, &ok) ; /* elbow room */ ok = ok && (s < Int_MAX) ; return (ok ? s : 0) ; } /* ========================================================================== */ /* === colamd_set_defaults ================================================== */ /* ========================================================================== */ /* The colamd_set_defaults routine sets the default values of the user- controllable parameters for colamd and symamd: Colamd: rows with more than max (16, knobs [0] * sqrt (n_col)) entries are removed prior to ordering. Columns with more than max (16, knobs [1] * sqrt (MIN (n_row,n_col))) entries are removed prior to ordering, and placed last in the output column ordering. Symamd: Rows and columns with more than max (16, knobs [0] * sqrt (n)) entries are removed prior to ordering, and placed last in the output ordering. knobs [0] dense row control knobs [1] dense column control knobs [2] if nonzero, do aggresive absorption knobs [3..19] unused, but future versions might use this */ PUBLIC void COLAMD_set_defaults ( /* === Parameters ======================================================= */ double knobs [COLAMD_KNOBS] /* knob array */ ) { /* === Local variables ================================================== */ Int i ; if (!knobs) { return ; /* no knobs to initialize */ } for (i = 0 ; i < COLAMD_KNOBS ; i++) { knobs [i] = 0 ; } knobs [COLAMD_DENSE_ROW] = 10 ; knobs [COLAMD_DENSE_COL] = 10 ; knobs [COLAMD_AGGRESSIVE] = TRUE ; /* default: do aggressive absorption*/ } /* ========================================================================== */ /* === symamd =============================================================== */ /* ========================================================================== */ PUBLIC Int SYMAMD_MAIN /* return TRUE if OK, FALSE otherwise */ ( /* === Parameters ======================================================= */ Int n, /* number of rows and columns of A */ Int A [], /* row indices of A */ Int p [], /* column pointers of A */ Int perm [], /* output permutation, size n+1 */ double knobs [COLAMD_KNOBS], /* parameters (uses defaults if NULL) */ Int stats [COLAMD_STATS], /* output statistics and error codes */ void * (*allocate) (size_t, size_t), /* pointer to calloc (ANSI C) or */ /* mxCalloc (for MATLAB mexFunction) */ void (*release) (void *) /* pointer to free (ANSI C) or */ /* mxFree (for MATLAB mexFunction) */ ) { /* === Local variables ================================================== */ Int *count ; /* length of each column of M, and col pointer*/ Int *mark ; /* mark array for finding duplicate entries */ Int *M ; /* row indices of matrix M */ size_t Mlen ; /* length of M */ Int n_row ; /* number of rows in M */ Int nnz ; /* number of entries in A */ Int i ; /* row index of A */ Int j ; /* column index of A */ Int k ; /* row index of M */ Int mnz ; /* number of nonzeros in M */ Int pp ; /* index into a column of A */ Int last_row ; /* last row seen in the current column */ Int length ; /* number of nonzeros in a column */ double cknobs [COLAMD_KNOBS] ; /* knobs for colamd */ double default_knobs [COLAMD_KNOBS] ; /* default knobs for colamd */ #ifndef NDEBUG colamd_get_debug ("symamd") ; #endif /* NDEBUG */ /* === Check the input arguments ======================================== */ if (!stats) { DEBUG0 (("symamd: stats not present\n")) ; return (FALSE) ; } for (i = 0 ; i < COLAMD_STATS ; i++) { stats [i] = 0 ; } stats [COLAMD_STATUS] = COLAMD_OK ; stats [COLAMD_INFO1] = -1 ; stats [COLAMD_INFO2] = -1 ; if (!A) { stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ; DEBUG0 (("symamd: A not present\n")) ; return (FALSE) ; } if (!p) /* p is not present */ { stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ; DEBUG0 (("symamd: p not present\n")) ; return (FALSE) ; } if (n < 0) /* n must be >= 0 */ { stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ; stats [COLAMD_INFO1] = n ; DEBUG0 (("symamd: n negative %d\n", n)) ; return (FALSE) ; } nnz = p [n] ; if (nnz < 0) /* nnz must be >= 0 */ { stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ; stats [COLAMD_INFO1] = nnz ; DEBUG0 (("symamd: number of entries negative %d\n", nnz)) ; return (FALSE) ; } if (p [0] != 0) { stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ; stats [COLAMD_INFO1] = p [0] ; DEBUG0 (("symamd: p[0] not zero %d\n", p [0])) ; return (FALSE) ; } /* === If no knobs, set default knobs =================================== */ if (!knobs) { COLAMD_set_defaults (default_knobs) ; knobs = default_knobs ; } /* === Allocate count and mark ========================================== */ count = (Int *) ((*allocate) (n+1, sizeof (Int))) ; if (!count) { stats [COLAMD_STATUS] = COLAMD_ERROR_out_of_memory ; DEBUG0 (("symamd: allocate count (size %d) failed\n", n+1)) ; return (FALSE) ; } mark = (Int *) ((*allocate) (n+1, sizeof (Int))) ; if (!mark) { stats [COLAMD_STATUS] = COLAMD_ERROR_out_of_memory ; (*release) ((void *) count) ; DEBUG0 (("symamd: allocate mark (size %d) failed\n", n+1)) ; return (FALSE) ; } /* === Compute column counts of M, check if A is valid ================== */ stats [COLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/ for (i = 0 ; i < n ; i++) { mark [i] = -1 ; } for (j = 0 ; j < n ; j++) { last_row = -1 ; length = p [j+1] - p [j] ; if (length < 0) { /* column pointers must be non-decreasing */ stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ; stats [COLAMD_INFO1] = j ; stats [COLAMD_INFO2] = length ; (*release) ((void *) count) ; (*release) ((void *) mark) ; DEBUG0 (("symamd: col %d negative length %d\n", j, length)) ; return (FALSE) ; } for (pp = p [j] ; pp < p [j+1] ; pp++) { i = A [pp] ; if (i < 0 || i >= n) { /* row index i, in column j, is out of bounds */ stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ; stats [COLAMD_INFO1] = j ; stats [COLAMD_INFO2] = i ; stats [COLAMD_INFO3] = n ; (*release) ((void *) count) ; (*release) ((void *) mark) ; DEBUG0 (("symamd: row %d col %d out of bounds\n", i, j)) ; return (FALSE) ; } if (i <= last_row || mark [i] == j) { /* row index is unsorted or repeated (or both), thus col */ /* is jumbled. This is a notice, not an error condition. */ stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ; stats [COLAMD_INFO1] = j ; stats [COLAMD_INFO2] = i ; (stats [COLAMD_INFO3]) ++ ; DEBUG1 (("symamd: row %d col %d unsorted/duplicate\n", i, j)) ; } if (i > j && mark [i] != j) { /* row k of M will contain column indices i and j */ count [i]++ ; count [j]++ ; } /* mark the row as having been seen in this column */ mark [i] = j ; last_row = i ; } } /* v2.4: removed free(mark) */ /* === Compute column pointers of M ===================================== */ /* use output permutation, perm, for column pointers of M */ perm [0] = 0 ; for (j = 1 ; j <= n ; j++) { perm [j] = perm [j-1] + count [j-1] ; } for (j = 0 ; j < n ; j++) { count [j] = perm [j] ; } /* === Construct M ====================================================== */ mnz = perm [n] ; n_row = mnz / 2 ; Mlen = COLAMD_recommended (mnz, n_row, n) ; M = (Int *) ((*allocate) (Mlen, sizeof (Int))) ; DEBUG0 (("symamd: M is %d-by-%d with %d entries, Mlen = %g\n", n_row, n, mnz, (double) Mlen)) ; if (!M) { stats [COLAMD_STATUS] = COLAMD_ERROR_out_of_memory ; (*release) ((void *) count) ; (*release) ((void *) mark) ; DEBUG0 (("symamd: allocate M (size %g) failed\n", (double) Mlen)) ; return (FALSE) ; } k = 0 ; if (stats [COLAMD_STATUS] == COLAMD_OK) { /* Matrix is OK */ for (j = 0 ; j < n ; j++) { ASSERT (p [j+1] - p [j] >= 0) ; for (pp = p [j] ; pp < p [j+1] ; pp++) { i = A [pp] ; ASSERT (i >= 0 && i < n) ; if (i > j) { /* row k of M contains column indices i and j */ M [count [i]++] = k ; M [count [j]++] = k ; k++ ; } } } } else { /* Matrix is jumbled. Do not add duplicates to M. Unsorted cols OK. */ DEBUG0 (("symamd: Duplicates in A.\n")) ; for (i = 0 ; i < n ; i++) { mark [i] = -1 ; } for (j = 0 ; j < n ; j++) { ASSERT (p [j+1] - p [j] >= 0) ; for (pp = p [j] ; pp < p [j+1] ; pp++) { i = A [pp] ; ASSERT (i >= 0 && i < n) ; if (i > j && mark [i] != j) { /* row k of M contains column indices i and j */ M [count [i]++] = k ; M [count [j]++] = k ; k++ ; mark [i] = j ; } } } /* v2.4: free(mark) moved below */ } /* count and mark no longer needed */ (*release) ((void *) count) ; (*release) ((void *) mark) ; /* v2.4: free (mark) moved here */ ASSERT (k == n_row) ; /* === Adjust the knobs for M =========================================== */ for (i = 0 ; i < COLAMD_KNOBS ; i++) { cknobs [i] = knobs [i] ; } /* there are no dense rows in M */ cknobs [COLAMD_DENSE_ROW] = -1 ; cknobs [COLAMD_DENSE_COL] = knobs [COLAMD_DENSE_ROW] ; /* === Order the columns of M =========================================== */ /* v2.4: colamd cannot fail here, so the error check is removed */ (void) COLAMD_MAIN (n_row, n, (Int) Mlen, M, perm, cknobs, stats) ; /* Note that the output permutation is now in perm */ /* === get the statistics for symamd from colamd ======================== */ /* a dense column in colamd means a dense row and col in symamd */ stats [COLAMD_DENSE_ROW] = stats [COLAMD_DENSE_COL] ; /* === Free M =========================================================== */ (*release) ((void *) M) ; DEBUG0 (("symamd: done.\n")) ; return (TRUE) ; } /* ========================================================================== */ /* === colamd =============================================================== */ /* ========================================================================== */ /* The colamd routine computes a column ordering Q of a sparse matrix A such that the LU factorization P(AQ) = LU remains sparse, where P is selected via partial pivoting. The routine can also be viewed as providing a permutation Q such that the Cholesky factorization (AQ)'(AQ) = LL' remains sparse. */ PUBLIC Int COLAMD_MAIN /* returns TRUE if successful, FALSE otherwise*/ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows in A */ Int n_col, /* number of columns in A */ Int Alen, /* length of A */ Int A [], /* row indices of A */ Int p [], /* pointers to columns in A */ double knobs [COLAMD_KNOBS],/* parameters (uses defaults if NULL) */ Int stats [COLAMD_STATS] /* output statistics and error codes */ ) { /* === Local variables ================================================== */ Int i ; /* loop index */ Int nnz ; /* nonzeros in A */ size_t Row_size ; /* size of Row [], in integers */ size_t Col_size ; /* size of Col [], in integers */ size_t need ; /* minimum required length of A */ Colamd_Row *Row ; /* pointer into A of Row [0..n_row] array */ Colamd_Col *Col ; /* pointer into A of Col [0..n_col] array */ Int n_col2 ; /* number of non-dense, non-empty columns */ Int n_row2 ; /* number of non-dense, non-empty rows */ Int ngarbage ; /* number of garbage collections performed */ Int max_deg ; /* maximum row degree */ double default_knobs [COLAMD_KNOBS] ; /* default knobs array */ Int aggressive ; /* do aggressive absorption */ int ok ; #ifndef NDEBUG colamd_get_debug ("colamd") ; #endif /* NDEBUG */ /* === Check the input arguments ======================================== */ if (!stats) { DEBUG0 (("colamd: stats not present\n")) ; return (FALSE) ; } for (i = 0 ; i < COLAMD_STATS ; i++) { stats [i] = 0 ; } stats [COLAMD_STATUS] = COLAMD_OK ; stats [COLAMD_INFO1] = -1 ; stats [COLAMD_INFO2] = -1 ; if (!A) /* A is not present */ { stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ; DEBUG0 (("colamd: A not present\n")) ; return (FALSE) ; } if (!p) /* p is not present */ { stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ; DEBUG0 (("colamd: p not present\n")) ; return (FALSE) ; } if (n_row < 0) /* n_row must be >= 0 */ { stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ; stats [COLAMD_INFO1] = n_row ; DEBUG0 (("colamd: nrow negative %d\n", n_row)) ; return (FALSE) ; } if (n_col < 0) /* n_col must be >= 0 */ { stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ; stats [COLAMD_INFO1] = n_col ; DEBUG0 (("colamd: ncol negative %d\n", n_col)) ; return (FALSE) ; } nnz = p [n_col] ; if (nnz < 0) /* nnz must be >= 0 */ { stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ; stats [COLAMD_INFO1] = nnz ; DEBUG0 (("colamd: number of entries negative %d\n", nnz)) ; return (FALSE) ; } if (p [0] != 0) { stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ; stats [COLAMD_INFO1] = p [0] ; DEBUG0 (("colamd: p[0] not zero %d\n", p [0])) ; return (FALSE) ; } /* === If no knobs, set default knobs =================================== */ if (!knobs) { COLAMD_set_defaults (default_knobs) ; knobs = default_knobs ; } aggressive = (knobs [COLAMD_AGGRESSIVE] != FALSE) ; /* === Allocate the Row and Col arrays from array A ===================== */ ok = TRUE ; Col_size = COLAMD_C (n_col, &ok) ; /* size of Col array of structs */ Row_size = COLAMD_R (n_row, &ok) ; /* size of Row array of structs */ /* need = 2*nnz + n_col + Col_size + Row_size ; */ need = t_mult (nnz, 2, &ok) ; need = t_add (need, n_col, &ok) ; need = t_add (need, Col_size, &ok) ; need = t_add (need, Row_size, &ok) ; if (!ok || need > (size_t) Alen || need > Int_MAX) { /* not enough space in array A to perform the ordering */ stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ; stats [COLAMD_INFO1] = need ; stats [COLAMD_INFO2] = Alen ; DEBUG0 (("colamd: Need Alen >= %d, given only Alen = %d\n", need,Alen)); return (FALSE) ; } Alen -= Col_size + Row_size ; Col = (Colamd_Col *) &A [Alen] ; Row = (Colamd_Row *) &A [Alen + Col_size] ; /* === Construct the row and column data structures ===================== */ if (!init_rows_cols (n_row, n_col, Row, Col, A, p, stats)) { /* input matrix is invalid */ DEBUG0 (("colamd: Matrix invalid\n")) ; return (FALSE) ; } /* === Initialize scores, kill dense rows/columns ======================= */ init_scoring (n_row, n_col, Row, Col, A, p, knobs, &n_row2, &n_col2, &max_deg) ; /* === Order the supercolumns =========================================== */ ngarbage = find_ordering (n_row, n_col, Alen, Row, Col, A, p, n_col2, max_deg, 2*nnz, aggressive) ; /* === Order the non-principal columns ================================== */ order_children (n_col, Col, p) ; /* === Return statistics in stats ======================================= */ stats [COLAMD_DENSE_ROW] = n_row - n_row2 ; stats [COLAMD_DENSE_COL] = n_col - n_col2 ; stats [COLAMD_DEFRAG_COUNT] = ngarbage ; DEBUG0 (("colamd: done.\n")) ; return (TRUE) ; } /* ========================================================================== */ /* === colamd_report ======================================================== */ /* ========================================================================== */ PUBLIC void COLAMD_report ( Int stats [COLAMD_STATS] ) { print_report ("colamd", stats) ; } /* ========================================================================== */ /* === symamd_report ======================================================== */ /* ========================================================================== */ PUBLIC void SYMAMD_report ( Int stats [COLAMD_STATS] ) { print_report ("symamd", stats) ; } /* ========================================================================== */ /* === NON-USER-CALLABLE ROUTINES: ========================================== */ /* ========================================================================== */ /* There are no user-callable routines beyond this point in the file */ /* ========================================================================== */ /* === init_rows_cols ======================================================= */ /* ========================================================================== */ /* Takes the column form of the matrix in A and creates the row form of the matrix. Also, row and column attributes are stored in the Col and Row structs. If the columns are un-sorted or contain duplicate row indices, this routine will also sort and remove duplicate row indices from the column form of the matrix. Returns FALSE if the matrix is invalid, TRUE otherwise. Not user-callable. */ PRIVATE Int init_rows_cols /* returns TRUE if OK, or FALSE otherwise */ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows of A */ Int n_col, /* number of columns of A */ Colamd_Row Row [], /* of size n_row+1 */ Colamd_Col Col [], /* of size n_col+1 */ Int A [], /* row indices of A, of size Alen */ Int p [], /* pointers to columns in A, of size n_col+1 */ Int stats [COLAMD_STATS] /* colamd statistics */ ) { /* === Local variables ================================================== */ Int col ; /* a column index */ Int row ; /* a row index */ Int *cp ; /* a column pointer */ Int *cp_end ; /* a pointer to the end of a column */ Int *rp ; /* a row pointer */ Int *rp_end ; /* a pointer to the end of a row */ Int last_row ; /* previous row */ /* === Initialize columns, and check column pointers ==================== */ for (col = 0 ; col < n_col ; col++) { Col [col].start = p [col] ; Col [col].length = p [col+1] - p [col] ; if (Col [col].length < 0) { /* column pointers must be non-decreasing */ stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ; stats [COLAMD_INFO1] = col ; stats [COLAMD_INFO2] = Col [col].length ; DEBUG0 (("colamd: col %d length %d < 0\n", col, Col [col].length)) ; return (FALSE) ; } Col [col].shared1.thickness = 1 ; Col [col].shared2.score = 0 ; Col [col].shared3.prev = EMPTY ; Col [col].shared4.degree_next = EMPTY ; } /* p [0..n_col] no longer needed, used as "head" in subsequent routines */ /* === Scan columns, compute row degrees, and check row indices ========= */ stats [COLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/ for (row = 0 ; row < n_row ; row++) { Row [row].length = 0 ; Row [row].shared2.mark = -1 ; } for (col = 0 ; col < n_col ; col++) { last_row = -1 ; cp = &A [p [col]] ; cp_end = &A [p [col+1]] ; while (cp < cp_end) { row = *cp++ ; /* make sure row indices within range */ if (row < 0 || row >= n_row) { stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ; stats [COLAMD_INFO1] = col ; stats [COLAMD_INFO2] = row ; stats [COLAMD_INFO3] = n_row ; DEBUG0 (("colamd: row %d col %d out of bounds\n", row, col)) ; return (FALSE) ; } if (row <= last_row || Row [row].shared2.mark == col) { /* row index are unsorted or repeated (or both), thus col */ /* is jumbled. This is a notice, not an error condition. */ stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ; stats [COLAMD_INFO1] = col ; stats [COLAMD_INFO2] = row ; (stats [COLAMD_INFO3]) ++ ; DEBUG1 (("colamd: row %d col %d unsorted/duplicate\n",row,col)); } if (Row [row].shared2.mark != col) { Row [row].length++ ; } else { /* this is a repeated entry in the column, */ /* it will be removed */ Col [col].length-- ; } /* mark the row as having been seen in this column */ Row [row].shared2.mark = col ; last_row = row ; } } /* === Compute row pointers ============================================= */ /* row form of the matrix starts directly after the column */ /* form of matrix in A */ Row [0].start = p [n_col] ; Row [0].shared1.p = Row [0].start ; Row [0].shared2.mark = -1 ; for (row = 1 ; row < n_row ; row++) { Row [row].start = Row [row-1].start + Row [row-1].length ; Row [row].shared1.p = Row [row].start ; Row [row].shared2.mark = -1 ; } /* === Create row form ================================================== */ if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED) { /* if cols jumbled, watch for repeated row indices */ for (col = 0 ; col < n_col ; col++) { cp = &A [p [col]] ; cp_end = &A [p [col+1]] ; while (cp < cp_end) { row = *cp++ ; if (Row [row].shared2.mark != col) { A [(Row [row].shared1.p)++] = col ; Row [row].shared2.mark = col ; } } } } else { /* if cols not jumbled, we don't need the mark (this is faster) */ for (col = 0 ; col < n_col ; col++) { cp = &A [p [col]] ; cp_end = &A [p [col+1]] ; while (cp < cp_end) { A [(Row [*cp++].shared1.p)++] = col ; } } } /* === Clear the row marks and set row degrees ========================== */ for (row = 0 ; row < n_row ; row++) { Row [row].shared2.mark = 0 ; Row [row].shared1.degree = Row [row].length ; } /* === See if we need to re-create columns ============================== */ if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED) { DEBUG0 (("colamd: reconstructing column form, matrix jumbled\n")) ; #ifndef NDEBUG /* make sure column lengths are correct */ for (col = 0 ; col < n_col ; col++) { p [col] = Col [col].length ; } for (row = 0 ; row < n_row ; row++) { rp = &A [Row [row].start] ; rp_end = rp + Row [row].length ; while (rp < rp_end) { p [*rp++]-- ; } } for (col = 0 ; col < n_col ; col++) { ASSERT (p [col] == 0) ; } /* now p is all zero (different than when debugging is turned off) */ #endif /* NDEBUG */ /* === Compute col pointers ========================================= */ /* col form of the matrix starts at A [0]. */ /* Note, we may have a gap between the col form and the row */ /* form if there were duplicate entries, if so, it will be */ /* removed upon the first garbage collection */ Col [0].start = 0 ; p [0] = Col [0].start ; for (col = 1 ; col < n_col ; col++) { /* note that the lengths here are for pruned columns, i.e. */ /* no duplicate row indices will exist for these columns */ Col [col].start = Col [col-1].start + Col [col-1].length ; p [col] = Col [col].start ; } /* === Re-create col form =========================================== */ for (row = 0 ; row < n_row ; row++) { rp = &A [Row [row].start] ; rp_end = rp + Row [row].length ; while (rp < rp_end) { A [(p [*rp++])++] = row ; } } } /* === Done. Matrix is not (or no longer) jumbled ====================== */ return (TRUE) ; } /* ========================================================================== */ /* === init_scoring ========================================================= */ /* ========================================================================== */ /* Kills dense or empty columns and rows, calculates an initial score for each column, and places all columns in the degree lists. Not user-callable. */ PRIVATE void init_scoring ( /* === Parameters ======================================================= */ Int n_row, /* number of rows of A */ Int n_col, /* number of columns of A */ Colamd_Row Row [], /* of size n_row+1 */ Colamd_Col Col [], /* of size n_col+1 */ Int A [], /* column form and row form of A */ Int head [], /* of size n_col+1 */ double knobs [COLAMD_KNOBS],/* parameters */ Int *p_n_row2, /* number of non-dense, non-empty rows */ Int *p_n_col2, /* number of non-dense, non-empty columns */ Int *p_max_deg /* maximum row degree */ ) { /* === Local variables ================================================== */ Int c ; /* a column index */ Int r, row ; /* a row index */ Int *cp ; /* a column pointer */ Int deg ; /* degree of a row or column */ Int *cp_end ; /* a pointer to the end of a column */ Int *new_cp ; /* new column pointer */ Int col_length ; /* length of pruned column */ Int score ; /* current column score */ Int n_col2 ; /* number of non-dense, non-empty columns */ Int n_row2 ; /* number of non-dense, non-empty rows */ Int dense_row_count ; /* remove rows with more entries than this */ Int dense_col_count ; /* remove cols with more entries than this */ Int min_score ; /* smallest column score */ Int max_deg ; /* maximum row degree */ Int next_col ; /* Used to add to degree list.*/ #ifndef NDEBUG Int debug_count ; /* debug only. */ #endif /* NDEBUG */ /* === Extract knobs ==================================================== */ /* Note: if knobs contains a NaN, this is undefined: */ if (knobs [COLAMD_DENSE_ROW] < 0) { /* only remove completely dense rows */ dense_row_count = n_col-1 ; } else { dense_row_count = DENSE_DEGREE (knobs [COLAMD_DENSE_ROW], n_col) ; } if (knobs [COLAMD_DENSE_COL] < 0) { /* only remove completely dense columns */ dense_col_count = n_row-1 ; } else { dense_col_count = DENSE_DEGREE (knobs [COLAMD_DENSE_COL], MIN (n_row, n_col)) ; } DEBUG1 (("colamd: densecount: %d %d\n", dense_row_count, dense_col_count)) ; max_deg = 0 ; n_col2 = n_col ; n_row2 = n_row ; /* === Kill empty columns =============================================== */ /* Put the empty columns at the end in their natural order, so that LU */ /* factorization can proceed as far as possible. */ for (c = n_col-1 ; c >= 0 ; c--) { deg = Col [c].length ; if (deg == 0) { /* this is a empty column, kill and order it last */ Col [c].shared2.order = --n_col2 ; KILL_PRINCIPAL_COL (c) ; } } DEBUG1 (("colamd: null columns killed: %d\n", n_col - n_col2)) ; /* === Kill dense columns =============================================== */ /* Put the dense columns at the end, in their natural order */ for (c = n_col-1 ; c >= 0 ; c--) { /* skip any dead columns */ if (COL_IS_DEAD (c)) { continue ; } deg = Col [c].length ; if (deg > dense_col_count) { /* this is a dense column, kill and order it last */ Col [c].shared2.order = --n_col2 ; /* decrement the row degrees */ cp = &A [Col [c].start] ; cp_end = cp + Col [c].length ; while (cp < cp_end) { Row [*cp++].shared1.degree-- ; } KILL_PRINCIPAL_COL (c) ; } } DEBUG1 (("colamd: Dense and null columns killed: %d\n", n_col - n_col2)) ; /* === Kill dense and empty rows ======================================== */ for (r = 0 ; r < n_row ; r++) { deg = Row [r].shared1.degree ; ASSERT (deg >= 0 && deg <= n_col) ; if (deg > dense_row_count || deg == 0) { /* kill a dense or empty row */ KILL_ROW (r) ; --n_row2 ; } else { /* keep track of max degree of remaining rows */ max_deg = MAX (max_deg, deg) ; } } DEBUG1 (("colamd: Dense and null rows killed: %d\n", n_row - n_row2)) ; /* === Compute initial column scores ==================================== */ /* At this point the row degrees are accurate. They reflect the number */ /* of "live" (non-dense) columns in each row. No empty rows exist. */ /* Some "live" columns may contain only dead rows, however. These are */ /* pruned in the code below. */ /* now find the initial matlab score for each column */ for (c = n_col-1 ; c >= 0 ; c--) { /* skip dead column */ if (COL_IS_DEAD (c)) { continue ; } score = 0 ; cp = &A [Col [c].start] ; new_cp = cp ; cp_end = cp + Col [c].length ; while (cp < cp_end) { /* get a row */ row = *cp++ ; /* skip if dead */ if (ROW_IS_DEAD (row)) { continue ; } /* compact the column */ *new_cp++ = row ; /* add row's external degree */ score += Row [row].shared1.degree - 1 ; /* guard against integer overflow */ score = MIN (score, n_col) ; } /* determine pruned column length */ col_length = (Int) (new_cp - &A [Col [c].start]) ; if (col_length == 0) { /* a newly-made null column (all rows in this col are "dense" */ /* and have already been killed) */ DEBUG2 (("Newly null killed: %d\n", c)) ; Col [c].shared2.order = --n_col2 ; KILL_PRINCIPAL_COL (c) ; } else { /* set column length and set score */ ASSERT (score >= 0) ; ASSERT (score <= n_col) ; Col [c].length = col_length ; Col [c].shared2.score = score ; } } DEBUG1 (("colamd: Dense, null, and newly-null columns killed: %d\n", n_col-n_col2)) ; /* At this point, all empty rows and columns are dead. All live columns */ /* are "clean" (containing no dead rows) and simplicial (no supercolumns */ /* yet). Rows may contain dead columns, but all live rows contain at */ /* least one live column. */ #ifndef NDEBUG debug_structures (n_row, n_col, Row, Col, A, n_col2) ; #endif /* NDEBUG */ /* === Initialize degree lists ========================================== */ #ifndef NDEBUG debug_count = 0 ; #endif /* NDEBUG */ /* clear the hash buckets */ for (c = 0 ; c <= n_col ; c++) { head [c] = EMPTY ; } min_score = n_col ; /* place in reverse order, so low column indices are at the front */ /* of the lists. This is to encourage natural tie-breaking */ for (c = n_col-1 ; c >= 0 ; c--) { /* only add principal columns to degree lists */ if (COL_IS_ALIVE (c)) { DEBUG4 (("place %d score %d minscore %d ncol %d\n", c, Col [c].shared2.score, min_score, n_col)) ; /* === Add columns score to DList =============================== */ score = Col [c].shared2.score ; ASSERT (min_score >= 0) ; ASSERT (min_score <= n_col) ; ASSERT (score >= 0) ; ASSERT (score <= n_col) ; ASSERT (head [score] >= EMPTY) ; /* now add this column to dList at proper score location */ next_col = head [score] ; Col [c].shared3.prev = EMPTY ; Col [c].shared4.degree_next = next_col ; /* if there already was a column with the same score, set its */ /* previous pointer to this new column */ if (next_col != EMPTY) { Col [next_col].shared3.prev = c ; } head [score] = c ; /* see if this score is less than current min */ min_score = MIN (min_score, score) ; #ifndef NDEBUG debug_count++ ; #endif /* NDEBUG */ } } #ifndef NDEBUG DEBUG1 (("colamd: Live cols %d out of %d, non-princ: %d\n", debug_count, n_col, n_col-debug_count)) ; ASSERT (debug_count == n_col2) ; debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2, max_deg) ; #endif /* NDEBUG */ /* === Return number of remaining columns, and max row degree =========== */ *p_n_col2 = n_col2 ; *p_n_row2 = n_row2 ; *p_max_deg = max_deg ; } /* ========================================================================== */ /* === find_ordering ======================================================== */ /* ========================================================================== */ /* Order the principal columns of the supercolumn form of the matrix (no supercolumns on input). Uses a minimum approximate column minimum degree ordering method. Not user-callable. */ PRIVATE Int find_ordering /* return the number of garbage collections */ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows of A */ Int n_col, /* number of columns of A */ Int Alen, /* size of A, 2*nnz + n_col or larger */ Colamd_Row Row [], /* of size n_row+1 */ Colamd_Col Col [], /* of size n_col+1 */ Int A [], /* column form and row form of A */ Int head [], /* of size n_col+1 */ Int n_col2, /* Remaining columns to order */ Int max_deg, /* Maximum row degree */ Int pfree, /* index of first free slot (2*nnz on entry) */ Int aggressive ) { /* === Local variables ================================================== */ Int k ; /* current pivot ordering step */ Int pivot_col ; /* current pivot column */ Int *cp ; /* a column pointer */ Int *rp ; /* a row pointer */ Int pivot_row ; /* current pivot row */ Int *new_cp ; /* modified column pointer */ Int *new_rp ; /* modified row pointer */ Int pivot_row_start ; /* pointer to start of pivot row */ Int pivot_row_degree ; /* number of columns in pivot row */ Int pivot_row_length ; /* number of supercolumns in pivot row */ Int pivot_col_score ; /* score of pivot column */ Int needed_memory ; /* free space needed for pivot row */ Int *cp_end ; /* pointer to the end of a column */ Int *rp_end ; /* pointer to the end of a row */ Int row ; /* a row index */ Int col ; /* a column index */ Int max_score ; /* maximum possible score */ Int cur_score ; /* score of current column */ unsigned Int hash ; /* hash value for supernode detection */ Int head_column ; /* head of hash bucket */ Int first_col ; /* first column in hash bucket */ Int tag_mark ; /* marker value for mark array */ Int row_mark ; /* Row [row].shared2.mark */ Int set_difference ; /* set difference size of row with pivot row */ Int min_score ; /* smallest column score */ Int col_thickness ; /* "thickness" (no. of columns in a supercol) */ Int max_mark ; /* maximum value of tag_mark */ Int pivot_col_thickness ; /* number of columns represented by pivot col */ Int prev_col ; /* Used by Dlist operations. */ Int next_col ; /* Used by Dlist operations. */ Int ngarbage ; /* number of garbage collections performed */ #ifndef NDEBUG Int debug_d ; /* debug loop counter */ Int debug_step = 0 ; /* debug loop counter */ #endif /* NDEBUG */ /* === Initialization and clear mark ==================================== */ max_mark = INT_MAX - n_col ; /* INT_MAX defined in */ tag_mark = clear_mark (0, max_mark, n_row, Row) ; min_score = 0 ; ngarbage = 0 ; DEBUG1 (("colamd: Ordering, n_col2=%d\n", n_col2)) ; /* === Order the columns ================================================ */ for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */) { #ifndef NDEBUG if (debug_step % 100 == 0) { DEBUG2 (("\n... Step k: %d out of n_col2: %d\n", k, n_col2)) ; } else { DEBUG3 (("\n----------Step k: %d out of n_col2: %d\n", k, n_col2)) ; } debug_step++ ; debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2-k, max_deg) ; debug_matrix (n_row, n_col, Row, Col, A) ; #endif /* NDEBUG */ /* === Select pivot column, and order it ============================ */ /* make sure degree list isn't empty */ ASSERT (min_score >= 0) ; ASSERT (min_score <= n_col) ; ASSERT (head [min_score] >= EMPTY) ; #ifndef NDEBUG for (debug_d = 0 ; debug_d < min_score ; debug_d++) { ASSERT (head [debug_d] == EMPTY) ; } #endif /* NDEBUG */ /* get pivot column from head of minimum degree list */ while (head [min_score] == EMPTY && min_score < n_col) { min_score++ ; } pivot_col = head [min_score] ; ASSERT (pivot_col >= 0 && pivot_col <= n_col) ; next_col = Col [pivot_col].shared4.degree_next ; head [min_score] = next_col ; if (next_col != EMPTY) { Col [next_col].shared3.prev = EMPTY ; } ASSERT (COL_IS_ALIVE (pivot_col)) ; /* remember score for defrag check */ pivot_col_score = Col [pivot_col].shared2.score ; /* the pivot column is the kth column in the pivot order */ Col [pivot_col].shared2.order = k ; /* increment order count by column thickness */ pivot_col_thickness = Col [pivot_col].shared1.thickness ; k += pivot_col_thickness ; ASSERT (pivot_col_thickness > 0) ; DEBUG3 (("Pivot col: %d thick %d\n", pivot_col, pivot_col_thickness)) ; /* === Garbage_collection, if necessary ============================= */ needed_memory = MIN (pivot_col_score, n_col - k) ; if (pfree + needed_memory >= Alen) { pfree = garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ; ngarbage++ ; /* after garbage collection we will have enough */ ASSERT (pfree + needed_memory < Alen) ; /* garbage collection has wiped out the Row[].shared2.mark array */ tag_mark = clear_mark (0, max_mark, n_row, Row) ; #ifndef NDEBUG debug_matrix (n_row, n_col, Row, Col, A) ; #endif /* NDEBUG */ } /* === Compute pivot row pattern ==================================== */ /* get starting location for this new merged row */ pivot_row_start = pfree ; /* initialize new row counts to zero */ pivot_row_degree = 0 ; /* tag pivot column as having been visited so it isn't included */ /* in merged pivot row */ Col [pivot_col].shared1.thickness = -pivot_col_thickness ; /* pivot row is the union of all rows in the pivot column pattern */ cp = &A [Col [pivot_col].start] ; cp_end = cp + Col [pivot_col].length ; while (cp < cp_end) { /* get a row */ row = *cp++ ; DEBUG4 (("Pivot col pattern %d %d\n", ROW_IS_ALIVE (row), row)) ; /* skip if row is dead */ if (ROW_IS_ALIVE (row)) { rp = &A [Row [row].start] ; rp_end = rp + Row [row].length ; while (rp < rp_end) { /* get a column */ col = *rp++ ; /* add the column, if alive and untagged */ col_thickness = Col [col].shared1.thickness ; if (col_thickness > 0 && COL_IS_ALIVE (col)) { /* tag column in pivot row */ Col [col].shared1.thickness = -col_thickness ; ASSERT (pfree < Alen) ; /* place column in pivot row */ A [pfree++] = col ; pivot_row_degree += col_thickness ; } } } } /* clear tag on pivot column */ Col [pivot_col].shared1.thickness = pivot_col_thickness ; max_deg = MAX (max_deg, pivot_row_degree) ; #ifndef NDEBUG DEBUG3 (("check2\n")) ; debug_mark (n_row, Row, tag_mark, max_mark) ; #endif /* NDEBUG */ /* === Kill all rows used to construct pivot row ==================== */ /* also kill pivot row, temporarily */ cp = &A [Col [pivot_col].start] ; cp_end = cp + Col [pivot_col].length ; while (cp < cp_end) { /* may be killing an already dead row */ row = *cp++ ; DEBUG3 (("Kill row in pivot col: %d\n", row)) ; KILL_ROW (row) ; } /* === Select a row index to use as the new pivot row =============== */ pivot_row_length = pfree - pivot_row_start ; if (pivot_row_length > 0) { /* pick the "pivot" row arbitrarily (first row in col) */ pivot_row = A [Col [pivot_col].start] ; DEBUG3 (("Pivotal row is %d\n", pivot_row)) ; } else { /* there is no pivot row, since it is of zero length */ pivot_row = EMPTY ; ASSERT (pivot_row_length == 0) ; } ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ; /* === Approximate degree computation =============================== */ /* Here begins the computation of the approximate degree. The column */ /* score is the sum of the pivot row "length", plus the size of the */ /* set differences of each row in the column minus the pattern of the */ /* pivot row itself. The column ("thickness") itself is also */ /* excluded from the column score (we thus use an approximate */ /* external degree). */ /* The time taken by the following code (compute set differences, and */ /* add them up) is proportional to the size of the data structure */ /* being scanned - that is, the sum of the sizes of each column in */ /* the pivot row. Thus, the amortized time to compute a column score */ /* is proportional to the size of that column (where size, in this */ /* context, is the column "length", or the number of row indices */ /* in that column). The number of row indices in a column is */ /* monotonically non-decreasing, from the length of the original */ /* column on input to colamd. */ /* === Compute set differences ====================================== */ DEBUG3 (("** Computing set differences phase. **\n")) ; /* pivot row is currently dead - it will be revived later. */ DEBUG3 (("Pivot row: ")) ; /* for each column in pivot row */ rp = &A [pivot_row_start] ; rp_end = rp + pivot_row_length ; while (rp < rp_end) { col = *rp++ ; ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; DEBUG3 (("Col: %d\n", col)) ; /* clear tags used to construct pivot row pattern */ col_thickness = -Col [col].shared1.thickness ; ASSERT (col_thickness > 0) ; Col [col].shared1.thickness = col_thickness ; /* === Remove column from degree list =========================== */ cur_score = Col [col].shared2.score ; prev_col = Col [col].shared3.prev ; next_col = Col [col].shared4.degree_next ; ASSERT (cur_score >= 0) ; ASSERT (cur_score <= n_col) ; ASSERT (cur_score >= EMPTY) ; if (prev_col == EMPTY) { head [cur_score] = next_col ; } else { Col [prev_col].shared4.degree_next = next_col ; } if (next_col != EMPTY) { Col [next_col].shared3.prev = prev_col ; } /* === Scan the column ========================================== */ cp = &A [Col [col].start] ; cp_end = cp + Col [col].length ; while (cp < cp_end) { /* get a row */ row = *cp++ ; row_mark = Row [row].shared2.mark ; /* skip if dead */ if (ROW_IS_MARKED_DEAD (row_mark)) { continue ; } ASSERT (row != pivot_row) ; set_difference = row_mark - tag_mark ; /* check if the row has been seen yet */ if (set_difference < 0) { ASSERT (Row [row].shared1.degree <= max_deg) ; set_difference = Row [row].shared1.degree ; } /* subtract column thickness from this row's set difference */ set_difference -= col_thickness ; ASSERT (set_difference >= 0) ; /* absorb this row if the set difference becomes zero */ if (set_difference == 0 && aggressive) { DEBUG3 (("aggressive absorption. Row: %d\n", row)) ; KILL_ROW (row) ; } else { /* save the new mark */ Row [row].shared2.mark = set_difference + tag_mark ; } } } #ifndef NDEBUG debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2-k-pivot_row_degree, max_deg) ; #endif /* NDEBUG */ /* === Add up set differences for each column ======================= */ DEBUG3 (("** Adding set differences phase. **\n")) ; /* for each column in pivot row */ rp = &A [pivot_row_start] ; rp_end = rp + pivot_row_length ; while (rp < rp_end) { /* get a column */ col = *rp++ ; ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; hash = 0 ; cur_score = 0 ; cp = &A [Col [col].start] ; /* compact the column */ new_cp = cp ; cp_end = cp + Col [col].length ; DEBUG4 (("Adding set diffs for Col: %d.\n", col)) ; while (cp < cp_end) { /* get a row */ row = *cp++ ; ASSERT(row >= 0 && row < n_row) ; row_mark = Row [row].shared2.mark ; /* skip if dead */ if (ROW_IS_MARKED_DEAD (row_mark)) { DEBUG4 ((" Row %d, dead\n", row)) ; continue ; } DEBUG4 ((" Row %d, set diff %d\n", row, row_mark-tag_mark)); ASSERT (row_mark >= tag_mark) ; /* compact the column */ *new_cp++ = row ; /* compute hash function */ hash += row ; /* add set difference */ cur_score += row_mark - tag_mark ; /* integer overflow... */ cur_score = MIN (cur_score, n_col) ; } /* recompute the column's length */ Col [col].length = (Int) (new_cp - &A [Col [col].start]) ; /* === Further mass elimination ================================= */ if (Col [col].length == 0) { DEBUG4 (("further mass elimination. Col: %d\n", col)) ; /* nothing left but the pivot row in this column */ KILL_PRINCIPAL_COL (col) ; pivot_row_degree -= Col [col].shared1.thickness ; ASSERT (pivot_row_degree >= 0) ; /* order it */ Col [col].shared2.order = k ; /* increment order count by column thickness */ k += Col [col].shared1.thickness ; } else { /* === Prepare for supercolumn detection ==================== */ DEBUG4 (("Preparing supercol detection for Col: %d.\n", col)) ; /* save score so far */ Col [col].shared2.score = cur_score ; /* add column to hash table, for supercolumn detection */ hash %= n_col + 1 ; DEBUG4 ((" Hash = %d, n_col = %d.\n", hash, n_col)) ; ASSERT (((Int) hash) <= n_col) ; head_column = head [hash] ; if (head_column > EMPTY) { /* degree list "hash" is non-empty, use prev (shared3) of */ /* first column in degree list as head of hash bucket */ first_col = Col [head_column].shared3.headhash ; Col [head_column].shared3.headhash = col ; } else { /* degree list "hash" is empty, use head as hash bucket */ first_col = - (head_column + 2) ; head [hash] = - (col + 2) ; } Col [col].shared4.hash_next = first_col ; /* save hash function in Col [col].shared3.hash */ Col [col].shared3.hash = (Int) hash ; ASSERT (COL_IS_ALIVE (col)) ; } } /* The approximate external column degree is now computed. */ /* === Supercolumn detection ======================================== */ DEBUG3 (("** Supercolumn detection phase. **\n")) ; detect_super_cols ( #ifndef NDEBUG n_col, Row, #endif /* NDEBUG */ Col, A, head, pivot_row_start, pivot_row_length) ; /* === Kill the pivotal column ====================================== */ KILL_PRINCIPAL_COL (pivot_col) ; /* === Clear mark =================================================== */ tag_mark = clear_mark (tag_mark+max_deg+1, max_mark, n_row, Row) ; #ifndef NDEBUG DEBUG3 (("check3\n")) ; debug_mark (n_row, Row, tag_mark, max_mark) ; #endif /* NDEBUG */ /* === Finalize the new pivot row, and column scores ================ */ DEBUG3 (("** Finalize scores phase. **\n")) ; /* for each column in pivot row */ rp = &A [pivot_row_start] ; /* compact the pivot row */ new_rp = rp ; rp_end = rp + pivot_row_length ; while (rp < rp_end) { col = *rp++ ; /* skip dead columns */ if (COL_IS_DEAD (col)) { continue ; } *new_rp++ = col ; /* add new pivot row to column */ A [Col [col].start + (Col [col].length++)] = pivot_row ; /* retrieve score so far and add on pivot row's degree. */ /* (we wait until here for this in case the pivot */ /* row's degree was reduced due to mass elimination). */ cur_score = Col [col].shared2.score + pivot_row_degree ; /* calculate the max possible score as the number of */ /* external columns minus the 'k' value minus the */ /* columns thickness */ max_score = n_col - k - Col [col].shared1.thickness ; /* make the score the external degree of the union-of-rows */ cur_score -= Col [col].shared1.thickness ; /* make sure score is less or equal than the max score */ cur_score = MIN (cur_score, max_score) ; ASSERT (cur_score >= 0) ; /* store updated score */ Col [col].shared2.score = cur_score ; /* === Place column back in degree list ========================= */ ASSERT (min_score >= 0) ; ASSERT (min_score <= n_col) ; ASSERT (cur_score >= 0) ; ASSERT (cur_score <= n_col) ; ASSERT (head [cur_score] >= EMPTY) ; next_col = head [cur_score] ; Col [col].shared4.degree_next = next_col ; Col [col].shared3.prev = EMPTY ; if (next_col != EMPTY) { Col [next_col].shared3.prev = col ; } head [cur_score] = col ; /* see if this score is less than current min */ min_score = MIN (min_score, cur_score) ; } #ifndef NDEBUG debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2-k, max_deg) ; #endif /* NDEBUG */ /* === Resurrect the new pivot row ================================== */ if (pivot_row_degree > 0) { /* update pivot row length to reflect any cols that were killed */ /* during super-col detection and mass elimination */ Row [pivot_row].start = pivot_row_start ; Row [pivot_row].length = (Int) (new_rp - &A[pivot_row_start]) ; ASSERT (Row [pivot_row].length > 0) ; Row [pivot_row].shared1.degree = pivot_row_degree ; Row [pivot_row].shared2.mark = 0 ; /* pivot row is no longer dead */ DEBUG1 (("Resurrect Pivot_row %d deg: %d\n", pivot_row, pivot_row_degree)) ; } } /* === All principal columns have now been ordered ====================== */ return (ngarbage) ; } /* ========================================================================== */ /* === order_children ======================================================= */ /* ========================================================================== */ /* The find_ordering routine has ordered all of the principal columns (the representatives of the supercolumns). The non-principal columns have not yet been ordered. This routine orders those columns by walking up the parent tree (a column is a child of the column which absorbed it). The final permutation vector is then placed in p [0 ... n_col-1], with p [0] being the first column, and p [n_col-1] being the last. It doesn't look like it at first glance, but be assured that this routine takes time linear in the number of columns. Although not immediately obvious, the time taken by this routine is O (n_col), that is, linear in the number of columns. Not user-callable. */ PRIVATE void order_children ( /* === Parameters ======================================================= */ Int n_col, /* number of columns of A */ Colamd_Col Col [], /* of size n_col+1 */ Int p [] /* p [0 ... n_col-1] is the column permutation*/ ) { /* === Local variables ================================================== */ Int i ; /* loop counter for all columns */ Int c ; /* column index */ Int parent ; /* index of column's parent */ Int order ; /* column's order */ /* === Order each non-principal column ================================== */ for (i = 0 ; i < n_col ; i++) { /* find an un-ordered non-principal column */ ASSERT (COL_IS_DEAD (i)) ; if (!COL_IS_DEAD_PRINCIPAL (i) && Col [i].shared2.order == EMPTY) { parent = i ; /* once found, find its principal parent */ do { parent = Col [parent].shared1.parent ; } while (!COL_IS_DEAD_PRINCIPAL (parent)) ; /* now, order all un-ordered non-principal columns along path */ /* to this parent. collapse tree at the same time */ c = i ; /* get order of parent */ order = Col [parent].shared2.order ; do { ASSERT (Col [c].shared2.order == EMPTY) ; /* order this column */ Col [c].shared2.order = order++ ; /* collaps tree */ Col [c].shared1.parent = parent ; /* get immediate parent of this column */ c = Col [c].shared1.parent ; /* continue until we hit an ordered column. There are */ /* guarranteed not to be anymore unordered columns */ /* above an ordered column */ } while (Col [c].shared2.order == EMPTY) ; /* re-order the super_col parent to largest order for this group */ Col [parent].shared2.order = order ; } } /* === Generate the permutation ========================================= */ for (c = 0 ; c < n_col ; c++) { p [Col [c].shared2.order] = c ; } } /* ========================================================================== */ /* === detect_super_cols ==================================================== */ /* ========================================================================== */ /* Detects supercolumns by finding matches between columns in the hash buckets. Check amongst columns in the set A [row_start ... row_start + row_length-1]. The columns under consideration are currently *not* in the degree lists, and have already been placed in the hash buckets. The hash bucket for columns whose hash function is equal to h is stored as follows: if head [h] is >= 0, then head [h] contains a degree list, so: head [h] is the first column in degree bucket h. Col [head [h]].headhash gives the first column in hash bucket h. otherwise, the degree list is empty, and: -(head [h] + 2) is the first column in hash bucket h. For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous column" pointer. Col [c].shared3.hash is used instead as the hash number for that column. The value of Col [c].shared4.hash_next is the next column in the same hash bucket. Assuming no, or "few" hash collisions, the time taken by this routine is linear in the sum of the sizes (lengths) of each column whose score has just been computed in the approximate degree computation. Not user-callable. */ PRIVATE void detect_super_cols ( /* === Parameters ======================================================= */ #ifndef NDEBUG /* these two parameters are only needed when debugging is enabled: */ Int n_col, /* number of columns of A */ Colamd_Row Row [], /* of size n_row+1 */ #endif /* NDEBUG */ Colamd_Col Col [], /* of size n_col+1 */ Int A [], /* row indices of A */ Int head [], /* head of degree lists and hash buckets */ Int row_start, /* pointer to set of columns to check */ Int row_length /* number of columns to check */ ) { /* === Local variables ================================================== */ Int hash ; /* hash value for a column */ Int *rp ; /* pointer to a row */ Int c ; /* a column index */ Int super_c ; /* column index of the column to absorb into */ Int *cp1 ; /* column pointer for column super_c */ Int *cp2 ; /* column pointer for column c */ Int length ; /* length of column super_c */ Int prev_c ; /* column preceding c in hash bucket */ Int i ; /* loop counter */ Int *rp_end ; /* pointer to the end of the row */ Int col ; /* a column index in the row to check */ Int head_column ; /* first column in hash bucket or degree list */ Int first_col ; /* first column in hash bucket */ /* === Consider each column in the row ================================== */ rp = &A [row_start] ; rp_end = rp + row_length ; while (rp < rp_end) { col = *rp++ ; if (COL_IS_DEAD (col)) { continue ; } /* get hash number for this column */ hash = Col [col].shared3.hash ; ASSERT (hash <= n_col) ; /* === Get the first column in this hash bucket ===================== */ head_column = head [hash] ; if (head_column > EMPTY) { first_col = Col [head_column].shared3.headhash ; } else { first_col = - (head_column + 2) ; } /* === Consider each column in the hash bucket ====================== */ for (super_c = first_col ; super_c != EMPTY ; super_c = Col [super_c].shared4.hash_next) { ASSERT (COL_IS_ALIVE (super_c)) ; ASSERT (Col [super_c].shared3.hash == hash) ; length = Col [super_c].length ; /* prev_c is the column preceding column c in the hash bucket */ prev_c = super_c ; /* === Compare super_c with all columns after it ================ */ for (c = Col [super_c].shared4.hash_next ; c != EMPTY ; c = Col [c].shared4.hash_next) { ASSERT (c != super_c) ; ASSERT (COL_IS_ALIVE (c)) ; ASSERT (Col [c].shared3.hash == hash) ; /* not identical if lengths or scores are different */ if (Col [c].length != length || Col [c].shared2.score != Col [super_c].shared2.score) { prev_c = c ; continue ; } /* compare the two columns */ cp1 = &A [Col [super_c].start] ; cp2 = &A [Col [c].start] ; for (i = 0 ; i < length ; i++) { /* the columns are "clean" (no dead rows) */ ASSERT (ROW_IS_ALIVE (*cp1)) ; ASSERT (ROW_IS_ALIVE (*cp2)) ; /* row indices will same order for both supercols, */ /* no gather scatter nessasary */ if (*cp1++ != *cp2++) { break ; } } /* the two columns are different if the for-loop "broke" */ if (i != length) { prev_c = c ; continue ; } /* === Got it! two columns are identical =================== */ ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ; Col [super_c].shared1.thickness += Col [c].shared1.thickness ; Col [c].shared1.parent = super_c ; KILL_NON_PRINCIPAL_COL (c) ; /* order c later, in order_children() */ Col [c].shared2.order = EMPTY ; /* remove c from hash bucket */ Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ; } } /* === Empty this hash bucket ======================================= */ if (head_column > EMPTY) { /* corresponding degree list "hash" is not empty */ Col [head_column].shared3.headhash = EMPTY ; } else { /* corresponding degree list "hash" is empty */ head [hash] = EMPTY ; } } } /* ========================================================================== */ /* === garbage_collection =================================================== */ /* ========================================================================== */ /* Defragments and compacts columns and rows in the workspace A. Used when all avaliable memory has been used while performing row merging. Returns the index of the first free position in A, after garbage collection. The time taken by this routine is linear is the size of the array A, which is itself linear in the number of nonzeros in the input matrix. Not user-callable. */ PRIVATE Int garbage_collection /* returns the new value of pfree */ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows */ Int n_col, /* number of columns */ Colamd_Row Row [], /* row info */ Colamd_Col Col [], /* column info */ Int A [], /* A [0 ... Alen-1] holds the matrix */ Int *pfree /* &A [0] ... pfree is in use */ ) { /* === Local variables ================================================== */ Int *psrc ; /* source pointer */ Int *pdest ; /* destination pointer */ Int j ; /* counter */ Int r ; /* a row index */ Int c ; /* a column index */ Int length ; /* length of a row or column */ #ifndef NDEBUG Int debug_rows ; DEBUG2 (("Defrag..\n")) ; for (psrc = &A[0] ; psrc < pfree ; psrc++) ASSERT (*psrc >= 0) ; debug_rows = 0 ; #endif /* NDEBUG */ /* === Defragment the columns =========================================== */ pdest = &A[0] ; for (c = 0 ; c < n_col ; c++) { if (COL_IS_ALIVE (c)) { psrc = &A [Col [c].start] ; /* move and compact the column */ ASSERT (pdest <= psrc) ; Col [c].start = (Int) (pdest - &A [0]) ; length = Col [c].length ; for (j = 0 ; j < length ; j++) { r = *psrc++ ; if (ROW_IS_ALIVE (r)) { *pdest++ = r ; } } Col [c].length = (Int) (pdest - &A [Col [c].start]) ; } } /* === Prepare to defragment the rows =================================== */ for (r = 0 ; r < n_row ; r++) { if (ROW_IS_DEAD (r) || (Row [r].length == 0)) { /* This row is already dead, or is of zero length. Cannot compact * a row of zero length, so kill it. NOTE: in the current version, * there are no zero-length live rows. Kill the row (for the first * time, or again) just to be safe. */ KILL_ROW (r) ; } else { /* save first column index in Row [r].shared2.first_column */ psrc = &A [Row [r].start] ; Row [r].shared2.first_column = *psrc ; ASSERT (ROW_IS_ALIVE (r)) ; /* flag the start of the row with the one's complement of row */ *psrc = ONES_COMPLEMENT (r) ; #ifndef NDEBUG debug_rows++ ; #endif /* NDEBUG */ } } /* === Defragment the rows ============================================== */ psrc = pdest ; while (psrc < pfree) { /* find a negative number ... the start of a row */ if (*psrc++ < 0) { psrc-- ; /* get the row index */ r = ONES_COMPLEMENT (*psrc) ; ASSERT (r >= 0 && r < n_row) ; /* restore first column index */ *psrc = Row [r].shared2.first_column ; ASSERT (ROW_IS_ALIVE (r)) ; ASSERT (Row [r].length > 0) ; /* move and compact the row */ ASSERT (pdest <= psrc) ; Row [r].start = (Int) (pdest - &A [0]) ; length = Row [r].length ; for (j = 0 ; j < length ; j++) { c = *psrc++ ; if (COL_IS_ALIVE (c)) { *pdest++ = c ; } } Row [r].length = (Int) (pdest - &A [Row [r].start]) ; ASSERT (Row [r].length > 0) ; #ifndef NDEBUG debug_rows-- ; #endif /* NDEBUG */ } } /* ensure we found all the rows */ ASSERT (debug_rows == 0) ; /* === Return the new value of pfree ==================================== */ return ((Int) (pdest - &A [0])) ; } /* ========================================================================== */ /* === clear_mark =========================================================== */ /* ========================================================================== */ /* Clears the Row [].shared2.mark array, and returns the new tag_mark. Return value is the new tag_mark. Not user-callable. */ PRIVATE Int clear_mark /* return the new value for tag_mark */ ( /* === Parameters ======================================================= */ Int tag_mark, /* new value of tag_mark */ Int max_mark, /* max allowed value of tag_mark */ Int n_row, /* number of rows in A */ Colamd_Row Row [] /* Row [0 ... n_row-1].shared2.mark is set to zero */ ) { /* === Local variables ================================================== */ Int r ; if (tag_mark <= 0 || tag_mark >= max_mark) { for (r = 0 ; r < n_row ; r++) { if (ROW_IS_ALIVE (r)) { Row [r].shared2.mark = 0 ; } } tag_mark = 1 ; } return (tag_mark) ; } /* ========================================================================== */ /* === print_report ========================================================= */ /* ========================================================================== */ PRIVATE void print_report ( char *method, Int stats [COLAMD_STATS] ) { Int i1, i2, i3 ; PRINTF (("\n%s version %d.%d, %s: ", method, COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE)) ; if (!stats) { PRINTF (("No statistics available.\n")) ; return ; } i1 = stats [COLAMD_INFO1] ; i2 = stats [COLAMD_INFO2] ; i3 = stats [COLAMD_INFO3] ; if (stats [COLAMD_STATUS] >= 0) { PRINTF (("OK. ")) ; } else { PRINTF (("ERROR. ")) ; } switch (stats [COLAMD_STATUS]) { case COLAMD_OK_BUT_JUMBLED: PRINTF(("Matrix has unsorted or duplicate row indices.\n")) ; PRINTF(("%s: number of duplicate or out-of-order row indices: %d\n", method, i3)) ; PRINTF(("%s: last seen duplicate or out-of-order row index: %d\n", method, INDEX (i2))) ; PRINTF(("%s: last seen in column: %d", method, INDEX (i1))) ; /* no break - fall through to next case instead */ case COLAMD_OK: PRINTF(("\n")) ; PRINTF(("%s: number of dense or empty rows ignored: %d\n", method, stats [COLAMD_DENSE_ROW])) ; PRINTF(("%s: number of dense or empty columns ignored: %d\n", method, stats [COLAMD_DENSE_COL])) ; PRINTF(("%s: number of garbage collections performed: %d\n", method, stats [COLAMD_DEFRAG_COUNT])) ; break ; case COLAMD_ERROR_A_not_present: PRINTF(("Array A (row indices of matrix) not present.\n")) ; break ; case COLAMD_ERROR_p_not_present: PRINTF(("Array p (column pointers for matrix) not present.\n")) ; break ; case COLAMD_ERROR_nrow_negative: PRINTF(("Invalid number of rows (%d).\n", i1)) ; break ; case COLAMD_ERROR_ncol_negative: PRINTF(("Invalid number of columns (%d).\n", i1)) ; break ; case COLAMD_ERROR_nnz_negative: PRINTF(("Invalid number of nonzero entries (%d).\n", i1)) ; break ; case COLAMD_ERROR_p0_nonzero: PRINTF(("Invalid column pointer, p [0] = %d, must be zero.\n", i1)); break ; case COLAMD_ERROR_A_too_small: PRINTF(("Array A too small.\n")) ; PRINTF((" Need Alen >= %d, but given only Alen = %d.\n", i1, i2)) ; break ; case COLAMD_ERROR_col_length_negative: PRINTF (("Column %d has a negative number of nonzero entries (%d).\n", INDEX (i1), i2)) ; break ; case COLAMD_ERROR_row_index_out_of_bounds: PRINTF (("Row index (row %d) out of bounds (%d to %d) in column %d.\n", INDEX (i2), INDEX (0), INDEX (i3-1), INDEX (i1))) ; break ; case COLAMD_ERROR_out_of_memory: PRINTF(("Out of memory.\n")) ; break ; /* v2.4: internal-error case deleted */ } } /* ========================================================================== */ /* === colamd debugging routines ============================================ */ /* ========================================================================== */ /* When debugging is disabled, the remainder of this file is ignored. */ #ifndef NDEBUG /* ========================================================================== */ /* === debug_structures ===================================================== */ /* ========================================================================== */ /* At this point, all empty rows and columns are dead. All live columns are "clean" (containing no dead rows) and simplicial (no supercolumns yet). Rows may contain dead columns, but all live rows contain at least one live column. */ PRIVATE void debug_structures ( /* === Parameters ======================================================= */ Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int n_col2 ) { /* === Local variables ================================================== */ Int i ; Int c ; Int *cp ; Int *cp_end ; Int len ; Int score ; Int r ; Int *rp ; Int *rp_end ; Int deg ; /* === Check A, Row, and Col ============================================ */ for (c = 0 ; c < n_col ; c++) { if (COL_IS_ALIVE (c)) { len = Col [c].length ; score = Col [c].shared2.score ; DEBUG4 (("initial live col %5d %5d %5d\n", c, len, score)) ; ASSERT (len > 0) ; ASSERT (score >= 0) ; ASSERT (Col [c].shared1.thickness == 1) ; cp = &A [Col [c].start] ; cp_end = cp + len ; while (cp < cp_end) { r = *cp++ ; ASSERT (ROW_IS_ALIVE (r)) ; } } else { i = Col [c].shared2.order ; ASSERT (i >= n_col2 && i < n_col) ; } } for (r = 0 ; r < n_row ; r++) { if (ROW_IS_ALIVE (r)) { i = 0 ; len = Row [r].length ; deg = Row [r].shared1.degree ; ASSERT (len > 0) ; ASSERT (deg > 0) ; rp = &A [Row [r].start] ; rp_end = rp + len ; while (rp < rp_end) { c = *rp++ ; if (COL_IS_ALIVE (c)) { i++ ; } } ASSERT (i > 0) ; } } } /* ========================================================================== */ /* === debug_deg_lists ====================================================== */ /* ========================================================================== */ /* Prints the contents of the degree lists. Counts the number of columns in the degree list and compares it to the total it should have. Also checks the row degrees. */ PRIVATE void debug_deg_lists ( /* === Parameters ======================================================= */ Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int head [], Int min_score, Int should, Int max_deg ) { /* === Local variables ================================================== */ Int deg ; Int col ; Int have ; Int row ; /* === Check the degree lists =========================================== */ if (n_col > 10000 && colamd_debug <= 0) { return ; } have = 0 ; DEBUG4 (("Degree lists: %d\n", min_score)) ; for (deg = 0 ; deg <= n_col ; deg++) { col = head [deg] ; if (col == EMPTY) { continue ; } DEBUG4 (("%d:", deg)) ; while (col != EMPTY) { DEBUG4 ((" %d", col)) ; have += Col [col].shared1.thickness ; ASSERT (COL_IS_ALIVE (col)) ; col = Col [col].shared4.degree_next ; } DEBUG4 (("\n")) ; } DEBUG4 (("should %d have %d\n", should, have)) ; ASSERT (should == have) ; /* === Check the row degrees ============================================ */ if (n_row > 10000 && colamd_debug <= 0) { return ; } for (row = 0 ; row < n_row ; row++) { if (ROW_IS_ALIVE (row)) { ASSERT (Row [row].shared1.degree <= max_deg) ; } } } /* ========================================================================== */ /* === debug_mark =========================================================== */ /* ========================================================================== */ /* Ensures that the tag_mark is less that the maximum and also ensures that each entry in the mark array is less than the tag mark. */ PRIVATE void debug_mark ( /* === Parameters ======================================================= */ Int n_row, Colamd_Row Row [], Int tag_mark, Int max_mark ) { /* === Local variables ================================================== */ Int r ; /* === Check the Row marks ============================================== */ ASSERT (tag_mark > 0 && tag_mark <= max_mark) ; if (n_row > 10000 && colamd_debug <= 0) { return ; } for (r = 0 ; r < n_row ; r++) { ASSERT (Row [r].shared2.mark < tag_mark) ; } } /* ========================================================================== */ /* === debug_matrix ========================================================= */ /* ========================================================================== */ /* Prints out the contents of the columns and the rows. */ PRIVATE void debug_matrix ( /* === Parameters ======================================================= */ Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [] ) { /* === Local variables ================================================== */ Int r ; Int c ; Int *rp ; Int *rp_end ; Int *cp ; Int *cp_end ; /* === Dump the rows and columns of the matrix ========================== */ if (colamd_debug < 3) { return ; } DEBUG3 (("DUMP MATRIX:\n")) ; for (r = 0 ; r < n_row ; r++) { DEBUG3 (("Row %d alive? %d\n", r, ROW_IS_ALIVE (r))) ; if (ROW_IS_DEAD (r)) { continue ; } DEBUG3 (("start %d length %d degree %d\n", Row [r].start, Row [r].length, Row [r].shared1.degree)) ; rp = &A [Row [r].start] ; rp_end = rp + Row [r].length ; while (rp < rp_end) { c = *rp++ ; DEBUG4 ((" %d col %d\n", COL_IS_ALIVE (c), c)) ; } } for (c = 0 ; c < n_col ; c++) { DEBUG3 (("Col %d alive? %d\n", c, COL_IS_ALIVE (c))) ; if (COL_IS_DEAD (c)) { continue ; } DEBUG3 (("start %d length %d shared1 %d shared2 %d\n", Col [c].start, Col [c].length, Col [c].shared1.thickness, Col [c].shared2.score)) ; cp = &A [Col [c].start] ; cp_end = cp + Col [c].length ; while (cp < cp_end) { r = *cp++ ; DEBUG4 ((" %d row %d\n", ROW_IS_ALIVE (r), r)) ; } } } PRIVATE void colamd_get_debug ( char *method ) { FILE *f ; colamd_debug = 0 ; /* no debug printing */ f = fopen ("debug", "r") ; if (f == (FILE *) NULL) { colamd_debug = 0 ; } else { fscanf (f, "%d", &colamd_debug) ; fclose (f) ; } DEBUG0 (("%s: debug version, D = %d (THIS WILL BE SLOW!)\n", method, colamd_debug)) ; } #endif /* NDEBUG */ Matrix/src/COLAMD/Source/Makefile0000644000175100001440000000057512271765436016206 0ustar hornikusersinclude $(MkInclude) PKG_CPPFLAGS = -I../Include -I../../SuiteSparse_config LIB = ../../COLAMD.a lib: $(LIB) colamd_l.o: colamd.c $(CC) $(ALL_CPPFLAGS) $(ALL_CFLAGS) -I../Include -DDLONG -c colamd.c -o $@ $(LIB): colamd_global.o colamd.o colamd_l.o $(AR) -rucs $(LIB) colamd_global.o colamd.o colamd_l.o mostlyclean: clean clean: @-rm -rf .libs _libs $(LIB) @-rm -f *.o Matrix/src/COLAMD/Source/colamd_global.c0000644000175100001440000000164112271765436017464 0ustar hornikusers/* ========================================================================== */ /* === colamd_global.c ====================================================== */ /* ========================================================================== */ /* ---------------------------------------------------------------------------- * COLAMD, Copyright (C) 2007, Timothy A. Davis. * See License.txt for the Version 2.1 of the GNU Lesser General Public License * http://www.suitesparse.com * -------------------------------------------------------------------------- */ /* Global variables for COLAMD */ #ifndef NPRINT #ifdef MATLAB_MEX_FILE #include "mex.h" int (*colamd_printf) (const char *, ...) = mexPrintf ; #else #include // For use with R package 'Matrix': #include void (*colamd_printf) (const char *, ...) = Rprintf ; #endif #else int (*colamd_printf) (const char *, ...) = ((void *) 0) ; #endif Matrix/src/COLAMD/Makefile0000644000175100001440000000027612271765436014744 0ustar hornikusers# compile just the C-callable library library: ( cd Source ; $(MAKE) lib ) # remove object files, but keep the compiled programs and library archives clean: ( cd Source ; $(MAKE) clean ) Matrix/src/COLAMD/Include/0000755000175100001440000000000012271765426014661 5ustar hornikusersMatrix/src/COLAMD/Include/colamd.h0000644000175100001440000002121012271765436016266 0ustar hornikusers/* ========================================================================== */ /* === colamd/symamd prototypes and definitions ============================= */ /* ========================================================================== */ /* COLAMD / SYMAMD include file You must include this file (colamd.h) in any routine that uses colamd, symamd, or the related macros and definitions. Authors: The authors of the code itself are Stefan I. Larimore and Timothy A. Davis (DrTimothyAldenDavis@gmail.com). The algorithm was developed in collaboration with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974 and DMS-9803599. Notice: Copyright (c) 1998-2007, Timothy A. Davis, All Rights Reserved. THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. Permission is hereby granted to use, copy, modify, and/or distribute this program, provided that the Copyright, this License, and the Availability of the original version is retained on all copies and made accessible to the end-user of any code or package that includes COLAMD or any modified version of COLAMD. Availability: The colamd/symamd library is available at http://www.suitesparse.com This file is required by the colamd.c, colamdmex.c, and symamdmex.c files, and by any C code that calls the routines whose prototypes are listed below, or that uses the colamd/symamd definitions listed below. */ #ifndef COLAMD_H #define COLAMD_H /* make it easy for C++ programs to include COLAMD */ #ifdef __cplusplus extern "C" { #endif /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include /* ========================================================================== */ /* === COLAMD version ======================================================= */ /* ========================================================================== */ /* COLAMD Version 2.4 and later will include the following definitions. * As an example, to test if the version you are using is 2.4 or later: * * #ifdef COLAMD_VERSION * if (COLAMD_VERSION >= COLAMD_VERSION_CODE (2,4)) ... * #endif * * This also works during compile-time: * * #if defined(COLAMD_VERSION) && (COLAMD_VERSION >= COLAMD_VERSION_CODE (2,4)) * printf ("This is version 2.4 or later\n") ; * #else * printf ("This is an early version\n") ; * #endif * * Versions 2.3 and earlier of COLAMD do not include a #define'd version number. */ #define COLAMD_DATE "Jun 1, 2012" #define COLAMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub)) #define COLAMD_MAIN_VERSION 2 #define COLAMD_SUB_VERSION 8 #define COLAMD_SUBSUB_VERSION 0 #define COLAMD_VERSION \ COLAMD_VERSION_CODE(COLAMD_MAIN_VERSION,COLAMD_SUB_VERSION) /* ========================================================================== */ /* === Knob and statistics definitions ====================================== */ /* ========================================================================== */ /* size of the knobs [ ] array. Only knobs [0..1] are currently used. */ #define COLAMD_KNOBS 20 /* number of output statistics. Only stats [0..6] are currently used. */ #define COLAMD_STATS 20 /* knobs [0] and stats [0]: dense row knob and output statistic. */ #define COLAMD_DENSE_ROW 0 /* knobs [1] and stats [1]: dense column knob and output statistic. */ #define COLAMD_DENSE_COL 1 /* knobs [2]: aggressive absorption */ #define COLAMD_AGGRESSIVE 2 /* stats [2]: memory defragmentation count output statistic */ #define COLAMD_DEFRAG_COUNT 2 /* stats [3]: colamd status: zero OK, > 0 warning or notice, < 0 error */ #define COLAMD_STATUS 3 /* stats [4..6]: error info, or info on jumbled columns */ #define COLAMD_INFO1 4 #define COLAMD_INFO2 5 #define COLAMD_INFO3 6 /* error codes returned in stats [3]: */ #define COLAMD_OK (0) #define COLAMD_OK_BUT_JUMBLED (1) #define COLAMD_ERROR_A_not_present (-1) #define COLAMD_ERROR_p_not_present (-2) #define COLAMD_ERROR_nrow_negative (-3) #define COLAMD_ERROR_ncol_negative (-4) #define COLAMD_ERROR_nnz_negative (-5) #define COLAMD_ERROR_p0_nonzero (-6) #define COLAMD_ERROR_A_too_small (-7) #define COLAMD_ERROR_col_length_negative (-8) #define COLAMD_ERROR_row_index_out_of_bounds (-9) #define COLAMD_ERROR_out_of_memory (-10) #define COLAMD_ERROR_internal_error (-999) /* ========================================================================== */ /* === Prototypes of user-callable routines ================================= */ /* ========================================================================== */ #include "SuiteSparse_config.h" size_t colamd_recommended /* returns recommended value of Alen, */ /* or 0 if input arguments are erroneous */ ( int nnz, /* nonzeros in A */ int n_row, /* number of rows in A */ int n_col /* number of columns in A */ ) ; size_t colamd_l_recommended /* returns recommended value of Alen, */ /* or 0 if input arguments are erroneous */ ( SuiteSparse_long nnz, /* nonzeros in A */ SuiteSparse_long n_row, /* number of rows in A */ SuiteSparse_long n_col /* number of columns in A */ ) ; void colamd_set_defaults /* sets default parameters */ ( /* knobs argument is modified on output */ double knobs [COLAMD_KNOBS] /* parameter settings for colamd */ ) ; void colamd_l_set_defaults /* sets default parameters */ ( /* knobs argument is modified on output */ double knobs [COLAMD_KNOBS] /* parameter settings for colamd */ ) ; int colamd /* returns (1) if successful, (0) otherwise*/ ( /* A and p arguments are modified on output */ int n_row, /* number of rows in A */ int n_col, /* number of columns in A */ int Alen, /* size of the array A */ int A [], /* row indices of A, of size Alen */ int p [], /* column pointers of A, of size n_col+1 */ double knobs [COLAMD_KNOBS],/* parameter settings for colamd */ int stats [COLAMD_STATS] /* colamd output statistics and error codes */ ) ; SuiteSparse_long colamd_l /* returns (1) if successful, (0) otherwise*/ ( /* A and p arguments are modified on output */ SuiteSparse_long n_row, /* number of rows in A */ SuiteSparse_long n_col, /* number of columns in A */ SuiteSparse_long Alen, /* size of the array A */ SuiteSparse_long A [], /* row indices of A, of size Alen */ SuiteSparse_long p [], /* column pointers of A, of size n_col+1 */ double knobs [COLAMD_KNOBS],/* parameter settings for colamd */ SuiteSparse_long stats [COLAMD_STATS] /* colamd output statistics * and error codes */ ) ; int symamd /* return (1) if OK, (0) otherwise */ ( int n, /* number of rows and columns of A */ int A [], /* row indices of A */ int p [], /* column pointers of A */ int perm [], /* output permutation, size n_col+1 */ double knobs [COLAMD_KNOBS], /* parameters (uses defaults if NULL) */ int stats [COLAMD_STATS], /* output statistics and error codes */ void * (*allocate) (size_t, size_t), /* pointer to calloc (ANSI C) or */ /* mxCalloc (for MATLAB mexFunction) */ void (*release) (void *) /* pointer to free (ANSI C) or */ /* mxFree (for MATLAB mexFunction) */ ) ; SuiteSparse_long symamd_l /* return (1) if OK, (0) otherwise */ ( SuiteSparse_long n, /* number of rows and columns of A */ SuiteSparse_long A [], /* row indices of A */ SuiteSparse_long p [], /* column pointers of A */ SuiteSparse_long perm [], /* output permutation, size n_col+1 */ double knobs [COLAMD_KNOBS], /* parameters (uses defaults if NULL) */ SuiteSparse_long stats [COLAMD_STATS], /* output stats and error codes */ void * (*allocate) (size_t, size_t), /* pointer to calloc (ANSI C) or */ /* mxCalloc (for MATLAB mexFunction) */ void (*release) (void *) /* pointer to free (ANSI C) or */ /* mxFree (for MATLAB mexFunction) */ ) ; void colamd_report ( int stats [COLAMD_STATS] ) ; void colamd_l_report ( SuiteSparse_long stats [COLAMD_STATS] ) ; void symamd_report ( int stats [COLAMD_STATS] ) ; void symamd_l_report ( SuiteSparse_long stats [COLAMD_STATS] ) ; #ifndef EXTERN #define EXTERN extern #endif EXTERN int (*colamd_printf) (const char *, ...) ; #ifdef __cplusplus } #endif #endif /* COLAMD_H */ Matrix/src/sparseQR.c0000644000175100001440000001512712271765436014252 0ustar hornikusers#include "sparseQR.h" SEXP sparseQR_validate(SEXP x) { CSP V = AS_CSP__(GET_SLOT(x, install("V"))), R = AS_CSP__(GET_SLOT(x, install("R"))); SEXP beta = GET_SLOT(x, install("beta")), p = GET_SLOT(x, Matrix_pSym), q = GET_SLOT(x, install("q")); R_CheckStack(); if (LENGTH(p) != V->m) return mkString(_("length(p) must match nrow(V)")); if (LENGTH(beta) != V->n) return mkString(_("length(beta) must match ncol(V)")); int lq = LENGTH(q); if (lq && lq != R->n) return mkString(_("length(q) must be zero or ncol(R)")); if (V->n != R->n) return mkString("ncol(V) != ncol(R)"); /* FIXME: Check that the permutations are permutations */ return ScalarLogical(1); } /** * Apply Householder transformations and the row permutation P to y * * @param V sparse matrix containing the vectors defining the * Householder transformations * @param beta scaling factors for the Householder transformations * @param p 0-based permutation vector of length V->m * @param trans logical value - if TRUE create Q'y[p] otherwise Qy[p] * @param y contents of a V->m by nrhs, i.e. dim(y) == ydims[0:1], dense matrix * Note that V->m = m2 : V may contain "spurious 0 rows" (structural rank deficiency) * @param ydims dimensions of y */ static void sparseQR_Qmult(cs *V, double *beta, int *p, int trans, double *y, int *ydims) { int j, k, m = V->m, n = V->n; double *x = Alloca(m, double); /* workspace */ R_CheckStack(); if (ydims[0] != m) error(_("sparseQR_Qmult(): nrow(y) = %d != %d = nrow(V)"), ydims[0], m); for (j = 0; j < ydims[1]; j++) { double *yj = y + j * m; if (trans) { cs_pvec(p, yj, x, m); /* x(0:m-1) = y(p(0:m-1), j) */ Memcpy(yj, x, m); /* replace it */ for (k = 0 ; k < n ; k++) /* apply H[1]...H[n] */ cs_happly(V, k, beta[k], yj); } else { for (k = n - 1 ; k >= 0 ; k--) /* apply H[n]...H[1] */ cs_happly(V, k, beta[k], yj); cs_ipvec(p, yj, x, m); /* inverse permutation */ Memcpy(yj, x, m); } } } /** * Given a sparse QR decomposition and y, compute Q y or Q'y * * @param qr a "sparseQR" object * @param y a (dense) Matrix * @param trans logical, if TRUE compute Q'y else Q y * @return Q'y ("qty") or Qy ("qy") */ SEXP sparseQR_qty(SEXP qr, SEXP y, SEXP trans) { //--- will be prepended also to other sparseQR_..() functions below ----------- #define INIT_sparseQR_ \ CSP V = AS_CSP__(GET_SLOT(qr, install("V"))); \ R_CheckStack(); \ SEXP ans, aa; \ PROTECT_INDEX ipx; \ PROTECT_WITH_INDEX(ans = dup_mMatrix_as_dgeMatrix(y), &ipx); \ int *ydims = INTEGER(GET_SLOT(ans, Matrix_DimSym)), \ m = ydims[0], n = ydims[1], M = V->m, *d_a; \ Rboolean rank_def = (m < M); \ if(rank_def) { /* must add 0-rows to y, i.e. ans, and remove them *before* return */ \ aa = PROTECT(NEW_OBJECT(MAKE_CLASS("dgeMatrix"))); \ d_a = INTEGER(GET_SLOT(aa, Matrix_DimSym)); d_a[0] = M; d_a[1] = n; \ SEXP dn = GET_SLOT(aa, Matrix_DimNamesSym); \ SET_VECTOR_ELT(dn, 1, \ duplicate(VECTOR_ELT(GET_SLOT(ans, Matrix_DimNamesSym), 1))); \ SET_SLOT(aa, Matrix_DimNamesSym, dn); \ double *yy = REAL( GET_SLOT(ans, Matrix_xSym)); /* m * n */ \ double *xx = REAL(ALLOC_SLOT(aa, Matrix_xSym, REALSXP, M * n)); \ for(int j = 0; j < n; j++) { /* j-th column */ \ Memcpy(xx + j*M, yy + j*m, m); /* copy x[ 1:m , j ] := yy[,j] */ \ for(int i = m; i < M; i++) xx[i + j*M] = 0.;/* x[(m+1):M, j ] := 0 */ \ } \ REPROTECT(ans = duplicate(aa), ipx); /* is M x n now */ \ ydims = INTEGER(GET_SLOT(ans, Matrix_DimSym)); \ } //--- end {INIT_sparseQR_} ----------------------------------------------------- INIT_sparseQR_ sparseQR_Qmult(V, REAL(GET_SLOT(qr, install("beta"))), INTEGER(GET_SLOT(qr, Matrix_pSym)), asLogical(trans), REAL(GET_SLOT(ans, Matrix_xSym)), ydims); #define EXIT_sparseQR_ \ /* remove the extra rows from ans */ \ d_a[0] = m;/* -> @Dim is ok; @Dimnames (i.e. colnames) still are */ \ double *yy = REAL( GET_SLOT(ans, Matrix_xSym)); /* is M x n */ \ double *xx = REAL(ALLOC_SLOT(aa, Matrix_xSym, REALSXP, m * n)); \ for(int j = 0; j < n; j++) { /* j-th column */ \ Memcpy(xx + j*m, yy + j*M, m); /* copy x[ 1:m, j ] := yy[,j] */ \ } \ ans = duplicate(aa); /* m x n finally */ \ UNPROTECT(1) if(rank_def) { warning(_("%s(): structurally rank deficient case: possibly WRONG zeros"), "sparseQR_qty"); EXIT_sparseQR_; } UNPROTECT(1); return ans; } // Compute qr.coef(qr, y) := R^{-1} Q' y {modulo row and column permutations} SEXP sparseQR_coef(SEXP qr, SEXP y) { SEXP qslot = GET_SLOT(qr, install("q")); CSP R = AS_CSP__(GET_SLOT(qr, install("R"))); INIT_sparseQR_ ; double *ax = REAL(GET_SLOT(ans, Matrix_xSym)); // M x n (M = V->m = R->m) /* apply row permutation and multiply by Q' */ sparseQR_Qmult(V, REAL(GET_SLOT(qr, install("beta"))), INTEGER(GET_SLOT(qr, Matrix_pSym)), /* trans = */ TRUE, ax, ydims); // FIXME: check n_R, M (= R->m) vs n, m int *q = INTEGER(qslot), lq = LENGTH(qslot), n_R = R->n; double *x = Alloca(M, double); R_CheckStack(); for (int j = 0; j < n; j++) { double *aj = ax + j * M; cs_usolve(R, aj); if (lq) { cs_ipvec(q, aj, x, n_R); Memcpy(aj, x, n_R); } } if(rank_def) { warning(_("%s(): structurally rank deficient case: possibly WRONG zeros"), "sparseQR_coef"); EXIT_sparseQR_; } UNPROTECT(1); return ans; } /** Compute qr.resid(qr, y) or qr.fitted(qr, y) */ SEXP sparseQR_resid_fitted(SEXP qr, SEXP y, SEXP want_resid) { int *p = INTEGER(GET_SLOT(qr, Matrix_pSym)), resid = asLogical(want_resid); double *beta = REAL(GET_SLOT(qr, install("beta"))); INIT_sparseQR_ double *ax = REAL(GET_SLOT(ans, Matrix_xSym)); /* apply row permutation and multiply by Q' */ sparseQR_Qmult(V, beta, p, /* trans = */ TRUE, ax, ydims); // FIXME (n,m) := dim(y) vs (N,M) := dim(V) -- ok ?? int N = V->n; // M = V->m (in INIT_.. above) for (int j = 0; j < n; j++) { if (resid) // qr.resid(): zero first N rows for (int i = 0; i < N; i++) ax[i + j * M] = 0; else // qr.fitted(): zero last M - N rows for (int i = N; i < M; i++) ax[i + j * M] = 0; } /* multiply by Q and apply inverse row permutation */ sparseQR_Qmult(V, beta, p, /* trans = */ FALSE, ax, ydims); if(rank_def) { warning(_("%s(): structurally rank deficient case: possibly WRONG zeros"), "sparseQR_resid_fitted"); EXIT_sparseQR_; } UNPROTECT(1); return ans; } Matrix/src/t_sparseVector.c0000644000175100001440000000672412271765436015520 0ustar hornikusers/*------ Definition of a template for [dilnz]sparseVector_sub(...) : * * -------- ~~~~~~~~~~~~~~~~~~~~~~ * i.e., included several times from ./Mutils.h * ~~~~~~~~ */ /* for all cases with an 'x' slot -- i.e. almost all cases ; * just redefine this in the other cases: */ #ifdef _dspV_ # define sparseVector_sub dsparseVector_sub # define _DOUBLE_ans # define _has_x_slot_ # undef _dspV_ #elif defined (_ispV_) # define sparseVector_sub isparseVector_sub # define _INT_ans # define _has_x_slot_ # undef _ispV_ #elif defined (_lspV_) # define sparseVector_sub lsparseVector_sub # define _LGL_ans # define _has_x_slot_ # undef _lspV_ #elif defined (_nspV_) # define sparseVector_sub nsparseVector_sub # define _LGL_ans /* withOUT 'x' slot */ # undef _nspV_ #elif defined (_zspV_) # define sparseVector_sub zsparseVector_sub # define _CPLX_ans # define _has_x_slot_ # undef _zspV_ #else # error "no valid _[dilnz]spV_ option" #endif /* - - - - - - - - - - - - - - - - - - - - */ #ifdef _DOUBLE_ans # define Type_ans double # define STYP_ans REAL # define NA_ans NA_REAL # define z_ans (0.) # define SXP_ans REALSXP #undef _DOUBLE_ans #elif defined (_INT_ans) # define Type_ans int # define STYP_ans INTEGER # define NA_ans NA_INTEGER # define z_ans (0) # define SXP_ans INTSXP #undef _INT_ans #elif defined (_LGL_ans) # define Type_ans int # define STYP_ans LOGICAL # define NA_ans NA_LOGICAL # define z_ans (0) # define SXP_ans LGLSXP #undef _LGL_ans #elif defined (_CPLX_ans) static Rcomplex cmplx_zero() { Rcomplex z; z.r = z.i = 0.; return z; } #ifdef _using_NA_ans // <-- get rid of "non-used" warning message static Rcomplex cmplx_NA() { Rcomplex z; z.r = z.i = NA_REAL; return z; } #endif # define Type_ans Rcomplex # define STYP_ans COMPLEX # define NA_ans cmplx_NA(); // "FIXME": NA_COMPLEX does not yet exist # define z_ans cmplx_zero(); # define SXP_ans CPLXSXP #undef _CPLX_ans #else # error "invalid macro logic" #endif /* - - - - - - - - - - - - - - - - - - - - */ #ifdef _has_x_slot_ /* currently have x slot always double (cholmod restriction): */ # define is_NA_x_(u) ISNAN(u) #endif /* Now the template which depends on the above macros : */ /** * Indexing a sparseVector 'vec', including recycling it (conceptually), i.e. * return vec[i] * * @param i index (0-based, contrary to the i-slot) * @param nnz_v the number of non-zero entries of 'vec' == length(vec@ i) * @param v_i (a int * pointer to) the 'i' slot of 'vec' * @param v_x (a ... * pointer to) the 'x' slot of 'vec' * @param len_v integer = the 'length' slot of 'vec * * @return */ static R_INLINE Type_ans sparseVector_sub(int64_t i, int nnz_v, double* v_i, Type_ans* v_x, int64_t len_v) { // double *v_i = INTEGER(GET_SLOT(vec, Matrix_iSym)); // double *v_x = REAL (GET_SLOT(vec, Matrix_xSym)); -- try to be agnostic about type // int64_t len_v = (int64_t) asReal(GET_SLOT(vec, Matrix_lengthSym)); int64_t i1 = (i % len_v) +1; // NB: Rely on the "validity": the i-slot v_i[] is strictly sorted increasingly for(int j=0; j < nnz_v; j++) { if(i1 > v_i[j]) continue; // else: i1 <= v_i[j] if(i1 == v_i[j]) // have a match #ifdef _has_x_slot_ return v_x[j]; #else return 1; #endif else // no match: the element is zero return z_ans; } return z_ans; } #undef Type_ans #undef STYP_ans #undef NA_ans #undef z_ans #undef SXP_ans #undef _has_x_slot_ #undef sparseVector_sub Matrix/src/TMatrix_as.h0000644000175100001440000000062712271765436014571 0ustar hornikusers#ifndef MATRIX_TRS_H #define MATRIX_TRS_H #include "Mutils.h" SEXP dsTMatrix_as_dsyMatrix(SEXP x); SEXP lsTMatrix_as_lsyMatrix(SEXP x); SEXP nsTMatrix_as_nsyMatrix(SEXP x); SEXP dtTMatrix_as_dtrMatrix(SEXP x); SEXP ltTMatrix_as_ltrMatrix(SEXP x); SEXP ntTMatrix_as_ntrMatrix(SEXP x); SEXP dsTMatrix_as_dgTMatrix(SEXP x); SEXP lsTMatrix_as_lgTMatrix(SEXP x); SEXP nsTMatrix_as_ngTMatrix(SEXP x); #endif Matrix/src/dgCMatrix.h0000644000175100001440000000201412271765436014370 0ustar hornikusers#ifndef MATRIX_DGCMATRIX_H #define MATRIX_DGCMATRIX_H #include #include "Mutils.h" #include "cs_utils.h" SEXP xCMatrix_validate(SEXP x); SEXP xRMatrix_validate(SEXP x); SEXP compressed_to_TMatrix(SEXP x, SEXP colP); SEXP compressed_non_0_ij(SEXP x, SEXP colP); SEXP R_to_CMatrix(SEXP x); SEXP dgCMatrix_colSums(SEXP x, SEXP NArm, SEXP spRes, SEXP trans, SEXP means); SEXP igCMatrix_colSums(SEXP x, SEXP NArm, SEXP spRes, SEXP trans, SEXP means); SEXP lgCMatrix_colSums(SEXP x, SEXP NArm, SEXP spRes, SEXP trans, SEXP means); SEXP ngCMatrix_colSums(SEXP x, SEXP NArm, SEXP spRes, SEXP trans, SEXP means); /* SEXP dgCMatrix_lusol(SEXP x, SEXP y); */ SEXP dgCMatrix_qrsol(SEXP x, SEXP y, SEXP ord); SEXP dgCMatrix_cholsol(SEXP x, SEXP y); SEXP dgCMatrix_QR(SEXP Ap, SEXP order); #ifdef Matrix_with_SPQR SEXP dgCMatrix_SPQR(SEXP Ap, SEXP ordering, SEXP econ, SEXP tol); #endif SEXP dgCMatrix_LU(SEXP Ap, SEXP orderp, SEXP tolp, SEXP error_on_sing); SEXP dgCMatrix_matrix_solve(SEXP Ap, SEXP bp, SEXP give_sparse); #endif Matrix/src/cs_utils.c0000644000175100001440000002336312271765436014340 0ustar hornikusers#include "cs_utils.h" /* Borrowed from one of Tim Davis' examples in the CSparse Demo directory */ /* 1 if A is square & upper tri., -1 if square & lower tri., 0 otherwise */ static int is_sym (cs *A) { int is_upper, is_lower, j, p, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i ; if (m != n) return (0) ; is_upper = 1 ; is_lower = 1 ; for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { if (Ai [p] > j) is_upper = 0 ; if (Ai [p] < j) is_lower = 0 ; } } return (is_upper ? 1 : (is_lower ? -1 : 0)) ; } /** * Create an identity matrix of size n as a cs struct. The structure * must be freed with cs_free by the caller. * * @param n size of identity matrix to construct. * * @return pointer to a cs object that contains the identity matrix. */ static CSP csp_eye(int n) { CSP eye = cs_spalloc(n, n, n, 1, 0); int *ep = eye->p, *ei = eye->i; double *ex = eye->x; if (n <= 0) error(_("csp_eye argument n must be positive")); eye->nz = -1; /* compressed column storage */ for (int j = 0; j < n; j++) { ep[j] = ei[j] = j; ex[j] = 1; } eye->nzmax = ep[n] = n; return eye; } /** * Create a cs object with the contents of x. Typically called via AS_CSP() * * @param ans pointer to a cs struct. This is allocated in the caller * so it is easier to keep track of where it should be freed - in many * applications the memory can be allocated with alloca and * automatically freed on exit from the caller. * @param x pointer to an object that inherits from CsparseMatrix * @param check_Udiag boolean - should a check for (and consequent * expansion of) a unit diagonal be performed. * * @return pointer to a cs object that contains pointers * to the slots of x. */ cs *Matrix_as_cs(cs *ans, SEXP x, Rboolean check_Udiag) { static const char *valid[] = {"dgCMatrix", "dtCMatrix", ""}; /* had also "dsCMatrix", but that only stores one triangle */ int *dims, ctype = Matrix_check_class_etc(x, valid); SEXP islot; if (ctype < 0) error(_("invalid class of 'x' in Matrix_as_cs(a, x)")); /* dimensions and nzmax */ dims = INTEGER(GET_SLOT(x, Matrix_DimSym)); ans->m = dims[0]; ans->n = dims[1]; islot = GET_SLOT(x, Matrix_iSym); ans->nz = -1; /* indicates compressed column storage */ ans->nzmax = LENGTH(islot); ans->i = INTEGER(islot); ans->p = INTEGER(GET_SLOT(x, Matrix_pSym)); ans->x = REAL(GET_SLOT(x, Matrix_xSym)); if(check_Udiag && ctype == 1 && (*diag_P(x) == 'U')) { /* diagU2N(.) : */ int n = dims[0]; CSP I_n = csp_eye(n); /* tmp := 1*ans + 1*eye -- result is newly allocated in cs_add(): */ CSP tmp = cs_add(ans, I_n, 1., 1.), t2; int nz = (tmp->p)[n]; /* double transpose trick to sort the columns */ cs_spfree(I_n); t2 = cs_transpose(tmp, 1); /* transpose including values */ cs_spfree(tmp); tmp = cs_transpose(t2, 1); cs_spfree(t2); /* content(ans) := content(tmp) : */ ans->nzmax = nz; /* The ans "slots" were pointers to x@ ; all need new content now: */ ans->p = Memcpy(( int*) R_alloc(sizeof( int), n+1), ( int*) tmp->p, n+1); ans->i = Memcpy(( int*) R_alloc(sizeof( int), nz), ( int*) tmp->i, nz); ans->x = Memcpy((double*) R_alloc(sizeof(double), nz), (double*) tmp->x, nz); cs_spfree(tmp); } return ans; } /** * Copy the contents of a to an appropriate CsparseMatrix object and, * optionally, free a or free both a and the pointers to its contents. * * @param a matrix to be converted * @param cl the name of the S4 class of the object to be generated * @param dofree 0 - don't free a; > 0 cs_free a; < 0 Free a * * @return SEXP containing a copy of a */ /* FIXME: Change API : May need object, not just class */ SEXP Matrix_cs_to_SEXP(cs *a, char *cl, int dofree) { static const char *valid[] = {"dgCMatrix", "dsCMatrix", "dtCMatrix", ""}; int ctype = Matrix_check_class(cl, valid); if (ctype < 0) error(_("invalid class of object to %s"), "Matrix_cs_to_SEXP"); SEXP ans = PROTECT(NEW_OBJECT(MAKE_CLASS(cl))); /* allocate and copy common slots */ int *dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2)); dims[0] = a->m; dims[1] = a->n; Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_pSym, INTSXP, a->n + 1)), a->p, a->n + 1); int nz = a->p[a->n]; Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_iSym, INTSXP, nz)), a->i, nz); Memcpy(REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, nz)), a->x, nz); if (ctype > 0) { /* dsC or dtC */ int uplo = is_sym(a); if (!uplo) error(_("cs matrix not compatible with class '%s'"), valid[ctype]); if (ctype == 2) /* dtC* */ SET_SLOT(ans, Matrix_diagSym, mkString("N")); SET_SLOT(ans, Matrix_uploSym, mkString(uplo < 0 ? "L" : "U")); } if (dofree > 0) cs_spfree(a); if (dofree < 0) Free(a); UNPROTECT(1); return ans; } #if 0 /* unused ------------------------------------*/ /* -------------------------------------*/ /** * Populate a css object with the contents of x. * * @param ans pointer to a csn object * @param x pointer to an object of class css_LU or css_QR. * * @return pointer to a cs object that contains pointers * to the slots of x. */ css *Matrix_as_css(css *ans, SEXP x) { char *cl = class_P(x); static const char *valid[] = {"css_LU", "css_QR", ""}; int *nz = INTEGER(GET_SLOT(x, install("nz"))), ctype = Matrix_check_class(cl, valid); if (ctype < 0) error(_("invalid class of object to %s"), "Matrix_as_css"); ans->q = INTEGER(GET_SLOT(x, install("Q"))); ans->m2 = nz[0]; ans->lnz = nz[1]; ans->unz = nz[2]; switch(ctype) { case 0: /* css_LU */ ans->pinv = (int *) NULL; ans->parent = (int *) NULL; ans->cp = (int *) NULL; break; case 1: /* css_QR */ ans->pinv = INTEGER(GET_SLOT(x, install("Pinv"))); ans->parent = INTEGER(GET_SLOT(x, install("parent"))); ans->cp = INTEGER(GET_SLOT(x, install("cp"))); break; default: error(_("invalid class of object to %s"), "Matrix_as_css"); } return ans; } /** * Populate a csn object with the contents of x. * * @param ans pointer to a csn object * @param x pointer to an object of class csn_LU or csn_QR. * * @return pointer to a cs object that contains pointers * to the slots of x. */ csn *Matrix_as_csn(csn *ans, SEXP x) { static const char *valid[] = {"csn_LU", "csn_QR", ""}; int ctype = Matrix_check_class(class_P(x), valid); if (ctype < 0) error(_("invalid class of object to %s"), "Matrix_as_csn"); ans->U = Matrix_as_cs(GET_SLOT(x, install("U"))); ans->L = Matrix_as_cs(GET_SLOT(x, install("L"))); switch(ctype) { case 0: ans->B = (double*) NULL; ans->pinv = INTEGER(GET_SLOT(x, install("Pinv"))); break; case 1: ans->B = REAL(GET_SLOT(x, install("beta"))); ans->pinv = (int*) NULL; break; default: error(_("invalid class of object to %s"), "Matrix_as_csn"); } return ans; } /** * Copy the contents of S to a css_LU or css_QR object and, * optionally, free S or free both S and the pointers to its contents. * * @param a css object to be converted * @param cl the name of the S4 class of the object to be generated * @param dofree 0 - don't free a; > 0 cs_free a; < 0 Free a * @param m number of rows in original matrix * @param n number of columns in original matrix * * @return SEXP containing a copy of S */ SEXP Matrix_css_to_SEXP(css *S, char *cl, int dofree, int m, int n) { SEXP ans; static const char *valid[] = {"css_LU", "css_QR", ""}; int *nz, ctype = Matrix_check_class(cl, valid); if (ctype < 0) error(_("Inappropriate class cl='%s' in Matrix_css_to_SEXP(S, cl, ..)"), cl); ans = PROTECT(NEW_OBJECT(MAKE_CLASS(cl))); /* allocate and copy common slots */ Memcpy(INTEGER(ALLOC_SLOT(ans, install("Q"), INTSXP, n)), S->q, n); nz = INTEGER(ALLOC_SLOT(ans, install("nz"), INTSXP, 3)); nz[0] = S->m2; nz[1] = S->lnz; nz[2] = S->unz; switch(ctype) { case 0: break; case 1: Memcpy(INTEGER(ALLOC_SLOT(ans, install("Pinv"), INTSXP, m)), S->pinv, m); Memcpy(INTEGER(ALLOC_SLOT(ans, install("parent"), INTSXP, n)), S->parent, n); Memcpy(INTEGER(ALLOC_SLOT(ans, install("cp"), INTSXP, n)), S->cp, n); break; default: error(_("Inappropriate class cl='%s' in Matrix_css_to_SEXP(S, cl, ..)"), cl); } if (dofree > 0) cs_sfree(S); if (dofree < 0) Free(S); UNPROTECT(1); return ans; } /** * Copy the contents of N to a csn_LU or csn_QR object and, * optionally, free N or free both N and the pointers to its contents. * * @param a csn object to be converted * @param cl the name of the S4 class of the object to be generated * @param dofree 0 - don't free a; > 0 cs_free a; < 0 Free a * * @return SEXP containing a copy of S */ SEXP Matrix_csn_to_SEXP(csn *N, char *cl, int dofree) { SEXP ans; static const char *valid[] = {"csn_LU", "csn_QR", ""}; int ctype = Matrix_check_class(cl, valid), n = (N->U)->n; if (ctype < 0) error(_("Inappropriate class cl='%s' in Matrix_csn_to_SEXP(S, cl, ..)"), cl); ans = PROTECT(NEW_OBJECT(MAKE_CLASS(cl))); /* allocate and copy common slots */ /* FIXME: Use the triangular matrix classes for csn_LU */ SET_SLOT(ans, install("L"), /* these are free'd later if requested */ Matrix_cs_to_SEXP(N->L, "dgCMatrix", 0)); SET_SLOT(ans, install("U"), Matrix_cs_to_SEXP(N->U, "dgCMatrix", 0)); switch(ctype) { case 0: Memcpy(INTEGER(ALLOC_SLOT(ans, install("Pinv"), INTSXP, n)), N->pinv, n); break; case 1: Memcpy(REAL(ALLOC_SLOT(ans, install("beta"), REALSXP, n)), N->B, n); break; default: error(_("Inappropriate class cl='%s' in Matrix_csn_to_SEXP(S, cl, ..)"), cl); } if (dofree > 0) cs_nfree(N); if (dofree < 0) { Free(N->L); Free(N->U); Free(N); } UNPROTECT(1); return ans; } #endif /* unused */ Matrix/src/dtTMatrix.c0000644000175100001440000000175612271765436014435 0ustar hornikusers /* Sparse triangular matrices in triplet format */ #include "dtTMatrix.h" #include "dgTMatrix.h" /* xTMatrix_validate */ /* This should be use for *BOTH* triangular and symmetric Tsparse: */ SEXP tTMatrix_validate(SEXP x) { SEXP val = xTMatrix_validate(x);/* checks x slot */ if(isString(val)) return(val); else { SEXP islot = GET_SLOT(x, Matrix_iSym), jslot = GET_SLOT(x, Matrix_jSym); int uploT = (*uplo_P(x) == 'U'), k, nnz = length(islot), *xj = INTEGER(jslot), *xi = INTEGER(islot); /* Maybe FIXME: ">" should be ">=" for diag = 'U' (uplo = 'U') */ if(uploT) { for (k = 0; k < nnz; k++) if(xi[k] > xj[k]) return mkString(_("uplo='U' must not have sparse entries below the diagonal")); } else { for (k = 0; k < nnz; k++) if(xi[k] < xj[k]) return mkString(_("uplo='L' must not have sparse entries above the diagonal")); } return ScalarLogical(1); } } /* SEXP dtTMatrix_as_dtrMatrix(SEXP x) ---> now in ./TMatrix_as.c */ Matrix/src/t_Csparse_subassign.c0000644000175100001440000003212312271765436016506 0ustar hornikusers/*------ Definition of a template for [diln]Csparse_subassign(...) : * * -------- ~~~~~~~~~~~~~~~~~~~~~~ * i.e., included several times from ./Csparse.c * ~~~~~~~~~~~ * _slot_kind : use the integer codes matching x_slot_kind in ./Mutils.h * ~~~~~~~~ */ #ifdef _d_Csp_ # define Csparse_subassign dCsparse_subassign # define x_CLASSES "dgCMatrix",/* 0 */ "dtCMatrix" /* 1 */ # define sparseVECTOR "dsparseVector" # define slot_kind_x 0 # define _DOUBLE_x # define _has_x_slot_ # undef _d_Csp_ #elif defined (_l_Csp_) # define Csparse_subassign lCsparse_subassign # define x_CLASSES "lgCMatrix",/* 0 */ "ltCMatrix" /* 1 */ # define sparseVECTOR "lsparseVector" # define slot_kind_x 1 # define _LGL_x # define _has_x_slot_ # undef _l_Csp_ #elif defined (_i_Csp_) # define Csparse_subassign iCsparse_subassign # define x_CLASSES "igCMatrix",/* 0 */ "itCMatrix" /* 1 */ # define sparseVECTOR "isparseVector" # define slot_kind_x 2 # define _INT_x # define _has_x_slot_ # undef _i_Csp_ #elif defined (_n_Csp_) # define Csparse_subassign nCsparse_subassign # define x_CLASSES "ngCMatrix",/* 0 */ "ntCMatrix" /* 1 */ # define sparseVECTOR "nsparseVector" # define slot_kind_x -1 # define _INT_x /* withOUT 'x' slot -- CARE! we assume that this is the *ONLY* case w/o x slot */ # undef _n_Csp_ #elif defined (_z_Csp_) // # error "zgC* not yet implemented" # define Csparse_subassign zCsparse_subassign # define x_CLASSES "zgCMatrix",/* 0 */ "ztCMatrix" /* 1 */ # define sparseVECTOR "zsparseVector" # define slot_kind_x 3 # define _CPLX_x # define _has_x_slot_ # undef _z_Csp_ #else # error "no valid _[dilnz]gC_ option" #endif // ------------------------------------------------- #ifdef _DOUBLE_x # define Type_x double # define Type_x_0_init(_VAR_) double _VAR_ = 0. # define Type_x_1_init(_VAR_) double _VAR_ = 1. # define STYP_x REAL # define SXP_x REALSXP #undef _DOUBLE_x #elif defined (_LGL_x) # define Type_x int # define Type_x_0_init(_VAR_) int _VAR_ = 0 # define Type_x_1_init(_VAR_) int _VAR_ = 1 # define STYP_x LOGICAL # define SXP_x LGLSXP #undef _LGL_x #elif defined (_INT_x) # define Type_x int # define Type_x_0_init(_VAR_) int _VAR_ = 0 # define Type_x_1_init(_VAR_) int _VAR_ = 1 # define STYP_x INTEGER # define SXP_x INTSXP #undef _INT_x #elif defined (_CPLX_x) # define Type_x Rcomplex # define Type_x_0_init(_VAR_) Rcomplex _VAR_; _VAR_.r = _VAR_.i = 0. # define Type_x_1_init(_VAR_) Rcomplex _VAR_; _VAR_.r = 1.; _VAR_.i = 0. # define STYP_x COMPLEX # define SXP_x CPLXSXP #else # error "invalid macro logic" #endif /** * Subassignment: x[i,j] <- value * * @param x * @param i_ integer row index 0-origin vector (as returned from R .ind.prep2()) * @param j_ integer column index 0-origin vector * @param value must be a [dln]sparseVector {which is recycled if needed} * * @return a Csparse matrix like x, but with the values replaced */ SEXP Csparse_subassign(SEXP x, SEXP i_, SEXP j_, SEXP value) { // TODO: for other classes consider using a trick as RallocedReal() in ./chm_common.c static const char *valid_cM [] = { // the only ones, for "the moment". FIXME: extend (!) x_CLASSES, ""}, // value: assume a "dsparseVector" for now -- slots: (i, length, x) *valid_spv[] = { sparseVECTOR, // = "the one with the same slot-class" // all others: ctype_v slot_kind "nsparseVector",// 1 -1 "lsparseVector",// 2 1 "isparseVector",// 3 2 "dsparseVector",// 4 0 "zsparseVector",// 5 3 ""}; int ctype_x = Matrix_check_class_etc(x, valid_cM), ctype_v = Matrix_check_class_etc(value, valid_spv); if (ctype_x < 0) error(_("invalid class of 'x' in Csparse_subassign()")); if (ctype_v < 0) error(_("invalid class of 'value' in Csparse_subassign()")); Rboolean value_is_nsp = ctype_v == 1; #ifndef _has_x_slot_ // i.e. "n.CMatrix" : sparseVECTOR == "nsparseVector" if(!value_is_nsp) value_is_nsp = (ctype_v == 0); #endif SEXP islot = GET_SLOT(x, Matrix_iSym), dimslot = GET_SLOT(x, Matrix_DimSym), i_cp = PROTECT(coerceVector(i_, INTSXP)), j_cp = PROTECT(coerceVector(j_, INTSXP)); // for d.CMatrix and l.CMatrix but not n.CMatrix: int *dims = INTEGER(dimslot), ncol = dims[1], /* nrow = dims[0], */ *i = INTEGER(i_cp), len_i = LENGTH(i_cp), *j = INTEGER(j_cp), len_j = LENGTH(j_cp), k, nnz_x = LENGTH(islot); int nnz = nnz_x; #define MATRIX_SUBASSIGN_VERBOSE // Temporary hack for debugging --- remove eventually -- FIXME #ifdef MATRIX_SUBASSIGN_VERBOSE Rboolean verbose = i[0] < 0; if(verbose) { i[0] = -i[0]; REprintf("Csparse_subassign() x[i,j] <- val; x is \"%s\"; value \"%s\" is_nsp=%d\n", valid_cM[ctype_x], valid_spv[ctype_v], (int)value_is_nsp); } #endif SEXP val_i_slot, val_x_slot; val_i_slot = PROTECT(coerceVector(GET_SLOT(value, Matrix_iSym), REALSXP)); double *val_i = REAL(val_i_slot); int nnz_val = LENGTH(GET_SLOT(value, Matrix_iSym)), n_prot = 4; Type_x *val_x = NULL; if(!value_is_nsp) { if(ctype_v) { // matrix 'x' and 'value' are of different kinds switch((enum x_slot_kind) slot_kind_x) { case x_pattern:// "n" case x_logical:// "l" if(ctype_v >= 3) warning(_("x[] <- val: val is coerced to logical for \"%s\" x"), valid_cM[ctype_x]); break; case x_integer: if(ctype_v >= 4) error(_("x[] <- val: val should be integer or logical, is coerced to integer, for \"%s\" x"), valid_cM[ctype_x]); break; case x_double: case x_complex: // coercion should be tried (and fail for complex -> double) below break; default: error(_("programming error in Csparse_subassign() should never happen")); } // otherwise: "coerce" : as(., ) : val_x_slot = PROTECT(coerceVector(GET_SLOT(value, Matrix_xSym), SXP_x)); n_prot++; val_x = STYP_x(val_x_slot); } else { val_x = STYP_x( GET_SLOT(value, Matrix_xSym)); } } int64_t len_val = (int64_t) asReal(GET_SLOT(value, Matrix_lengthSym)); /* llen_i = (int64_t) len_i; */ SEXP ans; /* Instead of simple "duplicate": PROTECT(ans = duplicate(x)) , build up: */ // Assuming that ans will have the same basic Matrix type as x : ans = PROTECT(NEW_OBJECT(MAKE_CLASS(valid_cM[ctype_x]))); SET_SLOT(ans, Matrix_DimSym, duplicate(dimslot)); SET_SLOT(ans, Matrix_DimNamesSym, duplicate(GET_SLOT(x, Matrix_DimNamesSym))); SET_SLOT(ans, Matrix_pSym, duplicate(GET_SLOT(x, Matrix_pSym))); SEXP r_pslot = GET_SLOT(ans, Matrix_pSym); // and assign the i- and x- slots at the end, as they are potentially modified // not just in content, but also in their *length* int *rp = INTEGER(r_pslot), *ri = Calloc(nnz_x, int); // to contain the final i - slot Memcpy(ri, INTEGER(islot), nnz_x); Type_x_0_init(z_ans); Type_x_1_init(one_ans); #ifdef _has_x_slot_ Type_x *rx = Calloc(nnz_x, Type_x); // to contain the final x - slot Memcpy(rx, STYP_x(GET_SLOT(x, Matrix_xSym)), nnz_x); #endif // NB: nnz_x : will always be the "current allocated length" of (i, x) slots // -- nnz : the current *used* length; always nnz <= nnz_x int jj, j_val = 0; // in "running" conceptionally through all value[i+ jj*len_i] // values, we are "below"/"before" the (j_val)-th non-zero one. // e.g. if value = (0,0,...,0), have nnz_val == 0, j_val must remain == 0 int64_t ii_val;// == "running" index (i + jj*len_i) % len_val for value[] for(jj = 0, ii_val=0; jj < len_j; jj++) { int j__ = j[jj]; /* int64_t j_l = jj * llen_i; */ R_CheckUserInterrupt(); for(int ii = 0; ii < len_i; ii++, ii_val++) { int i__ = i[ii], p1, p2; if(nnz_val && ii_val >= len_val) { // "recycle" indexing into value[] ii_val -= len_val; // = (ii + jj*len_i) % len_val j_val = 0; } int64_t ii_v1;//= ii_val + 1; Type_x v, /* := value[(ii + j_l) % len_val] = .sparseVector_sub((ii + j_l) % len_val, nnz_val, val_i, val_x, len_val) */ M_ij; int ind; Rboolean have_entry = FALSE; // note that rp[]'s may have *changed* even when 'j' remained! // "FIXME": do this only *when* rp[] has changed p1 = rp[j__], p2 = rp[j__ + 1]; // v := value[(ii + j_l) % len_val] = value[ii_val] v = z_ans; if(j_val < nnz_val) { // maybe find v := non-zero value[ii_val] ii_v1 = ii_val + 1; if(ii_v1 < val_i[j_val]) { // typical case: are still in zero-stretch // v = z_ans (== 0) } else if(ii_v1 == val_i[j_val]) { // have a match v = (value_is_nsp) ? one_ans : val_x[j_val]; j_val++;// from now on, look at the next non-zero entry } else { // ii_v1 > val_i[j_val] REprintf("programming thinko in Csparse_subassign(*, i=%d,j=%d): ii_v=%d, v@i[j_val=%ld]=%g\n", i__,j__, ii_v1, j_val, val_i[j_val]); j_val++;// from now on, look at the next non-zero entry } } // --------------- M_ij := getM(i., j.) -------------------------------- M_ij = z_ans; // as in ./t_sparseVector.c for(ind = p1; ind < p2; ind++) { if(ri[ind] >= i__) { if(ri[ind] == i__) { #ifdef _has_x_slot_ M_ij = rx[ind]; #else M_ij = 1; #endif #ifdef MATRIX_SUBASSIGN_VERBOSE if(verbose) REprintf("have entry x[%d, %d] = %g\n", i__, j__, # ifdef _CPLX_x (double)M_ij.r); # else (double)M_ij); # endif #endif have_entry = TRUE; } else { // ri[ind] > i__ #ifdef MATRIX_SUBASSIGN_VERBOSE if(verbose) REprintf("@i > i__ = %d --> ind-- = %d\n", i__, ind); #endif } break; } } //-- R: if(getM(i., j.) != (v <- getV(ii, jj))) // if(contents differ) ==> value needs to be changed : #ifdef _CPLX_x if(M_ij.r != v.r || M_ij.i != v.i) { #else if(M_ij != v) { #endif #ifdef MATRIX_SUBASSIGN_VERBOSE if(verbose) REprintf("setting x[%d, %d] <- %g", i__,j__, # ifdef _CPLX_x (double) v.r); # else (double) v); # endif #endif // (otherwise: nothing to do): // setM(i__, j__, v) // ---------------------------------------------------------- #ifndef _has_x_slot_ if(v == z_ans) { // Case I ----- remove x[i, j] = M_ij which we know is *non*-zero // BUT it is more efficient (memory-management!) *NOT* to remove, /// but --- in the case of x slot put a 0 zero there, and only at the very end drop them, // currently using drop0() in R code // we know : have_entry = TRUE ; // ri[ind] == i__; M_ij = rx[ind]; #ifdef MATRIX_SUBASSIGN_VERBOSE if(verbose) REprintf(" rm ind=%d\n", ind); #endif // remove the 'ind'-th element from x@i and x@x : nnz-- ; for(k=ind; k < nnz; k++) { ri[k] = ri[k+1]; #ifdef _has_x_slot_ rx[k] = rx[k+1]; #endif } for(k=j__ + 1; k <= ncol; k++) { rp[k] = rp[k] - 1; } } else #endif if(have_entry) { // Case II ----- replace (non-empty) x[i,j] by v ------- #ifdef MATRIX_SUBASSIGN_VERBOSE if(verbose) REprintf(" repl. ind=%d\n", ind); #endif #ifdef _has_x_slot_ rx[ind] = v; #endif } else { // Case III ----- v != 0 : insert v into "empty" x[i,j] ---- // extend the i and x slot by one entry : --------------------- if(nnz+1 > nnz_x) { // need to reallocate: #ifdef MATRIX_SUBASSIGN_VERBOSE if(verbose) REprintf(" Realloc()ing: nnz_x=%d", nnz_x); #endif // do it "only" 1x,..4x at the very most increasing by the // nnz-length of "value": nnz_x += (1 + nnz_val / 4); #ifdef MATRIX_SUBASSIGN_VERBOSE if(verbose) REprintf("(nnz_v=%d) --> %d ", nnz_val, nnz_x); #endif // C doc on realloc() says that the old content is *preserve*d ri = Realloc(ri, nnz_x, int); #ifdef _has_x_slot_ rx = Realloc(rx, nnz_x, Type_x); #endif } // 3) fill them ... int i1 = ind; #ifdef MATRIX_SUBASSIGN_VERBOSE if(verbose) REprintf(" INSERT p12=(%d,%d) -> ind=%d -> i1 = %d\n", p1,p2, ind, i1); #endif // shift the "upper values" *before* the insertion: for(int l = nnz-1; l >= i1; l--) { ri[l+1] = ri[l]; #ifdef _has_x_slot_ rx[l+1] = rx[l]; #endif } ri[i1] = i__; #ifdef _has_x_slot_ rx[i1] = v; #endif nnz++; // the columns j "right" of the current one : for(k=j__ + 1; k <= ncol; k++) rp[k]++; } } #ifdef MATRIX_SUBASSIGN_VERBOSE else if(verbose) REprintf("M_ij == v = %g\n", # ifdef _CPLX_x (double) v.r); # else (double) v); # endif #endif }// for( ii ) }// for( jj ) if(ctype_x == 1) { // triangularMatrix: copy the 'diag' and 'uplo' slots SET_SLOT(ans, Matrix_uploSym, duplicate(GET_SLOT(x, Matrix_uploSym))); SET_SLOT(ans, Matrix_diagSym, duplicate(GET_SLOT(x, Matrix_diagSym))); } // now assign the i- and x- slots, free memory and return : Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_iSym, INTSXP, nnz)), ri, nnz); #ifdef _has_x_slot_ Memcpy( STYP_x(ALLOC_SLOT(ans, Matrix_xSym, SXP_x, nnz)), rx, nnz); Free(rx); #endif Free(ri); UNPROTECT(n_prot); return ans; } #undef Csparse_subassign #undef x_CLASSES #undef sparseVECTOR #undef Type_x #undef STYP_x #undef SXP_x #undef Type_x_0_init #undef Type_x_1_init #undef _has_x_slot_ #undef slot_kind_x #ifdef _CPLX_x # undef _CPLX_x #endif Matrix/src/dspMatrix.h0000644000175100001440000000114212271765436014462 0ustar hornikusers#ifndef MATRIX_SPMATRIX_H #define MATRIX_SPMATRIX_H #include "dgeMatrix.h" #include "R_ext/Lapack.h" SEXP dspMatrix_validate(SEXP obj); double get_norm_sp(SEXP obj, const char *typstr); SEXP dspMatrix_norm(SEXP obj, SEXP type); SEXP dspMatrix_rcond(SEXP obj, SEXP type); SEXP dspMatrix_solve(SEXP a); SEXP dspMatrix_matrix_solve(SEXP a, SEXP b); SEXP dspMatrix_getDiag(SEXP x); SEXP lspMatrix_getDiag(SEXP x); SEXP dspMatrix_setDiag(SEXP x, SEXP d); SEXP lspMatrix_setDiag(SEXP x, SEXP d); SEXP dspMatrix_as_dsyMatrix(SEXP from); SEXP dspMatrix_matrix_mm(SEXP a, SEXP b); SEXP dspMatrix_trf(SEXP x); #endif Matrix/src/dpoMatrix.c0000644000175100001440000000761512271765436014464 0ustar hornikusers#include "dpoMatrix.h" SEXP dpoMatrix_validate(SEXP obj) { int i, n = INTEGER(GET_SLOT(obj, Matrix_DimSym))[0]; int np1 = n + 1; double *x = REAL(GET_SLOT(obj, Matrix_xSym)); /* quick but nondefinitive check on positive definiteness */ for (i = 0; i < n; i++) if (x[i * np1] < 0) return mkString(_("dpoMatrix is not positive definite")); return ScalarLogical(1); } SEXP dpoMatrix_chol(SEXP x) { SEXP val = get_factors(x, "Cholesky"), dimP = GET_SLOT(x, Matrix_DimSym), uploP = GET_SLOT(x, Matrix_uploSym); const char *uplo = CHAR(STRING_ELT(uploP, 0)); int *dims = INTEGER(dimP), info; int n = dims[0]; double *vx; if (val != R_NilValue) return val;// use x@factors$Cholesky if available dims = INTEGER(dimP); val = PROTECT(NEW_OBJECT(MAKE_CLASS("Cholesky"))); SET_SLOT(val, Matrix_uploSym, duplicate(uploP)); SET_SLOT(val, Matrix_diagSym, mkString("N")); SET_SLOT(val, Matrix_DimSym, duplicate(dimP)); vx = REAL(ALLOC_SLOT(val, Matrix_xSym, REALSXP, n * n)); AZERO(vx, n * n); F77_CALL(dlacpy)(uplo, &n, &n, REAL(GET_SLOT(x, Matrix_xSym)), &n, vx, &n); if (n > 0) { F77_CALL(dpotrf)(uplo, &n, vx, &n, &info); if (info) { if(info > 0) error(_("the leading minor of order %d is not positive definite"), info); else /* should never happen! */ error(_("Lapack routine %s returned error code %d"), "dpotrf", info); } } UNPROTECT(1); return set_factors(x, val, "Cholesky"); } SEXP dpoMatrix_rcond(SEXP obj, SEXP type) { SEXP Chol = dpoMatrix_chol(obj); const char typnm[] = {'O', '\0'}; /* always use the one norm */ int *dims = INTEGER(GET_SLOT(Chol, Matrix_DimSym)), info; double anorm = get_norm_sy(obj, typnm), rcond; F77_CALL(dpocon)(uplo_P(Chol), dims, REAL(GET_SLOT(Chol, Matrix_xSym)), dims, &anorm, &rcond, (double *) R_alloc(3*dims[0], sizeof(double)), (int *) R_alloc(dims[0], sizeof(int)), &info); return ScalarReal(rcond); } SEXP dpoMatrix_solve(SEXP x) { SEXP Chol = dpoMatrix_chol(x); SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dpoMatrix"))); int *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)), info; SET_SLOT(val, Matrix_factorSym, allocVector(VECSXP, 0)); slot_dup(val, Chol, Matrix_uploSym); slot_dup(val, Chol, Matrix_xSym); slot_dup(val, Chol, Matrix_DimSym); SET_SLOT(val, Matrix_DimNamesSym, duplicate(GET_SLOT(x, Matrix_DimNamesSym))); F77_CALL(dpotri)(uplo_P(val), dims, REAL(GET_SLOT(val, Matrix_xSym)), dims, &info); UNPROTECT(1); return val; } SEXP dpoMatrix_dgeMatrix_solve(SEXP a, SEXP b) { SEXP Chol = dpoMatrix_chol(a), val = PROTECT(NEW_OBJECT(MAKE_CLASS("dgeMatrix"))); int *adims = INTEGER(GET_SLOT(a, Matrix_DimSym)), *bdims = INTEGER(GET_SLOT(b, Matrix_DimSym)), info; if (adims[1] != bdims[0]) error(_("Dimensions of system to be solved are inconsistent")); if (adims[0] < 1 || bdims[1] < 1) error(_("Cannot solve() for matrices with zero extents")); SET_SLOT(val, Matrix_factorSym, allocVector(VECSXP, 0)); slot_dup(val, b, Matrix_DimSym); slot_dup(val, b, Matrix_xSym); F77_CALL(dpotrs)(uplo_P(Chol), adims, bdims + 1, REAL(GET_SLOT(Chol, Matrix_xSym)), adims, REAL(GET_SLOT(val, Matrix_xSym)), bdims, &info); UNPROTECT(1); return val; } SEXP dpoMatrix_matrix_solve(SEXP a, SEXP b) { SEXP Chol = dpoMatrix_chol(a), val = PROTECT(duplicate(b)); int *adims = INTEGER(GET_SLOT(a, Matrix_DimSym)), *bdims = INTEGER(getAttrib(b, R_DimSymbol)), info; if (!(isReal(b) && isMatrix(b))) error(_("Argument b must be a numeric matrix")); if (*adims != *bdims || bdims[1] < 1 || *adims < 1) error(_("Dimensions of system to be solved are inconsistent")); F77_CALL(dpotrs)(uplo_P(Chol), adims, bdims + 1, REAL(GET_SLOT(Chol, Matrix_xSym)), adims, REAL(val), bdims, &info); UNPROTECT(1); return val; } Matrix/src/t_Csparse_validate.c0000644000175100001440000000557412271765436016313 0ustar hornikusers/* Included from ./Csparse.c * ---------- */ #ifdef _t_Csparse_sort # define CSPARSE_VAL_RES_TYPE static int # define CSPARSE_VAL_FN_NAME Csparse_sort_2 # define CSPARSE_VAL_RETURN_TRUE return 1 # define CSPARSE_VAL_RETURN_STRING(STR) return 0 # undef _t_Csparse_sort #elif defined (_t_Csparse_validate) # define CSPARSE_VAL_RES_TYPE SEXP # define CSPARSE_VAL_FN_NAME Csparse_validate_ # define CSPARSE_VAL_RETURN_TRUE return ScalarLogical(1) # define CSPARSE_VAL_RETURN_STRING(STR) return mkString(_(STR)) # undef _t_Csparse_validate #else # error "no valid _t_Csparse_* option" #endif CSPARSE_VAL_RES_TYPE CSPARSE_VAL_FN_NAME(SEXP x, Rboolean maybe_modify) { /* NB: we do *NOT* check a potential 'x' slot here, at all */ SEXP pslot = GET_SLOT(x, Matrix_pSym), islot = GET_SLOT(x, Matrix_iSym); Rboolean sorted, strictly; int j, k, *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)), nrow = dims[0], ncol = dims[1], *xp = INTEGER(pslot), *xi = INTEGER(islot); if (length(pslot) != dims[1] + 1) CSPARSE_VAL_RETURN_STRING("slot p must have length = ncol(.) + 1"); if (xp[0] != 0) CSPARSE_VAL_RETURN_STRING("first element of slot p must be zero"); if (length(islot) < xp[ncol]) /* allow larger slots from over-allocation!*/ CSPARSE_VAL_RETURN_STRING("last element of slot p must match length of slots i and x"); for (j = 0; j < xp[ncol]; j++) { if (xi[j] < 0 || xi[j] >= nrow) CSPARSE_VAL_RETURN_STRING("all row indices must be between 0 and nrow-1"); } sorted = TRUE; strictly = TRUE; for (j = 0; j < ncol; j++) { if (xp[j] > xp[j + 1]) CSPARSE_VAL_RETURN_STRING("slot p must be non-decreasing"); if(sorted) /* only act if >= 2 entries in column j : */ for (k = xp[j] + 1; k < xp[j + 1]; k++) { if (xi[k] < xi[k - 1]) sorted = FALSE; else if (xi[k] == xi[k - 1]) strictly = FALSE; } } if (!sorted) { if(maybe_modify) { CHM_SP chx = (CHM_SP) alloca(sizeof(cholmod_sparse)); R_CheckStack(); as_cholmod_sparse(chx, x, FALSE, TRUE);/*-> cholmod_l_sort() ! */ /* as chx = AS_CHM_SP__(x) but ^^^^ sorting x in_place !!! */ /* Now re-check that row indices are *strictly* increasing * (and not just increasing) within each column : */ for (j = 0; j < ncol; j++) { for (k = xp[j] + 1; k < xp[j + 1]; k++) if (xi[k] == xi[k - 1]) CSPARSE_VAL_RETURN_STRING("slot i is not *strictly* increasing inside a column (even after cholmod_l_sort)"); } } else { /* no modifying sorting : */ CSPARSE_VAL_RETURN_STRING("row indices are not sorted within columns"); } } else if(!strictly) { /* sorted, but not strictly */ CSPARSE_VAL_RETURN_STRING("slot i is not *strictly* increasing inside a column"); } CSPARSE_VAL_RETURN_TRUE; } #undef CSPARSE_VAL_RES_TYPE #undef CSPARSE_VAL_FN_NAME #undef CSPARSE_VAL_RETURN_TRUE #undef CSPARSE_VAL_RETURN_STRING Matrix/src/dgTMatrix.c0000644000175100001440000001133312271765436014410 0ustar hornikusers#include /* for R_LEN... */ #include "dgTMatrix.h" #include "chm_common.h" #include "Tsparse.h" SEXP xTMatrix_validate(SEXP x) { /* Almost everything now in Tsparse_validate ( ./Tsparse.c ) * *but* the checking of the 'x' slot : */ if (LENGTH(GET_SLOT(x, Matrix_iSym)) != LENGTH(GET_SLOT(x, Matrix_xSym))) return mkString(_("lengths of slots i and x must match")); return ScalarLogical(1); } static void d_insert_triplets_in_array(int m, int n, int nnz, const int xi[], const int xj[], const double xx[], double vx[]) { int i; memset(vx, 0, sizeof(double) * m * n); for (i = 0; i < nnz; i++) { vx[xi[i] + xj[i] * m] += xx[i]; /* allow redundant entries in x */ } } static void l_insert_triplets_in_array(int m, int n, int nnz, const int xi[], const int xj[], const int xx[], int vx[]) { int i; memset(vx, 0, sizeof(int) * m * n); for (i = 0; i < nnz; i++) { vx[xi[i] + xj[i] * m] += xx[i]; /* allow redundant entries in x */ } } #define MAKE_gTMatrix_to_geMatrix(_t1_, _SEXPTYPE_, _SEXP_) \ SEXP _t1_ ## gTMatrix_to_ ## _t1_ ## geMatrix(SEXP x) \ { \ SEXP dd = GET_SLOT(x, Matrix_DimSym), \ islot = GET_SLOT(x, Matrix_iSym), \ ans = PROTECT(NEW_OBJECT(MAKE_CLASS(#_t1_ "geMatrix"))); \ \ int *dims = INTEGER(dd), \ m = dims[0], \ n = dims[1]; \ double len = m * (double)n; \ \ if (len > R_LEN_T_MAX) \ error(_("Cannot coerce to too large *geMatrix with %.0f entries"), \ len); \ \ SET_SLOT(ans, Matrix_factorSym, allocVector(VECSXP, 0)); \ SET_SLOT(ans, Matrix_DimSym, duplicate(dd)); \ SET_DimNames(ans, x); \ SET_SLOT(ans, Matrix_xSym, allocVector(_SEXPTYPE_, (R_len_t)len)); \ _t1_ ## _insert_triplets_in_array(m, n, length(islot), \ INTEGER(islot), \ INTEGER(GET_SLOT(x, Matrix_jSym)),\ _SEXP_(GET_SLOT(x, Matrix_xSym)), \ _SEXP_(GET_SLOT(ans, Matrix_xSym))); \ UNPROTECT(1); \ return ans; \ } MAKE_gTMatrix_to_geMatrix(d, REALSXP, REAL) MAKE_gTMatrix_to_geMatrix(l, LGLSXP, LOGICAL) #undef MAKE_gTMatrix_to_geMatrix #define MAKE_gTMatrix_to_matrix(_t1_, _SEXPTYPE_, _SEXP_) \ SEXP _t1_ ## gTMatrix_to_matrix(SEXP x) \ { \ SEXP dd = GET_SLOT(x, Matrix_DimSym), \ dn = GET_SLOT(x, Matrix_DimNamesSym), \ islot = GET_SLOT(x, Matrix_iSym); \ int m = INTEGER(dd)[0], \ n = INTEGER(dd)[1]; \ SEXP ans = PROTECT(allocMatrix(_SEXPTYPE_, m, n)); \ if(VECTOR_ELT(dn, 0) != R_NilValue || VECTOR_ELT(dn, 1) != R_NilValue) \ /* matrix() with non-trivial dimnames */ \ setAttrib(ans, R_DimNamesSymbol, duplicate(dn)); \ _t1_ ## _insert_triplets_in_array(m, n, length(islot), \ INTEGER(islot), \ INTEGER(GET_SLOT(x, Matrix_jSym)),\ _SEXP_(GET_SLOT(x, Matrix_xSym)), \ _SEXP_(ans)); \ UNPROTECT(1); \ return ans; \ } MAKE_gTMatrix_to_matrix(d, REALSXP, REAL) MAKE_gTMatrix_to_matrix(l, LGLSXP, LOGICAL) #undef MAKE_gTMatrix_to_matrix #ifdef _valid_only_for_old_graph_package SEXP graphNEL_as_dgTMatrix(SEXP x, SEXP symmetric) { int sym = asLogical(symmetric); SEXP nodes = GET_SLOT(x, install("nodes")), edgeL = GET_SLOT(x, install("edgeL")), ans = PROTECT(NEW_OBJECT(MAKE_CLASS(sym ? "dsTMatrix" : "dgTMatrix"))); int *ii, *jj, *dims, i, j, nnd = LENGTH(nodes), pos, totl; double *xx; totl = 0; for (i = 0; i < nnd; i++) totl += LENGTH(Matrix_getElement(VECTOR_ELT(edgeL, i), "edges")); dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2)); dims[0] = dims[1] = nnd; if (isString(nodes)) { SEXP dnms = ALLOC_SLOT(ans, Matrix_DimNamesSym, VECSXP, 2); SET_VECTOR_ELT(dnms, 0, duplicate(nodes)); SET_VECTOR_ELT(dnms, 1, duplicate(nodes)); } ii = Alloca(totl, int); jj = Alloca(totl, int); xx = Alloca(totl, double); R_CheckStack(); pos = 0; for (i = 0; i < nnd; i++) { SEXP edg = VECTOR_ELT(edgeL, i); SEXP edges = Matrix_getElement(edg, "edges"), weights = Matrix_getElement(edg, "weights"); int *edgs = INTEGER(PROTECT(coerceVector(edges, INTSXP))), nedg = LENGTH(edges); double *wts = REAL(weights); for (j = 0; j < nedg; j++) { int j1 = edgs[j] - 1; /* symmetric case stores upper triangle only */ if ((!sym) || i <= j1) { ii[pos] = i; jj[pos] = j1; xx[pos] = wts[j]; pos++; } } UNPROTECT(1); } Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_iSym, INTSXP, pos)), ii, pos); Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_jSym, INTSXP, pos)), jj, pos); Memcpy(REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, pos)), xx, pos); UNPROTECT(1); return ans; } #endif Matrix/src/dtrMatrix.h0000644000175100001440000000143312271765436014470 0ustar hornikusers#ifndef MATRIX_TRMATRIX_H #define MATRIX_TRMATRIX_H #include #include "Mutils.h" SEXP dtrMatrix_validate(SEXP obj); SEXP dtrMatrix_norm(SEXP obj, SEXP type); SEXP dtrMatrix_rcond(SEXP obj, SEXP type); SEXP dtrMatrix_solve(SEXP a); SEXP dtrMatrix_chol2inv(SEXP a); SEXP dtrMatrix_matrix_solve(SEXP a, SEXP b); SEXP dtrMatrix_matrix_mm (SEXP a, SEXP b, SEXP right, SEXP trans); SEXP dtrMatrix_dtrMatrix_mm(SEXP a, SEXP b, SEXP right, SEXP trans); SEXP dtrMatrix_as_dgeMatrix(SEXP from); SEXP dtrMatrix_as_matrix(SEXP from, SEXP keep_dimnames); SEXP dtrMatrix_as_dtpMatrix(SEXP from); SEXP dtrMatrix_addDiag(SEXP x, SEXP d); SEXP dtrMatrix_getDiag(SEXP x); SEXP ltrMatrix_getDiag(SEXP x); SEXP dtrMatrix_setDiag(SEXP x, SEXP d); SEXP ltrMatrix_setDiag(SEXP x, SEXP d); #endif Matrix/src/dsCMatrix.h0000644000175100001440000000110212271765436014401 0ustar hornikusers#ifndef MATRIX_SSC_H #define MATRIX_SSC_H #include "Mutils.h" #include "Csparse.h" /* -> diag_tC() */ #include "chm_common.h" SEXP R_chkName_Cholesky(SEXP nm, SEXP perm, SEXP LDL, SEXP super); SEXP R_chm_factor_name ( SEXP perm, SEXP LDL, SEXP super); SEXP dsCMatrix_Cholesky(SEXP A, SEXP perm, SEXP LDL, SEXP super, SEXP Imult); SEXP dsCMatrix_LDL_D(SEXP Ap, SEXP permP, SEXP resultKind); SEXP dsCMatrix_chol(SEXP x, SEXP pivot); SEXP dsCMatrix_Csparse_solve(SEXP a, SEXP b); SEXP dsCMatrix_matrix_solve(SEXP a, SEXP b); SEXP dsCMatrix_to_dgTMatrix(SEXP x); #endif Matrix/src/cs.c0000644000175100001440000025106012271765436013115 0ustar hornikusers#include "cs.h" /* C = alpha*A + beta*B */ cs *cs_add (const cs *A, const cs *B, double alpha, double beta) { csi p, j, nz = 0, anz, *Cp, *Ci, *Bp, m, n, bnz, *w, values ; double *x, *Bx, *Cx ; cs *C ; if (!CS_CSC (A) || !CS_CSC (B)) return (NULL) ; /* check inputs */ if (A->m != B->m || A->n != B->n) return (NULL) ; m = A->m ; anz = A->p [A->n] ; n = B->n ; Bp = B->p ; Bx = B->x ; bnz = Bp [n] ; w = cs_calloc (m, sizeof (csi)) ; /* get workspace */ values = (A->x != NULL) && (Bx != NULL) ; x = values ? cs_malloc (m, sizeof (double)) : NULL ; /* get workspace */ C = cs_spalloc (m, n, anz + bnz, values, 0) ; /* allocate result*/ if (!C || !w || (values && !x)) return (cs_done (C, w, x, 0)) ; Cp = C->p ; Ci = C->i ; Cx = C->x ; for (j = 0 ; j < n ; j++) { Cp [j] = nz ; /* column j of C starts here */ nz = cs_scatter (A, j, alpha, w, x, j+1, C, nz) ; /* alpha*A(:,j)*/ nz = cs_scatter (B, j, beta, w, x, j+1, C, nz) ; /* beta*B(:,j) */ if (values) for (p = Cp [j] ; p < nz ; p++) Cx [p] = x [Ci [p]] ; } Cp [n] = nz ; /* finalize the last column of C */ cs_sprealloc (C, 0) ; /* remove extra space from C */ return (cs_done (C, w, x, 1)) ; /* success; free workspace, return C */ } /* clear w */ static csi cs_wclear (csi mark, csi lemax, csi *w, csi n) { csi k ; if (mark < 2 || (mark + lemax < 0)) { for (k = 0 ; k < n ; k++) if (w [k] != 0) w [k] = 1 ; mark = 2 ; } return (mark) ; /* at this point, w [0..n-1] < mark holds */ } /* keep off-diagonal entries; drop diagonal entries */ static csi cs_diag (csi i, csi j, double aij, void *other) { return (i != j) ; } /* p = amd(A+A') if symmetric is true, or amd(A'A) otherwise */ csi *cs_amd (csi order, const cs *A) /* order 0:natural, 1:Chol, 2:LU, 3:QR */ { cs *C, *A2, *AT ; csi *Cp, *Ci, *last, *W, *len, *nv, *next, *P, *head, *elen, *degree, *w, *hhead, *ATp, *ATi, d, dk, dext, lemax = 0, e, elenk, eln, i, j, k, k1, k2, k3, jlast, ln, dense, nzmax, mindeg = 0, nvi, nvj, nvk, mark, wnvi, ok, cnz, nel = 0, p, p1, p2, p3, p4, pj, pk, pk1, pk2, pn, q, n, m, t ; csi h ; /* --- Construct matrix C ----------------------------------------------- */ if (!CS_CSC (A) || order <= 0 || order > 3) return (NULL) ; /* check */ AT = cs_transpose (A, 0) ; /* compute A' */ if (!AT) return (NULL) ; m = A->m ; n = A->n ; dense = CS_MAX (16, 10 * sqrt ((double) n)) ; /* find dense threshold */ dense = CS_MIN (n-2, dense) ; if (order == 1 && n == m) { C = cs_add (A, AT, 0, 0) ; /* C = A+A' */ } else if (order == 2) { ATp = AT->p ; /* drop dense columns from AT */ ATi = AT->i ; for (p2 = 0, j = 0 ; j < m ; j++) { p = ATp [j] ; /* column j of AT starts here */ ATp [j] = p2 ; /* new column j starts here */ if (ATp [j+1] - p > dense) continue ; /* skip dense col j */ for ( ; p < ATp [j+1] ; p++) ATi [p2++] = ATi [p] ; } ATp [m] = p2 ; /* finalize AT */ A2 = cs_transpose (AT, 0) ; /* A2 = AT' */ C = A2 ? cs_multiply (AT, A2) : NULL ; /* C=A'*A with no dense rows */ cs_spfree (A2) ; } else { C = cs_multiply (AT, A) ; /* C=A'*A */ } cs_spfree (AT) ; if (!C) return (NULL) ; cs_fkeep (C, &cs_diag, NULL) ; /* drop diagonal entries */ Cp = C->p ; cnz = Cp [n] ; P = cs_malloc (n+1, sizeof (csi)) ; /* allocate result */ W = cs_malloc (8*(n+1), sizeof (csi)) ; /* get workspace */ t = cnz + cnz/5 + 2*n ; /* add elbow room to C */ if (!P || !W || !cs_sprealloc (C, t)) return (cs_idone (P, C, W, 0)) ; len = W ; nv = W + (n+1) ; next = W + 2*(n+1) ; head = W + 3*(n+1) ; elen = W + 4*(n+1) ; degree = W + 5*(n+1) ; w = W + 6*(n+1) ; hhead = W + 7*(n+1) ; last = P ; /* use P as workspace for last */ /* --- Initialize quotient graph ---------------------------------------- */ for (k = 0 ; k < n ; k++) len [k] = Cp [k+1] - Cp [k] ; len [n] = 0 ; nzmax = C->nzmax ; Ci = C->i ; for (i = 0 ; i <= n ; i++) { head [i] = -1 ; /* degree list i is empty */ last [i] = -1 ; next [i] = -1 ; hhead [i] = -1 ; /* hash list i is empty */ nv [i] = 1 ; /* node i is just one node */ w [i] = 1 ; /* node i is alive */ elen [i] = 0 ; /* Ek of node i is empty */ degree [i] = len [i] ; /* degree of node i */ } mark = cs_wclear (0, 0, w, n) ; /* clear w */ elen [n] = -2 ; /* n is a dead element */ Cp [n] = -1 ; /* n is a root of assembly tree */ w [n] = 0 ; /* n is a dead element */ /* --- Initialize degree lists ------------------------------------------ */ for (i = 0 ; i < n ; i++) { d = degree [i] ; if (d == 0) /* node i is empty */ { elen [i] = -2 ; /* element i is dead */ nel++ ; Cp [i] = -1 ; /* i is a root of assembly tree */ w [i] = 0 ; } else if (d > dense) /* node i is dense */ { nv [i] = 0 ; /* absorb i into element n */ elen [i] = -1 ; /* node i is dead */ nel++ ; Cp [i] = CS_FLIP (n) ; nv [n]++ ; } else { if (head [d] != -1) last [head [d]] = i ; next [i] = head [d] ; /* put node i in degree list d */ head [d] = i ; } } while (nel < n) /* while (selecting pivots) do */ { /* --- Select node of minimum approximate degree -------------------- */ for (k = -1 ; mindeg < n && (k = head [mindeg]) == -1 ; mindeg++) ; if (next [k] != -1) last [next [k]] = -1 ; head [mindeg] = next [k] ; /* remove k from degree list */ elenk = elen [k] ; /* elenk = |Ek| */ nvk = nv [k] ; /* # of nodes k represents */ nel += nvk ; /* nv[k] nodes of A eliminated */ /* --- Garbage collection ------------------------------------------- */ if (elenk > 0 && cnz + mindeg >= nzmax) { for (j = 0 ; j < n ; j++) { if ((p = Cp [j]) >= 0) /* j is a live node or element */ { Cp [j] = Ci [p] ; /* save first entry of object */ Ci [p] = CS_FLIP (j) ; /* first entry is now CS_FLIP(j) */ } } for (q = 0, p = 0 ; p < cnz ; ) /* scan all of memory */ { if ((j = CS_FLIP (Ci [p++])) >= 0) /* found object j */ { Ci [q] = Cp [j] ; /* restore first entry of object */ Cp [j] = q++ ; /* new pointer to object j */ for (k3 = 0 ; k3 < len [j]-1 ; k3++) Ci [q++] = Ci [p++] ; } } cnz = q ; /* Ci [cnz...nzmax-1] now free */ } /* --- Construct new element ---------------------------------------- */ dk = 0 ; nv [k] = -nvk ; /* flag k as in Lk */ p = Cp [k] ; pk1 = (elenk == 0) ? p : cnz ; /* do in place if elen[k] == 0 */ pk2 = pk1 ; for (k1 = 1 ; k1 <= elenk + 1 ; k1++) { if (k1 > elenk) { e = k ; /* search the nodes in k */ pj = p ; /* list of nodes starts at Ci[pj]*/ ln = len [k] - elenk ; /* length of list of nodes in k */ } else { e = Ci [p++] ; /* search the nodes in e */ pj = Cp [e] ; ln = len [e] ; /* length of list of nodes in e */ } for (k2 = 1 ; k2 <= ln ; k2++) { i = Ci [pj++] ; if ((nvi = nv [i]) <= 0) continue ; /* node i dead, or seen */ dk += nvi ; /* degree[Lk] += size of node i */ nv [i] = -nvi ; /* negate nv[i] to denote i in Lk*/ Ci [pk2++] = i ; /* place i in Lk */ if (next [i] != -1) last [next [i]] = last [i] ; if (last [i] != -1) /* remove i from degree list */ { next [last [i]] = next [i] ; } else { head [degree [i]] = next [i] ; } } if (e != k) { Cp [e] = CS_FLIP (k) ; /* absorb e into k */ w [e] = 0 ; /* e is now a dead element */ } } if (elenk != 0) cnz = pk2 ; /* Ci [cnz...nzmax] is free */ degree [k] = dk ; /* external degree of k - |Lk\i| */ Cp [k] = pk1 ; /* element k is in Ci[pk1..pk2-1] */ len [k] = pk2 - pk1 ; elen [k] = -2 ; /* k is now an element */ /* --- Find set differences ----------------------------------------- */ mark = cs_wclear (mark, lemax, w, n) ; /* clear w if necessary */ for (pk = pk1 ; pk < pk2 ; pk++) /* scan 1: find |Le\Lk| */ { i = Ci [pk] ; if ((eln = elen [i]) <= 0) continue ;/* skip if elen[i] empty */ nvi = -nv [i] ; /* nv [i] was negated */ wnvi = mark - nvi ; for (p = Cp [i] ; p <= Cp [i] + eln - 1 ; p++) /* scan Ei */ { e = Ci [p] ; if (w [e] >= mark) { w [e] -= nvi ; /* decrement |Le\Lk| */ } else if (w [e] != 0) /* ensure e is a live element */ { w [e] = degree [e] + wnvi ; /* 1st time e seen in scan 1 */ } } } /* --- Degree update ------------------------------------------------ */ for (pk = pk1 ; pk < pk2 ; pk++) /* scan2: degree update */ { i = Ci [pk] ; /* consider node i in Lk */ p1 = Cp [i] ; p2 = p1 + elen [i] - 1 ; pn = p1 ; for (h = 0, d = 0, p = p1 ; p <= p2 ; p++) /* scan Ei */ { e = Ci [p] ; if (w [e] != 0) /* e is an unabsorbed element */ { dext = w [e] - mark ; /* dext = |Le\Lk| */ if (dext > 0) { d += dext ; /* sum up the set differences */ Ci [pn++] = e ; /* keep e in Ei */ h += e ; /* compute the hash of node i */ } else { Cp [e] = CS_FLIP (k) ; /* aggressive absorb. e->k */ w [e] = 0 ; /* e is a dead element */ } } } elen [i] = pn - p1 + 1 ; /* elen[i] = |Ei| */ p3 = pn ; p4 = p1 + len [i] ; for (p = p2 + 1 ; p < p4 ; p++) /* prune edges in Ai */ { j = Ci [p] ; if ((nvj = nv [j]) <= 0) continue ; /* node j dead or in Lk */ d += nvj ; /* degree(i) += |j| */ Ci [pn++] = j ; /* place j in node list of i */ h += j ; /* compute hash for node i */ } if (d == 0) /* check for mass elimination */ { Cp [i] = CS_FLIP (k) ; /* absorb i into k */ nvi = -nv [i] ; dk -= nvi ; /* |Lk| -= |i| */ nvk += nvi ; /* |k| += nv[i] */ nel += nvi ; nv [i] = 0 ; elen [i] = -1 ; /* node i is dead */ } else { degree [i] = CS_MIN (degree [i], d) ; /* update degree(i) */ Ci [pn] = Ci [p3] ; /* move first node to end */ Ci [p3] = Ci [p1] ; /* move 1st el. to end of Ei */ Ci [p1] = k ; /* add k as 1st element in of Ei */ len [i] = pn - p1 + 1 ; /* new len of adj. list of node i */ h = ((h<0) ? (-h):h) % n ; /* finalize hash of i */ next [i] = hhead [h] ; /* place i in hash bucket */ hhead [h] = i ; last [i] = h ; /* save hash of i in last[i] */ } } /* scan2 is done */ degree [k] = dk ; /* finalize |Lk| */ lemax = CS_MAX (lemax, dk) ; mark = cs_wclear (mark+lemax, lemax, w, n) ; /* clear w */ /* --- Supernode detection ------------------------------------------ */ for (pk = pk1 ; pk < pk2 ; pk++) { i = Ci [pk] ; if (nv [i] >= 0) continue ; /* skip if i is dead */ h = last [i] ; /* scan hash bucket of node i */ i = hhead [h] ; hhead [h] = -1 ; /* hash bucket will be empty */ for ( ; i != -1 && next [i] != -1 ; i = next [i], mark++) { ln = len [i] ; eln = elen [i] ; for (p = Cp [i]+1 ; p <= Cp [i] + ln-1 ; p++) w [Ci [p]] = mark; jlast = i ; for (j = next [i] ; j != -1 ; ) /* compare i with all j */ { ok = (len [j] == ln) && (elen [j] == eln) ; for (p = Cp [j] + 1 ; ok && p <= Cp [j] + ln - 1 ; p++) { if (w [Ci [p]] != mark) ok = 0 ; /* compare i and j*/ } if (ok) /* i and j are identical */ { Cp [j] = CS_FLIP (i) ; /* absorb j into i */ nv [i] += nv [j] ; nv [j] = 0 ; elen [j] = -1 ; /* node j is dead */ j = next [j] ; /* delete j from hash bucket */ next [jlast] = j ; } else { jlast = j ; /* j and i are different */ j = next [j] ; } } } } /* --- Finalize new element------------------------------------------ */ for (p = pk1, pk = pk1 ; pk < pk2 ; pk++) /* finalize Lk */ { i = Ci [pk] ; if ((nvi = -nv [i]) <= 0) continue ;/* skip if i is dead */ nv [i] = nvi ; /* restore nv[i] */ d = degree [i] + dk - nvi ; /* compute external degree(i) */ d = CS_MIN (d, n - nel - nvi) ; if (head [d] != -1) last [head [d]] = i ; next [i] = head [d] ; /* put i back in degree list */ last [i] = -1 ; head [d] = i ; mindeg = CS_MIN (mindeg, d) ; /* find new minimum degree */ degree [i] = d ; Ci [p++] = i ; /* place i in Lk */ } nv [k] = nvk ; /* # nodes absorbed into k */ if ((len [k] = p-pk1) == 0) /* length of adj list of element k*/ { Cp [k] = -1 ; /* k is a root of the tree */ w [k] = 0 ; /* k is now a dead element */ } if (elenk != 0) cnz = p ; /* free unused space in Lk */ } /* --- Postordering ----------------------------------------------------- */ for (i = 0 ; i < n ; i++) Cp [i] = CS_FLIP (Cp [i]) ;/* fix assembly tree */ for (j = 0 ; j <= n ; j++) head [j] = -1 ; for (j = n ; j >= 0 ; j--) /* place unordered nodes in lists */ { if (nv [j] > 0) continue ; /* skip if j is an element */ next [j] = head [Cp [j]] ; /* place j in list of its parent */ head [Cp [j]] = j ; } for (e = n ; e >= 0 ; e--) /* place elements in lists */ { if (nv [e] <= 0) continue ; /* skip unless e is an element */ if (Cp [e] != -1) { next [e] = head [Cp [e]] ; /* place e in list of its parent */ head [Cp [e]] = e ; } } for (k = 0, i = 0 ; i <= n ; i++) /* postorder the assembly tree */ { if (Cp [i] == -1) k = cs_tdfs (i, k, head, next, P, w) ; } return (cs_idone (P, C, W, 1)) ; } /* L = chol (A, [pinv parent cp]), pinv is optional */ csn *cs_chol (const cs *A, const css *S) { double d, lki, *Lx, *x, *Cx ; csi top, i, p, k, n, *Li, *Lp, *cp, *pinv, *s, *c, *parent, *Cp, *Ci ; cs *L, *C, *E ; csn *N ; if (!CS_CSC (A) || !S || !S->cp || !S->parent) return (NULL) ; n = A->n ; N = cs_calloc (1, sizeof (csn)) ; /* allocate result */ c = cs_malloc (2*n, sizeof (csi)) ; /* get csi workspace */ x = cs_malloc (n, sizeof (double)) ; /* get double workspace */ cp = S->cp ; pinv = S->pinv ; parent = S->parent ; C = pinv ? cs_symperm (A, pinv, 1) : ((cs *) A) ; E = pinv ? C : NULL ; /* E is alias for A, or a copy E=A(p,p) */ if (!N || !c || !x || !C) return (cs_ndone (N, E, c, x, 0)) ; s = c + n ; Cp = C->p ; Ci = C->i ; Cx = C->x ; N->L = L = cs_spalloc (n, n, cp [n], 1, 0) ; /* allocate result */ if (!L) return (cs_ndone (N, E, c, x, 0)) ; Lp = L->p ; Li = L->i ; Lx = L->x ; for (k = 0 ; k < n ; k++) Lp [k] = c [k] = cp [k] ; for (k = 0 ; k < n ; k++) /* compute L(k,:) for L*L' = C */ { /* --- Nonzero pattern of L(k,:) ------------------------------------ */ top = cs_ereach (C, k, parent, s, c) ; /* find pattern of L(k,:) */ x [k] = 0 ; /* x (0:k) is now zero */ for (p = Cp [k] ; p < Cp [k+1] ; p++) /* x = full(triu(C(:,k))) */ { if (Ci [p] <= k) x [Ci [p]] = Cx [p] ; } d = x [k] ; /* d = C(k,k) */ x [k] = 0 ; /* clear x for k+1st iteration */ /* --- Triangular solve --------------------------------------------- */ for ( ; top < n ; top++) /* solve L(0:k-1,0:k-1) * x = C(:,k) */ { i = s [top] ; /* s [top..n-1] is pattern of L(k,:) */ lki = x [i] / Lx [Lp [i]] ; /* L(k,i) = x (i) / L(i,i) */ x [i] = 0 ; /* clear x for k+1st iteration */ for (p = Lp [i] + 1 ; p < c [i] ; p++) { x [Li [p]] -= Lx [p] * lki ; } d -= lki * lki ; /* d = d - L(k,i)*L(k,i) */ p = c [i]++ ; Li [p] = k ; /* store L(k,i) in column i */ Lx [p] = lki ; } /* --- Compute L(k,k) ----------------------------------------------- */ if (d <= 0) return (cs_ndone (N, E, c, x, 0)) ; /* not pos def */ p = c [k]++ ; Li [p] = k ; /* store L(k,k) = sqrt (d) in column k */ Lx [p] = sqrt (d) ; } Lp [n] = cp [n] ; /* finalize L */ return (cs_ndone (N, E, c, x, 1)) ; /* success: free E,s,x; return N */ } /* x=A\b where A is symmetric positive definite; b overwritten with solution */ csi cs_cholsol (csi order, const cs *A, double *b) { double *x ; css *S ; csn *N ; csi n, ok ; if (!CS_CSC (A) || !b) return (0) ; /* check inputs */ n = A->n ; S = cs_schol (order, A) ; /* ordering and symbolic analysis */ N = cs_chol (A, S) ; /* numeric Cholesky factorization */ x = cs_malloc (n, sizeof (double)) ; /* get workspace */ ok = (S && N && x) ; if (ok) { cs_ipvec (S->pinv, b, x, n) ; /* x = P*b */ cs_lsolve (N->L, x) ; /* x = L\x */ cs_ltsolve (N->L, x) ; /* x = L'\x */ cs_pvec (S->pinv, x, b, n) ; /* b = P'*x */ } cs_free (x) ; cs_sfree (S) ; cs_nfree (N) ; return (ok) ; } /* C = compressed-column form of a triplet matrix T */ cs *cs_compress (const cs *T) { csi m, n, nz, p, k, *Cp, *Ci, *w, *Ti, *Tj ; double *Cx, *Tx ; cs *C ; if (!CS_TRIPLET (T)) return (NULL) ; /* check inputs */ m = T->m ; n = T->n ; Ti = T->i ; Tj = T->p ; Tx = T->x ; nz = T->nz ; C = cs_spalloc (m, n, nz, Tx != NULL, 0) ; /* allocate result */ w = cs_calloc (n, sizeof (csi)) ; /* get workspace */ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */ Cp = C->p ; Ci = C->i ; Cx = C->x ; for (k = 0 ; k < nz ; k++) w [Tj [k]]++ ; /* column counts */ cs_cumsum (Cp, w, n) ; /* column pointers */ for (k = 0 ; k < nz ; k++) { Ci [p = w [Tj [k]]++] = Ti [k] ; /* A(i,j) is the pth entry in C */ if (Cx) Cx [p] = Tx [k] ; } return (cs_done (C, w, NULL, 1)) ; /* success; free w and return C */ } /* column counts of LL'=A or LL'=A'A, given parent & post ordering */ #define HEAD(k,j) (ata ? head [k] : j) #define NEXT(J) (ata ? next [J] : -1) static void init_ata (cs *AT, const csi *post, csi *w, csi **head, csi **next) { csi i, k, p, m = AT->n, n = AT->m, *ATp = AT->p, *ATi = AT->i ; *head = w+4*n, *next = w+5*n+1 ; for (k = 0 ; k < n ; k++) w [post [k]] = k ; /* invert post */ for (i = 0 ; i < m ; i++) { for (k = n, p = ATp[i] ; p < ATp[i+1] ; p++) k = CS_MIN (k, w [ATi[p]]); (*next) [i] = (*head) [k] ; /* place row i in linked list k */ (*head) [k] = i ; } } csi *cs_counts (const cs *A, const csi *parent, const csi *post, csi ata) { csi i, j, k, n, m, J, s, p, q, jleaf, *ATp, *ATi, *maxfirst, *prevleaf, *ancestor, *head = NULL, *next = NULL, *colcount, *w, *first, *delta ; cs *AT ; if (!CS_CSC (A) || !parent || !post) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; s = 4*n + (ata ? (n+m+1) : 0) ; delta = colcount = cs_malloc (n, sizeof (csi)) ; /* allocate result */ w = cs_malloc (s, sizeof (csi)) ; /* get workspace */ AT = cs_transpose (A, 0) ; /* AT = A' */ if (!AT || !colcount || !w) return (cs_idone (colcount, AT, w, 0)) ; ancestor = w ; maxfirst = w+n ; prevleaf = w+2*n ; first = w+3*n ; for (k = 0 ; k < s ; k++) w [k] = -1 ; /* clear workspace w [0..s-1] */ for (k = 0 ; k < n ; k++) /* find first [j] */ { j = post [k] ; delta [j] = (first [j] == -1) ? 1 : 0 ; /* delta[j]=1 if j is a leaf */ for ( ; j != -1 && first [j] == -1 ; j = parent [j]) first [j] = k ; } ATp = AT->p ; ATi = AT->i ; if (ata) init_ata (AT, post, w, &head, &next) ; for (i = 0 ; i < n ; i++) ancestor [i] = i ; /* each node in its own set */ for (k = 0 ; k < n ; k++) { j = post [k] ; /* j is the kth node in postordered etree */ if (parent [j] != -1) delta [parent [j]]-- ; /* j is not a root */ for (J = HEAD (k,j) ; J != -1 ; J = NEXT (J)) /* J=j for LL'=A case */ { for (p = ATp [J] ; p < ATp [J+1] ; p++) { i = ATi [p] ; q = cs_leaf (i, j, first, maxfirst, prevleaf, ancestor, &jleaf); if (jleaf >= 1) delta [j]++ ; /* A(i,j) is in skeleton */ if (jleaf == 2) delta [q]-- ; /* account for overlap in q */ } } if (parent [j] != -1) ancestor [j] = parent [j] ; } for (j = 0 ; j < n ; j++) /* sum up delta's of each child */ { if (parent [j] != -1) colcount [parent [j]] += colcount [j] ; } return (cs_idone (colcount, AT, w, 1)) ; /* success: free workspace */ } /* p [0..n] = cumulative sum of c [0..n-1], and then copy p [0..n-1] into c */ double cs_cumsum (csi *p, csi *c, csi n) { csi i, nz = 0 ; double nz2 = 0 ; if (!p || !c) return (-1) ; /* check inputs */ for (i = 0 ; i < n ; i++) { p [i] = nz ; nz += c [i] ; nz2 += c [i] ; /* also in double to avoid csi overflow */ c [i] = p [i] ; /* also copy p[0..n-1] back into c[0..n-1]*/ } p [n] = nz ; return (nz2) ; /* return sum (c [0..n-1]) */ } /* depth-first-search of the graph of a matrix, starting at node j */ csi cs_dfs (csi j, cs *G, csi top, csi *xi, csi *pstack, const csi *pinv) { csi i, p, p2, done, jnew, head = 0, *Gp, *Gi ; if (!CS_CSC (G) || !xi || !pstack) return (-1) ; /* check inputs */ Gp = G->p ; Gi = G->i ; xi [0] = j ; /* initialize the recursion stack */ while (head >= 0) { j = xi [head] ; /* get j from the top of the recursion stack */ jnew = pinv ? (pinv [j]) : j ; if (!CS_MARKED (Gp, j)) { CS_MARK (Gp, j) ; /* mark node j as visited */ pstack [head] = (jnew < 0) ? 0 : CS_UNFLIP (Gp [jnew]) ; } done = 1 ; /* node j done if no unvisited neighbors */ p2 = (jnew < 0) ? 0 : CS_UNFLIP (Gp [jnew+1]) ; for (p = pstack [head] ; p < p2 ; p++) /* examine all neighbors of j */ { i = Gi [p] ; /* consider neighbor node i */ if (CS_MARKED (Gp, i)) continue ; /* skip visited node i */ pstack [head] = p ; /* pause depth-first search of node j */ xi [++head] = i ; /* start dfs at node i */ done = 0 ; /* node j is not done */ break ; /* break, to start dfs (i) */ } if (done) /* depth-first search at node j is done */ { head-- ; /* remove j from the recursion stack */ xi [--top] = j ; /* and place in the output stack */ } } return (top) ; } /* breadth-first search for coarse decomposition (C0,C1,R1 or R0,R3,C3) */ static csi cs_bfs (const cs *A, csi n, csi *wi, csi *wj, csi *queue, const csi *imatch, const csi *jmatch, csi mark) { csi *Ap, *Ai, head = 0, tail = 0, j, i, p, j2 ; cs *C ; for (j = 0 ; j < n ; j++) /* place all unmatched nodes in queue */ { if (imatch [j] >= 0) continue ; /* skip j if matched */ wj [j] = 0 ; /* j in set C0 (R0 if transpose) */ queue [tail++] = j ; /* place unmatched col j in queue */ } if (tail == 0) return (1) ; /* quick return if no unmatched nodes */ C = (mark == 1) ? ((cs *) A) : cs_transpose (A, 0) ; if (!C) return (0) ; /* bfs of C=A' to find R3,C3 from R0 */ Ap = C->p ; Ai = C->i ; while (head < tail) /* while queue is not empty */ { j = queue [head++] ; /* get the head of the queue */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; if (wi [i] >= 0) continue ; /* skip if i is marked */ wi [i] = mark ; /* i in set R1 (C3 if transpose) */ j2 = jmatch [i] ; /* traverse alternating path to j2 */ if (wj [j2] >= 0) continue ;/* skip j2 if it is marked */ wj [j2] = mark ; /* j2 in set C1 (R3 if transpose) */ queue [tail++] = j2 ; /* add j2 to queue */ } } if (mark != 1) cs_spfree (C) ; /* free A' if it was created */ return (1) ; } /* collect matched rows and columns into p and q */ static void cs_matched (csi n, const csi *wj, const csi *imatch, csi *p, csi *q, csi *cc, csi *rr, csi set, csi mark) { csi kc = cc [set], j ; csi kr = rr [set-1] ; for (j = 0 ; j < n ; j++) { if (wj [j] != mark) continue ; /* skip if j is not in C set */ p [kr++] = imatch [j] ; q [kc++] = j ; } cc [set+1] = kc ; rr [set] = kr ; } /* collect unmatched rows into the permutation vector p */ static void cs_unmatched (csi m, const csi *wi, csi *p, csi *rr, csi set) { csi i, kr = rr [set] ; for (i = 0 ; i < m ; i++) if (wi [i] == 0) p [kr++] = i ; rr [set+1] = kr ; } /* return 1 if row i is in R2 */ static csi cs_rprune (csi i, csi j, double aij, void *other) { csi *rr = (csi *) other ; return (i >= rr [1] && i < rr [2]) ; } /* Given A, compute coarse and then fine dmperm */ csd *cs_dmperm (const cs *A, csi seed) { csi m, n, i, j, k, cnz, nc, *jmatch, *imatch, *wi, *wj, *pinv, *Cp, *Ci, *ps, *rs, nb1, nb2, *p, *q, *cc, *rr, *r, *s, ok ; cs *C ; csd *D, *scc ; /* --- Maximum matching ------------------------------------------------- */ if (!CS_CSC (A)) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; D = cs_dalloc (m, n) ; /* allocate result */ if (!D) return (NULL) ; p = D->p ; q = D->q ; r = D->r ; s = D->s ; cc = D->cc ; rr = D->rr ; jmatch = cs_maxtrans (A, seed) ; /* max transversal */ imatch = jmatch + m ; /* imatch = inverse of jmatch */ if (!jmatch) return (cs_ddone (D, NULL, jmatch, 0)) ; /* --- Coarse decomposition --------------------------------------------- */ wi = r ; wj = s ; /* use r and s as workspace */ for (j = 0 ; j < n ; j++) wj [j] = -1 ; /* unmark all cols for bfs */ for (i = 0 ; i < m ; i++) wi [i] = -1 ; /* unmark all rows for bfs */ cs_bfs (A, n, wi, wj, q, imatch, jmatch, 1) ; /* find C1, R1 from C0*/ ok = cs_bfs (A, m, wj, wi, p, jmatch, imatch, 3) ; /* find R3, C3 from R0*/ if (!ok) return (cs_ddone (D, NULL, jmatch, 0)) ; cs_unmatched (n, wj, q, cc, 0) ; /* unmatched set C0 */ cs_matched (n, wj, imatch, p, q, cc, rr, 1, 1) ; /* set R1 and C1 */ cs_matched (n, wj, imatch, p, q, cc, rr, 2, -1) ; /* set R2 and C2 */ cs_matched (n, wj, imatch, p, q, cc, rr, 3, 3) ; /* set R3 and C3 */ cs_unmatched (m, wi, p, rr, 3) ; /* unmatched set R0 */ cs_free (jmatch) ; /* --- Fine decomposition ----------------------------------------------- */ pinv = cs_pinv (p, m) ; /* pinv=p' */ if (!pinv) return (cs_ddone (D, NULL, NULL, 0)) ; C = cs_permute (A, pinv, q, 0) ;/* C=A(p,q) (it will hold A(R2,C2)) */ cs_free (pinv) ; if (!C) return (cs_ddone (D, NULL, NULL, 0)) ; Cp = C->p ; nc = cc [3] - cc [2] ; /* delete cols C0, C1, and C3 from C */ if (cc [2] > 0) for (j = cc [2] ; j <= cc [3] ; j++) Cp [j-cc[2]] = Cp [j] ; C->n = nc ; if (rr [2] - rr [1] < m) /* delete rows R0, R1, and R3 from C */ { cs_fkeep (C, cs_rprune, rr) ; cnz = Cp [nc] ; Ci = C->i ; if (rr [1] > 0) for (k = 0 ; k < cnz ; k++) Ci [k] -= rr [1] ; } C->m = nc ; scc = cs_scc (C) ; /* find strongly connected components of C*/ if (!scc) return (cs_ddone (D, C, NULL, 0)) ; /* --- Combine coarse and fine decompositions --------------------------- */ ps = scc->p ; /* C(ps,ps) is the permuted matrix */ rs = scc->r ; /* kth block is rs[k]..rs[k+1]-1 */ nb1 = scc->nb ; /* # of blocks of A(R2,C2) */ for (k = 0 ; k < nc ; k++) wj [k] = q [ps [k] + cc [2]] ; for (k = 0 ; k < nc ; k++) q [k + cc [2]] = wj [k] ; for (k = 0 ; k < nc ; k++) wi [k] = p [ps [k] + rr [1]] ; for (k = 0 ; k < nc ; k++) p [k + rr [1]] = wi [k] ; nb2 = 0 ; /* create the fine block partitions */ r [0] = s [0] = 0 ; if (cc [2] > 0) nb2++ ; /* leading coarse block A (R1, [C0 C1]) */ for (k = 0 ; k < nb1 ; k++) /* coarse block A (R2,C2) */ { r [nb2] = rs [k] + rr [1] ; /* A (R2,C2) splits into nb1 fine blocks */ s [nb2] = rs [k] + cc [2] ; nb2++ ; } if (rr [2] < m) { r [nb2] = rr [2] ; /* trailing coarse block A ([R3 R0], C3) */ s [nb2] = cc [3] ; nb2++ ; } r [nb2] = m ; s [nb2] = n ; D->nb = nb2 ; cs_dfree (scc) ; return (cs_ddone (D, C, NULL, 1)) ; } static csi cs_tol (csi i, csi j, double aij, void *tol) { return (fabs (aij) > *((double *) tol)) ; } csi cs_droptol (cs *A, double tol) { return (cs_fkeep (A, &cs_tol, &tol)) ; /* keep all large entries */ } static csi cs_nonzero (csi i, csi j, double aij, void *other) { return (aij != 0) ; } csi cs_dropzeros (cs *A) { return (cs_fkeep (A, &cs_nonzero, NULL)) ; /* keep all nonzero entries */ } /* remove duplicate entries from A */ csi cs_dupl (cs *A) { csi i, j, p, q, nz = 0, n, m, *Ap, *Ai, *w ; double *Ax ; if (!CS_CSC (A)) return (0) ; /* check inputs */ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; w = cs_malloc (m, sizeof (csi)) ; /* get workspace */ if (!w) return (0) ; /* out of memory */ for (i = 0 ; i < m ; i++) w [i] = -1 ; /* row i not yet seen */ for (j = 0 ; j < n ; j++) { q = nz ; /* column j will start at q */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; /* A(i,j) is nonzero */ if (w [i] >= q) { Ax [w [i]] += Ax [p] ; /* A(i,j) is a duplicate */ } else { w [i] = nz ; /* record where row i occurs */ Ai [nz] = i ; /* keep A(i,j) */ Ax [nz++] = Ax [p] ; } } Ap [j] = q ; /* record start of column j */ } Ap [n] = nz ; /* finalize A */ cs_free (w) ; /* free workspace */ return (cs_sprealloc (A, 0)) ; /* remove extra space from A */ } /* add an entry to a triplet matrix; return 1 if ok, 0 otherwise */ csi cs_entry (cs *T, csi i, csi j, double x) { if (!CS_TRIPLET (T) || i < 0 || j < 0) return (0) ; /* check inputs */ if (T->nz >= T->nzmax && !cs_sprealloc (T,2*(T->nzmax))) return (0) ; if (T->x) T->x [T->nz] = x ; T->i [T->nz] = i ; T->p [T->nz++] = j ; T->m = CS_MAX (T->m, i+1) ; T->n = CS_MAX (T->n, j+1) ; return (1) ; } /* find nonzero pattern of Cholesky L(k,1:k-1) using etree and triu(A(:,k)) */ csi cs_ereach (const cs *A, csi k, const csi *parent, csi *s, csi *w) { csi i, p, n, len, top, *Ap, *Ai ; if (!CS_CSC (A) || !parent || !s || !w) return (-1) ; /* check inputs */ top = n = A->n ; Ap = A->p ; Ai = A->i ; CS_MARK (w, k) ; /* mark node k as visited */ for (p = Ap [k] ; p < Ap [k+1] ; p++) { i = Ai [p] ; /* A(i,k) is nonzero */ if (i > k) continue ; /* only use upper triangular part of A */ for (len = 0 ; !CS_MARKED (w,i) ; i = parent [i]) /* traverse up etree*/ { s [len++] = i ; /* L(k,i) is nonzero */ CS_MARK (w, i) ; /* mark i as visited */ } while (len > 0) s [--top] = s [--len] ; /* push path onto stack */ } for (p = top ; p < n ; p++) CS_MARK (w, s [p]) ; /* unmark all nodes */ CS_MARK (w, k) ; /* unmark node k */ return (top) ; /* s [top..n-1] contains pattern of L(k,:)*/ } /* compute the etree of A (using triu(A), or A'A without forming A'A */ csi *cs_etree (const cs *A, csi ata) { csi i, k, p, m, n, inext, *Ap, *Ai, *w, *parent, *ancestor, *prev ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; parent = cs_malloc (n, sizeof (csi)) ; /* allocate result */ w = cs_malloc (n + (ata ? m : 0), sizeof (csi)) ; /* get workspace */ if (!w || !parent) return (cs_idone (parent, NULL, w, 0)) ; ancestor = w ; prev = w + n ; if (ata) for (i = 0 ; i < m ; i++) prev [i] = -1 ; for (k = 0 ; k < n ; k++) { parent [k] = -1 ; /* node k has no parent yet */ ancestor [k] = -1 ; /* nor does k have an ancestor */ for (p = Ap [k] ; p < Ap [k+1] ; p++) { i = ata ? (prev [Ai [p]]) : (Ai [p]) ; for ( ; i != -1 && i < k ; i = inext) /* traverse from i to k */ { inext = ancestor [i] ; /* inext = ancestor of i */ ancestor [i] = k ; /* path compression */ if (inext == -1) parent [i] = k ; /* no anc., parent is k */ } if (ata) prev [Ai [p]] = k ; } } return (cs_idone (parent, NULL, w, 1)) ; } /* drop entries for which fkeep(A(i,j)) is false; return nz if OK, else -1 */ csi cs_fkeep (cs *A, csi (*fkeep) (csi, csi, double, void *), void *other) { csi j, p, nz = 0, n, *Ap, *Ai ; double *Ax ; if (!CS_CSC (A) || !fkeep) return (-1) ; /* check inputs */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; for (j = 0 ; j < n ; j++) { p = Ap [j] ; /* get current location of col j */ Ap [j] = nz ; /* record new location of col j */ for ( ; p < Ap [j+1] ; p++) { if (fkeep (Ai [p], j, Ax ? Ax [p] : 1, other)) { if (Ax) Ax [nz] = Ax [p] ; /* keep A(i,j) */ Ai [nz++] = Ai [p] ; } } } Ap [n] = nz ; /* finalize A */ cs_sprealloc (A, 0) ; /* remove extra space from A */ return (nz) ; } /* y = A*x+y */ csi cs_gaxpy (const cs *A, const double *x, double *y) { csi p, j, n, *Ap, *Ai ; double *Ax ; if (!CS_CSC (A) || !x || !y) return (0) ; /* check inputs */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { y [Ai [p]] += Ax [p] * x [j] ; } } return (1) ; } /* apply the ith Householder vector to x */ csi cs_happly (const cs *V, csi i, double beta, double *x) { csi p, *Vp, *Vi ; double *Vx, tau = 0 ; if (!CS_CSC (V) || !x) return (0) ; /* check inputs */ Vp = V->p ; Vi = V->i ; Vx = V->x ; for (p = Vp [i] ; p < Vp [i+1] ; p++) /* tau = v'*x */ { tau += Vx [p] * x [Vi [p]] ; } tau *= beta ; /* tau = beta*(v'*x) */ for (p = Vp [i] ; p < Vp [i+1] ; p++) /* x = x - v*tau */ { x [Vi [p]] -= Vx [p] * tau ; } return (1) ; } /* create a Householder reflection [v,beta,s]=house(x), overwrite x with v, * where (I-beta*v*v')*x = s*e1. See Algo 5.1.1, Golub & Van Loan, 3rd ed. */ double cs_house (double *x, double *beta, csi n) { double s, sigma = 0 ; csi i ; if (!x || !beta) return (-1) ; /* check inputs */ for (i = 1 ; i < n ; i++) sigma += x [i] * x [i] ; if (sigma == 0) { s = fabs (x [0]) ; /* s = |x(0)| */ (*beta) = (x [0] <= 0) ? 2 : 0 ; x [0] = 1 ; } else { s = sqrt (x [0] * x [0] + sigma) ; /* s = norm (x) */ x [0] = (x [0] <= 0) ? (x [0] - s) : (-sigma / (x [0] + s)) ; (*beta) = -1. / (s * x [0]) ; } return (s) ; } /* x(p) = b, for dense vectors x and b; p=NULL denotes identity */ csi cs_ipvec (const csi *p, const double *b, double *x, csi n) { csi k ; if (!x || !b) return (0) ; /* check inputs */ for (k = 0 ; k < n ; k++) x [p ? p [k] : k] = b [k] ; return (1) ; } /* consider A(i,j), node j in ith row subtree and return lca(jprev,j) */ csi cs_leaf (csi i, csi j, const csi *first, csi *maxfirst, csi *prevleaf, csi *ancestor, csi *jleaf) { csi q, s, sparent, jprev ; if (!first || !maxfirst || !prevleaf || !ancestor || !jleaf) return (-1) ; *jleaf = 0 ; if (i <= j || first [j] <= maxfirst [i]) return (-1) ; /* j not a leaf */ maxfirst [i] = first [j] ; /* update max first[j] seen so far */ jprev = prevleaf [i] ; /* jprev = previous leaf of ith subtree */ prevleaf [i] = j ; *jleaf = (jprev == -1) ? 1: 2 ; /* j is first or subsequent leaf */ if (*jleaf == 1) return (i) ; /* if 1st leaf, q = root of ith subtree */ for (q = jprev ; q != ancestor [q] ; q = ancestor [q]) ; for (s = jprev ; s != q ; s = sparent) { sparent = ancestor [s] ; /* path compression */ ancestor [s] = q ; } return (q) ; /* q = least common ancester (jprev,j) */ } /* load a triplet matrix from a file */ cs *cs_load (FILE *f) { double i, j ; /* use double for integers to avoid csi conflicts */ double x ; cs *T ; if (!f) return (NULL) ; /* check inputs */ T = cs_spalloc (0, 0, 1, 1, 1) ; /* allocate result */ while (fscanf (f, "%lg %lg %lg\n", &i, &j, &x) == 3) { if (!cs_entry (T, (csi) i, (csi) j, x)) return (cs_spfree (T)) ; } return (T) ; } /* solve Lx=b where x and b are dense. x=b on input, solution on output. */ csi cs_lsolve (const cs *L, double *x) { csi p, j, n, *Lp, *Li ; double *Lx ; if (!CS_CSC (L) || !x) return (0) ; /* check inputs */ n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ; for (j = 0 ; j < n ; j++) { x [j] /= Lx [Lp [j]] ; for (p = Lp [j]+1 ; p < Lp [j+1] ; p++) { x [Li [p]] -= Lx [p] * x [j] ; } } return (1) ; } /* solve L'x=b where x and b are dense. x=b on input, solution on output. */ csi cs_ltsolve (const cs *L, double *x) { csi p, j, n, *Lp, *Li ; double *Lx ; if (!CS_CSC (L) || !x) return (0) ; /* check inputs */ n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ; for (j = n-1 ; j >= 0 ; j--) { for (p = Lp [j]+1 ; p < Lp [j+1] ; p++) { x [j] -= Lx [p] * x [Li [p]] ; } x [j] /= Lx [Lp [j]] ; } return (1) ; } /* [L,U,pinv]=lu(A, [q lnz unz]). lnz and unz can be guess */ csn *cs_lu (const cs *A, const css *S, double tol) { cs *L, *U ; csn *N ; double pivot, *Lx, *Ux, *x, a, t ; csi *Lp, *Li, *Up, *Ui, *pinv, *xi, *q, n, ipiv, k, top, p, i, col, lnz,unz; if (!CS_CSC (A) || !S) return (NULL) ; /* check inputs */ n = A->n ; q = S->q ; lnz = S->lnz ; unz = S->unz ; x = cs_malloc (n, sizeof (double)) ; /* get double workspace */ xi = cs_malloc (2*n, sizeof (csi)) ; /* get csi workspace */ N = cs_calloc (1, sizeof (csn)) ; /* allocate result */ if (!x || !xi || !N) return (cs_ndone (N, NULL, xi, x, 0)) ; N->L = L = cs_spalloc (n, n, lnz, 1, 0) ; /* allocate result L */ N->U = U = cs_spalloc (n, n, unz, 1, 0) ; /* allocate result U */ N->pinv = pinv = cs_malloc (n, sizeof (csi)) ; /* allocate result pinv */ if (!L || !U || !pinv) return (cs_ndone (N, NULL, xi, x, 0)) ; Lp = L->p ; Up = U->p ; for (i = 0 ; i < n ; i++) x [i] = 0 ; /* clear workspace */ for (i = 0 ; i < n ; i++) pinv [i] = -1 ; /* no rows pivotal yet */ for (k = 0 ; k <= n ; k++) Lp [k] = 0 ; /* no cols of L yet */ lnz = unz = 0 ; for (k = 0 ; k < n ; k++) /* compute L(:,k) and U(:,k) */ { /* --- Triangular solve --------------------------------------------- */ Lp [k] = lnz ; /* L(:,k) starts here */ Up [k] = unz ; /* U(:,k) starts here */ if ((lnz + n > L->nzmax && !cs_sprealloc (L, 2*L->nzmax + n)) || (unz + n > U->nzmax && !cs_sprealloc (U, 2*U->nzmax + n))) { return (cs_ndone (N, NULL, xi, x, 0)) ; } Li = L->i ; Lx = L->x ; Ui = U->i ; Ux = U->x ; col = q ? (q [k]) : k ; top = cs_spsolve (L, A, col, xi, x, pinv, 1) ; /* x = L\A(:,col) */ /* --- Find pivot --------------------------------------------------- */ ipiv = -1 ; a = -1 ; for (p = top ; p < n ; p++) { i = xi [p] ; /* x(i) is nonzero */ if (pinv [i] < 0) /* row i is not yet pivotal */ { if ((t = fabs (x [i])) > a) { a = t ; /* largest pivot candidate so far */ ipiv = i ; } } else /* x(i) is the entry U(pinv[i],k) */ { Ui [unz] = pinv [i] ; Ux [unz++] = x [i] ; } } if (ipiv == -1 || a <= 0) return (cs_ndone (N, NULL, xi, x, 0)) ; if (pinv [col] < 0 && fabs (x [col]) >= a*tol) ipiv = col ; /* --- Divide by pivot ---------------------------------------------- */ pivot = x [ipiv] ; /* the chosen pivot */ Ui [unz] = k ; /* last entry in U(:,k) is U(k,k) */ Ux [unz++] = pivot ; pinv [ipiv] = k ; /* ipiv is the kth pivot row */ Li [lnz] = ipiv ; /* first entry in L(:,k) is L(k,k) = 1 */ Lx [lnz++] = 1 ; for (p = top ; p < n ; p++) /* L(k+1:n,k) = x / pivot */ { i = xi [p] ; if (pinv [i] < 0) /* x(i) is an entry in L(:,k) */ { Li [lnz] = i ; /* save unpermuted row in L */ Lx [lnz++] = x [i] / pivot ; /* scale pivot column */ } x [i] = 0 ; /* x [0..n-1] = 0 for next k */ } } /* --- Finalize L and U ------------------------------------------------- */ Lp [n] = lnz ; Up [n] = unz ; Li = L->i ; /* fix row indices of L for final pinv */ for (p = 0 ; p < lnz ; p++) Li [p] = pinv [Li [p]] ; cs_sprealloc (L, 0) ; /* remove extra space from L and U */ cs_sprealloc (U, 0) ; return (cs_ndone (N, NULL, xi, x, 1)) ; /* success */ } /* x=A\b where A is unsymmetric; b overwritten with solution */ csi cs_lusol (csi order, const cs *A, double *b, double tol) { double *x ; css *S ; csn *N ; csi n, ok ; if (!CS_CSC (A) || !b) return (0) ; /* check inputs */ n = A->n ; S = cs_sqr (order, A, 0) ; /* ordering and symbolic analysis */ N = cs_lu (A, S, tol) ; /* numeric LU factorization */ x = cs_malloc (n, sizeof (double)) ; /* get workspace */ ok = (S && N && x) ; if (ok) { cs_ipvec (N->pinv, b, x, n) ; /* x = b(p) */ cs_lsolve (N->L, x) ; /* x = L\x */ cs_usolve (N->U, x) ; /* x = U\x */ cs_ipvec (S->q, x, b, n) ; /* b(q) = x */ } cs_free (x) ; cs_sfree (S) ; cs_nfree (N) ; return (ok) ; } #ifdef MATLAB_MEX_FILE #define malloc mxMalloc #define free mxFree #define realloc mxRealloc #define calloc mxCalloc #endif /* wrapper for malloc */ void *cs_malloc (csi n, size_t size) { return (malloc (CS_MAX (n,1) * size)) ; } /* wrapper for calloc */ void *cs_calloc (csi n, size_t size) { return (calloc (CS_MAX (n,1), size)) ; } /* wrapper for free */ void *cs_free (void *p) { if (p) free (p) ; /* free p if it is not already NULL */ return (NULL) ; /* return NULL to simplify the use of cs_free */ } /* wrapper for realloc */ void *cs_realloc (void *p, csi n, size_t size, csi *ok) { void *pnew ; pnew = realloc (p, CS_MAX (n,1) * size) ; /* realloc the block */ *ok = (pnew != NULL) ; /* realloc fails if pnew is NULL */ return ((*ok) ? pnew : p) ; /* return original p if failure */ } /* find an augmenting path starting at column k and extend the match if found */ static void cs_augment (csi k, const cs *A, csi *jmatch, csi *cheap, csi *w, csi *js, csi *is, csi *ps) { csi found = 0, p, i = -1, *Ap = A->p, *Ai = A->i, head = 0, j ; js [0] = k ; /* start with just node k in jstack */ while (head >= 0) { /* --- Start (or continue) depth-first-search at node j ------------- */ j = js [head] ; /* get j from top of jstack */ if (w [j] != k) /* 1st time j visited for kth path */ { w [j] = k ; /* mark j as visited for kth path */ for (p = cheap [j] ; p < Ap [j+1] && !found ; p++) { i = Ai [p] ; /* try a cheap assignment (i,j) */ found = (jmatch [i] == -1) ; } cheap [j] = p ; /* start here next time j is traversed*/ if (found) { is [head] = i ; /* column j matched with row i */ break ; /* end of augmenting path */ } ps [head] = Ap [j] ; /* no cheap match: start dfs for j */ } /* --- Depth-first-search of neighbors of j ------------------------- */ for (p = ps [head] ; p < Ap [j+1] ; p++) { i = Ai [p] ; /* consider row i */ if (w [jmatch [i]] == k) continue ; /* skip jmatch [i] if marked */ ps [head] = p + 1 ; /* pause dfs of node j */ is [head] = i ; /* i will be matched with j if found */ js [++head] = jmatch [i] ; /* start dfs at column jmatch [i] */ break ; } if (p == Ap [j+1]) head-- ; /* node j is done; pop from stack */ } /* augment the match if path found: */ if (found) for (p = head ; p >= 0 ; p--) jmatch [is [p]] = js [p] ; } /* find a maximum transveral */ csi *cs_maxtrans (const cs *A, csi seed) /*[jmatch [0..m-1]; imatch [0..n-1]]*/ { csi i, j, k, n, m, p, n2 = 0, m2 = 0, *Ap, *jimatch, *w, *cheap, *js, *is, *ps, *Ai, *Cp, *jmatch, *imatch, *q ; cs *C ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; m = A->m ; Ap = A->p ; Ai = A->i ; w = jimatch = cs_calloc (m+n, sizeof (csi)) ; /* allocate result */ if (!jimatch) return (NULL) ; for (k = 0, j = 0 ; j < n ; j++) /* count nonempty rows and columns */ { n2 += (Ap [j] < Ap [j+1]) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { w [Ai [p]] = 1 ; k += (j == Ai [p]) ; /* count entries already on diagonal */ } } if (k == CS_MIN (m,n)) /* quick return if diagonal zero-free */ { jmatch = jimatch ; imatch = jimatch + m ; for (i = 0 ; i < k ; i++) jmatch [i] = i ; for ( ; i < m ; i++) jmatch [i] = -1 ; for (j = 0 ; j < k ; j++) imatch [j] = j ; for ( ; j < n ; j++) imatch [j] = -1 ; return (cs_idone (jimatch, NULL, NULL, 1)) ; } for (i = 0 ; i < m ; i++) m2 += w [i] ; C = (m2 < n2) ? cs_transpose (A,0) : ((cs *) A) ; /* transpose if needed */ if (!C) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, NULL, 0)) ; n = C->n ; m = C->m ; Cp = C->p ; jmatch = (m2 < n2) ? jimatch + n : jimatch ; imatch = (m2 < n2) ? jimatch : jimatch + m ; w = cs_malloc (5*n, sizeof (csi)) ; /* get workspace */ if (!w) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 0)) ; cheap = w + n ; js = w + 2*n ; is = w + 3*n ; ps = w + 4*n ; for (j = 0 ; j < n ; j++) cheap [j] = Cp [j] ; /* for cheap assignment */ for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */ for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* nothing matched yet */ q = cs_randperm (n, seed) ; /* q = random permutation */ for (k = 0 ; k < n ; k++) /* augment, starting at column q[k] */ { cs_augment (q ? q [k]: k, C, jmatch, cheap, w, js, is, ps) ; } cs_free (q) ; for (j = 0 ; j < n ; j++) imatch [j] = -1 ; /* find row match */ for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ; return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 1)) ; } /* C = A*B */ cs *cs_multiply (const cs *A, const cs *B) { csi p, j, nz = 0, anz, *Cp, *Ci, *Bp, m, n, bnz, *w, values, *Bi ; double *x, *Bx, *Cx ; cs *C ; if (!CS_CSC (A) || !CS_CSC (B)) return (NULL) ; /* check inputs */ if (A->n != B->m) return (NULL) ; m = A->m ; anz = A->p [A->n] ; n = B->n ; Bp = B->p ; Bi = B->i ; Bx = B->x ; bnz = Bp [n] ; w = cs_calloc (m, sizeof (csi)) ; /* get workspace */ values = (A->x != NULL) && (Bx != NULL) ; x = values ? cs_malloc (m, sizeof (double)) : NULL ; /* get workspace */ C = cs_spalloc (m, n, anz + bnz, values, 0) ; /* allocate result */ if (!C || !w || (values && !x)) return (cs_done (C, w, x, 0)) ; Cp = C->p ; for (j = 0 ; j < n ; j++) { if (nz + m > C->nzmax && !cs_sprealloc (C, 2*(C->nzmax)+m)) { return (cs_done (C, w, x, 0)) ; /* out of memory */ } Ci = C->i ; Cx = C->x ; /* C->i and C->x may be reallocated */ Cp [j] = nz ; /* column j of C starts here */ for (p = Bp [j] ; p < Bp [j+1] ; p++) { nz = cs_scatter (A, Bi [p], Bx ? Bx [p] : 1, w, x, j+1, C, nz) ; } if (values) for (p = Cp [j] ; p < nz ; p++) Cx [p] = x [Ci [p]] ; } Cp [n] = nz ; /* finalize the last column of C */ cs_sprealloc (C, 0) ; /* remove extra space from C */ return (cs_done (C, w, x, 1)) ; /* success; free workspace, return C */ } /* 1-norm of a sparse matrix = max (sum (abs (A))), largest column sum */ double cs_norm (const cs *A) { csi p, j, n, *Ap ; double *Ax, norm = 0, s ; if (!CS_CSC (A) || !A->x) return (-1) ; /* check inputs */ n = A->n ; Ap = A->p ; Ax = A->x ; for (j = 0 ; j < n ; j++) { for (s = 0, p = Ap [j] ; p < Ap [j+1] ; p++) s += fabs (Ax [p]) ; norm = CS_MAX (norm, s) ; } return (norm) ; } /* C = A(p,q) where p and q are permutations of 0..m-1 and 0..n-1. */ cs *cs_permute (const cs *A, const csi *pinv, const csi *q, csi values) { csi t, j, k, nz = 0, m, n, *Ap, *Ai, *Cp, *Ci ; double *Cx, *Ax ; cs *C ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; C = cs_spalloc (m, n, Ap [n], values && Ax != NULL, 0) ; /* alloc result */ if (!C) return (cs_done (C, NULL, NULL, 0)) ; /* out of memory */ Cp = C->p ; Ci = C->i ; Cx = C->x ; for (k = 0 ; k < n ; k++) { Cp [k] = nz ; /* column k of C is column q[k] of A */ j = q ? (q [k]) : k ; for (t = Ap [j] ; t < Ap [j+1] ; t++) { if (Cx) Cx [nz] = Ax [t] ; /* row i of A is row pinv[i] of C */ Ci [nz++] = pinv ? (pinv [Ai [t]]) : Ai [t] ; } } Cp [n] = nz ; /* finalize the last column of C */ return (cs_done (C, NULL, NULL, 1)) ; } /* pinv = p', or p = pinv' */ csi *cs_pinv (csi const *p, csi n) { csi k, *pinv ; if (!p) return (NULL) ; /* p = NULL denotes identity */ pinv = cs_malloc (n, sizeof (csi)) ; /* allocate result */ if (!pinv) return (NULL) ; /* out of memory */ for (k = 0 ; k < n ; k++) pinv [p [k]] = k ;/* invert the permutation */ return (pinv) ; /* return result */ } /* post order a forest */ csi *cs_post (const csi *parent, csi n) { csi j, k = 0, *post, *w, *head, *next, *stack ; if (!parent) return (NULL) ; /* check inputs */ post = cs_malloc (n, sizeof (csi)) ; /* allocate result */ w = cs_malloc (3*n, sizeof (csi)) ; /* get workspace */ if (!w || !post) return (cs_idone (post, NULL, w, 0)) ; head = w ; next = w + n ; stack = w + 2*n ; for (j = 0 ; j < n ; j++) head [j] = -1 ; /* empty linked lists */ for (j = n-1 ; j >= 0 ; j--) /* traverse nodes in reverse order*/ { if (parent [j] == -1) continue ; /* j is a root */ next [j] = head [parent [j]] ; /* add j to list of its parent */ head [parent [j]] = j ; } for (j = 0 ; j < n ; j++) { if (parent [j] != -1) continue ; /* skip j if it is not a root */ k = cs_tdfs (j, k, head, next, post, stack) ; } return (cs_idone (post, NULL, w, 1)) ; /* success; free w, return post */ } /* print a sparse matrix; use %g for integers to avoid differences with csi */ csi cs_print (const cs *A, csi brief) { csi p, j, m, n, nzmax, nz, *Ap, *Ai ; double *Ax ; if (!A) { Rprintf ("(null)\n") ; return (0) ; } m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; nzmax = A->nzmax ; nz = A->nz ; Rprintf ("CSparse Version %d.%d.%d, %s. %s\n", CS_VER, CS_SUBVER, CS_SUBSUB, CS_DATE, CS_COPYRIGHT) ; if (nz < 0) { Rprintf ("%g-by-%g, nzmax: %g nnz: %g, 1-norm: %g\n", (double) m, (double) n, (double) nzmax, (double) (Ap [n]), cs_norm (A)) ; for (j = 0 ; j < n ; j++) { Rprintf (" col %g : locations %g to %g\n", (double) j, (double) (Ap [j]), (double) (Ap [j+1]-1)) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { Rprintf (" %g : %g\n", (double) (Ai [p]), Ax ? Ax [p] : 1) ; if (brief && p > 20) { Rprintf (" ...\n") ; return (1) ; } } } } else { Rprintf ("triplet: %g-by-%g, nzmax: %g nnz: %g\n", (double) m, (double) n, (double) nzmax, (double) nz) ; for (p = 0 ; p < nz ; p++) { Rprintf (" %g %g : %g\n", (double) (Ai [p]), (double) (Ap [p]), Ax ? Ax [p] : 1) ; if (brief && p > 20) { Rprintf (" ...\n") ; return (1) ; } } } return (1) ; } /* x = b(p), for dense vectors x and b; p=NULL denotes identity */ csi cs_pvec (const csi *p, const double *b, double *x, csi n) { csi k ; if (!x || !b) return (0) ; /* check inputs */ for (k = 0 ; k < n ; k++) x [k] = b [p ? p [k] : k] ; return (1) ; } /* sparse QR factorization [V,beta,pinv,R] = qr (A) */ csn *cs_qr (const cs *A, const css *S) { double *Rx, *Vx, *Ax, *x, *Beta ; csi i, k, p, m, n, vnz, p1, top, m2, len, col, rnz, *s, *leftmost, *Ap, *Ai, *parent, *Rp, *Ri, *Vp, *Vi, *w, *pinv, *q ; cs *R, *V ; csn *N ; // the result if (!CS_CSC (A) || !S) return (NULL) ; m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; q = S->q ; parent = S->parent ; pinv = S->pinv ; m2 = S->m2 ; vnz = S->lnz ; rnz = S->unz ; leftmost = S->leftmost ; w = cs_malloc (m2+n, sizeof (csi)) ; /* get csi workspace */ x = cs_malloc (m2, sizeof (double)) ; /* get double workspace */ N = cs_calloc (1, sizeof (csn)) ; /* allocate result */ if (!w || !x || !N) return (cs_ndone (N, NULL, w, x, 0)) ; s = w + m2 ; /* s is size n */ for (k = 0 ; k < m2 ; k++) x [k] = 0 ; /* clear workspace x */ N->L = V = cs_spalloc (m2, n, vnz, 1, 0) ; /* allocate result V */ N->U = R = cs_spalloc (m2, n, rnz, 1, 0) ; /* allocate result R */ N->B = Beta = cs_malloc (n, sizeof (double)) ; /* allocate result Beta */ if (!R || !V || !Beta) return (cs_ndone (N, NULL, w, x, 0)) ; Rp = R->p ; Ri = R->i ; Rx = R->x ; Vp = V->p ; Vi = V->i ; Vx = V->x ; for (i = 0 ; i < m2 ; i++) w [i] = -1 ; /* clear w, to mark nodes */ rnz = 0 ; vnz = 0 ; for (k = 0 ; k < n ; k++) /* compute V and R */ { Rp [k] = rnz ; /* R(:,k) starts here */ Vp [k] = p1 = vnz ; /* V(:,k) starts here */ w [k] = k ; /* add V(k,k) to pattern of V */ Vi [vnz++] = k ; top = n ; col = q ? q [k] : k ; for (p = Ap [col] ; p < Ap [col+1] ; p++) /* find R(:,k) pattern */ { i = leftmost [Ai [p]] ; /* i = min(find(A(i,q))) */ for (len = 0 ; w [i] != k ; i = parent [i]) /* traverse up to k */ { s [len++] = i ; w [i] = k ; } while (len > 0) s [--top] = s [--len] ; /* push path on stack */ i = pinv [Ai [p]] ; /* i = permuted row of A(:,col) */ x [i] = Ax [p] ; /* x (i) = A(:,col) */ if (i > k && w [i] < k) /* pattern of V(:,k) = x (k+1:m) */ { Vi [vnz++] = i ; /* add i to pattern of V(:,k) */ w [i] = k ; } } for (p = top ; p < n ; p++) /* for each i in pattern of R(:,k) */ { i = s [p] ; /* R(i,k) is nonzero */ cs_happly (V, i, Beta [i], x) ; /* apply (V(i),Beta(i)) to x */ Ri [rnz] = i ; /* R(i,k) = x(i) */ Rx [rnz++] = x [i] ; x [i] = 0 ; if (parent [i] == k) vnz = cs_scatter (V, i, 0, w, NULL, k, V, vnz); } for (p = p1 ; p < vnz ; p++) /* gather V(:,k) = x */ { Vx [p] = x [Vi [p]] ; x [Vi [p]] = 0 ; } Ri [rnz] = k ; /* R(k,k) = norm (x) */ Rx [rnz++] = cs_house (Vx+p1, Beta+k, vnz-p1) ; /* [v,beta]=house(x) */ } Rp [n] = rnz ; /* finalize R */ Vp [n] = vnz ; /* finalize V */ return (cs_ndone (N, NULL, w, x, 1)) ; /* success */ } /* x=A\b where A can be rectangular; b overwritten with solution */ csi cs_qrsol (csi order, const cs *A, double *b) { double *x ; css *S ; csn *N ; cs *AT = NULL ; csi k, m, n, ok ; if (!CS_CSC (A) || !b) return (0) ; /* check inputs */ n = A->n ; m = A->m ; if (m >= n) { S = cs_sqr (order, A, 1) ; /* ordering and symbolic analysis */ N = cs_qr (A, S) ; /* numeric QR factorization */ x = cs_calloc (S ? S->m2 : 1, sizeof (double)) ; /* get workspace */ ok = (S && N && x) ; if (ok) { cs_ipvec (S->pinv, b, x, m) ; /* x(0:m-1) = b(p(0:m-1) */ for (k = 0 ; k < n ; k++) /* apply Householder refl. to x */ { cs_happly (N->L, k, N->B [k], x) ; } cs_usolve (N->U, x) ; /* x = R\x */ cs_ipvec (S->q, x, b, n) ; /* b(q(0:n-1)) = x(0:n-1) */ } } else { AT = cs_transpose (A, 1) ; /* Ax=b is underdetermined */ S = cs_sqr (order, AT, 1) ; /* ordering and symbolic analysis */ N = cs_qr (AT, S) ; /* numeric QR factorization of A' */ x = cs_calloc (S ? S->m2 : 1, sizeof (double)) ; /* get workspace */ ok = (AT && S && N && x) ; if (ok) { cs_pvec (S->q, b, x, m) ; /* x(q(0:m-1)) = b(0:m-1) */ cs_utsolve (N->U, x) ; /* x = R'\x */ for (k = m-1 ; k >= 0 ; k--) /* apply Householder refl. to x */ { cs_happly (N->L, k, N->B [k], x) ; } cs_pvec (S->pinv, x, b, n) ; /* b(0:n-1) = x(p(0:n-1)) */ } } cs_free (x) ; cs_sfree (S) ; cs_nfree (N) ; cs_spfree (AT) ; return (ok) ; } /* return a random permutation vector, the identity perm, or p = n-1:-1:0. * seed = -1 means p = n-1:-1:0. seed = 0 means p = identity. otherwise * p = random permutation. */ csi *cs_randperm (csi n, csi seed) { csi *p, k, j, t ; if (seed == 0) return (NULL) ; /* return p = NULL (identity) */ p = cs_malloc (n, sizeof (csi)) ; /* allocate result */ if (!p) return (NULL) ; /* out of memory */ for (k = 0 ; k < n ; k++) p [k] = n-k-1 ; if (seed == -1) return (p) ; /* return reverse permutation */ srand (seed) ; /* get new random number seed */ for (k = 0 ; k < n ; k++) { j = k + (rand ( ) % (n-k)) ; /* j = rand integer in range k to n-1 */ t = p [j] ; /* swap p[k] and p[j] */ p [j] = p [k] ; p [k] = t ; } return (p) ; } /* xi [top...n-1] = nodes reachable from graph of G*P' via nodes in B(:,k). * xi [n...2n-1] used as workspace */ csi cs_reach (cs *G, const cs *B, csi k, csi *xi, const csi *pinv) { csi p, n, top, *Bp, *Bi, *Gp ; if (!CS_CSC (G) || !CS_CSC (B) || !xi) return (-1) ; /* check inputs */ n = G->n ; Bp = B->p ; Bi = B->i ; Gp = G->p ; top = n ; for (p = Bp [k] ; p < Bp [k+1] ; p++) { if (!CS_MARKED (Gp, Bi [p])) /* start a dfs at unmarked node i */ { top = cs_dfs (Bi [p], G, top, xi, xi+n, pinv) ; } } for (p = top ; p < n ; p++) CS_MARK (Gp, xi [p]) ; /* restore G */ return (top) ; } /* x = x + beta * A(:,j), where x is a dense vector and A(:,j) is sparse */ csi cs_scatter (const cs *A, csi j, double beta, csi *w, double *x, csi mark, cs *C, csi nz) { csi i, p, *Ap, *Ai, *Ci ; double *Ax ; if (!CS_CSC (A) || !w || !CS_CSC (C)) return (-1) ; /* check inputs */ Ap = A->p ; Ai = A->i ; Ax = A->x ; Ci = C->i ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; /* A(i,j) is nonzero */ if (w [i] < mark) { w [i] = mark ; /* i is new entry in column j */ Ci [nz++] = i ; /* add i to pattern of C(:,j) */ if (x) x [i] = beta * Ax [p] ; /* x(i) = beta*A(i,j) */ } else if (x) x [i] += beta * Ax [p] ; /* i exists in C(:,j) already */ } return (nz) ; } /* find the strongly connected components of a square matrix */ csd *cs_scc (cs *A) /* matrix A temporarily modified, then restored */ { csi n, i, k, b, nb = 0, top, *xi, *pstack, *p, *r, *Ap, *ATp, *rcopy, *Blk ; cs *AT ; csd *D ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; Ap = A->p ; D = cs_dalloc (n, 0) ; /* allocate result */ AT = cs_transpose (A, 0) ; /* AT = A' */ xi = cs_malloc (2*n+1, sizeof (csi)) ; /* get workspace */ if (!D || !AT || !xi) return (cs_ddone (D, AT, xi, 0)) ; Blk = xi ; rcopy = pstack = xi + n ; p = D->p ; r = D->r ; ATp = AT->p ; top = n ; for (i = 0 ; i < n ; i++) /* first dfs(A) to find finish times (xi) */ { if (!CS_MARKED (Ap, i)) top = cs_dfs (i, A, top, xi, pstack, NULL) ; } for (i = 0 ; i < n ; i++) CS_MARK (Ap, i) ; /* restore A; unmark all nodes*/ top = n ; nb = n ; for (k = 0 ; k < n ; k++) /* dfs(A') to find strongly connnected comp */ { i = xi [k] ; /* get i in reverse order of finish times */ if (CS_MARKED (ATp, i)) continue ; /* skip node i if already ordered */ r [nb--] = top ; /* node i is the start of a component in p */ top = cs_dfs (i, AT, top, p, pstack, NULL) ; } r [nb] = 0 ; /* first block starts at zero; shift r up */ for (k = nb ; k <= n ; k++) r [k-nb] = r [k] ; D->nb = nb = n-nb ; /* nb = # of strongly connected components */ for (b = 0 ; b < nb ; b++) /* sort each block in natural order */ { for (k = r [b] ; k < r [b+1] ; k++) Blk [p [k]] = b ; } for (b = 0 ; b <= nb ; b++) rcopy [b] = r [b] ; for (i = 0 ; i < n ; i++) p [rcopy [Blk [i]]++] = i ; return (cs_ddone (D, AT, xi, 1)) ; } /* ordering and symbolic analysis for a Cholesky factorization */ css *cs_schol (csi order, const cs *A) { csi n, *c, *post, *P ; cs *C ; css *S ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; S = cs_calloc (1, sizeof (css)) ; /* allocate result S */ if (!S) return (NULL) ; /* out of memory */ P = cs_amd (order, A) ; /* P = amd(A+A'), or natural */ S->pinv = cs_pinv (P, n) ; /* find inverse permutation */ cs_free (P) ; if (order && !S->pinv) return (cs_sfree (S)) ; C = cs_symperm (A, S->pinv, 0) ; /* C = spones(triu(A(P,P))) */ S->parent = cs_etree (C, 0) ; /* find etree of C */ post = cs_post (S->parent, n) ; /* postorder the etree */ c = cs_counts (C, S->parent, post, 0) ; /* find column counts of chol(C) */ cs_free (post) ; cs_spfree (C) ; S->cp = cs_malloc (n+1, sizeof (csi)) ; /* allocate result S->cp */ S->unz = S->lnz = cs_cumsum (S->cp, c, n) ; /* find column pointers for L */ cs_free (c) ; return ((S->lnz >= 0) ? S : cs_sfree (S)) ; } /* solve Gx=b(:,k), where G is either upper (lo=0) or lower (lo=1) triangular */ csi cs_spsolve (cs *G, const cs *B, csi k, csi *xi, double *x, const csi *pinv, csi lo) { csi j, J, p, q, px, top, n, *Gp, *Gi, *Bp, *Bi ; double *Gx, *Bx ; if (!CS_CSC (G) || !CS_CSC (B) || !xi || !x) return (-1) ; Gp = G->p ; Gi = G->i ; Gx = G->x ; n = G->n ; Bp = B->p ; Bi = B->i ; Bx = B->x ; top = cs_reach (G, B, k, xi, pinv) ; /* xi[top..n-1]=Reach(B(:,k)) */ for (p = top ; p < n ; p++) x [xi [p]] = 0 ; /* clear x */ for (p = Bp [k] ; p < Bp [k+1] ; p++) x [Bi [p]] = Bx [p] ; /* scatter B */ for (px = top ; px < n ; px++) { j = xi [px] ; /* x(j) is nonzero */ J = pinv ? (pinv [j]) : j ; /* j maps to col J of G */ if (J < 0) continue ; /* column J is empty */ x [j] /= Gx [lo ? (Gp [J]) : (Gp [J+1]-1)] ;/* x(j) /= G(j,j) */ p = lo ? (Gp [J]+1) : (Gp [J]) ; /* lo: L(j,j) 1st entry */ q = lo ? (Gp [J+1]) : (Gp [J+1]-1) ; /* up: U(j,j) last entry */ for ( ; p < q ; p++) { x [Gi [p]] -= Gx [p] * x [j] ; /* x(i) -= G(i,j) * x(j) */ } } return (top) ; /* return top of stack */ } /* compute nnz(V) = S->lnz, S->pinv, S->leftmost, S->m2 from A and S->parent */ static csi cs_vcount (const cs *A, css *S) { csi i, k, p, pa, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i, *next, *head, *tail, *nque, *pinv, *leftmost, *w, *parent = S->parent ; S->pinv = pinv = cs_malloc (m+n, sizeof (csi)) ; /* allocate pinv, */ S->leftmost = leftmost = cs_malloc (m, sizeof (csi)) ; /* and leftmost */ w = cs_malloc (m+3*n, sizeof (csi)) ; /* get workspace */ if (!pinv || !w || !leftmost) { cs_free (w) ; /* pinv and leftmost freed later */ return (0) ; /* out of memory */ } next = w ; head = w + m ; tail = w + m + n ; nque = w + m + 2*n ; for (k = 0 ; k < n ; k++) head [k] = -1 ; /* queue k is empty */ for (k = 0 ; k < n ; k++) tail [k] = -1 ; for (k = 0 ; k < n ; k++) nque [k] = 0 ; for (i = 0 ; i < m ; i++) leftmost [i] = -1 ; for (k = n-1 ; k >= 0 ; k--) { for (p = Ap [k] ; p < Ap [k+1] ; p++) { leftmost [Ai [p]] = k ; /* leftmost[i] = min(find(A(i,:)))*/ } } for (i = m-1 ; i >= 0 ; i--) /* scan rows in reverse order */ { pinv [i] = -1 ; /* row i is not yet ordered */ k = leftmost [i] ; if (k == -1) continue ; /* row i is empty */ if (nque [k]++ == 0) tail [k] = i ; /* first row in queue k */ next [i] = head [k] ; /* put i at head of queue k */ head [k] = i ; } S->lnz = 0 ; S->m2 = m ; for (k = 0 ; k < n ; k++) /* find row permutation and nnz(V)*/ { i = head [k] ; /* remove row i from queue k */ S->lnz++ ; /* count V(k,k) as nonzero */ if (i < 0) i = S->m2++ ; /* add a fictitious row */ pinv [i] = k ; /* associate row i with V(:,k) */ if (--nque [k] <= 0) continue ; /* skip if V(k+1:m,k) is empty */ S->lnz += nque [k] ; /* nque [k] is nnz (V(k+1:m,k)) */ if ((pa = parent [k]) != -1) /* move all rows to parent of k */ { if (nque [pa] == 0) tail [pa] = tail [k] ; next [tail [k]] = head [pa] ; head [pa] = next [i] ; nque [pa] += nque [k] ; } } for (i = 0 ; i < m ; i++) if (pinv [i] < 0) pinv [i] = k++ ; cs_free (w) ; return (1) ; } /* symbolic ordering and analysis for QR or LU */ css *cs_sqr (csi order, const cs *A, csi qr) { csi n, k, ok = 1, *post ; css *S ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; S = cs_calloc (1, sizeof (css)) ; /* allocate result S */ if (!S) return (NULL) ; /* out of memory */ S->q = cs_amd (order, A) ; /* fill-reducing ordering */ if (order && !S->q) return (cs_sfree (S)) ; if (qr) /* QR symbolic analysis */ { cs *C = order ? cs_permute (A, NULL, S->q, 0) : ((cs *) A) ; S->parent = cs_etree (C, 1) ; /* etree of C'*C, where C=A(:,q) */ post = cs_post (S->parent, n) ; S->cp = cs_counts (C, S->parent, post, 1) ; /* col counts chol(C'*C) */ cs_free (post) ; ok = C && S->parent && S->cp && cs_vcount (C, S) ; if (ok) for (S->unz = 0, k = 0 ; k < n ; k++) S->unz += S->cp [k] ; if (order) cs_spfree (C) ; } else { S->unz = 4*(A->p [n]) + n ; /* for LU factorization only, */ S->lnz = S->unz ; /* guess nnz(L) and nnz(U) */ } return (ok ? S : cs_sfree (S)) ; /* return result S */ } /* C = A(p,p) where A and C are symmetric the upper part stored; pinv not p */ cs *cs_symperm (const cs *A, const csi *pinv, csi values) { csi i, j, p, q, i2, j2, n, *Ap, *Ai, *Cp, *Ci, *w ; double *Cx, *Ax ; cs *C ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; C = cs_spalloc (n, n, Ap [n], values && (Ax != NULL), 0) ; /* alloc result*/ w = cs_calloc (n, sizeof (csi)) ; /* get workspace */ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */ Cp = C->p ; Ci = C->i ; Cx = C->x ; for (j = 0 ; j < n ; j++) /* count entries in each column of C */ { j2 = pinv ? pinv [j] : j ; /* column j of A is column j2 of C */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; if (i > j) continue ; /* skip lower triangular part of A */ i2 = pinv ? pinv [i] : i ; /* row i of A is row i2 of C */ w [CS_MAX (i2, j2)]++ ; /* column count of C */ } } cs_cumsum (Cp, w, n) ; /* compute column pointers of C */ for (j = 0 ; j < n ; j++) { j2 = pinv ? pinv [j] : j ; /* column j of A is column j2 of C */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; if (i > j) continue ; /* skip lower triangular part of A*/ i2 = pinv ? pinv [i] : i ; /* row i of A is row i2 of C */ Ci [q = w [CS_MAX (i2, j2)]++] = CS_MIN (i2, j2) ; if (Cx) Cx [q] = Ax [p] ; } } return (cs_done (C, w, NULL, 1)) ; /* success; free workspace, return C */ } /* depth-first search and postorder of a tree rooted at node j */ csi cs_tdfs (csi j, csi k, csi *head, const csi *next, csi *post, csi *stack) { csi i, p, top = 0 ; if (!head || !next || !post || !stack) return (-1) ; /* check inputs */ stack [0] = j ; /* place j on the stack */ while (top >= 0) /* while (stack is not empty) */ { p = stack [top] ; /* p = top of stack */ i = head [p] ; /* i = youngest child of p */ if (i == -1) { top-- ; /* p has no unordered children left */ post [k++] = p ; /* node p is the kth postordered node */ } else { head [p] = next [i] ; /* remove i from children of p */ stack [++top] = i ; /* start dfs on child node i */ } } return (k) ; } /* C = A' */ cs *cs_transpose (const cs *A, csi values) { csi p, q, j, *Cp, *Ci, n, m, *Ap, *Ai, *w ; double *Cx, *Ax ; cs *C ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; C = cs_spalloc (n, m, Ap [n], values && Ax, 0) ; /* allocate result */ w = cs_calloc (m, sizeof (csi)) ; /* get workspace */ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */ Cp = C->p ; Ci = C->i ; Cx = C->x ; for (p = 0 ; p < Ap [n] ; p++) w [Ai [p]]++ ; /* row counts */ cs_cumsum (Cp, w, m) ; /* row pointers */ for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { Ci [q = w [Ai [p]]++] = j ; /* place A(i,j) as entry C(j,i) */ if (Cx) Cx [q] = Ax [p] ; } } return (cs_done (C, w, NULL, 1)) ; /* success; free w and return C */ } /* sparse Cholesky update/downdate, L*L' + sigma*w*w' (sigma = +1 or -1) */ csi cs_updown (cs *L, csi sigma, const cs *C, const csi *parent) { csi n, p, f, j, *Lp, *Li, *Cp, *Ci ; double *Lx, *Cx, alpha, beta = 1, delta, gamma, w1, w2, *w, beta2 = 1 ; if (!CS_CSC (L) || !CS_CSC (C) || !parent) return (0) ; /* check inputs */ Lp = L->p ; Li = L->i ; Lx = L->x ; n = L->n ; Cp = C->p ; Ci = C->i ; Cx = C->x ; if ((p = Cp [0]) >= Cp [1]) return (1) ; /* return if C empty */ w = cs_malloc (n, sizeof (double)) ; /* get workspace */ if (!w) return (0) ; /* out of memory */ f = Ci [p] ; for ( ; p < Cp [1] ; p++) f = CS_MIN (f, Ci [p]) ; /* f = min (find (C)) */ for (j = f ; j != -1 ; j = parent [j]) w [j] = 0 ; /* clear workspace w */ for (p = Cp [0] ; p < Cp [1] ; p++) w [Ci [p]] = Cx [p] ; /* w = C */ for (j = f ; j != -1 ; j = parent [j]) /* walk path f up to root */ { p = Lp [j] ; alpha = w [j] / Lx [p] ; /* alpha = w(j) / L(j,j) */ beta2 = beta*beta + sigma*alpha*alpha ; if (beta2 <= 0) break ; /* not positive definite */ beta2 = sqrt (beta2) ; delta = (sigma > 0) ? (beta / beta2) : (beta2 / beta) ; gamma = sigma * alpha / (beta2 * beta) ; Lx [p] = delta * Lx [p] + ((sigma > 0) ? (gamma * w [j]) : 0) ; beta = beta2 ; for (p++ ; p < Lp [j+1] ; p++) { w1 = w [Li [p]] ; w [Li [p]] = w2 = w1 - alpha * Lx [p] ; Lx [p] = delta * Lx [p] + gamma * ((sigma > 0) ? w1 : w2) ; } } cs_free (w) ; return (beta2 > 0) ; } /* solve Ux=b where x and b are dense. x=b on input, solution on output. */ csi cs_usolve (const cs *U, double *x) { csi p, j, n, *Up, *Ui ; double *Ux ; if (!CS_CSC (U) || !x) return (0) ; /* check inputs */ n = U->n ; Up = U->p ; Ui = U->i ; Ux = U->x ; for (j = n-1 ; j >= 0 ; j--) { x [j] /= Ux [Up [j+1]-1] ; for (p = Up [j] ; p < Up [j+1]-1 ; p++) { x [Ui [p]] -= Ux [p] * x [j] ; } } return (1) ; } /* allocate a sparse matrix (triplet form or compressed-column form) */ cs *cs_spalloc (csi m, csi n, csi nzmax, csi values, csi triplet) { cs *A = cs_calloc (1, sizeof (cs)) ; /* allocate the cs struct */ if (!A) return (NULL) ; /* out of memory */ A->m = m ; /* define dimensions and nzmax */ A->n = n ; A->nzmax = nzmax = CS_MAX (nzmax, 1) ; A->nz = triplet ? 0 : -1 ; /* allocate triplet or comp.col */ A->p = cs_malloc (triplet ? nzmax : n+1, sizeof (csi)) ; A->i = cs_malloc (nzmax, sizeof (csi)) ; A->x = values ? cs_malloc (nzmax, sizeof (double)) : NULL ; return ((!A->p || !A->i || (values && !A->x)) ? cs_spfree (A) : A) ; } /* change the max # of entries sparse matrix */ csi cs_sprealloc (cs *A, csi nzmax) { csi ok, oki, okj = 1, okx = 1 ; if (!A) return (0) ; if (nzmax <= 0) nzmax = (CS_CSC (A)) ? (A->p [A->n]) : A->nz ; A->i = cs_realloc (A->i, nzmax, sizeof (csi), &oki) ; if (CS_TRIPLET (A)) A->p = cs_realloc (A->p, nzmax, sizeof (csi), &okj) ; if (A->x) A->x = cs_realloc (A->x, nzmax, sizeof (double), &okx) ; ok = (oki && okj && okx) ; if (ok) A->nzmax = nzmax ; return (ok) ; } /* free a sparse matrix */ cs *cs_spfree (cs *A) { if (!A) return (NULL) ; /* do nothing if A already NULL */ cs_free (A->p) ; cs_free (A->i) ; cs_free (A->x) ; return ((cs *) cs_free (A)) ; /* free the cs struct and return NULL */ } /* free a numeric factorization */ csn *cs_nfree (csn *N) { if (!N) return (NULL) ; /* do nothing if N already NULL */ cs_spfree (N->L) ; cs_spfree (N->U) ; cs_free (N->pinv) ; cs_free (N->B) ; return ((csn *) cs_free (N)) ; /* free the csn struct and return NULL */ } /* free a symbolic factorization */ css *cs_sfree (css *S) { if (!S) return (NULL) ; /* do nothing if S already NULL */ cs_free (S->pinv) ; cs_free (S->q) ; cs_free (S->parent) ; cs_free (S->cp) ; cs_free (S->leftmost) ; return ((css *) cs_free (S)) ; /* free the css struct and return NULL */ } /* allocate a cs_dmperm or cs_scc result */ csd *cs_dalloc (csi m, csi n) { csd *D ; D = cs_calloc (1, sizeof (csd)) ; if (!D) return (NULL) ; D->p = cs_malloc (m, sizeof (csi)) ; D->r = cs_malloc (m+6, sizeof (csi)) ; D->q = cs_malloc (n, sizeof (csi)) ; D->s = cs_malloc (n+6, sizeof (csi)) ; return ((!D->p || !D->r || !D->q || !D->s) ? cs_dfree (D) : D) ; } /* free a cs_dmperm or cs_scc result */ csd *cs_dfree (csd *D) { if (!D) return (NULL) ; /* do nothing if D already NULL */ cs_free (D->p) ; cs_free (D->q) ; cs_free (D->r) ; cs_free (D->s) ; return ((csd *) cs_free (D)) ; /* free the csd struct and return NULL */ } /* free workspace and return a sparse matrix result */ cs *cs_done (cs *C, void *w, void *x, csi ok) { cs_free (w) ; /* free workspace */ cs_free (x) ; return (ok ? C : cs_spfree (C)) ; /* return result if OK, else free it */ } /* free workspace and return csi array result */ csi *cs_idone (csi *p, cs *C, void *w, csi ok) { cs_spfree (C) ; /* free temporary matrix */ cs_free (w) ; /* free workspace */ return (ok ? p : (csi *) cs_free (p)) ; /* return result, or free it */ } /* free workspace and return a numeric factorization (Cholesky, LU, or QR) */ csn *cs_ndone (csn *N, cs *C, void *w, void *x, csi ok) { cs_spfree (C) ; /* free temporary matrix */ cs_free (w) ; /* free workspace */ cs_free (x) ; return (ok ? N : cs_nfree (N)) ; /* return result if OK, else free it */ } /* free workspace and return a csd result */ csd *cs_ddone (csd *D, cs *C, void *w, csi ok) { cs_spfree (C) ; /* free temporary matrix */ cs_free (w) ; /* free workspace */ return (ok ? D : cs_dfree (D)) ; /* return result if OK, else free it */ } /* solve U'x=b where x and b are dense. x=b on input, solution on output. */ csi cs_utsolve (const cs *U, double *x) { csi p, j, n, *Up, *Ui ; double *Ux ; if (!CS_CSC (U) || !x) return (0) ; /* check inputs */ n = U->n ; Up = U->p ; Ui = U->i ; Ux = U->x ; for (j = 0 ; j < n ; j++) { for (p = Up [j] ; p < Up [j+1]-1 ; p++) { x [j] -= Ux [p] * x [Ui [p]] ; } x [j] /= Ux [Up [j+1]-1] ; } return (1) ; } Matrix/NAMESPACE0000644000175100001440000001663712271746775013012 0ustar hornikusersuseDynLib(Matrix, .registration=TRUE) ## Import non-base functions we need explicitly, ## notably for which we define methods: importFrom("lattice", levelplot, panel.levelplot.raster) importFrom("graphics", image) importFrom("utils", head, tail, assignInNamespace) importFrom("stats", cov2cor, toeplitz, update#, vcov ) importFrom("grid", grid.rect, gpar, grob)# others via 'grid::' ## try to import all we need, but not more importFrom("methods", ## still needed {group generics needed to be explicitly imported} ? Ops, Arith, Compare, Logic, Math, Math2, Summary, Complex, ## generics for which we export new methods: cbind2, rbind2, coerce, show , kronecker ## things we call,.. necessary when Matrix is loaded, but not attached, as in ## Rscript --vanilla -e 'require(methods);(M <- Matrix::Matrix(0:1,3,3));as(M,"sparseMatrix")' , callGeneric, as, is, extends, new , getClass, getClassDef, validObject , setClass, setClassUnion, setMethod, setOldClass , setValidity, slot, "slot<-" , signature, representation, prototype) ## Generics and functions defined in this package export("Cholesky", ".SuiteSparse_version", "Diagonal", ".symDiagonal", ".sparseDiagonal", "Hilbert", "KhatriRao", "Matrix", "spMatrix", "sparseMatrix", "Schur", "abIseq", "abIseq1", "rep2abI", "band", "bandSparse", "bdiag", ".bdiag", ## no longer; implicit generics now ## "colMeans", "colSums", ## these needed a "..." added ## "rowMeans", "rowSums", "condest", "onenormest", "det",# << "identical" as base - but with correct determinant() ## "mkDet", # <- useful in other packages (Rmpfr, gmp) .. hmm --> 'stats' ? ".dsy2mat", ".dxC2mat", ".T2Cmat", "..2dge", ".diag.dsC",# -> R/dsCMatrix.R --has FIXME "diagN2U", "diagU2N", ".diagU2N", ".diag2tT", ".diag2sT", "drop0", "expand", "expm", "facmul", "fac2sparse", "fac2Sparse", "forceSymmetric", ## 'graph' package (and class) related: "T2graph", "graph2T", "isTriangular", "isDiagonal", "isLDL", "is.null.DN", "invPerm", "lu", "nearPD", "nnzero", "formatSpMatrix", "formatSparseM", ".formatSparseSimple", "printSpMatrix", "printSpMatrix2", "qrR", "rankMatrix", "readHB", "readMM", "sparse.model.matrix", "sparseVector", "symmpart", "skewpart", "tcrossprod", "tril", "triu", "updown", "pack", "unpack" , ".updateCHMfactor" , ".validateCsparse" , "writeMM" ) if(getRversion() < "2.15.0") export(".M.classEnv") ## substitute for using cbind() / rbind() export("cBind", "rBind") exportClasses( ## Class unions: "index", "replValue", # if we don't export it, things fail in dispatch "atomicVector", "number", ## LOGIC "logic", "abIndex", "rleDiff", ## --- 'Matrix' mother and all its daughters : --------------- "Matrix", ## also intermediate `virtual' ones: "dMatrix", "lMatrix", "nMatrix", ## not yet used, but as sub-classes; ## must provide them for 'hierarchy-analysis': "iMatrix", "zMatrix", "denseMatrix", "sparseMatrix", "compMatrix", "diagonalMatrix", "generalMatrix", "symmetricMatrix", "triangularMatrix", "dsparseMatrix", "lsparseMatrix", "nsparseMatrix", "TsparseMatrix", "CsparseMatrix", "RsparseMatrix", "ddenseMatrix", "ldenseMatrix", "ndenseMatrix", "dgCMatrix", "dgRMatrix", "dgTMatrix", "dgeMatrix", "dpoMatrix", "dppMatrix", "dsCMatrix", "dsRMatrix", "dsTMatrix", "dspMatrix", "dsyMatrix", "dtCMatrix", "dtRMatrix", "dtTMatrix", "dtpMatrix", "dtrMatrix", "ddiMatrix", "lgeMatrix", "lspMatrix", "lsyMatrix", "ltpMatrix", "ltrMatrix", "ldiMatrix", "ngeMatrix", "nspMatrix", "nsyMatrix", "ntpMatrix", "ntrMatrix", "lgCMatrix", "lgRMatrix", "lgTMatrix", "lsCMatrix", "lsRMatrix", "lsTMatrix", "ltCMatrix", "ltRMatrix", "ltTMatrix", "ngCMatrix", "ngRMatrix", "ngTMatrix", "nsCMatrix", "nsRMatrix", "nsTMatrix", "ntCMatrix", "ntRMatrix", "ntTMatrix", "indMatrix", "pMatrix", "corMatrix", # unused ## --- inheriting "Matrix", but also factorizations: "BunchKaufman", "pBunchKaufman", "Cholesky", "pCholesky", ## "LDL", ## --- 'MatrixFactorization' mother and all its daughters : --- "MatrixFactorization", "CholeskyFactorization", "LU", "denseLU", "sparseLU", "CHMfactor", "CHMsuper", "CHMsimpl", "dCHMsuper", "dCHMsimpl", "nCHMsuper",# unused "nCHMsimpl",# unused "sparseQR", ## "SPQR", "Schur", "sparseVector", ## --- and daughters : --- "dsparseVector", "isparseVector", "lsparseVector", "nsparseVector", "zsparseVector", "xsparseVector" # the class union of all 'x' lost sparseVector's ) exportMethods(## for both own and "other" generics: ## Group Methods "Arith", "Compare", "Logic", "Math", "Math2", "Ops", "Summary", ## re-export S4 methods, for "stats"-S3-generics: "cov2cor", "toeplitz", "update", "!", "+",# for dgT(Matrix) only "%*%", "all", "any", "all.equal", "BunchKaufman", "Cholesky", "Schur", "as.array", "as.matrix", "as.vector", "as.numeric", "as.integer", "as.logical", "band", "chol", "chol2inv", "colMeans", "colSums", "coerce", "crossprod", "determinant", "diag", "diag<-", "diff", "dim", "dim<-", "dimnames", "dimnames<-", "drop", "expand", "expm", "format", "head", "image", "forceSymmetric", "isSymmetric", "is.na", "is.finite", "is.infinite", "kronecker", "length", "mean", "norm", "nnzero", "print",# print(x, ...) when show(x) is not sufficient "qr", "qr.R", "qr.Q", "qr.qy", "qr.qty", "qr.coef", "qr.resid", "qr.fitted", "rep", "rcond", "rowMeans", "rowSums", "show", "solve", ## "spqr", "summary", "symmpart", "skewpart", "t", "tail", "tcrossprod", "tril", "triu", "updown", "unname", "which", "zapsmall" ) if(getRversion() > "3.1.0") exportMethods("anyNA") exportMethods("rbind2") exportMethods("cbind2") S3method(print, sparseSummary) S3method(print, diagSummary) S3method(c, abIndex)# < for now -- S4 method on c() seems "difficult" ## So that such dispatch also works inside base functions: S3method(as.array, Matrix) S3method(as.matrix, Matrix) S3method(as.vector, Matrix) Matrix/data/0000755000175100001440000000000012271765436012462 5ustar hornikusersMatrix/data/KNex.R0000644000175100001440000000051512221622413013431 0ustar hornikusersstopifnot(require(Matrix), require(methods)) # Matrix classes; new, slot<- KNex <- local({ load(system.file(file.path("external", "KNex_slots.rda"), package = "Matrix")) ## -> 'L' r <- list(mm = new("dgCMatrix"), y = L[["y"]]) for (n in c("Dim", "i","p","x")) ## needs methods::slot<- slot(r$mm, n) <- L[[n]] r }) Matrix/data/CAex.R0000644000175100001440000000077512221622413013414 0ustar hornikusersstopifnot(require(Matrix), require(methods)) # Matrix classes; new, slot<- CAex <- local({ load(system.file(file.path("external", "CAex_slots.rda"), package = "Matrix")) ## -> 'L' r <- new("dgCMatrix") for (n in c("Dim", "i","p","x")) slot(r, n) <- L[[n]] r }) ## The reverse { CAex |--> L } is if(FALSE) { sNms <- c("Dim", "i", "p", "x") L <- lapply(sNms, function(N) slot(CAex, N)); names(L) <- sNms save(L, file = "/u/maechler/R/Pkgs/Matrix/inst/external/CAex_slots.rda") } Matrix/data/USCounties.R0000644000175100001440000000064512221622413014631 0ustar hornikusersstopifnot(require(Matrix), require(methods)) # Matrix classes; new, slot<- USCounties <- local({ load(system.file(file.path("external", "USCounties_slots.rda"), package = "Matrix")) ## -> 'L' r <- new("dsCMatrix") for (n in c("Dim", "i","p","x")) slot(r, n) <- L[[n]] r }) ## The reverse: ## L <- list() ## for (n in c("Dim", "i","p","x")) L[[n]] <- slot(USCounties, n) Matrix/R/0000755000175100001440000000000012271765426011751 5ustar hornikusersMatrix/R/HBMM.R0000644000175100001440000001543612070371667012625 0ustar hornikusers## Utilities for the Harwell-Boeing and MatrixMarket formats readone <- function(ln, iwd, nper, conv) { ln <- gsub("D", "E", ln) inds <- seq(0, by = iwd, length = nper + 1) (conv)(substring(ln, 1 + inds[-length(inds)], inds[-1])) } readmany <- function(conn, nlines, nvals, fmt, conv) { if (!grep("[[:digit:]]+[DEFGI][[:digit:]]+", fmt)) stop("Not a valid format") Iind <- regexpr('[DEFGI]', fmt) nper <- as.integer(substr(fmt, regexpr('[[:digit:]]+[DEFGI]', fmt), Iind - 1)) iwd <- as.integer(substr(fmt, Iind + 1, regexpr('[\\.\\)]', fmt) - 1)) rem <- nvals %% nper full <- nvals %/% nper ans <- vector("list", nvals %/% nper) for (i in seq_len(full)) ans[[i]] <- readone(readLines(conn, 1, ok = FALSE), iwd, nper, conv) if (!rem) return(unlist(ans)) c(unlist(ans), readone(readLines(conn, 1, ok = FALSE), iwd, rem, conv)) } readHB <- function(file) { if (is.character(file)) file <- if (file == "") stdin() else file(file) if (!inherits(file, "connection")) stop("'file' must be a character string or connection") if (!isOpen(file)) { open(file) on.exit(close(file)) } hdr <- readLines(file, 4, ok = FALSE) Title <- sub('[[:space:]]+$', '', substr(hdr[1], 1, 72)) Key <- sub('[[:space:]]+$', '', substr(hdr[1], 73, 80)) totln <- as.integer(substr(hdr[2], 1, 14)) ptrln <- as.integer(substr(hdr[2], 15, 28)) indln <- as.integer(substr(hdr[2], 29, 42)) valln <- as.integer(substr(hdr[2], 43, 56)) rhsln <- as.integer(substr(hdr[2], 57, 70)) if (!(t1 <- substr(hdr[3], 1, 1)) %in% c('C', 'R', 'P')) stop(gettextf("Invalid storage type: %s", t1), domain=NA) if (t1 != 'R') stop("Only numeric sparse matrices allowed") ## _FIXME: Patterns should also be allowed if (!(t2 <- substr(hdr[3], 2, 2)) %in% c('H', 'R', 'S', 'U', 'Z')) stop(gettextf("Invalid storage format: %s", t2), domain=NA) if (!(t3 <- substr(hdr[3], 3, 3)) %in% c('A', 'E')) stop(gettextf("Invalid assembled indicator: %s", t3), domain=NA) nr <- as.integer(substr(hdr[3], 15, 28)) nc <- as.integer(substr(hdr[3], 29, 42)) nz <- as.integer(substr(hdr[3], 43, 56)) nel <- as.integer(substr(hdr[3], 57, 70)) ptrfmt <- toupper(sub('[[:space:]]+$', '', substr(hdr[4], 1, 16))) indfmt <- toupper(sub('[[:space:]]+$', '', substr(hdr[4], 17, 32))) valfmt <- toupper(sub('[[:space:]]+$', '', substr(hdr[4], 33, 52))) rhsfmt <- toupper(sub('[[:space:]]+$', '', substr(hdr[4], 53, 72))) if (!is.na(rhsln) && rhsln > 0) { h5 <- readLines(file, 1, ok = FALSE) } ptr <- readmany(file, ptrln, nc + 1, ptrfmt, as.integer) ind <- readmany(file, indln, nz, indfmt, as.integer) vals <- readmany(file, valln, nz, valfmt, as.numeric) if (t2 == 'S') new("dsCMatrix", uplo = "L", p = ptr - 1L, i = ind - 1L, x = vals, Dim = c(nr, nc)) else new("dgCMatrix", p = ptr - 1L, i = ind - 1L, x = vals, Dim = c(nr, nc)) } readMM <- function(file) { if (is.character(file)) file <- if(file == "") stdin() else file(file) if (!inherits(file, "connection")) stop("'file' must be a character string or connection") if (!isOpen(file)) { open(file) on.exit(close(file)) } scan1 <- function(what, ...) scan(file, nmax = 1, what = what, quiet = TRUE, ...) if ((hdr <- scan1(character())) != "%%MatrixMarket") stop("file is not a MatrixMarket file") if (!(typ <- tolower(scan1(character()))) %in% "matrix") stop(gettextf("type '%s' not recognized", typ), domain = NA) if (!(repr <- tolower(scan1(character()))) %in% c("coordinate", "array")) stop(gettextf("representation '%s' not recognized", repr), domain = NA) elt <- tolower(scan1(character())) if (!elt %in% c("real", "complex", "integer", "pattern")) stop(gettextf("element type '%s' not recognized", elt), domain = NA) sym <- tolower(scan1(character())) if (!sym %in% c("general", "symmetric", "skew-symmetric", "hermitian")) stop(gettextf("symmetry form '%s' not recognized", sym), domain = NA) nr <- scan1(integer(), comment.char = "%") nc <- scan1(integer()) nz <- scan1(integer()) checkIJ <- function(els) { if(els$i < 1 || els$i > nr) stop("readMM(): row values 'i' are not in 1:nr", call.=FALSE) if(els$j < 1 || els$j > nc) stop("readMM(): column values 'j' are not in 1:nc", call.=FALSE) } if (repr == "coordinate") { switch(elt, "real" = , "integer" = { ## TODO: the "integer" element type should be returned as ## an object of an "iMatrix" subclass--once there are els <- scan(file, nmax = nz, quiet = TRUE, what= list(i= integer(), j= integer(), x= numeric())) checkIJ(els) switch(sym, "general" = { new("dgTMatrix", Dim = c(nr, nc), i = els$i - 1L, j = els$j - 1L, x = els$x) }, "symmetric" = { new("dsTMatrix", uplo = "L", Dim = c(nr, nc), i = els$i - 1L, j = els$j - 1L, x = els$x) }, "skew-symmetric" = { stop("symmetry form 'skew-symmetric' not yet implemented for reading") ## FIXME: use dgT... but must expand the (i,j,x) slots! new("dgTMatrix", uplo = "L", Dim = c(nr, nc), i = els$i - 1L, j = els$j - 1L, x = els$x) }, "hermitian" = { stop("symmetry form 'hermitian' not yet implemented for reading") }, ## otherwise (not possible; just defensive programming): stop(gettextf("symmetry form '%s' is not yet implemented", sym), domain = NA) ) }, "pattern" = { els <- scan(file, nmax = nz, quiet = TRUE, what = list(i = integer(), j = integer())) checkIJ(els) switch(sym, "general" = { new("ngTMatrix", Dim = c(nr, nc), i = els$i - 1L, j = els$j - 1L) }, "symmetric" = { new("nsTMatrix", uplo = "L", Dim = c(nr, nc), i = els$i - 1L, j = els$j - 1L) }, "skew-symmetric" = { stop("symmetry form 'skew-symmetric' not yet implemented for reading") ## FIXME: use dgT... but must expand the (i,j,x) slots! new("ngTMatrix", uplo = "L", Dim = c(nr, nc), i = els$i - 1L, j = els$j - 1L) }, "hermitian" = { stop("symmetry form 'hermitian' not yet implemented for reading") }, ## otherwise (not possible; just defensive programming): stop(gettextf("symmetry form '%s' is not yet implemented", sym), domain = NA) ) }, "complex" = { stop("element type 'complex' not yet implemented") }, ## otherwise (not possible currently): stop(gettextf("'%s()' is not yet implemented for element type '%s'", "readMM", elt), domain = NA)) } else stop(gettextf("'%s()' is not yet implemented for representation '%s'", "readMM", repr), domain = NA) } Matrix/R/lsCMatrix.R0000644000175100001440000000415311004710547013770 0ustar hornikusers#### Logical Symmetric Sparse Matrices in Compressed column-oriented format ### contains = "lsparseMatrix" setAs("lsCMatrix", "matrix", function(from) as(as(from, "generalMatrix"), "matrix")) setAs("lsCMatrix", "lgCMatrix", function(from) .Call(Csparse_symmetric_to_general, from)) ## needed for indexing (still ?) setAs("lsCMatrix", "lgTMatrix", function(from) as(as(from, "generalMatrix"), "lgTMatrix")) aslsC.by.lgC <- function(from) as(as(from, "lgCMatrix"), "symmetricMatrix") setAs("lgTMatrix", "lsCMatrix", aslsC.by.lgC) # <-> needed for Matrix() setAs("matrix", "lsCMatrix", aslsC.by.lgC) ## Specific conversions, should they be necessary. Better to convert as ## as(x, "TsparseMatrix") or as(x, "denseMatrix") setAs("lsCMatrix", "lsTMatrix", function(from) .Call(Csparse_to_Tsparse, from, FALSE)) setAs("lsCMatrix", "dsCMatrix", function(from) new("dsCMatrix", i = from@i, p = from@p, x = as.double(from@x), uplo = from@uplo, Dim = from@Dim, Dimnames = from@Dimnames)) if(FALSE) # needed ? setAs("lsCMatrix", "dgTMatrix", function(from) as(as(from, "dsCMatrix"), "dgTMatrix")) ## have rather tril() and triu() methods than ## setAs("lsCMatrix", "ltCMatrix", ....) setMethod("tril", "lsCMatrix", function(x, k = 0, ...) { if(x@uplo == "L" && k == 0) ## same internal structure + diag new("ltCMatrix", uplo = x@uplo, i = x@i, p = x@p, x = x@x, Dim = x@Dim, Dimnames = x@Dimnames) else tril(as(x, "lgCMatrix"), k = k, ...) }) setMethod("triu", "lsCMatrix", function(x, k = 0, ...) { if(x@uplo == "U" && k == 0) new("ltCMatrix", uplo = x@uplo, i = x@i, p = x@p, x = x@x, Dim = x@Dim, Dimnames = x@Dimnames) else triu(as(x, "lgCMatrix"), k = k, ...) }) setMethod("chol", signature(x = "lsCMatrix"), function(x, pivot=FALSE, ...) chol(as(x, "dgCMatrix"), pivot=pivot, ...)) ## Use more general method from CsparseMatrix class ## setMethod("t", signature(x = "lsCMatrix"), ## function(x) ## .Call(lsCMatrix_trans, x), ## valueClass = "lsCMatrix") Matrix/R/sparseVector.R0000644000175100001440000007153112256112203014541 0ustar hornikusers#### All Methods in relation with the sparseVector (sub)classes ## atomicVector : classUnion (logical,integer,double,....) setAs("atomicVector", "sparseVector", function(from) { n <- length(from)# *is* integer for atomic vectors r <- new(paste0(.V.kind(from), "sparseVector"), length = n) ii <- isN0(from) r@x <- from[ii] r@i <- seq_len(n)[ii] r }) ## dsparseVector: currently important, as later potentially made into d..Matrix : setAs("atomicVector", "dsparseVector", function(from) { n <- length(from)# *is* integer for atomic vectors r <- new("dsparseVector", length = n) ii <- isN0(from) r@x <- as.numeric(from)[ii] r@i <- seq_len(n)[ii] r }) setAs("nsparseVector", "lsparseVector", function(from) new("lsparseVector", i = from@i, length = from@length, x = rep.int(TRUE, length(from@i)))) setAs("nsparseVector", "dsparseVector", function(from) as(as(from, "lsparseVector"), "dsparseVector")) setAs("nsparseVector", "isparseVector", function(from) as(as(from, "lsparseVector"), "isparseVector")) setAs("nsparseVector", "zsparseVector", function(from) as(as(from, "lsparseVector"), "zsparseVector")) ## "xsparseVector" : those with an 'x' slot (i.e., currently := not nsparse*) setAs("xsparseVector", "dsparseVector", function(from) new("dsparseVector", x= as.double(from@x) , i= from@i, length= from@length)) setAs("xsparseVector", "isparseVector", function(from) new("isparseVector", x= as.integer(from@x), i= from@i, length= from@length)) setAs("xsparseVector", "lsparseVector", function(from) new("lsparseVector", x= as.logical(from@x), i= from@i, length= from@length)) setAs("xsparseVector", "zsparseVector", function(from) new("zsparseVector", x= as.complex(from@x), i= from@i, length= from@length)) setAs("xsparseVector", "nsparseVector", function(from) { if(any(is.na(from@x))) stop("cannot coerce 'NA's to \"nsparseVector\"") new("nsparseVector", i = from@i, length = from@length) }) setMethod("is.na", signature(x = "nsparseVector"), function(x) new("nsparseVector", length = x@length))## all FALSE setMethod("is.na", signature(x = "sparseVector"), ## x is *not* "nsparse*" as that has own method function(x) new("nsparseVector", i = x@i[is.na(x@x)], length= x@length)) if(getRversion() > "3.1.0") { setMethod("anyNA", signature(x = "nsparseVector"), function(x) FALSE) setMethod("anyNA", signature(x = "sparseVector"), function(x) anyNA(x@x)) } setMethod("is.infinite", signature(x = "nsparseVector"), function(x) new("nsparseVector", length = x@length))## all FALSE setMethod("is.infinite", signature(x = "sparseVector"), ## x is *not* "nsparse*" as that has own method function(x) new("nsparseVector", i = x@i[is.infinite(x@x)], length= x@length)) setMethod("is.finite", signature(x = "nsparseVector"), function(x) rep.int(TRUE, x@length))## all TRUE setMethod("is.finite", signature(x = "sparseVector"), function(x) { ## x is *not* "nsparse*" as that has own method r <- rep.int(TRUE, x@length) ## mostly TRUE r[x@i[!is.finite(x@x)]] <- FALSE r }) sp2vec <- function(x, mode = .type.kind[substr(cl, 1,1)]) { ## sparseVector -> vector cl <- class(x) r <- vector(mode, x@length) r[x@i] <- if(cl != "nsparseVector") { # cheap test for 'has x slot' if(is(x@x, mode)) x@x else as(x@x, mode) } else TRUE r } ##' Construct new sparse vector , *dropping* zeros ##' @param class character, the sparseVector class ##' @param x numeric/logical/...: the 'x' slot ##' @param i integer: index of non-zero entries ##' @param length integer: the 'length' slot ##' @return a sparseVector, with 0-dropped 'x' (and 'i') newSpV <- function(class, x, i, length, drop0 = TRUE, checkSort = TRUE) { if(length(x) == 1 && (li <- length(i)) != 1) ## recycle x : x <- rep.int(x, li) if(drop0 && isTRUE(any(x0 <- x == 0))) { keep <- is.na(x) | !x0 x <- x[keep] i <- i[keep] } if(checkSort && is.unsorted(i)) { ii <- sort.list(i) x <- x[ii] i <- i[ii] } new(class, x = x, i = i, length = length) } ## a "version" of 'prev' with changed contents: newSpVec <- function(class, x, prev) newSpV(class, x=x, i=prev@i, length=prev@length) ## Exported: sparseVector <- function(x, i, length) { newSpV(class = paste0(.V.kind(x), "sparseVector"), x=x, i=i, length=length) } setAs("sparseVector", "vector", function(from) sp2vec(from)) setMethod("as.vector", signature(x = "sparseVector", mode = "missing"), sp2vec) setMethod("as.vector", signature(x = "sparseVector", mode = "character"), sp2vec) setMethod("as.numeric", "sparseVector", function(x) sp2vec(x, mode = "double")) setMethod("as.logical", "sparseVector", function(x) sp2vec(x, mode = "logical")) setAs("sparseVector", "numeric", function(from) sp2vec(from, mode = "double")) setAs("sparseVector", "integer", function(from) sp2vec(from, mode = "integer")) setAs("sparseVector", "logical", function(from) sp2vec(from, mode = "logical")) ## the "catch all remaining" method: setAs("ANY", "sparseVector", function(from) as(as.vector(from), "sparseVector")) ## "nsparse*" is special -- by default "lsparseVector" are produced setAs("ANY", "nsparseVector", function(from) as(as(from, "sparseVector"),"nsparseVector")) setAs("diagonalMatrix", "sparseVector", function(from) { kind <- .M.kind(from) ## currently only "l" and "d" --> have 'x' n <- nrow(from) n2 <- as.double(n) * n if(n2 > .Machine$integer.max) { ## double (i, length) ii <- seq(1, by = n+1, length.out = n) ## 1-based indexing } else { # integer ok n2 <- as.integer(n2) ii <- as.integer(seq(1L, by = n+1L, length.out = n)) } new(paste0(kind, "sparseVector"), length = n2, i = ii, x = if(from@diag != "U") from@x else rep.int(switch(kind, "d" = 1, "l" = TRUE, "i" = 1L, "z" = 1+0i), n)) }) setAs("sparseMatrix", "sparseVector", function(from) as(as(from, "TsparseMatrix"), "sparseVector")) setAs("CsparseMatrix", "sparseVector", ## could go via TsparseMatrix, but this is faster: function(from) { d <- dim(from) n <- prod(d) # -> numeric, no integer overflow cld <- getClassDef(class(from)) kind <- .M.kind(from, cld) if(extends(cld, "symmetricMatrix")) from <- as(from, "generalMatrix") else if(extends(cld, "triangularMatrix") && from@diag == "U") from <- .Call(Csparse_diagU2N, from) xj <- .Call(Matrix_expand_pointers, from@p) ii <- if(n < .Machine$integer.max) 1L + from@i + d[1] * xj else 1 + from@i + as.double(d[1]) * xj cl <- paste0(kind, "sparseVector") if(kind != "n") ## have 'x' slot new(cl, i = ii, length = n, x = from@x) else new(cl, i = ii, length = n) }) setAs("TsparseMatrix", "sparseVector", function(from) { d <- dim(from) n <- prod(d) # -> numeric, no integer overflow cld <- getClassDef(class(from)) kind <- .M.kind(from, cld) if(extends(cld, "symmetricMatrix")) from <- as(from, "generalMatrix") else if(extends(cld, "triangularMatrix") && from@diag == "U") from <- .Call(Tsparse_diagU2N, from) if(is_duplicatedT(from, di = d)) from <- uniqTsparse(from) ii <- if(n < .Machine$integer.max) 1L + from@i + d[1] * from@j else 1 + from@i + as.double(d[1]) * from@j cl <- paste0(kind, "sparseVector") if(kind != "n") ## have 'x' slot new(cl, i = ii, length = n, x = from@x) else new(cl, i = ii, length = n) }) ##' ##' ##'

## Utility -- used in `dim<-` below, but also in Matrix(.) : ##' @title sparseVector --> sparseMatrix constructor ##' @param x "sparseVector" object ##' @param nrow integer or missing, as in matrix(), see ?matrix ##' @param ncol (ditto) ##' @param byrow logical (see ?matrix) ##' @param check logical indicating if it needs to be checked that 'x' is a sparseVector ##' @param symmetric logical indicating if result must be "symmetricMatrix" ##' @return an object inheriting from "sparseMatrix" ##' @author Martin Maechler, May 2007 ff. spV2M <- function (x, nrow, ncol, byrow = FALSE, check = TRUE, symmetric = FALSE) { cx <- class(x) if(check && !extends(cx, "sparseVector")) stop("'x' must inherit from \"sparseVector\"") if(!missing(ncol)) { ncol <- as.integer(ncol) if(ncol < 0) stop("'ncol' must be >= 0") } if(!missing(nrow)) { nrow <- as.integer(nrow) if(nrow < 0) stop("'nrow' must be >= 0") } n <- length(x) if(symmetric) { if(missing(nrow)) stop("Must specify 'nrow' when 'symmetric' is true") if(!missing(ncol) && nrow != ncol) stop("'nrow' and 'ncol' must be the same when 'symmetric' is true") ## otherwise ncol will not used at all when (symmetric) if(check && as.double(nrow)^2 != n) stop("'x' must have length nrow^2 when 'symmetric' is true") ## x <- x[indTri(nrow, upper=TRUE, diag=TRUE)] } else if(missing(nrow)) { nrow <- as.integer( if(missing(ncol)) { ## both missing: --> (n x 1) ncol <- 1L n } else { if(n %% ncol != 0) warning("'ncol' is not a factor of length(x)") as.integer(ceiling(n / ncol)) }) } else if(missing(ncol)) { ncol <- if(symmetric) nrow else { if(n %% nrow != 0) warning("'nrow' is not a factor of length(x)") as.integer(ceiling(n / nrow)) } } else { ## both nrow and ncol specified n.n <- as.double(ncol) * nrow # no integer overflow if(n.n < n) stop("nrow * ncol < length(x)", domain = NA) if(n.n != n) warning("nrow * ncol != length(x)", domain = NA) } ## now nrow * ncol >= n (or 'symmetric') ## ~~~~~~~~~~~~~~~~ cld <- getClassDef(cx) kind <- .M.kindC(cld) # "d", "n", "l", "i", "z", ... has.x <- kind != "n" clStem <- if(symmetric) "sTMatrix" else "gTMatrix" ## "careful_new()" : cNam <- paste0(kind, clStem) chngCl <- is.null(slotNames(newCl <- getClass(cNam, .Force=TRUE))) if(chngCl) { ## e.g. "igTMatrix" is not yet implemented if(substr(cNam,1,1) == "z") stop(gettextf("Class %s is not yet implemented", dQuote(cNam)), domain=NA) ## coerce to "double": newCl <- getClass(paste0("d", clStem)) } r <- new(newCl, Dim = c(nrow, ncol)) ## now "compute" the (i,j,x) slots given x@(i,x) i0 <- x@i - 1L if(byrow) { ## need as.integer(.) since @ i can be double j <- as.integer(i0 %% ncol) i <- as.integer(i0 %/% ncol) } else { ## default{byrow = FALSE} i <- as.integer(i0 %% nrow) j <- as.integer(i0 %/% nrow) } if(has.x) x <- if(chngCl) as.numeric(x@x) else x@x if(symmetric) { ## using uplo = "U" i0 <- i <= j ## i.e., indTri(nrow, upper=TRUE, diag=TRUE) i <- i[i0] j <- j[i0] if(has.x) x <- x[i0] } r@j <- j r@i <- i if(has.x) r@x <- x r }## {spV2M} .sparseV2Mat <- function(from) spV2M(from, nrow=length(from), ncol=1L, check=FALSE) setAs("sparseVector","Matrix", .sparseV2Mat) setAs("sparseVector","sparseMatrix", .sparseV2Mat) setAs("sparseVector","TsparseMatrix", .sparseV2Mat) setAs("sparseVector","CsparseMatrix", function(from) .Call(Tsparse_to_Csparse, .sparseV2Mat(from), FALSE)) ## This is very similar to the 'x = "sparseMatrix"' method in ./sparseMatrix.R: setMethod("dim<-", signature(x = "sparseVector", value = "ANY"), function(x, value) { if(!is.numeric(value) || length(value) != 2) stop("dim(.) value must be numeric of length 2") if(length(x) != prod(value <- round(value))) stop("dimensions don't match the number of cells") spV2M(x, nrow=value[1], ncol=value[2]) }) setMethod("length", "sparseVector", function(x) x@length) setMethod("show", signature(object = "sparseVector"), function(object) { n <- object@length cl <- class(object) cat(sprintf('sparse vector (nnz/length = %d/%.0f) of class "%s"\n', length(object@i), as.double(n), cl)) maxp <- max(1, getOption("max.print")) if(n <= maxp) { prSpVector(object, maxp = maxp) } else { # n > maxp : will cut length of what we'll display : ## cannot easily show head(.) & tail(.) because of "[1] .." printing of tail prSpVector(head(object, maxp), maxp = maxp) cat(" ............................", "\n ........suppressing ", n - maxp, " entries in show(); maybe adjust 'options(max.print= *)'", "\n ............................\n\n", sep='') } invisible(object) }) prSpVector <- function(x, digits = getOption("digits"), maxp = getOption("max.print"), zero.print = ".") { cld <- getClassDef(class(x)) stopifnot(extends(cld, "sparseVector"), maxp >= 1) if(is.logical(zero.print)) zero.print <- if(zero.print) "0" else " " ## kind <- .M.kindC(cld) ## has.x <- kind != "n" n <- x@length if(n > 0) { if(n > maxp) { # n > maxp =: nn : will cut length of what we'll display : x <- head(x, maxp) n <- maxp } xi <- x@i is.n <- extends(cld, "nsparseVector") logi <- is.n || extends(cld, "lsparseVector") cx <- if(logi) rep.int("N", n) else character(n) cx[if(length(xi)) -xi else TRUE] <- zero.print cx[ xi] <- { if(is.n) "|" else if(logi) c(":","|")[x@x + 1L] else ## numeric (or --not yet-- complex): 'has.x' in any cases format(x@x, digits = digits) } ## right = TRUE : cheap attempt to get better "." alignment print(cx, quote = FALSE, right = TRUE, max = maxp) } invisible(x) # TODO? in case of n > maxp, "should" return original x } ## This is a simplified intI() {-> ./Tsparse.R } -- for sparseVector indexing: intIv <- function(i, n, cl.i = getClass(class(i))) { ### Note: undesirable to use this for negative indices; ### ---- using seq_len(n) below means we are NON-sparse ... ### Fixed, for "x[i] with negative i" at least. ## Purpose: translate numeric | logical index into 1-based integer ## -------------------------------------------------------------------- ## Arguments: i: index vector (numeric | logical) *OR* sparseVector ## n: array extent { == length(.) } if(missing(i)) return(seq_len(n)) ## else : if(extends(cl.i, "numeric")) { storage.mode(i) <- "integer" int2i(i,n) ##-> ./Tsparse.R } else if (extends(cl.i, "logical")) { seq_len(n)[i] } else if(extends(cl.i, "nsparseVector")) { i@i # the indices are already there ! } else if(extends(cl.i, "lsparseVector")) { i@i[i@x] # "drop0", i.e. FALSE; NAs ok } else if (extends(cl.i, "sparseVector")) { ## 'i'sparse, 'd'sparse (etc) as.integer(i@x[i@i]) } else stop("index must be numeric, logical or sparseVector for indexing sparseVectors") } ## intIv() setMethod("head", signature(x = "sparseVector"), function(x, n = 6, ...) { stopifnot(length(n) == 1) if(n >= (nx <- x@length)) return(x) if(is.integer(x@i)) n <- as.integer(n) else stopifnot(n == round(n)) if(n < 0) n <- max(0L, n + nx) ## now be careful to *NOT* use seq_len(n), as this be efficient for huge n ## n < x@length now. ## As we *know* that '@i' is sorted increasingly: [x@i <= n] <==> [1:kk] x@length <- n x@i <- x@i[ii <- seq_len(which.max(x@i > n) - 1L)] if(substr(class(x), 1,1) != "n") ## be fast, ... x@x <- x@x[ii] x }) setMethod("tail", signature(x = "sparseVector"), function(x, n = 6, ...) { stopifnot(length(n) == 1) if(n >= (nx <- x@length)) return(x) if(is.integer(x@i)) n <- as.integer(n) else stopifnot(n == round(n)) if(n < 0) n <- max(0L, n + nx) ## now be careful to *NOT* use seq_len(n), as this be efficient for huge n ## n < x@length now. ## As we *know* '@i' is sorted increasingly: [x@i > nx-n] <==> [kk:nx] x@length <- n n <- nx-n # and keep indices > n N <- length(x@i) ii <- if(any(G <- x@i > n)) which.max(G):N else FALSE x@i <- x@i[ii] - n if(substr(class(x), 1,1) != "n") ## be fast, ... x@x <- x@x[ii] x }) setMethod("[", signature(x = "sparseVector", i = "index"), function (x, i, j, ..., drop) { cld <- getClassDef(class(x)) has.x <- !extends(cld, "nsparseVector") n <- x@length if(extends(cl.i <- getClass(class(i)), "numeric") && any(i < 0)) { ## negative indices - remain sparse --> *not* using intIv() if(any(i > 0)) stop("you cannot mix negative and positive indices") if(any(z <- i == 0)) i <- i[!z] ## all (i < 0) : ## FIXME: an efficient solution would use C here i <- unique(sort(-i)) # so we need to drop the 'i's if(any(nom <- is.na(m <- match(x@i, i)))) { ## eliminate those with non-0 match x@i <- x@i[nom] if(has.x) x@x <- x@x[nom] } ii <- findInterval(x@i, i) ## subtract that : x@i <- x@i - ii x@length <- x@length - length(i) } else { ii <- intIv(i, n, cl.i=cl.i) m <- match(x@i, ii, nomatch = 0) sel <- m > 0L x@length <- length(ii) x@i <- m[sel] if(any(iDup <- duplicated(ii))) { i.i <- match(ii[iDup], ii) jm <- lapply(i.i, function(.) which(. == m)) sel <- c(which(sel), unlist(jm)) x@i <- c(x@i, rep.int(which(iDup), sapply(jm, length))) } if (has.x) x@x <- x@x[sel] } x }) setMethod("[", signature(x = "sparseVector", i = "lsparseVector"), function (x, i, j, ..., drop) x[sort.int(i@i[i@x])]) setMethod("[", signature(x = "sparseVector", i = "nsparseVector"), function (x, i, j, ..., drop) x[sort.int(i@i)]) ##--- Something else: Allow v[ ] -- exactly similarly: if(FALSE) { ## R_FIXME: Not working, as internal "[" only dispatches on 1st argument setMethod("[", signature(x = "atomicVector", i = "lsparseVector"), function (x, i, j, ..., drop) x[sort.int(i@i[i@x])]) setMethod("[", signature(x = "atomicVector", i = "nsparseVector"), function (x, i, j, ..., drop) x[sort.int(i@i)]) } ##' Implement x[i] <- value ##' @param x a "sparseVector" ##' @param i an "index" (integer, logical, ..) ##' @param value ##' @return a "sparseVector" of the same length as 'x' ## This is much analogous to replTmat in ./Tsparse.R: replSPvec <- function (x, i, value) { n <- x@length ii <- intIv(i, n) lenRepl <- length(ii) lenV <- length(value) if(lenV == 0) { if(lenRepl != 0) stop("nothing to replace with") else return(x) } ## else: lenV := length(value) > 0 if(lenRepl %% lenV != 0) stop("number of items to replace is not a multiple of replacement length") if(anyDuplicated(ii)) { ## multiple *replacement* indices: last one wins ## TODO: in R 2.6.0 use duplicate(*, fromLast=TRUE) ir <- lenRepl:1 keep <- match(ii, ii[ir]) == ir ii <- ii[keep] lenV <- length(value <- rep(value, length = lenRepl)[keep]) lenRepl <- length(ii) } cld <- getClassDef(class(x)) has.x <- !extends(cld, "nsparseVector") m <- match(x@i, ii, nomatch = 0) sel <- m > 0L ## the simplest case if(all0(value)) { ## just drop the non-zero entries if(any(sel)) { ## non-zero there x@i <- x@i[!sel] if(has.x) x@x <- x@x[!sel] } return(x) } ## else -- some( value != 0 ) -- if(lenV > lenRepl) stop("too many replacement values") else if(lenV < lenRepl) value <- rep(value, length = lenRepl) ## now: length(value) == lenRepl v0 <- is0(value) ## value[1:lenRepl]: which are structural 0 now, which not? if(any(sel)) { ## indices of non-zero entries -- WRT to subvector iN0 <- m[sel] ## == match(x@i[sel], ii) ## 1a) replace those that are already non-zero with new val. vN0 <- !v0[iN0] if(any(vN0) && has.x) x@x[sel][vN0] <- value[iN0[vN0]] ## 1b) replace non-zeros with 0 --> drop entries if(any(!vN0)) { i <- which(sel)[!vN0] if(has.x) x@x <- x@x[-i] x@i <- x@i[-i] } iI0 <- if(length(iN0) < lenRepl) seq_len(lenRepl)[-iN0] } else iI0 <- seq_len(lenRepl) if(length(iI0) && any(vN0 <- !v0[iI0])) { ## 2) add those that were structural 0 (where value != 0) ij0 <- iI0[vN0] x@i <- c(x@i, ii[ij0]) if(has.x) x@x <- c(x@x, value[ij0]) } x } setReplaceMethod("[", signature(x = "sparseVector", i = "index", j = "missing", value = "replValue"), replSPvec) setReplaceMethod("[", signature(x = "sparseVector", i = "sparseVector", j = "missing", value = "replValue"), ## BTW, the important case: 'i' a *logical* sparseVector replSPvec) ## Something else: Also allow x[ ] <- v e.g. for atomic x : if(FALSE) { ## R_FIXME: Not working, as internal "[<-" only dispatches on 1st argument ## Now "the work is done" inside intIv() : setReplaceMethod("[", signature(x = "atomicVector", i = "sparseVector", j = "missing", value = "replValue"), function (x, i, value) callGeneric(x, i = intIv(i, x@length), value=value)) } ## a "method" for c(<(sparse)Vector>, <(sparse)Vector>): ## FIXME: This is not exported, nor used (nor documented) c2v <- function(x, y) { ## these as(., "sp..V..") check input implicitly: cx <- class(x <- as(x, "sparseVector")) cy <- class(y <- as(y, "sparseVector")) if(cx != cy) { ## find "common" class; result does have 'x' slot cxy <- c(cx,cy) commType <- { if(all(cxy %in% c("nsparseVector", "lsparseVector"))) "lsparseVector" else { # ==> "numeric" ("integer") or "complex" xslot1 <- function(u, cl.u) if(cl.u != "nsparseVector") u@x[1] else TRUE switch(typeof(xslot1(x, cx) + xslot1(y, cy)), ## "integer", "double", or "complex" "integer" = "isparseVector", "double" = "dsparseVector", "complex" = "zsparseVector") } } if(cx != commType) x <- as(x, commType) if(cy != commType) y <- as(y, commType) cx <- commType } ## now *have* common type -- transform 'x' into result: nx <- x@length x@length <- nx + y@length x@i <- c(x@i, nx + y@i) if(cx != "nsparseVector") x@x <- c(x@x, y@x) x } ## sort.default() does ## x[order(x, na.last = na.last, decreasing = decreasing)] ## but that uses a *dense* integer order vector ## ==> need direct sort() method for "sparseVector" for mean(*,trim), median(),.. sortSparseV <- function(x, decreasing = FALSE, na.last = NA) { if(length(ina <- which(is.na(x)))) { if(is.na(na.last)) x <- x[-ina] } ## TODO .NotYetImplemented() } all.equal.sparseV <- function(target, current, ...) { if(!is(target, "sparseVector") || !is(current, "sparseVector")) { return(paste0("target is ", data.class(target), ", current is ", data.class(current))) } lt <- length(target) lc <- length(current) if(lt != lc) { return(paste0("sparseVector", ": lengths (", lt, ", ", lc, ") differ")) } t.has.x <- class(target) != "nsparseVector" c.has.x <- class(current) != "nsparseVector" nz.t <- length(i.t <- target @i) nz.c <- length(i.c <- current@i) t.x <- if(t.has.x) target@x else rep.int(TRUE, nz.t) c.x <- if(c.has.x) current@x else rep.int(TRUE, nz.c) if(nz.t != nz.c || any(i.t != i.c)) { ## "work" if indices are not the same i1.c <- setdiff(i.t, i.c)# those in i.t, not yet in i.c i1.t <- setdiff(i.c, i.t) if((n1t <- length(i1.t))) { target@i <- i.t <- c(i.t, i1.t) t.x <- c(t.x, rep.int(if(t.has.x) 0 else 0L, n1t)) } if((n1c <- length(i1.c))) { current@i <- i.c <- c(i.c, i1.c) c.x <- c(c.x, rep.int(if(c.has.x) 0 else 0L, n1c)) } } if(is.unsorted(i.t)) { ## method="quick" {"radix" not ok for large range} ii <- sort.list(i.t, method = "quick", na.last=NA) target@i <- i.t <- i.t[ii] t.x <- t.x[ii] } if(is.unsorted(i.c)) { ii <- sort.list(i.c, method = "quick", na.last=NA) current@i <- i.c <- i.c[ii] c.x <- c.x[ii] } ## Now, we have extended both target and current ## *and* have sorted the respective i-slot, the i-slots should match! stopifnot(all(i.c == i.t)) all.equal.numeric(c.x, t.x, ...) } ## all.equal.sparseV ## For these, we remain sparse: setMethod("all.equal", c(target = "sparseVector", current = "sparseVector"), all.equal.sparseV) setMethod("all.equal", c(target = "sparseVector", current = "sparseMatrix"), function(target, current, ...) all.equal.sparseV(target, as(current, "sparseVector"), ...)) setMethod("all.equal", c(target = "sparseMatrix", current = "sparseVector"), function(target, current, ...) all.equal.sparseV(as(target, "sparseVector"), current, ...)) ## For the others, where one is "dense", "go to" dense rather now than later: setMethod("all.equal", c(target = "ANY", current = "sparseVector"), function(target, current, ...) all.equal(target, as.vector(current), ...)) setMethod("all.equal", c(target = "sparseVector", current = "ANY"), function(target, current, ...) all.equal(as.vector(target), current, ...)) ### rep(x, ...) -- rep() is primitive with internal default method with these args: ### ----------- ### till R 2.3.1, it had rep.default() which we use as 'model' here. repSpV <- function(x, times) { ## == rep.int(, times)" times <- as.integer(times)# truncating as rep.default() n <- x@length has.x <- substr(class(x), 1,1) != "n" ## fast, but hackish ## just assign new correct slots: if(times <= 1) { ## be quick for {0, 1} times if(times < 0) stop("'times >= 0' is required") if(times == 0) { x@length <- 0L x@i <- integer(0) if(has.x) x@x <- rep.int(x@x, 0) } return(x) } n. <- as.double(n) if(n. * times >= .Machine$integer.max) n <- n. # so won't have overflow in subsequent multiplys x@length <- n * times x@i <- rep.int(x@i, times) + n * rep(0:(times-1L), each=length(x@i)) ## := outer(x@i, 0:(times-1) * n, "+") but a bit faster if(has.x) x@x <- rep.int(x@x, times) x } setMethod("rep", "sparseVector", function(x, times, length.out, each, ...) { if (length(x) == 0) return(if(missing(length.out)) x else head(x, length.out)) if (!missing(each)) { tm <- rep.int(each, length(x)) x <- rep(x, tm) # "recursively" if(missing(length.out) && missing(times)) return(x) } ## else : if (!missing(length.out)) # takes precedence over times times <- ceiling(length.out/length(x)) r <- repSpV(x, times) if (!missing(length.out) && length(r) != length.out) { if(length.out > 0) head(r, length.out) else r[integer(0)] } else r }) ### Group Methods (!) ## "Ops" : ["Arith", "Compare", "Logic"]: ---> in ./Ops.R ## ------- ## "Summary" group : "max" "min" "range" "prod" "sum" "any" "all" setMethod("Summary", signature(x = "nsparseVector", na.rm = "ANY"), function(x, ..., na.rm) { ## no 'x' slot, no NA's .. n <- x@length l.x <- length(x@i) if(l.x == n) callGeneric(rep.int(TRUE, n), ..., na.rm = na.rm) else ## l.x < n : has some FALSE entries switch(.Generic, "prod" = 0, "min" = 0L, "all" = FALSE, "any" = l.x > 0, "sum" = l.x, "max" = as.integer(l.x > 0), "range" = c(0L, as.integer(l.x > 0))) }) ## The "other" "sparseVector"s ("d", "l", "i" ..): all have an 'x' slot : setMethod("Summary", signature(x = "sparseVector", na.rm = "ANY"), function(x, ..., na.rm) { n <- x@length l.x <- length(x@x) if(l.x == n) ## fully non-zero (and "general") - very rare but quick callGeneric(x@x, ..., na.rm = na.rm) else if(.Generic != "prod") { logicF <- .Generic %in% c("any","all") ## we rely on (x, NULL, y, ..) :== (x, y, ..): callGeneric(x@x, if(logicF) FALSE else 0, ..., na.rm = na.rm) } else { ## prod() if(any(is.na(x@x))) NaN else 0 } }) setMethod("solve", signature(a = "Matrix", b = "sparseVector"), function(a, b, ...) callGeneric(a, as(b, "sparseMatrix"))) ## the 'i' slot is 1-based *and* has no NA's: setMethod("which", "nsparseVector", function(x, arr.ind) x@i) setMethod("which", "lsparseVector", function(x, arr.ind) x@i[is1(x@x)]) ## and *error* for "dsparseVector", "i*", ... ##' indices of vector x[] to construct Toeplitz matrix ##' FIXME: write in C, port to R('stats' package), and use in stats::toeplitz() ind4toeplitz <- function(n) { A <- matrix(raw(), n, n) abs(as.vector(col(A) - row(A))) + 1L } .toeplitz.spV <- function(x, symmetric=TRUE, giveCsparse=TRUE) { ## semantically "identical" to stats::toeplitz n <- length(x) r <- spV2M(x[ind4toeplitz(n)], n,n, symmetric=symmetric, check=FALSE) if (giveCsparse) as(r, "CsparseMatrix") else r } setMethod("toeplitz", "sparseVector", .toeplitz.spV) Matrix/R/Csparse.R0000644000175100001440000004451112267246663013503 0ustar hornikusers#### Methods for the virtual class 'CsparseMatrix' of sparse matrices stored in #### "column compressed" format. #### -- many more specific things are e.g. in ./dgCMatrix.R setAs("CsparseMatrix", "TsparseMatrix", function(from) ## |-> cholmod_C -> cholmod_T -> chm_triplet_to_SEXP ## modified to support triangular (../src/Csparse.c) .Call(Csparse_to_Tsparse, from, is(from, "triangularMatrix"))) ## special cases (when a specific "to" class is specified) setAs("dgCMatrix", "dgTMatrix", function(from) .Call(Csparse_to_Tsparse, from, FALSE)) setAs("dsCMatrix", "dsTMatrix", function(from) .Call(Csparse_to_Tsparse, from, FALSE)) setAs("dsCMatrix", "dgCMatrix", function(from) .Call(Csparse_symmetric_to_general, from)) for(prefix in c("d", "l", "n")) setAs(paste0(prefix,"sCMatrix"), "generalMatrix", function(from) .Call(Csparse_symmetric_to_general, from)) rm(prefix) setAs("dtCMatrix", "dtTMatrix", function(from) .Call(Csparse_to_Tsparse, from, TRUE)) setAs("CsparseMatrix", "denseMatrix", function(from) { ## |-> cholmod_C -> cholmod_dense -> chm_dense_to_dense cld <- getClassDef(class(from)) if (extends(cld, "generalMatrix")) .Call(Csparse_to_dense, from) else { ## Csparse_to_dense loses symmetry and triangularity properties. ## With suitable changes to chm_dense_to_SEXP (../src/chm_common.c) ## we could do this in C code -- or do differently in C {FIXME!} if (extends(cld, "triangularMatrix") && from@diag == "U") from <- .Call(Csparse_diagU2N, from) as(.Call(Csparse_to_dense, from), # -> "[dln]geMatrix" paste0(.M.kind(from, cld), .dense.prefixes[.M.shape(from, cld)], "Matrix")) } }) ## special cases (when a specific "to" class is specified) setAs("dgCMatrix", "dgeMatrix", function(from) .Call(Csparse_to_dense, from)) setAs("dgCMatrix", "vector", function(from) .Call(Csparse_to_vector, from)) setAs("dsCMatrix", "vector", function(from) .Call(Csparse_to_vector, from)) setMethod("as.vector", signature(x = "dgCMatrix", mode = "missing"), function(x, mode) .Call(Csparse_to_vector, x)) setMethod("as.vector", signature(x = "dsCMatrix", mode = "missing"), function(x, mode) .Call(Csparse_to_vector, x)) ## could do these and more for as(., "numeric") ... but we *do* recommend as(*,"vector"): ## setAs("dgCMatrix", "numeric", Csp2vec) ## setAs("dsCMatrix", "numeric", Csp2vec) ## |-> cholmod_C -> cholmod_dense -> chm_dense_to_matrix ## cholmod_sparse_to_dense converts symmetric storage to general ## storage so symmetric classes are ok for conversion to matrix. ## unit triangular needs special handling .dxC2mat <- function(from, chkUdiag=TRUE) .Call(Csparse_to_matrix, from, chkUdiag) setAs("dgCMatrix", "matrix", function(from) .Call(Csparse_to_matrix, from, FALSE)) setAs("dsCMatrix", "matrix", function(from) .Call(Csparse_to_matrix, from, FALSE)) setAs("dtCMatrix", "matrix", function(from) .Call(Csparse_to_matrix, from, TRUE)) ## NB: Would *not* be ok for l*Matrix or n*Matrix, ## --------- as cholmod coerces to "REAL" aka "double" setAs("CsparseMatrix", "symmetricMatrix", function(from) { if(isSymmetric(from)) forceCspSymmetric(from) else stop("not a symmetric matrix; consider forceSymmetric() or symmpart()") }) .validateCsparse <- function(x, sort.if.needed = FALSE) .Call(Csparse_validate2, x, sort.if.needed) ##-> to be used in sparseMatrix(.), e.g. --- but is unused currently ## NB: 'sort.if.needed' is called 'maybe_modify' in C -- so be careful ## more useful: .sortCsparse <- function(x) .Call(Csparse_sort, x) ## modifies 'x' !! ### Some group methods: setMethod("Math", signature(x = "CsparseMatrix"), function(x) { f0 <- callGeneric(0.) if(is0(f0)) { ## sparseness, symm., triang.,... preserved cl <- class(x) has.x <- !extends(cl, "nsparseMatrix") ## has.x <==> *not* nonzero-pattern == "nMatrix" if(has.x) { type <- storage.mode(x@x) r <- callGeneric(x@x) } else { ## nsparseMatrix type <- "" r <- rep.int(as.double(callGeneric(TRUE)), switch(.sp.class(cl), CsparseMatrix = length(x@i), TsparseMatrix = length(x@i), RsparseMatrix = length(x@j))) } if(type == storage.mode(r)) { x@x <- r x } else { ## e.g. abs( ) --> integer Csparse ## FIXME: when we have 'i*' classes, use them here: rx <- new(sub("^.", "d", cl)) rx@x <- as.double(r) ## result is "same" sNams <- slotNames(cl) for(nm in sNams[sNams != "x"]) slot(rx, nm) <- slot(x, nm) rx } } else { ## no sparseness callGeneric(as_dense(x)) } }) ## {Math} ### Subsetting -- basic things (drop = "missing") are done in ./Matrix.R ### ---------- "[" and (currently) also ./sparseMatrix.R subCsp_cols <- function(x, j, drop) { ## x[ , j, drop=drop] where we know that x is Csparse* dn <- x@Dimnames jj <- intI(j, n = x@Dim[2], dn[[2]], give.dn = FALSE) r <- .Call(Csparse_submatrix, x, NULL, jj) if(!is.null(n <- dn[[1]])) r@Dimnames[[1]] <- n if(!is.null(n <- dn[[2]])) r@Dimnames[[2]] <- n[jj+1L] if(drop && any(r@Dim == 1L)) drop(as(r, "matrix")) else r } subCsp_rows <- function(x, i, drop)# , cl = getClassDef(class(x)) { ## x[ i, drop=drop] where we know that x is Csparse* dn <- x@Dimnames ii <- intI(i, n = x@Dim[1], dn[[1]], give.dn = FALSE) r <- .Call(Csparse_submatrix, x, ii, NULL) if(!is.null(n <- dn[[1]])) r@Dimnames[[1]] <- n[ii+1L] if(!is.null(n <- dn[[2]])) r@Dimnames[[2]] <- n if(drop && any(r@Dim == 1L)) drop(as(r, "matrix")) else r } subCsp_ij <- function(x, i, j, drop) { ## x[i, j, drop=drop] where we know that x is Csparse* d <- x@Dim dn <- x@Dimnames ## Take care that x[i,i] for symmetricM* stays symmetric i.eq.j <- identical(i,j) # < want fast check ii <- intI(i, n = d[1], dn[[1]], give.dn = FALSE) jj <- if(i.eq.j && d[1] == d[2]) ii else intI(j, n = d[2], dn[[2]], give.dn = FALSE) r <- .Call(Csparse_submatrix, x, ii, jj) if(!is.null(n <- dn[[1]])) r@Dimnames[[1]] <- n[ii + 1L] if(!is.null(n <- dn[[2]])) r@Dimnames[[2]] <- n[jj + 1L] if(!i.eq.j) { if(drop && any(r@Dim == 1L)) drop(as(r, "matrix")) else r } else { ## i == j if(drop) drop <- any(r@Dim == 1L) if(drop) drop(as(r, "matrix")) else if(extends((cx <- getClassDef(class(x))), "symmetricMatrix")) ## TODO? make more efficient: .gC2sym(r, uplo = x@uplo)## preserve uplo ! else if(extends(cx, "triangularMatrix") && !is.unsorted(ii)) as(r, "triangularMatrix") else r } } setMethod("[", signature(x = "CsparseMatrix", i = "index", j = "missing", drop = "logical"), function (x, i,j, ..., drop) { na <- nargs() Matrix.msg("Csp[i,m,l] : nargs()=",na, .M.level = 2) if(na == 4) subCsp_rows(x, i, drop=drop) else if(na == 3) .M.vectorSub(x, i) # as(x, "TsparseMatrix")[i, drop=drop] else ## should not happen stop("Matrix-internal error in [i,,d]; please report") }) setMethod("[", signature(x = "CsparseMatrix", i = "missing", j = "index", drop = "logical"), function (x,i,j, ..., drop) { Matrix.msg("Csp[m,i,l] : nargs()=",nargs(), .M.level = 2) subCsp_cols(x, j, drop=drop) }) setMethod("[", signature(x = "CsparseMatrix", i = "index", j = "index", drop = "logical"), function (x, i, j, ..., drop) { Matrix.msg("Csp[i,i,l] : nargs()=",nargs(), .M.level = 2) subCsp_ij(x, i, j, drop=drop) }) ## workhorse for "[<-" -- for d*, l*, and n..C-sparse matrices : ## --------- ----- replCmat <- function (x, i, j, ..., value) { di <- dim(x) dn <- dimnames(x) iMi <- missing(i) jMi <- missing(j) spV <- is(value, "sparseVector") na <- nargs() Matrix.msg("replCmat[x,i,j,.., val] : nargs()=", na,"; ", if(iMi | jMi) sprintf("missing (i,j) = (%d,%d)", iMi,jMi), .M.level = 2) if(na == 3) { ## "vector (or 2-col) indexing" M[i] <- v x <- as(x, "TsparseMatrix") x[i] <- value # may change class e.g. from dtT* to dgT* clx <- sub(".Matrix$", "CMatrix", (c.x <- class(x))) if("x" %in% .slotNames(c.x) && any0(x@x)) ## drop all values that "happen to be 0" drop0(x, is.Csparse=FALSE) else as_CspClass(x, clx) } else ## nargs() == 4 : replCmat4(x, i1 = if(iMi) 0:(di[1] - 1L) else .ind.prep2(i, 1, di, dn), i2 = if(jMi) 0:(di[2] - 1L) else .ind.prep2(j, 2, di, dn), iMi=iMi, jMi=jMi, value=value, spV=spV) } ## replCmat replCmat4 <- function(x, i1, i2, iMi, jMi, value, spV = is(value,"sparseVector")) { dind <- c(length(i1), length(i2)) # dimension of replacement region lenRepl <- prod(dind) lenV <- length(value) if(lenV == 0) { if(lenRepl != 0) stop("nothing to replace with") else return(x) } ## else: lenV := length(value) is > 0 if(lenRepl %% lenV != 0) stop("number of items to replace is not a multiple of replacement length") if(lenV > lenRepl) stop("too many replacement values") clx <- class(x) clDx <- getClassDef(clx) # extends() , is() etc all use the class definition ## keep "symmetry" if changed here: x.sym <- extends(clDx, "symmetricMatrix") if(x.sym) { ## only half the indices are there.. ## using array() for large dind is a disaster... mkArray <- if(spV) # TODO: room for improvement function(v, dim) spV2M(v, dim[1],dim[2]) else array x.sym <- (dind[1] == dind[2] && all(i1 == i2) && (lenRepl == 1 || lenV == 1 || isSymmetric(mkArray(value, dim=dind)))) ## x.sym : result is *still* symmetric x <- .Call(Csparse_symmetric_to_general, x) ## but do *not* redefine clx! } else if(extends(clDx, "triangularMatrix")) { xU <- x@uplo == "U" r.tri <- ((any(dind == 1) || dind[1] == dind[2]) && if(xU) max(i1) <= min(i2) else max(i2) <= min(i1)) if(r.tri) { ## result is *still* triangular if(any(i1 == i2)) # diagonal will be changed x <- diagU2N(x) # keeps class (!) } else { # go to "generalMatrix" and continue x <- as(x, paste0(.M.kind(x), "gCMatrix")) ## & do not redefine clx! } } ## Temporary hack for debugging --- remove eventually -- FIXME : ## see also MATRIX_SUBASSIGN_VERBOSE in ../src/t_Csparse_subassign.c if(!is.null(v <- getOption("Matrix.subassign.verbose")) && v) { op <- options(Matrix.verbose = 2); on.exit(options(op)) ## the "hack" to signal "verbose" to the C code: i1[1] <- -i1[1] if(i1[1] == 0) warning("i1[1] == 0 ==> C-level verbosity will not happen!") } if(extends(clDx, "dMatrix")) { has.x <- TRUE x <- .Call(dCsparse_subassign, if(clx %in% c("dgCMatrix", "dtCMatrix"))x else as(x, "dgCMatrix"), i1, i2, as(value, "sparseVector")) } else if(extends(clDx, "lMatrix")) { has.x <- TRUE x <- .Call(lCsparse_subassign, if(clx %in% c("lgCMatrix", "ltCMatrix"))x else as(x, "lgCMatrix"), i1, i2, as(value, "sparseVector")) } else if(extends(clDx, "nMatrix")) { has.x <- FALSE x <- .Call(nCsparse_subassign, if(clx %in% c("ngCMatrix", "ntCMatrix"))x else as(x, "ngCMatrix"), i1, i2, as(value, "sparseVector")) } else if(extends(clDx, "iMatrix")) { has.x <- TRUE x <- .Call(iCsparse_subassign, if(clx %in% c("igCMatrix", "itCMatrix"))x else as(x, "igCMatrix"), i1, i2, as(value, "sparseVector")) } else if(extends(clDx, "zMatrix")) { has.x <- TRUE x <- .Call(zCsparse_subassign, if(clx %in% c("zgCMatrix", "ztCMatrix"))x else as(x, "zgCMatrix"), i1, i2, ## here we only want zsparseVector {to not have to do this in C}: as(value, "zsparseVector")) } else { ## use "old" code ... ## does this happen ? ==> if(identical(Sys.getenv("USER"),"maechler"))## does it still happen? __ FIXME __ stop("using \"old code\" part in Csparse subassignment") ## else warning("using \"old code\" part in Csparse subassignment\n", " >>> please report to Matrix-authors@r-project.org", immediate. = TRUE, domain = NA) xj <- .Call(Matrix_expand_pointers, x@p) sel <- (!is.na(match(x@i, i1)) & !is.na(match( xj, i2))) has.x <- "x" %in% slotNames(clDx)# === slotNames(x), ## has.x <==> *not* nonzero-pattern == "nMatrix" if(has.x && sum(sel) == lenRepl) { ## all entries to be replaced are non-zero: ## need indices instead of just 'sel', for, e.g., A[2:1, 2:1] <- v non0 <- cbind(match(x@i[sel], i1), match(xj [sel], i2)) - 1L iN0 <- 1L + .Call(m_encodeInd, non0, di = dind, checkBounds = FALSE) has0 <- if(spV) length(value@i) < lenV else any(value[!is.na(value)] == 0) if(lenV < lenRepl) value <- rep_len(value, lenRepl) ## Ideally we only replace them where value != 0 and drop the value==0 ## ones; FIXME: see Davis(2006) "2.7 Removing entries", p.16, e.g. use cs_dropzeros() ## but really could be faster and write something like cs_drop_k(A, k) ## v0 <- 0 == value ## if (lenRepl == 1) and v0 is TRUE, the following is not doing anything ##- --> ./dgTMatrix.R and its replTmat() ## x@x[sel[!v0]] <- value[!v0] x@x[sel] <- as.vector(value[iN0]) if(extends(clDx, "compMatrix") && length(x@factors)) # drop cashed ones x@factors <- list() if(has0) x <- .Call(Csparse_drop, x, 0) return(if(x.sym) as_CspClass(x, clx) else x) } ## else go via Tsparse.. {FIXME: a waste! - we already have 'xj' ..} ## and inside Tsparse... the above i1, i2,..., sel are *all* redone! ## Happens too often {not anymore, I hope!} ## Matrix.msg("wasteful C -> T -> C in replCmat(x,i,j,v) for [i,j] <- v") x <- as(x, "TsparseMatrix") if(iMi) x[ ,i2+1L] <- value else if(jMi) x[i1+1L, ] <- value else x[i1+1L,i2+1L] <- value if(extends(clDx, "compMatrix") && length(x@factors)) # drop cashed ones x@factors <- list() }# else{ not using new memory-sparse code if(has.x && any0(x@x)) ## drop all values that "happen to be 0" as_CspClass(drop0(x), clx) else as_CspClass(x, clx) } ## replCmat4 setReplaceMethod("[", signature(x = "CsparseMatrix", i = "index", j = "missing", value = "replValue"), replCmat) setReplaceMethod("[", signature(x = "CsparseMatrix", i = "missing", j = "index", value = "replValue"), replCmat) setReplaceMethod("[", signature(x = "CsparseMatrix", i = "index", j = "index", value = "replValue"), replCmat) ### When the RHS 'value' is a sparseVector, now can use replCmat as well setReplaceMethod("[", signature(x = "CsparseMatrix", i = "missing", j = "index", value = "sparseVector"), replCmat) setReplaceMethod("[", signature(x = "CsparseMatrix", i = "index", j = "missing", value = "sparseVector"), replCmat) setReplaceMethod("[", signature(x = "CsparseMatrix", i = "index", j = "index", value = "sparseVector"), replCmat) ## A[ ij ] <- value, where ij is (i,j) 2-column matrix setReplaceMethod("[", signature(x = "CsparseMatrix", i = "matrix", j = "missing", value = "replValue"), function(x, i, j, ..., value) ## goto Tsparse modify and convert back: as(.TM.repl.i.mat(as(x, "TsparseMatrix"), i=i, value=value), "CsparseMatrix")) ## more in ./sparseMatrix.R (and ./Matrix.R ) setReplaceMethod("[", signature(x = "CsparseMatrix", i = "Matrix", j = "missing", value = "replValue"), function(x, i, j, ..., value) ## goto Tsparse modify and convert back: as(.TM.repl.i.mat(as(x, "TsparseMatrix"), i=i, value=value), "CsparseMatrix")) setMethod("t", signature(x = "CsparseMatrix"), function(x) .Call(Csparse_transpose, x, is(x, "triangularMatrix"))) ## NB: have extra tril(), triu() methods for symmetric ["dsC" and "lsC"] and ## NB: for all triangular ones, where the latter may 'callNextMethod()' these: setMethod("tril", "CsparseMatrix", function(x, k = 0, ...) { k <- as.integer(k[1]) dd <- dim(x); sqr <- dd[1] == dd[2] stopifnot(-dd[1] <= k, k <= dd[1]) # had k <= 0 r <- .Call(Csparse_band, x, -dd[1], k) ## return "lower triangular" if k <= 0 if(sqr && k <= 0) as(r, paste0(.M.kind(x), "tCMatrix")) else r }) setMethod("triu", "CsparseMatrix", function(x, k = 0, ...) { k <- as.integer(k[1]) dd <- dim(x); sqr <- dd[1] == dd[2] stopifnot(-dd[1] <= k, k <= dd[1]) # had k >= 0 r <- .Call(Csparse_band, x, k, dd[2]) ## return "upper triangular" if k >= 0 if(sqr && k >= 0) as(r, paste0(.M.kind(x), "tCMatrix")) else r }) setMethod("band", "CsparseMatrix", function(x, k1, k2, ...) { k1 <- as.integer(k1[1]) k2 <- as.integer(k2[1]) dd <- dim(x); sqr <- dd[1] == dd[2] stopifnot(-dd[1] <= k1, k1 <= k2, k2 <= dd[2]) r <- .Call(Csparse_band, diagU2N(x), k1, k2) if(sqr && k1 * k2 >= 0) ## triangular as(r, paste0(.M.kind(x), "tCMatrix")) else if (k1 < 0 && k1 == -k2 && isSymmetric(x)) ## symmetric as(r, paste0(.M.kind(x), "sCMatrix")) else r }) setMethod("diag", "CsparseMatrix", function(x, nrow, ncol) { ## "FIXME": could be more efficient; creates new ..CMatrix: dm <- .Call(Csparse_band, diagU2N(x), 0, 0) dlen <- min(dm@Dim) ind1 <- dm@i + 1L # 1-based index vector if (is(dm, "nMatrix")) { val <- rep.int(FALSE, dlen) val[ind1] <- TRUE } else if (is(dm, "lMatrix")) { val <- rep.int(FALSE, dlen) val[ind1] <- as.logical(dm@x) } else { val <- rep.int(0, dlen) ## cMatrix not yet active but for future expansion if (is(dm, "cMatrix")) val <- as.complex(val) val[ind1] <- dm@x } val }) setMethod("writeMM", "CsparseMatrix", function(obj, file, ...) .Call(Csparse_MatrixMarket, obj, path.expand(as.character(file)))) setMethod("Cholesky", signature(A = "CsparseMatrix"), function(A, perm = TRUE, LDL = !super, super = FALSE, Imult = 0, ...) Cholesky(as(A, "symmetricMatrix"), perm=perm, LDL=LDL, super=super, Imult=Imult, ...)) ## TODO (in ../TODO for quite a while .....): setMethod("Cholesky", signature(A = "nsparseMatrix"), function(A, perm = TRUE, LDL = !super, super = FALSE, Imult = 0, ...) stop("Cholesky() -> *symbolic* factorization -- not yet implemented")) Matrix/R/bind2.R0000644000175100001440000003675212253554012013072 0ustar hornikusers#### Containing all cbind2() and rbind2() methods for all our Matrices ###-- General ----------------------------------------------------------- ###-- Dense, incl Diagonal ---------------------------------------------- ###-- Sparse ------------------------------------------------------------ setMethod("cbind2", signature(x = "sparseMatrix", y = "matrix"), function(x, y) cbind2(x, .Call(dense_to_Csparse, y))) setMethod("cbind2", signature(x = "matrix", y = "sparseMatrix"), function(x, y) cbind2(.Call(dense_to_Csparse, x), y)) setMethod("rbind2", signature(x = "sparseMatrix", y = "matrix"), function(x, y) rbind2(x, .Call(dense_to_Csparse, y))) setMethod("rbind2", signature(x = "matrix", y = "sparseMatrix"), function(x, y) rbind2(.Call(dense_to_Csparse, x), y)) ## originally from ./Matrix.R : ------------------------------- ## The trivial methods : setMethod("cbind2", signature(x = "Matrix", y = "NULL"), function(x, y) x) setMethod("cbind2", signature(x = "Matrix", y = "missing"), function(x, y) x) setMethod("cbind2", signature(x = "NULL", y="Matrix"), function(x, y) x) ## using "atomicVector" not just "numeric" setMethod("cbind2", signature(x = "Matrix", y = "atomicVector"), function(x, y) cbind2(x, matrix(y, nrow = nrow(x)))) setMethod("cbind2", signature(x = "atomicVector", y = "Matrix"), function(x, y) cbind2(matrix(x, nrow = nrow(y)), y)) setMethod("cbind2", signature(x = "ANY", y = "Matrix"), function(x, y) .bail.out.2(.Generic, class(x), class(y))) setMethod("cbind2", signature(x = "Matrix", y = "ANY"), function(x, y) .bail.out.2(.Generic, class(x), class(y))) setMethod("rbind2", signature(x = "Matrix", y = "NULL"), function(x, y) x) setMethod("rbind2", signature(x = "Matrix", y = "missing"), function(x, y) x) setMethod("rbind2", signature(x = "NULL", y="Matrix"), function(x, y) x) setMethod("rbind2", signature(x = "Matrix", y = "atomicVector"), function(x, y) rbind2(x, matrix(y, ncol = ncol(x)))) setMethod("rbind2", signature(x = "atomicVector", y = "Matrix"), function(x, y) rbind2(matrix(x, ncol = ncol(y)), y)) setMethod("rbind2", signature(x = "ANY", y = "Matrix"), function(x, y) .bail.out.2(.Generic, class(x), class(y))) setMethod("rbind2", signature(x = "Matrix", y = "ANY"), function(x, y) .bail.out.2(.Generic, class(x), class(y))) ## Makes sure one gets x decent error message for the unimplemented cases: setMethod("cbind2", signature(x = "Matrix", y = "Matrix"), function(x, y) { rowCheck(x,y) .bail.out.2("cbind2", class(x), class(y)) }) ## Use a working fall back {particularly useful for sparse}: ## FIXME: implement rbind2 via "cholmod" for C* and Tsparse ones setMethod("rbind2", signature(x = "Matrix", y = "Matrix"), function(x, y) { colCheck(x,y) t(cbind2(t(x), t(y))) }) ## originally from ./denseMatrix.R : ------------------------------- ### cbind2 setMethod("cbind2", signature(x = "denseMatrix", y = "numeric"), function(x, y) { d <- dim(x); nr <- d[1]; nc <- d[2] y <- rep_len(y, nr) # 'silent procrustes' ## beware of (packed) triangular, symmetric, ... x <- as(x, geClass(x)) x@x <- c(x@x, as.double(y)) x@Dim[2] <- nc + 1L if(is.character(dn <- x@Dimnames[[2]])) x@Dimnames[[2]] <- c(dn, "") x }) ## the same, (x,y) <-> (y,x): setMethod("cbind2", signature(x = "numeric", y = "denseMatrix"), function(x, y) { d <- dim(y); nr <- d[1]; nc <- d[2] x <- rep_len(x, nr) y <- as(y, geClass(y)) y@x <- c(as.double(x), y@x) y@Dim[2] <- nc + 1L if(is.character(dn <- y@Dimnames[[2]])) y@Dimnames[[2]] <- c("", dn) y }) setMethod("cbind2", signature(x = "denseMatrix", y = "matrix"), function(x, y) cbind2(x, as_geSimpl(y))) setMethod("cbind2", signature(x = "matrix", y = "denseMatrix"), function(x, y) cbind2(as_geSimpl(x), y)) cbind2DN <- function(dnx,dny, ncx,ncy) { ## R and S+ are different in which names they take ## if they differ -- but there's no warning in any case rn <- if(!is.null(dnx[[1]])) dnx[[1]] else dny[[1]] cx <- dnx[[2]] ; cy <- dny[[2]] cn <- if(is.null(cx) && is.null(cy)) NULL else c(if(!is.null(cx)) cx else character(ncx), if(!is.null(cy)) cy else character(ncy)) list(rn, cn) } setMethod("cbind2", signature(x = "denseMatrix", y = "denseMatrix"), function(x, y) { nr <- rowCheck(x,y) ncx <- x@Dim[2] ncy <- y@Dim[2] ## beware of (packed) triangular, symmetric, ... hasDN <- !is.null.DN(dnx <- dimnames(x)) | !is.null.DN(dny <- dimnames(y)) x <- as(x, geClass(x)) y <- as(y, geClass(y)) x@x <- c(x@x, y@x) x@Dim[2] <- ncx + ncy if(hasDN) x@Dimnames <- cbind2DN(dnx,dny, ncx,ncy) x }) ### rbind2 -- analogous to cbind2 --- more to do for @x though: setMethod("rbind2", signature(x = "denseMatrix", y = "numeric"), function(x, y) { if(is.character(dn <- x@Dimnames[[1]])) dn <- c(dn, "") y <- rbind2(as(x,"matrix"), y) new(paste0(.M.kind(y), "geMatrix"), x = c(y), Dim = x@Dim + 1:0, Dimnames = list(dn, x@Dimnames[[2]])) }) ## the same, (x,y) <-> (y,x): setMethod("rbind2", signature(x = "numeric", y = "denseMatrix"), function(x, y) { if(is.character(dn <- y@Dimnames[[1]])) dn <- c("", dn) x <- rbind2(x, as(y,"matrix")) new(paste0(.M.kind(x), "geMatrix"), x = c(x), Dim = y@Dim + 1:0, Dimnames = list(dn, y@Dimnames[[2]])) }) setMethod("rbind2", signature(x = "denseMatrix", y = "matrix"), function(x, y) rbind2(x, as_geSimpl(y))) setMethod("rbind2", signature(x = "matrix", y = "denseMatrix"), function(x, y) rbind2(as_geSimpl(x), y)) rbind2DN <- function(dnx, dny, nrx,nry) { if(!is.null.DN(dnx) || !is.null.DN(dny)) { ## R and S+ are different in which names they take ## if they differ -- but there's no warning in any case list(if(is.null(rx <- dnx[[1]]) & is.null(ry <- dny[[1]])) NULL else c(if(!is.null(rx)) rx else character(nrx), if(!is.null(ry)) ry else character(nry)), if(!is.null(dnx[[2]])) dnx[[2]] else dny[[2]]) } else list(NULL, NULL) } setMethod("rbind2", signature(x = "denseMatrix", y = "denseMatrix"), function(x, y) { nc <- colCheck(x,y) nrx <- x@Dim[1] nry <- y@Dim[1] dnx <- dimnames(x) ## beware of (packed) triangular, symmetric, -> "cheap" (FIXME): x <- rbind2(as(x,"matrix"), as(y,"matrix")) new(paste0(.M.kind(x), "geMatrix"), x = c(x), Dim = c(nrx + nry, nc), Dimnames = rbind2DN(dnx, dimnames(y), nrx,nry)) }) ## originally from ./diagMatrix.R : -------------------------------------- ## For diagonalMatrix: preserve sparseness {not always optimal, but "the law"} ## hack to suppress the obnoxious dispatch ambiguity warnings: diag2Sp <- function(x) suppressWarnings(as(x, "CsparseMatrix")) setMethod("cbind2", signature(x = "diagonalMatrix", y = "sparseMatrix"), function(x,y) cbind2(diag2Sp(x), as(y,"CsparseMatrix"))) setMethod("cbind2", signature(x = "sparseMatrix", y = "diagonalMatrix"), function(x,y) cbind2(as(x,"CsparseMatrix"), diag2Sp(y))) setMethod("rbind2", signature(x = "diagonalMatrix", y = "sparseMatrix"), function(x,y) rbind2(diag2Sp(x), as(y,"CsparseMatrix"))) setMethod("rbind2", signature(x = "sparseMatrix", y = "diagonalMatrix"), function(x,y) rbind2(as(x,"CsparseMatrix"), diag2Sp(y))) ## in order to evade method dispatch ambiguity, but still remain "general" ## we use this hack instead of signature x = "diagonalMatrix" for(cls in names(getClass("diagonalMatrix")@subclasses)) { setMethod("cbind2", signature(x = cls, y = "matrix"), function(x,y) cbind2(diag2Sp(x), .Call(dense_to_Csparse, y))) setMethod("cbind2", signature(x = "matrix", y = cls), function(x,y) cbind2(.Call(dense_to_Csparse, x), diag2Sp(y))) setMethod("rbind2", signature(x = cls, y = "matrix"), function(x,y) rbind2(diag2Sp(x), .Call(dense_to_Csparse, y))) setMethod("rbind2", signature(x = "matrix", y = cls), function(x,y) rbind2(.Call(dense_to_Csparse, x), diag2Sp(y))) ## These are already defined for "Matrix" ## -- repeated here for method dispatch disambiguation {"design-FIXME" ?} setMethod("cbind2", signature(x = cls, y = "atomicVector"), function(x, y) cbind2(x, matrix(y, nrow = nrow(x)))) setMethod("cbind2", signature(x = "atomicVector", y = cls), function(x, y) cbind2(matrix(x, nrow = nrow(y)), y)) setMethod("rbind2", signature(x = cls, y = "atomicVector"), function(x, y) rbind2(x, matrix(y, ncol = ncol(x)))) setMethod("rbind2", signature(x = "atomicVector", y = cls), function(x, y) rbind2(matrix(x, ncol = ncol(y)), y)) } ## originally from ./dsparseMatrix.R : -------------------------------- ## FIXME: dimnames() handling should happen in C code ## ------> ../src/Csparse.c ## Fast - almost non-checking methods .cbind2Csp <- function(x,y) .Call(Csparse_horzcat, as_Csp2(x), as_Csp2(y)) .rbind2Csp <- function(x,y) .Call(Csparse_vertcat, as_Csp2(x), as_Csp2(y)) cbind2Sparse <- function(x,y) { ## beware of (packed) triangular, symmetric, ... if(identical(c(dnx <- dimnames(x), dny <- dimnames(y)), list(NULL,NULL,NULL,NULL))) ## keep empty dimnames .cbind2Csp(x,y) else { ## R and S+ are different in which names they take ## if they differ -- but there's no warning in any case rn <- if(!is.null(dnx[[1]])) dnx[[1]] else dny[[1]] cx <- dnx[[2]] ; cy <- dny[[2]] cn <- if(is.null(cx) && is.null(cy)) NULL else c(if(!is.null(cx)) cx else character(ncol(x)), if(!is.null(cy)) cy else character(ncol(y))) ans <- .cbind2Csp(x,y) ans@Dimnames <- list(rn, cn) ans } } setMethod("cbind2", signature(x = "sparseMatrix", y = "sparseMatrix"), function(x, y) { nr <- rowCheck(x,y) cbind2Sparse(x,y) }) rbind2Sparse <- function(x,y) { ## beware of (packed) triangular, symmetric, ... if(identical(c(dnx <- dimnames(x), dny <- dimnames(y)), list(NULL,NULL,NULL,NULL))) ## keep empty dimnames .rbind2Csp(x,y) else { ## R and S+ are different in which names they take ## if they differ -- but there's no warning in any case cn <- if(!is.null(dnx[[2]])) dnx[[2]] else dny[[2]] rx <- dnx[[1]] ; ry <- dny[[1]] rn <- if(is.null(rx) && is.null(ry)) NULL else c(if(!is.null(rx)) rx else character(nrow(x)), if(!is.null(ry)) ry else character(nrow(y))) ans <- .rbind2Csp(x,y) ans@Dimnames <- list(rn, cn) ans } } setMethod("rbind2", signature(x = "sparseMatrix", y = "sparseMatrix"), function(x, y) { nc <- colCheck(x,y) rbind2Sparse(x,y) }) if(length(formals(cbind2)) >= 3) { ## newer R -- can use optional 'sparse = NA' setMethod("cbind2", signature(x = "sparseMatrix", y = "denseMatrix"), function(x, y, sparse = NA) { nr <- rowCheck(x,y) if(is.na(sparse)) # result is sparse if "enough zeros" <==> sparseDefault() in Matrix() sparse <- (nnzero(x)+nnzero(y)) * 2 < nr * (ncol(x)+ncol(y)) if(sparse) cbind2Sparse(x,y) else cbind2(as(x, "denseMatrix"), y) }) setMethod("cbind2", signature(x = "denseMatrix", y = "sparseMatrix"), function(x, y, sparse = NA) { nr <- rowCheck(x,y) if(is.na(sparse)) # result is sparse if "enough zeros" <==> sparseDefault() in Matrix() sparse <- (nnzero(x)+nnzero(y)) * 2 < nr * (ncol(x)+ncol(y)) if(sparse) cbind2Sparse(x,y) else cbind2(x, as(y, "denseMatrix")) }) setMethod("rbind2", signature(x = "sparseMatrix", y = "denseMatrix"), function(x, y, sparse = NA) { nc <- colCheck(x,y) if(is.na(sparse)) # result is sparse if "enough zeros" <==> sparseDefault() in Matrix() sparse <- (nnzero(x)+nnzero(y)) * 2 < (nrow(x)+nrow(y)) * nc if(sparse) rbind2Sparse(x,y) else rbind2(as(x, "denseMatrix"), y) }) setMethod("rbind2", signature(x = "denseMatrix", y = "sparseMatrix"), function(x, y, sparse = NA) { nc <- colCheck(x,y) if(is.na(sparse)) # result is sparse if "enough zeros" <==> sparseDefault() in Matrix() sparse <- (nnzero(x)+nnzero(y)) * 2 < (nrow(x)+nrow(y)) * nc if(sparse) rbind2Sparse(x,y) else rbind2(x, as(y, "denseMatrix")) }) } else { ## older version of R -- cbind2() has no "..." setMethod("cbind2", signature(x = "sparseMatrix", y = "denseMatrix"), function(x, y) { nr <- rowCheck(x,y) ## result is sparse if "enough zeros" <==> sparseDefault() in Matrix() sparse <- (nnzero(x)+nnzero(y)) * 2 < nr * (ncol(x)+ncol(y)) if(sparse) cbind2Sparse(x,y) else cbind2(as(x, "denseMatrix"), y) }) setMethod("cbind2", signature(x = "denseMatrix", y = "sparseMatrix"), function(x, y) { nr <- rowCheck(x,y) ## result is sparse if "enough zeros" <==> sparseDefault() in Matrix() sparse <- (nnzero(x)+nnzero(y)) * 2 < nr * (ncol(x)+ncol(y)) if(sparse) cbind2Sparse(x,y) else cbind2(x, as(y, "denseMatrix")) }) setMethod("rbind2", signature(x = "sparseMatrix", y = "denseMatrix"), function(x, y) { nc <- colCheck(x,y) ## result is sparse if "enough zeros" <==> sparseDefault() in Matrix() sparse <- (nnzero(x)+nnzero(y)) * 2 < (nrow(x)+nrow(y)) * nc if(sparse) rbind2Sparse(x,y) else rbind2(as(x, "denseMatrix"), y) }) setMethod("rbind2", signature(x = "denseMatrix", y = "sparseMatrix"), function(x, y) { nc <- colCheck(x,y) ## result is sparse if "enough zeros" <==> sparseDefault() in Matrix() sparse <- (nnzero(x)+nnzero(y)) * 2 < (nrow(x)+nrow(y)) * nc if(sparse) rbind2Sparse(x,y) else rbind2(x, as(y, "denseMatrix")) }) }# older R -- no "sparse = NA" if(FALSE) { ## FIXME ##------------- maybe a bit faster --- but too much to maintain ## would have to be done for "rbind2" as well ... setMethod("cbind2", signature(x = "sparseMatrix", y = "numeric"), function(x, y) { d <- dim(x); nr <- d[1]; nc <- d[2]; cl <- class(x) x <- as(x, "CsparseMatrix") if(nr > 0) { y <- rep_len(y, nr) # 'silent procrustes' n0y <- y != 0 n.e <- length(x@i) x@i <- c(x@i, (0:(nr-1))[n0y]) x@p <- c(x@p, n.e + sum(n0y)) x@x <- c(x@x, y[n0y]) } else { ## nr == 0 } x@Dim[2] <- nc + 1L if(is.character(dn <- x@Dimnames[[2]])) x@Dimnames[[2]] <- c(dn, "") x }) ## the same, (x,y) <-> (y,x): setMethod("cbind2", signature(x = "numeric", y = "sparseMatrix"), function(x, y) { d <- dim(y); nr <- d[1]; nc <- d[2]; cl <- class(y) y <- as(y, "CsparseMatrix") if(nr > 0) { x <- rep_len(x, nr) # 'silent procrustes' n0x <- x != 0 y@i <- c((0:(nr-1))[n0x], y@i) y@p <- c(0L, sum(n0x) + y@p) y@x <- c(x[n0x], y@x) } else { ## nr == 0 } y@Dim[2] <- nc + 1L if(is.character(dn <- y@Dimnames[[2]])) y@Dimnames[[2]] <- c(dn, "") y }) }## -- no longer ## Can be made very efficient setMethod("rbind2", signature(x = "indMatrix", y = "indMatrix"), function(x, y) { dx <- x@Dim dy <- y@Dim if(dx[2] != dy[2]) stop(gettextf("Matrices must have same number of columns in %s", deparse(sys.call(sys.parent()))), call. = FALSE, domain=NA) new("indMatrix", Dim = c(dx[1]+dy[1], dx[2]), perm = c(x@perm,y@perm), Dimnames = rbind2DN(dimnames(x), dimnames(y), dx[1],dy[1])) }) Matrix/R/Auxiliaries.R0000644000175100001440000013561312254575000014350 0ustar hornikusers#### "Namespace private" Auxiliaries such as method functions #### (called from more than one place --> need to be defined early) ## Need to consider NAs ; "== 0" even works for logical & complex: ## Note that "!x" is faster than "x == 0", but does not (yet!) work for complex ## if we did these in C, would gain a factor 2 (or so): is0 <- function(x) !is.na(x) & x == 0 isN0 <- function(x) is.na(x) | x != 0 is1 <- function(x) !is.na(x) & x # also == "isTRUE componentwise" ## ##all0 <- function(x) !any(is.na(x)) && all(!x) ## ~= allFalse all0 <- function(x) .Call(R_all0, x) ## any0 <- function(x) isTRUE(any(x == 0)) ## ~= anyFalse any0 <- function(x) .Call(R_any0, x) ## These work "identically" for 1 ('==' TRUE) and 0 ('==' FALSE) ## (but give a warning for "double" 1 or 0) ## TODO: C versions of these would be faster allTrue <- function(x) all(x) && !any(is.na(x)) ##allFalse <- function(x) !any(x) && !any(is.na(x))## ~= all0, but allFalse(NULL) = TRUE w/warning allFalse <- function(x) .Call(R_all0, x) ##anyFalse <- function(x) isTRUE(any(!x)) ## ~= any0 anyFalse <- function(x) .Call(R_any0, x) as1 <- function(x, mod=mode(x)) switch(mod, "integer"= 1L, "double"=, "numeric"= 1, "logical"= TRUE, "complex"= 1+0i, stop(gettextf("invalid 'mod': %s", mod), domain = NA)) as0 <- function(x, mod=mode(x)) switch(mod, "integer"= 0L, "double"=, "numeric"= 0, "logical"= FALSE, "complex"= 0+0i, stop(gettextf("invalid 'mod': %s", mod), domain = NA)) .M.DN <- function(x) if(!is.null(dn <- dimnames(x))) dn else list(NULL,NULL) .has.DN <- ## has non-trivial Dimnames slot? function(x) !identical(list(NULL,NULL), x@Dimnames) ## This is exported now ( -> ../man/is.null.DN.Rd ): is.null.DN <- function(dn) { is.null(dn) || { if(!is.null(names(dn))) names(dn) <- NULL ch0 <- character(0) identical(dn, list(NULL,NULL)) || identical(dn, list(ch0, NULL)) || identical(dn, list(NULL, ch0)) || identical(dn, list(ch0, ch0)) } } .if.NULL <- function(x, orElse) if(!is.null(x)) x else orElse ## not %in% : `%nin%` <- function (x, table) is.na(match(x, table)) ##' @title Check identical(i, 0:n) {or identical(i, 1:n) when Ostart is false} ##' @param i an integer vector, to be compared with 0:n or 1:n ##' @param n an integer number ##' @param Ostart logical indicating if comparison with 0:n or 1:n should be made ##' @return TRUE or FALSE ##' @author Martin Maechler isSeq <- function(i, n, Ostart = TRUE) { ## FIXME: Port to C, use simple .Call() which is must faster notably in FALSE cases ## and then *export* (and hence document) identical(i, if(Ostart) 0L:n else seq_len(n)) } .bail.out.1 <- function(fun, cl) { stop(gettextf('not-yet-implemented method for %s(<%s>).\n ->> Ask the package authors to implement the missing feature.', fun, cl), call. = FALSE, domain=NA) } .bail.out.2 <- function(fun, cl1, cl2) { stop(gettextf('not-yet-implemented method for %s(<%s>, <%s>).\n ->> Ask the package authors to implement the missing feature.', fun, cl1, cl2), call. = FALSE, domain=NA) } Matrix.msg <- function(..., .M.level = 1) { if(!is.null(v <- getOption("Matrix.verbose")) && v >= .M.level) message(...) } ## we can set this to FALSE and possibly measure speedup: .copyClass.check <- TRUE ## This should be done in C and be exported by 'methods': [FIXME - ask JMC ] copyClass <- function(x, newCl, sNames = intersect(slotNames(newCl), slotNames(x)), check = .copyClass.check) { r <- new(newCl) ## Equivalent of ## for(n in sNames) slot(r, n, check=check) <- slot(x, n) : if(check) for(n in sNames) slot(r, n) <- slot(x, n) else for(n in sNames) # don't check, be fast ## .Call("R_set_slot", r, n, slot(x,n), PACKAGE = "methods") ## "ugly", but not using .Call(*, "methods") attr(r, n) <- attr(x, n) r } MatrixClass <- function(cl, cld = getClassDef(cl), ...Matrix = TRUE, dropVirtual = TRUE, ...) { ## Purpose: return the (maybe super-)class of class 'cl' from "Matrix", ## returning character(0) if there is none. ## ---------------------------------------------------------------------- ## Arguments: cl: string, class name ## cld: its class definition ## ...Matrix: if TRUE, the result must be of pattern "[dlniz]..Matrix" ## where the first letter "[dlniz]" denotes the content kind. ## ..... : other arguments are passed to .selectSuperClasses() ## ---------------------------------------------------------------------- ## Author: Martin Maechler, Date: 24 Mar 2009 ## stopifnot(is.character(cl)) ## Hmm, packageSlot(cl) *can* be misleading --> use cld@package first: if(is.null(pkg <- cld@package)) { if(is.null(pkg <- packageSlot(cl))) return(character()) ## else we use 'pkg' } if(identical(pkg, "Matrix") && (!...Matrix || (cl != "indMatrix" && identical(1L, grep("^[dlniz]..Matrix$", cl))))) cl else { ## possibly recursively r <- .selectSuperClasses(cld@contains, dropVirtual = dropVirtual, namesOnly = TRUE, ...) if(length(r)) Recall(r[1], ...Matrix = ...Matrix, dropVirtual = dropVirtual) else r } } attrSlotNames <- function(m, factors = TRUE) { ## slotnames of Matrix objects which are *not* directly content related sn <- slotNames(m); sn[sn %nin% c("x","i","j","p", if(!factors) "factors")] } ##' @param m ##' @return the slots of 'm' which are "attributes" of some kind. attrSlots <- function(m, factors = TRUE) sapply(attrSlotNames(m, factors=factors), function(sn) slot(m, sn), simplify = FALSE) ##' @return { NULL | TRUE | character | list(.) } attr.all_Mat <- function(target, current, check.attributes = TRUE, factorsCheck = FALSE, ...) { msg <- if(check.attributes) all.equal(attrSlots(target, factors=factorsCheck), attrSlots(current, factors=factorsCheck), check.attributes = TRUE, ...) ## else NULL if((c1 <- class(target)) != (c2 <- class(current))) ## list(): so we can easily check for this list(c(if(!isTRUE(msg)) msg, paste0("class(target) is ", c1, ", current is ", c2))) else msg } ##' @return combination for all.equal() functions in ./Matrix.R & ./sparseMatrix.R .a.e.comb <- function(msg, r) { if((is.null(msg) || isTRUE(msg)) & (r.ok <- isTRUE(r))) TRUE else c(if(!isTRUE(msg)) msg, if(!r.ok) r) } ## chol() via "dpoMatrix" ## This will only be called for *dense* matrices cholMat <- function(x, pivot = FALSE, ...) { packed <- length(x@x) < prod(dim(x)) ## is it packed? nmCh <- if(packed) "pCholesky" else "Cholesky" if(!is.null(ch <- x@factors[[nmCh]])) return(ch) ## use the cache px <- as(x, if(packed) "dppMatrix" else "dpoMatrix") if (isTRUE(validObject(px, test=TRUE))) ## 'pivot' is not used for dpoMatrix .set.factors(x, nmCh, chol(px, pivot, ...)) else stop("'x' is not positive definite -- chol() undefined.") } invPerm.R <- function(p) { p[p] <- seq_along(p) ; p } ## how much faster would this be in C? -- less than a factor of two? invPerm <- function(p, zero.p = FALSE, zero.res = FALSE) .Call(inv_permutation, p, zero.p, zero.res) ## sign( ) == determinant( ) signPerm <- function(p) { ## Purpose: sign() via the cycles ## ---------------------------------------------------------------------- ## Arguments: a permutation of 1:n ## ---------------------------------------------------------------------- ## Author: Peter Dalgaard, 14 Apr 2008 // speedup: Martin Maechler 2008-04-16 n <- length(p) x <- integer(n) ii <- seq_len(n) for (i in ii) { z <- ii[!x][1] # index of first unmarked x[] entry if (is.na(z)) break repeat { ## mark x[] <- i for those in i-th cycle x[z] <- i z <- p[z] if (x[z]) break } } ## Now, table(x) gives the cycle lengths, ## where split(seq_len(n), x) would give the cycles list ## tabulate(x, i - 1L) is quite a bit faster than the equivalent ## table(x) clen <- tabulate(x, i - 1L) ## The sign is -1 (<==> permutation is odd) iff ## the cycle factorization contains an odd number of even-length cycles: 1L - (sum(clen %% 2 == 0) %% 2L)*2L } detSparseLU <- function(x, logarithm = TRUE, ...) { ## Purpose: Compute determinant() from lu.x = lu(x) ## ---------------------------------------------------------------------- ## Author: Martin Maechler, Date: 15 Apr 2008 if(any(x@Dim == 0)) return(mkDet(numeric(0))) ll <- lu(x, errSing = FALSE) ## ^^^^^^^^^^^^^^^ no error in case of singularity if(identical(NA, ll)) { ## LU-decomposition failed with singularity return(mkDet(ldet=if(any(is.na(x))) NaN else -Inf, logarithm=logarithm, sig = 1L)) } ## else stopifnot(all(c("L","U") %in% slotNames(ll))) # ensure we have *sparse* LU r <- mkDet(diag(ll@U), logarithm) ## Det(x) == Det(P L U Q) == Det(P) * 1 * Det(U) * Det(Q); where Det(P), Det(Q) in {-1,1} r$sign <- r$sign * signPerm(ll@p + 1L) * signPerm(ll@q + 1L) r } ## Log(Determinant) from diagonal ... used several times mkDet <- function(d, logarithm = TRUE, ldet = sum(log(abs(d))), sig = -1L+2L*as.integer(prod(sign(d)) >= 0)) { # sig: -1 or +1 (not 0 !) modulus <- if (logarithm) ldet else exp(ldet) attr(modulus, "logarithm") <- logarithm val <- list(modulus = modulus, sign = sig) class(val) <- "det" val } dimCheck <- function(a, b) { da <- dim(a) db <- dim(b) if(any(da != db)) stop(gettextf("Matrices must have same dimensions in %s", deparse(sys.call(sys.parent()))), call. = FALSE, domain=NA) da } mmultCheck <- function(a, b, kind = 1L) { ## Check matching matrix dimensions and return that matching dim ## 1) %*% : [n x m] , [m x k] ## 2) crossprod: [m x n] , [m x k] ## 3) tcrossprod: [n x m] , [k x m] ## switch(kind, ## { ## %*% (kind = 1) ## ca <- dim(a)[2L] ## rb <- dim(b)[1L] ## }, ## { ## crossprod (kind = 2) ## ca <- dim(a)[1L] ## rb <- dim(b)[1L] ## }, ## { ## tcrossprod (kind = 3) ## ca <- dim(a)[2L] ## rb <- dim(b)[2L] ## }) ca <- dim(a)[1L + (kind %% 2L)] rb <- dim(b)[1L + (kind > 2)] if(ca != rb) stop(gettextf("non-conformable matrix dimensions in %s", deparse(sys.call(sys.parent()))), call. = FALSE, domain=NA) ca } dimNamesCheck <- function(a, b) { ## Constructs "sensical" dimnames for something like a + b ; ## assume dimCheck() has happened before nullDN <- list(NULL,NULL) h.a <- !identical(nullDN, dna <- dimnames(a)) h.b <- !identical(nullDN, dnb <- dimnames(b)) if(h.a || h.b) { if (!h.b) dna else if(!h.a) dnb else { ## both have non-trivial dimnames r <- dna # "default" result for(j in 1:2) if(!is.null(dn <- dnb[[j]])) { if(is.null(r[[j]])) r[[j]] <- dn else if(!identical(r[[j]], dn)) warning(gettextf("dimnames [%d] mismatch in %s", j, deparse(sys.call(sys.parent()))), call. = FALSE, domain=NA) } r } } else nullDN } rowCheck <- function(a, b) { da <- dim(a) db <- dim(b) if(da[1] != db[1]) stop(gettextf("Matrices must have same number of rows in %s", deparse(sys.call(sys.parent()))), call. = FALSE, domain=NA) ## return the common nrow() da[1] } colCheck <- function(a, b) { da <- dim(a) db <- dim(b) if(da[2] != db[2]) stop(gettextf("Matrices must have same number of columns in %s", deparse(sys.call(sys.parent()))), call. = FALSE, domain=NA) ## return the common ncol() da[2] } ## is.na() is FALSE everywhere. Consequently, this function ## just gives an "all-FALSE" nCsparseMatrix of same form as x ##' ##' @title all FALSE nCsparseMatrix "as x" ##' @param x Matrix ##' @return n.CsparseMatrix "as \code{x}" ##' @author Martin Maechler is.na_nsp <- function(x) { d <- x@Dim dn <- x@Dimnames ## step-wise construction ==> no validity check for speedup r <- new(if(d[1] == d[2] && identical(dn[[1]], dn[[2]])) "nsCMatrix" else "ngCMatrix") r@Dim <- d r@Dimnames <- dn r@p <- rep.int(0L, d[2]+1L) r } allTrueMat <- function(x, sym = (d[1] == d[2] && identical(dn[[1]], dn[[2]])), packed=TRUE) { d <- x@Dim dn <- x@Dimnames r <- new("ngeMatrix", Dim=d, Dimnames=dn, x = rep.int(TRUE, prod(d))) if(sym) as(r, if(packed) "nspMatrix" else "nsyMatrix") else r } allTrueMatrix <- function(x) allTrueMat(x) ## Note: !isPacked(.) i.e. `full' still contains ## ---- "*sy" and "*tr" which have "undefined" lower or upper part isPacked <- function(x) { ## Is 'x' a packed (dense) matrix ? is(x, "denseMatrix") && ## unneeded(!): any("x" == slotNames(x)) && length(x@x) < prod(dim(x)) } ##" Is 'x' a packed (dense) matrix -- "no-check" version .isPacked <- function(x) length(x@x) < prod(dim(x)) emptyColnames <- function(x, msg.if.not.empty = FALSE) { ## Useful for compact printing of (parts) of sparse matrices ## possibly dimnames(x) "==" NULL : dn <- dimnames(x) nc <- ncol(x) if(msg.if.not.empty && is.list(dn) && length(dn) >= 2 && is.character(cn <- dn[[2]]) && any(cn != "")) { lc <- length(cn) message(if(lc > 3) gettextf(" [[ suppressing %d column names %s ... ]]", nc, paste(sQuote(cn[1:3]), collapse = ", ")) else gettextf(" [[ suppressing %d column names %s ]]", nc, paste(sQuote(cn[1:lc]), collapse = ", ")), domain=NA) } dimnames(x) <- list(dn[[1]], character(nc)) x } ## The i-th unit vector e[1:n] with e[j] = \delta_{i,j} ## .E.i.log <- function(i,n) i == (1:n) ## .E.i <- function(i,n) ## r <- numeric(n) ## r[i] <- 1. ## r ## } idiag <- function(n, p=n) { ## Purpose: diag() returning *integer* ## -------------------------------------------------------- ## Author: Martin Maechler, Date: 8 Dec 2007, 23:13 r <- matrix(0L, n,p) if ((m <- min(n, p)) > 0) r[1 + 0:(m - 1) * (n + 1)] <- 1L r } ldiag <- function(n, p=n) { ## Purpose: diag() returning *logical* r <- matrix(FALSE, n,p) if ((m <- min(n, p)) > 0) r[1 + 0:(m - 1) * (n + 1)] <- TRUE r } ## The indices of the diagonal entries of an n x n matrix, n >= 1 ## i.e. indDiag(n) === which(diag(n) == 1) indDiag <- function(n) cumsum(c(1L, rep.int(n+1L, n-1))) ### TODO: write in C and port to base (or 'utils') R ### ----- ### "Theory" behind this: /u/maechler/R/MM/MISC/lower-tri-w.o-matrix.R ## NB: also have "abIndex" version: abIindTri() --> ./abIndex.R indTri <- function(n, upper = TRUE, diag = FALSE) { ## Indices of (strict) upper/lower triangular part ## == which(upper.tri(diag(n), diag=diag) or ## which(lower.tri(diag(n), diag=diag) -- but ## more efficiently for largish 'n' stopifnot(length(n) == 1, n == (n. <- as.integer(n)), (n <- n.) >= 0) if(n <= 2) { if(n == 0) return(integer(0)) if(n == 1) return(if(diag) 1L else integer(0)) ## else n == 2 v <- if(upper) 3L else 2L return(if(diag) c(1L, v, 4L) else v) } ## n >= 3 [also for n == 2 && diag (==TRUE)] : ## First, compute the 'diff(.)' of the result [fast, using integers] n. <- if(diag) n else n - 1L n1 <- n. - 1L ## all '1' but a few r <- rep.int(1L, choose(n.+1, 2) - 1) tt <- if(diag) 2L else 3L r[cumsum(if(upper) 1:n1 else n.:2)] <- if(upper) n:tt else tt:n ## now have differences; revert to "original": cumsum(c(if(diag) 1L else if(upper) n+1L else 2L, r)) } prTriang <- function(x, digits = getOption("digits"), maxp = getOption("max.print"), justify = "none", right = TRUE) { ## modeled along stats:::print.dist upper <- x@uplo == "U" m <- as(x, "matrix") cf <- format(m, digits = digits, justify = justify) cf[if(upper) row(cf) > col(cf) else row(cf) < col(cf)] <- "." print(cf, quote = FALSE, right = right, max = maxp) invisible(x) } prMatrix <- function(x, digits = getOption("digits"), maxp = getOption("max.print")) { d <- dim(x) cl <- class(x) ## cld <- getClassDef(cl) tri <- extends(cl, "triangularMatrix") xtra <- if(tri && x@diag == "U") " (unitriangular)" else "" cat(sprintf('%d x %d Matrix of class "%s"%s\n', d[1], d[2], cl, xtra)) if(prod(d) <= maxp) { if(tri) prTriang(x, digits = digits, maxp = maxp) else print(as(x, "matrix"), digits = digits, max = maxp) } else { ## d[1] > maxp / d[2] >= nr : m <- as(x, "matrix") nr <- maxp %/% d[2] n2 <- ceiling(nr / 2) print(head(m, max(1, n2))) cat("\n ..........\n\n") print(tail(m, max(1, nr - n2))) cat("\n ..........\n\n") } ## DEBUG: cat("str(.):\n") ; str(x) invisible(x)# as print() S3 methods do } nonFALSE <- function(x) { ## typically used for lMatrices: (TRUE,NA,FALSE) |-> (TRUE,TRUE,FALSE) if(any(ix <- is.na(x))) x[ix] <- TRUE x } nz.NA <- function(x, na.value) { ## Non-Zeros of x ## na.value: TRUE: NA's give TRUE, they are not 0 ## NA: NA's are not known ==> result := NA ## FALSE: NA's give FALSE, could be 0 stopifnot(is.logical(na.value), length(na.value) == 1) if(is.na(na.value)) x != 0 else if(na.value) isN0(x) else x != 0 & !is.na(x) } ### This assumes that e.g. the i-slot in Csparse is *not* over-allocated: nnzSparse <- function(x, cl = class(x), cld = getClassDef(cl)) { ## Purpose: number of *stored* / structural non-zeros {NA's counted too} ## ---------------------------------------------------------------------- ## Arguments: x sparseMatrix ## ---------------------------------------------------------------------- ## Author: Martin Maechler, 18 Apr 2008 if(extends(cld, "CsparseMatrix") || extends(cld, "TsparseMatrix")) length(x@i) else if(extends(cld, "RsparseMatrix")) length(x@j) else if(extends(cld, "indMatrix")) # is "sparse" too x@Dim[1] else stop(gettext("'x' must be \"sparseMatrix\""), domain=NA) } ## For sparseness handling, return a ## 2-column (i,j) matrix of 0-based indices of non-zero entries: non0.i <- function(M, cM = class(M), uniqT=TRUE) { if(extends(cM, "TsparseMatrix")) { if(uniqT && is_not_uniqT(M)) .Call(compressed_non_0_ij, as(M,"CsparseMatrix"), TRUE) else cbind(M@i, M@j) } else if(extends(cM, "indMatrix")) { cbind(seq_len(nrow(M)), M@perm) - 1L } else { ## C* or R* .Call(compressed_non_0_ij, M, extends(cM, "CsparseMatrix")) } } non0ind <- function(x, cld = getClassDef(class(x)), uniqT = TRUE, xtendSymm = TRUE, check.Udiag = TRUE) { if(is.numeric(x)) return(if((n <- length(x))) { if(is.matrix(x)) arrayInd(seq_len(n)[isN0(x)], dim(x)) - 1L else (0:(n-1))[isN0(x)] } else integer(0)) ## else stopifnot(extends(cld, "sparseMatrix")) ij <- non0.i(x, cld, uniqT=uniqT) if(xtendSymm && extends(cld, "symmetricMatrix")) { # also get "other" triangle notdiag <- ij[,1] != ij[,2]# but not the diagonals again rbind(ij, ij[notdiag, 2:1], deparse.level=0) } else if(check.Udiag && extends(cld, "triangularMatrix")) { # check for "U" diag if(x@diag == "U") { i <- seq_len(dim(x)[1]) - 1L rbind(ij, cbind(i,i, deparse.level=0), deparse.level=0) } else ij } else ij } if(FALSE) { ## -- now have .Call(m_encodeInd, ...) etc : ## nr= nrow: since i in {0,1,.., nrow-1} these are 1L "decimal" encodings: ## Further, these map to and from the usual "Fortran-indexing" (but 0-based) ## __ care against integer overflow __ encodeInd <- function(ij, di) { stopifnot(length(di) == 2) nr <- di[1L] if(prod(di) >= .Machine$integer.max) nr <- as.double(nr) ij[,1] + ij[,2] * nr } encodeInd2 <- function(i,j, di) { stopifnot(length(di) == 2) nr <- di[1L] if(prod(di) >= .Machine$integer.max) nr <- as.double(nr) i + j * nr } }## no more needed ## 'code' is 0-based; as.integer(.) because encode*() may produce double decodeInd <- function(code, nr) cbind(as.integer(code %% nr), as.integer(code %/% nr)) complementInd <- function(ij, dim, checkBnds=FALSE) { ## Purpose: Compute the complement of the 2-column 0-based ij-matrix ## but as 1-based indices n <- prod(dim) if(n == 0) return(integer(0)) seq_len(n)[-(1L + .Call(m_encodeInd, ij, dim, checkBnds))] } unionInd <- function(ij1, ij2) unique(rbind(ij1, ij2)) intersectInd <- function(ij1, ij2, di, checkBnds=FALSE) { ## from 2-column (i,j) matrices where i in {0,.., nrow-1}, ## return only the *common* entries decodeInd(intersect(.Call(m_encodeInd, ij1, di, checkBnds), .Call(m_encodeInd, ij2, di, checkBnds)), nr=di[1]) } WhichintersectInd <- function(ij1, ij2, di, checkBnds=FALSE) { ## from 2-column (i,j) matrices where i \in {0,.., nrow-1}, ## find *where* common entries are in ij1 & ij2 m1 <- match(.Call(m_encodeInd, ij1, di, checkBnds), .Call(m_encodeInd, ij2, di, checkBnds)) ni <- !is.na(m1) list(which(ni), m1[ni]) } ### There is a test on this in ../tests/dgTMatrix.R ! uniqTsparse <- function(x, class.x = c(class(x))) { ## Purpose: produce a *unique* triplet representation: ## by having (i,j) sorted and unique ## ----------------------------------------------------------- ## The following is not quite efficient {but easy to program, ## and as() are based on C code (all of them?) ## ## FIXME: Do it fast for the case where 'x' is already 'uniq' switch(class.x, "dgTMatrix" = as(as(x, "dgCMatrix"), "dgTMatrix"), "dsTMatrix" = as(as(x, "dsCMatrix"), "dsTMatrix"), "dtTMatrix" = as(as(x, "dtCMatrix"), "dtTMatrix"), ## do we need this for "logical" ones, there's no sum() there! "lgTMatrix" = as(as(x, "lgCMatrix"), "lgTMatrix"), "lsTMatrix" = as(as(x, "lsCMatrix"), "lsTMatrix"), "ltTMatrix" = as(as(x, "ltCMatrix"), "ltTMatrix"), ## do we need this for "logical" ones, there's no sum() there! "ngTMatrix" = as(as(x, "ngCMatrix"), "ngTMatrix"), "nsTMatrix" = as(as(x, "nsCMatrix"), "nsTMatrix"), "ntTMatrix" = as(as(x, "ntCMatrix"), "ntTMatrix"), ## otherwise: stop(gettextf("not yet implemented for class %s", dQuote(class.x)), domain = NA)) } ## Note: maybe, using ## ---- xj <- .Call(Matrix_expand_pointers, x@p) ## would be slightly more efficient than as( , "dgTMatrix") ## but really efficient would be to use only one .Call(.) for uniq(.) ! ## Earlier was: ## drop0 <- function(x, clx = c(class(x)), tol = 0) { drop0 <- function(x, tol = 0, is.Csparse = NA) { .Call(Csparse_drop, if(isTRUE(is.Csparse) || is.na(is.Csparse) && is(x, "CsparseMatrix")) x else as(x, "CsparseMatrix"), tol) } uniq <- function(x) { if(is(x, "TsparseMatrix")) uniqTsparse(x) else if(is(x, "sparseMatrix")) drop0(x) else x } asTuniq <- function(x) { if(is(x, "TsparseMatrix")) uniqTsparse(x) else as(x,"TsparseMatrix") } ## is 'x' a uniq Tsparse Matrix ? is_not_uniqT <- function(x, di = dim(x)) is.unsorted(x@j) || anyDuplicated(.Call(m_encodeInd2, x@i, x@j, di, FALSE)) ## is 'x' a TsparseMatrix with duplicated entries (to be *added* for uniq): is_duplicatedT <- function(x, di = dim(x)) anyDuplicated(.Call(m_encodeInd2, x@i, x@j, di, FALSE)) t_geMatrix <- function(x) { x@x <- as.vector(t(array(x@x, dim = x@Dim))) # no dimnames here x@Dim <- x@Dim[2:1] x@Dimnames <- x@Dimnames[2:1] x@factors <- list() ## FIXME -- do better, e.g., for "LU"? x } ## t( [dl]trMatrix ) and t( [dl]syMatrix ) : t_trMatrix <- function(x) { x@x <- as.vector(t(as(x, "matrix"))) x@Dim <- x@Dim[2:1] x@Dimnames <- x@Dimnames[2:1] x@uplo <- if (x@uplo == "U") "L" else "U" # and keep x@diag x } fixupDense <- function(m, from, cldm = getClassDef(class(m))) { if(extends(cldm, "triangularMatrix")) { m@uplo <- from@uplo m@diag <- from@diag } else if(extends(cldm, "symmetricMatrix")) { m@uplo <- from@uplo } m } ## -> ./ldenseMatrix.R : l2d_Matrix <- function(from, cl = MatrixClass(class(from)), cld = getClassDef(cl)) { ## stopifnot(is(from, "lMatrix")) fixupDense(new(sub("^l", "d", cl), x = as.double(from@x), Dim = from@Dim, Dimnames = from@Dimnames), from, cld) ## FIXME: treat 'factors' smartly {not for triangular!} } ## -> ./ndenseMatrix.R : n2d_Matrix <- function(from, cl = MatrixClass(class(from)), cld = getClassDef(cl)) { ## stopifnot(is(from, "nMatrix")) fixupDense(new(sub("^n", "d", cl), x = as.double(from@x), Dim = from@Dim, Dimnames = from@Dimnames), from, cld) ## FIXME: treat 'factors' smartly {not for triangular!} } n2l_Matrix <- function(from, cl = MatrixClass(class(from)), cld = getClassDef(cl)) { fixupDense(new(sub("^n", "l", cl), x = from@x, Dim = from@Dim, Dimnames = from@Dimnames), from, cld) ## FIXME: treat 'factors' smartly {not for triangular!} } ## -> ./ddenseMatrix.R : d2l_Matrix <- function(from, cl = MatrixClass(class(from)), cld = getClassDef(cl)) { fixupDense(new(sub("^d", "l", cl), x = as.logical(from@x), Dim = from@Dim, Dimnames = from@Dimnames), from, cld) ## FIXME: treat 'factors' smartly {not for triangular!} } n2l_spMatrix <- function(from) { ## stopifnot(is(from, "nMatrix")) new(sub("^n", "l", MatrixClass(class(from))), ##x = as.double(from@x), Dim = from@Dim, Dimnames = from@Dimnames) } tT2gT <- function(x, cl = class(x), toClass, cld = getClassDef(cl)) { ## coerce *tTMatrix to *gTMatrix {triangular -> general} d <- x@Dim if(uDiag <- x@diag == "U") # unit diagonal, need to add '1's uDiag <- (n <- d[1]) > 0 if(missing(toClass)) { do.n <- extends(cld, "nMatrix") toKind <- if(do.n) "n" else substr(MatrixClass(cl), 1,1) # "d" | "l"|"i"|"z" toClass <- paste0(toKind, "gTMatrix") } else { do.n <- extends(toClass, "nMatrix") toKind <- if(do.n) "n" else substr(toClass, 1,1) } if(do.n) ## no 'x' slot new(toClass, # == "ngTMatrix" Dim = d, Dimnames = x@Dimnames, i = c(x@i, if(uDiag) 0:(n-1)), j = c(x@j, if(uDiag) 0:(n-1))) else new(toClass, Dim = d, Dimnames = x@Dimnames, i = c(x@i, if(uDiag) 0:(n-1)), j = c(x@j, if(uDiag) 0:(n-1)), x = c(x@x, if(uDiag) rep.int(if(toKind == "l") TRUE else 1, n))) } ## __TODO__ ## Hack for the above, possibly considerably faster: ## Just *modify* the 'x' object , using attr(x, "class') <- toClass ## Fast very special one ## .gT2tC <- function(x, uplo, diag) .Call(Tsparse_to_tCsparse, x, uplo, diag) gT2tT <- function(x, uplo, diag, toClass, do.n = extends(toClass, "nMatrix")) { ## coerce *gTMatrix to *tTMatrix {general -> triangular} i <- x@i j <- x@j sel <- if(uplo == "U") { if(diag == "U") i < j else i <= j } else { if(diag == "U") i > j else i >= j } i <- i[sel] j <- j[sel] if(do.n) ## no 'x' slot new("ntTMatrix", i = i, j = j, uplo = uplo, diag = diag, Dim = x@Dim, Dimnames = x@Dimnames) else new(toClass, i = i, j = j, uplo = uplo, diag = diag, x = x@x[sel], Dim = x@Dim, Dimnames = x@Dimnames) } check.gT2tT <- function(from, toClass, do.n = extends(toClass, "nMatrix")) { if(isTr <- isTriangular(from)) { gT2tT(from, uplo = .if.NULL(attr(isTr, "kind"), "U"), diag = "N", ## improve: also test for unit diagonal toClass = toClass, do.n = do.n) } else stop("not a triangular matrix") } gT2sT <- function(x, toClass, do.n = extends(toClass, "nMatrix")) { upper <- x@i <= x@j i <- x@i[upper] j <- x@j[upper] if(do.n) ## no 'x' slot new("nsTMatrix", Dim = x@Dim, Dimnames = x@Dimnames, i = i, j = j, uplo = "U") else new(toClass, Dim = x@Dim, Dimnames = x@Dimnames, i = i, j = j, x = x@x[upper], uplo = "U") } check.gT2sT <- function(x, toClass, do.n = extends(toClass, "nMatrix")) { if(isSymmetric(x)) gT2sT(x, toClass, do.n) else stop("not a symmetric matrix; consider forceSymmetric() or symmpart()") } if(FALSE)# unused l2d_meth <- function(x) { cl <- MatrixClass(class(x)) as(callGeneric(as(x, sub("^l", "d", cl))), cl) } ## return "d" or "l" or "n" or "z" .M.kind <- function(x, clx = class(x)) { ## 'clx': class() *or* class definition of x if(is.matrix(x) || is.atomic(x)) { ## 'old style' matrix or vector if (is.numeric(x)) "d" ## also for integer: see .V.kind(), .M.kindC() else if(is.logical(x)) "l" ## FIXME ? "n" if no NA ?? else if(is.complex(x)) "z" else stop(gettextf("not yet implemented for matrix with typeof %s", typeof(x)), domain = NA) } else .M.kindC(clx) } ## the same as .M.kind, but also knows "i" .V.kind <- function(x, clx = class(x)) { ## 'clx': class() *or* class definition of x if(is.matrix(x) || is.atomic(x)) { ## 'old style' matrix or vector if (is.integer(x)) "i" else if(is.numeric(x)) "d" else if(is.logical(x)) "l" ## FIXME ? "n" if no NA ?? else if(is.complex(x)) "z" else stop(gettextf("not yet implemented for matrix with typeof %s", typeof(x)), domain = NA) } else .M.kindC(clx) } .M.kindC <- function(clx) { ## 'clx': class() *or* classdefinition if(is.character(clx)) # < speedup: get it once clx <- getClassDef(clx) if(extends(clx, "sparseVector")) ## shortcut substr(as.character(clx@className), 1,1) else if(extends(clx, "dMatrix")) "d" else if(extends(clx, "nMatrix")) "n" else if(extends(clx, "lMatrix")) "l" else if(extends(clx, "indMatrix")) "n" # permutation -> pattern else if(extends(clx, "zMatrix")) "z" else if(extends(clx, "iMatrix")) "i" else stop(gettextf(" not yet implemented for %s", clx@className), domain = NA) } ## typically used as .type.kind[.M.kind(x)]: .type.kind <- c("d" = "double", "i" = "integer", "l" = "logical", "n" = "logical", "z" = "complex") ## the reverse, a "version of" .M.kind(.): .kind.type <- names(.type.kind); names(.kind.type) <- as.vector(.type.kind) .M.shape <- function(x, clx = class(x)) { ## 'clx': class() *or* class definition of x if(is.matrix(x)) { ## 'old style matrix' if (isDiagonal (x)) "d" else if(isTriangular(x)) "t" else if(isSymmetric (x)) "s" else "g" # general } else { if(is.character(clx)) # < speedup: get it once clx <- getClassDef(clx) if(extends(clx, "diagonalMatrix")) "d" else if(extends(clx, "triangularMatrix"))"t" else if(extends(clx, "symmetricMatrix")) "s" else "g" } } ## a faster simpler version [for sparse matrices, i.e., never diagonal] .M.shapeC <- function(x, clx = class(x)) { if(is.character(clx)) # < speedup: get it once clx <- getClassDef(clx) if (extends(clx, "triangularMatrix")) "t" else if(extends(clx, "symmetricMatrix")) "s" else "g" } class2 <- function(cl, kind = "l", do.sub = TRUE) { ## Find "corresponding" class; since pos.def. matrices have no pendant: cl <- MatrixClass(cl) if(cl %in% c("dpoMatrix","corMatrix")) paste0(kind, "syMatrix") else if(cl == "dppMatrix") paste0(kind, "spMatrix") else if(do.sub) sub("^[a-z]", kind, cl) else cl } ## see also as_smartClass() below geClass <- function(x) { if (is(x, "dMatrix")) "dgeMatrix" else if(is(x, "lMatrix")) "lgeMatrix" else if(is(x, "nMatrix") || is(x, "indMatrix")) "ngeMatrix" else if(is(x, "zMatrix")) "zgeMatrix" else stop(gettextf("general Matrix class not yet implemented for %s", dQuote(class(x))), domain = NA) } .dense.prefixes <- c("d" = "tr", ## map diagonal to triangular "t" = "tr", "s" = "sy", "g" = "ge") .sparse.prefixes <- c("d" = "t", ## map diagonal to triangular "t" = "t", "s" = "s", "g" = "g") as_M.kind <- function(x, clx) { if(is.character(clx)) # < speedup: get it once clx <- getClassDef(clx) if(is(x, clx)) x else as(x, paste0(.M.kindC(clx), "Matrix")) } ## Used, e.g. after subsetting: Try to use specific class -- if feasible : as_dense <- function(x, cld = if(isS4(x)) getClassDef(class(x))) { as(x, paste0(.M.kind(x, cld), .dense.prefixes[.M.shape(x, cld)], "Matrix")) } ## This is "general" but slower than the next definition if(FALSE) .sp.class <- function(x) { ## find and return the "sparseness class" if(!is.character(x)) x <- class(x) for(cl in paste0(c("C","T","R"), "sparseMatrix")) if(extends(x, cl)) return(cl) ## else (should rarely happen) NA_character_ } .sp.class <- function(x) { ## find and return the "sparseness class" x <- if(!is.character(x)) MatrixClass(class(x)) else MatrixClass(x) if(any((ch <- substr(x,3,3)) == c("C","T","R"))) return(paste0(ch, "sparseMatrix")) ## else NA_character_ } ### Goal: Eventually get rid of these --- want to foster coercions ### ---- *to* virtual classes whenever possible, e.g. as(*, "CsparseMatrix") ## 2007-12: better goal: use them only for "matrix" [maybe speed them up later] ## Here, getting the class definition and passing it, should be faster as_Csparse <- function(x, cld = if(isS4(x)) getClassDef(class(x))) { as(x, paste0(.M.kind(x, cld), .sparse.prefixes[.M.shape(x, cld)], "CMatrix")) } if(FALSE) # replaced by .Call(dense_to_Csparse, *) which is perfect for "matrix" as_Csparse2 <- function(x, cld = if(isS4(x)) getClassDef(class(x))) { ## Csparse + U2N when needed sh <- .M.shape(x, cld) x <- as(x, paste0(.M.kind(x, cld), .sparse.prefixes[sh], "CMatrix")) if(sh == "t") .Call(Csparse_diagU2N, x) else x } ## *do* use this where applicable as_Csp2 <- function(x) { ## Csparse + U2N when needed x <- as(x, "CsparseMatrix") if(is(x, "triangularMatrix")) .Call(Csparse_diagU2N, x) else x } .gC2sym <- function(x, uplo) .Call(Csparse_general_to_symmetric, x, uplo) ## 'cl' : class() *or* class definition of from as_gCsimpl2 <- function(from, cl = class(from)) as(from, paste0(.M.kind(from, cl), "gCMatrix")) ## to be used directly in setAs(.) needs one-argument-only (from) : as_gCsimpl <- function(from) as(from, paste0(.M.kind(from), "gCMatrix")) ## slightly smarter: as_Sp <- function(from, shape, cl = class(from)) { if(is.character(cl)) cl <- getClassDef(cl) as(from, paste0(.M.kind(from, cl), shape, if(extends(cl, "TsparseMatrix")) "TMatrix" else "CMatrix")) } ## These are used in ./sparseMatrix.R: as_gSparse <- function(from) as_Sp(from, "g", getClassDef(class(from))) as_sSparse <- function(from) as_Sp(from, "s", getClassDef(class(from))) as_tSparse <- function(from) as_Sp(from, "t", getClassDef(class(from))) as_geSimpl2 <- function(from, cl = class(from)) as(from, paste0(.M.kind(from, cl), "geMatrix")) ## to be used directly in setAs(.) needs one-argument-only (from) : as_geSimpl <- function(from) as(from, paste0(.M.kind(from), "geMatrix")) ## Smarter, (but sometimes too smart!) compared to geClass() above: as_smartClass <- function(x, cl, cld = getClassDef(cl)) { if(missing(cl)) return(as_geSimpl(x)) ## else if(extends(cld, "diagonalMatrix") && isDiagonal(x)) ## diagonal* result: as(x, cl) else if(extends(cld, "symmetricMatrix") && isSymmetric(x)) { ## symmetric* result: kind <- .M.kind(x, cld) as(x, class2(cl, kind, do.sub= kind != "d")) } else if(extends(cld, "triangularMatrix") && isTriangular(x)) as(x, cl) else ## revert to as_geSimpl2(x, cld) } as_CspClass <- function(x, cl) { ## NOTE: diagonal is *not* sparse: cld <- getClassDef(cl) ##(extends(cld, "diagonalMatrix") && isDiagonal(x)) || if (extends(cld, "symmetricMatrix") && isSymmetric(x)) forceSymmetric(as(x,"CsparseMatrix")) else if (extends(cld, "triangularMatrix") && (iT <- isTriangular(x))) as(x, cl) else if(is(x, "CsparseMatrix")) x else as(x, paste0(.M.kind(x, cld), "gCMatrix")) } asTri <- function(from, newclass) { ## TODO: also check for unit-diagonal: 'diag = "U"' isTri <- isTriangular(from) if(isTri) new(newclass, x = from@x, Dim = from@Dim, Dimnames = from@Dimnames, uplo = attr(isTri, "kind")) else stop("not a triangular matrix") } try_as <- function(x, classes, tryAnyway = FALSE) { if(!tryAnyway && !is(x, "Matrix")) return(x) ## else ok <- canCoerce(x, classes[1]) while(!ok && length(classes <- classes[-1])) { ok <- canCoerce(x, classes[1]) } if(ok) as(x, classes[1]) else x } ## For *dense* matrices isTriMat <- function(object, upper = NA) { ## pretest: is it square? d <- dim(object) if(d[1] != d[2]) return(FALSE) TRUE.U <- structure(TRUE, kind = "U") if(d[1] == 0) return(TRUE.U) ## else slower test TRUE.L <- structure(TRUE, kind = "L") if(!is.matrix(object)) object <- as(object,"matrix") if(is.na(upper)) { if(all0(object[lower.tri(object)])) TRUE.U else if(all0(object[upper.tri(object)])) TRUE.L else FALSE } else if(upper) if(all0(object[lower.tri(object)])) TRUE.U else FALSE else ## upper is FALSE if(all0(object[upper.tri(object)])) TRUE.L else FALSE } ## For Tsparse matrices: isTriT <- function(object, upper = NA) { ## pretest: is it square? d <- dim(object) if(d[1] != d[2]) return(FALSE) ## else TRUE.U <- structure(TRUE, kind = "U") if(d[1] == 0) return(TRUE.U) TRUE.L <- structure(TRUE, kind = "L") if(is.na(upper)) { if(all(object@i <= object@j)) TRUE.U else if(all(object@i >= object@j)) TRUE.L else FALSE } else if(upper) { if(all(object@i <= object@j)) TRUE.U else FALSE } else { ## 'lower' if(all(object@i >= object@j)) TRUE.L else FALSE } } ## For Csparse matrices isTriC <- function(object, upper = NA) { ## pretest: is it square? d <- dim(object) if(d[1] != d[2]) return(FALSE) ## else TRUE.U <- structure(TRUE, kind = "U") if((n <- d[1]) == 0) return(TRUE.U) TRUE.L <- structure(TRUE, kind = "L") ## Need this, since 'i' slot of symmetric looks like triangular : if(is(object, "symmetricMatrix")) # triangular only iff diagonal : return(if(length(oi <- object@i) == n && isSeq(oi, n-1L) && isSeq(object@p, n)) structure(TRUE, kind = object@uplo) else FALSE) ## else ni <- 1:n ## the row indices split according to column: ilist <- split(object@i, factor(rep.int(ni, diff(object@p)), levels= ni)) lil <- unlist(lapply(ilist, length), use.names = FALSE) if(any(lil == 0)) { pos <- lil > 0 if(!any(pos)) ## matrix of all 0's return(TRUE.U) ilist <- ilist[pos] ni <- ni[pos] } ni0 <- ni - 1L # '0-based ni' if(is.na(upper)) { if(all(sapply(ilist, max, USE.NAMES = FALSE) <= ni0)) TRUE.U else if(all(sapply(ilist, min, USE.NAMES = FALSE) >= ni0)) TRUE.L else FALSE } else if(upper) { if(all(sapply(ilist, max, USE.NAMES = FALSE) <= ni0)) TRUE.U else FALSE } else { ## 'lower' if(all(sapply(ilist, min, USE.NAMES = FALSE) >= ni0)) TRUE.L else FALSE } } ## When the matrix is known to be [n x n] aka "square" ## (need "vector-indexing" work for 'M'): .is.diagonal.sq.matrix <- function(M, n = dim(M)[1L]) all0(M[rep_len(c(FALSE, rep.int(TRUE,n)), n^2)]) .is.diagonal <- function(object) { ## "matrix" or "denseMatrix" (but not "diagonalMatrix") d <- dim(object) if(d[1L] != (n <- d[2L])) FALSE else if(is.matrix(object)) .is.diagonal.sq.matrix(object, n) else ## "denseMatrix" -- packed or unpacked if(is(object, "generalMatrix")) # "dge", "lge", ... .is.diagonal.sq.matrix(object@x, n) else { ## "dense" but not {diag, general}, i.e. triangular or symmetric: ## -> has 'uplo' differentiate between packed and unpacked ### .......... FIXME ............... packed <- isPacked(object) if(object@uplo == "U") { } else { ## uplo == "L" } ### very cheap workaround all0(as.matrix(object)[rep_len(c(FALSE, rep.int(TRUE,n)), n^2)]) } } ## Purpose: Transform a *unit diagonal* sparse triangular matrix ## into one with explicit diagonal entries '1' ## for "dtC*", "ltC* ..: directly xtC.diagU2N <- function(x) if(x@diag == "U") .Call(Csparse_diagU2N, x) else x ##' @title uni-diagonal to "regular" triangular Matrix ##' ##' NOTE: class is *not* checked here! {speed} ##' @param x a dense unidiagonal (x@diag == "U") triangular Matrix ##' ("ltrMatrix", "dtpMatrix", ...). ##' @param kind character indicating content kind: "d","l",.. ##' @param isPacked logical indicating if 'x' is packed ##' @return Matrix "like" x, but with x@diag == "N" (and 1 or TRUE values "filled" in .@x) ##' @author Martin Maechler .dense.diagU2N <- function(x, kind = .M.kind(x), isPacked = length(x@x) < n^2) { ### FIXME: Move this to C ----- (possibly with an option of *not* copying) ## For denseMatrix, .@diag = "U" means the 'x' slot can have wrong values ## which are documented to never be accessed n <- x@Dim[1] if(n > 0) { one <- if(kind == "d") 1. else TRUE if(isPacked) { ## { == isPacked(x)) } : dtp-, ltp-, or "ntpMatrix": ## x@x is of length n*(n+1)/2 if(n == 1) x@x <- one else { di <- if(x@uplo == "U") seq_len(n) else c(1L,n:2L) x@x[cumsum(di)] <- one } } else { ## okay: now have 'x' slot of length n x n x@x[1L+ (0:(n-1L))*(n+1L)] <- one # even for "n..Matrix" } } x@diag <- "N" x } .diagU2N <- function(x, cl, checkDense = FALSE) { ## fast "no-test" version --- we *KNOW* 'x' is 'triangularMatrix' if(extends(cl, "CsparseMatrix")) .Call(Csparse_diagU2N, x) else if(extends(cl, "TsparseMatrix")) .Call(Tsparse_diagU2N, x) else { kind <- .M.kind(x, cl) if(checkDense && extends(cl,"denseMatrix")) { .dense.diagU2N(x, kind) } else { ## possibly dense, not [CT]sparseMatrix ==> Rsparse* .Call(Tsparse_diagU2N, as(as(x, paste0(kind, "Matrix")), "TsparseMatrix")) ## leave it as T* - the caller can always coerce to C* if needed } } } ## .diagU2N() diagU2N <- function(x, cl = getClassDef(class(x)), checkDense = FALSE) { if(extends(cl, "triangularMatrix") && x@diag == "U") .diagU2N(x, cl, checkDense=checkDense) else x } ##' @title coerce triangular Matrix to uni-diagonal ##' ##' NOTE: class is *not* checked here! {speed} ##' @param x a dense triangular Matrix ("ltrMatrix", "dtpMatrix", ...). ##' @return Matrix "like" x, but with x@diag == "U" .dense.diagN2U <- function(x) { ## as we promise that the diagonal entries are not accessed when ## diag = "U", we don't even need to set them to one !! x@diag <- "U" x } diagN2U <- function(x, cl = getClassDef(class(x)), checkDense = FALSE) { if(!(extends(cl, "triangularMatrix") && x@diag == "N")) return(x) if(checkDense && extends(cl,"denseMatrix")) { .dense.diagN2U(x) } else ## still possibly dense .Call(Csparse_diagN2U, as(x, "CsparseMatrix")) } .dgC.0.factors <- function(x) if(!length(x@factors)) x else { x@factors <- list() ; x } .as.dgC.0.factors <- function(x) { if(!is(x, "dgCMatrix")) as(x, "dgCMatrix") # will not have 'factors' else ## dgCMatrix .dgC.0.factors(x) } .set.factors <- function(x, name, value) .Call(R_set_factors, x, value, name) ### Fast, much simplified version of tapply() tapply1 <- function (X, INDEX, FUN = NULL, ..., simplify = TRUE) { sapply(unname(split(X, INDEX)), FUN, ..., simplify = simplify, USE.NAMES = FALSE) } ## tapply.x <- function (X, n, INDEX, FUN = NULL, ..., simplify = TRUE) { ## tapply1(X, factor(INDEX, 0:(n-1)), FUN = FUN, ..., simplify = simplify) ## } ### MM: Unfortunately, these are still pretty slow for large sparse ... sparsapply <- function(x, MARGIN, FUN, sparseResult = TRUE, ...) { ## Purpose: "Sparse Apply": better utility than tapply1() for colSums() etc : ## NOTE: Only applicable sum()-like where the "zeros do not count" ## ---------------------------------------------------------------------- ## Arguments: x: sparseMatrix; others as in *apply() ## ---------------------------------------------------------------------- ## Author: Martin Maechler, Date: 16 May 2007 stopifnot(MARGIN %in% 1:2) xi <- if(MARGIN == 1) x@i else x@j ui <- unique(xi) n <- x@Dim[MARGIN] ## FIXME: Here we assume 'FUN' to return 'numeric' ! r <- if(sparseResult) new("dsparseVector", length = n) else numeric(n) r[ui + 1L] <- sapply(ui, function(i) FUN(x@x[xi == i], ...)) r } sp.colMeans <- function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) { nr <- nrow(x) if(na.rm) ## use less than nrow(.) in case of NAs nr <- nr - sparsapply(x, 2, function(u) sum(is.na(u)), sparseResult=sparseResult) sparsapply(x, 2, sum, sparseResult=sparseResult, na.rm=na.rm) / nr } sp.rowMeans <- function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) { nc <- ncol(x) if(na.rm) ## use less than ncol(.) in case of NAs nc <- nc - sparsapply(x, 1, function(u) sum(is.na(u)), sparseResult=sparseResult) sparsapply(x, 1, sum, sparseResult=sparseResult, na.rm=na.rm) / nc } all0Matrix <- function(n,m) { ## an all-0 matrix -- chose what Matrix() also gives -- "most efficiently" n <- as.integer(n) m <- as.integer(m) new(if(n == m) "dsCMatrix" else "dgCMatrix", Dim = c(n,m), p = rep.int(0L, m+1L)) } setZero <- function(x) { ## all-0 matrix from x which must inherit from 'Matrix' d <- x@Dim new(if(d[1] == d[2]) "dsCMatrix" else "dgCMatrix", Dim = d, Dimnames = x@Dimnames, p = rep.int(0L, d[2]+1L)) } .M.vectorSub <- function(x,i) { ## e.g. M[0] , M[TRUE], M[1:2] if(any(as.logical(i)) || prod(dim(x)) == 0) ## FIXME: for *large sparse*, use sparseVector ! as(x, "matrix")[i] else ## save memory (for large sparse M): as.vector(x[1,1])[FALSE] } ##' Compute the three "parts" of two sets: ##' @param x arbitrary vector; possibly with duplicated values, ##' @param y (ditto) ##' @param uniqueCheck ##' @param check ##' ##' @return list(x.only = setdiff(x,y), ##' y.only = setdiff(y,x), ##' int = intersect(x,y)) setparts <- function(x,y, uniqueCheck = TRUE, check = TRUE) { if(check) { x <- as.vector(x) y <- as.vector(y) } if(uniqueCheck) { x <- unique.default(x) y <- unique.default(y) } .setparts(x,y) } .setparts <- function(x,y) { n1 <- length(m1 <- match(x,y, 0L)) n2 <- length(m2 <- match(y,x, 0L)) ix <- seq_len(n1)[m1 == 0L] iy <- seq_len(n2)[m2 == 0L] list(x.only = x[ix], ix.only = ix, mx = m1, y.only = y[iy], iy.only = iy, my = m2, int = if(n1 < n2) y[m1] else x[m2]) } ##' @title Warn about extraneous arguments in the "..." (of its caller) ## TODO NOTE: R/src/library/base/R/seq.R uses a simpler approach, ## *and* ngettext(.) {-> singular/plural *and* translatable} ##' @return ##' @author Martin Maechler, June 2012 chk.s <- function(...) { if(length(list(...))) warning(gettextf("arguments %s are disregarded in\n %s", sub(")$", '', sub("^list\\(", '', deparse(list(...), control=c()))), deparse(sys.call(-1), control=c())), call. = FALSE, domain=NA) } ##' *Only* to be used as function in ##' setMethod("Compare", ...., .Cmp.swap) --> ./Ops.R & ./diagMatrix.R .Cmp.swap <- function(e1,e2) { ## "swap RHS and LHS" and use the method below: switch(.Generic, "==" =, "!=" = callGeneric(e2, e1), "<" = e2 > e1, "<=" = e2 >= e1, ">" = e2 < e1, ">=" = e2 <= e1) } Matrix/R/dsparseMatrix.R0000644000175100001440000000442012211131516014677 0ustar hornikusers### d(ouble)sparseMatrix methods : setMethod("image", "dsparseMatrix", function(x, ...) image(as(x, "dgTMatrix"), ...)) setMethod("chol", signature(x = "dsparseMatrix"), function(x, pivot=FALSE, cache=TRUE, ...) { nm <- if(pivot) "sPdCholesky" else "spdCholesky" if(!is.null(ch <- x@factors[[nm]])) return(ch) ## use the cache px <- as(x, "symmetricMatrix") if (isTRUE(validObject(px, test=TRUE))) { if(cache) .set.factors(x, nm, chol(as(px, "CsparseMatrix"), pivot=pivot, ...)) else chol(as(px, "CsparseMatrix"), pivot=pivot, ...) } else stop("'x' is not positive definite -- chol() undefined.") }) setMethod("determinant", signature(x = "dsparseMatrix", logarithm = "logical"), function(x, logarithm = TRUE, ...) determinant(as(x,"CsparseMatrix"), logarithm, ...)) ##-> now dgC or dsC or dtC .. which *have* their methods setMethod("lu", signature(x = "dsparseMatrix"), function(x, cache=TRUE, ...) if(cache) .set.factors(x, "lu", lu(as(x, "dgCMatrix"), ...)) else lu(as(x, "dgCMatrix"), ...)) setMethod("is.finite", signature(x = "dsparseMatrix"), function(x) { if(any(!is.finite(x@x))) { r <- allTrueMat(x, packed = FALSE) x <- as(as(as(x,"CsparseMatrix"), "dgCMatrix"),"dgTMatrix") notF <- which(!is.finite(x@x)) r[cbind(x@i[notF], x@j[notF]) + 1L] <- FALSE r } else allTrueMat(x) }) setMethod("is.infinite", signature(x = "dsparseMatrix"), function(x) { if(any((isInf <- is.infinite(x@x)))) { cld <- getClassDef(class(x)) if(extends(cld, "triangularMatrix") && x@diag == "U") isInf <- is.infinite((x <- .diagU2N(x, cld))@x) r <- as(x, "lMatrix") # will be "lsparseMatrix" - *has* x slot r@x <- if(length(isInf) == length(r@x)) isInf else is.infinite(r@x) if(!extends(cld, "CsparseMatrix")) r <- as(r, "CsparseMatrix") as(.Call(Csparse_drop, r, 0), "nMatrix") # a 'pattern matrix } else is.na_nsp(x) }) ## Group Methods, see ?Arith (e.g.): "Ops" --> ./Ops.R ## ----- ## others moved to ./Csparse.R (and 'up' to ./sparseMatrix.R): ## "Math2" is in ./dMatrix.R Matrix/R/denseMatrix.R0000644000175100001440000002142412070371667014357 0ustar hornikusers### Simple fallback methods for all dense matrices ### These are "cheap" to program, but potentially far from efficient; ### Methods for specific subclasses will overwrite these: setAs("ANY", "denseMatrix", function(from) Matrix(from, sparse=FALSE)) ## Conceivably, could write ## setAs("matrix", "denseMatrix", ....) which was slightly more efficient than ## Matrix(.) but would have many things in common setAs(from = "denseMatrix", to = "generalMatrix", as_geSimpl) ## dense to sparse: ## : if we do this, do it "right", i.e. preserve symmetric/triangular! ## setAs("denseMatrix", "dsparseMatrix", ## ## MM thought that as() will take the ``closest'' match; but that fails! ## ## function(from) as(as(from, "dgeMatrix"), "dsparseMatrix")) ## function(from) as(as(from, "dgeMatrix"), "dgCMatrix")) .dense2C <- function(from) { cl <- class(from) cld <- getClassDef(cl) ## get it once (speedup) r <- .Call(dense_to_Csparse, from)# goes via "generalMatrix" ## FIXME: for symmetric / triangular matrices, this is a waste, notably if packed if (extends(cld, "generalMatrix")) r else if(extends(cld, "symmetricMatrix")) forceSymmetric(r) else if(extends(cld, "diagonalMatrix")) stop("diagonalMatrix in .dense2C() -- should never happen, please report!") else { ## we have "triangular" : if (extends(cld,"dMatrix")) as(r, "dtCMatrix") else if (extends(cld,"lMatrix")) as(r, "ltCMatrix") else if (extends(cld,"nMatrix")) as(r, "ntCMatrix") else if (extends(cld,"zMatrix")) as(r, "ztCMatrix") else stop(gettextf("undefined method for class %s", dQuote(cl)), domain=NA) } } setAs("denseMatrix", "CsparseMatrix", .dense2C) ## This sometimes fails (eg. for "lsyMatrix"), and we really want to ## use the generic ``go via Csparse'' (top of ./sparseMatrix.R) instead ## setAs("denseMatrix", "sparseMatrix", ## function(from) { ## cl <- class(from) ## cld <- getClassDef(cl) ## if (extends(cld, "generalMatrix")) ## .Call(dense_to_Csparse, from) ## else ## i.e. triangular | symmetric ## as_Csparse(from, cld) ## }) setAs("denseMatrix", "TsparseMatrix", function(from) as(.dense2C(from), "TsparseMatrix")) setMethod("show", signature(object = "denseMatrix"), function(object) prMatrix(object)) ##- ## FIXME: The following is only for the "dMatrix" objects that are not ##- ## "dense" nor "sparse" -- i.e. "packed" ones : ##- ## But these could be printed better -- "." for structural zeros. ##- setMethod("show", signature(object = "dMatrix"), prMatrix) ##- ## and improve this as well: ##- setMethod("show", signature(object = "pMatrix"), prMatrix) ##- ## this should now be superfluous [keep for safety for the moment]: setMethod("dim<-", signature(x = "denseMatrix", value = "ANY"), function(x, value) { if(!is.numeric(value) || length(value) != 2) stop("dim(.) value must be numeric of length 2") if(prod(dim(x)) != prod(value <- as.integer(value))) stop("dimensions don't match the number of cells") clx <- as.character(MatrixClass(class(x))) # as.*(): drop attr if(substring(clx,2) == "geMatrix") { x@Dim <- value if(length(x@factors) > 0) x@factors <- list() x } else { ## other "denseMatrix" x <- as_geSimpl2(x, clx) dim(x) <- value x } }) ## Using "index" for indices should allow ## integer (numeric), logical, or character (names!) indices : ## use geClass() when 'i' or 'j' are missing: ## since symmetric, triangular, .. will not be preserved anyway: setMethod("[", signature(x = "denseMatrix", i = "index", j = "missing", drop = "logical"), function (x, i, j, ..., drop) { if((na <- nargs()) == 3) r <- as(x, "matrix")[i, drop=drop] else if(na == 4) r <- as(x, "matrix")[i, , drop=drop] else stop(gettextf("invalid nargs()= %d", na), domain=NA) if(is.null(dim(r))) r else as(r, geClass(x)) }) setMethod("[", signature(x = "denseMatrix", i = "missing", j = "index", drop = "logical"), function (x, i, j, ..., drop) { r <- as(x, "matrix")[, j, drop=drop] if(is.null(dim(r))) r else as(r, geClass(x)) }) setMethod("[", signature(x = "denseMatrix", i = "index", j = "index", drop = "logical"), function (x, i, j, ..., drop) { r <- callGeneric(x = as(x, "matrix"), i=i, j=j, drop=drop) if(is.null(dim(r))) r else { cld <- getClassDef(cl <- class(x)) if(extends(cld, "symmetricMatrix") && length(i) == length(j) && isTRUE(all(i == j))) ## keep original symmetric class (but not "dpo") as(r, class2(cl, .M.kindC(cld))) else as_smartClass(r, cl) } }) .dense.sub.i.2col <- function(x, i, j, ..., drop) { r <- as(x, "matrix")[ i ] if(is.null(dim(r))) r else as(r, geClass(x)) } setMethod("[", signature(x = "denseMatrix", i = "matrix", j = "missing"),#drop="ANY" .dense.sub.i.2col) setMethod("[", signature(x = "denseMatrix", i = "matrix", j = "missing", drop="missing"), .dense.sub.i.2col) ## Now the "[<-" ones --- see also those in ./Matrix.R ## It's recommended to use setReplaceMethod() rather than setMethod("[<-",.) ## even though the former is currently just a wrapper for the latter ## x[] <- value : setReplaceMethod("[", signature(x = "denseMatrix", i = "missing", j = "missing", value = "ANY"),## double/logical/... function (x, value) { x <- as(x, "generalMatrix") x@x[] <- value validObject(x)# check if type and lengths above match x }) ## FIXME: 1) These are far from efficient ## ----- setReplaceMethod("[", signature(x = "denseMatrix", i = "index", j = "missing", value = "replValue"), function (x, i, j, ..., value) { r <- as(x, "matrix") ## message("`[<-` with nargs()= ",nargs()) if((na <- nargs()) == 3) r[i] <- value else if(na == 4) r[i, ] <- value else stop(gettextf("invalid nargs()= %d", na), domain=NA) as(r, geClass(x)) }) setReplaceMethod("[", signature(x = "denseMatrix", i = "missing", j = "index", value = "replValue"), function (x, i, j, ..., value) { r <- as(x, "matrix") r[, j] <- value as(r, geClass(x)) }) setReplaceMethod("[", signature(x = "denseMatrix", i = "index", j = "index", value = "replValue"), function (x, i, j, ..., value) { r <- as(x, "matrix") r[i, j] <- value as_smartClass(r, class(x)) ## was as(r, class(x)) }) setReplaceMethod("[", signature(x = "denseMatrix", i = "matrix", # 2-col.matrix j = "missing", value = "replValue"), function(x, i, j, ..., value) { r <- as(x, "matrix") r[ i ] <- value as(r, geClass(x)) }) setMethod("isSymmetric", signature(object = "denseMatrix"), function(object, tol = 100*.Machine$double.eps, ...) { ## pretest: is it square? d <- dim(object) if(d[1] != d[2]) return(FALSE) ## else slower test if (is(object,"dMatrix")) isTRUE(all.equal(as(object, "dgeMatrix"), as(t(object), "dgeMatrix"), tol = tol, ...)) else if (is(object, "nMatrix")) identical(as(object, "ngeMatrix"), as(t(object), "ngeMatrix")) else if (is(object, "lMatrix"))# not possible currently ## test for exact equality; FIXME(?): identical() too strict? identical(as(object, "lgeMatrix"), as(t(object), "lgeMatrix")) else if (is(object, "zMatrix")) ## will error out here identical(as(object, "zgeMatrix"), as(t(object), "zgeMatrix")) else if (is(object, "iMatrix")) ## will error out here identical(as(object, "igeMatrix"), as(t(object), "igeMatrix")) }) setMethod("isTriangular", signature(object = "triangularMatrix"), function(object, ...) TRUE) setMethod("isTriangular", signature(object = "denseMatrix"), isTriMat) setMethod("isDiagonal", signature(object = "denseMatrix"), .is.diagonal) ## FIXME: Once we have integer (idense..), sign(), abs(.) may need different: setMethod("Math", signature(x = "denseMatrix"), function(x) callGeneric(as(x, "dMatrix"))) # -> ./ddenseMatrix.R has next method setMethod("rcond", signature(x = "denseMatrix", norm = "character"), function(x, norm, ...) rcond(as(as(x, "dMatrix"), "dgeMatrix"), norm=norm, ...)) setMethod("symmpart", signature(x = "denseMatrix"), function(x) symmpart(as(x, "dMatrix"))) setMethod("skewpart", signature(x = "denseMatrix"), function(x) skewpart(as(x, "dMatrix"))) setMethod("is.na", signature(x = "denseMatrix"), function(x) { if(any((inax <- is.na(x@x)))) { r <- as(x, "lMatrix")#-> logical x-slot r@x <- inax as(r, "nMatrix") } else { d <- x@Dim new("ngCMatrix", Dim = d, Dimnames = dimnames(x), i = integer(0), p = rep.int(0L, d[2]+1L)) } }) Matrix/R/Hilbert.R0000644000175100001440000000027110615611763013457 0ustar hornikusersHilbert <- function(n) { ## generate the Hilbert matrix of dimension n n <- as.integer(n) i <- seq_len(n) new("dpoMatrix", x = c(1/outer(i - 1L, i, "+")), Dim = c(n,n)) } Matrix/R/ddenseMatrix.R0000644000175100001440000001542012211131516014502 0ustar hornikusers### Define Methods that can be inherited for all subclasses ## This replaces many "d..Matrix" -> "dgeMatrix" ones ## >> but << needs all sub(sub(sub)) classes of "ddenseMatrix" listed ## ----- in ../src/Mutils.c setAs("ddenseMatrix", "dgeMatrix", function(from) .Call(dup_mMatrix_as_dgeMatrix, from)) setAs("ddenseMatrix", "matrix", function(from) as(as(from, "dgeMatrix"), "matrix")) ## d(ouble) to l(ogical): setAs("dgeMatrix", "lgeMatrix", function(from) d2l_Matrix(from, "dgeMatrix")) setAs("dsyMatrix", "lsyMatrix", function(from) d2l_Matrix(from, "dsyMatrix")) setAs("dspMatrix", "lspMatrix", function(from) d2l_Matrix(from, "dspMatrix")) setAs("dtrMatrix", "ltrMatrix", function(from) d2l_Matrix(from, "dtrMatrix")) setAs("dtpMatrix", "ltpMatrix", function(from) d2l_Matrix(from, "dtpMatrix")) if(FALSE) ## FIXME, this fails for ("dtpMatrix" -> "CsparseMatrix") where .dense2C() works setAs("ddenseMatrix", "CsparseMatrix", function(from) { if (class(from) != "dgeMatrix") # don't lose symmetry/triangularity/... as_Csparse(from) else .Call(dense_to_Csparse, from) }) ## special case setAs("dgeMatrix", "dgCMatrix", function(from) .Call(dense_to_Csparse, from)) setAs("matrix", "CsparseMatrix", function(from) .Call(dense_to_Csparse, from)) ## function(from) { ## if(is.numeric(from)) ## .Call(dense_to_Csparse, .Call(dup_mMatrix_as_dgeMatrix, from)) ## else if(is.logical(from)) ## FIXME: this works, but maybe wastefully ## as(Matrix(from, sparse=TRUE), "CsparseMatrix") ## else stop('not-yet-implemented coercion to "CsparseMatrix"') ## }) ## special case needed in the Matrix function setAs("matrix", "dgCMatrix", function(from) { storage.mode(from) <- "double" .Call(dense_to_Csparse, from) }) setAs("numeric", "CsparseMatrix", function(from) .Call(dense_to_Csparse, .Call(dup_mMatrix_as_dgeMatrix, from))) setMethod("as.numeric", signature(x = "ddenseMatrix"), function(x, ...) as(x, "dgeMatrix")@x) ## -- see also ./Matrix.R e.g., for a show() method ## These methods are the 'fallback' methods for all dense numeric ## matrices in that they simply coerce the ddenseMatrix to a ## dgeMatrix. Methods for special forms override these. setMethod("norm", signature(x = "ddenseMatrix", type = "missing"), function(x, type, ...) norm(as(x, "dgeMatrix"))) setMethod("norm", signature(x = "ddenseMatrix", type = "character"), function(x, type, ...) norm(as(x, "dgeMatrix"), type)) setMethod("rcond", signature(x = "ddenseMatrix", norm = "missing"), function(x, norm, ...) rcond(as(x, "dgeMatrix"), ...)) setMethod("rcond", signature(x = "ddenseMatrix", norm = "character"), function(x, norm, ...) rcond(as(x, "dgeMatrix"), norm, ...)) ## Not really useful; now require *identical* class for result: ## setMethod("t", signature(x = "ddenseMatrix"), ## function(x) callGeneric(as(x, "dgeMatrix"))) ## "diag" --> specific methods for dge, dtr,dtp, dsy,dsp setMethod("solve", signature(a = "ddenseMatrix", b = "missing"), function(a, b, ...) solve(as(a, "dgeMatrix"))) for(.b in c("Matrix","ANY")) ## << against ambiguity notes setMethod("solve", signature(a = "ddenseMatrix", b = .b), function(a, b, ...) solve(as(a, "dgeMatrix"), b)) for(.b in c("matrix","numeric")) ## << against ambiguity notes setMethod("solve", signature(a = "ddenseMatrix", b = .b), function(a, b, ...) solve(as(a, "dgeMatrix"), Matrix(b))) rm(.b) setMethod("lu", signature(x = "ddenseMatrix"), function(x, ...) .set.factors(x, "LU", lu(as(x, "dgeMatrix"), ...))) setMethod("chol", signature(x = "ddenseMatrix"), cholMat) setMethod("determinant", signature(x = "ddenseMatrix", logarithm = "missing"), function(x, logarithm, ...) determinant(as(x, "dgeMatrix"))) setMethod("determinant", signature(x = "ddenseMatrix", logarithm = "logical"), function(x, logarithm, ...) determinant(as(x, "dgeMatrix"), logarithm)) ## now done for "dMatrix": ## setMethod("expm", signature(x = "ddenseMatrix"), ## function(x) callGeneric(as(x, "dgeMatrix"))) setMethod("Math", signature(x = "ddenseMatrix"), function(x) callGeneric(as(x, "dgeMatrix"))) .trilDense <- function(x, k = 0, ...) { k <- as.integer(k[1]) d <- dim(x) stopifnot(-d[1] <= k, k <= d[1]) # had k <= 0 ## returns "lower triangular" if k <= 0 && sqr .Call(dense_band, x, -d[1], k) } ## NB: have extra tril(), triu() methods for symmetric ["dsy" and "dsp"] and ## for triangular ["dtr" and "dtp"] setMethod("tril", "denseMatrix", .trilDense) setMethod("tril", "matrix", .trilDense) .triuDense <- function(x, k = 0, ...) { k <- as.integer(k[1]) d <- dim(x) stopifnot(-d[1] <= k, k <= d[1]) # had k >= 0 ## returns "upper triangular" if k >= 0 .Call(dense_band, x, k, d[2]) } setMethod("triu", "denseMatrix", .triuDense) setMethod("triu", "matrix", .triuDense) .bandDense <- function(x, k1, k2, ...) { k1 <- as.integer(k1[1]) k2 <- as.integer(k2[1]) dd <- dim(x) sqr <- dd[1] == dd[2] stopifnot(-dd[1] <= k1, k1 <= k2, k2 <= dd[2]) r <- .Call(dense_band, x, k1, k2) if (sqr && k1 < 0 && k1 == -k2 && isSymmetric(x)) ## symmetric forceSymmetric(r) else r } setMethod("band", "denseMatrix", .bandDense) setMethod("band", "matrix", .bandDense) setMethod("symmpart", signature(x = "ddenseMatrix"), function(x) .Call(ddense_symmpart, x)) setMethod("skewpart", signature(x = "ddenseMatrix"), function(x) .Call(ddense_skewpart, x)) setMethod("is.finite", signature(x = "dgeMatrix"), function(x) { if(all(ifin <- is.finite(x@x))) allTrueMat(x) else if(any(ifin)) { r <- as(x, "lMatrix") #-> logical x-slot r@x <- ifin as(r, "nMatrix") } else is.na_nsp(x) }) ## TODO? -- rather methods for specific subclasses of ddenseMatrix setMethod("is.finite", signature(x = "ddenseMatrix"), function(x) { if(all(ifin <- is.finite(x@x))) return(allTrueMat(x)) ## *NOT* dge, i.e., either triangular or symmetric ## (possibly packed): has finite 0-triangle cdx <- getClassDef(class(x)) r <- new(if(extends(cdx,"symmetricMatrix"))"nsyMatrix" else "ngeMatrix") r@Dim <- (d <- x@Dim) r@Dimnames <- x@Dimnames isPacked <- (le <- prod(d)) > length(ifin) r@x <- rep.int(TRUE, le) iTr <- indTri(d[1], upper= x@uplo == "U", diag= TRUE) if(isPacked) { ## x@x is "usable" r@x[iTr] <- ifin } else { r@x[iTr] <- ifin[iTr] } r }) setMethod("is.infinite", signature(x = "ddenseMatrix"), function(x) { if(any((isInf <- is.infinite(x@x)))) { r <- as(x, "lMatrix")#-> logical x-slot; 0 |--> FALSE r@x <- isInf as(r, "nMatrix")# often sparse .. better way? } else is.na_nsp(x) }) Matrix/R/triangularMatrix.R0000644000175100001440000000335012211131516015407 0ustar hornikusers#### Methods for the virtual class 'triangularMatrix' of triangular matrices #### Note that specific methods are in (8 different) ./?t?Matrix.R setAs("triangularMatrix", "symmetricMatrix", function(from) as(as(from, "generalMatrix"), "symmetricMatrix")) setAs("dgeMatrix", "triangularMatrix", function(from) asTri(from, "dtrMatrix")) setAs("lgeMatrix", "triangularMatrix", function(from) asTri(from, "ltrMatrix")) setAs("ngeMatrix", "triangularMatrix", function(from) asTri(from, "ntrMatrix")) .tril.tr <- function(x, k = 0, ...) { # are always square k <- as.integer(k[1]) dd <- dim(x) stopifnot(-dd[1] <= k, k <= dd[1]) # had k <= 0 if(k == 0 && x@uplo == "L") x else { ## more to do if(x@diag == "U") x <- .diagU2N(x, class(x), checkDense = TRUE) callNextMethod() } } .triu.tr <- function(x, k = 0, ...) { # are always square k <- as.integer(k[1]) dd <- dim(x) stopifnot(-dd[1] <= k, k <= dd[1]) # had k >= 0 if(k == 0 && x@uplo == "U") x else { ## more to do if(x@diag == "U") x <- .diagU2N(x, class(x), checkDense = TRUE) callNextMethod() } } ## In order to evade method dispatch ambiguity (with [CTR]sparse* and ddense*), ## but still remain "general" ## we use this hack instead of signature x = "triangularMatrix" : trCls <- names(getClass("triangularMatrix")@subclasses) trCls. <- trCls[grep(".t.Matrix", trCls)] # not "*Cholesky", "*Kaufman" .. for(cls in trCls.) { setMethod("tril", cls, .tril.tr) setMethod("triu", cls, .triu.tr) } ## ditto here: for(cls in trCls) setMethod("isTriangular", signature(object = cls), function(object, ...) TRUE) ## instead of just for .... signature(object = "triangularMatrix") rm(trCls, cls) Matrix/R/dgCMatrix.R0000644000175100001440000001205612215114135013741 0ustar hornikusers#### Sparse Matrices in Compressed column-oriented format ### contains = "dsparseMatrix", "CsparseMatrix" ## Specific conversions, should they be necessary. Better to convert as ## as(x, "TsparseMatrix") or as(x, "denseMatrix") ## Moved to ./Csparse.R : ## setAs("dgCMatrix", "dgTMatrix", .... ## setAs("dgCMatrix", "dgeMatrix", .... ## setAs("dgeMatrix", "dgCMatrix", .... setAs("dgCMatrix", "ngCMatrix", function(from) .Call(Csparse_to_nz_pattern, from, FALSE)) ## rather use Csparse* to lsparse* in ./lsparseMatrix.R , ## but this is for "back-compatibility" (have had tests for it..): setAs("dgCMatrix", "lgCMatrix", function(from) { ## FIXME use .Call() too! r <- new("lgCMatrix") r@x <- as.logical(from@x) ## and copy the other slots for(nm in c("i", "p", "Dim", "Dimnames")) slot(r, nm) <- slot(from, nm) r }) setMethod("image", "dgCMatrix", function(x, ...) { x <- as(x, "dgTMatrix") callGeneric() }) ## Group Methods, see ?Arith (e.g.) ## ----- ## ## "Arith" is now in ./Ops.R ## ## "Math" is up in ./Csparse.R ## ## "Math2" is up in ./dMatrix.R ###---- end {Group Methods} ----------------- ## "[<-" methods { setReplaceMethod()s } are now in ./Csparse.R ## setMethod("writeHB", signature(obj = "dgCMatrix"), ## function(obj, file, ...) { ## .Deprecated("writeMM") ## .Call(Matrix_writeHarwellBoeing, obj, ## as.character(file), "DGC") ## }) ##-> ./colSums.R for colSums,... rowMeans setMethod("t", signature(x = "dgCMatrix"), function(x) .Call(Csparse_transpose, x, FALSE), valueClass = "dgCMatrix") setMethod("determinant", signature(x = "dgCMatrix", logarithm = "logical"), detSparseLU) # using mkDet() --> ./Auxiliaries.R setMethod("qr", signature(x = "dgCMatrix"), function(x, tol = 1e-07, LAPACK = FALSE) .Call(dgCMatrix_QR, # -> cs_sqr() and cs_qr() >> ../src/dgCMatrix.c x, ## order = if(!is.null(v <- getOption("Matrix.verbose")) && v >= 1) -1L else TRUE)) setMethod("qr", signature(x = "sparseMatrix"), function(x, ...) qr(as(as(as(x, "CsparseMatrix"), "dsparseMatrix"), "dgCMatrix"), ...)) LU.dgC <- function(x, errSing = TRUE, order = TRUE, tol = 1.0, ...) .Call(dgCMatrix_LU, x, order, tol, errSing) setMethod("lu", signature(x = "dgCMatrix"), LU.dgC) setMethod("lu", signature(x = "sparseMatrix"), function(x, ...) .set.factors(x, "lu", lu(as(as(as(x, "CsparseMatrix"), "dsparseMatrix"), "dgCMatrix"), ...))) .solve.sparse.dgC <- function(a, b, tol = .Machine$double.eps) { ## @MM: see also solveSparse() in ~/R/MM/Pkg-ex/Matrix/Doran-A.R lu.a <- LU.dgC(a) if(tol > 0) { rU <- range(abs(diag(lu.a@U))) if(rU[1] / rU[2] < tol) stop(gettextf("LU computationally singular: ratio of extreme entries in |diag(U)| = %9.4g", rU[1] / rU[2]), domain=NA) } b.isMat <- if((b.miss <- missing(b))) { ## default b = Identity = Diagonal(nrow(a)), however more efficiently b <- .sparseDiagonal(dim(a)[1L]) TRUE } else !is.null(dim(b)) ## bp := P %*% b bp <- if(b.isMat) b[lu.a@p+1L, ] else b[lu.a@p+1L] ## R:= U^{-1} L^{-1} P b R <- solve(lu.a@U, solve(lu.a@L, bp)) ## result = Q'R = Q' U^{-1} L^{-1} P b = A^{-1} b, as A = P'LUQ R[invPerm(lu.a@q, zero.p=TRUE), ] } ## FIXME: workaround, till .Call(dgCMatrix_matrix_solve, a, b, sparse=TRUE) works: .solve.dgC <- function(a, b, sparse, tol = .Machine$double.eps) if(sparse) .solve.sparse.dgC(a, b, tol=tol) else .Call(dgCMatrix_matrix_solve, a, b, FALSE) .solve.dgC.mat <- function(a, b, sparse=FALSE, tol = .Machine$double.eps, ...) { chk.s(...) if(sparse) .solve.sparse.dgC(a, b, tol=tol) else .Call(dgCMatrix_matrix_solve, a, b, FALSE) } setMethod("solve", signature(a = "dgCMatrix", b = "matrix"), .solve.dgC.mat) setMethod("solve", signature(a = "dgCMatrix", b = "ddenseMatrix"), .solve.dgC.mat) setMethod("solve", signature(a = "dgCMatrix", b = "dsparseMatrix"), function(a, b, sparse=NA, tol = .Machine$double.eps, ...) { chk.s(...) if(is.na(sparse)) { if(isSymmetric(a)) ## TODO: fast cholmod_symmetric() for Cholesky return(solve(forceCspSymmetric(a, isTri=FALSE), b)) #-> sparse result ## else sparse <- FALSE # (old default) } ## FIXME: be better when sparse=TRUE (?) .solve.dgC(a, as(b, "denseMatrix"), tol=tol, sparse=sparse) }) ## This is a really dumb method but some people apparently want it ## (MM: a bit less dumb now with possibility of staying sparse) setMethod("solve", signature(a = "dgCMatrix", b = "missing"), function(a, b, sparse=NA, tol = .Machine$double.eps, ...) { chk.s(...) if(is.na(sparse)) { if(isSymmetric(a)) ## TODO: fast cholmod_symmetric() for Cholesky return(solve(forceCspSymmetric(a, isTri=FALSE), b = Diagonal(nrow(a)))) #-> sparse result ## else sparse <- FALSE # (old default) } if(sparse) .solve.sparse.dgC(a, tol=tol) # -> "smart" diagonal b else .Call(dgCMatrix_matrix_solve, a, b=diag(nrow(a)), FALSE) }) Matrix/R/bandSparse.R0000644000175100001440000000615312203431175014145 0ustar hornikusersbandSparse <- function(n, m = n, k, diagonals, symmetric = FALSE, giveCsparse = TRUE) { ## Purpose: Compute a band-matrix by speciyfying its (sub-)diagonal(s) ## ---------------------------------------------------------------------- ## Arguments: (n,m) : Matrix dimension ## k : integer vector of "diagonal numbers", with identical ## meaning as in band(*, k) ## diagonals: (optional!) list of (sub/super)diagonals ## symmetric: if TRUE, specify only upper or lower triangle; ## ---------------------------------------------------------------------- ## Author: Martin Maechler, Date: 20 Feb 2009, 22:42 if(use.x <- !missing(diagonals)) # when specified, must be matrix or list diag.isMat <- is.matrix(diagonals) len.k <- length(k) stopifnot(!use.x || is.list(diagonals) || diag.isMat, k == as.integer(k), n == as.integer(n), m == as.integer(m)) k <- as.integer(k) n <- as.integer(n) m <- as.integer(m) stopifnot(n >= 0, m >= 0, -n+1 <= k, k <= m - 1) if(use.x) { if(diag.isMat) { if(ncol(diagonals) != len.k) stop(gettextf("'diagonals' matrix must have %d columns (= length(k) )", len.k), domain=NA) getD <- function(j) diagonals[,j] } else { ## is.list(diagonals): if(length(diagonals) != len.k) stop(gettextf("'diagonals' must have the same length (%d) as 'k'", len.k), domain=NA) getD <- function(j) diagonals[[j]] } } if(symmetric && any(k < 0) && any(k > 0)) stop("for symmetric band matrix, only specify upper or lower triangle\n hence, all k must have the same sign") dims <- c(n,m) k.lengths <- ## This is a bit "ugly"; I got the cases "by inspection" if(n >= m) { ifelse(k >= m-n, m - pmax(0,k), n+k) } else { ## n < m ifelse(k >= -n+1, n + pmin(0,k), m-k) } i <- j <- integer(sum(k.lengths)) if(use.x) x <- if(len.k > 0) # carefully getting correct type/mode rep.int(getD(1)[1], length(i)) off.i <- 0L for(s in seq_len(len.k)) { kk <- k[s] ## *is* integer l.kk <- k.lengths[s] ## == length of (sub-)diagonal kk ii1 <- seq_len(l.kk) ind <- ii1 + off.i if(kk >= 0) { i[ind] <- ii1 j[ind] <- ii1 + kk } else { ## k < 0 i[ind] <- ii1 - kk j[ind] <- ii1 } if(use.x) { xx <- getD(s) if(length(xx) < l.kk) warning(gettextf("the %d-th (sub)-diagonal (k = %d) is too short; filling with NA's", s, kk), domain=NA) x[ind] <- xx[ii1] } off.i <- off.i + l.kk } if(symmetric) { ## we should have smarter sparseMatrix() UpLo <- if(min(k) >= 0) "U" else "L" T <- if(use.x) { if(is.integer(x)) x <- as.double(x) cc <- paste0(.M.kind(x), "sTMatrix") new(cc, i= i-1L, j= j-1L, x = x, Dim= dims, uplo=UpLo) } else new("nsTMatrix", i= i-1L, j= j-1L, Dim= dims, uplo=UpLo) if(giveCsparse) as(T, "CsparseMatrix") else T } else { ## general, not symmetric if(use.x) sparseMatrix(i=i, j=j, x=x, dims=dims, giveCsparse=giveCsparse) else sparseMatrix(i=i, j=j, dims=dims, giveCsparse=giveCsparse) } } Matrix/R/MatrixFactorization.R0000644000175100001440000000241710772211561016067 0ustar hornikusers#### The "mother" of all Matrix factorizations ## use a "fits all" bail-out method -- eventually this should not happen anymore setMethod("expand", "MatrixFactorization", function(x, ...) .bail.out.1(.Generic, class(x))) setMethod("show", "MatrixFactorization", function(object) { ## cheap one -- can have better for sub-classes ## cl <- class(object) ## cat(sprintf("'MatrixFactorization' of class \"%s\"\n", cl)) cat("'MatrixFactorization' of ") str(object) }) setMethod("show", "BunchKaufman", function(object) { cat("'Bunch-Kaufman' factorization of ") str(object) }) setMethod("show", "pBunchKaufman", function(object) { cat("packed 'Bunch-Kaufman' factorization of ") str(object) }) setMethod("dim", "MatrixFactorization", function(x) x@Dim) ## e.g., for (CHMfactor, ): setMethod("solve", signature(a = "MatrixFactorization", b = "numeric"), function(a, b, ...) callGeneric(a, Matrix(b))) ## catch others, otherwise base::solve is. setMethod("solve", signature(a = "MatrixFactorization", b = "ANY"), function(a, b, ...) .bail.out.2("solve", class(a), class(b))) setMethod("solve", signature(a = "MatrixFactorization", b = "missing"), function(a, b, ...) .bail.out.1("solve", class(a))) Matrix/R/dtpMatrix.R0000644000175100001440000000537512254575000014046 0ustar hornikusers#### Triangular Packed Matrices -- Coercion and Methods setAs("dtpMatrix", "dtrMatrix", function(from) .Call(dtpMatrix_as_dtrMatrix, from)) ## Is this needed? already have coercion to "TsparseMatrix" {FIXME} setAs("dtpMatrix", "dtTMatrix", function(from) { x <- as(from, "TsparseMatrix") cld <- getClassDef(class(x)) if(extends(cld, "dtTMatrix")) x else { ## triangularity lost: should not have happened warning("inefficient coercion (lost triangularity); please report") gT2tT(as(x, "dgTMatrix"), uplo = from@uplo, diag = from@diag, toClass = "dtTMatrix", do.n = FALSE) } }) setAs("dtpMatrix", "matrix", function(from) as(as(from, "dtrMatrix"), "matrix")) setAs("matrix", "dtpMatrix", function(from) as(as(from, "dtrMatrix"), "dtpMatrix")) setAs("pCholesky", "lMatrix", function(from) as(as(from, "dtpMatrix"), "lMatrix")) setAs("pBunchKaufman", "lMatrix", function(from) as(as(from, "dtpMatrix"), "lMatrix")) setMethod("determinant", signature(x = "dtpMatrix", logarithm = "missing"), function(x, logarithm, ...) determinant(x, TRUE)) setMethod("determinant", signature(x = "dtpMatrix", logarithm = "logical"), function(x, logarithm, ...) mkDet(diag(x), logarithm)) setMethod("diag", signature(x = "dtpMatrix"), function(x, nrow, ncol) .Call(dtpMatrix_getDiag, x), valueClass = "numeric") setMethod("diag<-", signature(x = "dtpMatrix"), function(x, value) { .Call(dtpMatrix_setDiag, if(x@diag == "U") .dense.diagU2N(x, "d", isPacked=TRUE) else x, value) }) setMethod("norm", signature(x = "dtpMatrix", type = "character"), function(x, type, ...) .Call(dtpMatrix_norm, x, type), valueClass = "numeric") setMethod("norm", signature(x = "dtpMatrix", type = "missing"), function(x, type, ...) .Call(dtpMatrix_norm, x, "O"), valueClass = "numeric") setMethod("rcond", signature(x = "dtpMatrix", norm = "character"), function(x, norm, ...) .Call(dtpMatrix_rcond, x, norm), valueClass = "numeric") setMethod("rcond", signature(x = "dtpMatrix", norm = "missing"), function(x, norm, ...) .Call(dtpMatrix_rcond, x, "O"), valueClass = "numeric") setMethod("solve", signature(a = "dtpMatrix", b="missing"), function(a, b, ...) .Call(dtpMatrix_solve, a), valueClass = "dtpMatrix") setMethod("solve", signature(a = "dtpMatrix", b="ddenseMatrix"), function(a, b, ...) .Call(dtpMatrix_matrix_solve, a, b), valueClass = "dgeMatrix") setMethod("solve", signature(a = "dtpMatrix", b="matrix"), function(a, b, ...) .Call(dtpMatrix_matrix_solve, a, b), valueClass = "dgeMatrix") ## FIXME: speed up setMethod("t", signature(x = "dtpMatrix"), function(x) as(t(as(x, "dtrMatrix")), "dtpMatrix"), valueClass = "dtpMatrix") Matrix/R/lsTMatrix.R0000644000175100001440000000163011004710614014001 0ustar hornikusers#### Logical Sparse Symmetric Matrices in Triplet format ### contains = "lsparseMatrix" setAs("lsTMatrix", "matrix", function(from) as(as(from, "lgTMatrix"), "matrix")) setAs("lsTMatrix", "lgCMatrix", # for diag function(from) as(as(from, "lsCMatrix"), "lgCMatrix")) setAs("lsTMatrix", "lgTMatrix", function(from) .Call(lsTMatrix_as_lgTMatrix, from)) if(FALSE) # should use as(., "dMatrix") setAs("lsTMatrix", "dsTMatrix", function(from) new("dsTMatrix", i = from@i, j = from@j, uplo = from@uplo, x = as.double(from@x), # *not* just 1; from@x *can* have FALSE Dim = from@Dim, Dimnames = from@Dimnames)) setAs("lsTMatrix", "lsyMatrix", function(from) .Call(lsTMatrix_as_lsyMatrix, from)) setMethod("t", "lsTMatrix", function(x) new("lsTMatrix", Dim = x@Dim, Dimnames = x@Dimnames, i = x@j, j = x@i, x = x@x, uplo = if (x@uplo == "U") "L" else "U")) Matrix/R/ntCMatrix.R0000644000175100001440000000320012213574105013764 0ustar hornikusers#### Logical Sparse Triangular Matrices in Compressed column-oriented format setAs("ntCMatrix", "matrix", function(from) as(copyClass(diagU2N(from), "ngCMatrix"), "matrix")) setAs("matrix", "ntCMatrix", function(from) as(as(from, "dtCMatrix"), "ntCMatrix")) setAs("ntCMatrix", "TsparseMatrix", function(from) .Call(Csparse_to_Tsparse, from, TRUE)) setAs("ntCMatrix", "ngCMatrix", function(from) copyClass(diagU2N(from), "ngCMatrix")) ## --- these now happen using "nCsparseMatrix" -- in ./ngCMatrix.R ## ## .ntC2d <- function(from) ## new("dtCMatrix", i = from@i, p = from@p, ## x = rep.int(1, length(from@i)), uplo = from@uplo, ## diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames) ## .ntC2l <- function(from) ## new("ltCMatrix", i = from@i, p = from@p, ## x = rep.int(TRUE, length(from@i)), uplo = from@uplo, ## diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames) ## Not needed, once we use "nCsparseMatrix" (-> ./ngCMatrix.R ): setAs("ntCMatrix", "dMatrix", nC2d) setAs("ntCMatrix", "dsparseMatrix", nC2d) setAs("ntCMatrix", "dtCMatrix", nC2d) ## setAs("ntCMatrix", "lMatrix", nC2l) setAs("ntCMatrix", "lsparseMatrix", nC2l) setAs("ntCMatrix", "ltCMatrix", nC2l) ## rm(.ntC2d,.ntC2l) # don't even keep "hidden" setAs("ngCMatrix", "ntCMatrix", # to triangular, needed for triu,.. function(from) as(as(as(from, "TsparseMatrix"), "ntTMatrix"), "ntCMatrix")) ## setAs("ntCMatrix", "generalMatrix", ## function(from) ......) ## setMethod("t", signature(x = "ntCMatrix"), ## function(x) .Call(ntCMatrix_trans, x), ## valueClass = "ntCMatrix") Matrix/R/nsparseMatrix.R0000644000175100001440000000332012164774573014736 0ustar hornikusers#### Superclass Methods for all sparse nonzero-pattern matrices setAs("CsparseMatrix", "nsparseMatrix", function(from) .Call(Csparse_to_nz_pattern, from, is(from, "triangularMatrix"))) setAs("CsparseMatrix", "nMatrix", function(from) .Call(Csparse_to_nz_pattern, from, is(from, "triangularMatrix"))) setAs("nsparseMatrix", "dsparseMatrix", function(from) as(from, "dMatrix")) ###------- Work via as(*, lgC) : ------------ setMethod("is.na", signature(x = "nsparseMatrix"), is.na_nsp) if(getRversion() > "3.1.0") setMethod("anyNA", signature(x = "nsparseMatrix"), function(x) FALSE) setMethod("all", signature(x = "nsparseMatrix"), function(x, ..., na.rm = FALSE) { pd <- prod(d <- dim(x)) if(pd == 0) return(TRUE) cld <- getClassDef(class(x)) if(extends(cld, "triangularMatrix")) return(FALSE) ## else if(extends(cld, "TsparseMatrix")) cld <- getClassDef(class(x <- as(x, "CsparseMatrix"))) ## now have Csparse or Rsparse: length of index slot = no.{TRUE} l.x <- length(if(extends(cld, "CsparseMatrix")) x@i else x@j) (l.x == pd) || ## fully non-zero (extends(cld, "symmetricMatrix") && l.x == choose(d[1]+1, 2)) ## else FALSE }) setMethod("any", signature(x = "nsparseMatrix"), function(x, ..., na.rm = FALSE) { if(any(dim(x) == 0)) return(FALSE) cld <- getClassDef(class(x)) if(extends(cld, "triangularMatrix") && x@diag == "U") TRUE # unit-diagonal else if(extends(cld, "CsparseMatrix") || extends(cld, "TsparseMatrix")) length(x@i) > 0 else # RsparseMatrix length(x@j) > 0 }) setMethod("image", "nsparseMatrix", function(x, ...) image(as(x,"dMatrix"))) Matrix/R/pMatrix.R0000644000175100001440000000671112211567675013525 0ustar hornikusers#### Permutation Matrices -- Coercion and Methods ### NB "pMatrix" extends "indMatrix" and inherits methods --> indMatrix.R ## The typical 'constructor' : coerce from 'index' setAs("integer", "pMatrix", function(from) { nn <- names(from) new("pMatrix", Dim = rep.int(length(from), 2L), Dimnames = list(nn,nn), perm = from) }) setAs("numeric", "pMatrix", function(from) if(all(from == (i <- as.integer(from)))) as(i, "pMatrix") else stop("coercion to \"pMatrix\" only works from integer numeric")) setAs("nMatrix", "pMatrix", function(from) { from <- as(as(from, "TsparseMatrix"), "ngTMatrix") n <- (d <- from@Dim)[1] if(n != d[2]) stop("not a square matrix") if(length(i <- from@i) != n) stop("the number of non-zero entries differs from nrow(.)") if((need.sort <- is.unsorted(i))) { ii <- sort.list(i) i <- i[ii] } if(n >= 1 && !identical(i, 0:(n - 1))) stop("must have exactly one non-zero entry per row") new("pMatrix", ## validity checking checks the 'perm' slot: perm = 1L + if(need.sort) from@j[ii] else from@j, Dim = d, Dimnames = from@Dimnames) }) setAs("matrix", "pMatrix", function(from) as(as(from, "nMatrix"), "pMatrix")) setMethod("solve", signature(a = "pMatrix", b = "missing"), function(a, b, ...) { a@perm <- invPerm(a@perm) a@Dimnames <- a@Dimnames[2:1] a }) setMethod("solve", signature(a = "pMatrix", b = "Matrix"), function(a, b, ...) crossprod(a, b)) setMethod("solve", signature(a = "pMatrix", b = "matrix"), function(a, b, ...) crossprod(a, b)) setMethod("solve", signature(a = "Matrix", b = "pMatrix"), function(a, b, ...) ## Or alternatively solve(a, as(b, "CsparseMatrix")) solve(a)[, invPerm(b@perm)]) setMethod("determinant", signature(x = "pMatrix", logarithm = "logical"), function(x, logarithm, ...) { if(any(x@Dim == 0)) mkDet(numeric(0)) else mkDet(logarithm=logarithm, ldet = 0, sig = signPerm(x@perm)) }) ## t(pM) is == the inverse pM^(-1): setMethod("t", signature(x = "pMatrix"), function(x) solve(x)) setMethod("%*%", signature(x = "matrix", y = "pMatrix"), function(x, y) { mmultCheck(x,y); x[, invPerm(y@perm)] }) setMethod("%*%", signature(x = "Matrix", y = "pMatrix"), function(x, y) { mmultCheck(x,y); x[, invPerm(y@perm)] }) setMethod("%*%", signature(x = "pMatrix", y = "pMatrix"), function(x, y) { stopifnot(identical(d <- x@Dim, y@Dim)) ## n <- d[1] ## FIXME: dimnames dealing: as with S3 matrix's %*% x@perm <- x@perm[y@perm] x }) setMethod("crossprod", signature(x = "pMatrix", y = "matrix"), function(x, y) { mmultCheck(x,y, 2L); y[invPerm(x@perm) ,]}) setMethod("crossprod", signature(x = "pMatrix", y = "Matrix"), function(x, y) { mmultCheck(x,y, 2L); y[invPerm(x@perm) ,]}) setMethod("crossprod", signature(x = "pMatrix", y = "pMatrix"), function(x, y) { stopifnot(identical(x@Dim, y@Dim)) x@perm <- invPerm(x@perm)[y@perm] x }) setMethod("tcrossprod", signature(x = "pMatrix", y = "pMatrix"), function(x, y) { stopifnot(identical(x@Dim, y@Dim)) x@perm <- x@perm[invPerm(y@perm)] x }) setMethod("crossprod", signature(x = "pMatrix", y = "missing"), function(x, y=NULL) Diagonal(nrow(x))) setMethod("tcrossprod", signature(x = "pMatrix", y = "missing"), function(x, y=NULL) Diagonal(nrow(x))) Matrix/R/dppMatrix.R0000644000175100001440000000555712203431175014042 0ustar hornikusers#### Positive-definite Symmetric Packed Matrices -- Coercion and Methods setAs("dppMatrix", "dpoMatrix", function(from) copyClass(.Call(dspMatrix_as_dsyMatrix, from), "dpoMatrix", sNames = c("x", "Dim", "Dimnames", "uplo", "factors"))) dpp2sC <- function(from) as(.Call(dspMatrix_as_dsyMatrix, from), "dsCMatrix") ## setAs("dppMatrix", "dsCMatrix", dpp2sC) setAs("dppMatrix", "CsparseMatrix", dpp2sC) setAs("dppMatrix", "sparseMatrix", dpp2sC) setAs("dppMatrix", "lMatrix", function(from) as(as(from, "dsyMatrix"), "lMatrix")) setAs("dppMatrix", "nMatrix", function(from) as(as(from, "dsyMatrix"), "nMatrix")) to_dpp <- function(from) as(as(as(as(from, "symmetricMatrix"), "dMatrix"), "dpoMatrix"), "dppMatrix") setAs("Matrix", "dppMatrix", to_dpp)# some may fail, but this tries setAs("matrix", "dppMatrix", to_dpp) setAs("dspMatrix", "dppMatrix", function(from){ if(is.null(tryCatch(.Call(dppMatrix_chol, from), error = function(e) NULL))) stop("not a positive definite matrix") ## else copyClass(from, "dppMatrix", sNames = c("x", "Dim", "Dimnames", "uplo", "factors")) }) setMethod("chol", signature(x = "dppMatrix"), function(x, pivot, LINPACK) .Call(dppMatrix_chol, x)) setMethod("determinant", signature(x = "dppMatrix", logarithm = "logical"), mkDet.via.chol) setMethod("determinant", signature(x = "dppMatrix", logarithm = "missing"), function(x, logarithm, ...) mkDet.via.chol(x, logarithm=TRUE)) setMethod("rcond", signature(x = "dppMatrix", norm = "character"), function(x, norm, ...) .Call(dppMatrix_rcond, x, norm), valueClass = "numeric") setMethod("rcond", signature(x = "dppMatrix", norm = "missing"), function(x, norm, ...) .Call(dppMatrix_rcond, x, "O"), valueClass = "numeric") setMethod("solve", signature(a = "dppMatrix", b = "missing"), function(a, b, ...) .Call(dppMatrix_solve, a), valueClass = "dppMatrix") setMethod("solve", signature(a = "dppMatrix", b = "dgeMatrix"), function(a, b, ...) .Call(dppMatrix_matrix_solve, a, b), valueClass = "dgeMatrix") setMethod("solve", signature(a = "dppMatrix", b = "matrix"), function(a, b, ...) .Call(dppMatrix_matrix_solve, a, b), valueClass = "dgeMatrix") ##setMethod("solve", signature(a = "dppMatrix", b = "numeric"), ## function(a, b, ...) ## .Call(dppMatrix_matrix_solve, a, as.matrix(b)), ## valueClass = "dgeMatrix") setMethod("solve", signature(a = "dppMatrix", b = "integer"), function(a, b, ...) { storage.mode(b) <- "double" .Call(dppMatrix_matrix_solve, a, as.matrix(b)) }, valueClass = "dgeMatrix") setMethod("t", signature(x = "dppMatrix"), function(x) as(t(as(x, "dspMatrix")), "dppMatrix"), valueClass = "dppMatrix") Matrix/R/diagMatrix.R0000644000175100001440000012102012254575000014145 0ustar hornikusers#### All methods for "diagonalMatrix" and its subclasses, #### currently "ddiMatrix", "ldiMatrix" ## Purpose: Constructor of diagonal matrices -- ~= diag() , ## but *not* diag() extractor! Diagonal <- function(n, x = NULL) { ## Allow Diagonal(4), Diagonal(x=1:5), and Diagonal(4, TRUE) n <- if(missing(n)) length(x) else { stopifnot(length(n) == 1, n == as.integer(n), n >= 0) as.integer(n) } if(missing(x)) ## unit diagonal matrix new("ddiMatrix", Dim = c(n,n), diag = "U") else { lx <- length(x) lx.1 <- lx == 1L stopifnot(lx.1 || lx == n) # but keep 'x' short for now if(is.logical(x)) cl <- "ldiMatrix" else if(is.numeric(x)) { cl <- "ddiMatrix" x <- as.numeric(x) } else if(is.complex(x)) { cl <- "zdiMatrix" # will not yet work } else stop("'x' has invalid data type") if(lx.1 && !is.na(x) && x == 1) # cheap check for uni-diagonal.. new(cl, Dim = c(n,n), diag = "U") else new(cl, Dim = c(n,n), diag = "N", x = if(lx.1) rep.int(x,n) else x) } } .sparseDiagonal <- function(n, x = 1, uplo = "U", shape = if(missing(cols)) "t" else "g", unitri, kind, cols = if(n) 0:(n - 1L) else integer(0)) { stopifnot(n == (n. <- as.integer(n)), (n <- n.) >= 0) if(!(mcols <- missing(cols))) stopifnot(0 <= (cols <- as.integer(cols)), cols < n) m <- length(cols) if(missing(kind)) kind <- if(is.double(x)) "d" else if(is.logical(x)) "l" else { ## for now storage.mode(x) <- "double" "d" } else stopifnot(any(kind == c("d","l","n"))) stopifnot(is.character(shape), nchar(shape) == 1, any(shape == c("t","s","g"))) # triangular / symmetric / general if((missing(unitri) || unitri) && shape == "t" && (mcols || cols == 0:(n-1L)) && ((any(kind == c("l", "n")) && allTrue(x)) || ( kind == "d" && allTrue(x == 1)))) { ## uni-triangular new(paste0(kind,"tCMatrix"), Dim = c(n,n), uplo = uplo, diag = "U", p = rep.int(0L, n+1L)) } else if(kind == "n") { if(shape == "g") new("ngCMatrix", Dim = c(n,m), i = cols, p = 0:m) else new(paste0("n", shape, "CMatrix"), Dim = c(n,m), uplo = uplo, i = cols, p = 0:m) } else { ## kind != "n" -- have x slot : if((lx <- length(x)) == 1) x <- rep.int(x, m) else if(lx != m) stop("length(x) must be either 1 or #{cols}") if(shape == "g") new(paste0(kind, "gCMatrix"), Dim = c(n,m), x = x, i = cols, p = 0:m) else new(paste0(kind, shape, "CMatrix"), Dim = c(n,m), uplo = uplo, x = x, i = cols, p = 0:m) } } ## Pkg 'spdep' had (relatively slow) versions of this as_dsCMatrix_I() .symDiagonal <- function(n, x = rep.int(1,n), uplo = "U") .sparseDiagonal(n, x, uplo, shape = "s") # instead of diagU2N(as(Diagonal(n), "CsparseMatrix")), diag = "N" in any case: .trDiagonal <- function(n, x = 1, uplo = "U", unitri=TRUE) .sparseDiagonal(n, x, uplo, shape = "t", unitri=unitri) ## This is modified from a post of Bert Gunter to R-help on 1 Sep 2005. ## Bert's code built on a post by Andy Liaw who most probably was influenced ## by earlier posts, notably one by Scott Chasalow on S-news, 16 Jan 2002 ## who posted his bdiag() function written in December 1995. if(FALSE)##--- no longer used: .bdiag <- function(lst) { ## block-diagonal matrix [a dgTMatrix] from list of matrices stopifnot(is.list(lst), length(lst) >= 1) dims <- vapply(lst, dim, 1L, USE.NAMES=FALSE) ## make sure we had all matrices: if(!(is.matrix(dims) && nrow(dims) == 2)) stop("some arguments are not matrices") csdim <- rbind(rep.int(0L, 2), apply(dims, 1, cumsum)) r <- new("dgTMatrix") r@Dim <- as.integer(csdim[nrow(csdim),]) add1 <- matrix(1:0, 2,2) for(i in seq_along(lst)) { indx <- apply(csdim[i:(i+1),] + add1, 2, function(n) n[1]:n[2]) if(is.null(dim(indx))) ## non-square matrix r[indx[[1]],indx[[2]]] <- lst[[i]] else ## square matrix r[indx[,1], indx[,2]] <- lst[[i]] } r } ## expand() needed something like bdiag() for lower-triangular ## (Tsparse) Matrices; hence Doug Bates provided a much more efficient ## implementation for those; now extended and generalized: .bdiag <- function(lst) { ## block-diagonal matrix [a dgTMatrix] from list of matrices stopifnot(is.list(lst), (nl <- length(lst)) >= 1) Tlst <- lapply(lapply(lst, as_Csp2), # includes "diagU2N" as, "TsparseMatrix") if(nl == 1) return(Tlst[[1]]) ## else i_off <- c(0L, cumsum(vapply(Tlst, nrow, 1L))) j_off <- c(0L, cumsum(vapply(Tlst, ncol, 1L))) clss <- vapply(Tlst, class, "") typ <- substr(clss, 2, 2) knd <- substr(clss, 1, 1) sym <- typ == "s" # symmetric ones tri <- typ == "t" # triangular ones use.n <- any(is.n <- knd == "n") if(use.n && !(use.n <- all(is.n))) { Tlst[is.n] <- lapply(Tlst[is.n], as, "lMatrix") knd [is.n] <- "l" } use.l <- !use.n && all(knd == "l") if(all(sym)) { ## result should be *symmetric* uplos <- vapply(Tlst, slot, ".", "uplo") ## either "U" or "L" tLU <- table(uplos)# of length 1 or 2 .. if(length(tLU) == 1) { ## all "U" or all "L" useU <- uplos[1] == "U" } else { ## length(tLU) == 2, counting "L" and "U" useU <- diff(tLU) >= 0 if(useU && (hasL <- tLU[1] > 0)) Tlst[hasL] <- lapply(Tlst[hasL], t) else if(!useU && (hasU <- tLU[2] > 0)) Tlst[hasU] <- lapply(Tlst[hasU], t) } if(use.n) { ## return nsparseMatrix : r <- new("nsTMatrix") } else { r <- new(paste0(if(use.l) "l" else "d", "sTMatrix")) r@x <- unlist(lapply(Tlst, slot, "x")) } r@uplo <- if(useU) "U" else "L" } else if(all(tri) && { ULs <- vapply(Tlst, slot, ".", "uplo")## "U" or "L" all(ULs[1L] == ULs[-1L]) } ## all upper or all lower ){ ## *triangular* result if(use.n) { ## return nsparseMatrix : r <- new("ntTMatrix") } else { r <- new(paste0(if(use.l) "l" else "d", "tTMatrix")) r@x <- unlist(lapply(Tlst, slot, "x")) } r@uplo <- ULs[1L] } else { if(any(sym)) Tlst[sym] <- lapply(Tlst[sym], as, "generalMatrix") if(use.n) { ## return nsparseMatrix : r <- new("ngTMatrix") } else { r <- new(paste0(if(use.l) "l" else "d", "gTMatrix")) r@x <- unlist(lapply(Tlst, slot, "x")) } } r@Dim <- c(i_off[nl+1], j_off[nl + 1]) r@i <- unlist(lapply(1:nl, function(k) Tlst[[k]]@i + i_off[k])) r@j <- unlist(lapply(1:nl, function(k) Tlst[[k]]@j + j_off[k])) r } bdiag <- function(...) { if((nA <- nargs()) == 0) return(new("dgCMatrix")) if(nA == 1 && !is.list(...)) return(as(..., "CsparseMatrix")) alis <- if(nA == 1 && is.list(..1)) ..1 else list(...) if(length(alis) == 1) return(as(alis[[1]], "CsparseMatrix")) ## else : two or more arguments as(.bdiag(alis), "CsparseMatrix") } .diag2tT <- function(from, uplo = "U", kind = .M.kind(from)) { ## to triangular Tsparse i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L new(paste0(kind, "tTMatrix"), diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames, uplo = uplo, x = from@x, # <- ok for diag = "U" and "N" (!) i = i, j = i) } .diag2sT <- function(from, uplo = "U", kind = .M.kind(from)) { ## to symmetric Tsparse n <- from@Dim[1] i <- seq_len(n) - 1L new(paste0(kind, "sTMatrix"), Dim = from@Dim, Dimnames = from@Dimnames, i = i, j = i, uplo = uplo, x = if(from@diag == "N") from@x else ## "U"-diag rep.int(switch(kind, "d" = 1., "l" =, "n" = TRUE, ## otherwise stop(gettextf("%s kind not yet implemented", sQuote(kind)), domain=NA)), n)) } ## diagonal -> triangular, upper / lower depending on "partner": diag2tT.u <- function(d, x, kind = .M.kind(d)) .diag2tT(d, uplo = if(is(x,"triangularMatrix")) x@uplo else "U", kind) ## diagonal -> sparse {triangular OR symmetric} (upper / lower) depending on "partner": diag2Tsmart <- function(d, x, kind = .M.kind(d)) { clx <- getClassDef(class(x)) if(extends(clx, "symmetricMatrix")) .diag2sT(d, uplo = x@uplo, kind) else .diag2tT(d, uplo = if(extends(clx,"triangularMatrix")) x@uplo else "U", kind) } ## FIXME: should not be needed {when ddi* is dsparse* etc}: setMethod("is.finite", signature(x = "diagonalMatrix"), function(x) is.finite(.diag2tT(x))) setMethod("is.infinite", signature(x = "diagonalMatrix"), function(x) is.infinite(.diag2tT(x))) ## In order to evade method dispatch ambiguity warnings, ## and because we can save a .M.kind() call, we use this explicit ## "hack" instead of signature x = "diagonalMatrix" : ## ## ddi*: di2tT <- function(from) .diag2tT(from, "U", "d") setAs("ddiMatrix", "triangularMatrix", di2tT) ##_no_longer_ setAs("ddiMatrix", "sparseMatrix", di2tT) ## needed too (otherwise -> Tsparse is taken): setAs("ddiMatrix", "TsparseMatrix", di2tT) setAs("ddiMatrix", "dsparseMatrix", di2tT) setAs("ddiMatrix", "CsparseMatrix", function(from) as(.diag2tT(from, "U", "d"), "CsparseMatrix")) setAs("ddiMatrix", "symmetricMatrix", function(from) .diag2sT(from, "U", "d")) ## ## ldi*: di2tT <- function(from) .diag2tT(from, "U", "l") setAs("ldiMatrix", "triangularMatrix", di2tT) ##_no_longer_ setAs("ldiMatrix", "sparseMatrix", di2tT) ## needed too (otherwise -> Tsparse is taken): setAs("ldiMatrix", "TsparseMatrix", di2tT) setAs("ldiMatrix", "lsparseMatrix", di2tT) setAs("ldiMatrix", "CsparseMatrix", function(from) as(.diag2tT(from, "U", "l"), "CsparseMatrix")) setAs("ldiMatrix", "symmetricMatrix", function(from) .diag2sT(from, "U", "l")) rm(di2tT) setAs("diagonalMatrix", "nMatrix", function(from) { n <- from@Dim[1] i <- if(from@diag == "U") integer(0) else which(isN0(from@x)) - 1L new("ntTMatrix", i = i, j = i, diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames) }) setAs("diagonalMatrix", "nsparseMatrix", function(from) as(from, "nMatrix")) ## Cheap fast substitute for diag() which *does* preserve the mode of x : mkDiag <- function(x, n) { y <- matrix(as0(mod=mode(x)), n,n) if (n > 0) y[1L + 0:(n - 1L) * (n + 1)] <- x y } setAs("diagonalMatrix", "matrix", function(from) { ## want "ldiMatrix" -> "matrix" : mkDiag(if(from@diag == "U") as1(from@x) else from@x, n = from@Dim[1]) }) setMethod("as.vector", signature(x = "diagonalMatrix", mode="missing"), function(x, mode) { n <- x@Dim[1] mod.x <- mode(x@x) r <- vector(mod.x, length = n^2) if(n) r[1 + 0:(n - 1L) * (n + 1)] <- if(x@diag == "U") as1(mod=mod.x) else x@x r }) setAs("diagonalMatrix", "generalMatrix", # prefer sparse: function(from) as(as(from, "CsparseMatrix"), "generalMatrix")) setAs("diagonalMatrix", "denseMatrix", function(from) as(as(from, "CsparseMatrix"), "denseMatrix")) ..diag.x <- function(m) rep.int(as1(m@x), m@Dim[1]) .diag.x <- function(m) if(m@diag == "U") rep.int(as1(m@x), m@Dim[1]) else m@x .diag.2N <- function(m) { if(m@diag == "U") m@diag <- "N" m } setAs("ddiMatrix", "dgeMatrix", function(from) .Call(dup_mMatrix_as_dgeMatrix, from)) setAs("ddiMatrix", "ddenseMatrix", function(from) as(as(from, "triangularMatrix"),"denseMatrix")) setAs("ldiMatrix", "ldenseMatrix", function(from) as(as(from, "triangularMatrix"),"denseMatrix")) setAs("matrix", "diagonalMatrix", function(from) { d <- dim(from) if(d[1] != (n <- d[2])) stop("non-square matrix") if(any(from[row(from) != col(from)] != 0)) stop("matrix with non-zero off-diagonals cannot be coerced to \"diagonalMatrix\"") x <- diag(from) if(is.logical(x)) { cl <- "ldiMatrix" uni <- allTrue(x) ## uni := {is it unit-diagonal ?} } else { cl <- "ddiMatrix" uni <- allTrue(x == 1) storage.mode(x) <- "double" } ## TODO: complex new(cl, Dim = c(n,n), diag = if(uni) "U" else "N", x = if(uni) x[FALSE] else x) }) ## ``generic'' coercion to diagonalMatrix : build on isDiagonal() and diag() setAs("Matrix", "diagonalMatrix", function(from) { d <- dim(from) if(d[1] != (n <- d[2])) stop("non-square matrix") if(!isDiagonal(from)) stop("matrix is not diagonal") ## else: x <- diag(from) if(is.logical(x)) { cl <- "ldiMatrix" uni <- allTrue(x) } else { cl <- "ddiMatrix" uni <- allTrue(x == 1) storage.mode(x) <- "double" } ## TODO: complex new(cl, Dim = c(n,n), diag = if(uni) "U" else "N", x = if(uni) x[FALSE] else x) }) setMethod("diag", signature(x = "diagonalMatrix"), function(x = 1, nrow, ncol) .diag.x(x)) subDiag <- function(x, i, j, ..., drop) { x <- as(x, "CsparseMatrix") ## << was "TsparseMatrix" (Csparse is faster now) x <- if(missing(i)) x[, j, drop=drop] else if(missing(j)) if(nargs() == 4) x[i, , drop=drop] else x[i, drop=drop] else x[i,j, drop=drop] if(isS4(x) && isDiagonal(x)) as(x, "diagonalMatrix") else x } setMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index", drop = "logical"), subDiag) setMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing", drop = "logical"), function(x, i, j, ..., drop) { na <- nargs() Matrix.msg("diag[i,m,l] : nargs()=", na, .M.level = 2) if(na == 4) subDiag(x, i=i, , drop=drop) else subDiag(x, i=i, drop=drop) }) setMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index", drop = "logical"), function(x, i, j, ..., drop) subDiag(x, j=j, drop=drop)) ## When you assign to a diagonalMatrix, the result should be ## diagonal or sparse --- ## FIXME: this now fails because the "denseMatrix" methods come first in dispatch ## Only(?) current bug: x[i] <- value is wrong when i is *vector* replDiag <- function(x, i, j, ..., value) { x <- as(x, "CsparseMatrix")# was "Tsparse.." till 2012-07 if(missing(i)) x[, j] <- value else if(missing(j)) { ## x[i , ] <- v *OR* x[i] <- v na <- nargs() ## message("diagnosing replDiag() -- nargs()= ", na) if(na == 4) x[i, ] <- value else if(na == 3) x[i] <- value else stop(gettextf("Internal bug: nargs()=%d; please report", na), domain=NA) } else x[i,j] <- value if(isDiagonal(x)) as(x, "diagonalMatrix") else x } setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index", value = "replValue"), replDiag) setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing", value = "replValue"), function(x,i,j, ..., value) { ## message("before replDiag() -- nargs()= ", nargs()) if(nargs() == 3) replDiag(x, i=i, value=value) else ## nargs() == 4 : replDiag(x, i=i, , value=value) }) setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index", value = "replValue"), function(x,i,j, ..., value) replDiag(x, j=j, value=value)) ## x[] <- value : setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "missing", value = "ANY"), function(x,i,j, ..., value) { if(all0(value)) { # be faster r <- new(paste0(.M.kindC(getClassDef(class(x))),"tTMatrix"))# of all "0" r@Dim <- x@Dim r@Dimnames <- x@Dimnames r } else { ## typically non-sense: assigning to full sparseMatrix x[TRUE] <- value x } }) setReplaceMethod("[", signature(x = "diagonalMatrix", i = "matrix", # 2-col.matrix j = "missing", value = "replValue"), function(x,i,j, ..., value) { if(ncol(i) == 2) { if(all((ii <- i[,1]) == i[,2])) { # replace in diagonal only if(x@diag == "U") { one <- as1(x@x) if(any(value != one | is.na(value))) { x@diag <- "N" x@x <- rep.int(one, x@Dim[1]) } else return(x) } x@x[ii] <- value x } else { ## no longer diagonal, but remain sparse: x <- as(x, "TsparseMatrix") x[i] <- value x } } else { # behave as "base R": use as if vector x <- as(x, "matrix") x[i] <- value Matrix(x) } }) ## value = "sparseMatrix": setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index", value = "sparseMatrix"), function (x, i, j, ..., value) callGeneric(x=x, , j=j, value = as(value, "sparseVector"))) setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing", value = "sparseMatrix"), function (x, i, j, ..., value) callGeneric(x=x, i=i, , value = as(value, "sparseVector"))) setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index", value = "sparseMatrix"), function (x, i, j, ..., value) callGeneric(x=x, i=i, j=j, value = as(value, "sparseVector"))) ## value = "sparseVector": setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index", value = "sparseVector"), replDiag) setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing", value = "sparseVector"), replDiag) setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index", value = "sparseVector"), replDiag) setMethod("t", signature(x = "diagonalMatrix"), function(x) { x@Dimnames <- x@Dimnames[2:1] ; x }) setMethod("isDiagonal", "diagonalMatrix", function(object) TRUE) setMethod("isTriangular", "diagonalMatrix", function(object, ...) TRUE) setMethod("isSymmetric", "diagonalMatrix", function(object, ...) TRUE) setMethod("symmpart", signature(x = "diagonalMatrix"), function(x) x) setMethod("skewpart", signature(x = "diagonalMatrix"), setZero) setMethod("chol", signature(x = "ddiMatrix"), function(x, pivot, ...) { if(x@diag == "U") return(x) ## else if(any(x@x < 0)) stop("chol() is undefined for diagonal matrix with negative entries") x@x <- sqrt(x@x) x }) ## chol(L) is L for logical diagonal: setMethod("chol", signature(x = "ldiMatrix"), function(x, pivot, ...) x) setMethod("determinant", signature(x = "diagonalMatrix", logarithm = "logical"), function(x, logarithm, ...) mkDet(.diag.x(x), logarithm)) setMethod("norm", signature(x = "diagonalMatrix", type = "character"), function(x, type, ...) { if((n <- x@Dim[1]) == 0) return(0) # as for "sparseMatrix" type <- toupper(substr(type[1], 1, 1)) isU <- (x@diag == "U") # unit-diagonal if(type == "F") sqrt(if(isU) n else sum(x@x^2)) else { ## norm == "I","1","O","M" : if(isU) 1 else max(abs(x@x)) } }) ## Basic Matrix Multiplication {many more to add} ## --------------------- ## Note that "ldi" logical are treated as numeric diagdiagprod <- function(x, y) { dimCheck(x,y) if(x@diag != "U") { if(y@diag != "U") { nx <- x@x * y@x if(is.numeric(nx) && !is.numeric(x@x)) x <- as(x, "dMatrix") x@x <- as.numeric(nx) } return(x) } else ## x is unit diagonal return(y) } setMethod("%*%", signature(x = "diagonalMatrix", y = "diagonalMatrix"), diagdiagprod, valueClass = "ddiMatrix") formals(diagdiagprod) <- alist(x=, y=x) setMethod("crossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"), diagdiagprod, valueClass = "ddiMatrix") setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"), diagdiagprod, valueClass = "ddiMatrix") setMethod("crossprod", signature(x = "diagonalMatrix", y = "missing"), diagdiagprod, valueClass = "ddiMatrix") setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "missing"), diagdiagprod, valueClass = "ddiMatrix") diagmatprod <- function(x, y) { ## x is diagonalMatrix dx <- dim(x) dy <- dim(y) if(dx[2] != dy[1]) stop("non-matching dimensions") as(if(x@diag == "U") y else x@x * y, "Matrix") } setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"), diagmatprod) ## sneaky .. : formals(diagmatprod) <- alist(x=, y=NULL) setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"), diagmatprod) diagGeprod <- function(x, y) { dx <- dim(x) dy <- dim(y) if(dx[2] != dy[1]) stop("non-matching dimensions") if(x@diag != "U") y@x <- x@x * y@x y } setMethod("%*%", signature(x= "diagonalMatrix", y= "dgeMatrix"), diagGeprod) setMethod("%*%", signature(x= "diagonalMatrix", y= "lgeMatrix"), diagGeprod) formals(diagGeprod) <- alist(x=, y=NULL) setMethod("crossprod", signature(x = "diagonalMatrix", y = "dgeMatrix"), diagGeprod, valueClass = "dgeMatrix") setMethod("crossprod", signature(x = "diagonalMatrix", y = "lgeMatrix"), diagGeprod) matdiagprod <- function(x, y) { dx <- dim(x) dy <- dim(y) if(dx[2] != dy[1]) stop("non-matching dimensions") Matrix(if(y@diag == "U") x else x * rep(y@x, each = dx[1])) } setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"), matdiagprod) formals(matdiagprod) <- alist(x=, y=NULL) setMethod("tcrossprod", signature(x = "matrix", y = "diagonalMatrix"), matdiagprod) gediagprod <- function(x, y) { dx <- dim(x) dy <- dim(y) if(dx[2] != dy[1]) stop("non-matching dimensions") if(y@diag == "N") x@x <- x@x * rep(y@x, each = dx[1]) x } setMethod("%*%", signature(x= "dgeMatrix", y= "diagonalMatrix"), gediagprod) setMethod("%*%", signature(x= "lgeMatrix", y= "diagonalMatrix"), gediagprod) formals(gediagprod) <- alist(x=, y=NULL) setMethod("tcrossprod", signature(x = "dgeMatrix", y = "diagonalMatrix"), gediagprod) setMethod("tcrossprod", signature(x = "lgeMatrix", y = "diagonalMatrix"), gediagprod) ## crossprod {more of these} ## tcrossprod --- all are not yet there: do the dense ones here: setMethod("%*%", signature(x = "diagonalMatrix", y = "denseMatrix"), function(x, y) if(x@diag == "U") y else x %*% as(y, "generalMatrix")) setMethod("%*%", signature(x = "denseMatrix", y = "diagonalMatrix"), function(x, y) if(y@diag == "U") x else as(x, "generalMatrix") %*% y) ## FIXME: ## setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"), ## function(x, y = NULL) { ## }) ##' @param x CsparseMatrix ##' @param y diagonalMatrix ##' @return x %*% y Cspdiagprod <- function(x, y) { dx <- dim(x <- .Call(Csparse_diagU2N, x)) dy <- dim(y) if(dx[2] != dy[1]) stop("non-matching dimensions") if(y@diag == "N") { ## otherwise: y == Diagonal(n) : multiplication is identity if(!all(y@x[1L] == y@x[-1L]) && is(x, "symmetricMatrix")) x <- as(x, "generalMatrix") ind <- rep.int(seq_len(dx[2]), x@p[-1] - x@p[-dx[2]-1L]) x@x <- x@x * y@x[ind] if(is(x, "compMatrix") && length(xf <- x@factors)) { ## instead of dropping all factors, be smart about some ## TODO ...... x@factors <- list() } } x } ##' @param x diagonalMatrix ##' @param y CsparseMatrix ##' @return x %*% y diagCspprod <- function(x, y) { dx <- dim(x) dy <- dim(y <- .Call(Csparse_diagU2N, y)) if(dx[2] != dy[1]) stop("non-matching dimensions") if(x@diag == "N") { if(!all(x@x[1L] == x@x[-1L]) && is(y, "symmetricMatrix")) y <- as(y, "generalMatrix") y@x <- y@x * x@x[y@i + 1L] if(is(y, "compMatrix") && length(yf <- y@factors)) { ## TODO if(FALSE) { ## instead of dropping all factors, be smart about some keep <- character() if(any(iLU <- names(yf) == "LU")) { keep <- "LU" } y@factors <- yf[keep] } else y@factors <- list() ## for now } } y } setMethod("crossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"), function(x, y = NULL) diagCspprod(x, y)) setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"), function(x, y = NULL) diagCspprod(x, as(y, "CsparseMatrix"))) ## Prefer calling diagCspprod to Cspdiagprod if going to transpose anyway ## x'y == (y'x)' setMethod("crossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"), function(x, y = NULL) t(diagCspprod(y, x))) setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"), function(x, y = NULL) t(diagCspprod(y, as(x, "Csparsematrix")))) setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"), function(x, y = NULL) diagCspprod(x, t(y))) setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"), function(x, y = NULL) diagCspprod(x, t(as(y, "CsparseMatrix")))) setMethod("tcrossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"), function(x, y = NULL) Cspdiagprod(x, y)) setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"), function(x, y = NULL) Cspdiagprod(as(x, "CsparseMatrix"), y)) setMethod("%*%", signature(x = "diagonalMatrix", y = "CsparseMatrix"), function(x, y) diagCspprod(x, y)) ## instead of "sparseMatrix", use: [RT]sparse.. ("closer" in method dispatch) for(cl in c("TsparseMatrix", "RsparseMatrix")) { setMethod("%*%", signature(x = "diagonalMatrix", y = "sparseMatrix"), function(x, y) diagCspprod(as(x, "CsparseMatrix"), y)) setMethod("%*%", signature(x = "sparseMatrix", y = "diagonalMatrix"), function(x, y) Cspdiagprod(as(x, "CsparseMatrix"), y)) } setMethod("%*%", signature(x = "CsparseMatrix", y = "diagonalMatrix"), function(x, y) Cspdiagprod(x, y)) ## TODO: Write tests in ./tests/ which ensure that many "ops" with diagonal* ## do indeed work by going through sparse (and *not* ddense)! setMethod("solve", signature(a = "diagonalMatrix", b = "missing"), function(a, b, ...) { a@x <- 1/ a@x a@Dimnames <- a@Dimnames[2:1] a }) solveDiag <- function(a, b, ...) { if(a@Dim[1] != nrow(b)) stop("incompatible matrix dimensions") ## trivially invert a 'in place' and multiply: a@x <- 1/ a@x a@Dimnames <- a@Dimnames[2:1] a %*% b } setMethod("solve", signature(a = "diagonalMatrix", b = "matrix"), solveDiag) setMethod("solve", signature(a = "diagonalMatrix", b = "Matrix"), solveDiag) ## Schur() ---> ./eigen.R ###---------------- (, , ) ---------------------- ## Use function for several signatures, in order to evade diagOdiag <- function(e1,e2) { ## result should also be diagonal _ if possible _ r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible" ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...: r00 <- callGeneric(if(is.numeric(e1@x)) 0 else FALSE, if(is.numeric(e2@x)) 0 else FALSE) if(is0(r00)) { ## r00 == 0 or FALSE --- result *is* diagonal if(is.numeric(r)) { # "double" *or* "integer" if(is.numeric(e2@x)) { e2@x <- r; return(.diag.2N(e2)) } if(!is.numeric(e1@x)) ## e.g. e1, e2 are logical; e1 <- as(e1, "dMatrix") if(!is.double(r)) r <- as.double(r) } else if(is.logical(r)) e1 <- as(e1, "lMatrix") else stop(gettextf("intermediate 'r' is of type %s", typeof(r)), domain=NA) e1@x <- r .diag.2N(e1) } else { ## result not diagonal, but at least symmetric: ## e.g., m == m isNum <- (is.numeric(r) || is.numeric(r00)) isLog <- (is.logical(r) || is.logical(r00)) Matrix.msg("exploding o into dense matrix", .M.level = 2) d <- e1@Dim n <- d[1] stopifnot(length(r) == n) if(isNum && !is.double(r)) r <- as.double(r) xx <- as.vector(matrix(rbind(r, matrix(r00,n,n)), n,n)) newcl <- paste0(if(isNum) "d" else if(isLog) { if(!any(is.na(r)) && !any(is.na(r00))) "n" else "l" } else stop("not yet implemented .. please report"), "syMatrix") new(newcl, Dim = e1@Dim, Dimnames = e1@Dimnames, x = xx) } } ### This would be *the* way, but we get tons of "ambiguous method dispatch" ## we use this hack instead of signature x = "diagonalMatrix" : diCls <- names(getClass("diagonalMatrix")@subclasses) if(FALSE) { setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"), diagOdiag) } else { ## These are just for method disambiguation: for(c1 in diCls) for(c2 in diCls) setMethod("Ops", signature(e1 = c1, e2 = c2), diagOdiag) } ## diagonal o triangular |--> triangular ## diagonal o symmetric |--> symmetric ## {also when other is sparse: do these "here" -- ## before conversion to sparse, since that loses "diagonality"} diagOtri <- function(e1,e2) { ## result must be triangular r <- callGeneric(d1 <- .diag.x(e1), diag(e2)) # error if not "compatible" ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...: e1.0 <- if(.n1 <- is.numeric(d1 )) 0 else FALSE r00 <- callGeneric(e1.0, if(.n2 <- is.numeric(e2[0])) 0 else FALSE) if(is0(r00)) { ## r00 == 0 or FALSE --- result *is* triangular diag(e2) <- r ## check what happens "in the triangle" e2.2 <- if(.n2) 2 else TRUE if(!callGeneric(e1.0, e2.2) == e2.2) { # values "in triangle" can change: n <- dim(e2)[1L] it <- indTri(n, upper = (e2@uplo == "U")) e2[it] <- callGeneric(e1.0, e2[it]) } e2 } else { ## result not triangular ---> general rr <- as(e2, "generalMatrix") diag(rr) <- r rr } } setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "triangularMatrix"), diagOtri) ## For the reverse, Ops == "Arith" | "Compare" | "Logic" ## 'Arith' := '"+"', '"-"', '"*"', '"^"', '"%%"', '"%/%"', '"/"' setMethod("Arith", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"), function(e1,e2) { ## this must only trigger for *dense* e1 switch(.Generic, "+" = .Call(dtrMatrix_addDiag, as(e1,"dtrMatrix"), .diag.x(e2)), "-" = .Call(dtrMatrix_addDiag, as(e1,"dtrMatrix"), - .diag.x(e2)), "*" = { n <- e2@Dim[1L] d2 <- if(e2@diag == "U") { # unit-diagonal d <- rep.int(as1(e2@x), n) e2@x <- d e2@diag <- "N" d } else e2@x e2@x <- diag(e1) * d2 e2 }, "^" = { ## will be dense ( as ^ 0 == 1 ): e1 ^ as(e2, "denseMatrix") }, ## otherwise: callGeneric(e1, diag2Tsmart(e2,e1))) }) ## Compare --> 'swap' (e.g. e1 < e2 <==> e2 > e1 ): setMethod("Compare", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"), .Cmp.swap) ## '&' and "|' are commutative: setMethod("Logic", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"), function(e1,e2) callGeneric(e2, e1)) ## For almost everything else, diag* shall be treated "as sparse" : ## These are cheap implementations via coercion ## For disambiguation --- define this for "sparseMatrix" , then for "ANY"; ## and because we can save an .M.kind() call, we use this explicit ## "hack" for all diagonalMatrix *subclasses* instead of just "diagonalMatrix" : ## ## ddi*: setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "sparseMatrix"), function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2)) setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ddiMatrix"), function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d"))) ## ldi* setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "sparseMatrix"), function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2)) setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ldiMatrix"), function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l"))) ## Ops: Arith --> numeric : "dMatrix" ## Compare --> logical ## Logic --> logical: "lMatrix" ## Other = "numeric" : stay diagonal if possible ## ddi*: Arith: result numeric, potentially ddiMatrix for(arg2 in c("numeric","logical")) setMethod("Arith", signature(e1 = "ddiMatrix", e2 = arg2), function(e1,e2) { n <- e1@Dim[1] f0 <- callGeneric(0, e2) if(all0(f0)) { # remain diagonal L1 <- (le <- length(e2)) == 1L if(e1@diag == "U") { if(any((r <- callGeneric(1, e2)) != 1)) { e1@diag <- "N" e1@x[seq_len(n)] <- r # possibly recycling r } ## else: result = e1 (is "U" diag) } else { r <- callGeneric(e1@x, e2) ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix e1@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le] } e1 } else callGeneric(diag2tT.u(e1,e2, "d"), e2) }) for(arg1 in c("numeric","logical")) setMethod("Arith", signature(e1 = arg1, e2 = "ddiMatrix"), function(e1,e2) { n <- e2@Dim[1] f0 <- callGeneric(e1, 0) if(all0(f0)) { # remain diagonal L1 <- (le <- length(e1)) == 1L if(e2@diag == "U") { if(any((r <- callGeneric(e1, 1)) != 1)) { e2@diag <- "N" e2@x[seq_len(n)] <- r # possibly recycling r } ## else: result = e2 (is "U" diag) } else { r <- callGeneric(e1, e2@x) ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix e2@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le] } e2 } else callGeneric(e1, diag2tT.u(e2,e1, "d")) }) ## ldi* Arith --> result numeric, potentially ddiMatrix for(arg2 in c("numeric","logical")) setMethod("Arith", signature(e1 = "ldiMatrix", e2 = arg2), function(e1,e2) { n <- e1@Dim[1] f0 <- callGeneric(0, e2) if(all0(f0)) { # remain diagonal L1 <- (le <- length(e2)) == 1L E <- copyClass(e1, "ddiMatrix", c("diag", "Dim", "Dimnames"))#FIXME: if ok, check=FALSE ## E <- copyClass(e1, "ddiMatrix", check=FALSE) ## storage.mode(E@x) <- "double" if(e1@diag == "U") { if(any((r <- callGeneric(1, e2)) != 1)) { E@diag <- "N" E@x[seq_len(n)] <- r # possibly recycling r } ## else: result = E (is "U" diag) } else { r <- callGeneric(e1@x, e2) ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le] } E } else callGeneric(diag2tT.u(e1,e2, "l"), e2) }) for(arg1 in c("numeric","logical")) setMethod("Arith", signature(e1 = arg1, e2 = "ldiMatrix"), function(e1,e2) { n <- e2@Dim[1] f0 <- callGeneric(e1, 0) if(all0(f0)) { # remain diagonal L1 <- (le <- length(e1)) == 1L E <- copyClass(e2, "ddiMatrix", c("diag", "Dim", "Dimnames"))#FIXME: if ok, check=FALSE ## E <- copyClass(e2, "ddiMatrix", check=FALSE) ## storage.mode(E@x) <- "double" if(e2@diag == "U") { if(any((r <- callGeneric(e1, 1)) != 1)) { E@diag <- "N" E@x[seq_len(n)] <- r # possibly recycling r } ## else: result = E (is "U" diag) } else { r <- callGeneric(e1, e2@x) ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le] } E } else callGeneric(e1, diag2tT.u(e2,e1, "l")) }) ## ddi*: for "Ops" without "Arith": or --> result logical, potentially ldi ## ## Note that ("numeric", "ddiMatrix") is simply swapped, e.g., if(FALSE) { selectMethod("<", c("numeric","lMatrix"))# Compare selectMethod("&", c("numeric","lMatrix"))# Logic } ## so we don't need to define a method here : for(arg2 in c("numeric","logical")) setMethod("Ops", signature(e1 = "ddiMatrix", e2 = arg2), function(e1,e2) { n <- e1@Dim[1] f0 <- callGeneric(0, e2) if(all0(f0)) { # remain diagonal L1 <- (le <- length(e2)) == 1L E <- copyClass(e1, "ldiMatrix", c("diag", "Dim", "Dimnames"))#FIXME: if ok, check=FALSE ## E <- copyClass(e1, "ldiMatrix", check=FALSE) ## storage.mode(E@x) <- "logical" if(e1@diag == "U") { if(any((r <- callGeneric(1, e2)) != 1)) { E@diag <- "N" E@x[seq_len(n)] <- r # possibly recycling r } ## else: result = E (is "U" diag) } else { r <- callGeneric(e1@x, e2) ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le] } E } else callGeneric(diag2tT.u(e1,e2, "d"), e2) }) ## ldi*: for "Ops" without "Arith": or --> result logical, potentially ldi for(arg2 in c("numeric","logical")) setMethod("Ops", signature(e1 = "ldiMatrix", e2 = arg2), function(e1,e2) { n <- e1@Dim[1] f0 <- callGeneric(FALSE, e2) if(all0(f0)) { # remain diagonal L1 <- (le <- length(e2)) == 1L if(e1@diag == "U") { if(any((r <- callGeneric(TRUE, e2)) != 1)) { e1@diag <- "N" e1@x[seq_len(n)] <- r # possibly recycling r } ## else: result = e1 (is "U" diag) } else { r <- callGeneric(e1@x, e2) ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix e1@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le] } e1 } else callGeneric(diag2tT.u(e1,e2, "l"), e2) }) ## Not {"sparseMatrix", "numeric} : {"denseMatrix", "matrix", ... } for(other in c("ANY", "Matrix", "dMatrix")) { ## ddi*: setMethod("Ops", signature(e1 = "ddiMatrix", e2 = other), function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2)) setMethod("Ops", signature(e1 = other, e2 = "ddiMatrix"), function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d"))) ## ldi*: setMethod("Ops", signature(e1 = "ldiMatrix", e2 = other), function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2)) setMethod("Ops", signature(e1 = other, e2 = "ldiMatrix"), function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l"))) } ## Direct subclasses of "denseMatrix": currently ddenseMatrix, ldense... : dense.subCl <- local({ dM.scl <- getClass("denseMatrix")@subclasses names(dM.scl)[vapply(dM.scl, slot, 0, "distance") == 1] }) for(DI in diCls) { dMeth <- if(extends(DI, "dMatrix")) function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2) else # "lMatrix", the only other kind for now function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2) for(c2 in c(dense.subCl, "Matrix")) { for(Fun in c("*", "&")) { setMethod(Fun, signature(e1 = DI, e2 = c2), function(e1,e2) callGeneric(e1, Diagonal(x = diag(e2)))) setMethod(Fun, signature(e1 = c2, e2 = DI), function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2)) } setMethod("^", signature(e1 = c2, e2 = DI), function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2)) for(Fun in c("%%", "%/%", "/")) ## 0 0 |--> NaN for these. setMethod(Fun, signature(e1 = DI, e2 = c2), dMeth) } } ### "Summary" : "max" "min" "range" "prod" "sum" "any" "all" ### ---------- the last 4: separately here for(cl in diCls) { setMethod("any", cl, function (x, ..., na.rm) { if(any(x@Dim == 0)) FALSE else if(x@diag == "U") TRUE else any(x@x, ..., na.rm = na.rm) }) setMethod("all", cl, function (x, ..., na.rm) { n <- x@Dim[1] if(n >= 2) FALSE else if(n == 0 || x@diag == "U") TRUE else all(x@x, ..., na.rm = na.rm) }) setMethod("prod", cl, function (x, ..., na.rm) { n <- x@Dim[1] if(n >= 2) 0 else if(n == 0 || x@diag == "U") 1 else ## n == 1, diag = "N" : prod(x@x, ..., na.rm = na.rm) }) setMethod("sum", cl, function(x, ..., na.rm) { r <- sum(x@x, ..., na.rm = na.rm)# double or integer, correctly if(x@diag == "U" && !is.na(r)) r + x@Dim[1] else r }) } ## The remaining ones are max, min, range : setMethod("Summary", "ddiMatrix", function(x, ..., na.rm) { if(any(x@Dim == 0)) callGeneric(numeric(0), ..., na.rm=na.rm) else if(x@diag == "U") callGeneric(x@x, 0, 1, ..., na.rm=na.rm) else callGeneric(x@x, 0, ..., na.rm=na.rm) }) setMethod("Summary", "ldiMatrix", function(x, ..., na.rm) { if(any(x@Dim == 0)) callGeneric(logical(0), ..., na.rm=na.rm) else if(x@diag == "U") callGeneric(x@x, FALSE, TRUE, ..., na.rm=na.rm) else callGeneric(x@x, FALSE, ..., na.rm=na.rm) }) ## similar to prTriang() in ./Auxiliaries.R : prDiag <- function(x, digits = getOption("digits"), justify = "none", right = TRUE) { cf <- array(".", dim = x@Dim, dimnames = x@Dimnames) cf[row(cf) == col(cf)] <- sapply(diag(x), format, digits = digits, justify = justify) print(cf, quote = FALSE, right = right) invisible(x) } ## somewhat consistent with "print" for sparseMatrix : setMethod("print", signature(x = "diagonalMatrix"), prDiag) setMethod("show", signature(object = "diagonalMatrix"), function(object) { d <- dim(object) cl <- class(object) cat(sprintf('%d x %d diagonal matrix of class "%s"', d[1], d[2], cl)) if(d[1] < 50) { cat("\n") prDiag(object) } else { cat(", with diagonal entries\n") show(diag(object)) invisible(object) } }) rm(arg1, arg2, other, DI, cl, c1, c2, dense.subCl, diCls)# not used elsewhere setMethod("summary", signature(object = "diagonalMatrix"), function(object, ...) { d <- dim(object) r <- summary(object@x, ...) attr(r, "header") <- sprintf('%d x %d diagonal Matrix of class "%s"', d[1], d[2], class(object)) ## use ole' S3 technology for such a simple case class(r) <- c("diagSummary", class(r)) r }) print.diagSummary <- function (x, ...) { cat(attr(x, "header"),"\n") class(x) <- class(x)[-1] print(x, ...) invisible(x) } Matrix/R/AllClass.R0000644000175100001440000007573012231175655013601 0ustar hornikusers## --- New "logic" class -- currently using "raw" instead of "logical" ## LOGIC setClass("logic", contains = "raw") ## ------------- Virtual Classes ---------------------------------------- ## Mother class of all Matrix objects setClass("Matrix", representation(Dim = "integer", Dimnames = "list", "VIRTUAL"), prototype = prototype(Dim = integer(2), Dimnames = list(NULL,NULL)), validity = function(object) { Dim <- object@Dim if (length(Dim) != 2) return("Dim slot must be of length 2") if (any(Dim < 0)) return("Dim slot must contain non-negative values") Dn <- object@Dimnames if (!is.list(Dn) || length(Dn) != 2) return("'Dimnames' slot must be list of length 2") lDn <- sapply(Dn, length) if (lDn[1] > 0 && lDn[1] != Dim[1]) return("length(Dimnames[[1]])' must match Dim[1]") if (lDn[2] > 0 && lDn[2] != Dim[2]) return("length(Dimnames[[2]])' must match Dim[2]") ## 'else' ok : TRUE }) ## The class of composite matrices - i.e. those for which it makes sense to ## create a factorization setClass("compMatrix", representation(factors = "list", "VIRTUAL"), contains = "Matrix") ## Virtual classes of Matrices determined by above/below diagonal relationships setClass("generalMatrix", representation = "VIRTUAL", contains = "compMatrix") setClass("symmetricMatrix", representation(uplo = "character", "VIRTUAL"), contains = "compMatrix", prototype = prototype(uplo = "U"), validity = function(object) .Call(symmetricMatrix_validate, object)) setClass("triangularMatrix", representation(uplo = "character", diag = "character", "VIRTUAL"), contains = "Matrix", prototype = prototype(uplo = "U", diag = "N"), validity = function(object) .Call(triangularMatrix_validate, object)) ## Virtual class of numeric matrices setClass("dMatrix", representation(x = "numeric", "VIRTUAL"), contains = "Matrix", validity = function(object) .Call(dMatrix_validate, object)) ## Virtual class of integer matrices setClass("iMatrix", representation(x = "integer", "VIRTUAL"), contains = "Matrix") ## Virtual class of logical matrices setClass("lMatrix", ## LOGIC representation(x = "logic", "VIRTUAL"), contains = "Matrix") representation(x = "logical", "VIRTUAL"), contains = "Matrix") ## Virtual class of nonzero pattern matrices setClass("nMatrix", representation("VIRTUAL"), contains = "Matrix") ## aka 'pattern' matrices -- have no x slot ## Virtual class of complex matrices setClass("zMatrix", # letter 'z' is as in the names of Lapack subroutines representation(x = "complex", "VIRTUAL"), contains = "Matrix") ## Virtual class of dense matrices (including "packed") setClass("denseMatrix", representation("VIRTUAL"), contains = "Matrix") ## Virtual class of dense, numeric matrices setClass("ddenseMatrix", representation("VIRTUAL"), contains = c("dMatrix", "denseMatrix")) ## Virtual class of dense, logical matrices setClass("ldenseMatrix", representation("VIRTUAL"), contains = c("lMatrix", "denseMatrix")) if(FALSE) { ##--not yet-- setClass("idenseMatrix", representation("VIRTUAL"), contains = c("iMatrix", "denseMatrix")) } ## Virtual class of dense, nonzero pattern matrices - rarely used, for completeness setClass("ndenseMatrix", representation(x = "logical", "VIRTUAL"), contains = c("nMatrix", "denseMatrix")) ## virtual SPARSE ------------ setClass("sparseMatrix", representation("VIRTUAL"), contains = "Matrix") ## diagonal: has 'diag' slot; diag = "U" <--> have identity matrix setClass("diagonalMatrix", representation(diag = "character", "VIRTUAL"), contains = "sparseMatrix", ## NOTE: ^^^^^^ was dense Matrix, until 0.999375-11 (2008-07) validity = function(object) { d <- object@Dim if(d[1] != (n <- d[2])) return("matrix is not square") lx <- length(object@x) if(object@diag == "U") { if(lx != 0) return("diag = \"U\" (identity matrix) requires empty 'x' slot") } else if(object@diag == "N") { if(lx != n) return("diagonal matrix has 'x' slot of length != 'n'") } else return("diagonal matrix 'diag' slot must be \"U\" or \"N\"") TRUE }, prototype = prototype(diag = "N") ) ## sparse matrices in Triplet representation (dgT, lgT, ..): setClass("TsparseMatrix", representation(i = "integer", j = "integer", "VIRTUAL"), contains = "sparseMatrix", validity = function(object) .Call(Tsparse_validate, object) ) setClass("CsparseMatrix", representation(i = "integer", p = "integer", "VIRTUAL"), contains = "sparseMatrix", prototype = prototype(p = 0L),# to be valid validity = function(object) .Call(Csparse_validate, object) ) setClass("RsparseMatrix", representation(p = "integer", j = "integer", "VIRTUAL"), contains = "sparseMatrix", prototype = prototype(p = 0L),# to be valid validity = function(object) .Call(Rsparse_validate, object) ) setClass("dsparseMatrix", representation("VIRTUAL"), contains = c("dMatrix", "sparseMatrix")) setClass("lsparseMatrix", representation("VIRTUAL"), contains = c("lMatrix", "sparseMatrix")) if(FALSE) { ##--not yet-- setClass("isparseMatrix", representation("VIRTUAL"), contains = c("lMatrix", "sparseMatrix")) } ## these are the "pattern" matrices for "symbolic analysis" of sparse OPs: setClass("nsparseMatrix", representation("VIRTUAL"), contains = c("nMatrix", "sparseMatrix")) if(FALSE) { ##-- a nice idea --- but needs more careful method re-definitions ##-- such that the *correct* methods are dispatched: ## Trying to use more economical method defs: setClass("dCsparseMatrix", representation("VIRTUAL"), contains = c("CsparseMatrix", "dsparseMatrix")) setClass("lCsparseMatrix", representation("VIRTUAL"), contains = c("CsparseMatrix", "lsparseMatrix")) setClass("nCsparseMatrix", representation("VIRTUAL"), contains = c("CsparseMatrix", "nsparseMatrix")) } ## ------------------ Proper (non-virtual) Classes ---------------------------- ##---------------------- DENSE ----------------------------------------- ## numeric, dense, general matrices setClass("dgeMatrix", contains = c("ddenseMatrix", "generalMatrix"), ## checks that length( @ x) == prod( @ Dim): validity = function(object) .Call(dgeMatrix_validate, object) ) ## i.e. "dgeMatrix" cannot be packed, but "ddenseMatrix" can .. ## numeric, dense, non-packed, triangular matrices setClass("dtrMatrix", contains = c("ddenseMatrix", "triangularMatrix"), validity = function(object) .Call(dtrMatrix_validate, object) ) ## numeric, dense, packed, triangular matrices setClass("dtpMatrix", contains = c("ddenseMatrix", "triangularMatrix"), validity = function(object) .Call(dtpMatrix_validate, object) ) ## numeric, dense, non-packed symmetric matrices setClass("dsyMatrix", contains = c("ddenseMatrix", "symmetricMatrix"), validity = function(object) .Call(dsyMatrix_validate, object) ) ## numeric, dense, packed symmetric matrices setClass("dspMatrix", contains = c("ddenseMatrix", "symmetricMatrix"), validity = function(object) .Call(dspMatrix_validate, object) ) ## numeric, dense, non-packed, positive-definite, symmetric matrices setClass("dpoMatrix", contains = "dsyMatrix", validity = function(object) .Call(dpoMatrix_validate, object) ) ## numeric, dense, packed, positive-definite, symmetric matrices setClass("dppMatrix", contains = "dspMatrix", validity = function(object) .Call(dppMatrix_validate, object) ) ##----- logical dense Matrices -- e.g. as result of COMPARISON ## logical, dense, general matrices setClass("lgeMatrix", contains = c("ldenseMatrix", "generalMatrix"), ## checks that length( @ x) == prod( @ Dim): validity = function(object) stopifnot(length(object@x) == prod(object@Dim)) ) ## i.e. "lgeMatrix" cannot be packed, but "ldenseMatrix" can .. ## logical, dense, non-packed, triangular matrices setClass("ltrMatrix", contains = c("ldenseMatrix", "triangularMatrix")) ## logical, dense, packed, triangular matrices setClass("ltpMatrix", contains = c("ldenseMatrix", "triangularMatrix")) ## logical, dense, non-packed symmetric matrices setClass("lsyMatrix", contains = c("ldenseMatrix", "symmetricMatrix")) ## logical, dense, packed symmetric matrices setClass("lspMatrix", contains = c("ldenseMatrix", "symmetricMatrix"), validity = function(object) .Call(dspMatrix_validate, object) ## "dsp", "lsp" and "nsp" have the same validate ) ##----- nonzero pattern dense Matrices -- "for completeness" ## logical, dense, general matrices setClass("ngeMatrix", contains = c("ndenseMatrix", "generalMatrix"), ## checks that length( @ x) == prod( @ Dim): validity = function(object) stopifnot(length(object@x) == prod(object@Dim))) ## i.e. "ngeMatrix" cannot be packed, but "ndenseMatrix" can .. ## logical, dense, non-packed, triangular matrices setClass("ntrMatrix", contains = c("ndenseMatrix", "triangularMatrix")) ## logical, dense, packed, triangular matrices setClass("ntpMatrix", contains = c("ndenseMatrix", "triangularMatrix")) ## logical, dense, non-packed symmetric matrices setClass("nsyMatrix", contains = c("ndenseMatrix", "symmetricMatrix")) ## logical, dense, packed symmetric matrices setClass("nspMatrix", contains = c("ndenseMatrix", "symmetricMatrix"), validity = function(object) .Call(dspMatrix_validate, object) ## "dsp", "lsp" and "nsp" have the same validate ) ## 'diagonalMatrix' already has validity checking ## diagonal, numeric matrices; "d*" has 'x' slot : setClass("ddiMatrix", contains = c("diagonalMatrix", "dMatrix"))# or "dMatrix" ## diagonal, logical matrices; "ldense*" has 'x' slot : setClass("ldiMatrix", contains = c("diagonalMatrix", "lMatrix")) setClass("corMatrix", representation(sd = "numeric"), contains = "dpoMatrix", validity = function(object) { ## assuming that 'dpoMatrix' validity check has already happened: n <- object@Dim[2] if(length(sd <- object@sd) != n) return("'sd' slot must be of length 'dim(.)[1]'") if(any(!is.finite(sd)))# including NA return("'sd' slot has non-finite entries") if(any(sd < 0)) return("'sd' slot has negative entries") TRUE }) ##-------------------- S P A R S E (non-virtual) -------------------------- ##---------- numeric sparse matrix classes -------------------------------- ## numeric, sparse, triplet general matrices setClass("dgTMatrix", contains = c("TsparseMatrix", "dsparseMatrix", "generalMatrix"), validity = function(object) .Call(xTMatrix_validate, object) ) ## Should not have dtTMatrix inherit from dgTMatrix because a dtTMatrix could ## be less than fully stored if diag = "U". Methods for the dgTMatrix ## class would not produce correct results even though all the slots ## are present. ## numeric, sparse, triplet triangular matrices setClass("dtTMatrix", contains = c("TsparseMatrix", "dsparseMatrix", "triangularMatrix"), validity = function(object) .Call(tTMatrix_validate, object) ) ## numeric, sparse, triplet symmetric matrices(also only store one triangle) setClass("dsTMatrix", contains = c("TsparseMatrix", "dsparseMatrix", "symmetricMatrix"), validity = function(object) .Call(tTMatrix_validate, object) ) ## numeric, sparse, sorted compressed sparse column-oriented general matrices setClass("dgCMatrix", contains = c("CsparseMatrix", "dsparseMatrix", "generalMatrix"), validity = function(object) .Call(xCMatrix_validate, object) ) ## special case: indicator rows for a factor - needs more careful definition #setClass("indicators", representation(levels = "character"), # contains = "dgCMatrix") ## see comments for dtTMatrix above ## numeric, sparse, sorted compressed sparse column-oriented triangular matrices setClass("dtCMatrix", contains = c("CsparseMatrix", "dsparseMatrix", "triangularMatrix"), validity = function(object) .Call(tCMatrix_validate, object) ) ## see comments for dsTMatrix above ## numeric, sparse, sorted compressed sparse column-oriented symmetric matrices setClass("dsCMatrix", contains = c("CsparseMatrix", "dsparseMatrix", "symmetricMatrix"), validity = function(object) .Call(tCMatrix_validate, object) ) if(FALSE) ## TODO ??? Class of positive definite (Csparse symmetric) Matrices: setClass("dpCMatrix", contains = "dsCMatrix", validity = function(object) TODO("test for pos.definite ??")) ## numeric, sparse, sorted compressed sparse row-oriented general matrices setClass("dgRMatrix", contains = c("RsparseMatrix", "dsparseMatrix", "generalMatrix"), validity = function(object) .Call(xRMatrix_validate, object) ) ## numeric, sparse, sorted compressed sparse row-oriented triangular matrices setClass("dtRMatrix", contains = c("RsparseMatrix", "dsparseMatrix", "triangularMatrix"), validity = function(object) .Call(tRMatrix_validate, object) ) ## numeric, sparse, sorted compressed sparse row-oriented symmetric matrices setClass("dsRMatrix", contains = c("RsparseMatrix", "dsparseMatrix", "symmetricMatrix"), validity = function(object) .Call(tRMatrix_validate, object) ) ##---------- logical sparse matrix classes -------------------------------- ## these classes are typically result of Matrix comparisons, e.g., ## <..Matrix> >= v (and hence can have NA's) ## logical, sparse, triplet general matrices setClass("lgTMatrix", contains = c("TsparseMatrix", "lsparseMatrix", "generalMatrix"), validity = function(object) .Call(xTMatrix_validate, object) ) ## logical, sparse, triplet triangular matrices setClass("ltTMatrix", contains = c("TsparseMatrix", "lsparseMatrix", "triangularMatrix"), validity = function(object) .Call(tTMatrix_validate, object) ) ## logical, sparse, triplet symmetric matrices setClass("lsTMatrix", contains = c("TsparseMatrix", "lsparseMatrix", "symmetricMatrix"), validity = function(object) .Call(tTMatrix_validate, object) ) ## logical, sparse, sorted compressed sparse column-oriented general matrices setClass("lgCMatrix", contains = c("CsparseMatrix", "lsparseMatrix", "generalMatrix"), validity = function(object) .Call(xCMatrix_validate, object) ) ## logical, sparse, sorted compressed sparse column-oriented triangular matrices setClass("ltCMatrix", contains = c("CsparseMatrix", "lsparseMatrix", "triangularMatrix"), validity = function(object) .Call(xCMatrix_validate, object) ) ## logical, sparse, sorted compressed sparse column-oriented symmetric matrices setClass("lsCMatrix", contains = c("CsparseMatrix", "lsparseMatrix", "symmetricMatrix"), validity = function(object) .Call(xCMatrix_validate, object) ) ## logical, sparse, sorted compressed sparse row-oriented general matrices setClass("lgRMatrix", contains = c("RsparseMatrix", "lsparseMatrix", "generalMatrix"), validity = function(object) .Call(xRMatrix_validate, object) ) ## logical, sparse, sorted compressed sparse row-oriented triangular matrices setClass("ltRMatrix", contains = c("RsparseMatrix", "lsparseMatrix", "triangularMatrix"), validity = function(object) .Call(tRMatrix_validate, object) ) ## logical, sparse, sorted compressed sparse row-oriented symmetric matrices setClass("lsRMatrix", contains = c("RsparseMatrix", "lsparseMatrix", "symmetricMatrix"), validity = function(object) .Call(tRMatrix_validate, object) ) ##---------- nonzero pattern sparse matrix classes --------------------------- ## these classes are used in symbolic analysis to determine the ## locations of non-zero entries ## nonzero pattern, sparse, triplet general matrices setClass("ngTMatrix", contains = c("TsparseMatrix", "nsparseMatrix", "generalMatrix") ## validity: Tsparse_validate should be enough ) ## nonzero pattern, sparse, triplet triangular matrices setClass("ntTMatrix", contains = c("TsparseMatrix", "nsparseMatrix", "triangularMatrix"), ## validity: Tsparse_ and triangular*_validate should be enough ) ## nonzero pattern, sparse, triplet symmetric matrices setClass("nsTMatrix", contains = c("TsparseMatrix", "nsparseMatrix", "symmetricMatrix"), ## validity: Tsparse_ and symmetric*_validate should be enough ) ## nonzero pattern, sparse, sorted compressed column-oriented matrices setClass("ngCMatrix", contains = c("CsparseMatrix", "nsparseMatrix", "generalMatrix"), ## validity: Csparse_validate should be enough ) setClass("ngCMatrix", contains = c("CsparseMatrix", "nsparseMatrix", "generalMatrix"), ## validity: Csparse_validate should be enough ) ## nonzero pattern, sparse, sorted compressed column-oriented triangular matrices setClass("ntCMatrix", contains = c("CsparseMatrix", "nsparseMatrix", "triangularMatrix"), ## validity: Csparse_ and triangular*_validate should be enough ) ## nonzero pattern, sparse, sorted compressed column-oriented symmetric matrices setClass("nsCMatrix", contains = c("CsparseMatrix", "nsparseMatrix", "symmetricMatrix"), ## validity: Csparse_ and symmetric*_validate should be enough ) ## nonzero pattern, sparse, sorted compressed row-oriented general matrices setClass("ngRMatrix", contains = c("RsparseMatrix", "nsparseMatrix", "generalMatrix"), ) ## nonzero pattern, sparse, sorted compressed row-oriented triangular matrices setClass("ntRMatrix", contains = c("RsparseMatrix", "nsparseMatrix", "triangularMatrix"), ) ## nonzero pattern, sparse, sorted compressed row-oriented symmetric matrices setClass("nsRMatrix", contains = c("RsparseMatrix", "nsparseMatrix", "symmetricMatrix"), ) if(FALSE) { ##--not yet-- ##---------- integer sparse matrix classes -------------------------------- ## integer, sparse, triplet general matrices setClass("igTMatrix", contains = c("TsparseMatrix", "isparseMatrix", "generalMatrix"), validity = function(object) .Call(xTMatrix_validate, object) ) ## integer, sparse, triplet triangular matrices setClass("itTMatrix", contains = c("TsparseMatrix", "isparseMatrix", "triangularMatrix"), validity = function(object) .Call(tTMatrix_validate, object) ) ## integer, sparse, triplet symmetric matrices setClass("isTMatrix", contains = c("TsparseMatrix", "isparseMatrix", "symmetricMatrix"), validity = function(object) .Call(tTMatrix_validate, object) ) ## integer, sparse, sorted compressed sparse column-oriented general matrices setClass("igCMatrix", contains = c("CsparseMatrix", "isparseMatrix", "generalMatrix"), validity = function(object) .Call(xCMatrix_validate, object) ) ## integer, sparse, sorted compressed sparse column-oriented triangular matrices setClass("itCMatrix", contains = c("CsparseMatrix", "isparseMatrix", "triangularMatrix"), validity = function(object) .Call(xCMatrix_validate, object) ) ## integer, sparse, sorted compressed sparse column-oriented symmetric matrices setClass("isCMatrix", contains = c("CsparseMatrix", "isparseMatrix", "symmetricMatrix"), validity = function(object) .Call(xCMatrix_validate, object) ) ## integer, sparse, sorted compressed sparse row-oriented general matrices setClass("igRMatrix", contains = c("RsparseMatrix", "isparseMatrix", "generalMatrix"), validity = function(object) .Call(xRMatrix_validate, object) ) ## integer, sparse, sorted compressed sparse row-oriented triangular matrices setClass("itRMatrix", contains = c("RsparseMatrix", "isparseMatrix", "triangularMatrix"), validity = function(object) .Call(tRMatrix_validate, object) ) ## integer, sparse, sorted compressed sparse row-oriented symmetric matrices setClass("isRMatrix", contains = c("RsparseMatrix", "isparseMatrix", "symmetricMatrix"), validity = function(object) .Call(tRMatrix_validate, object) ) }##--not yet-- ##-------------------- index and permutation matrices-------------------------- setClass("indMatrix", representation(perm = "integer"), contains = c("sparseMatrix", "generalMatrix"), validity = function(object) { n <- object@Dim[1] d <- object@Dim[2] perm <- object@perm if (length(perm) != n) return(paste("length of 'perm' slot must be", n)) if(n > 0 && (any(perm > d) | any(perm < 1))) return("'perm' slot is not a valid index") TRUE }) setClass("pMatrix", representation(perm = "integer"), contains = c("indMatrix"), validity = function(object) { d <- object@Dim if (d[2] != (n <- d[1])) return("pMatrix must be square") perm <- object@perm if (length(perm) != n) return(paste("length of 'perm' slot must be", n)) if(n > 0 && !(all(range(perm) == c(1, n)) && length(unique(perm)) == n)) return("'perm' slot is not a valid permutation") TRUE }) ### Factorization classes --------------------------------------------- ## Mother class: setClass("MatrixFactorization", representation(Dim = "integer", "VIRTUAL")) setClass("CholeskyFactorization", representation = "VIRTUAL", contains = "MatrixFactorization") ## -- Those (exceptions) inheriting from "Matrix" : --- setClass("Cholesky", contains = c("dtrMatrix", "CholeskyFactorization")) #unUsed: setClass("LDL", contains = c("dtrMatrix", "CholeskyFactorization")) setClass("pCholesky", contains = c("dtpMatrix", "CholeskyFactorization")) ## These are currently only produced implicitly from *solve() setClass("BunchKaufman", contains = c("dtrMatrix", "MatrixFactorization"), representation(perm = "integer"), validity = function(object) .Call(BunchKaufman_validate, object) ) setClass("pBunchKaufman", contains = c("dtpMatrix", "MatrixFactorization"), representation(perm = "integer"), validity = function(object) .Call(pBunchKaufman_validate, object)) ## -- the usual ``non-Matrix'' factorizations : --------- setClass("CHMfactor", # cholmod_factor struct as S4 object contains = "CholeskyFactorization", representation(colcount = "integer", perm = "integer", type = "integer", "VIRTUAL"), validity = function(object) .Call(CHMfactor_validate, object)) setClass("CHMsuper", # supernodal cholmod_factor contains = "CHMfactor", representation(super = "integer", pi = "integer", px = "integer", s = "integer", "VIRTUAL"), validity = function(object) .Call(CHMsuper_validate, object)) setClass("CHMsimpl", # simplicial cholmod_factor contains = "CHMfactor", representation(p = "integer", i = "integer", nz = "integer", nxt = "integer", prv = "integer", "VIRTUAL"), validity = function(object) .Call(CHMsimpl_validate, object)) setClass("dCHMsuper", contains = "CHMsuper", representation(x = "numeric")) setClass("nCHMsuper", contains = "CHMsuper") setClass("dCHMsimpl", contains = "CHMsimpl", representation(x = "numeric")) setClass("nCHMsimpl", contains = "CHMsimpl") ##--- LU --- setClass("LU", contains = "MatrixFactorization", representation("VIRTUAL")) setClass("denseLU", contains = "LU", representation(x = "numeric", perm = "integer"), validity = function(object) .Call(LU_validate, object)) setClass("sparseLU", contains = "LU", representation(L = "dgCMatrix", U = "dgCMatrix", p = "integer", q = "integer")) ##--- QR --- setClass("sparseQR", contains = "MatrixFactorization", representation(V = "dgCMatrix", beta = "numeric", p = "integer", R = "dgCMatrix", q = "integer"), validity = function(object) .Call(sparseQR_validate, object)) ##-- "SPQR" ---> ./spqr.R for noew ## "denseQR" -- ? (``a version of'' S3 class "qr") if (FALSE) { ## unused classes setClass("csn_QR", representation(U = "dgCMatrix", L = "dgCMatrix", beta = "numeric")) setClass("csn_LU", representation(U = "dgCMatrix", L = "dgCMatrix", Pinv = "integer")) setClass("css_QR", representation(Pinv = "integer", Q = "integer", parent = "integer", cp = "integer", nz = "integer")) setClass("css_LU", representation(Q = "integer", nz = "integer")) } ##-- Schur --- ## non-"Matrix" Class 1 --- For Eigen values: setClassUnion("number", members = c("numeric", "complex")) setClass("Schur", contains = "MatrixFactorization", representation(T = "Matrix", # <- "block-triangular"; maybe triangular Q = "Matrix", EValues = "number"), validity = function(object) { dim <- object@Dim if((n <- dim[1]) != dim[2]) "'Dim' slot is not (n,n)" else if(any(dim(object@T) != n)) "'dim(T)' is incorrect" else if(any(dim(object@Q) != n)) "'dim(Q)' is incorrect" else if(length(object@EValues) != n) "'EValues' is not of correct length" else TRUE }) ### Class Union : no inheritance, but is(*, ) : setClassUnion("mMatrix", members = c("matrix", "Matrix")) ## CARE: Sometimes we'd want all those for which 'x' contains all the data. ## e.g. Diagonal() is "ddiMatrix" with 'x' slot of length 0, does *not* contain 1 setClassUnion("xMatrix", ## those Matrix classes with an 'x' slot c("dMatrix", "iMatrix", "lMatrix", "ndenseMatrix", "zMatrix")) ## Definition Packed := dense with length( . @x) < prod( . @Dim) ## ~~~~~~ ## REPLACED the following with isPacked() in ./Auxiliaries.R : ## setClassUnion("packedMatrix", ## members = c("dspMatrix", "dppMatrix", "dtpMatrix", ## "lspMatrix", "ltpMatrix", "diagonalMatrix")) ## --------------------- non-"Matrix" Classes -------------------------------- ## --- "General" (not Matrix at all) ---- ## e.g. for "Arith" methods: setClassUnion("numLike", members = c("numeric", "logical")) ##setClassUnion("numIndex", members = "numeric") ## Note "rle" is a sealed oldClass (and "virtual" as w/o prototype) setClass("rleDiff", representation(first = "numLike", rle = "rle"), prototype = prototype(first = integer(), ## workaround buglet in R <= 2.10.x: rle = rle(integer()) rle = structure(list(lengths = integer(0L), values = 0[0L]), class = "rle") ), validity = function(object) { if(length(object@first) != 1) return("'first' must be of length one") rl <- object@rle if(!is.list(rl) || length(rl) != 2 || !identical(sort(names(rl)), c("lengths", "values"))) return("'rle' must be a list (lengths = *, values = *)") if(length(lens <- rl$lengths) != length(vals <- rl$values)) return("'lengths' and 'values' differ in length") if(any(lens <= 0)) return("'lengths' must be positive") TRUE }) ### 2010-03-04 -- thinking about *implementing* some 'abIndex' methodology, ### I conclude that the following structure would probably be even more ### efficient than the "rleDiff" one : ### IDEA: Store subsequences in a numeric matrix of three rows, where ### ----- one column = [from, to, by] defining a sub seq()ence ## for now, at least use it, and [TODO!] define "seqMat" <--> "abIndex" coercions: setClass("seqMat", contains = "matrix", prototype = prototype(matrix(0, nrow = 3, ncol=0)), validity = function(object) { if(!is.numeric(object)) return("is not numeric") d <- dim(object) if(length(d) != 3 || d[1] != 3) return("not a 3 x n matrix") if(any(object != floor(object))) return("some entries are not integer valued") TRUE }) setClass("abIndex", # 'ABSTRact Index' representation(kind = "character", ## one of ("int32", "double", "rleDiff") # i.e., numeric or "rleDiff" x = "numLike", # for numeric [length 0 otherwise] rleD = "rleDiff"), # "rleDiff" result prototype = prototype(kind = "int32", x = integer(0)),# rleD = ... etc validity = function(object) { switch(object@kind, "int32" = if(!is.integer(object@x)) return("'x' slot must be integer when kind is 'int32'") , "double" = if(!is.double(object@x)) return("'x' slot must be double when kind is 'double'") , "rleDiff" = { if(length(object@x)) return("'x' slot must be empty when kind is 'rleDiff'") }, ## otherwise return("'kind' must be one of (\"int32\", \"double\", \"rleDiff\")") ) TRUE }) ## for 'i' in x[i] or A[i,] : (numeric = {double, integer}) ## TODO: allow "abIndex" as well ! setClassUnion("index", members = c("numeric", "logical", "character")) ## "atomic vectors" (-> ?is.atomic ) -- but note that is.atomic() ! ## --------------- those that we want to convert from old-style "matrix" setClassUnion("atomicVector", ## "double" is not needed, and not liked by some members = c("logical", "integer", "numeric", "complex", "raw", "character")) ## --- Matrix - related (but not "Matrix" nor "Decomposition/Factorization): ## for 'value' in x[..] <- value hence for all "contents" of our Matrices: setClassUnion("replValue", members = c("numeric", "logical", "complex", "raw")) ### Sparse Vectors ---- here use 1-based indexing ! ----------- ## 'longindex' should allow sparseVectors of "length" > 2^32, ## which is necessary e.g. when converted from large sparse matrices ## setClass("longindex", contains = "numeric") ## but we use "numeric" instead, for simplicity (efficiency?) setClass("sparseVector", representation(length = "numeric", i = "numeric", "VIRTUAL"), ## "longindex" "longindex" ## note that "numeric" contains "integer" (if I like it or not..) prototype = prototype(length = 0), validity = function(object) { n <- object@length if(any(!is.finite(i <- object@i)))# no NA's ! "'i' slot is not all finite" else if(any(i < 1) || any(i > n)) sprintf("'i' must be in 1:%d", n) else if(is.unsorted(i, strictly=TRUE)) "'i' must be sorted strictly increasingly" else TRUE }) ##' initialization -- ensuring that 'i' is sorted (and 'x' alongside) setMethod("initialize", "sparseVector", function(.Object, i, x, ...) { has.x <- !missing(x) if(!missing(i)) { .Object@i <- ## (be careful to assign in all cases) if(is.unsorted(i, strictly=TRUE)) { if(is(.Object, "xsparseVector") && has.x) { si <- sort.int(i, index.return=TRUE) x <- x[si$ix] si$x } else sort.int(i, method = "quick") } else i } if(has.x) .Object@x <- x callNextMethod() }) .validXspVec <- function(object) { ## n <- object@length if(length(object@i) != length(object@x)) "'i' and 'x' differ in length" else TRUE } setClass("dsparseVector", representation(x = "numeric"), contains = "sparseVector", validity = .validXspVec) setClass("isparseVector", representation(x = "integer"), contains = "sparseVector", validity = .validXspVec) setClass("lsparseVector", representation(x = "logical"), contains = "sparseVector", validity = .validXspVec) setClass("zsparseVector", representation(x = "complex"), contains = "sparseVector", validity = .validXspVec) ## nsparse has no new slot: 'i' just contains the locations! setClass("nsparseVector", contains = "sparseVector") setClassUnion("xsparseVector", ## those sparseVector's with an 'x' slot c("dsparseVector", "isparseVector", "lsparseVector", "zsparseVector")) setClass("determinant", representation(modulus = "numeric", logarithm = "logical", sign = "integer", call = "call")) Matrix/R/sparseMatrix.R0000644000175100001440000007666112254023262014560 0ustar hornikusers### Define Methods that can be inherited for all subclasses ### Idea: Coercion between *VIRTUAL* classes -- as() chooses "closest" classes ### ---- should also work e.g. for dense-triangular --> sparse-triangular ! ##-> see als ./dMatrix.R, ./ddenseMatrix.R and ./lMatrix.R setAs("ANY", "sparseMatrix", function(from) as(from, "CsparseMatrix")) ## If people did not use xtabs(), but table(): setAs("table", "sparseMatrix", function(from) { if(length(d <- dim(from)) != 2) stop("only 2-dimensional tables can be directly coerced to sparse matrices") as(unclass(from), "CsparseMatrix") }) setAs("sparseMatrix", "generalMatrix", as_gSparse) setAs("sparseMatrix", "symmetricMatrix", as_sSparse) setAs("sparseMatrix", "triangularMatrix", as_tSparse) spMatrix <- function(nrow, ncol, i = integer(), j = integer(), x = numeric()) { dim <- c(as.integer(nrow), as.integer(ncol)) ## The conformability of (i,j,x) with itself and with 'dim' ## is checked automatically by internal "validObject()" inside new(.): kind <- .M.kind(x) new(paste0(kind, "gTMatrix"), Dim = dim, x = if(kind == "d") as.double(x) else x, ## our "Tsparse" Matrices use 0-based indices : i = as.integer(i - 1L), j = as.integer(j - 1L)) } sparseMatrix <- function(i = ep, j = ep, p, x, dims, dimnames, symmetric = FALSE, index1 = TRUE, giveCsparse = TRUE, check = TRUE, use.last.ij = FALSE) { ## Purpose: user-level substitute for most new(, ..) calls ## Author: Douglas Bates, Date: 12 Jan 2009, based on Martin's version if((m.i <- missing(i)) + (m.j <- missing(j)) + (m.p <- missing(p)) != 1) stop("exactly one of 'i', 'j', or 'p' must be missing from call") if(!m.p) { p <- as.integer(p) if((lp <- length(p)) < 1 || p[1] != 0 || any((dp <- p[-1] - p[-lp]) < 0)) stop("'p' must be a non-decreasing vector (0, ...)") ep <- rep.int(seq_along(dp), dp) } ## i and j are now both defined (via default = ep). Make them 1-based indices. i1 <- as.logical(index1)[1] i <- as.integer(i + !(m.i || i1)) j <- as.integer(j + !(m.j || i1)) ## "minimal dimensions" from (i,j,p); no warnings from empty i or j : dims.min <- suppressWarnings(c(max(i), max(j))) if(any(is.na(dims.min))) stop("NA's in (i,j) are not allowed") if(missing(dims)) { dims <- dims.min } else { ## check dims stopifnot(all(dims >= dims.min)) dims <- as.integer(dims) } sx <- if(symmetric) { if(dims[1] != dims[2]) stop("symmetric matrix must be square") "s" } else "g" isPat <- missing(x) ## <-> patter"n" Matrix kx <- if(isPat) "n" else .M.kind(x) r <- new(paste0(kx, sx, "TMatrix")) r@Dim <- dims if(symmetric && all(i >= j)) r@uplo <- "L" # else "U", the default if(!isPat) { if(kx == "d" && !is.double(x)) x <- as.double(x) if(length(x) != (n <- length(i))) { ## recycle if(length(x) != 1 && n %% length(x) != 0) warning("length(i) is not a multiple of length(x)") x <- rep_len(x, n) } if(use.last.ij && (id <- anyDuplicated(cbind(i,j), fromLast=TRUE))) { i <- i[-id] j <- j[-id] x <- x[-id] if(any(idup <- duplicated(cbind(i,j), fromLast=TRUE))) { ndup <- -which(idup) i <- i[ndup] j <- j[ndup] x <- x[ndup] } } r@x <- x } r@i <- i - 1L r@j <- j - 1L if(!missing(dimnames)) r@Dimnames <- dimnames if(check) validObject(r) if(giveCsparse) as(r, "CsparseMatrix") else r } ## "graph" coercions -- this needs the graph package which is currently ## ----- *not* required on purpose ## Note: 'undirected' graph <==> 'symmetric' matrix ## Use 'graph::' as it is not impoted into Matrix, and may only be loaded, not attached: ## Add some utils that may no longer be needed in future versions of the 'graph' package graph.has.weights <- function(g) "weight" %in% names(graph::edgeDataDefaults(g)) graph.non.1.weights <- function(g) any(unlist(graph::edgeData(g, attr = "weight")) != 1) graph.wgtMatrix <- function(g) { ## Purpose: work around "graph" package's as(g, "matrix") bug ## ---------------------------------------------------------------------- ## Arguments: g: an object inheriting from (S4) class "graph" ## ---------------------------------------------------------------------- ## Author: Martin Maechler, based on Seth Falcon's code; Date: 12 May 2006 ## MM: another buglet for the case of "no edges": if(graph::numEdges(g) == 0) { p <- length(nd <- graph::nodes(g)) return( matrix(0, p,p, dimnames = list(nd, nd)) ) } ## Usual case, when there are edges: if(has.w <- graph.has.weights(g)) { ## graph.non.1.weights(g) : w <- unlist(graph::edgeData(g, attr = "weight")) has.w <- any(w != 1) } ## now 'has.w' is TRUE iff there are weights != 1 ## now 'has.w' is TRUE iff there are weights != 1 m <- as(g, "matrix") ## now is a 0/1 - matrix (instead of 0/wgts) with the 'graph' bug if(has.w) { ## fix it if needed tm <- t(m) tm[tm != 0] <- w t(tm) } else m } setAs("graphAM", "sparseMatrix", function(from) { symm <- graph::edgemode(from) == "undirected" && isSymmetric(from@adjMat) ## This is only ok if there are no weights... if(graph.has.weights(from)) { as(graph.wgtMatrix(from), if(symm) "dsTMatrix" else "dgTMatrix") } else { ## no weights: 0/1 matrix -> logical as(as(from, "matrix"), if(symm) "nsTMatrix" else "ngTMatrix") } }) setAs("graph", "CsparseMatrix", function(from) as(as(from, "graphNEL"), "CsparseMatrix")) setAs("graph", "Matrix", function(from) as(from, "CsparseMatrix")) setAs("graphNEL", "CsparseMatrix", function(from) as(as(from, "TsparseMatrix"), "CsparseMatrix")) graph2T <- function(from, use.weights = graph.has.weights(from) && graph.non.1.weights(from)) { nd <- graph::nodes(from); dnms <- list(nd,nd) dm <- rep.int(length(nd), 2) edge2i <- function(e) { ## return (0-based) row indices 'i' rep.int(0:(dm[1]-1L), ## lens <- vapply(e, length, 0)) } if(use.weights) { eWts <- graph::edgeWeights(from); names(eWts) <- NULL i <- edge2i(eWts) To <- unlist(lapply(eWts, names)) j <- as.integer(match(To,nd)) - 1L # columns indices (0-based) ## symm <- symm && : improbable ## if(symm) new("dsTMatrix", .....) else new("dgTMatrix", i = i, j = j, x = unlist(eWts), Dim = dm, Dimnames = dnms) } else { ## no weights: 0/1 matrix -> logical edges <- lapply(from@edgeL[nd], "[[", "edges") symm <- graph::edgemode(from) == "undirected" if(symm)# each edge appears twice; keep upper triangle only edges <- lapply(seq_along(edges), function(i) {e <- edges[[i]]; e[e >= i]}) i <- edge2i(edges) j <- as.integer(unlist(edges)) - 1L # column indices (0-based) ## if(symm) { # symmetric: ensure upper triangle ## tmp <- i ## flip <- i > j ## i[flip] <- j[flip] ## j[flip] <- tmp[flip] ## new("nsTMatrix", i = i, j = j, Dim = dm, Dimnames = dnms, uplo = "U") ## } else { ## new("ngTMatrix", i = i, j = j, Dim = dm, Dimnames = dnms) ## } new(if(symm) "nsTMatrix" else "ngTMatrix", i = i, j = j, Dim = dm, Dimnames = dnms)# uplo = "U" is default } } setAs("graphNEL", "TsparseMatrix", function(from) graph2T(from)) setAs("sparseMatrix", "graph", function(from) as(from, "graphNEL")) setAs("sparseMatrix", "graphNEL", ## since have specific method for Tsparse below, 'from' is *not*, ## i.e. do not need to "uniquify" the T* matrix: function(from) T2graph(as(from, "TsparseMatrix"), need.uniq=FALSE)) setAs("TsparseMatrix", "graphNEL", function(from) T2graph(from)) T2graph <- function(from, need.uniq = is_not_uniqT(from), edgemode = NULL) { d <- dim(from) if(d[1] != d[2]) stop("only square matrices can be used as incidence matrices for graphs") n <- d[1] if(n == 0) return(new("graphNEL")) if(is.null(rn <- dimnames(from)[[1]])) rn <- as.character(1:n) if(need.uniq) ## Need to 'uniquify' the triplets! from <- uniqTsparse(from) if(is.null(edgemode)) edgemode <- if(isSymmetric(from)) { # either "symmetricMatrix" or otherwise ##-> undirected graph: every edge only once! if(!is(from, "symmetricMatrix")) { ## a general matrix which happens to be symmetric ## ==> remove the double indices from <- tril(from) } "undirected" } else { "directed" } ## every edge is there only once, either upper or lower triangle ft1 <- cbind(rn[from@i + 1L], rn[from@j + 1L]) graph::ftM2graphNEL(ft1, W = if(.hasSlot(from,"x")) as.numeric(from@x), ## else NULL V = rn, edgemode=edgemode) } ### Subsetting -- basic things (drop = "missing") are done in ./Matrix.R ### FIXME : we defer to the "*gT" -- conveniently, but not efficient for gC ! ## [dl]sparse -> [dl]gT -- treat both in one via superclass ## -- more useful when have "z" (complex) and even more setMethod("[", signature(x = "sparseMatrix", i = "index", j = "missing", drop = "logical"), function (x, i,j, ..., drop) { Matrix.msg("sp[i,m,l] : nargs()=",nargs(), .M.level = 2) cld <- getClassDef(class(x)) na <- nargs() x <- if(na == 4) as(x, "TsparseMatrix")[i, , drop=drop] else if(na == 3) as(x, "TsparseMatrix")[i, drop=drop] else ## should not happen stop("Matrix-internal error in [i,,d]; please report") ## ## try_as(x, c(cl, sub("T","C", viaCl))) if(is(x, "Matrix") && extends(cld, "CsparseMatrix")) as(x, "CsparseMatrix") else x }) setMethod("[", signature(x = "sparseMatrix", i = "missing", j = "index", drop = "logical"), function (x,i,j, ..., drop) { Matrix.msg("sp[m,i,l] : nargs()=",nargs(), .M.level = 2) cld <- getClassDef(class(x)) ##> why should this be needed; can still happen in [..]: ##> if(!extends(cld, "generalMatrix")) x <- as(x, "generalMatrix") ## viaCl <- paste0(.M.kind(x, cld), "gTMatrix") x <- as(x, "TsparseMatrix")[, j, drop=drop] ##simpler than x <- callGeneric(x = as(x, "TsparseMatrix"), j=j, drop=drop) if(is(x, "Matrix") && extends(cld, "CsparseMatrix")) as(x, "CsparseMatrix") else x }) setMethod("[", signature(x = "sparseMatrix", i = "index", j = "index", drop = "logical"), function (x, i, j, ..., drop) { Matrix.msg("sp[i,i,l] : nargs()=",nargs(), .M.level = 2) cld <- getClassDef(class(x)) ## be smart to keep symmetric indexing of symmetric: ##> doSym <- (extends(cld, "symmetricMatrix") && ##> length(i) == length(j) && all(i == j)) ##> why should this be needed; can still happen in [..]: ##> if(!doSym && !extends(cld, "generalMatrix")) ##> x <- as(x, "generalMatrix") ## viaCl <- paste0(.M.kind(x, cld), ## if(doSym) "sTMatrix" else "gTMatrix") x <- as(x, "TsparseMatrix")[i, j, drop=drop] if(is(x, "Matrix") && extends(cld, "CsparseMatrix")) as(x, "CsparseMatrix") else x }) ### "[<-" : ----------------- ## setReplaceMethod("[", .........) ## -> ./Tsparse.R ## & ./Csparse.R & ./Rsparse.R {those go via Tsparse} ## x[] <- value : setReplaceMethod("[", signature(x = "sparseMatrix", i = "missing", j = "missing", value = "ANY"),## double/logical/... function (x, i,j,..., value) { if(all0(value)) { # be faster cld <- getClassDef(class(x)) x <- diagU2N(x, cl = cld) for(nm in intersect(nsl <- names(cld@slots), c("x", "i","j", "factors"))) length(slot(x, nm)) <- 0L if("p" %in% nsl) x@p <- rep.int(0L, ncol(x)+1L) } else { ## typically non-sense: assigning to full sparseMatrix x[TRUE] <- value } x }) ## Do not use as.vector() (see ./Matrix.R ) for sparse matrices : setReplaceMethod("[", signature(x = "sparseMatrix", i = "missing", j = "ANY", value = "sparseMatrix"), function (x, i, j, ..., value) callGeneric(x=x, , j=j, value = as(value, "sparseVector"))) setReplaceMethod("[", signature(x = "sparseMatrix", i = "ANY", j = "missing", value = "sparseMatrix"), function (x, i, j, ..., value) callGeneric(x=x, i=i, , value = as(value, "sparseVector"))) setReplaceMethod("[", signature(x = "sparseMatrix", i = "ANY", j = "ANY", value = "sparseMatrix"), function (x, i, j, ..., value) callGeneric(x=x, i=i, j=j, value = as(value, "sparseVector"))) ## Group Methods setMethod("Math", signature(x = "sparseMatrix"), function(x) callGeneric(as(x, "CsparseMatrix"))) ## further group methods -> see ./Ops.R {"Summary": ./dMatrix.R } ### --- print() and show() methods --- .formatSparseSimple <- function(m, asLogical=FALSE, digits=NULL, col.names, note.dropping.colnames = TRUE, dn=dimnames(m)) { stopifnot(is.logical(asLogical)) if(asLogical) cx <- array("N", dim(m), dimnames=dn) else { ## numeric (or --not yet implemented-- complex): cx <- apply(m, 2, format, digits=digits) if(is.null(dim(cx))) {# e.g. in 1 x 1 case dim(cx) <- dim(m) dimnames(cx) <- dn } } if (missing(col.names)) col.names <- { if(!is.null(cc <- getOption("sparse.colnames"))) cc else if(is.null(dn[[2]])) FALSE else { # has column names == dn[[2]] ncol(m) < 10 } } if(identical(col.names, FALSE)) cx <- emptyColnames(cx, msg.if.not.empty = note.dropping.colnames) else if(is.character(col.names)) { stopifnot(length(col.names) == 1) cn <- col.names switch(substr(cn, 1,3), "abb" = { iarg <- as.integer(sub("^[^0-9]*", '', cn)) colnames(cx) <- abbreviate(colnames(cx), minlength = iarg) }, "sub" = { iarg <- as.integer(sub("^[^0-9]*", '', cn)) colnames(cx) <- substr(colnames(cx), 1, iarg) }, stop(gettextf("invalid 'col.names' string: %s", cn), domain=NA)) } ## else: nothing to do for col.names == TRUE cx }## .formatSparseSimple ### NB: Want this to work also for logical or numeric traditional matrix 'x': formatSparseM <- function(x, zero.print = ".", align = c("fancy", "right"), m = as(x,"matrix"), asLogical=NULL, digits=NULL, cx, iN0, dn = dimnames(m)) { cld <- getClassDef(class(x)) if(is.null(asLogical)) { binary <- extends(cld,"nsparseMatrix") || extends(cld, "indMatrix")# -> simple T / F asLogical <- { binary || extends(cld,"lsparseMatrix") || extends(cld,"matrix") && is.logical(x) } # has NA and (non-)structural FALSE } if(missing(cx)) cx <- .formatSparseSimple(m, asLogical=asLogical, digits=digits, dn=dn) if(is.null(d <- dim(cx))) {# e.g. in 1 x 1 case d <- dim(cx) <- dim(m) dimnames(cx) <- dn } if(missing(iN0)) iN0 <- 1L + .Call(m_encodeInd, non0ind(x, cld), di = d, FALSE) ## ne <- length(iN0) if(asLogical) { cx[m] <- "|" if(!extends(cld, "sparseMatrix")) x <- as(x,"sparseMatrix") if(anyFalse(x@x)) { ## any (x@x == FALSE) ## Careful for *non-sorted* Tsparse, e.g. from U-diag if(extends(cld, "TsparseMatrix")) { ## have no "fast uniqTsparse(): x <- as(x, "CsparseMatrix") cld <- getClassDef(class(x)) } F. <- is0(x@x) # the 'FALSE' ones ### FIXME: have iN0 already above -- *really* need the following ??? --FIXME-- ij <- non0.i(x, cld, uniqT=FALSE) if(extends(cld, "symmetricMatrix")) { ## also get "other" triangle notdiag <- ij[,1] != ij[,2] # but not the diagonals again ij <- rbind(ij, ij[notdiag, 2:1], deparse.level=0) F. <- c(F., F.[notdiag]) } iN0 <- 1L + .Call(m_encodeInd, ij, di = d, FALSE) cx[iN0[F.]] <- ":" # non-structural FALSE (or "o", "," , "-" or "f")? } } else if(match.arg(align) == "fancy" && !is.integer(m)) { fi <- apply(m, 2, format.info) ## fi[3,] == 0 <==> not expo. ## now 'format' the zero.print by padding it with ' ' on the right: ## case 1: non-exponent: fi[2,] + as.logical(fi[2,] > 0) ## the column numbers of all 'zero' entries -- (*large*) cols <- 1L + (0:(prod(d)-1L))[-iN0] %/% d[1] pad <- ifelse(fi[3,] == 0, fi[2,] + as.logical(fi[2,] > 0), ## exponential: fi[2,] + fi[3,] + 4) ## now be efficient ; sprintf() is relatively slow ## and pad is much smaller than 'cols'; instead of "simply" ## zero.print <- sprintf("%-*s", pad[cols] + 1, zero.print) if(any(doP <- pad > 0)) { # ## only pad those that need padding - *before* expanding z.p.pad <- rep.int(zero.print, length(pad)) z.p.pad[doP] <- sprintf("%-*s", pad[doP] + 1, zero.print) zero.print <- z.p.pad[cols] } else zero.print <- rep.int(zero.print, length(cols)) } ## else "right" : nothing to do cx[-iN0] <- zero.print cx }## formatSparseM() ## utility used inside sparseMatrix print()ing which might be useful ## outside the Matrix package: formatSpMatrix <- function(x, digits = NULL, # getOption("digits"), maxp = 1e9, # ~ 1/2 * .Machine$integer.max, ## getOption("max.print"), cld = getClassDef(class(x)), zero.print = ".", col.names, note.dropping.colnames = TRUE, align = c("fancy", "right")) { stopifnot(extends(cld, "sparseMatrix")) validObject(x) # have seen seg.faults for invalid objects d <- dim(x) if(extends(cld, "triangularMatrix") && x@diag == "U") { if(extends(cld, "CsparseMatrix")) x <- .Call(Csparse_diagU2N, x) else if(extends(cld, "TsparseMatrix")) x <- .Call(Tsparse_diagU2N, x) else { kind <- .M.kind(x, cld) x <- .Call(Tsparse_diagU2N, as(as(x, paste0(kind, "Matrix")), "TsparseMatrix")) cld <- getClassDef(class(x)) } } ## TODO? Could note it is *unit*-diagonal, e.g., by using "I" instead of "1" ? if(prod(d) > maxp) { # "Large" => will be "cut" ## only coerce to dense that part which won't be cut : nr <- maxp %/% d[2] m <- as(x[1:max(1, nr), ,drop=FALSE], "matrix") } else { m <- as(x, "matrix") } dn <- dimnames(m) ## will be === dimnames(cx) binary <- extends(cld,"nsparseMatrix") || extends(cld, "indMatrix") # -> simple T / F logi <- binary || extends(cld,"lsparseMatrix") # has NA and (non-)structural FALSE cx <- .formatSparseSimple(m, asLogical = logi, digits=digits, col.names=col.names, note.dropping.colnames=note.dropping.colnames, dn=dn) if(is.logical(zero.print)) zero.print <- if(zero.print) "0" else " " if(binary) { cx[!m] <- zero.print cx[m] <- "|" } else { # non-binary ==> has 'x' slot ## show only "structural" zeros as 'zero.print', not all of them.. ## -> cannot use 'm' alone d <- dim(cx) ne <- length(iN0 <- 1L + .Call(m_encodeInd, non0ind(x, cld), di = d, FALSE)) if(0 < ne && (logi || ne < prod(d))) { cx <- formatSparseM(x, zero.print, align, m=m, asLogical=logi, digits=digits, cx=cx, iN0=iN0, dn=dn) } else if (ne == 0)# all zeroes cx[] <- zero.print } cx }## formatSpMatrix() ## FIXME(?) -- ``merge this'' (at least ``synchronize'') with ## - - - prMatrix() from ./Auxiliaries.R ## FIXME: prTriang() in ./Auxiliaries.R should also get align = "fancy" ## printSpMatrix <- function(x, digits = NULL, # getOption("digits"), maxp = getOption("max.print"), cld = getClassDef(class(x)), zero.print = ".", col.names, note.dropping.colnames = TRUE, col.trailer = '', align = c("fancy", "right")) { stopifnot(extends(cld, "sparseMatrix")) x.orig <- x # to be returned cx <- formatSpMatrix(x, digits=digits, maxp=maxp, cld=cld, zero.print=zero.print, col.names=col.names, note.dropping.colnames=note.dropping.colnames, align=align) if(col.trailer != '') cx <- cbind(cx, col.trailer, deparse.level = 0) ## right = TRUE : cheap attempt to get better "." alignment print(cx, quote = FALSE, right = TRUE, max = maxp) invisible(x.orig) } ## printSpMatrix() printSpMatrix2 <- function(x, digits = NULL, # getOption("digits"), maxp = getOption("max.print"), zero.print = ".", col.names, note.dropping.colnames = TRUE, suppRows = NULL, suppCols = NULL, col.trailer = if(suppCols) "......" else "", align = c("fancy", "right")) { d <- dim(x) cl <- class(x) cld <- getClassDef(cl) xtra <- if(extends(cld, "triangularMatrix") && x@diag == "U") " (unitriangular)" else "" cat(sprintf('%d x %d sparse Matrix of class "%s"%s\n', d[1], d[2], cl, xtra)) if((identical(suppRows,FALSE) && identical(suppCols, FALSE)) || (!isTRUE(suppRows) && !isTRUE(suppCols) && prod(d) <= maxp)) { if(missing(col.trailer) && is.null(suppCols)) suppCols <- FALSE # for 'col.trailer' printSpMatrix(x, cld=cld, digits=digits, maxp=maxp, zero.print=zero.print, col.names=col.names, note.dropping.colnames=note.dropping.colnames, col.trailer=col.trailer, align=align) } else { ## d[1] > maxp / d[2] >= nr : -- this needs [,] working: validObject(x) nR <- d[1] ## nrow useW <- getOption("width") - (format.info(nR, digits=digits)[1] + 3+1) ## space for "[,] " ## --> suppress rows and/or columns in printing ... if(is.null(suppCols)) suppCols <- (d[2] * 2 > useW) nc <- if(suppCols) (useW - (1 + nchar(col.trailer))) %/% 2 else d[2] nr <- maxp %/% nc if(is.null(suppRows)) suppRows <- (nr < nR) sTxt <- c("in show(); maybe adjust 'options(max.print= *)'", "\n ..............................\n") if(suppRows) { if(suppCols) x <- x[ , 1:nc, drop = FALSE] n2 <- ceiling(nr / 2) printSpMatrix(x[seq_len(min(nR, max(1, n2))), , drop=FALSE], digits=digits, maxp=maxp, zero.print=zero.print, col.names=col.names, note.dropping.colnames=note.dropping.colnames, col.trailer = col.trailer, align=align) cat("\n ..............................", "\n ........suppressing rows ", sTxt, "\n", sep='') ## tail() automagically uses "[..,]" rownames: printSpMatrix(tail(x, max(1, nr-n2)), digits=digits, maxp=maxp, zero.print=zero.print, col.names=col.names, note.dropping.colnames=note.dropping.colnames, col.trailer = col.trailer, align=align) } else if(suppCols) { printSpMatrix(x[ , 1:nc , drop = FALSE], digits=digits, maxp=maxp, zero.print=zero.print, col.names=col.names, note.dropping.colnames=note.dropping.colnames, col.trailer = col.trailer, align=align) cat("\n .....suppressing columns ", sTxt, sep='') } else stop("logic programming error in printSpMatrix2(), please report") invisible(x) } } ## printSpMatrix2 () setMethod("format", signature(x = "sparseMatrix"), formatSpMatrix) setMethod("print", signature(x = "sparseMatrix"), printSpMatrix2) setMethod("show", signature(object = "sparseMatrix"), function(object) printSpMatrix2(object)) ## For very large and very sparse matrices, the above show() ## is not really helpful; Use summary() as an alternative: setMethod("summary", signature(object = "sparseMatrix"), function(object, ...) { d <- dim(object) T <- as(object, "TsparseMatrix") ## return a data frame (int, int, {double|logical|...}) : r <- if(is(object,"nsparseMatrix")) data.frame(i = T@i + 1L, j = T@j + 1L) else data.frame(i = T@i + 1L, j = T@j + 1L, x = T@x) attr(r, "header") <- sprintf('%d x %d sparse Matrix of class "%s", with %d entries', d[1], d[2], class(object), length(T@i)) ## use ole' S3 technology for such a simple case class(r) <- c("sparseSummary", class(r)) r }) print.sparseSummary <- function (x, ...) { cat(attr(x, "header"),"\n") print.data.frame(x, ...) invisible(x) } ### FIXME [from ../TODO ]: Use cholmod_symmetry() -- ## Possibly even use 'option' as argument here for fast check to use sparse solve !! ##' This case should be particularly fast setMethod("isSymmetric", signature(object = "dgCMatrix"), function(object, tol = 100*.Machine$double.eps, ...) isTRUE(all.equal(.dgC.0.factors(object), t(object), tol = tol, ...))) setMethod("isSymmetric", signature(object = "sparseMatrix"), function(object, tol = 100*.Machine$double.eps, ...) { ## pretest: is it square? d <- dim(object) if(d[1] != d[2]) return(FALSE) ## else slower test using t() -- ## FIXME (for tol = 0): use cholmod_symmetry(A, 1, ...) ## for tol > 0 should modify cholmod_symmetry(..) to work with tol ## or slightly simpler, rename and export is_sym() in ../src/cs_utils.c if (is(object, "dMatrix")) ## use gC; "T" (triplet) is *not* unique! isTRUE(all.equal(.as.dgC.0.factors( object), .as.dgC.0.factors(t(object)), tol = tol, ...)) else if (is(object, "lMatrix")) ## test for exact equality; FIXME(?): identical() too strict? identical(as( object, "lgCMatrix"), as(t(object), "lgCMatrix")) else if (is(object, "nMatrix")) ## test for exact equality; FIXME(?): identical() too strict? identical(as( object, "ngCMatrix"), as(t(object), "ngCMatrix")) else stop("not yet implemented") }) setMethod("isTriangular", signature(object = "CsparseMatrix"), isTriC) setMethod("isTriangular", signature(object = "TsparseMatrix"), isTriT) setMethod("isDiagonal", signature(object = "sparseMatrix"), function(object) { d <- dim(object) if(d[1] != d[2]) return(FALSE) ## else gT <- as(object, "TsparseMatrix") all(gT@i == gT@j) }) setMethod("determinant", signature(x = "sparseMatrix", logarithm = "missing"), function(x, logarithm, ...) determinant(x, logarithm = TRUE, ...)) setMethod("determinant", signature(x = "sparseMatrix", logarithm = "logical"), function(x, logarithm = TRUE, ...) determinant(as(x,"dsparseMatrix"), logarithm, ...)) setMethod("Cholesky", signature(A = "sparseMatrix"), function(A, perm = TRUE, LDL = !super, super = FALSE, Imult = 0, ...) Cholesky(as(A, "CsparseMatrix"), perm=perm, LDL=LDL, super=super, Imult=Imult, ...)) setMethod("diag", signature(x = "sparseMatrix"), function(x, nrow, ncol) diag(as(x, "CsparseMatrix"))) setMethod("dim<-", signature(x = "sparseMatrix", value = "ANY"), function(x, value) { if(!is.numeric(value) || length(value) != 2) stop("dim(.) value must be numeric of length 2") if(prod(dim(x)) != prod(value <- round(value))) # *not* as.integer ! stop("dimensions don't match the number of cells") ## be careful to keep things sparse r <- spV2M(as(x, "sparseVector"), nrow=value[1], ncol=value[2]) ## r now is "dgTMatrix" if(is(x, "CsparseMatrix")) as(r, "CsparseMatrix") else r }) setMethod("norm", signature(x = "sparseMatrix", type = "character"), function(x, type, ...) { type <- toupper(substr(type[1], 1, 1)) switch(type, ## max(, 0) |--> 0 "O" = , "1" = max(colSums(abs(x)), 0), ## One-norm (L_1) "I" = max(rowSums(abs(x)), 0), ## L_Infinity "F" = sqrt(sum(x^2)), ## Frobenius "M" = max(abs(x), 0), ## Maximum modulus of all ## otherwise: stop("invalid 'type'")) }) ## FIXME: need a version of LAPACK's rcond() algorithm, using sparse-arithmetic setMethod("rcond", signature(x = "sparseMatrix", norm = "character"), function(x, norm, useInv=FALSE, ...) { ## as workaround, allow use of 1/(norm(A) * norm(solve(A))) if(!identical(FALSE,useInv)) { Ix <- if(isTRUE(useInv)) solve(x) else if(is(useInv, "Matrix")) useInv return( 1/(norm(x, type=norm) * norm(Ix, type=norm)) ) } ## else d <- dim(x) ## FIXME: qr.R(qr(.)) warns about differing R (permutation!) ## really fix qr.R() *or* go via dense even in those cases rcond(if(d[1] == d[2]) { warning("rcond(.) via sparse -> dense coercion") as(x, "denseMatrix") } else if(d[1] > d[2]) qr.R(qr(x)) else qr.R(qr(t(x))), norm = norm, ...) }) setMethod("cov2cor", signature(V = "sparseMatrix"), function(V) { ## like stats::cov2cor() but making sure all matrices stay sparse p <- (d <- dim(V))[1] if (p != d[2]) stop("'V' is not a *square* matrix") if(!is(V, "dMatrix")) V <- as(V, "dMatrix")# actually "dsparseMatrix" Is <- sqrt(1/diag(V)) if (any(!is.finite(Is))) ## original had 0 or NA warning("diag(.) had 0 or NA entries; non-finite result is doubtful") Is <- Diagonal(x = Is) r <- Is %*% V %*% Is r[cbind(1:p,1:p)] <- 1 # exact in diagonal as(r, "symmetricMatrix") }) setMethod("is.na", signature(x = "sparseMatrix"),## NB: nsparse* have own method! function(x) { if(any((inax <- is.na(x@x)))) { cld <- getClassDef(class(x)) if(extends(cld, "triangularMatrix") && x@diag == "U") inax <- is.na((x <- .diagU2N(x, cld))@x) r <- as(x, "lMatrix") # will be "lsparseMatrix" - *has* x slot r@x <- if(length(inax) == length(r@x)) inax else is.na(r@x) if(!extends(cld, "CsparseMatrix")) r <- as(r, "CsparseMatrix") as(.Call(Csparse_drop, r, 0), "nMatrix") # a 'pattern matrix } else is.na_nsp(x) }) ## all.equal(): similar to all.equal_Mat() in ./Matrix.R ; ## ----------- eventually defer to "sparseVector" methods: setMethod("all.equal", c(target = "sparseMatrix", current = "sparseMatrix"), function(target, current, check.attributes = TRUE, ...) { msg <- attr.all_Mat(target, current, check.attributes=check.attributes, ...) if(is.list(msg)) msg[[1]] else .a.e.comb(msg, all.equal(as(target, "sparseVector"), as(current, "sparseVector"), check.attributes=check.attributes, ...)) }) setMethod("all.equal", c(target = "sparseMatrix", current = "ANY"), function(target, current, check.attributes = TRUE, ...) { msg <- attr.all_Mat(target, current, check.attributes=check.attributes, ...) if(is.list(msg)) msg[[1]] else .a.e.comb(msg, all.equal(as(target, "sparseVector"), current, check.attributes=check.attributes, ...)) }) setMethod("all.equal", c(target = "ANY", current = "sparseMatrix"), function(target, current, check.attributes = TRUE, ...) { msg <- attr.all_Mat(target, current, check.attributes=check.attributes, ...) if(is.list(msg)) msg[[1]] else .a.e.comb(msg, all.equal(target, as(current, "sparseVector"), check.attributes=check.attributes, ...)) }) setMethod("writeMM", "sparseMatrix", function(obj, file, ...) writeMM(as(obj, "CsparseMatrix"), as.character(file), ...)) ### --- sparse model matrix, fac2sparse, etc ----> ./spModels.R ### xtabs(*, sparse = TRUE) ---> part of standard package 'stats' since R 2.10.0 Matrix/R/corMatrix.R0000644000175100001440000000124211004063753014026 0ustar hornikusers#### "corMatrix" (was "correlation" in 2005) --- #### ----------- correlation matrices, inheriting from "dpoMatrix" ## dpo* -> cor* is in ./dpoMatrix.R .M.2cor <- function(from) as(as(from, "dpoMatrix"), "corMatrix") setAs("Matrix", "corMatrix", .M.2cor) setAs("matrix", "corMatrix", .M.2cor) ## This is necessary : setAs("dsyMatrix", "corMatrix", .M.2cor) ## BUT only because __ MM thinks __ ## the *automatical* (by inheritance) coercion ### dsyMatrix -> corMatrix coercion is wrong: ## selectMethod(coerce, c("dsyMatrix","corMatrix")) # gives ## function (from, to) ## { ## obj <- new("corMatrix") ## as(obj, "dsyMatrix") <- from ## obj ## } rm(.M.2cor) Matrix/R/spModels.R0000644000175100001440000003622412221622413013650 0ustar hornikusers#### Utilities for Sparse Model Matrices ## The "first" version {no longer used}: fac2sparse <- function(from, to = c("d","i","l","n","z"), drop.unused.levels = FALSE) { ## factor(-like) --> sparseMatrix {also works for integer, character} fact <- if (drop.unused.levels) factor(from) else as.factor(from) levs <- levels(fact) n <- length(fact) to <- match.arg(to) ## MM: using new() and then assigning slots has efficiency "advantage" ## of *not* validity checking res <- new(paste0(to, "gCMatrix")) res@i <- as.integer(fact) - 1L # 0-based res@p <- 0:n res@Dim <- c(length(levs), n) res@Dimnames <- list(levs, NULL) if(to != "n") res@x <- rep.int(switch(to, "d" = 1., "i" = 1L, "l" = TRUE, "z" = 1+0i), n) res } ## This version can deal with NA's [maybe slightly less efficient (how much?)] : fac2sparse <- function(from, to = c("d","i","l","n","z"), drop.unused.levels = TRUE, giveCsparse = TRUE) { ## factor(-like) --> sparseMatrix {also works for integer, character} fact <- if (drop.unused.levels) factor(from) else as.factor(from) levs <- levels(fact) n <- length(fact) to <- match.arg(to) i <- as.integer(fact) - 1L ## 0-based indices df <- data.frame(i = i, j = if(n) 0:(n-1L) else integer())[!is.na(i),] if(to != "n") df$x <- rep.int(switch(to, "d" = 1., "i" = 1L, "l" = TRUE, "z" = 1+0i), nrow(df)) T <- do.call("new", c(list(Class = paste0(to, "gTMatrix"), Dim = c(length(levs), n), Dimnames = list(levs, names(fact))), df)) if(giveCsparse) .Call(Tsparse_to_Csparse, T, FALSE) else T } setAs("factor", "sparseMatrix", function(from) fac2sparse(from, to = "d")) ##' fac2Sparse() := fac2sparse w/ contrasts ##' ##' @param from factor of which we want the "contrasted" (indicator) ##' design matrix ##' @param to character string specifying the response type ##' @param drop.unused.level logical indicating if non-present factor ##' levels should be dropped, via factor(from) ##' @param factorPatt12 logical vector fp[] of length 2 ##' fp[1] : give contrasted t(X); fp[2] : give "dummy" t(X) [=fac2sparse()] ##' @param contrasts.arg character string or NULL or (coercable to) ##' sparseMatrix, specifying the contrast ##' ##' @return a list of length two, each with the corresponding t(model matrix), ##' when the corresponding factorPatt12 is true. fac2Sparse <- function(from, to = c("d","i","l","n","z"), drop.unused.levels = TRUE, giveCsparse = TRUE, factorPatt12, contrasts.arg = NULL) { stopifnot(is.logical(factorPatt12), length(factorPatt12) == 2) if(any(factorPatt12)) m <- fac2sparse(from, to=to, drop.unused.levels=drop.unused.levels, giveCsparse=giveCsparse) ## ## code '2' : keep dummy, i.e. no contrasts : ans <- list(NULL, if(factorPatt12[2]) m) ## if(factorPatt12[1]) { ## *do* use contrasts.arg if(is.null(contrasts.arg)) contrasts.arg <- getOption("contrasts")[if(is.ordered(from)) "ordered" else "unordered"] ans[[1]] <- crossprod(if(is.character(contrasts.arg)) { stopifnot(is.function(FUN <- get(contrasts.arg))) ## calling contr.*() with correct level names directly : FUN(rownames(m), sparse = TRUE) } else as(contrasts.arg, "sparseMatrix"), m) } ans } ## "Sparse model.matrix()" ## model.matrix(object, data = environment(object), ## contrasts.arg = NULL, xlev = NULL, ...) ## ## Originally: Cut'n'paste from model.matrix() ... just replacing small part at end: sparse.model.matrix <- function(object, data = environment(object), contrasts.arg = NULL, xlev = NULL, transpose = FALSE, drop.unused.levels = FALSE, row.names=TRUE, verbose=FALSE, ...) { t <- if(missing(data)) terms(object) else terms(object, data=data) if (is.null(attr(data, "terms"))) data <- model.frame(object, data, xlev=xlev) else { reorder <- match(sapply(attr(t,"variables"),deparse, width.cutoff=500)[-1L], names(data)) if (any(is.na(reorder))) stop("model frame and formula mismatch in model.matrix()") if(!isSeq(reorder, ncol(data), Ostart=FALSE)) data <- data[,reorder, drop=FALSE] } int <- attr(t, "response") if(length(data)) { # otherwise no rhs terms, so skip all this contr.funs <- as.character(getOption("contrasts")) namD <- names(data) ## turn any character columns into factors for(i in namD) if(is.character(data[[i]])) { data[[i]] <- factor(data[[i]]) warning(gettextf("variable '%s' converted to a factor", i), domain = NA) } isF <- sapply(data, function(x) is.factor(x) || is.logical(x) ) isF[int] <- FALSE isOF <- sapply(data, is.ordered) for(nn in namD[isF]) # drop response if(is.null(attr(data[[nn]], "contrasts"))) contrasts(data[[nn]]) <- contr.funs[1 + isOF[nn]] ## it might be safer to have numerical contrasts: ## get(contr.funs[1 + isOF[nn]])(nlevels(data[[nn]])) if (!is.null(contrasts.arg) && is.list(contrasts.arg)) { if (is.null(namC <- names(contrasts.arg))) stop("invalid 'contrasts.arg' argument") for (nn in namC) { if (is.na(ni <- match(nn, namD))) warning(gettextf("variable '%s' is absent, its contrast will be ignored", nn), domain = NA) else { ca <- contrasts.arg[[nn]] ## FIXME: work for *sparse* ca if(is.matrix(ca)) contrasts(data[[ni]], ncol(ca)) <- ca else contrasts(data[[ni]]) <- contrasts.arg[[nn]] } } } } else { # internal model.matrix needs some variable isF <- FALSE data <- cbind(data, x = 0) } ## src/library/stats/R/models.R has ## ans <- .Internal(model.matrix(t, data)) if(verbose) { cat("model.spmatrix(t, data, ..) with t =\n"); str(t,give.attr=FALSE) } ans <- model.spmatrix(t, data, transpose=transpose, ## ============== drop.unused.levels=drop.unused.levels, row.names=row.names, verbose=verbose) ## attr(ans, "contrasts") <- lapply(data[isF], function(x) attr(x, "contrasts")) ans } ## {sparse.model.matrix} ##' Produce the t(Z); Z = "design matrix" of (X : Y), where ##' --- t(Z) : aka rowwise -version : "r" ##' ##' @title sparse model matrix for 2-way interaction ##' @param X and Y either are numeric matrices {maybe 1-column} ##' @param Y or "as(, sparseM)" ##' @param do.names logical ##' @param forceSparse logical ##' @return ##' @author Martin Maechler sparse2int <- function(X, Y, do.names = TRUE, forceSparse = FALSE, verbose = FALSE) { if(do.names) { dnx <- dimnames(X) dny <- dimnames(Y) } dimnames(Y) <- dimnames(X) <- list(NULL,NULL) nx <- nrow(X) ny <- nrow(Y) r <- if((nX <- is.numeric(X)) | (nY <- is.numeric(Y))) { if(nX) { if (nY || nx > 1) { # both numeric, or X >=2 "columns" F <- if(forceSparse) function(m) .Call(dense_to_Csparse, m) else identity F((if(ny == 1) X else X[rep.int(seq_len(nx), ny) , ]) * (if(nx == 1) Y else Y[rep (seq_len(ny),each=nx), ])) } else { ## numeric X (1 "column"), sparseMatrix Y r <- Y dp <- Y@p[-1] - Y@p[-(Y@Dim[2]+1L)] ## stopifnot(all(dp %in% 0:1)) # just for now ## if(nx == 1) ## FIXME: similar trick would be applicable for nx > 2 r@x <- X[dp == 1L] * Y@x r } } else { ## sparseMatrix X, numeric Y if(ny == 1) { ## FIXME: similar trick would be applicable for ny > 2 r <- X dp <- X@p[-1] - X@p[-(X@Dim[2]+1L)] ## stopifnot(all(dp %in% 0:1)) # just for now - drop! - FIXME r@x <- Y[dp == 1L] * X@x r } else { ## ny > 1 -- *larger* matrix X[rep.int(seq_len(nx), ny) , ] * (if(nx == 1) Y else Y[rep(seq_len(ny),each=nx), ]) } } } else { ## X & Y are both sparseMatrix (if(ny == 1) X else X[rep.int(seq_len(nx), ny) , ]) * (if(nx == 1) Y else Y[rep (seq_len(ny),each=nx) , ]) } if(verbose) cat(sprintf(" sp..2int(%s[%d],%s[%d]) ", if(nX)"" else "", nx, if(nY)"" else "", ny)) if(do.names) { ## FIXME: This names business needs a good solution.. ## but maybe "up in the caller" if(!is.null(dim(r)) && !is.null(nX <- dnx[[1]]) && !is.null(nY <- dny[[1]])) rownames(r) <- outer(nX, nY, paste, sep = ":") } r } ##' Sparse Model Matrix for a (high order) interaction term A:B:x:C ##' ##' @param rList list(.) of (transposed) single-factor model matrices, ##' belonging to, say, factors a, b, c,... ##' @param do.names ##' @param forceSparse ##' @param verbose ##' @return the model matrix corresponding to a:b:... sparseInt.r <- function(rList, do.names = TRUE, forceSparse = FALSE, verbose=FALSE) { nl <- length(rList) if(forceSparse) F <- function(m) if(is.matrix(m)) .Call(dense_to_Csparse, m) else m if(verbose) cat("sparseInt.r([1:",nl,"], f.Sp=",forceSparse,"): is.mat()= (", paste(symnum(vapply(rList, is.matrix, NA)), collapse=""), ")\n", sep="") if(nl == 1) { if(forceSparse) F(rList[[1]]) else rList[[1]] } else { ## 'recursion' free: r <- rList[[1]] for(j in 2:nl) r <- sparse2int(r, rList[[j]], do.names=do.names, verbose=verbose) if(forceSparse) F(r) else r } } ## not used currently is.model.frame <- function(x) { ## Purpose: check if x is a "valid" model.frame ## ------------------------------------------------------------ ## Author: Martin Maechler, Date: 3 Jul 2009 is.data.frame(x) && !is.null(tms <- attr(x, "terms")) && inherits(tms, "terms") && ## is.terms() would be better inherits(tms, "formula") && is.matrix(attr(tms, "factors")) && is.language(vv <- attr(tms, "variables")) && vv[[1]] == as.symbol("list") && all((vars <- sapply(as.list(vv[-1]), as.character)) %in% colnames(x)) ## and we could go on testing vars } ##' Create a sparse model matrix from a model frame. ##' -- This version uses 'rBind' and returns X' i.e. t(X) : ##' ##' @title Sparse Model Matrix from Model Frame ##' @param trms a "terms" object ##' @param mf a data frame, typically resulting from model.frame() ##' @param transpose logical indicating if X' = t(X) {is faster!} ##' or X should be returned ##' @param drop.unused.levels logical indicating if unused factor ##' levels should be dropped ##' @param row.names ##' @return sparse matrix (class "dgCMatrix") ##' @author Martin Maechler model.spmatrix <- function(trms, mf, transpose=FALSE, drop.unused.levels = FALSE, row.names=TRUE, verbose=FALSE) { ## Author: Martin Maechler, Date: 7 Jul 2009 ## mf is a model frame or a "simple" data.frame [after reorder !] stopifnot(is.data.frame(mf)) n <- nrow(mf) if(row.names) rnames <- row.names(mf) ## mf: make into list, dropping all attributes (but the names) fnames <- names(mf <- unclass(mf)) attributes(mf) <- list(names = fnames) if(length(factorPattern <- attr(trms, "factors"))) { d <- dim(factorPattern) nVar <- d[1] nTrm <- d[2] n.fP <- dimnames(factorPattern) fnames <- n.fP[[1]] # == names of variables {incl. "F(var)"} in the model Names <- n.fP[[2]] # == colnames == names of terms: "a", "b:c", ... } else { ## degenerate, e.g. 'Y ~ 1' nVar <- nTrm <- 0L fnames <- Names <- character(0) } ## all the "variables in the model" are also in "mf", including "sin(x)"; ## actually, ..../src/main/model.c even assumes stopifnot((m <- length(mf)) >= nVar) if(verbose) cat(sprintf("model.spm..(): (n=%d, nVar=%d (m=%d), nTrm=%d)\n", n, nVar,m, nTrm)) if(m > nVar) mf <- mf[seq_len(nVar)] stopifnot(fnames == names(mf)) noVar <- nVar == 0 ##>> this seems wrong; we use 1:nVar for indexing mf[] below .. ##>> if(noVar) nVar <- 1L # (as in ~/R/D/r-devel/R/src/main/model.c) ## Note: "character" variables have been changed to factor in the caller; ## hence: both factor and *logical* should be dealt as factor : is.f <- if(noVar) logical(0) else vapply(mf, function(.) is.factor(.) | is.logical(.), NA) indF <- which(is.f) if(verbose) { cat(" --> indF =\n"); print(indF) } hasInt <- attr(trms, "intercept") == 1 ## the degree of interaction: ## intOrder <- attr(trms, "order") ## if(!hasInt && length(indF)) { ## change the '1' of the first factor into a '2' : if(any(i1 <- factorPattern[indF, ] == 1)) ## replace at the first '1' location: factorPattern[indF,][which.max(i1)] <- 2L else {} ## nothing to do } ## Convert "factors" to "Rowwise- sparseMatrix ("dummy"-matrix) ----------- ## Result: a list of sparse model matrices for the "factor"s : f.matr <- structure(vector("list", length = length(indF)), names = fnames[indF]) i.f <- 0 ## ---- For each variable in the model ------------------- for(i in seq_len(nVar)) { nam <- fnames[i] f <- mf[[i]] if(is.f[i]) { fp <- factorPattern[i,] ## == factorPattern[nam,] contr <- attr(f, "contrasts") f.matr[[(i.f <- i.f + 1)]] <- # a list of 2 lapply(fac2Sparse(f, to = "d", drop.unused.levels=drop.unused.levels, factorPatt12 = 1:2 %in% fp, contrasts.arg = contr), function(s) { if(is.null(s)) return(s) ## else rownames(s) <- paste0(nam, if(is.null(rownames(s))) ## for some contr.*(), have lost rownames; hmm.. seq_len(nrow(s)) else rownames(s)) s }) } else { ## continuous variable --> "matrix" - for all of them if(any(iA <- (cl <- class(f)) == "AsIs")) # drop "AsIs" class class(f) <- if(length(cl) > 1L) cl[!iA] nr <- if(is.matrix(f)) nrow(f <- t(f)) else (dim(f) <- c(1L, length(f)))[1] if(is.null(rownames(f))) rownames(f) <- if(nr == 1) nam else paste0(nam, seq_len(nr)) mf[[i]] <- f } } if(verbose) { cat(" ---> f.matr list :\n") str(f.matr, max = as.integer(verbose)) fNms <- format(dQuote(Names)) dim.string <- gsub('5', as.character(floor(1+log10(n))), " -- concatenating (r, rj): dim = (%5d,%5d) | (%5d,%5d)\n") } ## FIXME: do all this in C -- getR <- function(N) # using 'nm' if(!is.null(r <- f.matr[[N]])) r[[factorPattern[N, nm]]] else mf[[N]] vNms <- "(Intercept)"[hasInt] counts <- integer(nTrm) r <- if(hasInt) ## column of 1's - as sparse new("dgCMatrix", i = 0:(n-1L), p = c(0L, n), Dim = c(n, 1L), x = rep.int(1, n)) else new("dgCMatrix", Dim = c(n, 0L)) if(transpose) r <- t(r) iTrm <- seq_len(nTrm) for(j in iTrm) { ## j-th term nm <- Names[j] if(verbose) cat(sprintf("term[%2d] %s .. ", j, fNms[j])) nmSplits <- strsplit(nm, ":", fixed=TRUE)[[1]] ## NOTA BENE: This can be very slow when many terms are involved ## FIXME ??? why does it use *much* memory in those cases ?? rj <- sparseInt.r(lapply(nmSplits, getR), do.names=TRUE, forceSparse = TRUE, verbose=verbose)# or just (verbose >= 2)) if(verbose) cat(sprintf(dim.string, nrow(r), ncol(r), nrow(rj),ncol(rj))) ## fast version of cbind2() / rbind2(), w/o checks, dimnames, etc r <- if(transpose) .Call(Csparse_vertcat, r, rj) else .Call(Csparse_horzcat, r, t(rj)) ## if(verbose) cat(" [Ok]\n") vNms <- c(vNms, dimnames(rj)[[1]]) counts[j] <- nrow(rj) } rns <- if(row.names) rnames dimnames(r) <- if(transpose) list(vNms, rns) else list(rns, vNms) attr(r, "assign") <- c(if(hasInt) 0L, rep(iTrm, counts)) r } ## model.spmatrix() Matrix/R/kronecker.R0000644000175100001440000001231612254575000014046 0ustar hornikusers#### Collect methods for kronecker() here. #### =========== ### ... all but the ``fall back methods'' which are in ./Matrix.R ... ## ~~~~~~~~~~ ### Request: Should be *fast* particularly when used with Diagonal() ! tmp <- function (X, Y, FUN = "*", make.dimnames = FALSE, ...) { kronecker(as(X, "TsparseMatrix"), Y, FUN = FUN, make.dimnames = make.dimnames, ...) } setMethod("kronecker", signature(X="diagonalMatrix", Y="ANY" ), tmp) setMethod("kronecker", signature(X="diagonalMatrix", Y="Matrix" ), tmp) setMethod("kronecker", signature(X="ANY", Y="sparseMatrix" ), tmp) ## the above could recurse infinitely : setMethod("kronecker", signature(X="sparseMatrix", Y="TsparseMatrix"), tmp) tmp <- function (X, Y, FUN = "*", make.dimnames = FALSE, ...) { kronecker(X, as(Y, "TsparseMatrix"), FUN = FUN, make.dimnames = make.dimnames, ...) } setMethod("kronecker", signature(X="ANY", Y="diagonalMatrix"), tmp) setMethod("kronecker", signature(X="Matrix", Y="diagonalMatrix"), tmp) setMethod("kronecker", signature(X="sparseMatrix", Y="ANY" ), tmp) setMethod("kronecker", signature(X="TsparseMatrix", Y="sparseMatrix"), tmp) rm(tmp) ## from ./dgTMatrix.R : setMethod("kronecker", signature(X = "dgTMatrix", Y = "dgTMatrix"), function (X, Y, FUN = "*", make.dimnames = FALSE, ...) { if (FUN != "*") stop("kronecker method must use default 'FUN'") ## otherwise we don't know that many results will be zero ydim <- Y@Dim xi <- X@i xnnz <- length(xi) yi <- Y@i ynnz <- length(yi) new("dgTMatrix", Dim = X@Dim * ydim, i = rep.int(yi, xnnz) + ydim[1] * rep.int(xi, rep.int(ynnz, xnnz)), j = rep.int(Y@j, xnnz) + ydim[2] * rep.int(X@j, rep.int(ynnz, xnnz)), ## faster than x = as.vector(outer(Y@x, X@x, FUN = FUN) x = as.vector(Y@x %*% t(X@x))) }) ## triangularity -- should be preserved "when obvious": setMethod("kronecker", signature(X = "dtTMatrix", Y = "dtTMatrix"), function (X, Y, FUN = "*", make.dimnames = FALSE, ...) { if (FUN != "*") stop("kronecker method must use default 'FUN'") ## otherwise we don't know that many results will be zero if(X@uplo != Y@uplo) { ## result not triangular X <- as(X, "dgTMatrix") Y <- as(Y, "dgTMatrix") return(callGeneric()) } ## else: both 'uplo' are the same -- result *is* triangular ## d.U <- (dX <- X@diag == "U") && (dY <- Y@diag == "U") if(Y@diag == "U") Y <- .diagU2N(Y, "dtTMatrix") ydim <- Y@Dim if(X@diag != "U") { xi <- X@i xj <- X@j xx <- X@x } else { ## X@diag == "U" nx <- X@Dim[1] # triangular matrices are square ii <- seq_len(nx) - 1L xi <- c(X@i, ii) xj <- c(X@j, ii) xx <- c(X@x, rep.int(1, nx)) } xnnz <- length(xi) yi <- Y@i ynnz <- length(yi) new("dtTMatrix", Dim = X@Dim * ydim, i = rep.int(yi, xnnz) + ydim[1] * rep.int(xi, rep.int(ynnz, xnnz)), j = rep.int(Y@j, xnnz) + ydim[2] * rep.int(xj, rep.int(ynnz, xnnz)), ## faster than x = as.vector(outer(Y@x, X@x, FUN = FUN) x = as.vector(Y@x %*% t(xx)), uplo = X@uplo, diag = "N" # if(d.U) { "U" , but drop the entries} else "N" ) }) setMethod("kronecker", signature(X = "dtTMatrix", Y = "dgTMatrix"), function (X, Y, FUN = "*", make.dimnames = FALSE, ...) { if(trY <- isTriangular(Y)) { Y <- gT2tT(Y, uplo = .if.NULL(attr(trY, "kind"), "U"), diag = "N", ## improve: also test for unit diagonal toClass = "dtTMatrix", do.n= FALSE) } else { X <- as(X, "dgTMatrix") } callGeneric() #-> dtT o dtT or dgT o dgT }) setMethod("kronecker", signature(X = "dgTMatrix", Y = "dtTMatrix"), function (X, Y, FUN = "*", make.dimnames = FALSE, ...) { if(trX <- isTriangular(X)) { X <- gT2tT(X, uplo = .if.NULL(attr(trX, "kind"), "U"), diag = "N", ## improve: also test for unit diagonal toClass = "dtTMatrix", do.n= FALSE) } else { Y <- as(Y, "dgTMatrix") } callGeneric() #-> dtT o dtT or dgT o dgT }) setMethod("kronecker", signature(X = "TsparseMatrix", Y = "TsparseMatrix"), function (X, Y, FUN = "*", make.dimnames = FALSE, ...) { if(!is(X, "dMatrix")) X <- as(X, "dMatrix") if(!is(Y, "dMatrix")) Y <- as(Y, "dMatrix") if(is(X, "symmetricMatrix")) X <- as(X, "generalMatrix") if(is(Y, "symmetricMatrix")) Y <- as(Y, "generalMatrix") callGeneric() }) if(FALSE) # probably not needed setMethod("kronecker", signature(X = "dgTMatrix", Y = "TsparseMatrix"), function (X, Y, FUN = "*", make.dimnames = FALSE, ...) { ## a case where Y is neither "dgT" nor "dtT" : if(!is(Y, "dMatrix")) Y <- as(Y, "dMatrix") if(is(Y, "symmetricMatrix")) Y <- as(Y, "generalMatrix") callGeneric() }) ## from ./dsparseMatrix.R : setMethod("kronecker", signature(X = "dsparseMatrix", Y = "dsparseMatrix"), function (X, Y, FUN = "*", make.dimnames = FALSE, ...) { if(is(X, "symmetricMatrix")) X <- as(X, "generalMatrix") if(is(Y, "symmetricMatrix")) Y <- as(Y, "generalMatrix") kronecker(as(X, "TsparseMatrix"), as(Y, "TsparseMatrix"), FUN = FUN, make.dimnames = make.dimnames, ...) }) Matrix/R/nnzero.R0000644000175100001440000000577612207615512013413 0ustar hornikusers#### Number of "structural" non-zeros --- this is nnzmax() in Matlab #### of effectively non-zero values = nnz() " " ## Our nnzero() is like Matlab's nnz() -- but more sophisticated because of NAs ## New: generic function instead of if(..) ... else if(..) ...... ## ## na.counted: TRUE : NA's are counted, they are not 0 ## NA : NA's are not known (0 or not) ==> result := NA ## FALSE: NA's are omitted before counting ## "Default" : for non-"Matrix" (e.g. classical matrices): setMethod("nnzero", "ANY", function(x, na.counted = NA) sum(nz.NA(x, na.counted))) setMethod("nnzero", "diagonalMatrix", function(x, na.counted = NA) sum(nz.NA(diag(x), na.counted))) setMethod("nnzero", "indMatrix", function(x, na.counted = NA) x@Dim[1]) ## other (not "indMatrix", not "diagonalMatrix") "sparseMatrix": setMethod("nnzero", "sparseMatrix", function(x, na.counted = NA) { d <- x@Dim if(any(d == 0)) return(0L) cl <- class(x) ## speedup: cld <- getClassDef(cl) n <- d[1] iSym <- extends(cld, "symmetricMatrix") iTri <- if(iSym) FALSE else extends(cld, "triangularMatrix") nn <- switch(.sp.class(cl), "CsparseMatrix" = x@p[d[2]+1L],# == length(x@i) only if not over-alloc. "TsparseMatrix" = { if(is_duplicatedT(x, di = d)) x <- .Call(Tsparse_to_Csparse, x, iTri) length(x@i) }, "RsparseMatrix" = x@p[n+1L]) if(!extends(cld, "nMatrix")) # <==> has 'x' slot : consider NAs in it: nn <- sum(nz.NA(if(nn < length(x@x)) x@x[seq_len(nn)] else x@x, na.counted)) if(iSym) nn+nn - sum(nz.NA(diag(x), na.counted)) else if(iTri && x@diag == "U") nn + n else nn }) setMethod("nnzero", "denseMatrix", function(x, na.counted = NA) { d <- x@Dim if(any(d == 0)) return(0L) cl <- class(x) ## speedup: cld <- getClassDef(cl) n <- d[1] iSym <- extends(cld, "symmetricMatrix") ## dense, not diagonal: Can use 'x' slot; if(iSym || extends(cld, "triangularMatrix")) { ## now !iSym <==> "triangularMatrix" upper <- (x@uplo == "U") if(length(x@x) < n*n) { ## packed symmetric | triangular if(iSym) { ## indices of *diagonal* entries for packed : iDiag <- cumsum(if(upper) 1:n else c(1L, if(n > 1)n:2)) ## symmetric packed: count off-diagonals *twice* 2L* sum(nz.NA(x@x[-iDiag], na.counted)) + sum(nz.NA(x@x[ iDiag], na.counted)) } else ## triangular packed sum(nz.NA(x@x, na.counted)) } else { ## not packed, but may have "arbitrary" ## entries in the non-relevant upper/lower triangle s <- sum(nz.NA(x@x[indTri(n, upper=upper)], na.counted)) (if(iSym) 2L * s else s) + (if(!iSym && x@diag == "U") n else sum(nz.NA(x@x[indDiag(n)], na.counted))) } } else { ## dense general <--> .geMatrix sum(nz.NA(x@x, na.counted)) } }) ## Working via sparse*: setMethod("nnzero", "CHMfactor", function(x, na.counted = NA) nnzero(as(x,"sparseMatrix"), na.counted=na.counted)) Matrix/R/lMatrix.R0000644000175100001440000001036412003525364013504 0ustar hornikuserssetAs("matrix", "lMatrix", function(from) { storage.mode(from) <- "logical" ; Matrix(from) }) ## NOTE: This is *VERY* parallel to ("dMatrix" -> "nMatrix") in ./dMatrix.R : setAs("lMatrix", "nMatrix", function(from) { if(any(is.na(from@x))) stop("\"lMatrix\" object with NAs cannot be coerced to \"nMatrix\"") ## i.e. from@x are only TRUE or FALSE cld <- getClassDef(cl <- MatrixClass(class(from))) if(extends(cld, "diagonalMatrix")) { # have no "ndi*" etc class cl <- class(from <- as(from, "sparseMatrix")) isSp <- TRUE } else { isSp <- extends(cld, "sparseMatrix") if(isSp && !all(from@x)) { from <- drop0(from) # was drop0(from, cld) if(cl != (c. <- class(from))) cld <- getClassDef(cl <- c.) } } sNams <- slotNames(cld) copyClass(from, sub("^l", "n", cl), if(isSp) sNams[sNams != "x"] else sNams) }) ## and the reverse as well : setAs("nMatrix", "lMatrix", function(from) { cld <- getClassDef(cl <- MatrixClass(class(from))) r <- copyClass(from, sub("^n", "l", cl), slotNames(cld)) if(extends(cld, "sparseMatrix")) r@x <- rep.int(TRUE, length(if(!extends(cld, "RsparseMatrix")) from@i else from@j)) r }) setAs("dMatrix", "lMatrix", function(from) { cld <- getClassDef(newCl <- class2(cl <- class(from), "l")) sNams <- slotNames(cld) r <- copyClass(from, newCl, sNames = sNams[sNams != "x"]) r@x <- as.logical(from@x) r }) setAs("lMatrix", "dMatrix", function(from) { cld <- getClassDef(cl <- MatrixClass(class(from))) sNams <- slotNames(cld) r <- copyClass(from, newCl = sub("^l", "d", cl), sNames = sNams[sNams != "x"]) r@x <- as.double(from@x) r }) ## needed at least for lsparse* : setAs("lMatrix", "dgCMatrix", function(from) as(as(from, "lgCMatrix"), "dgCMatrix")) ###-------------- which( ) ----------------------------------------------------- ## "ldi: is both "sparseMatrix" and "lMatrix" but not "lsparseMatrix" setMethod("which", "ldiMatrix", function(x, arr.ind) { n <- x@Dim[1L] i <- if(x@diag == "U") seq_len(n) else which(x@x) if(arr.ind) cbind(i,i, deparse.level = 0) else i + n*(i - 1L) }) whichDense <- function(x, arr.ind = FALSE) { wh <- which(x@x) ## faster but "forbidden": .Internal(which(x@x)) if (arr.ind && !is.null(d <- dim(x))) arrayInd(wh, d, useNames=FALSE) else wh } setMethod("which", "ndenseMatrix", function(x, arr.ind) whichDense(as(x, "ngeMatrix"), arr.ind=arr.ind)) setMethod("which", "ldenseMatrix", function(x, arr.ind) whichDense(as(x, "lgeMatrix"), arr.ind=arr.ind)) setMethod("which", "nsparseMatrix", function(x, arr.ind) { if(arr.ind) which(as(x, "TsparseMatrix"), arr.ind=TRUE) else as(x, "sparseVector")@i }) setMethod("which", "lsparseMatrix", function(x, arr.ind) { if(arr.ind) which(as(x, "TsparseMatrix"), arr.ind=TRUE) else which(as(x, "sparseVector")) }) which.ngT <- function(x, arr.ind) if(arr.ind) cbind(x@i, x@j) + 1L else as(x, "sparseVector")@i setMethod("which", "ngTMatrix", which.ngT) setMethod("which", "ntTMatrix", function(x, arr.ind) which.ngT(.Call(Tsparse_diagU2N, x), arr.ind)) setMethod("which", "nsTMatrix", function(x, arr.ind) which.ngT(as(x, "generalMatrix"), arr.ind)) which.lgT <- function(x, arr.ind) { if(arr.ind) { iT <- is1(x@x) cbind(x@i[iT], x@j[iT]) + 1L } else which(as(x, "sparseVector")) } setMethod("which", "lgTMatrix", which.lgT) setMethod("which", "ltTMatrix", function(x, arr.ind) which.lgT(.Call(Tsparse_diagU2N, x), arr.ind)) setMethod("which", "lsTMatrix", function(x, arr.ind) which.lgT(as(x, "generalMatrix"), arr.ind)) ## all() methods ---> ldenseMatrix.R and lsparseMatrix.R setMethod("any", signature(x = "lMatrix"), function(x, ..., na.rm = FALSE) ## logical unit-triangular has TRUE diagonal: (prod(dim(x)) >= 1 && is(x, "triangularMatrix") && x@diag == "U") || any(x@x, ..., na.rm = na.rm)) setMethod("is.finite", signature(x = "lMatrix"), function(x) !is.na(x)) setMethod("is.finite", signature(x = "nMatrix"), allTrueMatrix) setMethod("is.infinite", signature(x = "lMatrix"), is.na_nsp)# all FALSE setMethod("is.infinite", signature(x = "nMatrix"), is.na_nsp)# all FALSE Matrix/R/dsTMatrix.R0000644000175100001440000000233611003616106013775 0ustar hornikusers### Coercion and Methods for Symmetric Triplet Matrices ## Now in ./Tsparse.R ## setAs("dsTMatrix", "dsCMatrix", ## function(from) .Call(Tsparse_to_Csparse, from, FALSE)) setAs("dsTMatrix", "dgTMatrix", function(from) .Call(dsTMatrix_as_dgTMatrix, from)) setAs("dsTMatrix", "lsTMatrix", function(from) new("lsTMatrix", i = from@i, j = from@j, uplo = from@uplo, Dim = from@Dim, Dimnames = from@Dimnames)) ## Conversion <--> dense storage is via dsyMatrix : setAs("dsTMatrix", "dsyMatrix", function(from) .Call(dsTMatrix_as_dsyMatrix, from)) setAs("dsTMatrix", "dgeMatrix", function(from) as(as(from, "dsyMatrix"), "dgeMatrix")) setAs("dsTMatrix", "matrix", function(from) as(as(from, "dsyMatrix"), "matrix")) to_dsT <- function(from) as(as(from, "dsyMatrix"), "dsTMatrix") setAs("dgeMatrix", "dsTMatrix", to_dsT) setAs("matrix", "dsTMatrix", to_dsT) setMethod("t", "dsTMatrix", function(x) new("dsTMatrix", Dim = x@Dim, Dimnames = x@Dimnames, i = x@j, j = x@i, x = x@x, uplo = if (x@uplo == "U") "L" else "U")) ## setMethod("writeHB", signature(obj = "dsTMatrix"), ## function(obj, file, ...) callGeneric(as(obj, "CsparseMatrix"), file, ...)) Matrix/R/colSums.R0000644000175100001440000002304212211567675013522 0ustar hornikusers#### Collect methods for colSums(), rowSums(), colMeans(), rowMeans() here. #### ======= ------- -------- -------- ## Utilities: ## .as.dgC.Fun <- function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) { ## x <- as(x, "dgCMatrix") ## callGeneric() ## } ## .as.dgT.Fun <- function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) { ## x <- as(x, "dgTMatrix") ## callGeneric() ## } .as.d.Fun <- function(x, na.rm = FALSE, dims = 1) { x <- as(x, "dMatrix") callGeneric() } .as.dge.Fun <- function(x, na.rm = FALSE, dims = 1) { x <- as(x, "dgeMatrix") callGeneric() } .as.gC.Fun <- function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) { x <- as_gCsimpl(x) callGeneric() } .as.C.Fun <- function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) { x <- as(x, "CsparseMatrix") ## or if necessary as_Csparse(.) callGeneric() } ### Dense Matrices: ------------------------------------------------- setMethod("colSums", signature(x = "denseMatrix"), .as.d.Fun) setMethod("colMeans", signature(x = "denseMatrix"), .as.d.Fun) setMethod("rowSums", signature(x = "denseMatrix"), .as.d.Fun) setMethod("rowMeans", signature(x = "denseMatrix"), .as.d.Fun) ## FIXME: "works" but not optimally for triangular/symmetric(packed)/.. setMethod("colSums", signature(x = "ddenseMatrix"), .as.dge.Fun) setMethod("colMeans", signature(x = "ddenseMatrix"), .as.dge.Fun) setMethod("rowSums", signature(x = "ddenseMatrix"), .as.dge.Fun) setMethod("rowMeans", signature(x = "ddenseMatrix"), .as.dge.Fun) setMethod("colSums", signature(x = "dgeMatrix"), function(x, na.rm = FALSE, dims = 1) .Call(dgeMatrix_colsums, x, na.rm, TRUE, FALSE), valueClass = "numeric") setMethod("colMeans", signature(x = "dgeMatrix"), function(x, na.rm = FALSE, dims = 1) .Call(dgeMatrix_colsums, x, na.rm, TRUE, TRUE), valueClass = "numeric") setMethod("rowSums", signature(x = "dgeMatrix"), function(x, na.rm = FALSE, dims = 1) .Call(dgeMatrix_colsums, x, na.rm, FALSE, FALSE), valueClass = "numeric") setMethod("rowMeans", signature(x = "dgeMatrix"), function(x, na.rm = FALSE, dims = 1) .Call(dgeMatrix_colsums, x, na.rm, FALSE, TRUE), valueClass = "numeric") ### Sparse Matrices: ------------------------------------------------- ## Diagonal ones: .diag.Sum <- function(x, na.rm = FALSE, dims = 1) if(x@diag == "U") rep(1, x@Dim[1]) else as.numeric(x@x) .diag.Mean <- function(x, na.rm = FALSE, dims = 1) { n <- x@Dim[1L] if(x@diag == "U") rep(1/n, n) else as.numeric(x@x)/n } setMethod("colSums", signature(x = "diagonalMatrix"), .diag.Sum) setMethod("rowSums", signature(x = "diagonalMatrix"), .diag.Sum) setMethod("colMeans", signature(x = "diagonalMatrix"), .diag.Mean) setMethod("rowMeans", signature(x = "diagonalMatrix"), .diag.Mean) rm(.diag.Sum, .diag.Mean) ### Csparse --- the fast workhorse ones ### 1) those with .Call(.), {d, i, l, n} gCMatrix x {col|row}{Sums|Means} : ## the last two arguments to dgCMatrix_colSums are `trans' and `means' setMethod("colSums", signature(x = "dgCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(dgCMatrix_colSums, x, na.rm, sparseResult, FALSE, FALSE)) setMethod("rowSums", signature(x = "dgCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(dgCMatrix_colSums, x, na.rm, sparseResult, TRUE, FALSE)) setMethod("colMeans", signature(x = "dgCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(dgCMatrix_colSums, x, na.rm, sparseResult, FALSE, TRUE)) setMethod("rowMeans", signature(x = "dgCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(dgCMatrix_colSums, x, na.rm, sparseResult, TRUE, TRUE)) setMethod("colSums", signature(x = "igCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(igCMatrix_colSums, x, na.rm, sparseResult, FALSE, FALSE)) setMethod("rowSums", signature(x = "igCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(igCMatrix_colSums, x, na.rm, sparseResult, TRUE, FALSE)) setMethod("colMeans", signature(x = "igCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(igCMatrix_colSums, x, na.rm, sparseResult, FALSE, TRUE)) setMethod("rowMeans", signature(x = "igCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(igCMatrix_colSums, x, na.rm, sparseResult, TRUE, TRUE)) setMethod("colSums", signature(x = "lgCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(lgCMatrix_colSums, x, na.rm, sparseResult, FALSE, FALSE)) setMethod("rowSums", signature(x = "lgCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(lgCMatrix_colSums, x, na.rm, sparseResult, TRUE, FALSE)) setMethod("colMeans", signature(x = "lgCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(lgCMatrix_colSums, x, na.rm, sparseResult, FALSE, TRUE)) setMethod("rowMeans", signature(x = "lgCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(lgCMatrix_colSums, x, na.rm, sparseResult, TRUE, TRUE)) setMethod("colSums", signature(x = "ngCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(ngCMatrix_colSums, x, na.rm, sparseResult, FALSE, FALSE)) setMethod("rowSums", signature(x = "ngCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(ngCMatrix_colSums, x, na.rm, sparseResult, TRUE, FALSE)) setMethod("colMeans", signature(x = "ngCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(ngCMatrix_colSums, x, na.rm, sparseResult, FALSE, TRUE)) setMethod("rowMeans", signature(x = "ngCMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) .Call(ngCMatrix_colSums, x, na.rm, sparseResult, TRUE, TRUE)) ### 2) the other Csparse ones are "just" coerced to a *gCMatrix : setMethod("colSums", signature(x = "CsparseMatrix"), .as.gC.Fun) setMethod("colMeans", signature(x = "CsparseMatrix"), .as.gC.Fun) setMethod("rowSums", signature(x = "CsparseMatrix"), .as.gC.Fun) setMethod("rowMeans", signature(x = "CsparseMatrix"), .as.gC.Fun) ##setMethod("rowSums", signature(x = "dgCMatrix"), ## function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) ## sparsapply(x, 1, sum, sparseResult = sparseResult, na.rm = na.rm)) ##setMethod("rowMeans", signature(x = "dgCMatrix"), sp.rowMeans) ## --- Tsparse ---- ## .as.C.Fun -- since there's now C code for dgCMatrix_colSums setMethod("colSums", signature(x = "TsparseMatrix"), .as.C.Fun) setMethod("colMeans", signature(x = "TsparseMatrix"), .as.C.Fun) setMethod("rowSums", signature(x = "TsparseMatrix"), .as.C.Fun) setMethod("rowMeans", signature(x = "TsparseMatrix"), .as.C.Fun) ## setMethod("colSums", signature(x = "TsparseMatrix"), .as.dgT.Fun, ## valueClass = "numeric") ## setMethod("colMeans", signature(x = "TsparseMatrix"), .as.dgT.Fun, ## valueClass = "numeric") ## ## setMethod("rowSums", signature(x = "TsparseMatrix"), .as.dgT.Fun, ## valueClass = "numeric") ## setMethod("rowMeans", signature(x = "TsparseMatrix"), .as.dgT.Fun, ## valueClass = "numeric") ## setMethod("colSums", signature(x = "dgTMatrix"), ## function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) ## sparsapply(x, 2, sum, sparseResult = sparseResult, na.rm = na.rm)) ## setMethod("rowSums", signature(x = "dgTMatrix"), ## function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) ## sparsapply(x, 1, sum, sparseResult = sparseResult, na.rm = na.rm)) ## setMethod("colMeans", signature(x = "dgTMatrix"), sp.colMeans) ## setMethod("rowMeans", signature(x = "dgTMatrix"), sp.rowMeans) ## --- Rsparse ---- ## row <-> col of the "transposed, seen as C" : setMethod("rowSums", signature(x = "RsparseMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) colSums(.tR.2.C(x), na.rm=na.rm, dims=dims, sparseResult=sparseResult)) setMethod("rowMeans", signature(x = "RsparseMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) colMeans(.tR.2.C(x), na.rm=na.rm, dims=dims, sparseResult=sparseResult)) setMethod("colSums", signature(x = "RsparseMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) rowSums(.tR.2.C(x), na.rm=na.rm, dims=dims, sparseResult=sparseResult)) setMethod("colMeans", signature(x = "RsparseMatrix"), function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) rowMeans(.tR.2.C(x), na.rm=na.rm, dims=dims, sparseResult=sparseResult)) ## ## These two are obviously more efficient than going through Tsparse: ## setMethod("colSums", signature(x = "dgRMatrix"), ## function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) ## sparsapply(x, 2, sum, sparseResult = sparseResult, na.rm = na.rm)) ## setMethod("colMeans", signature(x = "dgRMatrix"), sp.colMeans) ## --- indMatrix [incl pMatrix ] --- setMethod("colSums", signature(x = "indMatrix"), function(x, na.rm = FALSE, dims = 1) tabulate(x@perm, nbins=x@Dim[2])) setMethod("colMeans", signature(x = "indMatrix"), function(x, na.rm = FALSE, dims = 1) tabulate(x@perm, nbins=x@Dim[2])/x@Dim[1]) ## for completeness: setMethod("rowSums", signature(x = "indMatrix"), function(x, na.rm = FALSE, dims = 1) rep.int(1, x@Dim[1])) setMethod("rowMeans", signature(x = "indMatrix"), function(x, na.rm = FALSE, dims = 1) rep.int(1/x@Dim[2], x@Dim[1])) Matrix/R/not.R0000644000175100001440000000672211307004303012656 0ustar hornikusers#### --- All method definitions for "!" (not) --- ## Divert everything to "lMatrix" and its subclasses : setMethod("!", "Matrix", function(x) !as(x, "lMatrix")) ## -- diag --- setMethod("!", "ldiMatrix", function(x) { r <- copyClass(x, "lsyMatrix", c("Dim","Dimnames")) n <- x@Dim[1] if (n > 0) { ## off-diagonal: assign all and then reassign diagonals: rx <- rep.int(TRUE, n * n) ## diagonal entries: rx[1L + 0:(n - 1L) * (n + 1L)] <- { if(x@diag == "N") !x@x else FALSE ## "U" } r@x <- rx } r }) ## -- lsparse -- setMethod("!", "lsparseMatrix", ## turns FALSE to TRUE --> dense matrix function(x) !as(x, "denseMatrix"))# was "lgeMatrix" ## Use "Matrix" method !as(. , "lMatrix") ## setMethod("!", "nsparseMatrix", ## ## turns FALSE to TRUE --> dense matrix ## function(x) !as(x, "ngeMatrix")) ## -- ldense --- setMethod("!", "ltrMatrix", function(x) { x@x <- !x@x ## And now fill one triangle with '!FALSE' results : ## TODO: the following should be .Call using ## a variation of make_array_triangular: r <- as(x, "lgeMatrix") n <- x@Dim[1] if(x@diag == "U") r@x[indDiag(n)] <- FALSE ## result has diagonal all FALSE r@x[indTri(n, upper=x@uplo != "U")] <- TRUE r }) setMethod("!", "ltpMatrix", function(x) !as(x, "ltrMatrix")) ## for the other ldense* ones setMethod("!", "lgeMatrix", function(x) { x@x <- !x@x ; x }) setMethod("!", "ldenseMatrix", function(x) { if(is(x, "symmetricMatrix")) { # lsy | lsp x@x <- !x@x x } else ## triangular are dealt with above already : "general" here: !as(x, "lgeMatrix") }) ## -- ndense --- setMethod("!", "ntrMatrix", function(x) { x@x <- !x@x ## And now we must fill one triangle with '!FALSE' results : ## TODO: the following should be .Call using ## a variation of make_array_triangular: r <- as(x, "ngeMatrix") n <- x@Dim[1] coli <- rep(1:n, each=n) rowi <- rep(1:n, n) Udiag <- x@diag == "U" log.i <- if(x@uplo == "U") { if(Udiag) rowi >= coli else rowi > coli } else { if(Udiag) rowi <= coli else rowi < coli } r@x[log.i] <- TRUE r }) setMethod("!", "ntpMatrix", function(x) !as(x, "ntrMatrix")) ## for the other ldense* ones setMethod("!", "ngeMatrix", function(x) { x@x <- !x@x ; x }) setMethod("!", "ndenseMatrix", function(x) { if(is(x, "symmetricMatrix")) { # lsy | lsp x@x <- !x@x x } else ## triangular are dealt with above already : "general" here: !as(x, "ngeMatrix") }) ### ---- sparseVector ----- setMethod("!", "sparseVector", function(x) { n <- x@length if(2 * length(x@i) <= n) !sp2vec(x) else { ## sparse result ii <- seq_len(n)[-x@i] if((has.x <- !is(x, "nsparseVector"))) { xx <- rep.int(TRUE, (l.i <- length(ii))) if((.na <- any(x.na <- is.na(x@x))) | (.fa <- any(x.f <- !x.na & !x@x))) { ## deal with 'FALSE' and 'NA' in x slot if(.na) { ii <- c(ii, x@i[x.na]) xx <- c(xx, x@x[x.na]) } if(.fa) { ## any(x.f) x.f <- x.f & !x.na ii <- c(ii, x@i[x.f]) xx <- c(xx, rep.int(TRUE, sum(x.f))) } ## sort increasing in index: i.s <- sort.list(ii) ii <- ii[i.s] xx <- xx[i.s] } } if(has.x) newSpV("lsparseVector", x = xx, i = ii, length = n) else new("nsparseVector", i = ii, length = n) } }) Matrix/R/KhatriRao.R0000644000175100001440000000363012233417610013745 0ustar hornikusers# Efficient Khatri-Rao product for large sparse matrices # Assumes two matrices in CsparseMatrix format # Written by Michael Cysouw ## MM: there's a "public" Matlab version, at ## http://www.mathworks.com/matlabcentral/fileexchange/28872-khatri-rao-product/content/kr.m ## with documentation ## ## % Khatri-Rao product. ## ## % kr(A,B) returns the Khatri-Rao product of two matrices A and B, of ## % dimensions I-by-K and J-by-K respectively. The result is an I*J-by-K ## % matrix formed by the matching columnwise Kronecker products, i.e. ## % the k-th column of the Khatri-Rao product is defined as ## % kron(A(:,k),B(:,k)). KhatriRao <- function(X, Y = X, FUN = "*", make.dimnames = FALSE) { stopifnot((p <- ncol(X)) == ncol(Y)) X <- as(X,"CsparseMatrix") Y <- as(Y,"CsparseMatrix") xn <- diff( X@p) yn <- diff(yp <- Y@p) ## both of length p newp <- as.integer(diffinv(xn*yn)) xn.yp <- xn[ as.logical(yn) ] # xn "where" Y is present yj <- .Call(Matrix_expand_pointers, yp)## as(Y,"TsparseMatrix")@j yj <- factor(yj) # for split() below rep.yn <- rep.int(yn,xn) i1 <- rep.int(X@i, rep.yn) i2 <- unlist(rep(split.default(Y@i,yj), xn.yp)) n1 <- nrow(X); n2 <- nrow(Y) newi <- i1*n2 + i2 dim <- as.integer(c(n1*n2, p)) dns <- if (make.dimnames) { ## this is not good enough: dnx, dny may be NULL list(as.vector(outer(rownames(Y),rownames(X), FUN = "paste", sep = ":")), colnames(X)) } else list(NULL,NULL) if((nX <- is(X, "nMatrix")) & (nY <- is(Y, "nMatrix"))) new("ngCMatrix", Dim=dim, Dimnames=dns, i = newi, p = newp) else { ## at least one of 'X' and 'Y' has an "x" slot: if(nX) X <- as(X, "lgCMatrix") if(nY) Y <- as(Y, "lgCMatrix") x1 <- rep.int(X@x, rep.yn) x2 <- unlist(rep(split.default(Y@x,yj), xn.yp)) new("dgCMatrix", Dim=dim, Dimnames=dns, i = newi, p = newp, x = match.fun(FUN) (x1,x2)) } } Matrix/R/products.R0000644000175100001440000006034612271746775013756 0ustar hornikusers#### All %*%, crossprod() and tcrossprod() methods of the Matrix package #### ^^^ ---------------------------------------------------------- ### with EXCEPTIONS: ./diagMatrix.R ### ./indMatrix.R ./pMatrix.R ### NOTA BENE: vector %*% Matrix _and_ Matrix %*% vector ### --------- The k-vector is treated as (1,k)-matrix *or* (k,1)-matrix ### on both sides when ever it "helps fit" the matrix dimensions: ##--- ./products.Rout ## ~~~~~~~~~~~~~~~ ## ========> in a M.v or v.M operation , ## you *must* look at dim(M) to see how to treat v !!!!!!!!!!!!!!!! ## For %*% (M = Matrix; v = vector (double, integer,.. or "sparsevector"): ## Drawback / bug: for (dense)vectors, the *names* are lost [sparsevectors have no names!] .M.v <- function(x, y) { # dim(y) <- if(ncol(x) == (n <- length(y))) c(n, 1L) else c(1L, n) ## which works when m == 1, otherwise errors x %*% y } ## For %*% : .v.M <- function(x, y) { dim(x) <- if(nrow(y) == (n <- length(x))) c(1L, n) else c(n, 1L) x %*% y } ## For tcrossprod() : .v.Mt <- function(x, y) { dim(x) <- if(ncol(y) == (n <- length(x))) c(1L, n) else c(n, 1L) tcrossprod(x, y) } ###-- I --- %*% ------------------------------------------------------ ## General method for dense matrix multiplication in case specific methods ## have not been defined. setMethod("%*%", signature(x = "ddenseMatrix", y = "ddenseMatrix"), function(x, y) .Call(dgeMatrix_matrix_mm, .Call(dup_mMatrix_as_dgeMatrix, x), y, FALSE), valueClass = "dgeMatrix") setMethod("%*%", signature(x = "dgeMatrix", y = "dgeMatrix"), function(x, y) .Call(dgeMatrix_matrix_mm, x, y, FALSE), valueClass = "dgeMatrix") setMethod("%*%", signature(x = "dgeMatrix", y = "matrix"), function(x, y) .Call(dgeMatrix_matrix_mm, x, y, FALSE), valueClass = "dgeMatrix") setMethod("%*%", signature(x = "matrix", y = "dgeMatrix"), function(x, y) .Call(dgeMatrix_matrix_mm, y, x, TRUE), valueClass = "dgeMatrix") .dsy_m_mm <- function(x, y) .Call(dsyMatrix_matrix_mm, x, y, FALSE) setMethod("%*%", signature(x = "dsyMatrix", y = "matrix"), .dsy_m_mm) setMethod("%*%", signature(x = "dsyMatrix", y = "ddenseMatrix"), .dsy_m_mm) ## for disambiguity : setMethod("%*%", signature(x = "dsyMatrix", y = "dsyMatrix"), .dsy_m_mm) ## or even ## for(yCl in .directSubClasses(getClass("ddenseMatrix"))) ## setMethod("%*%", signature(x = "dsyMatrix", y = yCl), .dsy_m_mm) setMethod("%*%", signature(x = "ddenseMatrix", y = "dsyMatrix"), function(x, y) .Call(dsyMatrix_matrix_mm, y, x, TRUE)) setMethod("%*%", signature(x = "matrix", y = "dsyMatrix"), function(x, y) .Call(dsyMatrix_matrix_mm, y, x, TRUE)) setMethod("%*%", signature(x = "dspMatrix", y = "ddenseMatrix"), function(x, y) .Call(dspMatrix_matrix_mm, x, y), valueClass = "dgeMatrix") setMethod("%*%", signature(x = "dspMatrix", y = "matrix"), function(x, y) .Call(dspMatrix_matrix_mm, x, y), valueClass = "dgeMatrix") ## Not needed because of c("numeric", "Matrix") method ##setMethod("%*%", signature(x = "numeric", y = "CsparseMatrix"), ## function(x, y) t(.Call(Csparse_dense_crossprod, y, t(x))), ## valueClass = "dgeMatrix") ## FIXME -- do the "same" for "dtpMatrix" {also, with [t]crossprod()} ## all just like these "%*%" : setMethod("%*%", signature(x = "dtrMatrix", y = "dtrMatrix"), function(x, y) .Call(dtrMatrix_dtrMatrix_mm, x, y, FALSE, FALSE)) setMethod("%*%", signature(x = "dtrMatrix", y = "ddenseMatrix"), function(x, y) .Call(dtrMatrix_matrix_mm, x, y, FALSE, FALSE), valueClass = "dgeMatrix") setMethod("%*%", signature(x = "dtrMatrix", y = "matrix"), function(x, y) .Call(dtrMatrix_matrix_mm, x, y, FALSE, FALSE), valueClass = "dgeMatrix") setMethod("%*%", signature(x = "ddenseMatrix", y = "dtrMatrix"), function(x, y) .Call(dtrMatrix_matrix_mm, y, x, TRUE, FALSE), valueClass = "dgeMatrix") setMethod("%*%", signature(x = "matrix", y = "dtrMatrix"), function(x, y) .Call(dtrMatrix_matrix_mm, y, x, TRUE, FALSE), valueClass = "dgeMatrix") setMethod("%*%", signature(x = "dtpMatrix", y = "ddenseMatrix"), function(x, y) .Call(dtpMatrix_matrix_mm, x, y, FALSE, FALSE)) setMethod("%*%", signature(x = "dgeMatrix", y = "dtpMatrix"), function(x, y) .Call(dgeMatrix_dtpMatrix_mm, x, y)) ## dtpMatrix <-> matrix : will be used by the "numeric" one setMethod("%*%", signature(x = "dtpMatrix", y = "matrix"), function(x, y) .Call(dtpMatrix_matrix_mm, x, y, FALSE, FALSE)) setMethod("%*%", signature(x = "matrix", y = "dtpMatrix"), function(x, y) ..2dge(x) %*% y) ## dtpMatrix <-> numeric : the auxiliary functions are R version specific! ##setMethod("%*%", signature(x = "dtpMatrix", y = "numeric"), .M.v) ##setMethod("%*%", signature(x = "numeric", y = "dtpMatrix"), .v.M) ## For multiplication operations, sparseMatrix overrides other method ## selections. Coerce a ddensematrix argument to a lsparseMatrix. setMethod("%*%", signature(x = "lsparseMatrix", y = "ldenseMatrix"), function(x, y) x %*% as(y, "sparseMatrix")) setMethod("%*%", signature(x = "ldenseMatrix", y = "lsparseMatrix"), function(x, y) as(x, "sparseMatrix") %*% y) ## and coerce lsparse* to lgC* setMethod("%*%", signature(x = "lsparseMatrix", y = "lsparseMatrix"), function(x, y) as(x, "lgCMatrix") %*% as(y, "lgCMatrix")) for(c.x in c("lMatrix", "nMatrix")) { setMethod("%*%", signature(x = c.x, y = "dMatrix"), function(x, y) as(x, "dMatrix") %*% y) setMethod("%*%", signature(x = "dMatrix", y = c.x), function(x, y) x %*% as(y, "dMatrix")) for(c.y in c("lMatrix", "nMatrix")) setMethod("%*%", signature(x = c.x, y = c.y), function(x, y) as(x, "dMatrix") %*% as(y, "dMatrix")) }; rm(c.x, c.y) setMethod("%*%", signature(x = "CsparseMatrix", y = "CsparseMatrix"), function(x, y) .Call(Csparse_Csparse_prod, x, y)) setMethod("%*%", signature(x = "CsparseMatrix", y = "ddenseMatrix"), function(x, y) .Call(Csparse_dense_prod, x, y)) setMethod("%*%", signature(x = "CsparseMatrix", y = "matrix"), function(x, y) .Call(Csparse_dense_prod, x, y)) # was x %*% Matrix(y) setMethod("%*%", signature(x = "CsparseMatrix", y = "numeric"), function(x, y) .Call(Csparse_dense_prod, x, y)) ## Not yet. Don't have methods for y = "CsparseMatrix" and general x #setMethod("%*%", signature(x = "ANY", y = "TsparseMatrix"), # function(x, y) callGeneric(x, as(y, "CsparseMatrix"))) setMethod("%*%", signature(x = "TsparseMatrix", y = "ANY"), function(x, y) .T.2.C(x) %*% y) setMethod("%*%", signature(x = "ANY", y = "TsparseMatrix"), function(x, y) x %*% .T.2.C(y)) setMethod("%*%", signature(x = "TsparseMatrix", y = "Matrix"), function(x, y) .T.2.C(x) %*% y) setMethod("%*%", signature(x = "Matrix", y = "TsparseMatrix"), function(x, y) x %*% .T.2.C(y)) setMethod("%*%", signature(x = "TsparseMatrix", y = "TsparseMatrix"), function(x, y) .T.2.C(x) %*% .T.2.C(y)) ##-------- Work via as(*, lgC) : ------------ ## For multiplication operations, sparseMatrix overrides other method ## selections. Coerce a ddensematrix argument to a nsparseMatrix. setMethod("%*%", signature(x = "nsparseMatrix", y = "ndenseMatrix"), function(x, y) x %*% as(y, "nsparseMatrix")) setMethod("%*%", signature(x = "ndenseMatrix", y = "nsparseMatrix"), function(x, y) as(x, "nsparseMatrix") %*% y) ## and coerce nsparse* to lgC* setMethod("%*%", signature(x = "nsparseMatrix", y = "nsparseMatrix"), function(x, y) as(x, "ngCMatrix") %*% as(y, "ngCMatrix")) ## FIXME(2): These three are sub-optimal : has 2 x t() : ## *faster*: provide dense_Csparse_prod() ## x %*% y = t(crossprod(y, t(x))) unless when x is vector setMethod("%*%", signature(x = "ddenseMatrix", y = "CsparseMatrix"), function(x, y) t(.Call(Csparse_dense_crossprod, y, t(x))), valueClass = "dgeMatrix") setMethod("%*%", signature(x = "matrix", y = "CsparseMatrix"), function(x, y) t(.Call(Csparse_dense_crossprod, y, t(x))), valueClass = "dgeMatrix") setMethod("%*%", signature(x = "numLike", y = "CsparseMatrix"), function(x, y) t(.Call(Csparse_dense_crossprod, y, x)), valueClass = "dgeMatrix") ## "Matrix" ## Methods for operations where one argument is numeric setMethod("%*%", signature(x = "Matrix", y = "numLike"), .M.v) setMethod("%*%", signature(x = "numLike", y = "Matrix"), .v.M) setMethod("%*%", signature(x = "Matrix", y = "matrix"), function(x, y) x %*% Matrix(y)) setMethod("%*%", signature(x = "matrix", y = "Matrix"), function(x, y) Matrix(x) %*% y) ## bail-out methods in order to get better error messages .local.bail.out <- function (x, y) stop(gettextf('not-yet-implemented method for <%s> %%*%% <%s>', class(x), class(y)), domain=NA) setMethod("%*%", signature(x = "ANY", y = "Matrix"), .local.bail.out) setMethod("%*%", signature(x = "Matrix", y = "ANY"), .local.bail.out) ### sparseVector sp.x.sp <- function(x, y) Matrix(sum(x * y), 1L, 1L, sparse=FALSE) ## inner product -- no sense to return sparse! setMethod("%*%", signature(x = "Matrix", y = "sparseVector"), .M.v) setMethod("%*%", signature(x = "sparseVector", y = "Matrix"), .v.M) setMethod("%*%", signature(x = "sparseVector", y = "sparseVector"), sp.x.sp) ## setMethod("%*%", signature(x = "sparseMatrix", y = "sparseVector"), ## function(x, y) x %*% .sparseV2Mat(y)) ###--- II --- crossprod ----------------------------------------------------- setMethod("crossprod", signature(x = "dgeMatrix", y = "missing"), function(x, y = NULL) .Call(dgeMatrix_crossprod, x, FALSE), valueClass = "dpoMatrix") ## crossprod (x,y) setMethod("crossprod", signature(x = "dgeMatrix", y = "dgeMatrix"), function(x, y = NULL) .Call(dgeMatrix_dgeMatrix_crossprod, x, y, FALSE), valueClass = "dgeMatrix") setMethod("crossprod", signature(x = "dgeMatrix", y = "matrix"), function(x, y = NULL) .Call(dgeMatrix_matrix_crossprod, x, y, FALSE), valueClass = "dgeMatrix") setMethod("crossprod", signature(x = "dgeMatrix", y = "numeric"), function(x, y = NULL) .Call(dgeMatrix_matrix_crossprod, x, y, FALSE), valueClass = "dgeMatrix") setMethod("crossprod", signature(x = "matrix", y = "dgeMatrix"), function(x, y = NULL) crossprod(..2dge(x), y), valueClass = "dgeMatrix") setMethod("crossprod", signature(x = "numLike", y = "dgeMatrix"), function(x, y = NULL) crossprod(as.matrix(as.double(x)), y), valueClass = "dgeMatrix") setMethod("crossprod", signature(x = "ddenseMatrix", y = "missing"), function(x, y = NULL) crossprod(as(x, "dgeMatrix"))) setMethod("crossprod", signature(x = "dtrMatrix", y = "missing"), function(x, y = NULL) crossprod(as(x, "dgeMatrix")), valueClass = "dpoMatrix") ## "dtrMatrix" - remaining (uni)triangular if possible setMethod("crossprod", signature(x = "dtrMatrix", y = "dtrMatrix"), function(x, y) .Call(dtrMatrix_dtrMatrix_mm, x, y, FALSE, TRUE)) setMethod("crossprod", signature(x = "dtrMatrix", y = "ddenseMatrix"), function(x, y) .Call(dtrMatrix_matrix_mm, x, y, FALSE, TRUE), valueClass = "dgeMatrix") setMethod("crossprod", signature(x = "dtrMatrix", y = "matrix"), function(x, y) .Call(dtrMatrix_matrix_mm, x, y, FALSE, TRUE), valueClass = "dgeMatrix") ## "dtpMatrix" if(FALSE) ## not yet in C setMethod("crossprod", signature(x = "dtpMatrix", y = "dtpMatrix"), function(x, y) .Call(dtpMatrix_dtpMatrix_mm, x, y, FALSE, TRUE)) setMethod("crossprod", signature(x = "dtpMatrix", y = "ddenseMatrix"), function(x, y) .Call(dtpMatrix_matrix_mm, x, y, FALSE, TRUE), valueClass = "dgeMatrix") setMethod("crossprod", signature(x = "dtpMatrix", y = "matrix"), function(x, y) .Call(dtpMatrix_matrix_mm, x, y, FALSE, TRUE), valueClass = "dgeMatrix") ## "crossprod" methods too ... ## setMethod("crossprod", signature(x = "dgTMatrix", y = "missing"), ## function(x, y = NULL) ## .Call(csc_crossprod, as(x, "dgCMatrix"))) ## setMethod("crossprod", signature(x = "dgTMatrix", y = "matrix"), ## function(x, y = NULL) ## .Call(csc_matrix_crossprod, as(x, "dgCMatrix"), y)) ##setMethod("crossprod", signature(x = "dgTMatrix", y = "numeric"), ## function(x, y = NULL) ## .Call(csc_matrix_crossprod, as(x, "dgCMatrix"), as.matrix(y))) ## setMethod("tcrossprod", signature(x = "dgTMatrix", y = "missing"), ## function(x, y = NULL) ## .Call(csc_tcrossprod, as(x, "dgCMatrix"))) setMethod("crossprod", signature(x = "CsparseMatrix", y = "missing"), function(x, y = NULL) { if (is(x, "symmetricMatrix")) ## crossprod() should give "symmetric*": forceSymmetric(x %*% x, uplo = x@uplo) else .Call(Csparse_crossprod, x, trans = FALSE, triplet = FALSE) }) setMethod("crossprod", signature(x = "CsparseMatrix", y = "CsparseMatrix"), function(x, y = NULL) .Call(Csparse_Csparse_crossprod, x, y, trans = FALSE)) ## FIXME: Generalize the class of y. This specific method is to replace one ## in dgCMatrix.R setMethod("crossprod", signature(x = "CsparseMatrix", y = "ddenseMatrix"), function(x, y = NULL) .Call(Csparse_dense_crossprod, x, y)) setMethod("crossprod", signature(x = "CsparseMatrix", y = "matrix"), function(x, y = NULL) .Call(Csparse_dense_crossprod, x, y)) setMethod("crossprod", signature(x = "CsparseMatrix", y = "numeric"), function(x, y = NULL) .Call(Csparse_dense_crossprod, x, y)) setMethod("crossprod", signature(x = "TsparseMatrix", y = "missing"), function(x, y = NULL) { if (is(x, "symmetricMatrix")) ## crossprod() should give "symmetric*": forceSymmetric(x %*% x, uplo = x@uplo) else .Call(Csparse_crossprod, x, trans = FALSE, triplet = TRUE) }) setMethod("crossprod", signature(x = "TsparseMatrix", y = "ANY"), function(x, y = NULL) crossprod(.T.2.C(x), y)) setMethod("crossprod", signature(x = "ANY", y = "TsparseMatrix"), function(x, y = NULL) crossprod(x, .T.2.C(y))) setMethod("crossprod", signature(x = "TsparseMatrix", y = "Matrix"), function(x, y = NULL) crossprod(.T.2.C(x), y)) setMethod("crossprod", signature(x = "Matrix", y = "TsparseMatrix"), function(x, y = NULL) crossprod(x, .T.2.C(y))) setMethod("crossprod", signature(x = "TsparseMatrix", y = "TsparseMatrix"), function(x, y = NULL) crossprod(.T.2.C(x), .T.2.C(y))) setMethod("crossprod", signature(x = "dsparseMatrix", y = "ddenseMatrix"), function(x, y = NULL) .Call(Csparse_dense_crossprod, as(x, "CsparseMatrix"), y)) setMethod("crossprod", signature(x = "ddenseMatrix", y = "dgCMatrix"), function(x, y = NULL) t(.Call(Csparse_dense_crossprod, y, x))) setMethod("crossprod", signature(x = "ddenseMatrix", y = "dsparseMatrix"), function(x, y = NULL) t(.Call(Csparse_dense_crossprod, as(y, "CsparseMatrix"), x))) setMethod("crossprod", signature(x = "dgCMatrix", y = "dgeMatrix"), function(x, y = NULL) .Call(Csparse_dense_crossprod, x, y)) setMethod("crossprod", signature(x = "dsparseMatrix", y = "dgeMatrix"), function(x, y = NULL) .Call(Csparse_dense_crossprod, as(x, "CsparseMatrix"), y)) ## NB: there's already ## ("CsparseMatrix", "missing") and ("TsparseMatrix", "missing") methods ## infinite recursion: ## setMethod("crossprod", signature(x = "dgeMatrix", y = "dsparseMatrix"), ## function(x, y = NULL) crossprod(x, as(y, "dgCMatrix"))) setMethod("crossprod", signature(x = "lsparseMatrix", y = "ldenseMatrix"), function(x, y = NULL) crossprod(x, as(y, "sparseMatrix"))) setMethod("crossprod", signature(x = "ldenseMatrix", y = "lsparseMatrix"), function(x, y = NULL) crossprod(as(x, "sparseMatrix"), y)) setMethod("crossprod", signature(x = "lsparseMatrix", y = "lsparseMatrix"), function(x, y = NULL) crossprod(as(x, "lgCMatrix"), as(y, "lgCMatrix"))) setMethod("crossprod", signature(x = "nsparseMatrix", y = "ndenseMatrix"), function(x, y = NULL) crossprod(x, as(y, "sparseMatrix"))) setMethod("crossprod", signature(x = "ndenseMatrix", y = "nsparseMatrix"), function(x, y = NULL) crossprod(as(x, "sparseMatrix"), y)) setMethod("crossprod", signature(x = "nsparseMatrix", y = "nsparseMatrix"), function(x, y = NULL) crossprod(as(x, "ngCMatrix"), as(y, "ngCMatrix"))) ## FIXME(3): slightly sub-optimal : t() : setMethod("crossprod", signature(x = "ddenseMatrix", y = "CsparseMatrix"), function(x, y) t(.Call(Csparse_dense_crossprod, y, x))) setMethod("crossprod", signature(x = "matrix", y = "CsparseMatrix"), function(x, y) t(.Call(Csparse_dense_crossprod, y, x))) setMethod("crossprod", signature(x = "numeric", y = "CsparseMatrix"), function(x, y) t(.Call(Csparse_dense_crossprod, y, x))) ## "Matrix" : cbind(), rbind() do names -> dimnames setMethod("crossprod", signature(x = "Matrix", y = "numLike"), function(x, y) crossprod(x, cbind(y,deparse.level=0))) setMethod("crossprod", signature(x = "numLike", y = "Matrix"), function(x, y) crossprod(rbind(x,deparse.level=0), y)) setMethod("crossprod", signature(x = "Matrix", y = "matrix"), function(x, y) crossprod(x, Matrix(y))) setMethod("crossprod", signature(x = "matrix", y = "Matrix"), function(x, y) crossprod(Matrix(x), y)) ## sparseVector setMethod("crossprod", signature(x = "Matrix", y = "sparseVector"), function(x, y) crossprod(x, .sparseV2Mat(y))) setMethod("crossprod", signature(x = "sparseVector", y = "Matrix"), function(x, y) crossprod(spV2M(x, nrow = length(x), ncol = 1L, check = FALSE), y)) setMethod("crossprod", signature(x = "sparseVector", y = "sparseVector"), sp.x.sp) setMethod("crossprod", signature(x = "sparseVector", y = "missing"), function(x, y=NULL) sp.x.sp(x,x)) ## cheap fallbacks setMethod("crossprod", signature(x = "Matrix", y = "Matrix"), function(x, y) t(x) %*% y) setMethod("crossprod", signature(x = "Matrix", y = "missing"), function(x, y) t(x) %*% x) setMethod("crossprod", signature(x = "Matrix", y = "ANY"), function(x, y) t(x) %*% y) setMethod("crossprod", signature(x = "ANY", y = "Matrix"), function(x, y) t(x) %*% y) ###--- III --- tcrossprod --------------------------------------------------- setMethod("tcrossprod", signature(x = "dgeMatrix", y = "dgeMatrix"), function(x, y = NULL) .Call(dgeMatrix_dgeMatrix_crossprod, x, y, TRUE), valueClass = "dgeMatrix") setMethod("tcrossprod", signature(x = "dgeMatrix", y = "matrix"), function(x, y = NULL) .Call(dgeMatrix_matrix_crossprod, x, y, TRUE), valueClass = "dgeMatrix") setMethod("tcrossprod", signature(x = "dgeMatrix", y = "numLike"), function(x, y = NULL) .Call(dgeMatrix_matrix_crossprod, x, y, TRUE), valueClass = "dgeMatrix") setMethod("tcrossprod", signature(x = "matrix", y = "dgeMatrix"), function(x, y = NULL) tcrossprod(..2dge(x), y), valueClass = "dgeMatrix") setMethod("tcrossprod", signature(x = "numLike", y = "dgeMatrix"), .v.Mt, valueClass = "dgeMatrix") setMethod("tcrossprod", signature(x = "dgeMatrix", y = "missing"), function(x, y = NULL) .Call(dgeMatrix_crossprod, x, TRUE), valueClass = "dpoMatrix") if(FALSE) { ## this would mask 'base::tcrossprod' setMethod("tcrossprod", signature(x = "matrix", y = "missing"), function(x, y = NULL) .Call(dgeMatrix_crossprod, ..2dge(x), TRUE), valueClass = "dpoMatrix") setMethod("tcrossprod", signature(x = "numLike", y = "missing"), function(x, y = NULL) tcrossprod(as.matrix(as.double(x)))) } setMethod("tcrossprod", signature(x = "ddenseMatrix", y = "missing"), function(x, y = NULL) tcrossprod(as(x, "dgeMatrix"))) setMethod("tcrossprod", signature(x = "dtrMatrix", y = "dtrMatrix"), function(x, y) .Call(dtrMatrix_dtrMatrix_mm, y, x, TRUE, TRUE)) ## Must have 1st arg. = "dtrMatrix" in dtrMatrix_matrix_mm (): ## would need another way, to define tcrossprod() --- TODO? --- ## ## setMethod("tcrossprod", signature(x = "dtrMatrix", y = "ddenseMatrix"), ## function(x, y) .Call(dtrMatrix_matrix_mm, y, x, TRUE, TRUE)) ## setMethod("tcrossprod", signature(x = "dtrMatrix", y = "matrix"), ## function(x, y) .Call(dtrMatrix_matrix_mm, y, x, TRUE, TRUE)) setMethod("tcrossprod", signature(x = "ddenseMatrix", y = "dtrMatrix"), function(x, y) .Call(dtrMatrix_matrix_mm, y, x, TRUE, TRUE)) setMethod("tcrossprod", signature(x = "matrix", y = "dtrMatrix"), function(x, y) .Call(dtrMatrix_matrix_mm, y, x, TRUE, TRUE)) if(FALSE) { ## TODO in C setMethod("tcrossprod", signature(x = "ddenseMatrix", y = "dtpMatrix"), function(x, y) .Call(dtpMatrix_matrix_mm, y, x, TRUE, TRUE)) setMethod("tcrossprod", signature(x = "matrix", y = "dtpMatrix"), function(x, y) .Call(dtpMatrix_matrix_mm, y, x, TRUE, TRUE)) } setMethod("tcrossprod", signature(x = "CsparseMatrix", y = "CsparseMatrix"), function(x, y = NULL) .Call(Csparse_Csparse_crossprod, x, y, trans = TRUE)) setMethod("tcrossprod", signature(x = "CsparseMatrix", y = "missing"), function(x, y = NULL) { if (is(x, "symmetricMatrix")) ## tcrossprod() should give "symmetric*": forceSymmetric(x %*% x, uplo = x@uplo) else .Call(Csparse_crossprod, x, trans = TRUE, triplet = FALSE) }) ### FIXME (suboptimal): one t(): setMethod("tcrossprod", signature(x = "CsparseMatrix", y = "ddenseMatrix"), function(x, y) .Call(Csparse_dense_prod, x, t(y))) setMethod("tcrossprod", signature(x = "CsparseMatrix", y = "matrix"), function(x, y) .Call(Csparse_dense_prod, x, t(y))) setMethod("tcrossprod", signature(x = "CsparseMatrix", y = "numLike"), function(x, y) .Call(Csparse_dense_prod, x, rbind(y, deparse.level=0))) ### FIXME (speed): Csparse_dense_crossprod should also get a 'trans = TRUE' ## so we could have one less t() in this: ## -- xy' = (yx')' setMethod("tcrossprod", signature(x = "ddenseMatrix", y = "CsparseMatrix"), function(x, y) t(.Call(Csparse_dense_prod, y, t(x)))) setMethod("tcrossprod", signature(x = "matrix", y = "CsparseMatrix"), function(x, y) t(.Call(Csparse_dense_prod, y, t(x)))) setMethod("tcrossprod", signature(x = "numLike", y = "CsparseMatrix"), # x or t(x) depending on dimension of y ! .v.Mt)#<- FIXME more efficient setMethod("tcrossprod", signature(x = "TsparseMatrix", y = "missing"), function(x, y = NULL) { if (is(x, "symmetricMatrix")) ## tcrossprod() should give "symmetric*": forceSymmetric(x %*% x, uplo = x@uplo) else .Call(Csparse_crossprod, x, trans = TRUE, triplet = TRUE) }) setMethod("tcrossprod", signature(x = "ANY", y = "TsparseMatrix"), function(x, y = NULL) tcrossprod(x, .T.2.C(y))) setMethod("tcrossprod", signature(x = "TsparseMatrix", y = "ANY"), function(x, y = NULL) tcrossprod(.T.2.C(x), y)) setMethod("tcrossprod", signature(x = "Matrix", y = "TsparseMatrix"), function(x, y = NULL) tcrossprod(x, .T.2.C(y))) setMethod("tcrossprod", signature(x = "TsparseMatrix", y = "Matrix"), function(x, y = NULL) tcrossprod(.T.2.C(x), y)) setMethod("tcrossprod", signature(x = "TsparseMatrix", y = "TsparseMatrix"), function(x, y = NULL) tcrossprod(.T.2.C(x), .T.2.C(y))) ## "Matrix" setMethod("tcrossprod", signature(x = "Matrix", y = "numLike"), function(x, y) x %*% rbind(y,deparse.level=0)) setMethod("tcrossprod", signature(x = "numLike", y = "Matrix"), .v.Mt) setMethod("tcrossprod", signature(x = "Matrix", y = "matrix"), function(x, y = NULL) tcrossprod(x, Matrix(y))) setMethod("tcrossprod", signature(x = "matrix", y = "Matrix"), function(x, y = NULL) tcrossprod(Matrix(x), y)) ## sparseVector setMethod("tcrossprod", signature(x = "Matrix", y = "sparseVector"), function(x, y) tcrossprod(x, .sparseV2Mat(y))) setMethod("tcrossprod", signature(x = "sparseVector", y = "Matrix"), .v.Mt) setMethod("tcrossprod", signature(x = "sparseMatrix", y = "sparseVector"), function(x, y) tcrossprod(x, .sparseV2Mat(y))) setMethod("tcrossprod", signature(x = "sparseVector", y = "sparseMatrix"), .v.Mt) setMethod("tcrossprod", signature(x = "sparseVector", y = "sparseVector"), function(x, y) .sparseV2Mat(x) %*% spV2M(y, nrow=1L, ncol=length(y), check=FALSE)) setMethod("tcrossprod", signature(x = "sparseVector", y = "missing"), ## could be speeded: spV2M(x, *) called twice with different ncol/nrow function(x, y=NULL) .sparseV2Mat(x) %*% spV2M(x, nrow=1L, ncol=length(x), check=FALSE)) ## cheap fallbacks setMethod("tcrossprod", signature(x = "Matrix", y = "Matrix"), function(x, y = NULL) x %*% t(y)) setMethod("tcrossprod", signature(x = "Matrix", y = "missing"), function(x, y = NULL) x %*% t(x)) setMethod("tcrossprod", signature(x = "Matrix", y = "ANY"), function(x, y = NULL) x %*% t(y)) setMethod("tcrossprod", signature(x = "ANY", y = "Matrix"), function(x, y = NULL) x %*% t(y)) ## Local variables: ## mode: R ## page-delimiter: "^###---" ## End: Matrix/R/indMatrix.R0000644000175100001440000001410412211567675014033 0ustar hornikusers#### Index Matrices -- Coercion and Methods (--> ../man/indMatrix-class.Rd ) ## The typical 'constructor' : coerce from 'perm' setAs("integer", "indMatrix", function(from) new("indMatrix", Dim = c(length(from), max(from)), Dimnames = list(names(from), NULL), perm = from)) setAs("numeric", "indMatrix", function(from) if(all(from == (i <- as.integer(from)))) as(i, "indMatrix") else stop("coercion to \"indMatrix\" only works from integer numeric")) ## A constructor from a list giving the index ('perm') and the number of columns ## (need this for cases in which the value(s) represented by the last ## column(s) has no observations): .list2indMatrix <- function(from) { if(length(from) == 2 && all(from[[1]] == (i <- as.integer(from[[1]]))) && from[[2]] == (d <- as.integer(from[[2]])) && length(d) == 1 && d >= max(i)) { new("indMatrix", perm = i, Dim = c(length(i), d)) } else stop("coercion from list(i1,...,ik, d) to \"indMatrix\" failed. All entries must be integer valued and the number of columns, d, not smaller than the maximal index i*.") } setAs("list", "indMatrix", .list2indMatrix) setAs("indMatrix", "matrix", function(from) { fp <- from@perm r <- ldiag(n = from@Dim[2])[fp,] if(.has.DN(from)) dimnames(r) <- from@Dimnames r }) ## coerce to 0/1 sparse matrix, i.e. sparse pattern .ind2ngT <- function(from) { d <- from@Dim new("ngTMatrix", i = seq_len(d[1]) - 1L, j = from@perm - 1L, Dim = d, Dimnames = from@Dimnames) } setAs("indMatrix", "ngTMatrix", .ind2ngT) setAs("indMatrix", "TsparseMatrix", .ind2ngT) setAs("indMatrix", "nMatrix", .ind2ngT) setAs("indMatrix", "lMatrix", function(from) as(.ind2ngT(from), "lMatrix")) setAs("indMatrix", "dMatrix", function(from) as(.ind2ngT(from), "dMatrix")) setAs("indMatrix", "dsparseMatrix", function(from) as(from, "dMatrix")) setAs("indMatrix", "lsparseMatrix", function(from) as(from, "lMatrix")) setAs("indMatrix", "nsparseMatrix", .ind2ngT) setAs("indMatrix", "CsparseMatrix", function(from) as(.ind2ngT(from), "CsparseMatrix")) setAs("indMatrix", "ngeMatrix", function(from) as(.ind2ngT(from),"ngeMatrix")) setAs("nMatrix", "indMatrix", function(from) { from <- as(as(from, "TsparseMatrix"), "ngTMatrix") n <- (d <- from@Dim)[1] if(n < d[2]) stop("not a skinny matrix") if(length(i <- from@i) != n) stop("the number of non-zero entries differs from nrow(.)") if((need.sort <- is.unsorted(i))) { ii <- sort.list(i) i <- i[ii] } if(n >= 1 && !identical(i, 0:(n - 1))) stop("must have exactly one non-zero entry per row") new("indMatrix", ## validity checking checks the 'perm' slot: perm = 1L + if(need.sort) from@j[ii] else from@j, Dim = d, Dimnames = from@Dimnames) }) setAs("matrix", "indMatrix", function(from) as(as(from, "nMatrix"), "indMatrix")) setAs("indMatrix", "matrix", function(from) as(.ind2ngT(from), "matrix")) setAs("sparseMatrix", "indMatrix", function(from) as(as(from, "nsparseMatrix"), "indMatrix")) setMethod("is.na", signature(x = "indMatrix"), is.na_nsp) setMethod("is.infinite", signature(x = "indMatrix"), is.na_nsp) setMethod("is.finite", signature(x = "indMatrix"), allTrueMatrix) setMethod("t", signature(x = "indMatrix"), function(x) t(.ind2ngT(x))) setMethod("%*%", signature(x = "matrix", y = "indMatrix"), function(x, y) x %*% as(y, "lMatrix")) setMethod("%*%", signature(x = "Matrix", y = "indMatrix"), function(x, y) x %*% as(y, "lMatrix")) setMethod("%*%", signature(x = "indMatrix", y = "matrix"), function(x, y) { mmultCheck(x,y); y[x@perm ,] }) setMethod("%*%", signature(x = "indMatrix", y = "Matrix"), function(x, y) { mmultCheck(x,y); y[x@perm ,] }) setMethod("crossprod", signature(x = "indMatrix", y = "matrix"), function(x, y) as(t(x), "lMatrix") %*% y) setMethod("crossprod", signature(x = "indMatrix", y = "Matrix"), function(x, y) as(t(x), "lMatrix") %*% y) setMethod("crossprod", signature(x = "indMatrix", y = "indMatrix"), function(x, y) { mmultCheck(x,y, 2L) xy <- interaction(x@perm, y@perm) Matrix(data= tabulate(xy, nbins=nlevels(xy)), nrow= x@Dim[2L], ncol= y@Dim[2L]) }) setMethod("tcrossprod", signature(x = "matrix", y = "indMatrix"), function(x, y) { mmultCheck(x,y, 3L); x[, y@perm] }) setMethod("tcrossprod", signature(x = "Matrix", y = "indMatrix"), function(x, y) { mmultCheck(x,y, 3L); x[, y@perm] }) setMethod("tcrossprod", signature(x = "indMatrix", y = "indMatrix"), function(x, y) { mmultCheck(x,y, 3L); x[, y@perm] }) setMethod("crossprod", signature(x = "indMatrix", y = "missing"), function(x, y=NULL) Diagonal(x=as.numeric(table(x@perm)))) setMethod("tcrossprod", signature(x = "indMatrix", y = "missing"), function(x, y=NULL) x[,x@perm]) setMethod("kronecker", signature(X = "indMatrix", Y = "indMatrix"), function (X, Y, FUN = "*", make.dimnames = FALSE, ...) { if (FUN != "*") stop("kronecker method must use default 'FUN'") perm <- as.integer(interaction(rep(X@perm, each =Y@Dim[1]), rep(Y@perm, times=X@Dim[1]), lex.order=TRUE)) new("indMatrix", perm=perm, Dim=X@Dim*Y@Dim) }) setMethod("[", signature(x = "indMatrix", i = "index", j = "missing", drop = "logical"), function (x, i, j, ..., drop) { n <- length(newperm <- x@perm[i]) if(drop && n == 1) { ## -> logical unit vector newperm == seq_len(x@Dim[2]) } else { ## stay matrix if(!is.null((DN <- x@Dimnames)[[1]])) DN[[1]] <- DN[[1]][i] new("indMatrix", perm = newperm, Dim = c(n, x@Dim[2]), Dimnames = DN) } }) .indMat.nosense <- function (x, i, j, ..., value) stop('replacing "indMatrix" entries is not allowed, as rarely sensible') setReplaceMethod("[", signature(x = "indMatrix", i = "index"), .indMat.nosense) setReplaceMethod("[", signature(x = "indMatrix", i = "missing", j = "index"), .indMat.nosense) ## explicit ^^^^^^^^^^^^ for disambiguation setReplaceMethod("[", signature(x = "indMatrix", i = "missing", j = "missing"), .indMat.nosense) ### rbind2() method: --> bind2.R Matrix/R/abIndex.R0000644000175100001440000005715012255412673013451 0ustar hornikusers#### Methods for the "abIndex" := ``abstract Index'' class ### Note: this partly builds on ideas and code from Jens Oehlschlaegel, ### ---- as implemented (in the GPL'ed part of) package 'ff'. ## Basic idea: a vector x of integer indices often has long stretches ## i, i+1, i+2, ... such that diff(x) has stretches of '1'. ## Now keep x[1] =: first and diff(x) =: d, ## and use rle() to encode d. Here, use a C version for rle() rleMaybe <- function(i, force = FALSE) { ## TODO: move all this to a new C fnc., still keeping the *_i() and *_d() if(is.na(force <- as.logical(force))) stop("'force' must be (coercable to) TRUE or FALSE") int <- is.integer(i) || is.logical(i) || { i. <- suppressWarnings(as.integer(i)) if(r <- isTRUE(all(is.na(i) | i. == i))) i <- i. r } ## if(int), 'i' will be coerced to integer on C level ##N R-devel codetools get FP again: ##N Matrix.rle <- if(int) Matrix_rle_i else Matrix_rle_d ##N .Call(Matrix.rle, i, force) if(int) Matrix_rle_d <- Matrix_rle_i .Call(Matrix_rle_d, i, force) } .rle <- function(lengths, values) structure(list(lengths = lengths, values = values), class = "rle") ##' @param x ##' ##' @return diff(x), giving '0' for 'Inf - Inf' or similar .diff <- function(x) { ## TODO: considerably faster in C if((n <- length(x)) <= 1) return(x[0]) r <- (x1 <- x[-1]) - (x2 <- x[-n]) if(any(ina <- is.na(r))) r[ina & (x1 == x2 | (is.na(x1) & is.na(x2)))] <- 0 r } ##' @param from: logical or numeric vector ##' ##' @return an "abIndex" vector, "semantically equivalent" to 'from' vec2abI <- function(from, force = FALSE) { ans <- new("abIndex") r <- rleMaybe(.diff(from), force=force)## .diff(): also work for rep(Inf, *) if(is.null(r)) { ## no "compression" ans@kind <- if(is.integer(from)) "int32" else "double" ans@x <- from } else { ans@kind <- "rleDiff" ## ans@x <- integer(0) # <- prototype does that ans@rleD <- new("rleDiff", first = from[1], rle = r) } ans } ## "abIndex" version of indDiag(n) === which(diag(n) == 1) -> ./Auxiliaries.R abIindDiag <- function(n) { ## cumsum(c(1L, rep.int(n+1L, n-1))) stopifnot((n <- as.integer(n)) >= 1) rl <- if(n == 1) .rle(n[0],n[0]) else .rle(n-1L, n+1L) new("abIndex", kind = "rleDiff", rleD = new("rleDiff", first = 1, rle = rl)) } ## "abIndex" version of indTri(n) ... --> ./Auxiliaries.R abIindTri <- function(n, upper = TRUE, diag = FALSE) { ## Indices of strict upper/lower triangular part ## == which(upper.tri(diag(n), diag=diag) or ## which(lower.tri(diag(n), diag=diag) -- but as abIndex stopifnot(length(n) == 1, n == (n. <- as.integer(n)), (n <- n.) >= 0) if(n <= 2) { vec2abI( if(n == 0) integer(0) else if(n == 1) { if(diag) 1L else integer(0) } else { ## n == 2 v <- if(upper) 3L else 2L if(diag) c(1L, v, 4L) else v }) } else { ## n >= 3 [also for n == 2 && diag (==TRUE)] : ## First, compute the 'diff(.)' of the result [fast, using integers] n. <- if(diag) n else n - 1L n1 <- n. - 1L tt <- if(diag) 2L else 3L mk1s <- function(n,m) as.vector(rbind(1L, n:m)) mks1 <- function(n,m) as.vector(rbind(n:m, 1L)) rl <- .rle(lengths= if(upper) mk1s(1L,n1) else mks1(n1,1L), values = if(upper) mks1(n, tt) else mk1s(tt, n)) frst <- if(diag) 1L else if(upper) n+1L else 2L new("abIndex", kind = "rleDiff", rleD = new("rleDiff", first = frst, rle = rl)) } } setAs("numeric", "abIndex", function(from) vec2abI(from)) setAs("logical", "abIndex", function(from) vec2abI(from)) setMethod("show", "rleDiff", function(object) { cat(sprintf(## first can be 'NULL' --> cannot use %g " RLE difference (class 'rleDiff'): first = %s, \"rle\":%s", format(object@first), if(length(rl <- object@rle)) "\n" else " ")) print(rl, prefix = " ") invisible(object) }) setMethod("show", "abIndex", function(object) { knd <- object@kind cat(sprintf( "Abstract Index vector (class 'abIndex') of length %.0f, kind \"%s\"\n", length(object), knd)) if(knd == "rleDiff") { ### FIXME: show something like this is equivalent to c(2:10, 13:34, ...) cat(" and slot \"rleD\":\n") show(object@rleD) } else { cat(" and \"x\" slot\n") show(object@x) } invisible(object) }) ##' Constructor of "abIndex" version of n:m ##' @param from ##' @param to ##' ##' @return an "abIndex" object semantically equivalent to from:to abIseq1 <- function(from = 1, to = 1) { stopifnot(length(from) == 1L, length(to) == 1L) to <- to - from new("abIndex", kind="rleDiff", rleD = new("rleDiff", first = as.integer(from), rle = .rle(lengths = abs(to),# <- double : maybe > .Machine$integer.max values = as.integer(sign(to))))) } ## an "abIndex" version of seq(), i.e. seq.default(): abIseq <- function(from = 1, to = 1, by = ((to - from)/(length.out - 1)), length.out = NULL, along.with = NULL) { if((One <- nargs() == 1L) && !missing(from)) { lf <- length(from) return(if(mode(from) == "numeric" && lf == 1L) abIseq1(1L, from) else if(lf) abIseq1(1L, lf) else new("abIndex")) } if(!missing(along.with)) { length.out <- length(along.with) if(One) return(if(length.out) abIseq1(1L, length.out) else new("abIndex")) } else if(!missing(length.out)) length.out <- ceiling(length.out) if(is.null(length.out)) if(missing(by)) abIseq1(from,to) else { # dealing with 'by' del <- to - from if(del == 0 && to == 0) return(as(to, "abIndex")) n <- del/by if(!(length(n) && is.finite(n))) { if(length(by) && by == 0 && length(del) && del == 0) return(as(from, "abIndex")) stop("invalid (to - from)/by in seq(.)") } if(n < 0L) stop("wrong sign in 'by' argument") if(n > .Machine$integer.max) stop("'by' argument is much too small") dd <- abs(del)/max(abs(to), abs(from)) if (dd < 100*.Machine$double.eps) return(from) n <- as.integer(n + 1e-7) x <- from + abIseq1(0L,n) * by ## correct for overshot because of fuzz -- FIXME: need pmin() for "abIndex": if(by > 0) pmin(x, to) else pmax(x, to) } else if(!is.finite(length.out) || length.out < 0L) stop("length must be non-negative number") else if(length.out == 0L) new("abIndex") else if (One) abIseq1(1L, length.out) else if(missing(by)) { # if(from == to || length.out < 2) by <- 1 if(missing(to)) to <- from + length.out - 1L if(missing(from)) from <- to - length.out + 1L if(length.out > 2L) if(from == to) rep2abI(from, length.out) ## rep.int(from, length.out) else c(as(from,"abIndex"), from + abIseq1(1L, length.out - 2L) * by, to) else as(c(from, to)[seq_len(length.out)],"abIndex") } else if(missing(to)) from + abIseq1(0L, length.out - 1L) * by else if(missing(from)) to - abIseq1(length.out - 1L, 0L) * by else stop("too many arguments") } ##' rep.int(x, times) " as abIndex " ##' @param x numeric vector ##' @param times integer (valued) scalar: the number of repetitions ##' ##' @return an "abIndex" vector rep2abI <- function(x, times) { r <- new("abIndex") if((n <- length(x)) == 0) return(r) if(n == 1) { # clear case for compression r@kind <- "rleDiff" rD <- new("rleDiff") rD@first <- x[1L] rD@rle <- .rle(lengths = times - 1L, values = 0L) r@rleD <- rD } else { ## n >= 2 .. check if compression is worth it: ## .. say if compression of x itself is worth {FIXME? optimal cutoff} rr <- rleMaybe(.diff(x)) if(is.null(rr)) { r@kind <- if(is.integer(x)) "int32" else "double" r@x <- rep.int(x, times) } else { r@kind <- "rleDiff" rD <- new("rleDiff") rD@first <- x[1L] Dx <- x[1L] - x[length(x)] N <- (length(rr$lengths) + 1L)*times rD@rle <- .rle(lengths = rep.int(c(rr$lengths, 1L), times)[-N], values = rep.int(c(rr$values, Dx), times)[-N]) r@rleD <- rD } } r } combine_rleD <- function(rleList, m = length(rleList)) { ## Combine list of "rleDiff"s into a new one -- for c(..) ## auxiliary (and main working horse) for c.abIndex() ### TODO: really should do this in C i1 <- unlist(lapply(rleList, slot, "first")) rles <- lapply(rleList, slot, "rle") ## the list of vectors of 'lengths' and 'values' : lens <- lapply(rles, `[[`, "lengths") vals <- lapply(rles, `[[`, "values") ## the 'ends' are needed for the "jump sizes" in between: ends2 <- function(x) # related to ends.rleD() above x@first + c(0, with(x@rle, sum(lengths*values))) ends <- unlist(lapply(rleList, ends2))[-c(1, 2*m)] ii <- 2L*seq_len(m - 1) d.ends <- ends[ii] - ends[ii-1L] ## llen1 <- unlist(lapply(lens, length)) + 1L ## n <- sum(llen1) n <- m + sum(unlist(lapply(lens, length))) ## comb(): intersperse x2[[j]] between lis[[j] & lis[[j+1]] : comb <- function(lis, x2) unlist(mapply(c, lis, x2, SIMPLIFY=FALSE, USE.NAMES=FALSE)) n.len <- comb(lens, 1L)[-n] n.val <- comb(vals, c(d.ends,NA))[-n] new("rleDiff", first = i1[1], rle = .rle(lengths = n.len, values = n.val)) } ## {combine_rleD} ## For now -- S4 method on c(), i.e., setMethod("c", ...) ## seems "difficult", and this works "magically" ## when the first argument is an abIndex : c.abIndex <- function(...) { m <- length(list(...)) if(m <= 1) return(if(m == 0) new("abIndex") else as(..1, "abIndex")) ## else: have length m >= 2 labi <- lapply(list(...), as, Class = "abIndex") knd <- unlist(lapply(labi, slot, "kind")) ## Convention: Result kind should be the 'kind' of the first neq.k <- knd != (k1 <- knd[1]) if(any(neq.k)) { if(all(not.rD <- knd != "rleDiff")) { ## either "double" or "int32" .. using 'x' k1 <- "double" ## and it will just work to c(.) the 'x' slots } else { warning("c(,..) of different kinds, coercing all to 'rleDiff'") labi[not.rD] <- lapply(labi[not.rD], function(av) vec2abI(av@x, force=TRUE)) k1 <- "rleDiff" } } switch(k1, "rleDiff" = { new("abIndex", kind="rleDiff", rleD = combine_rleD(lapply(labi, slot, "rleD"), m)) }, "double" =, "int32" = { new("abIndex", kind = k1, x = do.call(c, lapply(labi, slot, "x"))) }) } setMethod("length", "abIndex", function(x) if(identical(x@kind, "rleDiff")) sum(x@rleD@rle$lengths)+ 1L else length(x@x)) abI2num <- function(from) { switch(from@kind, "rleDiff" = { x <- from@rleD ## as inverse.rle(): cumsum(c(x@first, rep.int(x@rle$values, x@rle$lengths))) }, "int32" =, "double" = from@x) } setAs("abIndex", "numeric", abI2num) setAs("abIndex", "vector", abI2num) setAs("abIndex", "integer", function(from) as.integer(abI2num(from))) ## for S3 lovers and back-compatibility: setMethod(as.integer, "abIndex", function(x) as.integer(abI2num(x))) setMethod(as.numeric, "abIndex", function(x) abI2num(x)) setMethod(as.vector, c(x = "abIndex", mode = "ANY"), function(x) abI2num(x)) setMethod(as.vector, c(x = "abIndex", mode = "character"), ## this is beautiful -- because of as() ! function(x, mode) as(abI2num(x), mode)) ## Need max(), min(), all( == ) any( == ) ## ---> Groups "Summary" and "Compare" (maybe all "Ops") ## For that, we really need "[" and/or "rep"() methods -- TODO -- ## setMethod("[", signature(x = "abIndex", i = "index"), function (x, i, j, ..., drop) { switch(x@kind, "rleDiff" = { ## intIv() in ./sparseVector.R -- not memory-efficient (??) n <- length(x) ii <- intIv(i, n) ## ii : 1-based integer indices d <- x@rleD ## Now work with the equivalent of ## cumsum(c(d@first, rep.int(d@rle$values, d@rle$lengths))) stop("[i] is not yet implemented") }, "int32" =, "double" = ## as it's not rle-packed, can remain simple: x@x[i]) }) ##' Endpoints of all linear stretches -- auxiliary for range(.) ##' @param x an "rleDiff" object ##' ##' @return numeric vector of end points of all linear stretches of x. ends.rleD <- function(x) { rl <- x@rle stopifnot(length(lens <- rl$lengths) == length(vals <- rl$values)) cumsum(c(x@first, lens*vals)) } ##' Collapse or "uniquify" an 'rle' object, i.e., ##' 1) drop 'lengths' 0 parts ##' 2) *merge* adjacent parts where 'values' are the same ##' ##' @param x an "rle" object ##' ##' @return an "rle" object, a "unique" version of the input 'x' rleCollapse <- function(x) { ## TODO: faster (and simpler!) in C ## TODO(2): move this to 'R base' L <- x$lengths V <- x$values chng <- FALSE if((chng <- any(i0 <- L == 0))) { ## drop 0 'lengths' parts L <- L[!i0] ; V <- V[!i0] } ## FIXME: This is not elegant nor efficient: while(any(i0 <- diff(V) == 0)) { ## merge adjacent parts with same values if(!chng) chng <- TRUE ## fix one stretch (and repeat), starting at ii0 and total length 1+ li0 ii0 <- which.max(i0)# index of first TRUE li0 <- if((l0 <- length(i0)) <= ii0) 1 else which.min(!i0[ii0:l0]) stopifnot(li0 >= 1)## <- for now L[ii0] <- sum(L[ii0+(0:li0)]) ii <- -(ii0 + seq_len(li0)) L <- L[ii] V <- V[ii] } if(chng) { x$lengths <- L ; x$values <- V } x } ## {rleCollapse} setMethod("drop", "abIndex", function(x) { if(x@kind == "rleDiff") x@rleD@rle <- rleCollapse(x@rleD@rle) x }) ## Summary: { max, min, range, prod, sum, any, all } : ## have 'summGener1' := those without prod, sum setMethod("Summary", signature(x = "abIndex", na.rm = "ANY"), function(x, ..., na.rm) { switch(x@kind, "rleDiff" = { d <- x@rleD if(.Generic %in% c("range","min","max")) { callGeneric(ends.rleD(d), ..., na.rm=na.rm) } else { ## "sum", "prod" : switch(.Generic, "all" = { ## these often, but *not* always come in pairs en <- ends.rleD(d) ## so maybe it does not really help! stop("all() is not yet implemented") ## all(c(d@first, d@rle$values), ..., na.rm=na.rm) }, "any" = any(c(d@first, d@rle$values), ..., na.rm=na.rm), "sum" = { stop("sum() is not yet implemented") }, "prod"= { stop("prod() is not yet implemented") }) } }, "int32" =, "double" = callGeneric(x@x, ..., na.rm = na.rm) ) }) ### "Ops" := sub-groups "Arith", "Compare", and "Logic" ## ## For now (*), only "Arith" does make sense ## --> keep "Ops" undefined and define "Arith" : ## ---- ## (*) : TODO: logical <-> abIndex --> "Compare" etc as well setMethod("Ops", signature(e1 = "abIndex", e2 = "abIndex"), function(e1, e2) { .bail.out.2(.Generic, class(e1), class(e2)) }) setMethod("Ops", signature(e1 = "abIndex", e2 = "ANY"), function(e1, e2) { .bail.out.2(.Generic, class(e1), class(e2)) }) setMethod("Ops", signature(e1 = "ANY", e2 = "abIndex"), function(e1, e2) { .bail.out.2(.Generic, class(e1), class(e2)) }) setMethod("Arith", signature(e1 = "abIndex", e2 = "abIndex"), function(e1, e2) { l1 <- length(e1) l2 <- length(e2) mM <- range(l1,l2) stop("not yet implemented") ## FIXME ------------------ if(mM[1] != mM[2]) { ## lengths differ if(mM[1] %% mM[2] != 0) ## identical warning as in main/arithmetic.c warning("longer object length\n\tis not a multiple of shorter object length") if(l1 < l2) { } else { ## l1 > l2 } } switch(e1@kind, "rleDiff" = { }, "int32" =, "double" = { }) }) ## numLike = {numeric, logical}: setMethod("Arith", signature(e1 = "abIndex", e2 = "numLike"), function(e1, e2) { if(!length(e1)) return(e1) if(e1@kind != "rleDiff") { # no compression e1@x <- callGeneric(e1@x, e2) if(e1@kind != "double" && is.double(e1@x)) e1@kind <- "double" return(e1) } if(length(e2) == 1) { ## scalar if(is.na(e2)) return(rep2abI(e2, length(e1))) ## else 'e2' is not NA and scalar switch(.Generic, "+" =, "-" = { e1@rleD@first <- callGeneric(e1@rleD@first, e2) e1 }, "*" = { e1@rleD@first <- e1@rleD@first * e2 r <- e1@rleD@rle$values * e2 if(is0(e2) && all0(r)) { ## result all 0: collapse e1@rleD@rle$values <- r[1L] e1@rleD@rle$lengths <- sum(e1@rleD@rle$lengths) } else ## normal case e1@rleD@rle$values <- r e1 }, "/" = { if(is0(e2) ## division by 0 && length(unique(sign(ee <- ends.rleD(e1@rleD)))) > 1) { ## at least one subsequence contains 0, i.e., changes sign: warning("x / 0 for an x with sign-change\n no longer representable as 'rleDiff'") return(vec2abI(abI2num(e1) / 0)) } e1@rleD@first <- e1@rleD@first / e2 e1@rleD@rle$values <- e1@rleD@rle$values / e2 e1 }, "^" = { if(e2 == 1) e1 else vec2abI(abI2num(e1) ^ e2) }, "%%" = , "%/%" = vec2abI(callGeneric(abI2num(e1), e2))) } else ## length(e2) != 1 callGeneric(e1, as(e2, "abIndex")) }) setMethod("Arith", signature(e1 = "numLike", e2 = "abIndex"), function(e1, e2) { if(!length(e2)) return(e2) if(e2@kind != "rleDiff") { # no compression e2@x <- callGeneric(e1, e2@x) if(e2@kind != "double" && is.double(e2@x)) e2@kind <- "double" return(e2) } if(length(e1) == 1) { ## scalar if(is.na(e1)) return(rep2abI(e1, length(e2))) ## else 'e1' is not NA and scalar switch(.Generic, "+" = { e2@rleD@first <- e1 + e2@rleD@first e2 }, "-" = { e2@rleD@first <- e1 - e2@rleD@first e2@rleD@rle$values <- -e2@rleD@rle$values e2 }, "*" = { e2@rleD@first <- e1 * e2@rleD@first r <- e1 * e2@rleD@rle$values if(is0(e1) && all0(r)) { ## result all 0: collapse e2@rleD@rle$values <- r[1L] e2@rleD@rle$lengths <- sum(e2@rleD@rle$lengths) } else ## normal case e2@rleD@rle$values <- r e2 }, "/" = , "^" =, "%%" = , "%/%" = vec2abI(callGeneric(e1, abI2num(e2)))) } else ## length(e1) != 1 callGeneric(as(e1, "abIndex"), e2) }) setMethod("is.na", signature(x = "abIndex"), function(x) { if(x@kind != "rleDiff") is.na(x@x) else { rd <- x@rleD rl <- rd@rle len <- 1+ sum(L <- rl$lengths) if(is.na(rd@first)) rep.int(TRUE, len) else { ## interesting case V <- rl$values if(!any(ina <- is.na(V))) rep.int(FALSE, len) else { ## at least one V is NA --> "x" is NA from then on: k <- match(TRUE,ina) # the first one l1 <- 1+ sum(L[seq_len(k-1)]) c(rep.int(FALSE, l1), rep.int(TRUE, len - l1)) } } } }) ## TODO ?? "is.nan" analogously ?? ## setMethod("is.finite", signature(x = "abIndex"), function(x) { if(x@kind != "rleDiff") is.finite(x@x) else { rd <- x@rleD rl <- rd@rle len <- 1+ sum(L <- rl$lengths) if(!is.finite(rd@first)) rep.int(FALSE, len) else { ## interesting case V <- rl$values if(all(iFin <- is.finite(V))) rep.int(TRUE, len) else { ## at least one V is +- Inf --> "x" is Inf/NaN from there k <- match(FALSE,iFin) # the first non-finite one l1 <- 1+ sum(L[seq_len(k-1)]) c(rep.int(TRUE, l1), rep.int(FALSE, len - l1)) } } } }) setMethod("is.infinite", signature(x = "abIndex"), function(x) { if(x@kind != "rleDiff") is.infinite(x@x) else { rd <- x@rleD rl <- rd@rle len <- 1+ sum(L <- rl$lengths) if(is.infinite(rd@first)) rep.int(TRUE, len) else { ## interesting case V <- rl$values if(!any(iInf <- is.infinite(V))) rep.int(FALSE, len) else { ## at least one V is +- Inf --> "x" is Inf/NaN from there k <- match(TRUE,iInf) # the first one l1 <- 1+ sum(L[seq_len(k-1)]) ## FIXME? do *not* consider 'NaN' (changing TRUE to FALSE): c(rep.int(FALSE, l1), rep.int(TRUE, len - l1)) } } } }) all.equal.abI <- function(target, current, ...) { if(!is(target, "abIndex") || !is(current, "abIndex")) return(paste0("target is ", data.class(target), ", current is ", data.class(current))) lt <- length(target) lc <- length(current) if(lt != lc) paste0("abIndex", ": lengths (", lt, ", ", lc, ") differ") else if(target@kind == current@kind) { all.equal.default(target, current, ...) } else ## different 'kinds' -- take "easy" exit: all.equal(abI2num(target), abI2num(current), ...) } ## {all.equal.abI} setMethod("all.equal", c(target = "abIndex", current = "abIndex"), all.equal.abI) setMethod("all.equal", c(target = "abIndex", current = "numLike"), function(target, current, ...) all.equal.abI(target, as(current, "abIndex"), ...)) setMethod("all.equal", c(target = "numLike", current = "abIndex"), function(target, current, ...) all.equal.abI(as(target, "abIndex"), current, ...)) ## Then I want something like get.ind.sel(.) [ ./Tsparse.R ] working, ## i.e. possibly match(i, , nomatch = 0) setAs("seqMat", "numeric", function(from) { do.call(c, lapply(seq_len(ncol(from)), function(j) seq(from=from[1L,j], to = from[2L,j]))) }) setAs("numeric", "seqMat", function(from) as(as(from, "abIndex"), "seqMat")) setAs("abIndex", "seqMat", function(from) { n <- length(from) d <- from@rleD va <- d@rle$values le <- d@rle$lengths m <- length(le) ## Now work the 'ends' are cumsum(c(d@first, le * va)) ## we need to care for the "length 1" stretches: if(any(nonPair <- le[2* seq_len(m2 <- m %/% 2)] != 1)) { ## an "easy" (but not so efficient when 'm' is "large") ## way would be to "make these" into pairs, then work for that case... } ## use ~/R/MM/Pkg-ex/Matrix/abIndex-experi.R for trying things ... stop(" --> is not yet implemented") }) setAs("seqMat", "abIndex", function(from) { stop(" --> is not yet implemented") }) Matrix/R/dgTMatrix.R0000644000175100001440000001634512256042001013764 0ustar hornikusers## Now in ./Tsparse.R ## setAs("dgTMatrix", "dgCMatrix", ## function(from) .Call(Tsparse_to_Csparse, from, FALSE) ## ) setAs("dgTMatrix", "dgeMatrix", function(from) .Call(dgTMatrix_to_dgeMatrix, from)) setAs("dgTMatrix", "matrix", function(from) .Call(dgTMatrix_to_matrix, from)) setAs("dgeMatrix", "dgTMatrix", function(from) as(as(from, "dgCMatrix"), "dgTMatrix")) if(FALSE) ## special case, relatively ugly, needed ?? setAs("dgTMatrix", "dsCMatrix", function(from) { if (!isSymmetric(from)) stop("cannot coerce non-symmetric \"dgTMatrix\" to \"dsCMatrix\" class") upper <- from@i <= from@j uC <- as(new("dgTMatrix", Dim = from@Dim, Dimnames = from@Dimnames, i = from@i[upper], j = from@j[upper], x = from@x[upper]), "dgCMatrix") new("dsCMatrix", Dim = uC@Dim, p = uC@p, i = uC@i, x = uC@x, uplo = "U") }) ## This is faster: setAs("dgTMatrix", "dtCMatrix", function(from) { if(!(iTri <- isTriangular(from))) stop("the matrix is not triangular") ## else stopifnot(is.character(uplo <- attr(iTri,"kind"))) .Call(Tsparse_to_tCsparse, from, uplo, "N") }) setAs("dgTMatrix", "dtTMatrix", function(from) check.gT2tT(from, toClass = "dtTMatrix", do.n=FALSE)) setAs("dgTMatrix", "triangularMatrix", function(from) check.gT2tT(from, toClass = "dtTMatrix", do.n=FALSE)) setAs("dgTMatrix", "dsTMatrix", function(from) check.gT2sT(from, toClass = "dsTMatrix", do.n=FALSE)) setAs("dgTMatrix", "symmetricMatrix", function(from) check.gT2sT(from, toClass = "dsTMatrix", do.n=FALSE)) mat2dgT <- function(from) { x <- as.double(from) nz <- isN0(x) new("dgTMatrix", Dim = dim(from), i = row(from)[nz] - 1L, j = col(from)[nz] - 1L, x = x[nz]) } setAs("matrix", "dgTMatrix", mat2dgT) ## "[" methods are now in ./Tsparse.R ## "[<-" methods { setReplaceMethod()s } too ... setMethod("image", "dgTMatrix", function(x, xlim = c(1, di[2]), ylim = c(di[1], 1), aspect = "iso", sub = sprintf("Dimensions: %d x %d", di[1], di[2]), xlab = "Column", ylab = "Row", cuts = 15, useRaster = FALSE, useAbs = NULL, colorkey = !useAbs, col.regions = NULL, lwd = NULL, ...) { ## 'at' can remain missing and be passed to levelplot di <- x@Dim xx <- x@x if(missing(useAbs)) ## use abs() when all values are non-neg useAbs <- min(xx, na.rm=TRUE) >= 0 else if(useAbs) xx <- abs(xx) rx <- range(xx, finite=TRUE) ## FIXME: make use of 'cuts' now ## and call levelplot() with 'at = ', making sure 0 is included and matching ## *exactly* - rather than approximately if(is.null(col.regions)) col.regions <- if(useAbs) { grey(seq(from = 0.7, to = 0, length = 100)) } else { ## no abs(.), rx[1] < 0 nn <- 100 n0 <- min(nn, max(0, round((0 - rx[1])/(rx[2]-rx[1]) * nn))) col.regions <- c(colorRampPalette(c("blue3", "gray80"))(n0), colorRampPalette(c("gray75","red3"))(nn - n0)) } if(!is.null(lwd) && !(is.numeric(lwd) && all(lwd >= 0))) # allow lwd=0 stop("'lwd' must be NULL or non-negative numeric") stopifnot(length(xlim) == 2, length(ylim) == 2) ## ylim: the rows count from top to bottom: ylim <- sort(ylim, decreasing=TRUE) if(all(xlim == round(xlim))) xlim <- xlim+ c(-.5, .5) if(all(ylim == round(ylim))) ylim <- ylim+ c(-.5, .5) levelplot(x@x ~ (x@j + 1L) * (x@i + 1L), sub = sub, xlab = xlab, ylab = ylab, xlim = xlim, ylim = ylim, aspect = aspect, colorkey = colorkey, col.regions = col.regions, cuts = cuts, par.settings = list(background = list(col = "transparent")), panel = if(useRaster) panel.levelplot.raster else function(x, y, z, subscripts, at, ..., col.regions) { ## a trimmed down version of lattice::panel.levelplot x <- as.numeric(x[subscripts]) y <- as.numeric(y[subscripts]) ## FIXME: use level.colors() here and 'at' from above -- ## ----- look at 'zcol' in panel.levelplot() numcol <- length(at) - 1 num.r <- length(col.regions) col.regions <- if (num.r <= numcol) rep_len(col.regions, numcol) else col.regions[1+ ((1:numcol-1)*(num.r-1)) %/% (numcol-1)] zcol <- rep.int(NA_integer_, length(z)) for (i in seq_along(col.regions)) zcol[!is.na(x) & !is.na(y) & !is.na(z) & at[i] <= z & z < at[i+1]] <- i zcol <- zcol[subscripts] if (any(subscripts)) { ## the line-width used in grid.rect() inside ## levelplot()'s panel for the *border* of the ## rectangles: levelplot()panel has lwd=1e-5: ## Here: use smart default ! if(is.null(lwd)) { wh <- grid::current.viewport()[c("width", "height")] ## wh : current viewport dimension in pixel wh <- c(grid::convertWidth(wh$width, "inches", valueOnly=TRUE), grid::convertHeight(wh$height, "inches", valueOnly=TRUE)) * par("cra") / par("cin") pSize <- wh/di ## size of one matrix-entry in pixels pA <- prod(pSize) # the "area" p1 <- min(pSize) lwd <- ## crude for now if(p1 < 2 || pA < 6) 0.01 # effectively 0 else if(p1 >= 4) 1 else if(p1 > 3) 0.5 else 0.2 ## browser() Matrix.msg("rectangle size ", paste(round(pSize,1), collapse=" x "), " [pixels]; --> lwd :", formatC(lwd)) } else stopifnot(is.numeric(lwd), all(lwd >= 0)) # allow 0 grid.rect(x = x, y = y, width = 1, height = 1, default.units = "native", gp = gpar(fill = col.regions[zcol], lwd = lwd, col = if(lwd < .01) NA)) } }, ...) }) ## Uses the triplet convention of *adding* entries with same (i,j): setMethod("+", signature(e1 = "dgTMatrix", e2 = "dgTMatrix"), function(e1, e2) { dimCheck(e1, e2) new("dgTMatrix", i = c(e1@i, e2@i), j = c(e1@j, e2@j), x = c(e1@x, e2@x), Dim = e1@Dim) }) ## setMethod("writeHB", signature(obj = "dgTMatrix"), ## function(obj, file, ...) callGeneric(as(obj, "CsparseMatrix"), file, ...)) Matrix/R/ngTMatrix.R0000644000175100001440000000535312254575000014003 0ustar hornikusers#### Nonzero Pattern Sparse Matrices in triplet format ### contains = "nsparseMatrix" ### ============= ---> superclass methods in ./nsparseMatrix.R setAs("ngTMatrix", "lgeMatrix", function(from) .Call(lgTMatrix_to_lgeMatrix, as(from,"lgTMatrix"))) setAs("ngTMatrix", "ngeMatrix", function(from) as(as(from, "lgeMatrix"), "nMatrix")) setAs("ngTMatrix", "generalMatrix", function(from) as(from, "ngeMatrix")) setAs("ngTMatrix", "matrix", function(from) .Call(lgTMatrix_to_matrix, as(from, "lgTMatrix"))) ## setAs("ngTMatrix", "matrix", # go via fast C code: ## function(from) as(as(from, "ngCMatrix"), "matrix")) setAs("matrix", "ngTMatrix", function(from) { if(!is.logical(from)) storage.mode(from) <- "logical" if(any(is.na(from))) stop("cannot coerce 'NA's to \"nsparseMatrix\"") dn <- dimnames(from) if(is.null.DN(dn)) dn <- list(NULL,NULL) else dimnames(from) <- NULL # such that which(.) does not see any: ij <- which(from, arr.ind = TRUE) - 1L if(length(ij) == 0) ij <- matrix(ij, 0, 2) new("ngTMatrix", i = ij[,1], j = ij[,2], Dim = as.integer(dim(from)), Dimnames = dn) }) setAs("matrix", "nMatrix", function(from) as(from, "ngTMatrix")) setAs("ngTMatrix", "dgTMatrix", function(from) ## more efficient than ## as(as(as(sM, "ngCMatrix"), "dgCMatrix"), "dgTMatrix") new("dgTMatrix", i = from@i, j = from@j, x = rep.int(1, length(from@i)), ## cannot copy factors, but can we use them? Dim = from@Dim, Dimnames= from@Dimnames)) setAs("ngTMatrix", "dMatrix", function(from) as(from, "dgTMatrix")) setAs("ngTMatrix", "dsparseMatrix", function(from) as(from, "dgTMatrix")) setAs("ngTMatrix", "lgTMatrix", function(from) new("lgTMatrix", i = from@i, j = from@j, x = rep.int(TRUE, length(from@i)), ## cannot copy factors, but can we use them? Dim = from@Dim, Dimnames= from@Dimnames)) setAs("ngTMatrix", "lMatrix", function(from) as(from, "lgTMatrix")) setAs("ngTMatrix", "triangularMatrix", function(from) check.gT2tT(from, toClass = "ntTMatrix", do.n=TRUE)) setAs("ngTMatrix", "ntTMatrix", function(from) check.gT2tT(from, toClass = "ntTMatrix", do.n=TRUE)) setAs("ngTMatrix", "symmetricMatrix", function(from) check.gT2sT(from, toClass = "nsTMatrix", do.n=TRUE)) ## We favor coercion to super-classes, here, "symmetricMatrix" ## setAs("ngTMatrix", "nsTMatrix", ## function(from) check.gT2sT(from, toClass = "nsTMatrix", do.n=TRUE)) if(FALSE) ## unneeded: use t. setMethod("t", signature(x = "ngTMatrix"), function(x) new("ngTMatrix", i = x@j, j = x@i, Dim = x@Dim[2:1], Dimnames= x@Dimnames[2:1]), valueClass = "ngTMatrix") Matrix/R/condest.R0000644000175100001440000003234112070371667013533 0ustar hornikusers#### This is a "translation" of GNU octave's #### ~/src/octave-3.2.4/scripts/linear-algebra/condest.m #### and ~/src/octave-3.2.4/scripts/linear-algebra/onenormest.m #### which have identical copyright and references (see below): #### ##__\begin{copyright clause}______________________________________________ ## Copyright (C) 2007, 2008, 2009 Regents of the University of California ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## Code originally licensed under ## ## Copyright (c) 2007, Regents of the University of California ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions ## are met: ## ## * Redistributions of source code must retain the above copyright ## notice, this list of conditions and the following disclaimer. ## ## * Redistributions in binary form must reproduce the above ## copyright notice, this list of conditions and the following ## disclaimer in the documentation and/or other materials provided ## with the distribution. ## ## * Neither the name of the University of California, Berkeley nor ## the names of its contributors may be used to endorse or promote ## products derived from this software without specific prior ## written permission. ## ## THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ## TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ## PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS AND ## CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, ## SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT ## LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF ## USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ## ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT ## OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF ## SUCH DAMAGE. ## Author: Jason Riedy ## Keywords: linear-algebra norm estimation ## Version: 0.2 ##__\end{copyright clause}________________________________________________ condest <- function(A, t = min (n, 5), normA = norm(A, "1"), silent = FALSE, quiet = TRUE) { ## Octave has further optional args and "calling sequences" ## may be implement at a later time point ## if(length(d <- dim(A)) != 2 || (n <- d[1]) != d[2]) stop("'A' must be a square matrix") luA <- lu(A) i.n <- seq_len(n) isSparse <- is(A, "sparseMatrix") if(isSparse) { ### FIXME: if A is not a Matrix, but already a "CHMfactor" as resulting from ### Cholesky() , then we can procede more efficiently , notably ### because of the solve(A, b, system = ".*") options ! ## luA = "sparseLU": slots (L, U, p,q, Dim); ## expand(luA) == list(P, L, U, Q) <----> A = P' L U Q ## where P A == A[p +1,] and A Q' == A[, q +1] ## <==> A^(-1) x = Q' U^-1 L^-1 P x = Q'y ## and A^(-T) x =(Q' U^-1 L^-1 P)' x = P' L^-T U^-T Q x = P'z q. <- q.i <- luA@q + 1L; q.i[q.i] <- i.n p. <- p.i <- luA@p + 1L; p.i[p.i] <- i.n ## q.i := inv(q.) & p.i := inv(p.), the inverse permutations Ut <- t(luA@U) Lt <- t(luA@L) f.solve <- function(x) solve(luA@U, solve(luA@L, x[p.,]))[q.i,] f.solve_t <- function(x) solve(Lt, solve(Ut, x[q.,]))[p.i,] ##Oct [L, U, P, Pc] = lu (A); ##Oct solve = @(x) Pc' * (U \ (L \ (P * x))); ##Oct solve_t = @(x) P' * (L' \ (U' \ (Pc * x))); } else { ## luA is "denseLU" : e.A <- expand(luA) ## == list(L, U, P), where A = PLU p. <- p.i <- luA@perm; p.i[p.i] <- i.n ## p.i := inv(p.), the inverse permutation Ut <- t(e.A$U) Lt <- t(e.A$L) ## A = PLU <--> A^{-1} x = U^-1 L^-1 P x ## A^{-T} x = (U^-1 L^-1 P)' x = P' L^-T U^-T x = P'z f.solve <- function(x) solve(e.A$U, solve(e.A$L, x[p.,])) f.solve_t <- function(x) solve(Lt, solve(Ut, x))[p.i,] ##Oct [L, U, P] = lu (A); ##Oct solve = @(x) U \ (L \ (P*x)); ##Oct solve_t = @(x) P' * (L' \ (U' \ x)); } n1.res <- ## onenormest (A^{-1}, t=t) -- of course,that's *NOT* what we want onenormest (A.x = f.solve, At.x = f.solve_t, t=t, n=n, quiet=quiet, silent=silent) ## [Ainv_norm, v, w] = onenormest (solve, solve_t, n, t); w <- n1.res[["w"]] list(est = normA * n1.res[["est"]], v = w / sum(abs(w))) # sum(|w|) = norm(w, "1") } ## %!demo ## %! N = 100; ## %! A = randn (N) + eye (N); ## %! condest (A) ## %! [L,U,P] = lu (A); ## %! condest (A, @(x) U\ (L\ (P*x)), @(x) P'*(L'\ (U'\x))) ## %! condest (@(x) A*x, @(x) A'*x, @(x) U\ (L\ (P*x)), @(x) P'*(L'\ (U'\x)), N) ## %! norm (inv (A), 1) * norm (A, 1) ### Yes, these test bounds are really loose. There's ### enough randomization to trigger odd cases with hilb(). ## %!test ## %! N = 6; ## %! A = hilb (N); ## %! cA = condest (A); ## %! cA_test = norm (inv (A), 1) * norm (A, 1); ## %! assert (cA, cA_test, -2^-8); ## %!test ## %! N = 6; ## %! A = hilb (N); ## %! solve = @(x) A\x; solve_t = @(x) A'\x; ## %! cA = condest (A, solve, solve_t); ## %! cA_test = norm (inv (A), 1) * norm (A, 1); ## %! assert (cA, cA_test, -2^-8); ## %!test ## %! N = 6; ## %! A = hilb (N); ## %! apply = @(x) A*x; apply_t = @(x) A'*x; ## %! solve = @(x) A\x; solve_t = @(x) A'\x; ## %! cA = condest (apply, apply_t, solve, solve_t, N); ## %! cA_test = norm (inv (A), 1) * norm (A, 1); ## %! assert (cA, cA_test, -2^-6); ## %!test ## %! N = 12; ## %! A = hilb (N); ## %! [rcondA, v] = condest (A); ## %! x = A*v; ## %! assert (norm(x, inf), 0, eps); ##------------ onenormest ------------------------------------------ onenormest <- function(A, t = min(n, 5), A.x, At.x, n, silent = FALSE, quiet = silent, iter.max = 10, eps = 4* .Machine$double.eps) { mi.A <- missing(A) mi.A.x <- missing(A.x) mi.At.x <- missing(At.x) no.A.x <- mi.A.x || !is.function(A.x) no.At.x <- mi.At.x || !is.function(At.x) if(mi.A && (no.A.x || no.At.x)) stop("must either specify 'A' or the functions 'A.x' and 'At.x'") if(!mi.A && (!mi.A.x || !mi.At.x)) warning("when 'A' is specified, 'A.x' and 'At.x' are disregarded") if(mi.A) { stopifnot(is.numeric(n), length(n) == 1, n == round(n), n >= 0) } else { ## using 'A' if(length(d <- dim(A)) != 2 || (n <- d[1]) != d[2]) stop("'A' must be a square matrix") rm(d) } stopifnot(is.numeric(t), length(t) == 1, t >= 1, iter.max >= 1) ## Initial test vectors X. X <- matrix(runif(n*t), n,t) # X = rand (n, t); ## scale X to have column sums == 1 : X <- X / rep(colSums(X), each=n) ## Track if a vertex has been visited. been_there <- logical(n) # zeros (n, 1); I.t <- diag(nrow = t) ## To check if the estimate has increased. est_old <- 0 ## Normalized vector of signs. S <- matrix(0, n, t) for(iter in 1:(iter.max + 1)) { Y <- if(mi.A) A.x(X) else A %*% X ## is n x t ## Find the initial estimate as the largest A*x. ## [est, imax] = max (sum (abs (Y), 1)) imax <- which.max(cY <- colSums(abs(Y))) est <- cY[imax] if (est > est_old || iter == 2) w <- Y[, imax] if (iter >= 2 && est < est_old) { ## No improvement, so stop. est <- est_old break } est_old <- est S_old <- S if (iter > iter.max) { ## Gone too far. Stop. if(!silent) warning(gettextf("not converged in %d iterations", iter.max), domain = NA) break } S <- sign (Y) ## n x t ## Test if any of S are approximately parallel to previous S ## vectors or current S vectors. If everything is parallel, ## stop. Otherwise, replace any parallel vectors with ## rand{-1,+1}. partest <- apply(abs(crossprod(S_old, S) - n) < eps*n, 2, any) if (all(partest)) { ## All the current vectors are parallel to old vectors. ## We've hit a cycle, so stop. if(!quiet) message("hit a cycle (1) -- stop iterations") break } if (any(partest)) { ## Some vectors are parallel to old ones and are cycling, ## but not all of them. Replace the parallel vectors with ## rand{-1,+1}. numpar <- sum (partest) replacements <- matrix(sample(c(-1,1), n*numpar,replace=TRUE), n, numpar) S[,partest] <- replacements } ## Now test for parallel vectors within S. partest <- apply(crossprod(S) - I.t == n, 2, any) if (any(partest)) { numpar <- sum(partest) replacements <- matrix(sample(c(-1,1), n*numpar,replace=TRUE), n, numpar) S[,partest] <- replacements } Z <- if(mi.A) At.x(S) else crossprod(A, S) ## -- n x t ## Now find the largest non-previously-visted index per vector. ## h = max(2, abs(Z)) ## -- n x t h <- pmax.int(2, as(abs(Z),"matrix")); dim(h) <- dim(Z) ## -- n x t ## [mh, mhi] = max (h) : for each column h[,j]: ## mh[j] = max(h[,j]); mhi = argmax(..) mhi <- apply(h, 2, which.max) ## mh <- h[cbind(mhi,1:t)] if (iter >= 2 && all(mhi == imax)) { ## (mhi == imax) : in octave this is only true when it's for all() ## Hit a cycle, stop. if(!quiet) message("hit a cycle (2) -- stop iterations") break } ## [h, ind] = sort (h, 'descend'): r <- apply(h, 2, sort.int, decreasing=TRUE, index.return=TRUE) #-> list h <- sapply(r, `[[`, "x") ind <- sapply(r, `[[`, "ix") #-> n x t {each column = permutation of 1:n} if (t > 1) { firstind <- ind[1:t] if (all (been_there[firstind])) { ## Visited all these before, so stop. break } ind <- ind[!been_there[ind]] ##-> now ind is a simple vector if(length(ind) < t) { ## There aren't enough new vectors, so we're practically ## in a cycle. Stop. if(!quiet) message("not enough new vecs -- stop iterations") break } } ## Visit the new indices. X <- matrix(0, n, t) X[cbind(ind[1:t], 1:t)] <- 1 ## for(zz in 1:t) X[ind[zz],zz] <- 1 been_there [ind[1:t]] <- TRUE } ## for(iter ...) ## The estimate est and vector w are set in the loop above. The ## vector v selects the imax column of A. v <- integer(n) v[imax] <- 1L list(est=est, v=v, w=w, iter=iter) }## {onenormest} ## %!demo ## %! N = 100; ## %! A = randn(N) + eye(N); ## %! [L,U,P] = lu(A); ## %! nm1inv = onenormest(@(x) U\(L\(P*x)), @(x) P'*(L'\(U'\x)), N, 30) ## %! norm(inv(A), 1) ## %!test ## %! N = 10; ## %! A = ones (N); ## %! [nm1, v1, w1] = onenormest (A); ## %! [nminf, vinf, winf] = onenormest (A', 6); ## %! assert (nm1, N, -2*eps); ## %! assert (nminf, N, -2*eps); ## %! assert (norm (w1, 1), nm1 * norm (v1, 1), -2*eps) ## %! assert (norm (winf, 1), nminf * norm (vinf, 1), -2*eps) ## %!test ## %! N = 10; ## %! A = ones (N); ## %! [nm1, v1, w1] = onenormest (@(x) A*x, @(x) A'*x, N, 3); ## %! [nminf, vinf, winf] = onenormest (@(x) A'*x, @(x) A*x, N, 3); ## %! assert (nm1, N, -2*eps); ## %! assert (nminf, N, -2*eps); ## %! assert (norm (w1, 1), nm1 * norm (v1, 1), -2*eps) ## %! assert (norm (winf, 1), nminf * norm (vinf, 1), -2*eps) ## %!test ## %! N = 5; ## %! A = hilb (N); ## %! [nm1, v1, w1] = onenormest (A); ## %! [nminf, vinf, winf] = onenormest (A', 6); ## %! assert (nm1, norm (A, 1), -2*eps); ## %! assert (nminf, norm (A, inf), -2*eps); ## %! assert (norm (w1, 1), nm1 * norm (v1, 1), -2*eps) ## %! assert (norm (winf, 1), nminf * norm (vinf, 1), -2*eps) ## ## Only likely to be within a factor of 10. ## %!test ## %! N = 100; ## %! A = rand (N); ## %! [nm1, v1, w1] = onenormest (A); ## %! [nminf, vinf, winf] = onenormest (A', 6); ## %! assert (nm1, norm (A, 1), -.1); ## %! assert (nminf, norm (A, inf), -.1); ## %! assert (norm (w1, 1), nm1 * norm (v1, 1), -2*eps) ## %! assert (norm (winf, 1), nminf * norm (vinf, 1), -2*eps) Matrix/R/CHMfactor.R0000644000175100001440000001620612211131516013664 0ustar hornikusers ### FIXME: We really want the separate parts (P,L,D) of A = P' L D L' P' ### ----- --> ~/R/MM/Pkg-ex/Matrix/chol-ex.R ---------------- setAs("CHMfactor", "sparseMatrix", function(from) .Call(CHMfactor_to_sparse, from)) setAs("CHMfactor", "Matrix", function(from) as(from, "sparseMatrix")) setAs("CHMfactor", "pMatrix", function(from) as(from@perm + 1L, "pMatrix")) setMethod("expand", signature(x = "CHMfactor"), function(x, ...) list(P = as(x, "pMatrix"), L = as(x, "sparseMatrix"))) ##' Determine if a CHMfactor object is LDL or LL ##' @param x - a CHMfactor object ##' @return TRUE if x is LDL, otherwise FALSE isLDL <- function(x) { stopifnot(is(x, "CHMfactor")) as.logical(! x@type[2])# "!" = not as type[2] := (cholmod_factor)->is_ll } .isLDL <- function(x) as.logical(! x@type[2])# "!" = not as type[2] := (cholmod_factor)->is_ll setMethod("image", "CHMfactor", function(x, ...) { x <- as(as(x, "sparseMatrix"), "dgTMatrix") callGeneric() }) .CHM_solve <- function(a, b, system = c("A", "LDLt", "LD", "DLt", "L", "Lt", "D", "P", "Pt"), ...) { chk.s(...) sysDef <- eval(formals()$system) .Call(CHMfactor_solve, ##-> cholmod_solve() in ../src/CHOLMOD/Cholesky/cholmod_solve.c a, b, ## integer in 1 ("A"), 2 ("LDLt"), ..., 9 ("Pt") : match(match.arg(system, sysDef), sysDef, nomatch = 0L)) } setMethod("solve", signature(a = "CHMfactor", b = "ddenseMatrix"), .CHM_solve, valueClass = "dgeMatrix") setMethod("solve", signature(a = "CHMfactor", b = "matrix"), .CHM_solve, valueClass = "dgeMatrix") setMethod("solve", signature(a = "CHMfactor", b = "numeric"), function(a, b, ...) .CHM_solve(a, matrix(if(is.double(b)) b else as.double(b), length(b), 1L), ...), valueClass = "dgeMatrix") setMethod("solve", signature(a = "CHMfactor", b = "dsparseMatrix"), function(a, b, system = c("A", "LDLt", "LD", "DLt", "L", "Lt", "D", "P", "Pt"), ...) { chk.s(...) sysDef <- eval(formals()$system) .Call(CHMfactor_spsolve, #--> cholmod_spsolve() in ../src/CHOLMOD/Cholesky/cholmod_spsolve.c a, as(as(b, "CsparseMatrix"), "dgCMatrix"), match(match.arg(system, sysDef), sysDef, nomatch = 0L)) }, valueClass = "CsparseMatrix")# < virtual value ? setMethod("solve", signature(a = "CHMfactor", b = "diagonalMatrix"), function(a, b, ...) solve(a, as(b, "dsparseMatrix"), ...)) setMethod("solve", signature(a = "CHMfactor", b = "missing"), ## <--> b = Diagonal(.) function(a, b, system = c("A", "LDLt", "LD","DLt", "L","Lt", "D", "P","Pt"), ...) { chk.s(...) sysDef <- eval(formals()$system) system <- match.arg(system, sysDef) i.sys <- match(system, sysDef, nomatch = 0L) as(.Call(CHMfactor_spsolve, a, .sparseDiagonal(a@Dim[1], shape="g"), i.sys), switch(system, A=, LDLt = "symmetricMatrix",# was "dsCMatrix" LD=, DLt=, L=, Lt =, D = "dtCMatrix", # < diagonal: still as "Csparse.." P=, Pt = "pMatrix")) }) ## Catch-all the rest : make sure 'system' is not lost setMethod("solve", signature(a = "CHMfactor", b = "ANY"), function(a, b, system = c("A", "LDLt", "LD","DLt", "L","Lt", "D", "P","Pt"), ...) solve(a, as(b, "dMatrix"), system, ...)) setMethod("chol2inv", signature(x = "CHMfactor"), function (x, ...) { chk.s(...) solve(x, system = "A") }) setMethod("determinant", signature(x = "CHMfactor", logarithm = "missing"), function(x, logarithm, ...) determinant(x, TRUE)) setMethod("determinant", signature(x = "CHMfactor", logarithm = "logical"), function(x, logarithm, ...) { ldet <- .Call(CHMfactor_ldetL2, x) / 2 mkDet(logarithm=logarithm, ldet=ldet, sig = 1L) }) setMethod("update", signature(object = "CHMfactor"), function(object, parent, mult = 0, ...) { stopifnot(extends(clp <- class(parent), "sparseMatrix")) d <- dim(parent) if(!extends(clp, "dsparseMatrix")) clp <- class(parent <- as(parent, "dsparseMatrix")) if(!extends(clp, "CsparseMatrix")) clp <- class(parent <- as(parent, "CsparseMatrix")) if(d[1] == d[2] && !extends(clp, "dsCMatrix") && !is.null(v <- getOption("Matrix.verbose")) && v >= 1) message(gettextf("Quadratic matrix '%s' (=: A) is not formally\n symmetric. Will be treated as A A' ", "parent"), domain=NA) chk.s(...) .Call(CHMfactor_update, object, parent, mult) }) ##' fast version, somewhat hidden; here parent *must* be 'd[sg]CMatrix' .updateCHMfactor <- function(object, parent, mult) .Call(CHMfactor_update, object, parent, mult) setMethod("updown", signature(update="ANY", C="ANY", L="ANY"), ## fallback method -- give a "good" error message: function(update,C,L) stop("'update' must be logical or '+' or '-'; 'C' a matrix, and 'L' a \"CHMfactor\"")) setMethod("updown", signature(update="logical", C="mMatrix", L="CHMfactor"), function(update,C,L){ bnew <- as(L,'pMatrix') %*% C .Call(CHMfactor_updown,update, as(bnew,'sparseMatrix'), L) }) setMethod("updown", signature(update="character", C="mMatrix", L="CHMfactor"), function(update,C,L){ if(! update %in% c("+","-")) stop("update must be TRUE/FALSE or '+' or '-'") update <- update=="+" bnew <- as(L,'pMatrix') %*% C .Call(CHMfactor_updown,update, as(bnew,'sparseMatrix'), L) }) ## Currently hidden: ldetL2up <- function(x, parent, Imult) { ## Purpose: compute log Det |A + m*I| for many values of m ## ---------------------------------------------------------------------- ## Arguments: x: CHMfactor to be updated ## parent : CsparseMatrix M; for symmetric M, A = M, otherwise A = MM' ## Imult : a numeric *vector* of 'm's (= I multipliers) ## ---------------------------------------------------------------------- ## Author: Doug Bates, Date: 19 Mar 2008 stopifnot(is(x, "CHMfactor"), is(parent, "CsparseMatrix"), nrow(x) == nrow(parent)) .Call(CHMfactor_ldetL2up, x, parent, as.double(Imult)) } ##' Update a sparse Cholesky factorization in place ##' @param L A sparse Cholesky factor that inherits from CHMfactor ##' @param parent a sparse matrix for updating the factor. Either a ##' dsCMatrix, in which case L is updated to the Cholesky ##' factorization of parent, or a dgCMatrix, in which case L is ##' updated to the Cholesky factorization of tcrossprod(parent) ##' @param Imult an optional positive scalar to be added to the ##' diagonal before factorization, ##' @return NULL. This function always returns NULL. It is called ##' for its side-effect of updating L in place. ##' @note This function violates the functional language semantics of ##' R in that it updates its argument L in place (i.e. without copying). ##' This is intentional but it means the function should be used ##' with caution. If the preceding sentences do not make sense to ##' you, you should not use this function,. destructive_Chol_update <- function(L, parent, Imult = 1) { stopifnot(is(L, "CHMfactor"), is(parent, "sparseMatrix")) .Call(destructive_CHM_update, L, parent, Imult) } Matrix/R/dtTMatrix.R0000644000175100001440000000304011003616106013767 0ustar hornikusers### Coercion and Methods for Triangular Triplet Matrices setAs("dtTMatrix", "dgTMatrix", function(from) tT2gT(from, cl = "dtTMatrix", toClass = "dgTMatrix")) setAs("dtTMatrix", "generalMatrix", function(from) tT2gT(from, cl = "dtTMatrix", toClass = "dgTMatrix")) if(FALSE) ## needed in ../tests/Class+Meth.R -- replaced by .T.2.l() in ./Tsparse.R setAs("dtTMatrix", "ltTMatrix", function(from) new("ltTMatrix", i = from@i, j = from@j, x = as.logical(from@x), uplo = from@uplo, diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames)) if(FALSE) ## needed in ../tests/Class+Meth.R -- replaced by .T.2.n() in ./Tsparse.R setAs("dtTMatrix", "ntTMatrix", function(from) new("ntTMatrix", i = from@i, j = from@j, uplo = from@uplo, diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames)) ## Conversion to dense storage is first to a dtrMatrix setAs("dtTMatrix", "dtrMatrix", function(from) .Call(dtTMatrix_as_dtrMatrix, from)) setAs("dtTMatrix", "matrix", function(from) as(as(from, "dtrMatrix"), "matrix")) setAs("dtTMatrix", "dgeMatrix", function(from) as(as(from, "dtrMatrix"), "dgeMatrix")) setAs("matrix", "dtTMatrix", function(from) as(as(from, "dtpMatrix"), "dtTMatrix")) setMethod("t", "dtTMatrix", function(x) new("dtTMatrix", Dim = x@Dim[2:1], Dimnames = x@Dimnames[2:1], i = x@j, j = x@i, x = x@x, diag = x@diag, uplo = if (x@uplo == "U") "L" else "U")) Matrix/R/Tsparse.R0000644000175100001440000007662112267246663013533 0ustar hornikusers#### "TsparseMatrix" : Virtual class of sparse matrices in triplet-format ## more efficient than going via Csparse: setAs("matrix", "TsparseMatrix", function(from) if(is.numeric(from)) mat2dgT(from) else if(is.logical(from)) as(Matrix(from, sparse=TRUE), "TsparseMatrix") else stop("not-yet-implemented coercion to \"TsparseMatrix\"")) setAs("numeric", "TsparseMatrix", function(from) as(as.matrix(from), "TsparseMatrix")) setAs("TsparseMatrix", "matrix", function(from) .Call(dgTMatrix_to_matrix, as(from, "dgTMatrix"))) ## in ../src/Tsparse.c : |-> cholmod_T -> cholmod_C -> chm_sparse_to_SEXP ## adjusted for triangular matrices not represented in cholmod .T.2.C <- function(from) .Call(Tsparse_to_Csparse, from, ## is(from, "triangularMatrix")) ## fast, exported for power users .T2Cmat <- function(from, isTri = is(from, "triangularMatrix")) .Call(Tsparse_to_Csparse, from, isTri) setAs("TsparseMatrix", "CsparseMatrix", .T.2.C) .T.2.n <- function(from) { ## No: coercing to n(sparse)Matrix gives the "full" pattern including 0's ## if(any(is0(from@x))) ## 0 or FALSE -- the following should have drop0Tsp(.) ## from <- as(drop0(from), "TsparseMatrix") if(is(from, "triangularMatrix")) # i.e. ?tTMatrix new("ntTMatrix", i = from@i, j = from@j, uplo = from@uplo, diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames) else if(is(from, "symmetricMatrix")) # i.e. ?sTMatrix new("nsTMatrix", i = from@i, j = from@j, uplo = from@uplo, Dim = from@Dim, Dimnames = from@Dimnames) else new("ngTMatrix", i = from@i, j = from@j, Dim = from@Dim, Dimnames = from@Dimnames) } setAs("TsparseMatrix", "nsparseMatrix", .T.2.n) setAs("TsparseMatrix", "nMatrix", .T.2.n) .T.2.l <- function(from) { cld <- getClassDef(class(from)) xx <- if(extends(cld, "nMatrix")) rep.int(TRUE, length(from@i)) else as.logical(from@x) if(extends(cld, "triangularMatrix")) # i.e. ?tTMatrix new("ltTMatrix", i = from@i, j = from@j, x = xx, uplo = from@uplo, diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames) else if(extends(cld, "symmetricMatrix")) # i.e. ?sTMatrix new("lsTMatrix", i = from@i, j = from@j, x = xx, uplo = from@uplo, Dim = from@Dim, Dimnames = from@Dimnames) else new("lgTMatrix", i = from@i, j = from@j, x = xx, Dim = from@Dim, Dimnames = from@Dimnames) } setAs("TsparseMatrix", "lsparseMatrix", .T.2.l) setAs("TsparseMatrix", "lMatrix", .T.2.l) ## Special cases ("d", "l", "n") %o% ("g", "s", "t") : ## used e.g. in triu() setAs("dgTMatrix", "dgCMatrix", function(from) .Call(Tsparse_to_Csparse, from, FALSE)) setAs("dsTMatrix", "dsCMatrix", function(from) .Call(Tsparse_to_Csparse, from, FALSE)) setAs("dtTMatrix", "dtCMatrix", function(from) .Call(Tsparse_to_Csparse, from, TRUE)) setAs("lgTMatrix", "lgCMatrix", function(from) .Call(Tsparse_to_Csparse, from, FALSE)) setAs("lsTMatrix", "lsCMatrix", function(from) .Call(Tsparse_to_Csparse, from, FALSE)) setAs("ltTMatrix", "ltCMatrix", function(from) .Call(Tsparse_to_Csparse, from, TRUE)) setAs("ngTMatrix", "ngCMatrix", function(from) .Call(Tsparse_to_Csparse, from, FALSE)) setAs("nsTMatrix", "nsCMatrix", function(from) .Call(Tsparse_to_Csparse, from, FALSE)) setAs("ntTMatrix", "ntCMatrix", function(from) .Call(Tsparse_to_Csparse, from, TRUE)) ### "[" : ### ----- ## Test for numeric/logical/character ## method-*internally* ; this is not strictly OO, but allows to use ## the following utility and hence much more compact code. ## Otherwise have to write methods for all possible combinations of ## (i , j) \in ## (numeric, logical, character, missing) x (numeric, log., char., miss.) ##' a simplified "subset" of intI() below int2i <- function(i, n) { if(any(i < 0L)) { if(any(i > 0L)) stop("you cannot mix negative and positive indices") seq_len(n)[i] } else { if(length(i) && max(i, na.rm=TRUE) > n) stop(gettextf("index larger than maximal %d", n), domain=NA) if(any(z <- i == 0)) i <- i[!z] i } } intI <- function(i, n, dn, give.dn = TRUE) { ## Purpose: translate numeric | logical | character index ## into 0-based integer ## ---------------------------------------------------------------------- ## Arguments: i: index vector (numeric | logical | character) ## n: array extent { == dim(.) [margin] } ## dn: character col/rownames or NULL { == dimnames(.)[[margin]] } ## ---------------------------------------------------------------------- ## Author: Martin Maechler, Date: 23 Apr 2007 has.dn <- !is.null.DN(dn) DN <- has.dn && give.dn if(is(i, "numeric")) { storage.mode(i) <- "integer" if(any(is.na(i))) stop("'NA' indices are not (yet?) supported for sparse Matrices") if(any(i < 0L)) { if(any(i > 0L)) stop("you cannot mix negative and positive indices") i0 <- (0:(n - 1L))[i] } else { if(length(i) && max(i, na.rm=TRUE) > n) stop(gettextf("index larger than maximal %d", n), domain=NA) if(any(z <- i == 0)) i <- i[!z] i0 <- i - 1L # transform to 0-indexing } if(DN) dn <- dn[i] } else if (is(i, "logical")) { if(length(i) > n) stop(gettextf("logical subscript too long (%d, should be %d)", length(i), n), domain=NA) i0 <- (0:(n - 1L))[i] if(DN) dn <- dn[i] } else { ## character if(!has.dn) stop("no 'dimnames[[.]]': cannot use character indexing") i0 <- match(i, dn) if(any(is.na(i0))) stop("invalid character indexing") if(DN) dn <- dn[i0] i0 <- i0 - 1L } if(!give.dn) i0 else list(i0 = i0, dn = dn) } ## {intI} .ind.prep <- function(xi, intIlist, iDup = duplicated(i0), anyDup = any(iDup)) { ## Purpose: do the ``common things'' for "*gTMatrix" indexing for 1 dim. ## and return match(.,.) + li = length of corresponding dimension ## ## xi = "x@i" ; intIlist = intI(i, dim(x)[margin], ....) i0 <- intIlist$i0 stopifnot(is.numeric(i0))# cheap fast check (i0 may have length 0 !) m <- match(xi, i0, nomatch=0) if(anyDup) { # assuming anyDup <- any(iDup <- duplicated(i0)) ## i0i: where in (non-duplicated) i0 are the duplicated ones i0i <- match(i0[iDup], i0) i.x <- which(iDup) - 1L jm <- lapply(i0i, function(.) which(. == m)) } c(list(m = m, li = length(i0), i0 = i0, anyDup = anyDup, dn = intIlist$dn), ## actually, iDup is rarely needed in calling code if(anyDup) list(iDup = iDup, i0i = i0i, i.x = i.x, jm = unlist(jm), i.xtra = rep.int(i.x, sapply(jm, length)))) } ## {.ind.prep} ##' ##' Do the ``common things'' for "*gTMatrix" sub-assignment ##' for 1 dimension, 'margin' , ##'
##' @title Indexing Preparation ##' @param i "index" ##' @param margin in {1,2}; ##' @param di = dim(x) { used when i is not character } ##' @param dn = dimnames(x) ##' @return match(.,.) + li = length of corresponding dimension ##' difference to .ind.prep(): use 1-indices; no match(xi,..), no dn at end ##' @author Martin Maechler .ind.prep2 <- function(i, margin, di, dn) { intI(i, n = di[margin], dn = dn[[margin]], give.dn = FALSE) } ## Select rows setMethod("[", signature(x = "TsparseMatrix", i = "index", j = "missing", drop = "logical"), function (x, i, j, ..., drop) { ## select rows na <- nargs() Matrix.msg("Tsp[i,m,l]: nargs()=", na, .M.level=2) if(na == 4) .as.Tsp(as(x,"CsparseMatrix")[i, , drop=drop], noCheck = !drop) else if(na == 3) ## e.g. M[0] , M[TRUE], M[1:2] .M.vectorSub(x,i) else ## should not happen stop("Matrix-internal error in [i,,d]; please report") }) ## Select columns setMethod("[", signature(x = "TsparseMatrix", i = "missing", j = "index", drop = "logical"), function (x, i, j, ..., drop) { ## select columns .as.Tsp(as(x,"CsparseMatrix")[, j, drop=drop], noCheck = !drop) }) setMethod("[", signature(x = "TsparseMatrix", i = "index", j = "index", drop = "logical"), function (x, i, j, ..., drop) .as.Tsp(as(x,"CsparseMatrix")[i, j, drop=drop], noCheck = !drop)) ## This is "just for now" -- Thinking of *not* doing this in the future .as.Tsp <- function(x, noCheck) if(noCheck || is(x,"sparseMatrix")) as(x, "TsparseMatrix") else x ## FIXME: Learn from .TM... below or rather .M.sub.i.2col(.) in ./Matrix.R ## ------ the following should be much more efficient than the ## subset.ij() based ./Matrix.R code : if(FALSE) ## A[ ij ] where ij is (i,j) 2-column matrix : setMethod("[", signature(x = "TsparseMatrix", i = "matrix", j = "missing"),# drop="ANY" function (x, i, j, ..., drop) { di <- dim(x) dn <- dimnames(x) ## TODO check i (= 2-column matrix of indices) --- ## as in .M.sub.i.2col() in ./Matrix.R j <- i[,2] i <- i[,1] if(is(x, "symmetricMatrix")) { isSym <- isTRUE(all(i == j))# work for i,j NA if(!isSym) x <- as(x, paste0(.M.kind(x), "gTMatrix")) } else isSym <- FALSE if(isSym) { offD <- x@i != x@j ip1 <- .ind.prep(c(x@i,x@j[offD]), intI(i, n= di[1], dn=dn[[1]])) ip2 <- .ind.prep(c(x@j,x@i[offD]), intI(j, n= di[2], dn=dn[[2]])) } else { ip1 <- .ind.prep(x@i, intI(i, n = di[1], dn = dn[[1]])) ip2 <- .ind.prep(x@j, intI(j, n = di[2], dn = dn[[2]])) } stop("FIXME: NOT YET FINISHED IMPLEMENTATION") ## The M[i_vec, j_vec] had -- we need "its diagonal" : sel <- ip1$m & ip2$m if(isSym) { # only those corresponding to upper/lower triangle sel <- sel & (if(x@uplo == "U") ip1$m <= ip2$m else ip2$m <= ip1$m) } x@i <- ip1$m[sel] - 1L x@j <- ip2$m[sel] - 1L if (!is(x, "nsparseMatrix")) x@x <- c(x@x, if(isSym) x@x[offD])[sel] if (drop && any(nd == 1)) drop(as(x,"matrix")) else x }) ###========= Sub-Assignment aka *Replace*Methods ========================= ### FIXME: make this `very fast' for the very very common case of ### ----- M[i,j] <- v with i,j = length-1-numeric; v= length-1 number ### *and* M[i,j] == 0 previously ## ## FIXME(2): keep in sync with replCmat() in ./Csparse.R ## FIXME(3): It's terribly slow when used e.g. from diag(M[,-1]) <- value ## ----- which has "workhorse" M[,-1] <- ## ## workhorse for "[<-" : replTmat <- function (x, i, j, ..., value) { ## NOTE: need '...', i.e., exact signature such that setMethod() ## does not use .local() such that nargs() will work correctly: di <- dim(x) dn <- dimnames(x) iMi <- missing(i) jMi <- missing(j) ## "FIXME": could pass this (and much ? more) when this function would not *be* a ## method but be *called* from methods clDv <- getClassDef(clV <- class(value)) spV <- extends(clDv, "sparseVector") ## own version of all0() that works both for sparseVector and atomic vectors: .all0 <- function(v) if(spV) length(v@i) == 0 else all0(v) delayedAssign("value.not.logical", !(if(spV) { extends(clDv, "lsparseVector") || extends(clDv, "nsparseVector") } else { is.logical(value) || is.logical(as.vector(value)) })) na <- nargs() if(na == 3) { ## i = vector (but *not* 2-col) indexing" M[i] <- v Matrix.msg("diagnosing replTmat(x,i,j,v): nargs()= 3; ", if(iMi | jMi) sprintf("missing (i,j) = (%d,%d)", iMi,jMi)) if(iMi) stop("internal bug: missing 'i' in replTmat(): please report") if(is.character(i)) stop("[ ] indexing not allowed: forgot a \",\" ?") if(is.matrix(i)) stop("internal bug: matrix 'i' in replTmat(): please report") ## Now: have M[i] <- v with vector logical or "integer" i : ## Tmatrix maybe non-unique, have an entry split into a sum of several ones: if(!is(x,"generalMatrix")) { cl <- class(x) x <- as(x, paste0(.M.kind(x), "gTMatrix")) Matrix.msg("'sub-optimal sparse 'x[i] <- v' assignment: Coercing class ", cl," to ",class(x)) } nr <- di[1] x.i <- .Call(m_encodeInd2, x@i, x@j, di=di, FALSE) if(anyDuplicated(x.i)) { ## == if(is_duplicatedT(x, di = di)) x <- uniqTsparse(x) x.i <- .Call(m_encodeInd2, x@i, x@j, di=di, FALSE) } n <- prod(di) i <- if(is.logical(i)) { # full-size logical indexing if(n) { if(length(i) < n) i <- rep_len(i, n) (0:(n-1))[i] # -> 0-based index vector as well {maybe LARGE!} } else integer(0) } else { ## also works with *negative* indices etc: int2i(as.integer(i), n) - 1L ## 0-based indices [to match m_encodeInd2()] } clx <- class(x) clDx <- getClassDef(clx) # extends(), is() etc all use the class definition has.x <- "x" %in% slotNames(clDx) # === slotNames(x) if(!has.x && # <==> "n.TMatrix" ((iNA <- any(ina <- is.na(value))) || value.not.logical)) { if(value.not.logical) value <- as.logical(value) if(iNA) { value[ina] <- TRUE warning( gettextf("x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced; NA |--> TRUE.", dQuote(clx)), domain=NA) } else warning( gettextf("x[.] <- val: x is %s, val not in {TRUE, FALSE} is coerced.", dQuote(clx)), domain=NA) } ## now have 0-based indices x.i (entries) and i (new entries) ## the simplest case: if(.all0(value)) { ## just drop the non-zero entries if(!all(sel <- is.na(match(x.i, i)))) { ## non-zero there x@i <- x@i[sel] x@j <- x@j[sel] if(has.x) x@x <- x@x[sel] if(extends(clDx, "compMatrix") && length(x@factors)) # drop cashed ones x@factors <- list() } return(x) } m <- length(i) if(length(value) != m) { ## use recycling rules if(m %% length(value) != 0) warning("number of items to replace is not a multiple of replacement length") value <- rep_len(value, m) } ## With duplicated entries i, only use the last ones! if(id <- anyDuplicated(i, fromLast=TRUE)) { i <- i[-id] value <- value[-id] if(any(id <- duplicated(i, fromLast=TRUE))) { nd <- -which(id) i <- i[nd] value <- value[nd] } } ## matching existing non-zeros and new entries; isE := "is Existing" ## isE <- i %in% x.i; mi <- {matching i's} isE <- !is.na(mi <- match(i, x.i)) ## => mi[isE] entries in (i,j,x) to be set to new value[]s ## 1) Change the matching non-zero entries if(has.x) x@x[mi[isE]] <- value[isE] else if(any0(value[isE])) { ## "n.TMatrix" : remove (i,j) where value is FALSE get0 <- !value[isE] ## x[i,j] is TRUE, should become FALSE i.rm <- - mi[isE][get0] x@i <- x@i[i.rm] x@j <- x@j[i.rm] } ## 2) add the new non-zero entries i <- i[!isE] xv <- value[!isE] if(has.x) { x@x <- c(x@x, xv) } else { # n.TMatrix : assign (i,j) only where value is TRUE: i <- i[xv] } x@i <- c(x@i, i %% nr) x@j <- c(x@j, i %/% nr) if(extends(clDx, "compMatrix") && length(x@factors)) # drop cashed ones x@factors <- list() return(x) } ## {nargs = 3; x[ii] <- value } ## nargs() == 4 : x[i,j] <- value ## -------------------------------------------------------------------------- lenV <- length(value) Matrix.msg(".. replTmat(x,i,j,v): nargs()= 4; cl.(x)=", class(x),"; len.(value)=", lenV,"; ", if(iMi | jMi) sprintf("missing (i,j) = (%d,%d)", iMi,jMi), .M.level = 2)# level 1 gives too many messages ## FIXME: use 'abIndex' or a better algorithm, e.g. if(iMi) i1 <- if(iMi) 0:(di[1] - 1L) else .ind.prep2(i, 1, di, dn) i2 <- if(jMi) 0:(di[2] - 1L) else .ind.prep2(j, 2, di, dn) dind <- c(length(i1), length(i2)) # dimension of replacement region lenRepl <- prod(dind) if(lenV == 0) { if(lenRepl != 0) stop("nothing to replace with") else return(x) } ## else: lenV := length(value) is > 0 if(lenRepl %% lenV != 0) stop("number of items to replace is not a multiple of replacement length") if(!spV && lenRepl > 2^16) { # (somewhat arbitrary cutoff) value <- as(value, "sparseVector")# so that subsequent rep(.) are fast spV <- TRUE } ## Now deal with duplicated / repeated indices: "last one wins" if(!iMi && any(dup <- duplicated(i1, fromLast = TRUE))) { ## duplicated rows keep <- !dup i1 <- i1[keep] ## keep is "internally" recycled below {and that's important: it is dense!} lenV <- length(value <- rep_len(value, lenRepl)[keep]) dind[1] <- length(i1) lenRepl <- prod(dind) } if(!jMi && any(dup <- duplicated(i2, fromLast = TRUE))) { ## duplicated columns iDup <- which(dup) ## The following is correct, but rep(keep,..) can be *HUGE* ## keep <- !dup ## i2 <- i2[keep] ## lenV <- length(value <- rep_len(value, lenRepl)[rep(keep, each=dind[1])]) ## solution: sv[-i] is efficient for sparseVector: i2 <- i2[- iDup] nr <- dind[1] iDup <- rep((iDup - 1)*nr, each=nr) + seq_len(nr) lenV <- length(value <- rep_len(value, lenRepl)[-iDup]) dind[2] <- length(i2) lenRepl <- prod(dind) } clx <- class(x) clDx <- getClassDef(clx) # extends() , is() etc all use the class definition stopifnot(extends(clDx, "TsparseMatrix")) ## Tmatrix maybe non-unique, have an entry split into a sum of several ones: if(is_duplicatedT(x, di = di)) x <- uniqTsparse(x) toGeneral <- r.sym <- FALSE if(extends(clDx, "symmetricMatrix")) { ## using array() for large dind is a disaster... mkArray <- if(spV) # TODO: room for improvement function(v, dim) spV2M(v, dim[1],dim[2]) else array r.sym <- (dind[1] == dind[2] && all(i1 == i2) && (lenRepl == 1 || lenV == 1 || isSymmetric(mkArray(value, dim=dind)))) if(r.sym) { ## result is *still* symmetric --> keep symmetry! xU <- x@uplo == "U" # later, we will consider only those indices above / below diagonal: } else toGeneral <- TRUE } else if(extends(clDx, "triangularMatrix")) { xU <- x@uplo == "U" r.tri <- ((any(dind == 1) || dind[1] == dind[2]) && if(xU) max(i1) <= min(i2) else max(i2) <= min(i1)) if(r.tri) { ## result is *still* triangular if(any(i1 == i2)) # diagonal will be changed x <- diagU2N(x) # keeps class (!) } else toGeneral <- TRUE } if(toGeneral) { # go to "generalMatrix" and continue if((.w <- isTRUE(getOption("Matrix.warn"))) || (!is.null(v <- getOption("Matrix.verbose")) && v >= 1)) (if(.w) warning else message)( "M[i,j] <- v : coercing symmetric M[] into non-symmetric") x <- as(x, paste0(.M.kind(x), "gTMatrix")) clDx <- getClassDef(clx <- class(x)) } ## TODO (efficiency): replace 'sel' by 'which(sel)' get.ind.sel <- function(ii,ij) (match(x@i, ii, nomatch = 0) & match(x@j, ij, nomatch = 0)) ## sel[k] := TRUE iff k-th non-zero entry (typically x@x[k]) is to be replaced sel <- get.ind.sel(i1,i2) has.x <- "x" %in% slotNames(clDx) # === slotNames(x) ## the simplest case: for all Tsparse, even for i or j missing if(.all0(value)) { ## just drop the non-zero entries if(any(sel)) { ## non-zero there x@i <- x@i[!sel] x@j <- x@j[!sel] if(has.x) x@x <- x@x[!sel] if(extends(clDx, "compMatrix") && length(x@factors)) # drop cashed ones x@factors <- list() } return(x) } ## else -- some( value != 0 ) -- if(lenV > lenRepl) stop("too many replacement values") ## now have lenV <= lenRepl if(!has.x && # <==> "n.TMatrix" ((iNA <- any(is.na(value))) || value.not.logical)) warning(if(iNA) gettextf("x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced NA |--> TRUE.", dQuote(clx)) else gettextf("x[.,.] <- val: x is %s, val not in {TRUE, FALSE} is coerced.", dQuote(clx)), domain=NA) ## another simple, typical case: if(lenRepl == 1) { if(spV && has.x) value <- as(value, "vector") if(any(sel)) { ## non-zero there if(has.x) x@x[sel] <- value } else { ## new non-zero x@i <- c(x@i, i1) x@j <- c(x@j, i2) if(has.x) x@x <- c(x@x, value) } if(extends(clDx, "compMatrix") && length(x@factors)) # drop cashed ones x@factors <- list() return(x) } ### Otherwise, for large lenRepl, we get into trouble below if(lenRepl > 2^20) { # (somewhat arbitrary cutoff) ## FIXME: just for testing !! ## if(identical(Sys.getenv("USER"),"maechler") ## if(lenRepl > 2) { # __________ ___ JUST for testing! _______________ if(is.null(v <- getOption("Matrix.quiet")) || !v) message(gettextf("x[.,.] <- val : x being coerced from Tsparse* to CsparseMatrix"), domain = NA) return(replCmat4(as(x,"CsparseMatrix"), i1, i2, iMi=iMi, jMi=jMi, value = if(spV) value else as(value, "sparseVector"), spV = TRUE)) } ## if(r.sym) # value already adjusted, see above ## lenRepl <- length(value) # shorter (since only "triangle") if(!r.sym && lenV < lenRepl) value <- rep_len(value, lenRepl) ## now: length(value) == lenRepl {but value is sparseVector if it's "long" !} ## value[1:lenRepl]: which are structural 0 now, which not? ## v0 <- is0(value) ## - replaced by using isN0(as.vector(.)) on a typical small subset value[.] ## --> more efficient for sparse 'value' & large 'lenRepl' : ## FIXME [= FIXME(3) above]: ## ----- The use of seq_len(lenRepl) below is *still* inefficient ## (or impossible e.g. when lenRepl == 50000^2) ## and the vN0 <- isN0(as.vector(value[iI0])) is even more ... ## One idea: use "abIndex", (a very efficient storage of index vectors which are ## a concatenation of only a few arithmetic seq()ences use.abI <- isTRUE(getOption("Matrix.use.abIndex")) ## This 'use.abI' should later depend on the *dimension* of things ! ##>>> But for that, we need to implement the following abIndex - "methods": ##>>> [-n], [ ] , intersect(, ) ## and for intersect(): typically sort(), unique() & similar iI0 <- if(use.abI) abIseq1(1L, lenRepl) else seq_len(lenRepl) if(any(sel)) { ## the 0-based indices of non-zero entries -- WRT to submatrix non0 <- cbind(match(x@i[sel], i1), match(x@j[sel], i2)) - 1L iN0 <- 1L + .Call(m_encodeInd, non0, di = dind, FALSE) ## 1a) replace those that are already non-zero with non-0 values vN0 <- isN0(value[iN0]) if(any(vN0) && has.x) { vv0 <- which(vN0) x@x[sel][vv0] <- as.vector(value[iN0[vv0]]) } ## 1b) replace non-zeros with 0 --> drop entries if(any(!vN0)) { ii <- which(sel)[!vN0] if(has.x) x@x <- x@x[-ii] x@i <- x@i[-ii] x@j <- x@j[-ii] } iI0 <- if(length(iN0) < lenRepl) iI0[-iN0] ## else NULL # == complementInd(non0, dind) } if(length(iI0)) { if(r.sym) { ## should only set new entries above / below diagonal, i.e., ## subset iI0 such as to contain only above/below .. iSel <- if(use.abI) abIindTri(dind[1], upper=xU, diag=TRUE) else indTri(dind[1], upper=xU, diag=TRUE) ## select also the corresponding triangle of values ### TODO for "abIndex" -- note we KNOW that both iI0 and iSel ### are strictly increasing : iI0 <- intersect(iI0, iSel) } full <- length(iI0) == lenRepl vN0 <- if(spV) ## "sparseVector" (if(full) value else value[iI0])@i else which(isN0(if(full) value else value[iI0])) if(length(vN0)) { ## 2) add those that were structural 0 (where value != 0) iIN0 <- if(full) vN0 else iI0[vN0] ij0 <- decodeInd(iIN0 - 1L, nr = dind[1]) x@i <- c(x@i, i1[ij0[,1] + 1L]) x@j <- c(x@j, i2[ij0[,2] + 1L]) if(has.x) x@x <- c(x@x, as.vector(value[iIN0])) } } if(extends(clDx, "compMatrix") && length(x@factors)) # drop cashed ones x@factors <- list() x } ## end{replTmat} ## A[ ij ] <- value, where ij is a matrix; typically (i,j) 2-column matrix : ## ---------------- ./Matrix.R has a general cheap method ## This one should become as fast as possible -- is also used from Csparse.R -- .TM.repl.i.mat <- function (x, i, j, ..., value) { nA <- nargs() if(nA != 3) stop(gettextf("nargs() = %d should never happen; please report.", nA), domain=NA) ## else: nA == 3 i.e., M [ cbind(ii,jj) ] <- value or M [ Lmat ] <- value if(is.logical(i)) { Matrix.msg(".TM.repl.i.mat(): drop 'matrix' case ...", .M.level=2) ## c(i) : drop "matrix" to logical vector x[as.vector(i)] <- value return(x) } else if(extends(cli <- getClassDef(class(i)),"lMatrix") || extends(cli, "nMatrix")) { Matrix.msg(".TM.repl.i.mat(): \"lMatrix\" case ...", .M.level=2) i <- which(as(i, if(extends(cli, "sparseMatrix")) "sparseVector" else "vector")) ## x[i] <- value ; return(x) return(`[<-`(x,i, value=value)) } else if(extends(cli, "Matrix")) { # "dMatrix" or "iMatrix" if(ncol(i) != 2) stop("such indexing must be by logical or 2-column numeric matrix") i <- as(i, "matrix") } else if(!is.numeric(i) || ncol(i) != 2) stop("such indexing must be by logical or 2-column numeric matrix") if(!is.integer(i)) storage.mode(i) <- "integer" if(any(i < 0)) stop("negative values are not allowed in a matrix subscript") if(any(is.na(i))) stop("NAs are not allowed in subscripted assignments") if(any(i0 <- (i == 0))) # remove them i <- i[ - which(i0, arr.ind = TRUE)[,"row"], ] if(length(attributes(i)) > 1) # more than just 'dim'; simplify: will use identical attributes(i) <- list(dim = dim(i)) ## now have integer i >= 1 m <- nrow(i) if(m == 0) return(x) if(length(value) == 0) stop("nothing to replace with") ## mod.x <- .type.kind[.M.kind(x)] if(length(value) != m) { ## use recycling rules if(m %% length(value) != 0) warning("number of items to replace is not a multiple of replacement length") value <- rep_len(value, m) } clx <- class(x) clDx <- getClassDef(clx) # extends() , is() etc all use the class definition stopifnot(extends(clDx, "TsparseMatrix")) di <- dim(x) nr <- di[1] nc <- di[2] i1 <- i[,1] i2 <- i[,2] if(any(i1 > nr)) stop(gettextf("row indices must be <= nrow(.) which is %d", nr), domain=NA) if(any(i2 > nc)) stop(gettextf("column indices must be <= ncol(.) which is %d", nc), domain=NA) ## Tmatrix maybe non-unique, have an entry split into a sum of several ones: if(is_duplicatedT(x, di = di)) x <- uniqTsparse(x) toGeneral <- FALSE isN <- extends(clDx, "nMatrix") if(r.sym <- extends(clDx, "symmetricMatrix")) { ## Tests to see if the assignments are symmetric as well r.sym <- all(i1 == i2) if(!r.sym) { # do have *some* Lower or Upper entries iL <- i1 > i2 iU <- i1 < i2 r.sym <- sum(iL) == sum(iU) # same number if(r.sym) { iLord <- order(i1[iL], i2[iL]) iUord <- order(i2[iU], i1[iU]) # row <-> col. ! r.sym <- { identical(i[iL, , drop=FALSE][iLord,], i[iU, 2:1, drop=FALSE][iUord,]) && all(value[iL][iLord] == value[iU][iUord]) } } } if(r.sym) { ## result is *still* symmetric --> keep symmetry! ## now consider only those indices above / below diagonal: useI <- if(x@uplo == "U") i1 <= i2 else i2 <= i1 i <- i[useI, , drop=FALSE] value <- value[useI] } else toGeneral <- TRUE } else if(extends(clDx, "triangularMatrix")) { r.tri <- all(if(x@uplo == "U") i1 <= i2 else i2 <= i1) if(r.tri) { ## result is *still* triangular if(any(ieq <- i1 == i2)) { # diagonal will be changed if(x@diag == "U" && all(ieq) && all(value == if(isN) TRUE else as1(x@x))) ## only diagonal values are set to 1 -- i.e. unchanged return(x) x <- diagU2N(x) # keeps class (!) } } else toGeneral <- TRUE } if(toGeneral) { # go to "generalMatrix" and continue if((.w <- isTRUE(getOption("Matrix.warn"))) || isTRUE(getOption("Matrix.verbose"))) (if(.w) warning else message)( "M[ij] <- v : coercing symmetric M[] into non-symmetric") x <- as(x, paste0(.M.kind(x), "gTMatrix")) clDx <- getClassDef(clx <- class(x)) } ii.v <- .Call(m_encodeInd, i - 1L, di, checkBounds = TRUE)# 0-indexing if(id <- anyDuplicated(ii.v, fromLast=TRUE)) { Matrix.msg("duplicate ij-entries in 'Matrix[ ij ] <- value'; using last", .M.level = 1) ii.v <- ii.v [-id] value <- value[-id] if(any(id <- duplicated(ii.v, fromLast=TRUE))) { nd <- -which(id) ii.v <- ii.v [nd] value <- value[nd] } } ii.x <- .Call(m_encodeInd2, x@i, x@j, di, FALSE) m1 <- match(ii.v, ii.x) i.repl <- !is.na(m1) # those that need to be *replaced* if(isN) { ## no 'x' slot isN <- all(value %in% c(FALSE, TRUE)) # will result remain "nMatrix" ? if(!isN) x <- as(x, paste0(if(extends(clDx, "lMatrix")) "l" else "d", .sparse.prefixes[.M.shape(x)], "TMatrix")) } has.x <- !isN ## isN <===> "remains pattern matrix" <===> has no 'x' slot if(any(i.repl)) { ## some to replace at matching (@i, @j) if(has.x) x@x[m1[i.repl]] <- value[i.repl] else { # nMatrix ; eliminate entries that are set to FALSE; keep others if(any(isF <- !value[i.repl])) { ii <- m1[i.repl][isF] x@i <- x@i[ -ii] x@j <- x@j[ -ii] } } } if(any(i.new <- !i.repl & isN0(value))) { ## some new entries i.j <- decodeInd(ii.v[i.new], nr) x@i <- c(x@i, i.j[,1]) x@j <- c(x@j, i.j[,2]) if(has.x) x@x <- c(x@x, value[i.new]) } if(extends(clDx, "compMatrix") && length(x@factors)) # drop cashed ones x@factors <- list() x } ## end{.TM.repl.i.mat} setReplaceMethod("[", signature(x = "TsparseMatrix", i = "index", j = "missing", value = "replValue"), replTmat) setReplaceMethod("[", signature(x = "TsparseMatrix", i = "missing", j = "index", value = "replValue"), replTmat) setReplaceMethod("[", signature(x = "TsparseMatrix", i = "index", j = "index", value = "replValue"), replTmat) setReplaceMethod("[", signature(x = "TsparseMatrix", i = "matrix", j = "missing", value = "replValue"), .TM.repl.i.mat) setReplaceMethod("[", signature(x = "TsparseMatrix", i = "Matrix", j = "missing", value = "replValue"), .TM.repl.i.mat) ### When the RHS 'value' is a sparseVector, now can use replTmat as well setReplaceMethod("[", signature(x = "TsparseMatrix", i = "missing", j = "index", value = "sparseVector"), replTmat) setReplaceMethod("[", signature(x = "TsparseMatrix", i = "index", j = "missing", value = "sparseVector"), replTmat) setReplaceMethod("[", signature(x = "TsparseMatrix", i = "index", j = "index", value = "sparseVector"), replTmat) setMethod("solve", signature(a = "TsparseMatrix", b = "ANY"), function(a, b, ...) solve(as(a, "CsparseMatrix"), b)) setMethod("solve", signature(a = "TsparseMatrix", b = "missing"), function(a, b, ...) solve(as(a, "CsparseMatrix"))) ## Want tril(), triu(), band() --- just as "indexing" --- ## return a "close" class: setMethod("tril", "TsparseMatrix", function(x, k = 0, ...) as(tril(.T.2.C(x), k = k, ...), "TsparseMatrix")) setMethod("triu", "TsparseMatrix", function(x, k = 0, ...) as(triu(.T.2.C(x), k = k, ...), "TsparseMatrix")) setMethod("band", "TsparseMatrix", function(x, k1, k2, ...) as(band(.T.2.C(x), k1 = k1, k2 = k2, ...), "TsparseMatrix")) ## For the "general" T ones (triangular & symmetric have special methods): setMethod("t", signature(x = "TsparseMatrix"), function(x) { cld <- getClassDef(class(x)) r <- new(cld) r@i <- x@j r@j <- x@i if(any("x" == slotNames(cld))) r@x <- x@x r@Dim <- x@Dim[2:1] r@Dimnames <- x@Dimnames[2:1] r }) Matrix/R/nsCMatrix.R0000644000175100001440000000426711500726523014002 0ustar hornikusers#### Logical Symmetric Sparse Matrices in Compressed column-oriented format ### contains = "nsparseMatrix" setAs("nsCMatrix", "matrix", function(from) as(as(from, "ngCMatrix"), "matrix")) setAs("nsCMatrix", "ngCMatrix", function(from) .Call(Csparse_symmetric_to_general, from)) ## Specific conversions, should they be necessary. Better to convert as ## as(x, "TsparseMatrix") or as(x, "denseMatrix") setAs("nsCMatrix", "nsTMatrix", function(from) .Call(Csparse_to_Tsparse, from, FALSE)) ## --- these now happen using "nCsparseMatrix" -- in ./ngCMatrix.R ## ## .nsC2d <- function(from) ## new("dsCMatrix", i = from@i, p = from@p, ## x = rep.int(1, length(from@i)), uplo = from@uplo, ## Dim = from@Dim, Dimnames = from@Dimnames) ## .nsC2l <- function(from) ## new("lsCMatrix", i = from@i, p = from@p, ## x = rep.int(TRUE, length(from@i)), uplo = from@uplo, ## Dim = from@Dim, Dimnames = from@Dimnames) ## Not needed, once we use "nCsparseMatrix" (-> ./ngCMatrix.R ): setAs("nsCMatrix", "dMatrix", nC2d) setAs("nsCMatrix", "dsparseMatrix", nC2d) setAs("nsCMatrix", "dsCMatrix", nC2d) ## setAs("nsCMatrix", "lMatrix", nC2l) setAs("nsCMatrix", "lsparseMatrix", nC2l) setAs("nsCMatrix", "lsCMatrix", nC2l) ## rm(.nsC2d,.nsC2l) # don't even keep "hidden" ## have rather tril() and triu() methods than ## setAs("nsCMatrix", "ntCMatrix", ....) setMethod("tril", "nsCMatrix", function(x, k = 0, ...) { if(x@uplo == "L" && k == 0) ## same internal structure + diag new("ntCMatrix", uplo = x@uplo, i = x@i, p = x@p, Dim = x@Dim, Dimnames = x@Dimnames) else tril(as(x, "ngCMatrix"), k = k, ...) }) setMethod("triu", "nsCMatrix", function(x, k = 0, ...) { if(x@uplo == "U" && k == 0) new("ntCMatrix", uplo = x@uplo, i = x@i, p = x@p, Dim = x@Dim, Dimnames = x@Dimnames) else triu(as(x, "ngCMatrix"), k = k, ...) }) setMethod("chol", signature(x = "nsCMatrix"), function(x, pivot=FALSE, ...) stop("temporarily disabled"))## FIXME ## Use more general method from CsparseMatrix class ## setMethod("t", signature(x = "nsCMatrix"), ## function(x) ## .Call(nsCMatrix_trans, x), ## valueClass = "nsCMatrix") Matrix/R/lsparseMatrix.R0000644000175100001440000000306411270663051014722 0ustar hornikusers#### Superclass Methods for all sparse logical matrices C2l <- function(from) { if(extends(cld <- getClassDef(cl <- class(from)), "lsparseMatrix")) return(from) ## else if(!(is.n <- extends(cld, "nsparseMatrix"))) { ## len.x <- length(from@x) from <- .Call(Csparse_drop, from, 0) ## did.drop <- length(from@x) != len.x } r <- as(.Call(Csparse_to_nz_pattern, from, extends(cld, "triangularMatrix")), "lsparseMatrix") if(!is.n && any(ina <- is.na(from@x))) { ## NAs must remain NA ## since we dropped, we "know" that the 'x' slots match: stopifnot(length(from@x) == length(r@x)) is.na(r@x) <- ina } r } setAs("CsparseMatrix", "lMatrix", C2l) setAs("CsparseMatrix", "lsparseMatrix", C2l) setAs("lsparseMatrix", "matrix", function(from) as(as(from, "ldenseMatrix"), "matrix")) setAs("lsparseMatrix", "dsparseMatrix", function(from) as(from, "dMatrix")) ###------- Work via as(*, lgC) : ------------ setMethod("all", signature(x = "lsparseMatrix"), function(x, ..., na.rm = FALSE) { d <- x@Dim l.x <- length(x@x) if(l.x == prod(d)) ## fully non-zero all(x@x, ..., na.rm = na.rm) else if(is(x, "symmetricMatrix") && l.x == choose(d[1]+1, 2)) { if(.Generic %in% summGener1) all(x@x, ..., na.rm = na.rm) else all(as(x, "generalMatrix")@x, ..., na.rm = na.rm) } else FALSE ## has at least one structural 0 }) ## setMethod("any", ) ---> ./lMatrix.R setMethod("image", "lsparseMatrix", function(x, ...) image(as(x,"dMatrix"))) Matrix/R/Matrix.R0000644000175100001440000007440412271746775013357 0ustar hornikusers#### Toplevel ``virtual'' class "Matrix" ### Virtual coercions -- via smart "helpers" (-> ./Auxiliaries.R) setAs("Matrix", "sparseMatrix", function(from) as(from, "CsparseMatrix")) setAs("Matrix", "CsparseMatrix", function(from) as_Csparse(from)) setAs("Matrix", "denseMatrix", function(from) as_dense(from)) ## Maybe TODO: ## setAs("Matrix", "nMatrix", function(from) ....) ## Most of these work; this is a last resort: setAs(from = "Matrix", to = "matrix", # do *not* call base::as.matrix() here: function(from) .bail.out.2("coerce", class(from), class(to))) setAs(from = "matrix", to = "Matrix", function(from) Matrix(from)) ## ## probably not needed eventually: ## setAs(from = "ddenseMatrix", to = "matrix", ## function(from) { ## if(length(d <- dim(from)) != 2) stop("dim(.) has not length 2") ## array(from@x, dim = d, dimnames = dimnames(from)) ## }) ## should propagate to all subclasses: setMethod("as.matrix", signature(x = "Matrix"), function(x) as(x, "matrix")) ## for 'Matrix' objects, as.array() should be equivalent: setMethod("as.array", signature(x = "Matrix"), function(x) as(x, "matrix")) ## Such that also base functions dispatch properly on our classes: as.array.Matrix <- as.matrix.Matrix <- function(x, ...) as(x, "matrix") ## head and tail apply to all Matrix objects for which subscripting is allowed: setMethod("head", signature(x = "Matrix"), utils::head.matrix) setMethod("tail", signature(x = "Matrix"), utils::tail.matrix) setMethod("drop", signature(x = "Matrix"), function(x) if(all(dim(x) != 1)) x else drop(as(x, "matrix"))) ## slow "fall back" method {subclasses should have faster ones}: setMethod("as.vector", signature(x = "Matrix", mode = "missing"), function(x, mode) as.vector(as(x, "matrix"), mode)) ## so base functions calling as.vector() work too: as.vector.Matrix <- function(x, mode) as.vector(as(x, "matrix"), mode) setAs("Matrix", "vector", function(from) as.vector (as(from, "matrix"))) setAs("Matrix", "numeric", function(from) as.numeric(as(from, "matrix"))) setAs("Matrix", "logical", function(from) as.logical(as(from, "matrix"))) setAs("Matrix", "integer", function(from) as.integer(as(from, "matrix"))) setAs("Matrix", "complex", function(from) as.complex(as(from, "matrix"))) ## mainly need these for "dMatrix" or "lMatrix" respectively, but why not general: setMethod("as.numeric", signature(x = "Matrix"), function(x, ...) as.numeric(as.vector(x))) setMethod("as.logical", signature(x = "Matrix"), function(x, ...) as.logical(as.vector(x))) setMethod("mean", signature(x = "sparseMatrix"), function(x, ...) mean(as(x,"sparseVector"), ...)) setMethod("mean", signature(x = "sparseVector"), function(x, trim = 0, na.rm = FALSE, ...) { if (na.rm) # remove NAs such that new length() is ok x <- x[!is.na(x)] # remains sparse! if(is0(trim)) sum(x) / length(x) else { ## fast trimmed mean for sparseVector: ## ---> we'd need fast & sparse sort(). ## Normally this means to define a xtfrm() method; ## however, that plus x[order(x, ..)] will NOT be sparse ## TODO: sortSparseVector(.) warning("trimmed mean of 'sparseVector' -- suboptimally using as.numeric(.)") mean(as.numeric(x), trim=trim) } }) ## for the non-"sparseMatrix" ones: setMethod("mean", signature(x = "Matrix"), function(x, trim = 0, na.rm = FALSE, ...) { if (na.rm) x <- x[!is.na(x)] if(is0(trim)) sum(x) / length(x) else mean(as.numeric(x), trim=trim) }) ## for non-"sparseMatrix" : setMethod("cov2cor", signature(V = "Matrix"), function(V) { ## was as(cov2cor(as(V, "matrix")), "dpoMatrix")) r <- V p <- (d <- dim(V))[1] if(p != d[2]) stop("'V' is not a square matrix") Is <- sqrt(1/diag(V)) # diag( 1/sigma_i ) if(any(!is.finite(Is))) warning("diag(.) had 0 or NA entries; non-finite result is doubtful") Is <- Diagonal(x = Is) r <- Is %*% V %*% Is r[cbind(1:p,1:p)] <- 1 # exact in diagonal as(forceSymmetric(r), "dpoMatrix") }) ## "base" has an isSymmetric() S3-generic since R 2.3.0 setMethod("isSymmetric", signature(object = "symmetricMatrix"), function(object, ...) TRUE) setMethod("isSymmetric", signature(object = "triangularMatrix"), ## TRUE iff diagonal: function(object, ...) isDiagonal(object)) setMethod("isTriangular", signature(object = "matrix"), isTriMat) setMethod("isDiagonal", signature(object = "matrix"), .is.diagonal) ## The "catch all" methods -- far from optimal: setMethod("symmpart", signature(x = "Matrix"), function(x) as((x + t(x))/2, "symmetricMatrix")) setMethod("skewpart", signature(x = "Matrix"), function(x) (x - t(x))/2) ## FIXME: do this (similarly as for "ddense.." in C setMethod("symmpart", signature(x = "matrix"), function(x) (x + t(x))/2) setMethod("skewpart", signature(x = "matrix"), function(x) (x - t(x))/2) if(getRversion() > "3.1.0") ## NB: "nsparseMatrix" has extra method setMethod("anyNA", signature(x = "xMatrix"), function(x) anyNA(x@x)) setMethod("dim", signature(x = "Matrix"), function(x) x@Dim, valueClass = "integer") setMethod("length", "Matrix", function(x) prod(dim(x))) setMethod("dimnames", signature(x = "Matrix"), function(x) x@Dimnames) ## not exported but used more than once for "dimnames<-" method : ## -- or do only once for all "Matrix" classes ?? dimnamesGets <- function (x, value) { d <- dim(x) if (!is.list(value) || length(value) != 2 || !(is.null(v1 <- value[[1]]) || length(v1) == d[1]) || !(is.null(v2 <- value[[2]]) || length(v2) == d[2])) stop(gettextf("invalid dimnames given for %s object", dQuote(class(x))), domain=NA) x@Dimnames <- list(if(!is.null(v1)) as.character(v1), if(!is.null(v2)) as.character(v2)) x } setMethod("dimnames<-", signature(x = "Matrix", value = "list"), dimnamesGets) setMethod("dimnames<-", signature(x = "Matrix", value = "NULL"), function(x, value) { message("dimnames(.) <- NULL: translated to \ndimnames(.) <- list(NULL,NULL) <==> unname(.)") x@Dimnames <- list(NULL,NULL) x }) setMethod("unname", signature("Matrix", force="missing"), function(obj) { obj@Dimnames <- list(NULL,NULL); obj}) Matrix <- function (data = NA, nrow = 1, ncol = 1, byrow = FALSE, dimnames = NULL, sparse = NULL, doDiag = TRUE, forceCheck = FALSE) { sparseDefault <- function(m) prod(dim(m)) > 2*sum(isN0(as(m, "matrix"))) i.M <- is(data, "Matrix") sM <- FALSE if(i.M) { if(is(data, "diagonalMatrix")) return(data) # in all cases sV <- FALSE } else if(inherits(data, "table")) # special treatment class(data) <- "matrix" # "matrix" first for S4 dispatch else if(is(data, "sparseVector")) { data <- spV2M(data, nrow, ncol, byrow=byrow) i.M <- sparse <- forceCheck <- sM <- sV <- TRUE } if(is.null(sparse1 <- sparse) && (i.M || is(data, "matrix"))) sparse <- sparseDefault(data) doDN <- TRUE if (i.M) { if (!sV) { if(!missing(nrow) || !missing(ncol)|| !missing(byrow)) warning("'nrow', 'ncol', etc, are disregarded when 'data' is \"Matrix\" already") sM <- is(data,"sparseMatrix") if(!forceCheck && ((sparse && sM) || (!sparse && !sM))) return(data) ## else : convert dense <-> sparse -> at end } } else if (!is.matrix(data)) { ## cut & paste from "base::matrix" : ## avoid copying to strip attributes in simple cases if (is.object(data) || !is.atomic(data)) data <- as.vector(data) if(length(data) == 1 && is0(data) && !identical(sparse, FALSE)) { ## Matrix(0, ...) : always sparse unless "sparse = FALSE": if(is.null(sparse)) sparse1 <- sparse <- TRUE i.M <- sM <- TRUE if (missing(nrow)) nrow <- ceiling(1/ncol) else if (missing(ncol)) ncol <- ceiling(1/nrow) isSym <- nrow == ncol ## will be sparse: do NOT construct full matrix! data <- new(paste0(if(is.numeric(data)) "d" else if(is.logical(data)) "l" else stop("invalid 'data'"), if(isSym) "s" else "g", "CMatrix"), p = rep.int(0L, ncol+1L), Dim = as.integer(c(nrow,ncol)), Dimnames = if(is.null.DN(dimnames)) list(NULL,NULL) else dimnames) } else { ## normal case ## Now 'forbidden' : ## data <- .Internal(matrix(data, nrow, ncol, byrow, dimnames, ## missing(nrow), missing(ncol))) data <- .External(Mmatrix, data, nrow, ncol, byrow, dimnames, missing(nrow), missing(ncol)) if(is.null(sparse)) sparse <- sparseDefault(data) } doDN <- FALSE } else if(!missing(nrow) || !missing(ncol)|| !missing(byrow)) warning("'nrow', 'ncol', etc, are disregarded for matrix 'data'") ## 'data' is now a "matrix" or "Matrix" if (doDN && !is.null(dimnames)) dimnames(data) <- dimnames ## check for symmetric / triangular / diagonal : isSym <- isSymmetric(data) if((isTri <- !isSym)) isTri <- isTriangular(data) isDiag <- isSym # cannot be diagonal if it isn't symmetric if(isDiag) # do not *build* 1 x 1 diagonalMatrix isDiag <- doDiag && !isTRUE(sparse1) && nrow(data) > 1 && isDiagonal(data) ## try to coerce ``via'' virtual classes if(isDiag) { ## diagonal is preferred to sparse ! data <- as(data, "diagonalMatrix") isSym <- FALSE } else if(sparse && !sM) data <- as(data, "sparseMatrix") else if(!sparse) { if(i.M) { ## data is 'Matrix' if(!is(data, "denseMatrix")) data <- as(data, "denseMatrix") } else { ## data is "matrix" (and result "dense" -> go via "general" ctype <- typeof(data) if (ctype == "complex") stop("complex matrices not yet implemented in Matrix package") if (ctype == "integer") ## integer Matrices not yet implemented storage.mode(data) <- "double" data <- new(paste0(.M.kind(data), "geMatrix"), Dim = dim(data), Dimnames = .M.DN(data), x = c(data)) } } if(isTri && !is(data, "triangularMatrix")) { data <- if(attr(isTri,"kind") == "L") tril(data) else triu(data) #was as(data, "triangularMatrix") } else if(isSym && !is(data, "symmetricMatrix")) data <- forceSymmetric(data) #was as(data, "symmetricMatrix") data } ## Methods for operations where one argument is numeric ## maybe not 100% optimal, but elegant: setMethod("solve", signature(a = "Matrix", b = "missing"), function(a, b, ...) solve(a, Diagonal(nrow(a)))) setMethod("solve", signature(a = "Matrix", b = "numeric"), function(a, b, ...) callGeneric(a, Matrix(b))) setMethod("solve", signature(a = "Matrix", b = "matrix"), function(a, b, ...) callGeneric(a, Matrix(b))) setMethod("solve", signature(a = "matrix", b = "Matrix"), function(a, b, ...) callGeneric(Matrix(a), b)) setMethod("solve", signature(a = "Matrix", b = "diagonalMatrix"), function(a, b, ...) callGeneric(a, as(b,"CsparseMatrix"))) ## when no sub-class method is found, bail out setMethod("solve", signature(a = "Matrix", b = "ANY"), function(a, b, ...) .bail.out.2("solve", class(a), class(b))) setMethod("solve", signature(a = "ANY", b = "Matrix"), function(a, b, ...) .bail.out.2("solve", class(a), class(b))) setMethod("chol2inv", signature(x = "denseMatrix"), function (x, ...) chol2inv(as(as(x, "dMatrix"), "dtrMatrix"), ...)) setMethod("chol2inv", signature(x = "diagonalMatrix"), function (x, ...) { chk.s(...) tcrossprod(solve(x)) }) setMethod("chol2inv", signature(x = "sparseMatrix"), function (x, ...) { chk.s(...) ## for now: tcrossprod(solve(as(x,"triangularMatrix"))) }) ## There are special sparse methods in ./kronecker.R ; this is a "fall back": setMethod("kronecker", signature(X = "Matrix", Y = "ANY", FUN = "ANY", make.dimnames = "ANY"), function(X, Y, FUN, make.dimnames, ...) { if(is(X, "sparseMatrix")) warning("using slow kronecker() method") X <- as(X, "matrix") ; Matrix(callGeneric()) }) setMethod("kronecker", signature(X = "ANY", Y = "Matrix", FUN = "ANY", make.dimnames = "ANY"), function(X, Y, FUN, make.dimnames, ...) { if(is(Y, "sparseMatrix")) warning("using slow kronecker() method") Y <- as(Y, "matrix") ; Matrix(callGeneric()) }) setMethod("determinant", signature(x = "Matrix", logarithm = "missing"), function(x, logarithm, ...) determinant(x, logarithm = TRUE, ...)) ## The ``Right Thing'' to do : ## base::det() calls [base::]determinant(); ## our det() should call our determinant() : det <- base::det environment(det) <- environment()## == asNamespace("Matrix") setMethod("Cholesky", signature(A = "Matrix"), function(A, perm = TRUE, LDL = !super, super = FALSE, Imult = 0, ...) stop(gettextf("Cholesky(A) called for 'A' of class \"%s\";\n\t it is currently defined for sparseMatrix only; consider using chol() instead", class(A)), call. = FALSE, domain=NA)) ## FIXME: All of these should never be called setMethod("chol", signature(x = "Matrix"), function(x, pivot, ...) .bail.out.1("chol", class(x))) setMethod("determinant", signature(x = "Matrix", logarithm = "logical"), function(x, logarithm, ...) determinant(as(x,"dMatrix"), logarithm=logarithm, ...)) setMethod("diag", signature(x = "Matrix"), function(x, nrow, ncol) .bail.out.1("diag", class(x))) if(FALSE)## TODO: activate later setMethod("diag<-", signature(x = "Matrix"), function(x, value) .bail.out.1("diag", class(x))) setMethod("t", signature(x = "Matrix"), function(x) .bail.out.1(.Generic, class(x))) setMethod("norm", signature(x = "Matrix", type = "character"), function(x, type, ...) .bail.out.1("norm", class(x))) setMethod("rcond", signature(x = "Matrix", norm = "character"), function(x, norm, ...) .bail.out.1("rcond", class(x))) ## for all : setMethod("norm", signature(x = "ANY", type = "missing"), function(x, type, ...) norm(x, type = "O", ...)) setMethod("rcond", signature(x = "ANY", norm = "missing"), function(x, norm, ...) rcond(x, norm = "O", ...)) setMethod("lu", "matrix", function(x, warnSing = TRUE, ...) lu(..2dge(x), warnSing=warnSing, ...)) ## We want to use all.equal.numeric() *and* make sure that uses ## not just base::as.vector but the generic with our methods: all.equal_num <- base::all.equal.numeric ## from /src/library/base/R/all.equal.R environment(all.equal_num) <- environment()## == as.environment("Matrix") all.equal_Mat <- function(target, current, check.attributes = TRUE, factorsCheck = FALSE, ...) { msg <- attr.all_Mat(target, current, check.attributes=check.attributes, factorsCheck=factorsCheck, ...) if(is.list(msg)) msg[[1]] else .a.e.comb(msg, all.equal_num(as.vector(target), as.vector(current), check.attributes=check.attributes, ...)) } ## The all.equal() methods for dense matrices (and fallback): setMethod("all.equal", c(target = "Matrix", current = "Matrix"), all.equal_Mat) setMethod("all.equal", c(target = "Matrix", current = "ANY"), all.equal_Mat) setMethod("all.equal", c(target = "ANY", current = "Matrix"), all.equal_Mat) ## -> ./sparseMatrix.R, ./sparseVector.R have specific methods ## MM: More or less "Cut & paste" from ## --- diff.default() from R/src/library/base/R/diff.R : setMethod("diff", signature(x = "Matrix"), function(x, lag = 1, differences = 1, ...) { if (length(lag) > 1 || length(differences) > 1 || lag < 1 || differences < 1) stop("'lag' and 'differences' must be integers >= 1") xlen <- nrow(x) if (lag * differences >= xlen) return(x[,FALSE][0]) # empty of proper mode i1 <- -1:-lag for (i in 1:differences) x <- x[i1, , drop = FALSE] - x[-nrow(x):-(nrow(x)-lag+1), , drop = FALSE] x }) setMethod("image", "Matrix", function(x, ...) { # coercing to sparse is not inefficient, ## since we need 'i' and 'j' for levelplot() x <- as(as(x, "sparseMatrix"), "dsparseMatrix") ## note that "ddiMatrix" is "sparse*" and "d*", but *not* dsparse callGeneric() }) ## Group Methods ## --- "Summary" ------- have "ddense*" and "dsparse*" ones in ---> ./dMatrix.R <--- ## ------- "diagMatrix" --> ./diagMatrix.R ~~~~~~~~~~~ ## For all other Matrix objects {and note that "all" and "any" have their own}: setMethod("all", signature(x = "Matrix"), function(x, ..., na.rm) callGeneric(as(x, "lMatrix"), ..., na.rm=na.rm)) setMethod("any", signature(x = "Matrix"), function(x, ..., na.rm) callGeneric(as(x, "lMatrix"), ..., na.rm=na.rm)) setMethod("Summary", signature(x = "Matrix", na.rm = "ANY"), function(x, ..., na.rm) callGeneric(as(x,"dMatrix"), ..., na.rm = na.rm)) ## Try to make min(1, ) work, i.e., not dispatch on first arg to .Primitive ## This for(..) gives {during installation} ## Error in setGeneric(F, signature = "...") : ## ‘max’ is a primitive function; methods can be defined, but the generic function is implicit, and cannot be changed. if(FALSE) for(F in c("max", "min", "range", "prod", "sum", "any", "all")) { setGeneric(F, signature = "...") } ### try on "min" for now --- ~/R/Pkgs/Rmpfr/R/mpfr.R is the example (for "pmin") if(FALSE)### This gives error message that the "ANY" is method is sealed ... setMethod("min", "ANY", function(..., na.rm = FALSE) { args <- list(...) if(all(isAtm <- vapply(args, is.atomic, NA))) return( base::min(..., na.rm = na.rm) ) ## else try to dispatch on an argument which is a Matrix.. or in a if(any(isM <- vapply(args, is, NA, class2="Matrix"))) { ## swap the Matrix with the first argument i <- which.max(isM)# the first "Matrix" if(i == 1) stop("programming error: min() should have dispatched w/ 1st arg much earlier") } else { ## if no "Matrix", take the first non-atomic argument ## (FIXME: should take the first for which there is a method !) i <- which.max(!isAtm) } ii <- seq_along(args) ii[c(1,i)] <- c(i,1) do.call(min, c(args[ii], list(na.rm=na.rm))) }) if(FALSE) { ## FIXME: it does *not* solve the problem anyway .. ## ## (m <- Matrix(c(0,0,2:0), 3,5)) ## min(1,m) ##-> error, as it calls the .Primitive min() and that does *not* dispatch on 2nd arg ## setMethod("Summary", signature(x = "ANY", na.rm = "ANY"), function(x, ..., na.rm) { if(!length(a <- list(...))) (get(.Generic, envir=baseenv()))(x, na.rm=na.rm) else { if(!is.null(v <- getOption("Matrix.verbose")) && v >= 1) message(sprintf("in Summary(, .): %s(<%s>, <%s>%s)\n", .Generic, class(x), class(a[[1]]), if(length(a) > 1)", ..." else ""), domain = NA) do.call(.Generic, c(x, a, list(na.rm=na.rm))) }}) } Summary.l <- function(x, ..., na.rm) { ## must be method directly if(.Generic %in% c("all", "any")) callGeneric(x@x, ..., na.rm = na.rm) else { r <- callGeneric(as(x,"dMatrix"), ..., na.rm = na.rm) if(!is.infinite(r) && .Generic != "prod") as.integer(r) else r } } ## almost identical: Summary.np <- function(x, ..., na.rm) { if(.Generic %in% c("all", "any")) callGeneric(as(x, "lMatrix"), ..., na.rm = na.rm) else { r <- callGeneric(as(x,"dMatrix"), ..., na.rm = na.rm) if(!is.infinite(r) && .Generic != "prod") as.integer(r) else r } } ## setMethod("Summary", signature(x = "lMatrix", na.rm = "ANY"), Summary.l) setMethod("Summary", signature(x = "nMatrix", na.rm = "ANY"), Summary.np) setMethod("Summary", signature(x = "indMatrix", na.rm = "ANY"), Summary.np) ## NOTE: "&" and "|" are now in group "Logic" c "Ops" --> ./Ops.R ## "!" is in ./not.R ## Further, see ./Ops.R ## ~~~~~ ### -------------------------------------------------------------------------- ### ### Subsetting "[" and ### SubAssign "[<-" : The "missing" cases can be dealt with here, "at the top": ## Using "index" for indices should allow ## integer (numeric), logical, or character (names!) indices : ## "x[]": setMethod("[", signature(x = "Matrix", i = "missing", j = "missing", drop = "ANY"), function (x, i, j, ..., drop) x) ## missing 'drop' --> 'drop = TRUE' ## ----------- ## select rows __ or __ vector indexing: setMethod("[", signature(x = "Matrix", i = "index", j = "missing", drop = "missing"), function(x,i,j, ..., drop) { Matrix.msg("M[i,m,m] : nargs()=",nargs(), .M.level = 2) if(nargs() == 2) { ## e.g. M[0] , M[TRUE], M[1:2] .M.vectorSub(x,i) } else { callGeneric(x, i=i, , drop=TRUE) ## ^^ } }) ## select columns setMethod("[", signature(x = "Matrix", i = "missing", j = "index", drop = "missing"), function(x,i,j, ..., drop) { Matrix.msg("M[m,i,m] : nargs()=",nargs(), .M.level = 2) callGeneric(x, j=j, drop= TRUE) }) setMethod("[", signature(x = "Matrix", i = "index", j = "index", drop = "missing"), function(x,i,j, ..., drop) { Matrix.msg("M[i,i,m] : nargs()=",nargs(), .M.level = 2) callGeneric(x, i=i, j=j, drop= TRUE) }) ## bail out if any of (i,j,drop) is "non-sense" setMethod("[", signature(x = "Matrix", i = "ANY", j = "ANY", drop = "ANY"), function(x,i,j, ..., drop) stop("invalid or not-yet-implemented 'Matrix' subsetting")) ## logical indexing, such as M[ M >= 7 ] *BUT* also M[ M[,1] >= 3,], ## The following is *both* for M [ ] ## and also for M [ , ] .M.sub.i.logical <- function (x, i, j, ..., drop) { nA <- nargs() # counts 'M[i]' as 2 arguments, 'M[i,]' as 3 if(nA == 2) { ## M [ M >= 7 ] ## FIXME: when both 'x' and 'i' are sparse, this can be very inefficient if(is(x, "sparseMatrix")) message("[ ] : .M.sub.i.logical() maybe inefficient") toC <- geClass(x) if(canCoerce(x, toC)) as(x, toC)@x[as.vector(i)] else as(as(as(x, "generalMatrix"), "denseMatrix"), toC)@x[as.vector(i)] ## -> error when lengths don't match } else if(nA == 3) { ## M[i, ] e.g., M [ M[,1, drop=FALSE] >= 7, ] ## Note: current method dispatch seems not to call this ever if(!any(is.na(i)) && all(i)) ## select everything x else ## not selecting all -> result is *NOT* diagonal/triangular/symmetric/.. ## keep j missing, but drop = "logical" callGeneric(as(x,"generalMatrix"), i = i, , drop = TRUE) } else stop(gettextf( "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.logical)?", nA), domain=NA) } ## instead of using 'drop = "ANY"' {against ambiguity notices}: for(ii in c("lMatrix", "logical")) setMethod("[", signature(x = "Matrix", i = ii, j = "missing", drop = "missing"), .M.sub.i.logical) rm(ii) ##' x[ ij ] where ij is (i,j) 2-column matrix ##' @note only called from .M.sub.i.2col(x, i) below subset.ij <- function(x, ij) { m <- nrow(ij) if(m > 3) { cld <- getClassDef(class(x)) sym.x <- extends(cld, "symmetricMatrix") if(sym.x) { W <- if(x@uplo == "U") # stored only [i,j] with i <= j ij[,1] > ij[,2] else ij[,1] < ij[,2] if(any(W)) ij[W,] <- ij[W, 2:1] } if(extends(cld, "sparseMatrix")) { ## do something smarter: di <- dim(x) if(!extends(cld, "CsparseMatrix")) { x <- as(x, "CsparseMatrix") # simpler; our standard cld <- getClassDef(class(x)) } tri.x <- extends(cld, "triangularMatrix") if(tri.x) { ## need these for the 'x' slot in any case if (x@diag == "U") x <- .Call(Csparse_diagU2N, x) ## slightly more efficient than non0.i() or non0ind(): ij.x <- .Call(compressed_non_0_ij, x, isC=TRUE) } else { ## symmetric / general : for symmetric, only "existing" part ij.x <- non0.i(x, cld) } m1 <- .Call(m_encodeInd, ij.x, di, checkBounds = FALSE) m2 <- .Call(m_encodeInd, ij -1L, di, checkBounds = TRUE) mi <- match(m2, m1, nomatch=0) mmi <- mi != 0L ## == (m2 %in% m1) ## Result: all FALSE or 0 apart from where we match non-zero entries ans <- vector(mode = .type.kind[.M.kindC(cld)], length = m) ## those that are *not* zero: ans[mmi] <- if(extends(cld, "nsparseMatrix")) TRUE else x@x[mi[mmi]] if(any(ina <- is.na(m2))) # has one or two NA in that (i,j) row is.na(ans) <- ina ans } else { ## non-sparse : dense ##---- NEVER happens: 'denseMatrix' has its own setMethod(.) ! message("m[ ]: inefficiently indexing single elements") i1 <- ij[,1] i2 <- ij[,2] ## very inefficient for large m unlist(lapply(seq_len(m), function(j) x[i1[j], i2[j]])) } } else { # 1 <= m <= 3 i1 <- ij[,1] i2 <- ij[,2] unlist(lapply(seq_len(m), function(j) x[i1[j], i2[j]])) } } ## A[ ij ] where ij is (i,j) 2-column matrix -- but also when that is logical mat! .M.sub.i.2col <- function (x, i, j, ..., drop) { nA <- nargs() if(nA != 2) stop(domain=NA, gettextf( "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' (i.2col)?", nA)) ## else: (nA == 2): M [ cbind(ii,jj) ] or M [ ] if(!is.integer(nc <- ncol(i))) stop(".M.sub.i.2col(): 'i' has no integer column number;\n should never happen; please report") if(is.logical(i)) return(.M.sub.i.logical(x, i=i)) # call with 2 args! else if(!is.numeric(i) || nc != 2) stop("such indexing must be by logical or 2-column numeric matrix") if(!nrow(i)) return(vector(mode = .type.kind[.M.kind(x)])) ## else subset.ij(x, i) } setMethod("[", signature(x = "Matrix", i = "matrix", j = "missing"),# drop="ANY" .M.sub.i.2col) ## just against ambiguity notices : setMethod("[", signature(x = "Matrix", i = "matrix", j = "missing", drop="missing"), .M.sub.i.2col) ### "[<-" : ----------------- ## A[ ij ] <- value, where ij is (i,j) 2-column matrix : ## ---------------- ## The cheap general method, now only used for "pMatrix","indMatrix" ## sparse all use .TM.repl.i.mat() ## NOTE: need '...' below such that setMethod() does ## not use .local() such that nargs() will work correctly: .M.repl.i.2col <- function (x, i, j, ..., value) { nA <- nargs() if(nA == 3) { ## M [ cbind(ii,jj) ] <- value or M [ Lmat ] <- value if(!is.integer(nc <- ncol(i))) stop(".M.repl.i.2col(): 'i' has no integer column number;\n should never happen; please report") else if(!is.numeric(i) || nc != 2) stop("such indexing must be by logical or 2-column numeric matrix") if(is.logical(i)) { message(".M.repl.i.2col(): drop 'matrix' case ...") ## c(i) : drop "matrix" to logical vector return( callGeneric(x, i=c(i), value=value) ) } if(!is.integer(i)) storage.mode(i) <- "integer" if(any(i < 0)) stop("negative values are not allowed in a matrix subscript") if(any(is.na(i))) stop("NAs are not allowed in subscripted assignments") if(any(i0 <- (i == 0))) # remove them i <- i[ - which(i0, arr.ind = TRUE)[,"row"], ] ## now have integer i >= 1 m <- nrow(i) ## mod.x <- .type.kind[.M.kind(x)] if(length(value) > 0 && m %% length(value) != 0) warning("number of items to replace is not a multiple of replacement length") ## recycle: value <- rep_len(value, m) i1 <- i[,1] i2 <- i[,2] if(m > 2) message("m[ ] <- v: inefficiently treating single elements") ## inefficient -- FIXME -- (also loses "symmetry" unnecessarily) for(k in seq_len(m)) x[i1[k], i2[k]] <- value[k] x } else stop(gettextf( "nargs() = %d. Extraneous illegal arguments inside '[ .. ]' ?", nA), domain=NA) } setReplaceMethod("[", signature(x = "Matrix", i = "matrix", j = "missing", value = "replValue"), .M.repl.i.2col) ## Three catch-all methods ... would be very inefficient for sparse* ## --> extra methods in ./sparseMatrix.R setReplaceMethod("[", signature(x = "Matrix", i = "missing", j = "ANY", value = "Matrix"), function (x, i, j, ..., value) callGeneric(x=x, , j=j, value = as.vector(value))) setReplaceMethod("[", signature(x = "Matrix", i = "ANY", j = "missing", value = "Matrix"), function (x, i, j, ..., value) callGeneric(x=x, i=i, , value = as.vector(value))) setReplaceMethod("[", signature(x = "Matrix", i = "ANY", j = "ANY", value = "Matrix"), function (x, i, j, ..., value) callGeneric(x=x, i=i, j=j, value = as.vector(value))) setReplaceMethod("[", signature(x = "Matrix", i = "missing", j = "ANY", value = "matrix"), function (x, i, j, ..., value) callGeneric(x=x, , j=j, value = c(value))) setReplaceMethod("[", signature(x = "Matrix", i = "ANY", j = "missing", value = "matrix"), function (x, i, j, ..., value) callGeneric(x=x, i=i, , value = c(value))) setReplaceMethod("[", signature(x = "Matrix", i = "ANY", j = "ANY", value = "matrix"), function (x, i, j, value) callGeneric(x=x, i=i, j=j, value = c(value))) ## M [ ] <- value; used notably for x = "CsparseMatrix" ------------------- .repl.i.lDMat <- function (x, i, j, ..., value) { ## nA <- nargs() ## if(nA != 3) stop(gettextf("nargs() = %d should never happen; please report.", nA), domain=NA) ## else: nA == 3 i.e., M [ Lmat ] <- value ## x[i] <- value ; return(x) `[<-`(x, i=which(as.vector(i)), value=value) } setReplaceMethod("[", signature(x = "Matrix", i = "ldenseMatrix", j = "missing", value = "replValue"), .repl.i.lDMat) setReplaceMethod("[", signature(x = "Matrix", i = "ndenseMatrix", j = "missing", value = "replValue"), .repl.i.lDMat) .repl.i.lSMat <- function (x, i, j, ..., value) { ## nA <- nargs() ## if(nA != 3) stop(gettextf("nargs() = %d should never happen; please report.", nA), domain=NA) ## else: nA == 3 i.e., M [ Lmat ] <- value ## x[i] <- value ; return(x) `[<-`(x, i=which(as(i, "sparseVector")), value=value) } setReplaceMethod("[", signature(x = "Matrix", i = "lsparseMatrix", j = "missing", value = "replValue"), .repl.i.lSMat) setReplaceMethod("[", signature(x = "Matrix", i = "nsparseMatrix", j = "missing", value = "replValue"), .repl.i.lSMat) ## (ANY,ANY,ANY) is used when no `real method' is implemented : setReplaceMethod("[", signature(x = "Matrix", i = "ANY", j = "ANY", value = "ANY"), function (x, i, j, value) { if(!is.atomic(value)) stop(gettextf( "RHS 'value' (class %s) matches 'ANY', but must match matrix class %s", class(value), class(x)), domain=NA) else stop("not-yet-implemented 'Matrix[<-' method") }) Matrix/R/ltCMatrix.R0000644000175100001440000000216711004710547013774 0ustar hornikusers#### Logical Sparse Triangular Matrices in Compressed column-oriented format setAs("ltCMatrix", "matrix", function(from) as(as(from, "lgCMatrix"), "matrix")) setAs("matrix", "ltCMatrix", function(from) as(as(from, "dtCMatrix"), "ltCMatrix")) setAs("ltCMatrix", "lgCMatrix", function(from) copyClass(diagU2N(from), "lgCMatrix", c("i", "p", "x", "Dim", "Dimnames"))) setAs("ltCMatrix", "ltTMatrix", function(from) .Call(Csparse_to_Tsparse, from, TRUE)) setAs("ltCMatrix", "dMatrix", # < instead of "dtCMatrix" function(from) new("dtCMatrix", i = from@i, p = from@p, x = as.double(from@x), uplo = from@uplo, diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames)) setAs("lgCMatrix", "ltCMatrix", # to triangular {needed in triu() } function(from) as(as(as(from, "lgTMatrix"), "ltTMatrix"), "ltCMatrix")) ## setAs("ltCMatrix", "generalMatrix", ## function(from) ......) ## setMethod("t", signature(x = "ltCMatrix"), ## function(x) .Call(ltCMatrix_trans, x), ## valueClass = "ltCMatrix") Matrix/R/rankMatrix.R0000644000175100001440000001112612257570015014205 0ustar hornikusers#### Determine *the* rank of a matrix #### -------------------------------- ## ## As this is not such a well-defined problem as people think, ## we provide *some* possibilities here, including the Matlab one. ## ## Ideas by Martin Maechler (April 2007) and Ravi Varadhan (October 2007) rankMatrix <- function(x, tol = NULL, method = c("tolNorm2", "qr.R", "qrLINPACK", "qr", "useGrad", "maybeGrad"), sval = svd(x, 0,0)$d, warn.t = TRUE) { ## Purpose: rank of a matrix ``as Matlab'' or "according to Ravi V" ## ---------------------------------------------------------------------- ## Arguments: x: a numerical matrix, maybe non-square ## tol: numerical tolerance (compared to singular values) ## sval: vector of non-increasing singular values of x ## (pass as argument if already known) ## ---------------------------------------------------------------------- ## Author: Martin Maechler, Date: 7 Apr 2007, 16:16 ## ---------------------------------------------------------------------- ## ## maybeGrad (Ravi V.): This algorithm determines the rank based on the ## "gradient" of the ## absolute, singular values, rather than enforcing a rigid ## tolerance criterion, ## ## Author: Ravi Varadhan, Date: 22 October 2007 // Tweaks: MM, Oct.23 ## ---------------------------------------------------------------------- stopifnot(length(d <- dim(x)) == 2) p <- min(d) miss.meth <- missing(method) method <- match.arg(method) if(useGrad <- (method %in% c("useGrad", "maybeGrad"))) { stopifnot(length(sval) == p, diff(sval) <= 0) # must be sorted non-increasingly: max = s..[1] ln.av <- log(abs(sval)) diff1 <- diff(ln.av) if(method == "maybeGrad") { grad <- (min(ln.av) - max(ln.av)) / p useGrad <- (min(diff1) <= min(-3, 10 * grad)) }# ------- } if(!useGrad) { x.dense <- is.numeric(x) || is(x,"denseMatrix") ## "qr" is allowed for backcompatibility [change @ 2013-11-24] if((Meth <- method) == "qr") method <- if(x.dense) "qrLINPACK" else "qr.R" else Meth <- substr(method, 1,2) if(Meth == "qr") { if(is.null(tol)) tol <- max(d) * .Machine$double.eps } else { ## (Meth != "qr"), i.e. "tolNorm2" if(is.null(tol)) { if(!x.dense && missing(sval) && prod(d) >= 100000L) warning(gettextf( "rankMatrix(, method = '%s') coerces to dense matrix. Probably should rather use method = 'qr' !?", method), immediate.=TRUE, domain=NA) ## the "Matlab" default: stopifnot(diff(sval) <= 0) #=> sval[1]= max(sval) tol <- max(d) * .Machine$double.eps } else stopifnot((tol <- as.numeric(tol)[[1]]) >= 0) } } structure(## rank : if(useGrad) which.min(diff1) else if(Meth == "qr") { if((do.t <- (d[1L] < d[2L])) && warn.t) warning(gettextf( "rankMatrix(x, method='qr'): computing t(x) as nrow(x) < ncol(x)")) q.r <- qr(if(do.t) t(x) else x, tol=tol, LAPACK = method != "qrLINPACK") if(x.dense && (method == "qrLINPACK")) q.r$rank else { ## else "qr.R" or sparse {or a problem) diagR <- if(x.dense) # faster than, but equivalent to diag(qr.R(q.r)) diag(q.r$qr) else ## FIXME: Here, we could be quite a bit faster, ## by not returning the full sparseQR, but just ## doing the following in C, and return the rank. diag(q.r@R) d.i <- abs(diagR) ## is abs(.) unneeded? [FIXME] ## declare those entries to be zero that are < tol*max(.) sum(d.i >= tol * max(d.i)) ## was sum(diag(q.r@R) != 0) } ## else stop(gettextf( ## "method %s not applicable for qr() result class %s", ## sQuote(method), dQuote(class(q.r)[1])), ## domain=NA) } else sum(sval >= tol * sval[1]), ## "tolNorm2" "method" = method, "useGrad" = useGrad, "tol" = if(useGrad) NA else tol) } ## Ravi's plot of the absolute singular values: if(FALSE) { ## if (plot.eigen) { plot(abs(sval), type = "b", xlab = "Index", xaxt = "n", log = "y", ylab = "|singular value| [log scaled]") axis(1, at = unique(c(axTicks(1), rank, p))) abline(v = rank, lty = 3) mtext(sprintf("rank = %d (used %s (%g))", rank, if(use.grad)"'gradient'" else "fixed tol.", if(use.grad) min(diff1) else tol)) } Matrix/R/dpoMatrix.R0000644000175100001440000000544312220123153014024 0ustar hornikusers#### Positive-definite Symmetric Matrices -- Coercion and Methods setAs("dpoMatrix", "dppMatrix", function(from) copyClass(.Call(dsyMatrix_as_dspMatrix, from), "dppMatrix", sNames = c("x", "Dim", "Dimnames", "uplo", "factors"))) setAs("dpoMatrix", "corMatrix", function(from) { if(!is.null(cm <- from@factors$correlation)) return(cm) ## else sd <- sqrt(diag(from)) if(is.null(names(sd)) && !is.null(nms <- from@Dimnames[[1]])) names(sd) <- nms Is <- Diagonal(x = 1/sd) .set.factors(from, "correlation", new("corMatrix", as(forceSymmetric(Is %*% from %*% Is), "dpoMatrix"), sd = unname(sd))) }) setAs("dpoMatrix", "lMatrix", function(from) as(as(from, "dsyMatrix"), "lMatrix")) setAs("dpoMatrix", "nMatrix", function(from) as(as(from, "dsyMatrix"), "nMatrix")) if(FALSE) # should no longer be needed setAs("corMatrix", "lMatrix", function(from) as(as(from, "dpoMatrix"), "lMatrix")) ## Needed *in addition* to the general to_dpo() method below: setAs("dspMatrix", "dpoMatrix", function(from) as(as(from,"dsyMatrix"), "dpoMatrix")) to_dpo <- function(from) # not coercing to "dsy*" explicitly: as(as(as(as(from, "symmetricMatrix"), "dMatrix"), "denseMatrix"), "dpoMatrix") setAs("Matrix", "dpoMatrix", to_dpo) setAs("matrix", "dpoMatrix", to_dpo) setMethod("chol", signature(x = "dpoMatrix"), function(x, pivot, ...) .Call(dpoMatrix_chol, x)) setMethod("rcond", signature(x = "dpoMatrix", norm = "character"), function(x, norm, ...) .Call(dpoMatrix_rcond, x, norm)) setMethod("rcond", signature(x = "dpoMatrix", norm = "missing"), function(x, norm, ...) .Call(dpoMatrix_rcond, x, "O")) setMethod("solve", signature(a = "dpoMatrix", b = "missing"), function(a, b, ...) .Call(dpoMatrix_solve, a), valueClass = "dpoMatrix") setMethod("solve", signature(a = "dpoMatrix", b = "dgeMatrix"), function(a, b, ...) .Call(dpoMatrix_dgeMatrix_solve, a, b), valueClass = "dgeMatrix") setMethod("solve", signature(a = "dpoMatrix", b = "matrix"), function(a, b, ...) .Call(dpoMatrix_matrix_solve, a, b), valueClass = "matrix") mkDet.via.chol <- function(x, logarithm, ...) mkDet(logarithm, ldet = 2*sum(log(abs(diag(chol(x))))), sig = 1L) setMethod("determinant", signature(x = "dpoMatrix", logarithm = "logical"), mkDet.via.chol) setMethod("determinant", signature(x = "dpoMatrix", logarithm = "missing"), function(x, logarithm, ...) mkDet.via.chol(x, logarithm=TRUE)) ## Is this usable / necessary? -- FIXME! ## setMethod("solve", signature(a = "dpoMatrix", b = "numeric"), ## function(a, b, ...) ## as.numeric(.Call(dpoMatrix_matrix_solve, ## a, as.matrix(b))), ## valueClass = "numeric") Matrix/R/dspMatrix.R0000644000175100001440000000634412001034107014026 0ustar hornikusers### Coercion and Methods for Symmetric Packed Matrices setAs("dspMatrix", "dsyMatrix", function(from) .Call(dspMatrix_as_dsyMatrix, from)) dsp2sC <- function(from) as(.Call(dspMatrix_as_dsyMatrix, from), "dsCMatrix") ## setAs("dspMatrix", "dsCMatrix", dsp2sC) setAs("dspMatrix", "CsparseMatrix", dsp2sC) setAs("dspMatrix", "sparseMatrix", dsp2sC) ## dge <--> dsp via dsy setAs("dgeMatrix", "dspMatrix", function(from) as(as(from, "dsyMatrix"), "dspMatrix")) ## S3-matrix <--> dsp via dsy setAs("dspMatrix", "matrix", function(from) as(as(from, "dsyMatrix"), "matrix")) setAs("matrix", "dspMatrix", function(from) as(as(from, "dsyMatrix"), "dspMatrix")) setMethod("rcond", signature(x = "dspMatrix", norm = "character"), function(x, norm, ...) .Call(dspMatrix_rcond, x, norm), valueClass = "numeric") setMethod("rcond", signature(x = "dspMatrix", norm = "missing"), function(x, norm, ...) .Call(dspMatrix_rcond, x, "O"), valueClass = "numeric") setMethod("BunchKaufman", signature(x = "dspMatrix"), function(x) .Call(dspMatrix_trf, x)) ## Should define multiplication from the right setMethod("solve", signature(a = "dspMatrix", b = "missing"), function(a, b, ...) .Call(dspMatrix_solve, a), valueClass = "dspMatrix") setMethod("solve", signature(a = "dspMatrix", b = "matrix"), function(a, b, ...) .Call(dspMatrix_matrix_solve, a, b), valueClass = "dgeMatrix") setMethod("solve", signature(a = "dspMatrix", b = "ddenseMatrix"), function(a, b, ...) .Call(dspMatrix_matrix_solve, a, b), valueClass = "dgeMatrix") ##setMethod("solve", signature(a = "dspMatrix", b = "numeric"), ## function(a, b, ...) ## .Call(dspMatrix_matrix_solve, a, as.matrix(b)), ## valueClass = "dgeMatrix") ## No longer needed ## setMethod("solve", signature(a = "dspMatrix", b = "integer"), ## function(a, b, ...) { ## storage.mode(b) <- "double" ## .Call(dspMatrix_matrix_solve, a, as.matrix(b)) ## }, valueClass = "dgeMatrix") setMethod("norm", signature(x = "dspMatrix", type = "character"), function(x, type, ...) .Call(dspMatrix_norm, x, type), valueClass = "numeric") setMethod("norm", signature(x = "dspMatrix", type = "missing"), function(x, type, ...) .Call(dspMatrix_norm, x, "O"), valueClass = "numeric") ## FIXME: speed up! setMethod("t", signature(x = "dspMatrix"), function(x) as(t(as(x, "dsyMatrix")), "dspMatrix"), valueClass = "dspMatrix") setMethod("diag", signature(x = "dspMatrix"), function(x, nrow, ncol) .Call(dspMatrix_getDiag, x)) setMethod("diag<-", signature(x = "dspMatrix"), function(x, value) .Call(dspMatrix_setDiag, x, value)) ## The following allows as(*, "dppMatrix"). ## However it *requires* that dppMatrix_chol() gives an error ## for non-positive-semi-definite matrices -- which it does since 2005-10-03 if(FALSE)## FIXME: This gives an error for singular pos.SEMI-def. matrices: setIs("dspMatrix", "dppMatrix", test = function(obj) "try-error" != class(try(.Call(dppMatrix_chol, obj), TRUE)), replace = function(obj, value) { ## copy all slots for(n in slotNames(obj)) slot(obj, n) <- slot(value, n) obj }) Matrix/R/nearPD.R0000644000175100001440000000752712176145760013255 0ustar hornikusers ## nearcor.R : ## Copyright (2007) Jens Oehlschlägel ## GPL licence, no warranty, use at your own risk nearPD <- ## Computes the nearest correlation matrix to an approximate ## correlation matrix, i.e. not positive semidefinite. function(x # n-by-n approx covariance/correlation matrix , corr = FALSE, keepDiag = FALSE , do2eigen = TRUE # if TRUE do a sfsmisc::posdefify() eigen step , doSym = FALSE # symmetrize after tcrossprod() , doDykstra = TRUE # do use Dykstra's correction , only.values = FALSE# if TRUE simply return lambda[j]. , ensureSymmetry = !isSymmetric(x)# so user can set to FALSE iff she knows.. , eig.tol = 1e-6 # defines relative positiveness of eigenvalues compared to largest , conv.tol = 1e-7 # convergence tolerance for algorithm , posd.tol = 1e-8 # tolerance for enforcing positive definiteness , maxit = 100 # maximum number of iterations allowed , conv.norm.type = "I" , trace = FALSE # set to TRUE (or 1 ..) to trace iterations ) { if(ensureSymmetry) { ## only if needed/wanted ... ## message("applying nearPD() to symmpart(x)") x <- symmpart(x) } n <- ncol(x) if(keepDiag) diagX0 <- diag(x) if(doDykstra) { ## D_S should be like x, but filled with '0' -- following also works for 'Matrix': D_S <- x; D_S[] <- 0 } X <- x iter <- 0 ; converged <- FALSE; conv <- Inf while (iter < maxit && !converged) { Y <- X if(doDykstra) R <- Y - D_S ## project onto PSD matrices X_k = P_S (R_k) e <- eigen(if(doDykstra) R else Y, symmetric = TRUE) ## Q <- e$vectors d <- e$values ## D <- diag(d) ## create mask from relative positive eigenvalues p <- d > eig.tol*d[1] if(!any(p)) stop("Matrix seems negative semi-definite") ## use p mask to only compute 'positive' part Q <- Q[,p,drop = FALSE] ## X <- Q %*% D[p,p,drop = FALSE] %*% t(Q) --- more efficiently : X <- tcrossprod(Q * rep(d[p], each=nrow(Q)), Q) if(doDykstra) ## update Dykstra's correction D_S = \Delta S_k D_S <- X - R ## project onto symmetric and possibly 'given diag' matrices: if(doSym) X <- (X + t(X))/2 if(corr) diag(X) <- 1 else if(keepDiag) diag(X) <- diagX0 conv <- norm(Y-X, conv.norm.type) / norm(Y, conv.norm.type) iter <- iter + 1 if (trace) cat(sprintf("iter %3d : #{p}=%d, ||Y-X|| / ||Y||= %11g\n", iter, sum(p), conv)) converged <- (conv <= conv.tol) } if(!converged) warning(gettextf("'nearPD()' did not converge in %d iterations", iter), domain = NA) ## force symmetry is *NEVER* needed, we have symmetric X here! ## X <- (X + t(X))/2 if(do2eigen || only.values) { ## begin from posdefify(sfsmisc) e <- eigen(X, symmetric = TRUE) d <- e$values Eps <- posd.tol * abs(d[1]) if (d[n] < Eps) { d[d < Eps] <- Eps if(!only.values) { Q <- e$vectors o.diag <- diag(X) X <- Q %*% (d * t(Q)) D <- sqrt(pmax(Eps, o.diag)/diag(X)) X[] <- D * X * rep(D, each = n) } } if(only.values) return(d) ## unneeded(?!): X <- (X + t(X))/2 if(corr) diag(X) <- 1 else if(keepDiag) diag(X) <- diagX0 } ## end from posdefify(sfsmisc) structure(list(mat = new("dpoMatrix", x = as.vector(X), Dim = c(n,n), Dimnames = .M.DN(x)), eigenvalues = d, corr = corr, normF = norm(x-X, "F"), iterations = iter, rel.tol = conv, converged = converged), class = "nearPD") } Matrix/R/ndenseMatrix.R0000644000175100001440000001462511003616106014523 0ustar hornikusers#### "ndenseMatrix" - virtual class of nonzero pattern dense matrices #### ------------ #### Contains nge*; ntr*, ntp*; nsy*, nsp*; ndi* ## Nonzero Pattern -> Double {of same structure}: setAs("ngeMatrix", "dgeMatrix", function(from) n2d_Matrix(from, "ngeMatrix")) setAs("nsyMatrix", "dsyMatrix", function(from) n2d_Matrix(from, "nsyMatrix")) setAs("nspMatrix", "dspMatrix", function(from) n2d_Matrix(from, "nspMatrix")) setAs("ntrMatrix", "dtrMatrix", function(from) n2d_Matrix(from, "ntrMatrix")) setAs("ntpMatrix", "dtpMatrix", function(from) n2d_Matrix(from, "ntpMatrix")) ### NOTA BENE: Much of this is *very* parallel to ./ldenseMatrix.R ### ~~~~~~~~~~~~~~~~ setAs("ndenseMatrix", "ldenseMatrix", function(from) n2l_Matrix(from)) setAs("ngeMatrix", "lgeMatrix", function(from) n2l_Matrix(from, "ngeMatrix")) setAs("nsyMatrix", "lsyMatrix", function(from) n2l_Matrix(from, "nsyMatrix")) setAs("nspMatrix", "lspMatrix", function(from) n2l_Matrix(from, "nspMatrix")) setAs("ntrMatrix", "ltrMatrix", function(from) n2l_Matrix(from, "ntrMatrix")) setAs("ntpMatrix", "ltpMatrix", function(from) n2l_Matrix(from, "ntpMatrix")) ## all need be coercable to "ngeMatrix": setAs("nsyMatrix", "ngeMatrix", function(from) .Call(lsyMatrix_as_lgeMatrix, from, 1L)) setAs("ntrMatrix", "ngeMatrix", function(from) .Call(ltrMatrix_as_lgeMatrix, from, 1L)) setAs("ntpMatrix", "ngeMatrix", function(from) as(as(from, "ntrMatrix"), "ngeMatrix")) setAs("nspMatrix", "ngeMatrix", function(from) as(as(from, "nsyMatrix"), "ngeMatrix")) ## and the reverse setAs("ngeMatrix", "ntpMatrix", function(from) as(as(from, "ntrMatrix"), "ntpMatrix")) setAs("ngeMatrix", "nspMatrix", function(from) as(as(from, "nsyMatrix"), "nspMatrix")) ## packed <-> non-packed : setAs("nspMatrix", "nsyMatrix", function(from) .Call(lspMatrix_as_lsyMatrix, from, 1L)) setAs("nsyMatrix", "nspMatrix", function(from) .Call(lsyMatrix_as_lspMatrix, from, 1L)) setAs("ntpMatrix", "ntrMatrix", function(from) .Call(ltpMatrix_as_ltrMatrix, from, 1L)) setAs("ntrMatrix", "ntpMatrix", function(from) .Call(ltrMatrix_as_ltpMatrix, from, 1L)) ### -> symmetric : if(FALSE) ## not sure if this is a good idea ... -- FIXME? setIs("ngeMatrix", "nsyMatrix", test = function(obj) isSymmetric(obj), replace = function(obj, value) { ## copy all slots for(n in slotNames(obj)) slot(obj, n) <- slot(value, n) }) ### Alternative (at least works): setAs("ngeMatrix", "nsyMatrix", function(from) { if(isSymmetric(from)) new("nsyMatrix", x = from@x, Dim = from@Dim, Dimnames = from@Dimnames, factors = from@factors) else stop("not a symmetric matrix; consider forceSymmetric() or symmpart()") }) setAs("ngeMatrix", "ntrMatrix", function(from) { if(isT <- isTriangular(from)) new("ntrMatrix", x = from@x, Dim = from@Dim, Dimnames = from@Dimnames, uplo = .if.NULL(attr(isT, "kind"), "U")) ## TODO: also check 'diag' else stop("not a triangular matrix") }) ### ldense* <-> "matrix" : ## 1) "nge* : setAs("ngeMatrix", "matrix", function(from) array(from@x, dim = from@Dim, dimnames = from@Dimnames)) setAs("matrix", "ngeMatrix", function(from) { new("ngeMatrix", x = as.logical(from), Dim = as.integer(dim(from)), Dimnames = .M.DN(from)) }) ## 2) base others on "nge*": setAs("matrix", "nsyMatrix", function(from) as(as(from, "ngeMatrix"), "nsyMatrix")) setAs("matrix", "nspMatrix", function(from) as(as(from, "nsyMatrix"), "nspMatrix")) setAs("matrix", "ntrMatrix", function(from) as(as(from, "ngeMatrix"), "ntrMatrix")) setAs("matrix", "ntpMatrix", function(from) as(as(from, "ntrMatrix"), "ntpMatrix")) ## Useful if this was called e.g. for as(*, "nsyMatrix"), but it isn't setAs("matrix", "ndenseMatrix", function(from) as(from, "ngeMatrix")) setAs("ndenseMatrix", "matrix", ## uses the above l*M. -> lgeM. function(from) as(as(from, "ngeMatrix"), "matrix")) ## dense |-> compressed : ## go via "l" because dense_to_Csparse can't be used for "n" [missing CHOLMOD function] setAs("ndenseMatrix", "CsparseMatrix", function(from) as(as(as(from, "lMatrix"), "CsparseMatrix"), "nMatrix")) ## setAs("ndenseMatrix", "sparseMatrix", ## function(from) as(as(as(from, "lMatrix"), "sparseMatrix"), "nMatrix")) setAs("ndenseMatrix", "TsparseMatrix", function(from) { if(is(from, "generalMatrix")) { ## cheap but not so efficient: ij <- which(as(from,"matrix"), arr.ind = TRUE) - 1L new("ngTMatrix", i = ij[,1], j = ij[,2], Dim = from@Dim, Dimnames = from@Dimnames, factors = from@factors) } else ## triangular or symmetric (have *no* diagonal nMatrix) ## is delicate {packed or not, upper /lower indices ..} -> easy way as(as(as(from, "lMatrix"), "TsparseMatrix"), "nMatrix") }) ## Not sure, if these are needed or more efficient than the above: ## First one probably is setAs("ngeMatrix", "ngTMatrix", function(from) { ## cheap but not so efficient: ij <- which(as(from,"matrix"), arr.ind = TRUE) - 1L new("ngTMatrix", i = ij[,1], j = ij[,2], Dim = from@Dim, Dimnames = from@Dimnames, factors = from@factors) }) setAs("ngeMatrix", "ngCMatrix", function(from) as(as(from, "ngTMatrix"), "ngCMatrix")) setMethod("as.logical", signature(x = "ndenseMatrix"), function(x, ...) as(x, "ngeMatrix")@x) ###---------------------------------------------------------------------- setMethod("t", signature(x = "ngeMatrix"), t_geMatrix) setMethod("t", signature(x = "ntrMatrix"), t_trMatrix) setMethod("t", signature(x = "nsyMatrix"), t_trMatrix) setMethod("t", signature(x = "ntpMatrix"), function(x) as(t(as(x, "ntrMatrix")), "ntpMatrix")) setMethod("t", signature(x = "nspMatrix"), function(x) as(t(as(x, "nsyMatrix")), "nspMatrix")) ## NOTE: "&" and "|" are now in group "Logic" c "Ops" --> ./Ops.R ## "!" is in ./not.R setMethod("as.vector", signature(x = "ndenseMatrix", mode = "missing"), function(x, mode) as(x, "ngeMatrix")@x) setMethod("norm", signature(x = "ndenseMatrix", type = "character"), function(x, type, ...) .Call(dgeMatrix_norm, as(as(x,"dMatrix"),"dgeMatrix"), type), valueClass = "numeric") setMethod("rcond", signature(x = "ndenseMatrix", norm = "character"), .rcond_via_d, valueClass = "numeric") Matrix/R/AllGeneric.R0000644000175100001440000000611412213673171014072 0ustar hornikusers#### Define those generics that we need, if they don't exist; #### not all will be exported setGeneric("expand", function(x, ...) standardGeneric("expand")) setGeneric("isDiagonal", function(object) standardGeneric("isDiagonal")) setGeneric("isTriangular", function(object, ...) ## 'upper = NA' standardGeneric("isTriangular")) ## isSymmetric is "S3 generic" in R's base/R/eigen.R setGeneric("facmul", function(x, factor, y, transpose, left, ...) standardGeneric("facmul")) setGeneric("BunchKaufman", function(x, ...) standardGeneric("BunchKaufman")) setGeneric("lu", function(x, ...) standardGeneric("lu")) ##NB ## do not redefine the "base signature" ##NB setGeneric("chol", def = function(x, pivot= FALSE,...) standardGeneric("chol"), ##NB useAsDefault= function(x, pivot= FALSE,...) base::chol(x, pivot, ...)) ##NB setGeneric("qr", def = function(x, tol=1e-7,...) standardGeneric("qr"), ##NB useAsDefault= function(x, tol=1e-7,...) base::qr(x, tol, ...)) setGeneric("Schur", function(x, vectors, ...) standardGeneric("Schur")) setGeneric("unpack", function(x, ...) standardGeneric("unpack")) setGeneric("pack", function(x, ...) standardGeneric("pack")) ##- setGeneric("%p%", function(a, b) standardGeneric("%p%")) setGeneric("expm", function(x) standardGeneric("expm")) setGeneric("writeMM", function(obj, file, ...) standardGeneric("writeMM")) setGeneric("tril", function(x, k = 0, ...) standardGeneric("tril")) setGeneric("triu", function(x, k = 0, ...) standardGeneric("triu")) setGeneric("band", function(x, k1, k2, ...) standardGeneric("band")) setGeneric("Cholesky", function(A, perm = TRUE, LDL = !super, super = FALSE, Imult = 0, ...) standardGeneric("Cholesky")) setGeneric("symmpart", function(x) standardGeneric("symmpart")) setGeneric("skewpart", function(x) standardGeneric("skewpart")) ## A version of coercion to "symmetric" which does *NOT* check, ## but just takes the ## upper (or lower) values and ## ``declares'' the symmetric: setGeneric("forceSymmetric", function(x, uplo) standardGeneric("forceSymmetric")) setGeneric("nnzero", function(x, na.counted = NA) standardGeneric("nnzero"), signature = "x") setGeneric("updown", function(update, C, L) standardGeneric("updown")) ##> must do this in any case, as long as this should *run* in R < 2.15.2 ##> if(as.numeric(R.version$`svn rev`) < 60620) setGeneric("toeplitz", function(x, ...) standardGeneric("toeplitz"), useAsDefault= function(x, ...) stats::toeplitz(x)) ## and an entry in ../man/sparseVector-class.Rd if(FALSE) ## only "need this", as 'Dvec' should not get its default from base::qr.Q : ## unfortunately, this masks base::qr.Q with a warning setGeneric("qr.Q", function(qr, complete = FALSE, Dvec) standardGeneric("qr.Q"), useAsDefault = function(qr, complete = FALSE, Dvec) { if(missing(Dvec)) base::qr.Q(qr, complete=complete) else base::qr.Q(qr, complete=complete, Dvec=Dvec) }) Matrix/R/ntTMatrix.R0000644000175100001440000000236211004710614014007 0ustar hornikusers#### Logical Sparse Triangular Matrices in Triplet format ### contains = "nsparseMatrix" setAs("matrix", "ntTMatrix", function(from) as(as(from, "ntrMatrix"), "TsparseMatrix")) setAs("ntTMatrix", "ngTMatrix", function(from) tT2gT(from, cl = "ntTMatrix", toClass = "ngTMatrix")) setAs("ntTMatrix", "generalMatrix", function(from) tT2gT(from, cl = "ntTMatrix", toClass = "ngTMatrix")) setAs("ntTMatrix", "ntCMatrix", function(from) .Call(Tsparse_to_Csparse, from, TRUE)) setAs("ntTMatrix", "ngCMatrix", function(from) as(.Call(Tsparse_to_Csparse, from, TRUE), "ngCMatrix")) setAs("ntTMatrix", "dtTMatrix", function(from) new("dtTMatrix", i = from@i, j = from@j, x = rep.int(1, length(from@i)), uplo = from@uplo, diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames)) setAs("ntTMatrix", "ntrMatrix", function(from) .Call(ntTMatrix_as_ntrMatrix, from)) setAs("ntTMatrix", "matrix", function(from) as(as(from, "ntrMatrix"), "matrix")) setMethod("t", "ntTMatrix", function(x) new("ntTMatrix", Dim = x@Dim[2:1], Dimnames = x@Dimnames[2:1], i = x@j, j = x@i, diag = x@diag, uplo = if (x@uplo == "U") "L" else "U")) Matrix/R/SparseM-conv.R0000644000175100001440000000574512050202345014401 0ustar hornikusers####----------- Minimal conversion utilities <--> "SparseM" ### I. The "natural pairs" between the two packages: setAs("matrix.csr", "dgRMatrix", function(from) { new("dgRMatrix", x = from@ra, j = from@ja - 1L, p = from@ia - 1L, Dim = from@dimension) }) setAs("dgRMatrix", "matrix.csr", function(from) { new("matrix.csr", ra = from@x, ja = from@j + 1L, ia = from@p + 1L, dimension = from@Dim) }) setAs("matrix.csc", "dgCMatrix", function(from) { new("dgCMatrix", x = from@ra, i = from@ja - 1L, p = from@ia - 1L, Dim = from@dimension) }) setAs("dgCMatrix", "matrix.csc", function(from) { new("matrix.csc", ra = from@x, ja = from@i + 1L, ia = from@p + 1L, dimension = from@Dim) }) setAs("matrix.coo", "dgTMatrix", function(from) { new("dgTMatrix", x = from@ra, i = from@ia - 1L, j = from@ja - 1L, Dim = from@dimension) }) setAs("dgTMatrix", "matrix.coo", function(from) { new("matrix.coo", ra = from@x, ia = from@i + 1L, ja = from@j + 1L, dimension = from@Dim) }) ### II. Enable coercion to the ``favorite'' of each package; ### --- ---------------------------- ### i.e., "dgCMatrix" and "matrix.csr" setAs("dsparseMatrix", "matrix.csr", function(from) as(as(as(from, "RsparseMatrix"), "dgRMatrix"), "matrix.csr")) ## setAs("matrix.csr", "dgCMatrix", function(from) as(as(from, "dgRMatrix"), "CsparseMatrix")) setAs("matrix.coo", "dgCMatrix", function(from) as(as(from, "dgTMatrix"), "dgCMatrix")) ### also define the virtual coercions that we (should) advertize: setAs("matrix.csr", "RsparseMatrix", function(from) as(from, "dgRMatrix")) setAs("matrix.csc", "CsparseMatrix", function(from) as(from, "dgCMatrix")) setAs("matrix.coo", "TsparseMatrix", function(from) as(from, "dgTMatrix")) ## to "Csparse*" and "Tsparse*" should work for all sparse: setAs("matrix.csr", "CsparseMatrix", function(from) as(as(from, "dgRMatrix"), "CsparseMatrix")) setAs("matrix.coo", "CsparseMatrix", function(from) as(as(from, "dgTMatrix"), "CsparseMatrix")) setAs("matrix.csc", "TsparseMatrix", function(from) as(as(from, "dgCMatrix"), "TsparseMatrix")) setAs("matrix.csr", "TsparseMatrix", function(from) as(as(from, "dgRMatrix"), "TsparseMatrix")) ## Also *from* (our favorite) Csparse should work to all 3 SparseM setAs("CsparseMatrix", "matrix.csr", function(from) as(as(from, "RsparseMatrix"), "matrix.csr")) setAs("CsparseMatrix", "matrix.coo", function(from) as(as(from, "TsparseMatrix"), "matrix.coo")) setAs("CsparseMatrix", "matrix.csc", function(from) as(as(from, "dgCMatrix"), "matrix.csc")) ## Easy coercion: just always use as( , "Matrix") : setAs("matrix.csr", "Matrix", function(from) as(from, "CsparseMatrix")) # we favor! setAs("matrix.coo", "Matrix", function(from) as(from, "TsparseMatrix")) setAs("matrix.csc", "Matrix", function(from) as(from, "CsparseMatrix")) Matrix/R/dgeMatrix.R0000644000175100001440000000704312271746775014032 0ustar hornikusers ##' works for vectors, matrix, .. ..2dge <- function(from) .Call(dup_mMatrix_as_dgeMatrix, from) setAs("matrix", "dgeMatrix", ..2dge) setAs("numLike", "dgeMatrix", ..2dge) setAs("dgeMatrix", "matrix", function(from) array(from@x, dim = from@Dim, dimnames = from@Dimnames)) ## Group Methods, see ?Math (e.g.) ## "Arith" is in ./Ops.R setMethod("Math", signature(x = "dgeMatrix"), function(x) { x@x <- callGeneric(x@x) x }) ## "Math2" is in ./dMatrix.R ## "Summary" ## "Compare" now happens in ./dMatrix.R ## -- end{group generics} ----------------------- ## "[" settings are "up in" Matrix.R & denseMatrix.R setMethod("as.vector", signature(x = "dgeMatrix", mode = "missing"), function(x, mode) x@x) setMethod("norm", signature(x = "dgeMatrix", type = "missing"), function(x, type, ...) norm(x, type = "O", ...)) setMethod("norm", signature(x = "dgeMatrix", type = "character"), function(x, type, ...) .Call(dgeMatrix_norm, x, type), valueClass = "numeric") setMethod("rcond", signature(x = "dgeMatrix", norm = "missing"), function(x, norm, ...) rcond(x, norm = "O", ...)) setMethod("rcond", signature(x = "dgeMatrix", norm = "character"), function(x, norm, ...) { if({d <- dim(x); d[1] == d[2]}) .Call(dgeMatrix_rcond, x, norm) else rcond(qr.R(qr(if(d[1] < d[2]) t(x) else x)), norm=norm, ...) }, valueClass = "numeric") ##> FIXME: R-devel (2.11.0) norm() is *wrong* for NAs, whereas this dgeMatrix ##> ----- one works, even though both should call the identical LAPACK 'dlange' ????? ##> Hence, keep the Matrix version active for now: ##> if(getRversion() < "2.11.0" || R.version$`svn rev` < 51018) ##--- the same for "traditional" 'matrix': setMethod("norm", signature(x = "matrix", type = "character"), function(x, type, ...) .Call(dgeMatrix_norm, ..2dge(x), type), valueClass = "numeric") setMethod("t", signature(x = "dgeMatrix"), t_geMatrix) .dge.diag <- function(x, nrow, ncol) .Call(dgeMatrix_getDiag, x) setMethod("diag", signature(x = "dgeMatrix"), .dge.diag) setMethod("diag<-", signature(x = "dgeMatrix"), function(x, value) .Call(dgeMatrix_setDiag, x, value)) setMethod("chol", signature(x = "dgeMatrix"), cholMat) setMethod("solve", signature(a = "dgeMatrix", b = "missing"), function(a, b, ...) .Call(dgeMatrix_solve, a), valueClass = "dgeMatrix") setMethod("solve", signature(a = "dgeMatrix", b = "ddenseMatrix"), function(a, b, ...) .Call(dgeMatrix_matrix_solve, a, b), valueClass = "dgeMatrix") setMethod("solve", signature(a = "dgeMatrix", b = "matrix"), function(a, b, ...) .Call(dgeMatrix_matrix_solve, a, b), valueClass = "dgeMatrix") setMethod("solve", signature(a = "dgeMatrix", b = "sparseMatrix"), function(a, b, ...) .Call(dgeMatrix_matrix_solve, a, as(b, "denseMatrix")), valueClass = "dgeMatrix") ## not needed - method for numeric defined for Matrix class ## setMethod("solve", signature(a = "dgeMatrix", b = "numeric"), ## function(a, b, ...) ## .Call(dgeMatrix_matrix_solve, a, as.matrix(as.double(b)))) setMethod("lu", signature(x = "dgeMatrix"), function(x, warnSing = TRUE, ...) .Call(dgeMatrix_LU, x, warnSing), valueClass = "denseLU") setMethod("determinant", signature(x = "dgeMatrix", logarithm = "missing"), function(x, logarithm, ...) .Call(dgeMatrix_determinant, x, TRUE)) setMethod("determinant", signature(x = "dgeMatrix", logarithm = "logical"), function(x, logarithm, ...) .Call(dgeMatrix_determinant, x, logarithm)) ##-> ./expm.R for expm() ##-> ./colSums.R for colSums,... rowMeans Matrix/R/dtrMatrix.R0000644000175100001440000000707712003525364014051 0ustar hornikusers#### Triangular Matrices -- Coercion and Methods ## or rather setIs() {since test can fail }? ## FIXME: get rid of this (coerce to "triangular..") ?!? setAs("dgeMatrix", "dtrMatrix", function(from) asTri(from, "dtrMatrix")) setAs("dtrMatrix", "dtpMatrix", function(from) .Call(dtrMatrix_as_dtpMatrix, from)) setAs("dtrMatrix", "sparseMatrix", .dense2C) setAs("dtrMatrix", "CsparseMatrix", .dense2C) ## needed for t() method setAs("dtrMatrix", "matrix", function(from) .Call(dtrMatrix_as_matrix, from, TRUE)) setAs("matrix", "dtrMatrix", function(from) as(.Call(dup_mMatrix_as_dgeMatrix, from), "dtrMatrix")) setAs("Cholesky", "lMatrix", function(from) as(as(from, "dtrMatrix"), "lMatrix")) setAs("BunchKaufman", "lMatrix", function(from) as(as(from, "dtrMatrix"), "lMatrix")) ## Group Methods: ## TODO: carefully check for the cases where the result remains triangular ## instead : inherit them from "dgeMatrix" via definition in ./dMatrix.R ## Note: Just *because* we have an explicit dtr -> dge coercion, ## show( ) is not okay, and we need our own: setMethod("show", "dtrMatrix", function(object) prMatrix(object)) setMethod("determinant", signature(x = "dtrMatrix", logarithm = "missing"), function(x, logarithm, ...) callGeneric(x, TRUE)) setMethod("determinant", signature(x = "dtrMatrix", logarithm = "logical"), function(x, logarithm, ...) mkDet(diag(x), logarithm)) setMethod("diag", signature(x = "dtrMatrix"), function(x, nrow, ncol) .Call(dtrMatrix_getDiag, x), valueClass = "numeric") setMethod("diag<-", signature(x = "dtrMatrix"), function(x, value) { .Call(dtrMatrix_setDiag, if(x@diag == "U") .dense.diagU2N(x, "d", isPacked=FALSE) else x, value) }) setMethod("norm", signature(x = "dtrMatrix", type = "character"), function(x, type, ...) .Call(dtrMatrix_norm, x, type), valueClass = "numeric") setMethod("norm", signature(x = "dtrMatrix", type = "missing"), function(x, type, ...) .Call(dtrMatrix_norm, x, "O"), valueClass = "numeric") setMethod("rcond", signature(x = "dtrMatrix", norm = "character"), function(x, norm, ...) .Call(dtrMatrix_rcond, x, norm), valueClass = "numeric") setMethod("rcond", signature(x = "dtrMatrix", norm = "missing"), function(x, norm, ...) .Call(dtrMatrix_rcond, x, "O"), valueClass = "numeric") setMethod("chol2inv", signature(x = "dtrMatrix"), function (x, ...) { chk.s(...) if (x@diag != "N") x <- diagU2N(x) .Call(dtrMatrix_chol2inv, x) }) setMethod("solve", signature(a = "dtrMatrix", b="missing"), function(a, b, ...) { ## warn, as e.g. CHMfactor have 'system' as third argument chk.s(...) .Call(dtrMatrix_solve, a) }, valueClass = "dtrMatrix") setMethod("solve", signature(a = "dtrMatrix", b="ddenseMatrix"), function(a, b, ...) { chk.s(...) .Call(dtrMatrix_matrix_solve, a, b) }, valueClass = "dgeMatrix") setMethod("solve", signature(a = "dtrMatrix", b="dMatrix"), function(a, b, ...) { chk.s(...) .Call(dtrMatrix_matrix_solve, a, as(b,"denseMatrix")) }, valueClass = "dgeMatrix") setMethod("solve", signature(a = "dtrMatrix", b="Matrix"), function(a, b, ...) { chk.s(...) .Call(dtrMatrix_matrix_solve, a, as(as(b, "dMatrix"), "denseMatrix")) }, valueClass = "dgeMatrix") setMethod("solve", signature(a = "dtrMatrix", b="matrix"), function(a, b, ...) { chk.s(...) .Call(dtrMatrix_matrix_solve, a, b) }, valueClass = "dgeMatrix") setMethod("t", signature(x = "dtrMatrix"), t_trMatrix) Matrix/R/ltTMatrix.R0000644000175100001440000000237311004710614014007 0ustar hornikusers#### Logical Sparse Triangular Matrices in Triplet format ### contains = "lsparseMatrix" setAs("matrix", "ltTMatrix", function(from) as(as(from, "ltrMatrix"), "TsparseMatrix")) setAs("ltTMatrix", "lgTMatrix", function(from) tT2gT(from, cl = "ltTMatrix", toClass = "lgTMatrix")) setAs("ltTMatrix", "generalMatrix", function(from) tT2gT(from, cl = "ltTMatrix", toClass = "lgTMatrix")) setAs("ltTMatrix", "ltCMatrix", function(from) .Call(Tsparse_to_Csparse, from, TRUE)) setAs("ltTMatrix", "lgCMatrix", function(from) as(.Call(Tsparse_to_Csparse, from, TRUE), "lgCMatrix")) setAs("ltTMatrix", "dtTMatrix", function(from) new("dtTMatrix", i = from@i, j = from@j, x = rep.int(1, length(from@i)), uplo = from@uplo, diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames)) setAs("ltTMatrix", "ltrMatrix", function(from) .Call(ltTMatrix_as_ltrMatrix, from)) setAs("ltTMatrix", "matrix", function(from) as(as(from, "ltrMatrix"), "matrix")) setMethod("t", "ltTMatrix", function(x) new("ltTMatrix", Dim = x@Dim[2:1], Dimnames = x@Dimnames[2:1], i = x@j, j = x@i, x = x@x, diag = x@diag, uplo = if (x@uplo == "U") "L" else "U")) Matrix/R/Ops.R0000644000175100001440000017356012271746775012657 0ustar hornikusers#### ------- All "Ops" group methods for all Matrix classes ------------ ### === ### Note that the "Ops" group consists of ### sub-groups "Arith", "Compare", and "Logic" ### ----- ------- ----- ### where 'Arith' := '"+"', '"-"', '"*"', '"^"', '"%%"', '"%/%"', '"/"' ### 'Compare' := '"=="', '">"', '"<"', '"!="', '"<="', '">="' ### 'Logic' := '"&"', '"|"' (( but *not* '"!"' since that has ### only one argument )) ## in shell, find them with ## egrep 'Method\("(Ops|Compare|Arith|Logic)"' R/*R ### "Ops" ---- remember Ops = {Arith, Compare, Logic} [Logic: since R 2.4.1] ### ----- ### Note: diagonalMatrix are handled by special methods -> ./diagMatrix.R ### -------------- ~~~~~~~~~~~~~~ ### Design decision for *sparseMatrix*: ### work via Csparse since Tsparse are not-unique (<-> slots not compatible) ### -- 0 -- (not dense *or* sparse) ----------------------------------- ##-------- originally from ./Matrix.R -------------------- ## Some ``Univariate'' "Arith": setMethod("+", signature(e1 = "Matrix", e2 = "missing"), function(e1,e2) e1) ## "fallback": setMethod("-", signature(e1 = "Matrix", e2 = "missing"), function(e1, e2) { warning("inefficient method used for \"- e1\"") 0-e1 }) setMethod("-", signature(e1 = "denseMatrix", e2 = "missing"), function(e1, e2) { e1@x <- -e1@x; e1 }) ## "diagonalMatrix" -- only two cases -- easiest to do both setMethod("-", signature(e1 = "ddiMatrix", e2 = "missing"), function(e1, e2) { if(e1@diag == "U") { e1@x <- rep.int(-1., e1@Dim[1]) e1@diag <- "N" } else ## diag == "N" -> using 'x' slot e1@x <- -e1@x e1 }) setMethod("-", signature(e1 = "ldiMatrix", e2 = "missing"), function(e1, e2) { d <- e1@Dim new("ddiMatrix", Dim = d, Dimnames = e1@Dimnames, diag = "N", x = if(e1@diag == "U") rep.int(-1, d[1]) else -e1@x) }) ## old-style matrices are made into new ones setMethod("Ops", signature(e1 = "Matrix", e2 = "matrix"), function(e1, e2) callGeneric(e1, Matrix(e2))) setMethod("Ops", signature(e1 = "matrix", e2 = "Matrix"), function(e1, e2) callGeneric(Matrix(e1), e2)) ## Note: things like callGeneric(Matrix(e1, sparse=is(e2,"sparseMatrix")), e2)) ## may *not* be better: e.g. Matrix(.) can give *diagonal* instead of sparse ## bail-outs -- on highest possible level, hence "Ops", not "Compare"/"Arith" : .bail.out.Ops <- function(e1, e2) { if(is(e1, "Matrix") && is(e2, "Matrix")) dimCheck(e1,e2) .bail.out.2(.Generic, class(e1), class(e2)) } setMethod("Ops", signature(e1 = "Matrix", e2 = "ANY"), .bail.out.Ops) setMethod("Ops", signature(e1 = "ANY", e2 = "Matrix"), .bail.out.Ops) rm(.bail.out.Ops) ## "General principle" ## - - - - - - - - - ## For "Arith" it is sufficient (though not optimal, once we have "iMatrix"!) ## to define "dMatrix" methods and coerce all other "[nli]Matrix" to "dMatrix" setMethod("Arith", signature(e1 = "Matrix", e2 = "Matrix"), function(e1, e2) callGeneric(as(e1, "dMatrix"), as(e2, "dMatrix"))) ## For "Compare", this would be feasible too, but is clearly suboptimal, ## particularly for "==" and "!=" ## and for "lMatrix" and "nMatrix" should not coerce at all if(FALSE) setMethod("Compare", signature(e1 = "Matrix", e2 = "Matrix"), function(e1, e2) { if(is.na(match(.Generic, c("==", "!=")))) callGeneric(as(e1, "dMatrix"), as(e2, "dMatrix")) else { ## no coercion needed for "==" or "!=" ## ## what now ? <<<<<<<<<<< FIXME >>>>>>>>> .bail.out.2(.Generic, class(e1), class(e2)) } }) ## Working entirely on "matching" x slot: ## can be done for matching-dim "*geMatrix", and also ## matching-{dim + uplo} for *packed* (only!) symmetric+triangular .Ops.via.x <- function(e1,e2) { d <- dimCheck(e1, e2) e1@x <- callGeneric(e1@x, e2@x) e1 } ###-------- originally from ./dMatrix.R -------------------- ## ## Note that there extra methods for o ! ## ## "Compare" -> returning logical Matrices; .Cmp.swap() is in ./Auxiliaries.R setMethod("Compare", signature(e1 = "numeric", e2 = "dMatrix"), .Cmp.swap) setMethod("Compare", signature(e1 = "logical", e2 = "dMatrix"), .Cmp.swap) setMethod("Compare", signature(e1 = "numeric", e2 = "lMatrix"), .Cmp.swap) setMethod("Compare", signature(e1 = "logical", e2 = "lMatrix"), .Cmp.swap) setMethod("Compare", signature(e1 = "numeric", e2 = "nMatrix"), .Cmp.swap) setMethod("Compare", signature(e1 = "logical", e2 = "nMatrix"), .Cmp.swap) ## This is parallel to Logic.Mat.atomic() below ---> __keep parallel__ ! Cmp.Mat.atomic <- function(e1, e2) { ## result will inherit from "lMatrix" d <- e1@Dim cl <- class(e1) if((l2 <- length(e2)) == 0) { if(prod(d) == 0) return(new(class2(cl, "l"), Dim= d)) else stop(gettextf(" %s %s is undefined", .Generic, paste0(class(e2),"(0)")), domain=NA) } cl1 <- getClassDef(cl) slots1 <- names(cl1@slots) has.x <- any("x" == slots1)# *fast* check for "x" slot presence if(l2 > 1 && has.x) ## e2 cannot simply be compared with e1@x --> use another method return(callGeneric(e1, Matrix(e2, nrow=d[1], ncol=d[2]))) ## else Udg <- extends(cl1, "triangularMatrix") && e1@diag == "U" r0 <- callGeneric(0, e2) ## Udg: append the diagonal at *end*, as diagU2N(): r <- callGeneric(if(Udg) c(e1@x,..diag.x(e1)) else if(has.x) e1@x else TRUE, e2) ## trivial case first (beware of NA) if(isTRUE(all(r0) && all(r))) { r <- new(if(d[1] == d[2]) "lsyMatrix" else "lgeMatrix") r@Dim <- d r@Dimnames <- e1@Dimnames r@x <- rep.int(TRUE, prod(d)) } else if(extends(cl1, "denseMatrix")) { full <- !.isPacked(e1) # << both "dtr" and "dsy" are 'full' if(full || allFalse(r0) || extends(cl1, "symmetricMatrix")) { isTri <- extends(cl1, "triangularMatrix") if(isTri) { if(extends(cl1,"Cholesky") || extends(cl1,"BunchKaufman")) cl1 <- getClassDef(cl <- class(e1 <- as(e1, "dtrMatrix"))) } ## FIXME? using copyClass() to copy "relevant" slots r <- new(class2(cl, "l"), x = r, Dim = d, Dimnames = dimnames(e1)) if(extends(cl1, "symmetricMatrix")) { r@uplo <- e1@uplo } else if(isTri) { r@uplo <- e1@uplo r@diag <- e1@diag } } else { ## packed matrix with structural 0 and r0 is not all FALSE: ##--> result cannot be packed anymore ## [dense & packed & not symmetric ] ==> must be "dtp*" : if(!extends(cl1, "dtpMatrix")) stop("internal bug in \"Compare\" method (Cmp.Mat.atomic); please report") rx <- rep_len(r0, prod(d)) rx[indTri(d[1], upper = (e1@uplo == "U"), diag=TRUE)] <- r r <- new("lgeMatrix", x = rx, Dim = d, Dimnames = dimnames(e1)) } } else { ##---- e1 is(. , sparseMatrix) ----------------- ## FIXME: remove this test eventually if(extends(cl1, "diagonalMatrix")) stop("Cmp.Mat.atomic() should not be called for diagonalMatrix") remainSparse <- allFalse(r0) ## <==> things remain sparse if(Udg) { # e1 *is* unit-diagonal (triangular sparse) r1 <- callGeneric(1, e2) Udg <- all(r1) # maybe Unit-diagonal (sparse) result ## if(!remainSparse) we'll use non0ind() which *has* unit-diag. indices at end ## if(Udg && remainSparse) { } else { ## result will not be unit-diagonal sparse e1 <- .diagU2N(e1, cl = cl1) # otherwise, result is U-diag if(extends(cl1, "CsparseMatrix")) { ## repeat computation if e1 has changed r <- callGeneric(if(has.x) e1@x else TRUE, e2) } } } if(remainSparse) { if(!any(is.na(r)) && ((Ar <- all(r)) || !any(r))) { lClass <- class2(cl, "l") # is "lsparse*" r <- new(lClass) r@Dim <- d r@Dimnames <- dimnames(e1) if(Ar) { # 'TRUE' instead of 'x': same sparsity: for(n in intersect(c("i","j","p","uplo","diag"), slots1)) slot(r, n) <- slot(e1, n) n <- if(has.x) length(e1@x) else if(any("p" == slots1)) e1@p[d[2]+1L] else length(e1@i) r@x <- rep.int(TRUE, n) } else { ## !any(r): all FALSE: keep empty 'r' matrix ## but may need a valid 'pointer' slot: if(extends(lClass, "CsparseMatrix")) r@p <- rep.int(0L, 1+ncol(r)) else if(extends(lClass, "RsparseMatrix")) r@p <- rep.int(0L, 1+nrow(r)) } } else { # some TRUE, FALSE, NA : go via unique 'Tsparse' M <- asTuniq(e1) nCl <- class2(class(M), 'l') # logical Tsparse sN <- slotNames(nCl) ## copy "the other slots" (important for "tr"/"sym"): r <- copyClass(M, nCl, sNames = sN[is.na(match(sN, "x"))]) r@x <- callGeneric(if(has.x) M@x else 1, e2) if(extends(cl1, "CsparseMatrix")) r <- as(r, "CsparseMatrix") else if(extends(cl1, "RsparseMatrix")) r <- as(r, "RsparseMatrix") } } else { ## non sparse result; triangularity also gone, typically lClass <- if(extends(cl1, "symmetricMatrix")) "lsyMatrix" else "lgeMatrix" Matrix.msg(sprintf("sparse to dense (%s) coercion in '%s' -> %s", lClass, .Generic, "Cmp.Mat.atomic"), .M.level = 2) rx <- rep_len(r0, prod(d)) ## Here, we assume that 'r' and the indices align (!) encI <- .Call(m_encodeInd, non0ind(e1, cl1, uniqT=FALSE, xtendSymm=FALSE), di = d, checkBounds = FALSE) rx[1L + encI] <- r r <- new(lClass, x = rx, Dim = d, Dimnames = dimnames(e1)) } } r } setMethod("Compare", signature(e1 = "dMatrix", e2 = "numeric"), Cmp.Mat.atomic) setMethod("Compare", signature(e1 = "dMatrix", e2 = "logical"), Cmp.Mat.atomic) setMethod("Compare", signature(e1 = "lMatrix", e2 = "numeric"), Cmp.Mat.atomic) setMethod("Compare", signature(e1 = "lMatrix", e2 = "logical"), Cmp.Mat.atomic) setMethod("Compare", signature(e1 = "nMatrix", e2 = "numeric"), Cmp.Mat.atomic) setMethod("Compare", signature(e1 = "nMatrix", e2 = "logical"), Cmp.Mat.atomic) ## "xMatrix <-> work with 'x' slot {was originally just for "Compare"}: ## ------- {also used for "Arith"}: Ops.x.x <- function(e1, e2) { d <- dimCheck(e1,e2) if((dens1 <- extends(c1 <- class(e1), "denseMatrix"))) gen1 <- extends(c1, "generalMatrix") if((dens2 <- extends(c2 <- class(e2), "denseMatrix"))) gen2 <- extends(c2, "generalMatrix") if(dens1 && dens2) { ## both inherit from ddense* geM <- TRUE if(!gen1) { if(!gen2) { ## consider preserving "triangular" / "symmetric" geM <- FALSE le <- prod(d) isPacked <- function(x) length(x@x) < le Mclass <- if(sym <- extends(c1, "symmetricMatrix") && extends(c2, "symmetricMatrix")) { if(e1@uplo != e2@uplo) ## one is upper, one is lower e2 <- t(e2) if((p1 <- isPacked(e1)) | (p2 <- isPacked(e2))) { ## at least one is packed if(p1 != p2) { # one is not packed --> *do* pack it: pack.sy <- function(x) if(is.numeric(x@x)) .Call(dsyMatrix_as_dspMatrix, x) else .Call(lsyMatrix_as_lspMatrix, x, 0L) if(p1) e2 <- pack.sy(e2) else e1 <- pack.sy(e1) } "spMatrix" } else "syMatrix" } else if(tri <- extends(c1, "triangularMatrix") && extends(c2, "triangularMatrix")) { if(!(geM <- e1@uplo != e2@uplo || isN0(callGeneric(0,0)))) { p1 <- isPacked(e1) p2 <- isPacked(e2) if(e1@diag == "U") e1 <- .dense.diagU2N(e1, isPacked=p1) if(e2@diag == "U") e2 <- .dense.diagU2N(e2, isPacked=p2) if(p1 | p2) { ## at least one is packed if(p1 != p2) { # one is not packed --> *do* pack it: pack.tr <- function(x) if(is.numeric(x@x)) .Call(dtrMatrix_as_dtpMatrix, x) else .Call(ltrMatrix_as_ltpMatrix, x, 0L) if(p1) e2 <- pack.tr(e2) else e1 <- pack.tr(e1) } "tpMatrix" } else "trMatrix" } } else { geM <- TRUE } if(geM) e2 <- as(e2, "generalMatrix") } if(geM) e1 <- as(e1, "generalMatrix") # was "dgeMatrix" } else { ## gen1 if(!gen2) e2 <- as(e2, "generalMatrix") } ## now, in all cases @x should be matching & correct {only "uplo" part is used} r <- callGeneric(e1@x, e2@x) if(geM) new(paste0(.M.kind(r), "geMatrix"), x = r, Dim = d, Dimnames = dimnames(e1)) else new(paste0(.M.kind(r), Mclass), x = r, Dim = d, Dimnames = dimnames(e1), uplo = e1@uplo) } else { r <- if(!dens1 && !dens2) ## both e1 _and_ e2 are sparse. ## Now (new method dispatch, 2009-01) *does* happen ## even though we have o methods callGeneric(as(e1, "CsparseMatrix"), as(e2, "CsparseMatrix")) else if(dens1 && !dens2) ## go to dense callGeneric(e1, as(e2, "denseMatrix")) else ## if(!dens1 && dens2) callGeneric(as(e1, "denseMatrix"), e2) ## criterion "2 * nnz(.) < ." as in sparseDefault() in Matrix() [./Matrix.R] : if(2 * nnzero(r, na.counted = TRUE) < prod(d)) as(r, "sparseMatrix") else r } } setMethod("Ops", signature(e1 = "dMatrix", e2 = "dMatrix"), Ops.x.x) setMethod("Ops", signature(e1 = "lMatrix", e2 = "lMatrix"), Ops.x.x) ## n*: for "Arith" go via dMatrix, for "Logic" via "lMatrix" setMethod("Compare", signature(e1 = "nMatrix", e2 = "nMatrix"), Ops.x.x) ## l o d : depends on *kind* of Ops -- but Ops.x.x works on slots - correctly: setMethod("Ops", signature(e1="lMatrix", e2="dMatrix"), Ops.x.x) setMethod("Ops", signature(e1="dMatrix", e2="lMatrix"), Ops.x.x) ## lMatrix & nMatrix ... probably should also just use "Matrix" ? ## ## Hmm, the coercion should differ, depending on subgroup ("Logic", "Arith",..) ## --> try to get rid of these setMethod("Ops", signature(e1="lMatrix", e2="numeric"), function(e1,e2) callGeneric(as(e1,"dMatrix"), e2)) setMethod("Ops", signature(e1="numeric", e2="lMatrix"), function(e1,e2) callGeneric(e1, as(e2,"dMatrix"))) setMethod("Ops", signature(e1="nMatrix", e2="numeric"), function(e1,e2) callGeneric(as(e1,"dMatrix"), e2)) setMethod("Ops", signature(e1="numeric", e2="nMatrix"), function(e1,e2) callGeneric(e1, as(e2,"dMatrix"))) ## setMethod("Ops", signature(e1="Matrix", e2="logical"), ## function(e1,e2) callGeneric(as(e1,"lMatrix"), e2)) ## setMethod("Ops", signature(e1="logical", e2="Matrix"), ## function(e1,e2) callGeneric(e1, as(e2,"lMatrix"))) ## "dpoMatrix" / "dppMatrix" : ## Positive-definiteness is lost with all "Ops" but some "Arith" cases for(cl in c("numeric", "logical")) { # "complex", "raw" : basically "replValue" setMethod("Arith", signature(e1 = cl, e2 = "dpoMatrix"), function(e1, e2) if(length(e1) <= 1 && any(.Generic == c("*","/","+")) && (e1 > 0)) { e2@x <- callGeneric(e1, e2@x) ; e2 # remains "dpo" } else ## in all other cases callGeneric(e1, as(e2, "dsyMatrix"))) setMethod("Arith", signature(e1 = cl, e2 = "dppMatrix"), function(e1, e2) if(length(e1) <= 1 && any(.Generic == c("*","/","+")) && (e1 > 0)) { e2@x <- callGeneric(e1, e2@x) ; e2 # remains "dpp" } else ## in all other cases callGeneric(e1, as(e2, "dspMatrix"))) setMethod("Arith", signature(e1 = "dpoMatrix", e2 = cl), function(e1, e2) if(length(e2) <= 1 && any(.Generic == c("*","/","+")) && (e2 > 0)) { e1@x <- callGeneric(e1@x, e2) ; e1 # remains "dpo" } else ## in all other cases callGeneric(as(e1, "dsyMatrix"), e2)) setMethod("Arith", signature(e1 = "dppMatrix", e2 = cl), function(e1, e2) if(length(e2) <= 1 && any(.Generic == c("*","/","+")) && (e2 > 0)) { e1@x <- callGeneric(e1@x, e2) ; e1 # remains "dpp" } else ## in all other cases callGeneric(as(e1, "dspMatrix"), e2)) setMethod("Ops", signature(e1 = cl, e2 = "dpoMatrix"), function(e1, e2) callGeneric(e1, as(e2, "dsyMatrix"))) setMethod("Ops", signature(e1 = cl, e2 = "dppMatrix"), function(e1, e2) callGeneric(e1, as(e2, "dspMatrix"))) setMethod("Ops", signature(e1 = "dpoMatrix", e2 = cl), function(e1, e2) callGeneric(as(e1, "dsyMatrix"), e2)) setMethod("Ops", signature(e1 = "dppMatrix", e2 = cl), function(e1, e2) callGeneric(as(e1, "dspMatrix"), e2)) }# for(cl...) ### -- I -- dense ----------------------------------------------------------- ##-------- originally from ./dgeMatrix.R -------------------- ## ----- only work with NAMESPACE importFrom(methods, ..) setMethod("Arith", signature(e1 = "dgeMatrix", e2 = "dgeMatrix"), ## "+", "-", "*", "^", "%%", "%/%", "/" function(e1, e2) { ## NB: triangular, symmetric, etc may need own method d1 <- e1@Dim d2 <- e2@Dim eqD <- d1 == d2 if (!eqD[1]) stop("Matrices must have same number of rows for arithmetic") same.dim <- eqD[2] if (same.dim) { d <- d1 dn <- dimNamesCheck(e1, e2) } else { # nrows differ ----> maybe recycling if(d2[2] %% d1[2] == 0) { # nrow(e2) is a multiple e1@x <- rep.int(e1@x, d2[2] %/% d1[2]) d <- d2 dn <- e2@Dimnames } else if(d1[2] %% d2[2] == 0) { # nrow(e1) is a multiple e2@x <- rep.int(e2@x, d1[2] %/% d2[2]) d <- d1 dn <- e1@Dimnames } else stop(gettextf("number of rows are not compatible for %s", .Generic), domain=NA) } new("dgeMatrix", Dim = d, Dimnames = dn, x = callGeneric(e1@x, e2@x)) }) A.M.n <- function(e1, e2) { d <- e1@Dim le <- length(e2) if(le == 1 || le == d[1] || prod(d) == le) { # matching dim e1@x <- callGeneric(e1@x, as.vector(e2)) e1 } else stop ("length of 2nd arg does not match dimension of first") } setMethod("Arith", signature(e1 = "dgeMatrix", e2 = "numeric"), A.M.n) setMethod("Arith", signature(e1 = "dgeMatrix", e2 = "logical"), A.M.n) setMethod("Arith", signature(e1 = "dgeMatrix", e2 = "sparseVector"), A.M.n) A.n.M <- function(e1, e2) { d <- e2@Dim le <- length(e1) if(le == 1 || le == d[1] || prod(d) == le) { # matching dim e2@x <- callGeneric(as.vector(e1), e2@x) e2 } else stop ("length of 1st arg does not match dimension of 2nd") } setMethod("Arith", signature(e1 = "numeric", e2 = "dgeMatrix"), A.n.M) setMethod("Arith", signature(e1 = "logical", e2 = "dgeMatrix"), A.n.M) setMethod("Arith", signature(e1 = "sparseVector", e2 = "dgeMatrix"), A.n.M) ## rm(A.M.n, A.n.M) ##-------- originally from ./ddenseMatrix.R -------------------- ## Cheap version: work via "dgeMatrix" and use the group methods there: if(FALSE)## preserve "symmetric", "triangular", --> rather use Ops.x.x setMethod("Arith", signature(e1 = "ddenseMatrix", e2 = "ddenseMatrix"), function(e1, e2) callGeneric(as(e1, "dgeMatrix"), as(e2, "dgeMatrix"))) .Arith.denseM.atom <- function(e1, e2) { ## since e1 = "dgeMatrix" has its own method, we have ## either symmetric or triangular ! d <- e1@Dim le <- length(e2 <- as.vector(e2)) if(le == 1 || le == d[1] || prod(d) == le) { # matching dim if(is(e1, "triangularMatrix")) { r0 <- callGeneric(0, e2) if(all0(r0)) { # result remains triangular if(e1@diag == "U" && !all(1 == callGeneric(1,e2))) e1 <- diagU2N(e1) e1@x <- callGeneric(e1@x, e2) e1 } else { ## result *general* callGeneric(as(e1,"dgeMatrix"), e2) } } else { ## symmetric if(le == 1) { ## result remains symmetric e1@x <- callGeneric(e1@x, e2) e1 } else { ## (le == d[1] || prod(d) == le) ## *might* remain symmetric, but 'x' may contain garbage ## *testing* for symmetry is also a bit expensive ==> simple: callGeneric(as(e1,"dgeMatrix"), e2) } } } else stop ("length of 2nd arg does not match dimension of first") } setMethod("Arith", signature(e1 = "ddenseMatrix", e2 = "numeric"), .Arith.denseM.atom) setMethod("Arith", signature(e1 = "ddenseMatrix", e2 = "logical"), .Arith.denseM.atom) setMethod("Arith", signature(e1 = "ddenseMatrix", e2 = "sparseVector"), .Arith.denseM.atom) .Arith.atom.denseM <- function(e1, e2) { d <- e2@Dim ## note that e2 is either symmetric or triangular here le <- length(e1 <- as.vector(e1)) if(le == 1 || le == d[1] || prod(d) == le) { # matching dim if(is(e2, "triangularMatrix")) { r0 <- callGeneric(e1, 0) if(all0(r0)) { # result remains triangular if(e2@diag == "U" && !all(1 == callGeneric(e1,1))) e2 <- diagU2N(e2) e2@x <- callGeneric(e1, e2@x) e2 } else { # result *general* callGeneric(e1, as(e2,"dgeMatrix")) } } else { ## symmetric if(le == 1) { # result remains symmetric e2@x <- callGeneric(e1, e2@x) e2 } else { ## (le == d[1] || prod(d) == le) ## *might* remain symmetric, but 'x' may contain garbage ## *testing* for symmetry is also a bit expensive ==> simple: callGeneric(e1, as(e2,"dgeMatrix")) } } } else stop ("length of 1st arg does not match dimension of 2nd") } ## setMethod("Arith", signature(e1 = "numeric", e2 = "ddenseMatrix"), ## function(e1, e2) callGeneric(e1, as(e2, "dgeMatrix"))) setMethod("Arith", signature(e1 = "numeric", e2 = "ddenseMatrix"), .Arith.atom.denseM) setMethod("Arith", signature(e1 = "logical", e2 = "ddenseMatrix"), .Arith.atom.denseM) setMethod("Arith", signature(e1 = "sparseVector", e2 = "ddenseMatrix"), .Arith.atom.denseM) ## "Logic" ## ------- ##-------- originally from ./ldenseMatrix.R -------------------- ## These all had "Logic", now also for "Compare", ## but "Arith" differs: result will be "dgeMatrix' : .Ops2dge.via.x <- function(e1,e2) { dimCheck(e1, e2) r <- copyClass(e1, "dgeMatrix", sNames = c("Dim","Dimnames")) r@x <- as.numeric(callGeneric(e1@x, e2@x)) r } setMethod("Compare", signature(e1="lgeMatrix", e2="lgeMatrix"), .Ops.via.x) setMethod("Logic", signature(e1="lgeMatrix", e2="lgeMatrix"), .Ops.via.x) setMethod("Arith", signature(e1="lgeMatrix", e2="lgeMatrix"), .Ops2dge.via.x) setMethod("Compare", signature(e1="ngeMatrix", e2="ngeMatrix"), .Ops.via.x) setMethod("Logic", signature(e1="ngeMatrix", e2="ngeMatrix"), .Ops.via.x) setMethod("Arith", signature(e1="ngeMatrix", e2="ngeMatrix"), .Ops2dge.via.x) ## FIXME: These lose symmmetry & triangularity setMethod("Ops", signature(e1="ldenseMatrix", e2="ldenseMatrix"), function(e1,e2) { dimCheck(e1, e2) callGeneric(as(e1, "lgeMatrix"), as(e2, "lgeMatrix")) }) setMethod("Ops", signature(e1="ndenseMatrix", e2="ndenseMatrix"), function(e1,e2) { dimCheck(e1, e2) callGeneric(as(e1, "ngeMatrix"), as(e2, "ngeMatrix")) }) ## nMatrix -> lMatrix conversions when "the other" is not nMatrix ## Use Ops.x.x unless both are sparse setMethod("Ops", signature(e1="nMatrix", e2="lMatrix"), Ops.x.x) setMethod("Ops", signature(e1="lMatrix", e2="nMatrix"), Ops.x.x) setMethod("Ops", signature(e1="nMatrix", e2="dMatrix"), Ops.x.x) setMethod("Ops", signature(e1="dMatrix", e2="nMatrix"), Ops.x.x) ## ... both are sparse: cannot use Ops.x.x setMethod("Ops", signature(e1="nsparseMatrix", e2="lsparseMatrix"), function(e1,e2) callGeneric(as(e1,"lMatrix"), e2)) setMethod("Ops", signature(e1="lsparseMatrix", e2="nsparseMatrix"), function(e1,e2) callGeneric(e1, as(e2,"lMatrix"))) setMethod("Ops", signature(e1="nsparseMatrix", e2="dsparseMatrix"), function(e1,e2) callGeneric(as(e1,"lMatrix"), e2)) setMethod("Ops", signature(e1="dsparseMatrix", e2="nsparseMatrix"), function(e1,e2) callGeneric(e1, as(e2,"lMatrix"))) ## Have this for "Ops" already above ## setMethod("Logic", signature(e1 = "logical", e2 = "Matrix"), ## function(e1, e2) callGeneric(e1, as(e2, "lMatrix"))) ## setMethod("Logic", signature(e1 = "Matrix", e2 = "logical"), ## function(e1, e2) callGeneric(as(e1, "lMatrix"), e2)) .ll <- function(e1, e2) callGeneric(as(e1,"lMatrix"), as(e2, "lMatrix")) setMethod("Logic", signature(e1 = "nMatrix", e2 = "Matrix"), .ll) setMethod("Logic", signature(e1 = "Matrix", e2 = "nMatrix"), .ll) setMethod("Logic", signature(e1 = "nMatrix", e2 = "nMatrix"), .ll) rm(.ll) ### "ANY" here means "any non-Matrix" (since "Ops"(ANY) has already bailout above): setMethod("Logic", signature(e1 = "ANY", e2 = "Matrix"), function(e1, e2) callGeneric(as.logical(e1), as(e2, "lMatrix"))) setMethod("Logic", signature(e1 = "Matrix", e2 = "ANY"), function(e1, e2) callGeneric(as(e1, "lMatrix"), as.logical(e2))) ## "swap RHS and LHS" and use the method below -- can do this, since ## "Logic" := { "&" , "|" } and both are commutative for(Mcl in c("lMatrix","nMatrix","dMatrix")) for(cl in c("logical", "numeric", "sparseVector")) setMethod("Logic", signature(e1 = cl, e2 = Mcl), function(e1,e2) callGeneric(e2, e1)) ## conceivably "numeric" could use callGeneric(e2, as.logical(e1)) ## but that's not useful at the moment, since Logic.Mat.atomic() does as.logical() ## This is parallel to Cmp.Mat.atomic() above ---> __keep parallel__ ! Logic.Mat.atomic <- function(e1, e2) { ## result will typically be "like" e1: e2 <- as.logical(e2) if(.Generic == "&" && allTrue (e2)) return(as(e1, "lMatrix")) if(.Generic == "|" && allFalse(e2)) return(as(e1, "lMatrix")) d <- e1@Dim cl <- class(e1) if((l2 <- length(e2)) == 0) { if(prod(d) == 0) return(new(class2(cl, "l"), Dim= d)) else stop(gettextf(" %s %s is undefined", .Generic, paste0(class(e2),"(0)")), domain=NA) } cl1 <- getClassDef(cl) slots1 <- names(cl1@slots) has.x <- any("x" == slots1)# *fast* check for "x" slot presence if(l2 > 1 && has.x) ## e2 cannot simply be compared with e1@x --> use another method return(callGeneric(e1, Matrix(e2, nrow=d[1], ncol=d[2]))) ## else Udg <- extends(cl1, "triangularMatrix") && e1@diag == "U" r0 <- callGeneric(0, e2) ## Udg: append the diagonal at *end*, as diagU2N(): r <- callGeneric(if(Udg) c(e1@x,..diag.x(e1)) else if(has.x) e1@x else TRUE, e2) ## trivial case first (beware of NA) if(isTRUE(all(r0) && all(r))) { r <- new(if(d[1] == d[2]) "lsyMatrix" else "lgeMatrix") r@Dim <- d r@Dimnames <- e1@Dimnames r@x <- rep.int(TRUE, prod(d)) } else if(extends(cl1, "denseMatrix")) { full <- !.isPacked(e1) # << both "dtr" and "dsy" are 'full' if(full || allFalse(r0) || extends(cl1, "symmetricMatrix")) { isTri <- extends(cl1, "triangularMatrix") if(isTri) { if(extends(cl1,"Cholesky") || extends(cl1,"BunchKaufman")) cl1 <- getClassDef(cl <- class(e1 <- as(e1, "dtrMatrix"))) } ## FIXME? using copyClass() to copy "relevant" slots r <- new(class2(cl, "l"), x = r, Dim = d, Dimnames = dimnames(e1)) if(extends(cl1, "symmetricMatrix")) { r@uplo <- e1@uplo } else if(isTri) { r@uplo <- e1@uplo r@diag <- e1@diag } } else { ## packed matrix with structural 0 and r0 is not all FALSE: ##--> result cannot be packed anymore ## [dense & packed & not symmetric ] ==> must be "ltp*" : if(!extends(cl1, "ltpMatrix")) stop("internal bug in \"Logic\" method (Logic.Mat.atomic); please report") rx <- rep_len(r0, prod(d)) rx[indTri(d[1], upper = (e1@uplo == "U"), diag=TRUE)] <- r r <- new("lgeMatrix", x = rx, Dim = d, Dimnames = dimnames(e1)) } } else { ##---- e1 is(. , sparseMatrix) ----------------- ## FIXME: remove this test eventually if(extends(cl1, "diagonalMatrix")) stop("Logic.Mat.atomic() should not be called for diagonalMatrix") remainSparse <- allFalse(r0) ## <==> things remain sparse if(Udg) { # e1 *is* unit-diagonal (triangular sparse) r1 <- callGeneric(1, e2) Udg <- all(r1) # maybe Unit-diagonal (sparse) result ## if(!remainSparse) we'll use non0ind() which *has* unit-diag. indices at end ## if(Udg && remainSparse) { } else { ## result will not be unit-diagonal sparse e1 <- .diagU2N(e1, cl = cl1) # otherwise, result is U-diag if(extends(cl1, "CsparseMatrix")) { ## repeat computation if e1 has changed r <- callGeneric(if(has.x) e1@x else TRUE, e2) } } } if(remainSparse) { if(!any(is.na(r)) && ((Ar <- all(r)) || !any(r))) { lClass <- class2(cl, "l") # is "lsparse*" r <- new(lClass) r@Dim <- d r@Dimnames <- dimnames(e1) if(Ar) { # 'TRUE' instead of 'x': same sparsity: for(n in intersect(c("i","j","p","uplo","diag"), slots1)) slot(r, n) <- slot(e1, n) n <- if(has.x) length(e1@x) else if(any("p" == slots1)) e1@p[d[2]+1L] else length(e1@i) r@x <- rep.int(TRUE, n) } else { ## !any(r): all FALSE: keep empty 'r' matrix ## but may need a valid 'pointer' slot: if(extends(lClass, "CsparseMatrix")) r@p <- rep.int(0L, 1+ncol(r)) else if(extends(lClass, "RsparseMatrix")) r@p <- rep.int(0L, 1+nrow(r)) } } else { # some TRUE, FALSE, NA : go via unique 'Tsparse' M <- asTuniq(e1) nCl <- class2(class(M), 'l') # logical Tsparse sN <- slotNames(nCl) ## copy "the other slots" (important for "tr"/"sym"): r <- copyClass(M, nCl, sNames = sN[is.na(match(sN, "x"))]) r@x <- callGeneric(if(has.x) M@x else TRUE, e2) if(extends(cl1, "CsparseMatrix")) r <- as(r, "CsparseMatrix") else if(extends(cl1, "RsparseMatrix")) r <- as(r, "RsparseMatrix") } } else { ## non sparse result lClass <- if(extends(cl1, "symmetricMatrix")) "lsyMatrix" else "lgeMatrix" Matrix.msg(sprintf("sparse to dense (%s) coercion in '%s' -> %s", lClass, .Generic, "Logic.Mat.atomic"), .M.level = 2) rx <- rep_len(r0, prod(d)) ## Here, we assume that 'r' and the indices align (!) encI <- .Call(m_encodeInd, non0ind(e1, cl1, uniqT=FALSE, xtendSymm=FALSE), di = d, checkBounds = FALSE) rx[1L + encI] <- r r <- new(lClass, x = rx, Dim = d, Dimnames = dimnames(e1)) } } r } for(Mcl in c("lMatrix","nMatrix","dMatrix")) for(cl in c("logical", "numeric", "sparseVector")) setMethod("Logic", signature(e1 = Mcl, e2 = cl), Logic.Mat.atomic) ### -- II -- sparse ---------------------------------------------------------- ## Have lgC o lgC and then lgT o lgT Logic - quite similarly - ## also lsC o * and ltC o * : ## Here's the common functionality .do.Logic.lsparse <- function(e1,e2, d, dn, isOR, ij1, ij2) { ## NB non-diagonalMatrix := Union{ general, symmetric, triangular} gen1 <- extends(cD1 <- getClassDef(class(e1)), "generalMatrix") gen2 <- extends(cD2 <- getClassDef(class(e2)), "generalMatrix") sym1 <- !gen1 && extends(cD1, "symmetricMatrix") sym2 <- !gen2 && extends(cD2, "symmetricMatrix") tri1 <- !gen1 && !sym1 tri2 <- !gen2 && !sym2 G <- gen1 && gen2 S <- sym1 && sym2 && e1@uplo == e2@uplo T <- tri1 && tri2 && e1@uplo == e2@uplo if(T && e1@diag != e2@diag) { ## one is "U" the other "N" if(e1@diag == "U") e1 <- diagU2N(e1) else ## (e2@diag == "U" e2 <- diagU2N(e2) shape <- "t" } else if(!G && !S && !T) { ## e.g. one symmetric, one general ## coerce to generalMatrix and go : if(!gen1) e1 <- as(e1, "generalMatrix", strict = FALSE) if(!gen2) e2 <- as(e2, "generalMatrix", strict = FALSE) shape <- "g" } else { shape <- if(T) "t" else if(S) "s" else "g" } ii <- WhichintersectInd(ij1, ij2, di=d) I1 <- ii[[1]] ; has1 <- length(I1) > 0 I2 <- ii[[2]] ; has2 <- length(I2) > 0 ## 1) common indices i <- ij1[I1, 1] j <- ij1[I1, 2] if(isOR) { ## i.e. .Generic == "|" i.e. not "&" x <- e1@x[I1] | e2@x[I2] ## 2) "e1 o FALSE": x2 <- if(has1) e1@x[- I1] else e1@x # == callGeneric(e1@x[- I1], FALSE) ## 3) "0 o e1": x3 <- if(has2) e2@x[- I2] else e2@x # == callGeneric(FALSE, e2@x[- I2]) i <- c(i, if(has1) ij1[-I1, 1] else ij1[, 1], if(has2) ij2[-I2, 1] else ij2[, 1]) j <- c(j, if(has1) ij1[-I1, 2] else ij1[, 2], if(has2) ij2[-I2, 2] else ij2[, 2]) x <- c(x, x2, x3) } else { ## AND x <- e1@x[I1] & e2@x[I2] } if(any(!(x. <- x | is.na(x)))) { ## drop 'FALSE's i <- i[x.] j <- j[x.] x <- x[x.] } new(paste0("l",shape,"TMatrix"), Dim = d, Dimnames = dn, i = i, j = j, x = x) } Logic.lCMat <- function(e1, e2, isOR) { stopifnot(is.logical(isOR)) d <- dimCheck(e1, e2) dn <- dimNamesCheck(e1, e2) ## Very easy case first : if(identical(e1@i, e2@i) && identical(e1@p, e2@p)) { e1@x <- if(isOR) e1@x | e2@x else e1@x & e2@x return(e1) } ## else : .Call(Tsparse_to_Csparse, .do.Logic.lsparse(e1, e2, d = d, dn = dn, isOR = isOR, ij1 = .Call(compressed_non_0_ij, e1, TRUE), ij2 = .Call(compressed_non_0_ij, e2, TRUE)), FALSE) } m.Logic.lCMat <- function(e1, e2) Logic.lCMat(e1, e2, isOR = .Generic == "|") Logic.lTMat <- function(e1,e2) { d <- dimCheck(e1, e2) dn <- dimNamesCheck(e1, e2) ## Very easy case first : if(identical(e1@i, e2@i) && identical(e1@j, e2@j)) { e1@x <- callGeneric(e1@x, e2@x) return(e1) } ## else : cld <- getClassDef(class(e1)) .do.Logic.lsparse(e1, e2, d = d, dn = dn, isOR = .Generic == "|", ij1 = non0ind(e1, cld), ij2 = non0ind(e2, cld)) } setMethod("Logic", signature(e1="lgCMatrix", e2="lgCMatrix"), m.Logic.lCMat) setMethod("Logic", signature(e1="lgTMatrix", e2="lgTMatrix"), Logic.lTMat) setMethod("Logic", signature(e1 = "lsCMatrix", e2 = "lsCMatrix"), function(e1, e2) { if(e1@uplo == e2@uplo) Logic.lCMat(e1, e2, isOR = .Generic == "|") else Logic.lCMat(e1, t(e2), isOR = .Generic == "|") }) setMethod("Logic", signature(e1 = "ltCMatrix", e2 = "ltCMatrix"), function(e1, e2) { if(e1@uplo == e2@uplo) { if(e1@diag == e2@diag) ## both "N" or both "U" (!) Logic.lCMat(e1, e2, isOR = .Generic == "|") else if(e1@diag == "U") Logic.lCMat(diagU2N(e1), e2, isOR = .Generic == "|") else ## e1@diag == "N" *and* e2@diag == "U" Logic.lCMat(e1, diagU2N(e2), isOR = .Generic == "|") } else { d <- dimCheck(e1, e2) ## differing triangle (upper <-> lower): ## all will be FALSE apart from diagonal as(.diag2tT(new("ldiMatrix", Dim=d, x = get(.Generic)(diag(e1), diag(e2))), uplo = e1@uplo, kind = "l"), "dtCMatrix") } }) ## Now the other "Ops" for the "lgT" and "lgC" cases: setMethod("Arith", signature(e1="lgCMatrix", e2="lgCMatrix"), function(e1, e2) callGeneric(as(e1, "dgCMatrix"), as(e2, "dgCMatrix"))) setMethod("Arith", signature(e1="lgTMatrix", e2="lgTMatrix"), function(e1, e2) callGeneric(as(e1, "dgTMatrix"), as(e2, "dgTMatrix"))) ## More generally: Arith: l* and n* via d* setMethod("Arith", signature(e1="lsparseMatrix", e2="Matrix"), function(e1, e2) callGeneric(as(e1, "dMatrix"), as(e2,"dMatrix"))) setMethod("Arith", signature(e1="Matrix", e2="lsparseMatrix"), function(e1, e2) callGeneric(as(e1, "dMatrix"), as(e2,"dMatrix"))) setMethod("Arith", signature(e1="nsparseMatrix", e2="Matrix"), function(e1, e2) callGeneric(as(e1, "dMatrix"), as(e2,"dMatrix"))) setMethod("Arith", signature(e1="Matrix", e2="nsparseMatrix"), function(e1, e2) callGeneric(as(e1, "dMatrix"), as(e2,"dMatrix"))) ## for(cl in c("numeric", "logical")) # "complex", "raw" : basically "replValue" for(Mcl in c("lMatrix", "nMatrix")) { setMethod("Arith", signature(e1=Mcl, e2=cl), function(e1, e2) callGeneric(as(e1, "dMatrix"), e2)) setMethod("Arith", signature(e1=cl, e2=Mcl), function(e1, e2) callGeneric(e1, as(e2,"dMatrix"))) } rm(cl, Mcl) ## FIXME: These are really too cheap: currently almost all go via dgC*() : ## setMethod("Compare", signature(e1="lgCMatrix", e2="lgCMatrix"), ## setMethod("Compare", signature(e1="lgTMatrix", e2="lgTMatrix"), ## setMethod("Compare", signature(e1="lsparseMatrix", e2="lsparseMatrix"), ## function(e1, e2) callGeneric(as(e1, "dgCMatrix"), as(e2, "dgCMatrix"))) ##. Have "Ops" below which only goes *conditionally* via Csparse ##. setMethod("Compare", signature(e1="lsparseMatrix", e2="lsparseMatrix"), ##. function(e1, e2) callGeneric(as(e1, "CsparseMatrix"), ##. as(e2, "CsparseMatrix"))) ## setMethod("Compare", signature(e1="lgTMatrix", e2="lgTMatrix"), ## coerce to Csparse ## function(e1, e2) callGeneric(as(e1, "dgCMatrix"), as(e2, "dgCMatrix"))) ###--- Sparse ... ---------- setMethod("Ops", signature(e1="lsparseMatrix", e2="lsparseMatrix"), function(e1,e2) callGeneric(as(e1, "CsparseMatrix"), as(e2, "CsparseMatrix"))) setMethod("Logic", signature(e1="lsparseMatrix", e2="ldenseMatrix"), function(e1,e2) callGeneric(as(e1, "generalMatrix"), as(e2, "sparseMatrix"))) setMethod("Logic", signature(e1="ldenseMatrix", e2="lsparseMatrix"), function(e1,e2) callGeneric(as(e1, "sparseMatrix"), as(e2, "generalMatrix"))) setMethod("Logic", signature(e1="lsparseMatrix", e2="lsparseMatrix"), function(e1,e2) { if(!is(e1,"generalMatrix")) callGeneric(as(as(e1, "generalMatrix"), "CsparseMatrix"), e2) else if(!is(e2,"generalMatrix")) callGeneric(e1, as(as(e2, "generalMatrix"), "CsparseMatrix")) else callGeneric(as(e1, "lgCMatrix"), as(e2, "lgCMatrix")) }) ## FIXME: also want (symmetric o symmetric) , (triangular o triangular) ## ----- setMethod("Arith", signature(e1 = "dsCMatrix", e2 = "dsCMatrix"), function(e1, e2) { Matrix.msg("suboptimal 'Arith' implementation of 'dsC* o dsC*'") forceSymmetric(callGeneric(as(e1, "dgCMatrix"), as(e2, "dgCMatrix"))) }) ##-------- originally from ./dgCMatrix.R -------------------- .Arith.Csparse <- function(e1, e2, Generic, class., triangular = FALSE) { ## Generic is one of "+", "-", "*", "^", "%%", "%/%", "/" ## triangular: TRUE iff e1,e2 are triangular _and_ e1@uplo == e2@uplo d <- dimCheck(e1, e2) dn <- dimNamesCheck(e1, e2) if(triangular) { ## need these for the 'x' slots in any case if (e1@diag == "U") e1 <- .Call(Csparse_diagU2N, e1) if (e2@diag == "U") e2 <- .Call(Csparse_diagU2N, e2) ## slightly more efficient than non0.i() or non0ind(): ij1 <- .Call(compressed_non_0_ij, e1, isC=TRUE) ij2 <- .Call(compressed_non_0_ij, e2, isC=TRUE) newTMat <- function(i,j,x) new("dtTMatrix", Dim = d, Dimnames = dn, i = i, j = j, x = x, uplo = e1@uplo) dmat <- "dtrMatrix" } else { cld <- getClassDef(class.) ij1 <- non0ind(e1, cld) ij2 <- non0ind(e2, cld) newTMat <- function(i,j,x) new("dgTMatrix", Dim = d, Dimnames = dn, i = i, j = j, x = x) dmat <- "dgeMatrix" } switch(Generic, "+" = , "-" = { ## care for over-allocated 'x' slot: nc1 <- d[2] + 1L if((nz <- e1@p[nc1]) < length(e1@x)) e1@x <- e1@x[seq_len(nz)] if((nz <- e2@p[nc1]) < length(e2@x)) e2@x <- e2@x[seq_len(nz)] ## special "T" convention: repeated entries are *summed* .Call(Tsparse_to_Csparse, newTMat(i = c(ij1[,1], ij2[,1]), j = c(ij1[,2], ij2[,2]), x = if(Generic == "+") c(e1@x, e2@x) else c(e1@x, - e2@x)), triangular) }, "*" = { ## X * 0 == 0 * X == 0 --> keep common non-0 ii <- WhichintersectInd(ij1, ij2, di=d) ij <- ij1[ii[[1]], , drop = FALSE] .Call(Tsparse_to_Csparse, newTMat(i = ij[,1], j = ij[,2], x = e1@x[ii[[1]]] * e2@x[ii[[2]]]), triangular) }, "^" = { ii <- WhichintersectInd(ij1, ij2, di=d) ## 3 cases: ## 1) X^0 := 1 (even for X=0) ==> dense ## 2) 0^Y := 0 for Y != 0 ===== ## 3) x^y : ## FIXME: dgeM[cbind(i,j)] <- V is not yet possible ## nor dgeM[ i_vect ] <- V ## r <- as(e2, "dgeMatrix") ## ... r <- as(e2, "matrix") Yis0 <- is0(r) r[complementInd(ij1, dim=d)] <- 0 ## 2) r[1L + ij2[ii[[2]], , drop=FALSE]] <- e1@x[ii[[1]]] ^ e2@x[ii[[2]]] ## 3) r[Yis0] <- 1 ## 1) as(r, dmat) }, "%%" = , "%/%" = , "/" = ## 0 op 0 |-> NaN => dense get(Generic)(as(e1, dmat), e2) )# end{switch(..)} } setMethod("Arith", signature(e1 = "dgCMatrix", e2 = "dgCMatrix"), function(e1,e2) .Arith.Csparse(e1,e2, .Generic, class.= "dgCMatrix")) setMethod("Arith", signature(e1 = "dtCMatrix", e2 = "dtCMatrix"), function(e1, e2) { U1 <- e1@uplo isTri <- U1 == e2@uplo && .Generic != "^" # will the result definitely be triangular? if(isTri) { .Arith.Csparse(e1,e2, .Generic, class. = "dtCMatrix", triangular = TRUE) } else { ## lowerTri o upperTri: |--> "all 0" {often} -- FIXME? .Arith.Csparse(as(e1, "dgCMatrix"), as(e2, "dgCMatrix"), .Generic, class.= "dgCMatrix") } }) ## TODO : Consider going a level up, and do this for all "Ops" ## ## NB: For "dgCMatrix" have special method ==> this is for dsC*, lgC*, ... ## now also for Tsparse etc {*must* as method directly: "callGeneric()"} .Arith.CM.atom <- function(e1, e2) { if(length(e2) == 1) { ## e.g., Mat ^ a f0 <- callGeneric(0, e2) if(is0(f0)) { ## remain sparse, symm., tri.,... e1 <- as(e1, "dMatrix") if(!extends(cld <- getClassDef(class(e1)), "CsparseMatrix")) cld <- getClassDef(class(e1 <- as(e1, "CsparseMatrix"))) if(extends(cld, "triangularMatrix") && e1@diag == "U" && !all(1 == callGeneric(1, e2))) e1 <- .diagU2N(e1, cld) e1@x <- callGeneric(e1@x, e2) if(extends(cld, "compMatrix") && length(e1@factors)) ## TODO: be much smarter and try *updating* (some) 'factors': e1@factors <- list() return(e1) } } ## all other (potentially non-sparse) cases: give up symm, tri,.. callGeneric(as(as(as(e1, "dMatrix"), "CsparseMatrix"), "dgCMatrix"), e2) } ## The same, e1 <-> e2 : .Arith.atom.CM <- function(e1, e2) { if(length(e1) == 1) { f0 <- callGeneric(e1, 0) if(is0(f0)) { e2 <- as(e2, "dMatrix") if(!extends(cld <- getClassDef(class(e2)), "CsparseMatrix")) cld <- getClassDef(class(e2 <- as(e2, "CsparseMatrix"))) if(extends(cld, "triangularMatrix") && e2@diag == "U" && !all(1 == callGeneric(e1, 1))) e2 <- .diagU2N(e2, cld) e2@x <- callGeneric(e1, e2@x) if(extends(cld, "compMatrix") && length(e2@factors)) ## TODO: be much smarter and try *updating* (some) 'factors': e2@factors <- list() return(e2) } } callGeneric(e1, as(as(as(e2, "dMatrix"), "CsparseMatrix"), "dgCMatrix")) } setMethod("Arith", signature(e1 = "CsparseMatrix", e2 = "numeric"), .Arith.CM.atom) setMethod("Arith", signature(e1 = "numeric", e2 = "CsparseMatrix"), .Arith.atom.CM) .Ops.recycle.ind <- function(spM, len) { n <- prod(d <- dim(spM)) if(n < len) stop("vector too long in Matrix - vector operation") if(n %% len != 0) ## identical warning as in main/arithmetic.c warning("longer object length\n\tis not a multiple of shorter object length") ## TODO(speedup!): construction of [1L + in0 %%len] via one .Call() in0 <- .Call(m_encodeInd, .Call(compressed_non_0_ij, spM, TRUE), d, FALSE) 1L + in0 %% len } A.M.n <- function(e1, e2) { if((l2 <- length(e2)) == 0) stop(gettextf(" %s %s is undefined", .Generic, paste0(class(e2),"(0)")), domain=NA) is0f <- is0(f0 <- callGeneric(0, e2)) if(all(is0f)) { ## result keeps sparseness structure of e1 if(l2 > 1) { # "recycle" e2 "carefully" e2 <- e2[.Ops.recycle.ind(e1, len = l2)] } e1@x <- callGeneric(e1@x, e2) if(length(e1@factors)) # TODO: be smarter and try *updating* (some) 'factors': e1@factors <- list() e1 } else if(mean(is0f) > 7/8) { ## remain sparse ['7/8' is *somewhat* arbitrary] if(l2 > 1) ## as not all callGeneric(0, e2) is 0, e2 is typically sparse callGeneric(e1, as(e2, "sparseVector")) else { ## l2 == 1: e2 is "scalar" e1@x <- callGeneric(e1@x, e2) if(length(e1@factors)) # TODO: be smarter (see above) e1@factors <- list() e1 } } else { ## non-sparse, since '0 o e2' is not (all) 0 r <- as(e1, "matrix") if(length(e2) == 1) { r[] <- f0 r[non0ind(e1, getClassDef("dgCMatrix")) + 1L] <- callGeneric(e1@x, e2) ..2dge(r) } else { as(callGeneric(r, e2), "dgeMatrix") } } } setMethod("Arith", signature(e1 = "dgCMatrix", e2 = "numeric"), A.M.n) setMethod("Arith", signature(e1 = "dgCMatrix", e2 = "logical"), A.M.n) ## coercing to "general*" / "dgC*" would e.g. lose symmetry of 'S * 3' setMethod("Arith", signature(e1 = "dsparseMatrix", e2 = "numeric"), .Arith.CM.atom) setMethod("Arith", signature(e1 = "dsparseMatrix", e2 = "logical"), .Arith.CM.atom) A.n.M <- function(e1, e2) { if((l1 <- length(e1)) == 0) stop(gettextf("%s %s is undefined", paste0(class(e2),"(0)"), .Generic), domain=NA) is0f <- is0(f0 <- callGeneric(e1, 0)) if(all(is0f)) { ## result keeps sparseness structure of e2 if(l1 > 1) { # "recycle" e1 "carefully" e1 <- e1[.Ops.recycle.ind(e2, len = l1)] } e2@x <- callGeneric(e1, e2@x) if(length(e2@factors))# TODO: be much smarter and try *updating* (some) 'factors': e2@factors <- list() e2 } else if(mean(is0f) > 7/8) { ## remain sparse ['7/8' is *somewhat* arbitrar if(l1 > 1) ## as not all callGeneric(e1, 0) is 0, e1 is typically sparse callGeneric(as(e1, "sparseVector"), e2) else { ## l1 == 1: e1 is "scalar" e2@x <- callGeneric(e1, e2@x) if(length(e2@factors))# TODO: be much smarter (see above) e2@factors <- list() e2 } } else { ## non-sparse, since '0 o e2' is not (all) 0 r <- as(e2, "matrix") if(length(e1) == 1) { r[] <- f0 r[non0ind(e2, getClassDef("dgCMatrix")) + 1L] <- callGeneric(e1, e2@x) ..2dge(r) } else { as(callGeneric(e1, r), "dgeMatrix") } } } setMethod("Arith", signature(e1 = "numeric", e2 = "dgCMatrix"), A.n.M) setMethod("Arith", signature(e1 = "logical", e2 = "dgCMatrix"), A.n.M) ## coercing to "general*" / "dgC*" would e.g. lose symmetry of '3 * S' setMethod("Arith", signature(e1 = "numeric", e2 = "dsparseMatrix"), .Arith.atom.CM) setMethod("Arith", signature(e1 = "logical", e2 = "dsparseMatrix"), .Arith.atom.CM) rm(A.M.n, A.n.M) ##-------- originally from ./Csparse.R -------------------- setMethod("Arith", signature(e1 = "CsparseMatrix", e2 = "CsparseMatrix"), function(e1, e2) { ## go via "symmetric" if both are symmetric, etc... s1 <- .M.shape(e1, getClassDef(class(e1))) s2 <- .M.shape(e2, getClassDef(class(e2))) viaCl <- paste0("d", if(s1 == s2) s1 else "g", "CMatrix") callGeneric(as(as(e1, "dMatrix"), viaCl), as(as(e2, "dMatrix"), viaCl)) }) setMethod("Logic", signature(e1 = "CsparseMatrix", e2 = "CsparseMatrix"), function(e1, e2) { ## go via "symmetric" if both are symmetric, etc... s1 <- .M.shape(e1, getClassDef(class(e1))) s2 <- .M.shape(e2, getClassDef(class(e2))) viaCl <- paste0("l", if(s1 == s2) s1 else "g", "CMatrix") callGeneric(as(as(e1, "lMatrix"), viaCl), as(as(e2, "lMatrix"), viaCl)) }) setMethod("Compare", signature(e1 = "CsparseMatrix", e2 = "CsparseMatrix"), function(e1, e2) { d <- dimCheck(e1,e2) ## How do the "0" or "FALSE" entries compare? ## Depends if we have an "EQuality RELation" or not: EQrel <- switch(.Generic, "==" =, "<=" =, ">=" = TRUE, "!=" =, "<" =, ">" = FALSE) if(EQrel) { ## The (0 op 0) or (FALSE op FALSE) comparison gives TRUE ## -> result becomes *dense*; the following may be suboptimal return( callGeneric(as(e1, "denseMatrix"), as(e2, "denseMatrix"))) } ## else: INequality: 0 op 0 gives FALSE ---> remain sparse! cD1 <- getClassDef(class(e1)) cD2 <- getClassDef(class(e2)) Matrix.msg(sprintf("Compare -- \"%s\" %s \"%s\" :\n", cD1@className, .Generic, cD2@className), .M.level = 2) ## NB non-diagonalMatrix := Union{ general, symmetric, triangular} gen1 <- extends(cD1, "generalMatrix") gen2 <- extends(cD2, "generalMatrix") sym1 <- !gen1 && extends(cD1, "symmetricMatrix") sym2 <- !gen2 && extends(cD2, "symmetricMatrix") tri1 <- !gen1 && !sym1 tri2 <- !gen2 && !sym2 G <- gen1 && gen2 S <- sym1 && sym2 && e1@uplo == e2@uplo T <- tri1 && tri2 && e1@uplo == e2@uplo if(T && e1@diag != e2@diag) { ## one is "U" the other "N" if(e1@diag == "U") e1 <- diagU2N(e1) else ## (e2@diag == "U" e2 <- diagU2N(e2) shape <- "t" } else if(!G && !S && !T) { ## e.g. one symmetric, one general ## coerce to generalMatrix and go : if(!gen1) e1 <- as(e1, "generalMatrix", strict = FALSE) if(!gen2) e2 <- as(e2, "generalMatrix", strict = FALSE) shape <- "g" } else { shape <- if(T) "t" else if(S) "s" else "g" } dn <- dimNamesCheck(e1, e2) ## the result object: newC <- sub("^.", "l", MatrixClass(class(e1))) ## FIXME: "n" result when e1 & e2 are "n", or even whenever possible r <- new(newC) e1is.n <- extends(cD1, "nMatrix") e2is.n <- extends(cD2, "nMatrix") ## Easy case: identical sparsity pattern if(identical(e1@i, e2@i) && identical(e1@p, e2@p)) { if(e1is.n) { if(e2is.n) ## non-equality of identical pattern matrices: all FALSE r@p <- rep.int(0L, d[2]+1L) # and r@i, r@x remain empty else { ## e1 pattern, e2@x rx <- callGeneric(TRUE, e2@x) if(allFalse(rx)) r@p <- rep.int(0L, d[2]+1L) # and r@i, r@x remain empty else { r@x <- rx r@i <- e2@i r@p <- e2@p } } } else if(e2is.n) { ## e1@x, e2 pattern rx <- callGeneric(e1@x, TRUE) if(allFalse(rx)) r@p <- rep.int(0L, d[2]+1L) # and r@i, r@x remain empty else { r@x <- rx r@i <- e1@i r@p <- e1@p } } else { # both have 'x' slot r@x <- callGeneric(e1@x, e2@x) ## and all others are '0 op 0' which give FALSE r@i <- e1@i r@p <- e1@p } r@Dim <- d r@Dimnames <- dn r } else { ## now the 'x' slots ``match'' insofar as they are for the ## same "space" (triangle for tri* and symm*; else rectangle) ## not non0ind() which gives more; ## want only those which correspond to 'x' slot ij1 <- .Call(compressed_non_0_ij, e1, TRUE) ij2 <- .Call(compressed_non_0_ij, e2, TRUE) ii <- WhichintersectInd(ij1, ij2, di=d) I1 <- ii[[1]]; has1 <- length(I1) > 0 I2 <- ii[[2]]; has2 <- length(I2) > 0 ## potentially could be faster for 'nsparse' but this is simple: e1x <- if(e1is.n) rep.int(1L, length(e1@i)) else e1@x e2x <- if(e2is.n) rep.int(1L, length(e2@i)) else e2@x ## 1) common x <- callGeneric(e1x[I1], e2x[I2]) ## 2) "e1 o 0": x2 <- callGeneric(if(has1) e1x[- I1] else e1x, 0) ## 3) "0 o e2": x3 <- callGeneric(0, if(has2) e2x[- I2] else e2x) i <- c(ij1[I1, 1], if(has1) ij1[-I1, 1] else ij1[, 1], if(has2) ij2[-I2, 1] else ij2[, 1]) j <- c(ij1[I1, 2], if(has1) ij1[-I1, 2] else ij1[, 2], if(has2) ij2[-I2, 2] else ij2[, 2]) x <- c(x, x2, x3) if(any(i0x <- is0(x))) { # drop 'FALSE's n0 <- !i0x i <- i[n0] j <- j[n0] x <- x[n0] } .Call(Tsparse_to_Csparse, if(e1is.n && e2is.n) new(paste0("n",shape,"TMatrix"), Dim = d, Dimnames = dn, i = i, j = j) else new(paste0("l",shape,"TMatrix"), Dim = d, Dimnames = dn, i = i, j = j, x = x), FALSE) } }) ##-------- originally from ./sparseMatrix.R -------------------- ## "Arith" short cuts / exceptions setMethod("-", signature(e1 = "sparseMatrix", e2 = "missing"), function(e1, e2) { e1 <- diagU2N(e1); e1@x <- -e1@x; e1 }) ## with the following exceptions: setMethod("-", signature(e1 = "nsparseMatrix", e2 = "missing"), function(e1,e2) callGeneric(as(as(as(e1, "CsparseMatrix"), "dMatrix"), "dgCMatrix"))) setMethod("-", signature(e1 = "pMatrix", e2 = "missing"), function(e1,e2) callGeneric(as(e1, "ngTMatrix"))) ## Group method "Arith" ## have CsparseMatrix methods above ## which may preserve "symmetric", "triangular" -- simply defer to those: setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "nsparseMatrix"), function(e1, e2) callGeneric(as(e1, "CsparseMatrix"), as(e2, "lsparseMatrix"))) setMethod("Ops", signature(e1 = "nsparseMatrix", e2 = "sparseMatrix"), function(e1, e2) callGeneric(as(e1, "lsparseMatrix"), as(e2, "CsparseMatrix"))) ## these were 'Arith', now generalized: if(FALSE) { ## just shifts the ambiguity warnings .. ## o more complicated - against PITA disambiguation warnings: setMethod("Ops", signature(e1 = "TsparseMatrix", e2 = "TsparseMatrix"), function(e1, e2) callGeneric(as(e1, "CsparseMatrix"), as(e2, "CsparseMatrix"))) setMethod("Ops", signature(e1 = "TsparseMatrix", e2 = "CsparseMatrix"), function(e1, e2) callGeneric(as(e1, "CsparseMatrix"), e2)) setMethod("Ops", signature(e1 = "CsparseMatrix", e2 = "TsparseMatrix"), function(e1, e2) callGeneric(e1, as(e2, "CsparseMatrix"))) } ## catch the rest: Rsparse* and T* o R* setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "sparseMatrix"), function(e1, e2) callGeneric(as(e1, "CsparseMatrix"), as(e2, "CsparseMatrix"))) setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "numeric"), function(e1, e2) callGeneric(as(e1, "CsparseMatrix"), e2)) setMethod("Ops", signature(e1 = "numeric", e2 = "sparseMatrix"), function(e1, e2) callGeneric(e1, as(e2, "CsparseMatrix"))) ## setMethod("Compare", signature(e1 = "sparseMatrix", e2 = "sparseMatrix"), ## function(e1, e2) callGeneric(as(e1, "CsparseMatrix"), ## as(e2, "CsparseMatrix"))) ###-------- sparseVector ------------- ###-------- ============ ------------- ## Catch all remaining setMethod("Ops", signature(e1 = "sparseVector", e2 = "ANY"), function(e1, e2) .bail.out.2(.Generic, class(e1), class(e2))) setMethod("Ops", signature(e1 = "ANY", e2 = "sparseVector"), function(e1, e2) .bail.out.2(.Generic, class(e1), class(e2))) ## 1) spVec o (sp)Vec : ------------- ## FIXME: ## 2. o should also happen directly and ## |-> sparse for o = {'*', "/", '&&', '==', ... setMethod("Ops", signature(e1 = "sparseVector", e2 = "atomicVector"), function(e1, e2) { if(length(e2) == 1) { ## scalar ------ special case - "fast" if(all0(rf <- callGeneric(FALSE, e2))) { # result remains sparse if(is(e1, "nsparseVector")) { # no 'x' slot, i.e. all TRUE r <- callGeneric(TRUE, e2) if(is.logical(r)) { if(isTRUE(at <- all(r))) # (could be NA) e1 # result unchanged else newSpVec("lsparseVector", x = r, e1) } else { newSpVec(paste0(if(is.integer(r)) "i" else "d", "sparseVector"), x = r, e1) } } else { # has x slot r <- callGeneric(e1@x, e2) if(identical(class(r), class(e1@x))) { e1@x <- r e1 } else { newSpVec(paste0(.V.kind(r), "sparseVector"), x = r, e1) } } } else ## non-sparse result callGeneric(sp2vec(e1), e2) } else ## e2 is not scalar callGeneric(e1, as(e2, "sparseVector")) }) setMethod("Ops", signature(e1 = "atomicVector", e2 = "sparseVector"), function(e1, e2) { if(length(e1) == 1) { ## scalar ------ special case - "fast" if(all0(rf <- callGeneric(e1, FALSE))) { # result remains sparse if(is(e2, "nsparseVector")) { # no 'x' slot, i.e. all TRUE r <- callGeneric(e1, TRUE) if(is.logical(r)) { if(isTRUE(at <- all(r))) # (could be NA) e2 # result unchanged else newSpVec("lsparseVector", x = r, e2) } else { newSpVec(paste0(if(is.integer(r)) "i" else "d", "sparseVector"), x = r, e2) } } else { # has x slot r <- callGeneric(e1, e2@x) if(identical(class(r), class(e2@x))) { e2@x <- r e2 } else { newSpVec(paste0(.V.kind(r), "sparseVector"), x = r, e2) } } } else ## non-sparse result callGeneric(e1, sp2vec(e2)) } else ## e1 is not scalar callGeneric(as(e1, "sparseVector"), e2) }) Ops.spV.spV <- function(e1, e2) { n1 <- e1@length n2 <- e2@length if(n1 != n2) { if(n1 < n2) { n <- n1 ; N <- n2 } else { n <- n2 ; N <- n1 } if(n == 1) { # simple case, do not really recycle if(n1 < n2) return(callGeneric(sp2vec(e1), e2)) else return(callGeneric(e1, sp2vec(e2))) } ## else : 2 <= n < N if(N %% n != 0) warning("longer object length\n\t", "is not a multiple of shorter object length") ## recycle the shorter one if(n1 < n2) { e1 <- rep(e1, length = N) } else { e2 <- rep(e2, length = N) } } else { ## n1 == n2 N <- n1 } ## ---- e1 & e2 now are both of length 'N' ---- ## First check the (0 o 0) result is1n <- extends(class(e1), "nsparseVector") is2n <- extends(class(e2), "nsparseVector") r00 <- callGeneric(if(is1n) FALSE else as0(e1@x), if(is2n) FALSE else as0(e2@x)) if(is0(r00)) { ## -> sparseVector e1x <- if(is1n) TRUE else e1@x e2x <- if(is2n) TRUE else e2@x sp <- .setparts(e1@i, e2@i) ## Idea: Modify 'e2' and return it : new.x <- c(callGeneric(e1x[sp[["ix.only"]]], 0), # e1-only callGeneric(0, e2x[sp[["iy.only"]]]), # e2-only callGeneric(e1x[sp[["my"]]], # common to both e2x[sp[["mx"]]])) i. <- c(sp[["x.only"]], sp[["y.only"]], sp[["int"]]) cl2x <- typeof(e2x) ## atomic "class"es - can use in is(), as(), too: if(!is2n && is(new.x, cl2x)) { i. <- sort.int(i., method = "quick", index.return=TRUE) e2@x <- as(new.x, cl2x)[i.$ix] e2@i <- i.$x e2 } else { newSpV(paste0(.kind.type[typeof(new.x)],"sparseVector"), x = new.x, i = i., length = e2@length) } } else { ## 0 o 0 is NOT in {0 , FALSE} --> "dense" result callGeneric(sp2vec(e1), sp2vec(e2)) } } ## {Ops.spV.spV} ## try to use it in all cases setMethod("Ops", signature(e1 = "sparseVector", e2 = "sparseVector"), Ops.spV.spV) ## was function(e1, e2) .bail.out.2(.Generic, class(e1), class(e2))) setMethod("Arith", signature(e1 = "sparseVector", e2 = "sparseVector"), function(e1, e2) callGeneric(as(e1, "dsparseVector"), as(e2, "dsparseVector"))) setMethod("Arith", signature(e1 = "dsparseVector", e2 = "dsparseVector"), Ops.spV.spV) ## "Arith" exception (shortcut) setMethod("-", signature(e1 = "dsparseVector", e2 = "missing"), function(e1) { e1@x <- -e1@x ; e1 }) setMethod("Logic", signature(e1 = "sparseVector", e2 = "sparseVector"), ## FIXME: this is suboptimal for "nsparseVector" !! function(e1, e2) callGeneric(as(e1, "lsparseVector"), as(e2, "lsparseVector"))) setMethod("Logic", signature(e1 = "lsparseVector", e2 = "lsparseVector"), Ops.spV.spV) ## "nsparse" have no 'x' slot --> version of Ops.spV.spV.. ## -------- but also for (nsp.. o lsp..) etc, when lsp... has no NA if(FALSE) ### FIXME setMethod("Logic", signature(e1 = "nsparseVector", e2 = "nsparseVector"), function(e1, e2) { .bail.out.2(.Generic, class(e1), class(e2)) }) ## 2) spVec o [Mm]atrix : ------------- Ops.M.spV <- function(e1, e2) { d <- e1@Dim n1 <- prod(d) n2 <- e2@length if(n1 != n2) { if(n1 < n2) { stop(sprintf( "dim [product %d] do not match the length of object [%d]", n1, n2)) } ## else n1 > n2 [vector] N <- n1 if(n2 == 1) ## simple case, do not really recycle return(callGeneric(e1, sp2vec(e2))) if(N %% n2 != 0) warning("longer object length\n\t", "is not a multiple of shorter object length") ## else : 2 <= n < N --- recycle the vector e2 <- rep(e2, length = N) } else { ## n1 == n2 N <- n1 } ## ---- e1 & e2 now are both of length 'N' ---- dim(e2) <- d #-> sparseMatrix (!) callGeneric(e1, e2) }## {Ops.M.spV} Ops.spV.M <- function(e1, e2) { n1 <- e1@length d <- e2@Dim n2 <- prod(d) if(n2 != n1) { if(n2 < n1) { stop(sprintf( "dim [product %d] do not match the length of object [%d]", n2, n1)) } ## else n2 > n1 [vector] N <- n2 if(n1 == 1) ## simple case, do not really recycle return(callGeneric(sp2vec(e1), e2)) if(N %% n1 != 0) warning("longer object length\n\t", "is not a multiple of shorter object length") ## else : 2 <= n < N --- recycle the vector e1 <- rep(e1, length = N) } else { ## n2 == n1 N <- n2 } ## ---- e2 & e1 now are both of length 'N' ---- dim(e1) <- d #-> sparseMatrix (!) callGeneric(e1, e2) }## {Ops.spV.M} ## try to use it in all cases setMethod("Ops", signature(e1 = "Matrix", e2 = "sparseVector"), Ops.M.spV) setMethod("Ops", signature(e1 = "sparseVector", e2 = "Matrix"), Ops.spV.M) Matrix/R/dsyMatrix.R0000644000175100001440000001055412271746775014073 0ustar hornikusers### Coercion and Methods for Dense Numeric Symmetric Matrices setAs("dgeMatrix", "dsyMatrix", function(from) { if(isSymmetric(from))# < with tolerance! .Call(dense_to_symmetric, from, "U", FALSE) else stop("not a symmetric matrix; consider forceSymmetric() or symmpart()") }) ## NB: The alternative, 'zero tolerance' { <=> isSymmetric(*, tol=0) } ## breaks too much previous code -- though it would be much faster -- ## setAs("dgeMatrix", "dsyMatrix", ## function(from) .Call(dense_to_symmetric, from, "U", TRUE)) setAs("matrix", "dsyMatrix", function(from) as(..2dge(from), "dsyMatrix")) .dsy2mat <- function(from, keep.dimnames=TRUE)# faster .Call(dsyMatrix_as_matrix, from, keep.dimnames) setAs("dsyMatrix", "matrix", function(from) .Call(dsyMatrix_as_matrix, from, TRUE)) setAs("dsyMatrix", "dspMatrix", function(from) .Call(dsyMatrix_as_dspMatrix, from)) setAs("dsyMatrix", "dsTMatrix", function(from) { # 'dsT': only store upper *or* lower uplo <- from@uplo if(any((d <- dim(from)) == 0)) { ij <- matrix(0L, 0,2) ; m <- from@x } else { ## FIXME! working via "matrix" is *not* efficient: ## the "other triangle" is filled, compared with 0, and then trashed: m <- .Call(dsyMatrix_as_matrix, from, FALSE) # no dimnames! ij <- which(m != 0, arr.ind = TRUE) ij <- ij[if(uplo == "U") ij[,1] <= ij[,2] else ij[,1] >= ij[,2] , , drop = FALSE] } new("dsTMatrix", i = ij[,1] - 1L, j = ij[,2] - 1L, x = as.vector(m[ij]), uplo = uplo, Dim = from@Dim, Dimnames = from@Dimnames) }) setAs("dsyMatrix", "dsCMatrix", function(from) as(as(from, "dsTMatrix"), "dsCMatrix")) ## Note: Just *because* we have an explicit dtr -> dge coercion, ## show( ) is not okay, and we need our own: setMethod("show", "dsyMatrix", function(object) prMatrix(object)) setMethod("rcond", signature(x = "dsyMatrix", norm = "character"), function(x, norm, ...) .Call(dsyMatrix_rcond, x, norm), valueClass = "numeric") setMethod("rcond", signature(x = "dsyMatrix", norm = "missing"), function(x, norm, ...) .Call(dsyMatrix_rcond, x, "O"), valueClass = "numeric") setMethod("solve", signature(a = "dsyMatrix", b = "missing"), function(a, b, ...) .Call(dsyMatrix_solve, a), valueClass = "dsyMatrix") setMethod("solve", signature(a = "dsyMatrix", b = "matrix"), function(a, b, ...) .Call(dsyMatrix_matrix_solve, a, b), valueClass = "dgeMatrix") setMethod("solve", signature(a = "dsyMatrix", b = "ddenseMatrix"), function(a, b, ...) .Call(dsyMatrix_matrix_solve, a, b)) setMethod("solve", signature(a = "dsyMatrix", b = "denseMatrix"), ## eg. for ddi* or ldi* function(a, b, ...) .Call(dsyMatrix_matrix_solve, a, as(b,"dMatrix"))) setMethod("norm", signature(x = "dsyMatrix", type = "character"), function(x, type, ...) .Call(dsyMatrix_norm, x, type), valueClass = "numeric") setMethod("norm", signature(x = "dsyMatrix", type = "missing"), function(x, type, ...) .Call(dsyMatrix_norm, x, "O"), valueClass = "numeric") ## *Should* create the opposite storage format: "U" -> "L" and vice-versa: setMethod("t", signature(x = "dsyMatrix"), t_trMatrix, valueClass = "dsyMatrix") setMethod("BunchKaufman", signature(x = "dsyMatrix"), function(x) .Call(dsyMatrix_trf, x)) setAs("dsyMatrix", "dpoMatrix", function(from){ if(is.null(tryCatch(.Call(dpoMatrix_chol, from), error = function(e) NULL))) stop("not a positive definite matrix") ## else copyClass(from, "dpoMatrix", sNames = c("x", "Dim", "Dimnames", "uplo", "factors")) }) setMethod("diag", signature(x = "dsyMatrix"), function(x, nrow, ncol) .Call(dgeMatrix_getDiag, x)) setMethod("diag<-", signature(x = "dsyMatrix"), function(x, value) .Call(dgeMatrix_setDiag, x, value)) ## Now that we have "chol", we can define "determinant" methods, ## exactly like in ./dsCMatrix.R ## DB - Probably figure out how to use the BunchKaufman decomposition instead ## {{FIXME: Shouldn't it be possible to have "determinant" work by ## default automatically for "Matrix"es when there's a "chol" method available? ## ..> work with ss <- selectMethod("chol", signature("dgCMatrix")) ## -- not have to define showMethod("determinant", ...) for all classes Matrix/R/dMatrix.R0000644000175100001440000001214112011566771013475 0ustar hornikusers### Define Methods that can be inherited for all subclasses ##-> "dMatrix" <--> "lMatrix" ---> ./lMatrix.R ## these two are parallel to "n <-> l" in the above : setAs("nMatrix", "dMatrix", function(from) { cld <- getClassDef(cl <- MatrixClass(class(from))) isSp <- extends(cld, "sparseMatrix") ## faster(not "nicer"): any(substr(cl,3,3) == c("C","T","R")) sNams <- slotNames(cld) r <- copyClass(from, sub("^n", "d", cl), if(isSp) sNams else sNams[sNams != "x"]) r@x <- if(isSp) rep.int(1., nnzSparse(from)) else as.double(from@x) r }) ## NOTE: This is *VERY* parallel to ("lMatrix" -> "nMatrix") in ./lMatrix.R : setAs("dMatrix", "nMatrix", function(from) { if(any(is.na(from@x))) stop("\"dMatrix\" object with NAs cannot be coerced to \"nMatrix\"") ## i.e. from@x are only TRUE (or FALSE in dense case) cld <- getClassDef(cl <- MatrixClass(class(from))) if(extends(cld, "diagonalMatrix")) { # have no "ndi*" etc class cl <- class(from <- as(from, "sparseMatrix")) isSp <- TRUE } else { isSp <- extends(cld, "sparseMatrix") if(isSp && any(from@x == 0)) { from <- drop0(from) # was drop0(from, cld) if(cl != (c. <- class(from))) cld <- getClassDef(cl <- c.) } } sNams <- slotNames(cld) r <- copyClass(from, sub("^d", "n", cl), sNams[sNams != "x"]) if(!isSp) # 'x' slot |--> logical r@x <- as.logical(from@x) r }) ## Group Methods, see ?Arith (e.g.) ## ----- ## >>> More specific methods for sub-classes (sparse), use these as "catch-all": ## the non-Ops ones : setMethod("Math2", ## Assume that Generic(u, k) |--> u for u in {0,1} ## which is true for round(), signif() ==> all structure maintained signature(x = "dMatrix"), function(x, digits) { x@x <- callGeneric(x@x, digits = digits) x }) ## at installation time: ## "max" "min" "range" "prod" "sum" "any" "all" : summGenerics <- getGroupMembers("Summary") ## w/o "prod" & "sum": summGener1 <- summGenerics[match(summGenerics, c("prod","sum"), 0) == 0] ## [also needs extra work in ./AllGeneric.R ] : setMethod("Summary", signature(x = "ddenseMatrix", na.rm = "ANY"), function(x, ..., na.rm) { d <- x@Dim if(any(d == 0)) return(callGeneric(numeric(0), ..., na.rm=na.rm)) clx <- getClassDef(class(x)) if(extends(clx, "generalMatrix")) callGeneric(x@x, ..., na.rm = na.rm) else if(extends(clx, "symmetricMatrix")) { # incl packed, pos.def. if(.Generic %in% summGener1) { callGeneric(if (length(x@x) < prod(d)) x@x else x@x[indTri(d[1], upper= x@uplo == "U", diag= TRUE)], ..., na.rm = na.rm) } else callGeneric(as(x, "dgeMatrix")@x, ..., na.rm = na.rm) } else { ## triangular , packed if(.Generic %in% summGener1) { if(.Generic %in% c("any","all")) { Zero <- FALSE; One <- TRUE } else { Zero <- 0; One <- 1 } callGeneric(x@x, Zero, if(x@diag == "U") One, ..., na.rm = na.rm) } else callGeneric(as(x, "dgeMatrix")@x, ..., na.rm = na.rm) } }) setMethod("Summary", signature(x = "dsparseMatrix", na.rm = "ANY"), function(x, ..., na.rm) { ne <- prod(d <- dim(x)) if(ne == 0) return(callGeneric(numeric(0), ..., na.rm=na.rm)) n <- d[1] clx <- getClassDef(class(x)) isTri <- extends(clx, "triangularMatrix") if(extends(clx, "TsparseMatrix") && is_duplicatedT(x, di = d)) x <- .Call(Tsparse_to_Csparse, x, isTri)# = as(x, "Csparsematrix") l.x <- length(x@x) if(l.x == ne) ## fully non-zero (and "general") - very rare but quick return( callGeneric(x@x, ..., na.rm = na.rm) ) ## else l.x < ne isSym <- !isTri && extends(clx, "symmetricMatrix") isU.tri <- isTri && x@diag == "U" ## "full": has *no* structural zero : very rare, but need to catch : full.x <- ((isSym && l.x == choose(n+1, 2)) || (n == 1 && (isU.tri || l.x == 1))) isGener1 <- .Generic %in% summGener1 if(isGener1) { ## not prod() or sum() -> no need check for symmetric logicF <- .Generic %in% c("any","all") ## we rely on (x, NULL, y, ..) :== (x, y, ..): callGeneric(x@x, if(!full.x) { if(logicF) FALSE else 0 }, if(isU.tri) { if(logicF) TRUE else 1 }, ..., na.rm = na.rm) } else { ## prod() or sum() : care for "symmetric" and U2N if(!full.x && .Generic == "prod") { if(any(is.na(x@x))) NaN else 0 } else callGeneric((if(isSym) as(x, "generalMatrix") else x)@x, if(!full.x) 0, # one 0 <==> many 0's if(isU.tri) rep.int(1, n), ..., na.rm = na.rm) } }) ## "Ops" ("Arith", "Compare", "Logic") --> ./Ops.R ## -- end{group generics} ----------------------- ## Methods for single-argument transformations setMethod("zapsmall", signature(x = "dMatrix"), function(x, digits = getOption("digits")) { x@x <- zapsmall(x@x, digits) x }) ## -- end(single-argument transformations) ------ Matrix/R/lgTMatrix.R0000644000175100001440000000367512254575000014006 0ustar hornikusers#### Logical Sparse Matrices in triplet format ### contains = "lsparseMatrix" ### ============= ---> superclass methods in ./lsparseMatrix.R setAs("lgTMatrix", "lgeMatrix", function(from) .Call(lgTMatrix_to_lgeMatrix, from)) setAs("lgTMatrix", "matrix", function(from) .Call(lgTMatrix_to_matrix, from)) ## setAs("lgTMatrix", "matrix", # go via fast C code: ## function(from) as(as(from, "lgCMatrix"), "matrix")) setAs("matrix", "lgTMatrix", function(from) { stopifnot(is.logical(from)) dn <- dimnames(from) if(is.null.DN(dn)) dn <- list(NULL,NULL) else dimnames(from) <- NULL TorNA <- is.na(from) | from ij <- which(TorNA, arr.ind = TRUE) - 1L if(length(ij) == 0) ij <- matrix(ij, 0, 2) new("lgTMatrix", i = ij[,1], j = ij[,2], x = from[TorNA], Dim = as.integer(dim(from)), Dimnames = dn) }) setAs("lgTMatrix", "dgTMatrix", function(from) ## more efficient than ## as(as(as(sM, "lgCMatrix"), "dgCMatrix"), "dgTMatrix") new("dgTMatrix", i = from@i, j = from@j, x = as.double(from@x), ## cannot copy factors, but can we use them? Dim = from@Dim, Dimnames= from@Dimnames)) setAs("lgTMatrix", "triangularMatrix", function(from) check.gT2tT(from, toClass = "ltTMatrix", do.n=FALSE)) setAs("lgTMatrix", "ltTMatrix", function(from) check.gT2tT(from, toClass = "ltTMatrix", do.n=FALSE)) setAs("lgTMatrix", "symmetricMatrix", function(from) check.gT2sT(from, toClass = "lsTMatrix", do.n=FALSE)) ## We favor coercion to super-classes, here, "symmetricMatrix" ## setAs("lgTMatrix", "lsTMatrix", ## function(from) check.gT2sT(from, toClass = "lsTMatrix", do.n=FALSE)) if(FALSE) ## unneeded: use t. setMethod("t", signature(x = "lgTMatrix"), function(x) new("lgTMatrix", i = x@j, j = x@i, x = x@x, Dim = x@Dim[2:1], Dimnames= x@Dimnames[2:1]), valueClass = "lgTMatrix") Matrix/R/ldenseMatrix.R0000644000175100001440000001705612003525364014530 0ustar hornikusers#### "ldenseMatrix" - virtual class of logical dense matrices #### ------------ #### Contains lge*; ltr*, ltp*; lsy*, lsp*; ldi* ## Logical -> Double {of same structure}: setAs("lgeMatrix", "dgeMatrix", function(from) l2d_Matrix(from, "lgeMatrix")) setAs("lsyMatrix", "dsyMatrix", function(from) l2d_Matrix(from, "lsyMatrix")) setAs("lspMatrix", "dspMatrix", function(from) l2d_Matrix(from, "lspMatrix")) setAs("ltrMatrix", "dtrMatrix", function(from) l2d_Matrix(from, "ltrMatrix")) setAs("ltpMatrix", "dtpMatrix", function(from) l2d_Matrix(from, "ltpMatrix")) ### NOTA BENE: Much of this is *very* parallel to ./ndenseMatrix.R ### ~~~~~~~~~~~~~~~~ ## all need be coercable to "lgeMatrix": setAs("lsyMatrix", "lgeMatrix", function(from) .Call(lsyMatrix_as_lgeMatrix, from, 0L)) setAs("ltrMatrix", "lgeMatrix", function(from) .Call(ltrMatrix_as_lgeMatrix, from, 0L)) setAs("ltpMatrix", "lgeMatrix", function(from) as(as(from, "ltrMatrix"), "lgeMatrix")) setAs("lspMatrix", "lgeMatrix", function(from) as(as(from, "lsyMatrix"), "lgeMatrix")) ## and the reverse setAs("lgeMatrix", "ltpMatrix", function(from) as(as(from, "ltrMatrix"), "ltpMatrix")) setAs("lgeMatrix", "lspMatrix", function(from) as(as(from, "lsyMatrix"), "lspMatrix")) ## packed <-> non-packed : setAs("lspMatrix", "lsyMatrix", function(from) .Call(lspMatrix_as_lsyMatrix, from, 0L)) setAs("lsyMatrix", "lspMatrix", function(from) .Call(lsyMatrix_as_lspMatrix, from, 0L)) setAs("ltpMatrix", "ltrMatrix", function(from) .Call(ltpMatrix_as_ltrMatrix, from, 0L)) setAs("ltrMatrix", "ltpMatrix", function(from) .Call(ltrMatrix_as_ltpMatrix, from, 0L)) ### -> symmetric : if(FALSE) ## not sure if this is a good idea ... -- FIXME? setIs("lgeMatrix", "lsyMatrix", test = function(obj) isSymmetric(obj), replace = function(obj, value) { ## copy all slots for(n in slotNames(obj)) slot(obj, n) <- slot(value, n) }) ### Alternative (at least works): setAs("lgeMatrix", "lsyMatrix", function(from) { if(isSymmetric(from)) new("lsyMatrix", x = from@x, Dim = from@Dim, Dimnames = from@Dimnames, factors = from@factors) else stop("not a symmetric matrix; consider forceSymmetric() or symmpart()") }) setAs("lgeMatrix", "ltrMatrix", function(from) { if(isT <- isTriangular(from)) new("ltrMatrix", x = from@x, Dim = from@Dim, Dimnames = from@Dimnames, uplo = .if.NULL(attr(isT, "kind"), "U")) ## TODO: also check 'diag' else stop("not a triangular matrix") }) ### ldense* <-> "matrix" : ## 1) "lge* : setAs("lgeMatrix", "matrix", function(from) array(from@x, dim = from@Dim, dimnames = from@Dimnames)) setAs("matrix", "lgeMatrix", function(from) { new("lgeMatrix", x = as.logical(from), Dim = as.integer(dim(from)), Dimnames = .M.DN(from)) }) ## 2) base others on "lge*": setAs("matrix", "lsyMatrix", function(from) as(as(from, "lgeMatrix"), "lsyMatrix")) setAs("matrix", "lspMatrix", function(from) as(as(from, "lsyMatrix"), "lspMatrix")) setAs("matrix", "ltrMatrix", function(from) as(as(from, "lgeMatrix"), "ltrMatrix")) setAs("matrix", "ltpMatrix", function(from) as(as(from, "ltrMatrix"), "ltpMatrix")) ## Useful if this was called e.g. for as(*, "lsyMatrix"), but it isn't setAs("matrix", "ldenseMatrix", function(from) as(from, "lgeMatrix")) setAs("ldenseMatrix", "matrix", ## uses the above l*M. -> lgeM. function(from) as(as(from, "lgeMatrix"), "matrix")) ## dense |-> compressed : setAs("lgeMatrix", "lgTMatrix", function(from) as(.dense2C(from), "lgTMatrix")) setAs("lgeMatrix", "lgCMatrix", function(from) as(as(from, "lgTMatrix"), "lgCMatrix")) setMethod("as.logical", signature(x = "ldenseMatrix"), function(x, ...) as(x, "lgeMatrix")@x) ###---------------------------------------------------------------------- setMethod("diag", signature(x = "lgeMatrix"), function(x, nrow, ncol) .Call(lgeMatrix_getDiag, x)) setMethod("diag", signature(x = "lsyMatrix"), function(x, nrow, ncol) .Call(lgeMatrix_getDiag, x)) setMethod("diag", signature(x = "lspMatrix"), function(x, nrow, ncol) .Call(lspMatrix_getDiag, x)) setMethod("diag", signature(x = "ltrMatrix"), function(x, nrow, ncol) .Call(ltrMatrix_getDiag, x)) setMethod("diag", signature(x = "ltpMatrix"), function(x, nrow, ncol) .Call(ltpMatrix_getDiag, x)) setMethod("diag", signature(x = "ndenseMatrix"),# << the "same" function(x, nrow, ncol) diag(as(x, "ldenseMatrix"))) ## --- *SETTING* of diagonal : diag(x) <- value --------- ## --- ===================== faster than default x[cbind[c(i,i)]] <- value setMethod("diag<-", signature(x = "lgeMatrix"), function(x, value) .Call(lgeMatrix_setDiag, x, value)) setMethod("diag<-", signature(x = "lsyMatrix"), function(x, value) .Call(lgeMatrix_setDiag, x, value)) setMethod("diag<-", signature(x = "lspMatrix"), function(x, value) .Call(lspMatrix_setDiag, x, value)) .diag.set.ltr <- function(x, value) { .Call(ltrMatrix_setDiag, if(x@diag == "U") .dense.diagU2N(x, "l", isPacked=FALSE) else x, value) } .diag.set.ltp <- function(x, value) { .Call(ltpMatrix_setDiag, if(x@diag == "U") .dense.diagU2N(x, "l", isPacked=TRUE) else x, value) } setMethod("diag<-", signature(x = "ltrMatrix"), .diag.set.ltr) setMethod("diag<-", signature(x = "ltpMatrix"), .diag.set.ltp) ## the *same* for the "ndenseMatrix" elements: setMethod("diag<-", signature(x = "ngeMatrix"), function(x, value) .Call(lgeMatrix_setDiag, x, value)) setMethod("diag<-", signature(x = "nsyMatrix"), function(x, value) .Call(lgeMatrix_setDiag, x, value)) setMethod("diag<-", signature(x = "nspMatrix"), function(x, value) .Call(lspMatrix_setDiag, x, value)) setMethod("diag<-", signature(x = "ntrMatrix"), .diag.set.ltr) setMethod("diag<-", signature(x = "ntpMatrix"), .diag.set.ltp) rm(.diag.set.ltr, .diag.set.ltp) setMethod("t", signature(x = "lgeMatrix"), t_geMatrix) setMethod("t", signature(x = "ltrMatrix"), t_trMatrix) setMethod("t", signature(x = "lsyMatrix"), t_trMatrix) setMethod("t", signature(x = "ltpMatrix"), function(x) as(t(as(x, "ltrMatrix")), "ltpMatrix")) setMethod("t", signature(x = "lspMatrix"), function(x) as(t(as(x, "lsyMatrix")), "lspMatrix")) ## NOTE: "&" and "|" are now in group "Logic" c "Ops" --> ./Ops.R ## "!" is in ./not.R setMethod("as.vector", signature(x = "ldenseMatrix", mode = "missing"), function(x, mode) as(x, "lgeMatrix")@x) setMethod("all", signature(x = "lsyMatrix"), function(x, ..., na.rm = FALSE) all(x@x, ..., na.rm = na.rm)) ## Note: the above "lsy*" method is needed [case below can be wrong] setMethod("all", signature(x = "ldenseMatrix"), function(x, ..., na.rm = FALSE) { if(prod(dim(x)) >= 1) (!is(x, "triangularMatrix") && !is(x, "diagonalMatrix") && all(x@x, ..., na.rm = na.rm)) else all(x@x, ..., na.rm = na.rm) }) ## setMethod("any", ) ---> ./lMatrix.R ## setMethod("any", signature(x = "ldenseMatrix"), ## function(x, ..., na.rm = FALSE) ## (prod(dim(x)) >= 1 && is(x, "triangularMatrix") && x@diag == "U") || ## any(x@x, ..., na.rm = na.rm)) setMethod("norm", signature(x = "ldenseMatrix", type = "character"), function(x, type, ...) .Call(dgeMatrix_norm, as(as(x,"dMatrix"),"dgeMatrix"), type), valueClass = "numeric") .rcond_via_d <- function(x, norm, ...) rcond(as(as(x, "dMatrix"), "dgeMatrix"), norm=norm, ...) setMethod("rcond", signature(x = "ldenseMatrix", norm = "character"), .rcond_via_d, valueClass = "numeric") Matrix/R/nsTMatrix.R0000644000175100001440000000151111004710614014001 0ustar hornikusers#### Sparse Symmetric non-zero pattern Matrices in Triplet format ### contains = "nsparseMatrix" setAs("nsTMatrix", "matrix", function(from) as(as(from, "ngTMatrix"), "matrix")) setAs("nsTMatrix", "ngCMatrix", # for diag function(from) as(as(from, "nsCMatrix"), "ngCMatrix")) setAs("nsTMatrix", "ngTMatrix", function(from) .Call(nsTMatrix_as_ngTMatrix, from)) setAs("nsTMatrix", "dsTMatrix", function(from) new("dsTMatrix", i = from@i, j = from@j, uplo = from@uplo, x = rep.int(1., length(from@i)), Dim = from@Dim, Dimnames = from@Dimnames)) setAs("nsTMatrix", "nsyMatrix", function(from) .Call(nsTMatrix_as_nsyMatrix, from)) setMethod("t", "nsTMatrix", function(x) new("nsTMatrix", Dim = x@Dim, Dimnames = x@Dimnames, i = x@j, j = x@i, uplo = if (x@uplo == "U") "L" else "U")) Matrix/R/LU.R0000644000175100001440000000101411054545144012377 0ustar hornikuserssetMethod("expand", signature(x = "denseLU"), function(x, ...) .Call(LU_expand, x)) setMethod("solve", signature(a = "denseLU", b = "missing"), function(a, b, ...) { ll <- expand(a) #-> list(L, U, P); orig x = P %*% L %*% U ## too expensive: with(lapply(ll, solve), U %*% L %*% P) solve(ll$U, solve(ll$L, ll$P)) }) setMethod("expand", signature(x = "sparseLU"), function(x, ...) list(P = as(x@p + 1L, "pMatrix"), L = x@L, U = x@U, Q = as(x@q + 1L, "pMatrix"))) Matrix/R/expm.R0000644000175100001440000000222011004063604013017 0ustar hornikusers#### All methods for expm() , the Matrix Exponential setMethod("expm", signature(x = "dgeMatrix"), function(x) .Call(dgeMatrix_exp, x)) setMethod("expm", signature(x = "Matrix"), function(x) expm(as(x, "dMatrix"))) setMethod("expm", signature(x = "dMatrix"),function(x) expm(as(x, "dgeMatrix"))) ## but these trigger first: expmSpec <- function(x, newClass) { r <- copyClass(x, newClass, c("uplo", "Dim", "Dimnames")) r@x <- expm(as(as(x, "dMatrix"),"generalMatrix"))@x r } setMethod("expm", signature(x = "triangularMatrix"), function(x) expmSpec(x, "dtrMatrix")) setMethod("expm", signature(x = "symmetricMatrix"), function(x) expmSpec(x, "dsyMatrix")) setMethod("expm", signature(x = "ddiMatrix"), function(x) { if(x@diag == "U") { x@diag <- "N" x@x <- rep.int(exp(1), x@Dim[1]) } else { x@x <- exp(x@x) } x }) ## Not necessary (and there's no direct ldi -> ddi coercion anyway: ## setMethod("expm", signature(x = "ldiMatrix"), ## function(x) expm(as(x,"ddiMatrix"))) ## As long as this is not "in R" : setMethod("expm", signature(x = "matrix"), function(x) expm(Matrix(x))) Matrix/R/sparseQR.R0000644000175100001440000001213412244416541013624 0ustar hornikusers#### Methods for the sparse QR decomposition ## TODO: qr.R() generic that allows optional args ['backPermute'] ## --- so we can add it to our qr.R() method, *instead* of this : qrR <- function(qr, complete = FALSE, backPermute = TRUE) { ir <- seq_len(qr@Dim[if(complete) 1L else 2L]) r <- if(backPermute <- backPermute && (n <- length(qr@q)) && !isSeq(qr@q, n-1L)) qr@R[ir, order(qr@q), drop = FALSE] else qr@R[ir, , drop = FALSE] if(complete || backPermute) r else as(r, "triangularMatrix") } setMethod("qr.R", signature(qr = "sparseQR"), function(qr, complete = FALSE) { if((is.null(v <- getOption("Matrix.quiet.qr.R")) || !v) && (is.null(v <- getOption("Matrix.quiet")) || !v)) warning("qr.R() may differ from qr.R() because of permutations. Possibly use our qrR() instead") qrR(qr, complete=complete, backPermute=FALSE) }) ## if(identical("", as.character(formals(qr.Q)$Dvec))) { # "new" setMethod("qr.Q", "sparseQR", function(qr, complete=FALSE, Dvec) { d <- qr@Dim ir <- seq_len(d[k <- if(complete) 1L else 2L]) if(missing(Dvec)) Dvec <- rep.int(1, if(complete) d[1] else min(d)) D <- .sparseDiagonal(d[1], x=Dvec, cols=0L:(d[k] -1L)) qr.qy(qr, D) }) ## } else { ## setMethod("qr.Q", "sparseQR", ## function(qr, complete=FALSE, Dvec = rep.int(1, if(complete) d[1] else min(d))) ## { ## d <- qr@Dim ## ir <- seq_len(d[k <- if(complete) 1L else 2L]) ## D <- .sparseDiagonal(d[1], x=Dvec, cols=0L:(d[k] -1L)) ## qr.qy(qr, D) ## }) ## } setMethod("qr.qy", signature(qr = "sparseQR", y = "ddenseMatrix"), function(qr, y) .Call(sparseQR_qty, qr, y, FALSE), valueClass = "dgeMatrix") setMethod("qr.qy", signature(qr = "sparseQR", y = "matrix"), function(qr, y) .Call(sparseQR_qty, qr, y, FALSE), valueClass = "dgeMatrix") setMethod("qr.qy", signature(qr = "sparseQR", y = "numeric"), ## drop to vector {to be 100% standard-R-matrix compatible} : function(qr, y) .Call(sparseQR_qty, qr, y, FALSE)@x) setMethod("qr.qy", signature(qr = "sparseQR", y = "Matrix"), function(qr, y) .Call(sparseQR_qty, qr, as(as(y, "denseMatrix"),"dgeMatrix"), FALSE), valueClass = "dgeMatrix") setMethod("qr.qty", signature(qr = "sparseQR", y = "ddenseMatrix"), function(qr, y) .Call(sparseQR_qty, qr, y, TRUE), valueClass = "dgeMatrix") setMethod("qr.qty", signature(qr = "sparseQR", y = "matrix"), function(qr, y) .Call(sparseQR_qty, qr, y, TRUE), valueClass = "dgeMatrix") setMethod("qr.qty", signature(qr = "sparseQR", y = "numeric"), function(qr, y) .Call(sparseQR_qty, qr, y, TRUE)@x) setMethod("qr.qty", signature(qr = "sparseQR", y = "Matrix"), function(qr, y) .Call(sparseQR_qty, qr, as(as(y, "denseMatrix"),"dgeMatrix"), TRUE), valueClass = "dgeMatrix") .coef.trunc <- function(qr, res, drop=FALSE) res[seq_len(ncol(qr@R)),,drop=drop] setMethod("qr.coef", signature(qr = "sparseQR", y = "ddenseMatrix"), function(qr, y) .coef.trunc(qr, .Call(sparseQR_coef, qr, y)), valueClass = "dgeMatrix") setMethod("qr.coef", signature(qr = "sparseQR", y = "matrix"), function(qr, y) .coef.trunc(qr, .Call(sparseQR_coef, qr, y)), valueClass = "dgeMatrix") setMethod("qr.coef", signature(qr = "sparseQR", y = "numeric"), function(qr, y) .coef.trunc(qr, .Call(sparseQR_coef, qr, y), drop=TRUE)) setMethod("qr.coef", signature(qr = "sparseQR", y = "Matrix"), function(qr, y) .coef.trunc(qr, .Call(sparseQR_coef, qr, as(as(y, "denseMatrix"),"dgeMatrix"))), valueClass = "dgeMatrix") setMethod("qr.resid", signature(qr = "sparseQR", y = "ddenseMatrix"), function(qr, y) .Call(sparseQR_resid_fitted, qr, y, TRUE), valueClass = "dgeMatrix") setMethod("qr.resid", signature(qr = "sparseQR", y = "matrix"), function(qr, y) .Call(sparseQR_resid_fitted, qr, y, TRUE), valueClass = "dgeMatrix") setMethod("qr.resid", signature(qr = "sparseQR", y = "numeric"), function(qr, y) .Call(sparseQR_resid_fitted, qr, y, TRUE)@x) setMethod("qr.resid", signature(qr = "sparseQR", y = "Matrix"), function(qr, y) .Call(sparseQR_resid_fitted, qr, as(as(y, "denseMatrix"),"dgeMatrix"), TRUE), valueClass = "dgeMatrix") setMethod("qr.fitted", signature(qr = "sparseQR", y = "ddenseMatrix"), function(qr, y, k) .Call(sparseQR_resid_fitted, qr, y, FALSE), valueClass = "dgeMatrix") setMethod("qr.fitted", signature(qr = "sparseQR", y = "matrix"), function(qr, y, k) .Call(sparseQR_resid_fitted, qr, y, FALSE), valueClass = "dgeMatrix") setMethod("qr.fitted", signature(qr = "sparseQR", y = "numeric"), function(qr, y, k) .Call(sparseQR_resid_fitted, qr, y, FALSE)@x) setMethod("qr.fitted", signature(qr = "sparseQR", y = "Matrix"), function(qr, y, k) .Call(sparseQR_resid_fitted, qr, as(as(y, "denseMatrix"),"dgeMatrix"), FALSE), valueClass = "dgeMatrix") ## setMethod("solve", signature(a = "sparseQR", b = "ANY"), function(a, b, ...) qr.coef(a, b)) Matrix/R/dtCMatrix.R0000644000175100001440000001000712201004116013740 0ustar hornikusers#### Triangular Sparse Matrices in compressed column-oriented format setAs("dtCMatrix", "ltCMatrix", function(from) new("ltCMatrix", i = from@i, p = from@p, uplo = from@uplo, diag = from@diag, x = as.logical(from@x), ## FIXME?: use from@factors smartly Dim = from@Dim, Dimnames = from@Dimnames)) setAs("dtCMatrix", "ntCMatrix", # just drop 'x' slot: function(from) new("ntCMatrix", i = from@i, p = from@p, uplo = from@uplo, diag = from@diag, ## FIXME?: use from@factors smartly Dim = from@Dim, Dimnames = from@Dimnames)) setAs("matrix", "dtCMatrix", function(from) as(as(from, "dtTMatrix"), "dtCMatrix")) setAs("dtCMatrix", "dgCMatrix", function(from) { if (from@diag == "U") from <- .Call(Csparse_diagU2N, from) new("dgCMatrix", i = from@i, p = from@p, x = from@x, Dim = from@Dim, Dimnames = from@Dimnames) }) setAs("dtCMatrix", "dsCMatrix", function(from) as(from, "symmetricMatrix")) setAs("dtCMatrix", "dgTMatrix", function(from) { if (from@diag == "U") from <- .Call(Csparse_diagU2N, from) ## ignore triangularity in conversion to TsparseMatrix .Call(Csparse_to_Tsparse, from, FALSE) }) ## FIXME: make more efficient ## ----- and as(., "triangularMatrix") is even worse via as_Sp() setAs("dgCMatrix", "dtCMatrix", # to triangular, needed for triu,.. function(from) as(.Call(Csparse_to_Tsparse, from, FALSE), "dtCMatrix")) setAs("dtCMatrix", "dgeMatrix", function(from) as(as(from, "dgTMatrix"), "dgeMatrix")) ## These are all needed because cholmod doesn't support triangular: ## (see end of ./Csparse.R ), e.g. for triu() setAs("dtCMatrix", "dtTMatrix", function(from) .Call(Csparse_to_Tsparse, from, TRUE)) ## {# and this is not elegant: ## x <- as(from, "dgTMatrix") ## if (from@diag == "U") { ## drop diagonal entries '1': ## i <- x@i; j <- x@j ## nonD <- i != j ## xx <- x@x[nonD] ; i <- i[nonD] ; j <- j[nonD] ## } else { ## xx <- x@x; i <- x@i; j <- x@j ## } ## new("dtTMatrix", x = xx, i = i, j = j, Dim = x@Dim, ## Dimnames = x@Dimnames, uplo = from@uplo, diag = from@diag) ## }) ## Now that we support triangular matrices use the inherited method. ## setAs("dtCMatrix", "TsparseMatrix", function(from) as(from, "dtTMatrix")) setAs("dtCMatrix", "dtrMatrix", function(from) as(as(from, "dtTMatrix"), "dtrMatrix")) setMethod("determinant", signature(x = "dtCMatrix", logarithm = "logical"), function(x, logarithm = TRUE, ...) { if(x@diag == "N") mkDet(diag(x), logarithm) else structure(list(modulus = structure(if (logarithm) 0 else 1, "logarithm" = logarithm), sign = 1L), class = "det") }) setMethod("solve", signature(a = "dtCMatrix", b = "missing"), function(a, b, ...) { stopifnot((n <- nrow(a)) == ncol(a)) as(.Call(dtCMatrix_sparse_solve, a, .trDiagonal(n, unitri=FALSE)), "dtCMatrix") }, valueClass = "dtCMatrix") setMethod("solve", signature(a = "dtCMatrix", b = "dgeMatrix"), function(a, b, ...) .Call(dtCMatrix_matrix_solve, a, b, TRUE), valueClass = "dgeMatrix") setMethod("solve", signature(a = "dtCMatrix", b = "CsparseMatrix"), function(a, b, ...) .sortCsparse(.Call(dtCMatrix_sparse_solve, a, b)), ## ------------ TODO: both in C code valueClass = "dgCMatrix") setMethod("solve", signature(a = "dtCMatrix", b = "matrix"), function(a, b, ...) { storage.mode(b) <- "double" .Call(dtCMatrix_matrix_solve, a, b, FALSE) }, valueClass = "dgeMatrix") ## Isn't this case handled by the method for (a = "Matrix', b = ## "numeric") in ./Matrix.R? Or is this method defined here for ## the as.double coercion? setMethod("solve", signature(a = "dtCMatrix", b = "numeric"), function(a, b, ...) .Call(dtCMatrix_matrix_solve, a, as.matrix(as.double(b)), FALSE), valueClass = "dgeMatrix") Matrix/R/zzz.R0000644000175100001440000000170012253554012012712 0ustar hornikusers### Note that "in theory" even base::as.vector() should be overloaded. ### In practice that could be too much of a performance penalty in some cases. .MatrixEnv <- new.env(parent=emptyenv()) ## as long as it's small, no 'hash = TRUE' .chm_common <- new.env(parent = emptyenv()) ## environment in which to store some settings from cholmod_common .onLoad <- function(libname, pkgname) { .Call(CHM_set_common_env, .chm_common) } ## Instead, simply re-assign the [cr]bind()s which are recursively ## based on [cr]bind2 : ## ## save to cBind / rBind ("rename") cBind <- methods:::cbind rBind <- methods:::rbind .onUnload <- function(libpath) { library.dynam.unload("Matrix", libpath) } .SuiteSparse_version <- function() { ssv <- .Call(get_SuiteSparse_version) package_version(list(major = ssv[1], minor = paste(ssv[2:3], collapse="."))) } if(getRversion() < "3.0.0") { rep_len <- function(x, length.out) rep(x, length.out=length.out) } Matrix/R/eigen.R0000644000175100001440000001036212103255600013143 0ustar hornikusers#### eigen() , Schur() etc #### ===== ===== ## eigen() is not even generic, and we haven't any C code, ## but rather base::eigen() "magically" works via as.matrix() if (FALSE) { setMethod("eigen", signature(x = "dgeMatrix", only.values = "missing"), function(x, symmetric, only.values, EISPACK) # << must match generic .Call(dgeMatrix_eigen, x, FALSE)) setMethod("eigen", signature(x = "dgeMatrix", only.values = "logical"), function(x, symmetric, only.values, EISPACK) .Call(dgeMatrix_eigen, x, only.values)) } #not yet .dgeSchur <- function(x, vectors, ...) { cl <- .Call(dgeMatrix_Schur, x, TRUE, TRUE) realEV <- all(cl$WI == 0) ## TODO: do all this in C new("Schur", Dim = x@Dim, Q = as(cl$Z, "dgeMatrix"), T = as(cl$T, if(realEV)"dtrMatrix" else "dgeMatrix"), EValues = if(realEV) cl$WR else complex(real = cl$WR, imaginary = cl$WI)) } setMethod("Schur", signature(x = "dgeMatrix", vectors = "missing"), .dgeSchur) setMethod("Schur", signature(x = "dgeMatrix", vectors = "logical"), function(x, vectors, ...) { if(vectors) .dgeSchur(x) else { cl <- .Call(dgeMatrix_Schur, x, FALSE, TRUE) realEV <- all(cl$WI == 0) list(T = as(cl$T, if(realEV) "dtrMatrix" else "dgeMatrix"), EValues = if(realEV) cl$WR else complex(real = cl$WR, imaginary = cl$WI)) }}) ## Ok, for the faint of heart, also provide "matrix" methods : .mSchur <- function(x, vectors, ...) { cl <- .Call(dgeMatrix_Schur, x, TRUE, FALSE) list(Q = cl$Z, T = cl$T, EValues = if(all(cl$WI == 0)) cl$WR else complex(real = cl$WR, imaginary = cl$WI)) } setMethod("Schur", signature(x = "matrix", vectors = "missing"), .mSchur) setMethod("Schur", signature(x = "matrix", vectors = "logical"), function(x, vectors, ...) { if(vectors) .mSchur(x) else { cl <- .Call(dgeMatrix_Schur, x, FALSE, FALSE) EV <- if(all(cl$WI == 0)) cl$WR else complex(real = cl$WR, imaginary = cl$WI) cl$WR <- cl$WI <- NULL cl$EValues <- EV cl }}) Schur.dsy <- function(x, vectors, ...) { if(missing(vectors)) vectors <- TRUE ## TODO: do all this in C ## Should directly call LAPACK dsyev() evl <- eigen(x, only.values = !vectors) eVals <- evl$values if(vectors) new("Schur", Dim = x@Dim, Q = as(evl$vectors, "dgeMatrix"), T = Diagonal(x = eVals), EValues = eVals) else list(T = Diagonal(x = eVals), EValues = eVals) } setMethod("Schur", signature(x = "dsyMatrix", vectors = "ANY"), Schur.dsy) ## FIXME(?) these coerce from sparse to *dense* setMethod("Schur", signature(x = "generalMatrix", vectors = "missing"), function(x, vectors, ...) callGeneric(as(x, "dgeMatrix"))) setMethod("Schur", signature(x = "generalMatrix", vectors = "logical"), function(x, vectors, ...) callGeneric(as(x, "dgeMatrix"), vectors)) setMethod("Schur", signature(x = "symmetricMatrix", vectors = "missing"), function(x, vectors, ...) Schur.dsy(as(x, "dsyMatrix"))) setMethod("Schur", signature(x = "symmetricMatrix", vectors = "logical"), function(x, vectors, ...) Schur.dsy(as(x, "dsyMatrix"), vectors)) ## Schur() : {Note that the Schur decomposition is not unique here} .simpleSchur <- function(x, vectors, ...) { x <- as(x, "dMatrix") d <- dim(x) new("Schur", Dim = d, Q = Diagonal(d[1]), T = x, EValues = diag(x)) } setMethod("Schur", signature(x = "diagonalMatrix", vectors = "missing"), .simpleSchur) setMethod("Schur", signature(x = "diagonalMatrix", vectors = "logical"), function(x, vectors, ...) { if(vectors) .simpleSchur(x) else { x <- as(x, "dMatrix") list(T = x, EValues = x@x) }}) .triSchur <- function(x, vectors, ...) { x <- as(x, "dMatrix") d <- dim(x) n <- d[1] if(x@uplo == "U" || n == 0) new("Schur", Dim = d, Q = Diagonal(n), T = x, EValues = diag(x)) else { i <- n:1 new("Schur", Dim = d, Q = as(i, "pMatrix"), T = t(t(x)[i,i]), EValues = diag(x)[i]) } } setMethod("Schur", signature(x = "triangularMatrix", vectors = "missing"), .triSchur) setMethod("Schur", signature(x = "triangularMatrix", vectors = "logical"), function(x, vectors, ...) { if(vectors) .triSchur(x) else { x <- as(x, "dMatrix") list(T = x, EValues = x@x) }}) Matrix/R/dsCMatrix.R0000644000175100001440000001772212215114135013762 0ustar hornikusers#### Symmetric Sparse Matrices in compressed column-oriented format setAs("dgCMatrix", "dsCMatrix", function(from) { ## r2130 ... | 2008-03-14 | added deprecation warning warning("as(.,\"dsCMatrix\") is deprecated (since 2008); do use as(., \"symmetricMatrix\")") as(from, "symmetricMatrix") }) ## Specific conversions, should they be necessary. Better to convert as ## as(x, "TsparseMatrix") or as(x, "denseMatrix") ## Moved to ./Csparse.R ## setAs("dsCMatrix", "dsTMatrix", ## function(from) .Call(Csparse_to_Tsparse, from, FALSE)) setAs("dsCMatrix", "dgTMatrix", # needed for show(), image() function(from) ## pre-Cholmod -- FIXME: get rid of .Call(dsCMatrix_to_dgTMatrix, from)) setAs("dsCMatrix", "dgeMatrix", function(from) as(as(from, "dgTMatrix"), "dgeMatrix")) setAs("dsCMatrix", "matrix", function(from) as(as(from, "generalMatrix"), "matrix")) setAs("matrix", "dsCMatrix", function(from) as(as(as(from, "CsparseMatrix"), "symmetricMatrix"), "dMatrix")) setAs("dsCMatrix", "lsCMatrix", function(from) new("lsCMatrix", i = from@i, p = from@p, uplo = from@uplo, x = as.logical(from@x), Dim = from@Dim, Dimnames = from@Dimnames)) setAs("dsCMatrix", "nsCMatrix", function(from) new("nsCMatrix", i = from@i, p = from@p, uplo = from@uplo, Dim = from@Dim, Dimnames = from@Dimnames)) setAs("dsCMatrix", "dgCMatrix", function(from) .Call(Csparse_symmetric_to_general, from)) setAs("dsCMatrix", "dsyMatrix", function(from) as(from, "denseMatrix")) ##' Check if \code{name} (== "[sS][pP][dD]Cholesky") fits the values of the ##' logicals (perm, LDL, super). ##' @param name a string such as "sPdCholesky" ##' @param perm also known as \code{pivot} ##' @param LDL ##' @param super ##' @return logical: TRUE if the name matches .chkName.CHM <- function(name, perm, LDL, super) .Call(R_chkName_Cholesky, name, perm, LDL, super) ## ../src/dsCMatrix.c .CHM.factor.name <- function(perm, LDL, super) .Call(R_chm_factor_name, perm, LDL, super) ## have rather tril() and triu() methods than ## setAs("dsCMatrix", "dtCMatrix", ....) setMethod("tril", "dsCMatrix", function(x, k = 0, ...) { if(x@uplo == "L" && k == 0) ## same internal structure (speedup potential !?) new("dtCMatrix", uplo = x@uplo, i = x@i, p = x@p, x = x@x, Dim = x@Dim, Dimnames = x@Dimnames) else tril(as(x, "dgCMatrix"), k = k, ...) }) setMethod("triu", "dsCMatrix", function(x, k = 0, ...) { if(x@uplo == "U" && k == 0) ## same internal structure (speedup potential !?) new("dtCMatrix", uplo = x@uplo, i = x@i, p = x@p, x = x@x, Dim = x@Dim, Dimnames = x@Dimnames) else triu(as(x, "dgCMatrix"), k = k, ...) }) solve.dsC.mat <- function(a,b, tol = .Machine$double.eps) { r <- tryCatch(.Call(dsCMatrix_matrix_solve, a, b), error=function(e)NULL, warning=function(w)NULL) if(is.null(r)) { ## cholmod factorization was not ok Matrix.msg("solve.dsC.mat(): Cholmod factorization unsuccessful --> using LU()") .solve.sparse.dgC(as(a,"dgCMatrix"), b=b, tol=tol) } else r } ## ``Fully-sparse'' solve() {different Cholmod routine, otherwise "the same"}: solve.dsC.dC <- function(a,b, tol = .Machine$double.eps) { r <- tryCatch(.Call(dsCMatrix_Csparse_solve, a, b), error=function(e)NULL, warning=function(w)NULL) if(is.null(r)) { ## cholmod factorization was not ok Matrix.msg("solve.dsC.dC(): Cholmod factorization unsuccessful --> using LU()") .solve.sparse.dgC(as(a,"dgCMatrix"), b=b, tol=tol) } else r } ## . ------------------------ setMethod("solve", signature(a = "dsCMatrix", b = "ddenseMatrix"), function(a, b, ...) { if (class(b) != "dgeMatrix") b <- .Call(dup_mMatrix_as_dgeMatrix, b) solve.dsC.mat(a,b) }, valueClass = "dgeMatrix") setMethod("solve", signature(a = "dsCMatrix", b = "denseMatrix"), ## only triggers for diagonal*, ldense*.. (but *not* ddense: above) function(a, b, ...) solve.dsC.mat(a, as(.Call(dup_mMatrix_as_geMatrix, b), "dgeMatrix"))) setMethod("solve", signature(a = "dsCMatrix", b = "matrix"), function(a, b, ...) solve.dsC.mat(a, .Call(dup_mMatrix_as_dgeMatrix, b)), valueClass = "dgeMatrix") setMethod("solve", signature(a = "dsCMatrix", b = "numeric"), function(a, b, ...) solve.dsC.mat(a, .Call(dup_mMatrix_as_dgeMatrix, b)), valueClass = "dgeMatrix") ## . ------------------------ setMethod("solve", signature(a = "dsCMatrix", b = "dsparseMatrix"), function(a, b, ...) { cb <- getClassDef(class(b)) if (!extends(cb, "CsparseMatrix")) cb <- getClassDef(class(b <- as(b, "CsparseMatrix"))) if (extends(cb, "symmetricMatrix")) ## not supported (yet) by cholmod_spsolve b <- as(b, "dgCMatrix") solve.dsC.dC(a,b) }) setMethod("solve", signature(a = "dsCMatrix", b = "missing"), function(a, b, ...) solve(a, .trDiagonal(nrow(a), unitri=FALSE), ...)) setMethod("chol", signature(x = "dsCMatrix"), function(x, pivot = FALSE, ...) .Call(dsCMatrix_chol, x, pivot), valueClass = "dtCMatrix") setMethod("Cholesky", signature(A = "dsCMatrix"), ## signature(): leaving away (perm, LDL,..), but specify below: ## <==> all "ANY" function(A, perm = TRUE, LDL = !super, super = FALSE, Imult = 0, ...) .Call(dsCMatrix_Cholesky, A, perm, LDL, super, Imult)) setMethod("t", signature(x = "dsCMatrix"), function(x) .Call(Csparse_transpose, x, FALSE), valueClass = "dsCMatrix") ### These two are very similar, the first one has the advantage to be applicable to 'Chx' directly: .diag.dsC <- function(x, Chx = Cholesky(x, LDL=TRUE), res.kind = "diag") { force(Chx) if(!missing(Chx)) stopifnot(.isLDL(Chx), is.integer(Chx@p), is.double(Chx@x)) .Call(diag_tC, Chx@p, Chx@x, Chx@perm, res.kind) ## ^^^^^^^ from ../src/Csparse.c } ## here, we *could* allow a 'mult = 0' factor : .CHM.LDL.D <- function(x, perm = TRUE, res.kind = "diag") { .Call(dsCMatrix_LDL_D, x, perm, res.kind) ## ^^^^^^^^^^^^^^^^ from ../src/dsCMatrix.c } ## FIXME: kind = "diagBack" is not yet implemented ## would be much more efficient, but there's no CHOLMOD UI (?) ## ## Note: for det(), permutation is unimportant; ## for diag(), apply *inverse* permutation ## q <- p ; q[q] <- seq_along(q); q ldet1.dsC <- function(x, ...) .Call(CHMfactor_ldetL2, Cholesky(x, ...)) ## these are slightly faster (ca. 3 to 4 %): ldet2.dsC <- function(x, ...) { Ch <- Cholesky(x, super = FALSE, ...) .Call(diag_tC, Ch@p, Ch@x, Ch@perm, "sumLog") } ## only very slightly ( ~ < 1% ) faster (than "ldet2"): ldet3.dsC <- function(x, perm = TRUE) .Call(dsCMatrix_LDL_D, x, perm=perm, "sumLog") setMethod("determinant", signature(x = "dsCMatrix", logarithm = "missing"), function(x, logarithm, ...) determinant(x, TRUE)) setMethod("determinant", signature(x = "dsCMatrix", logarithm = "logical"), function(x, logarithm, ...) { if((n <- x@Dim[1]) <= 1) return(mkDet(diag(x), logarithm)) Chx <- tryCatch(suppressWarnings(Cholesky(x, LDL=TRUE)), error = function(e) NULL) ## or ## ldet <- .Call("CHMfactor_ldetL2", Chx) # which would also work ## when Chx <- Cholesky(x, super=TRUE) ## ldet <- tryCatch(.Call(dsCMatrix_LDL_D, x, perm=TRUE, "sumLog"), ## if(is.null(ldet)) if(is.null(Chx)) ## we do *not* have a positive definite matrix detSparseLU(x, logarithm) else { d <- .Call(diag_tC, Chx@p, Chx@x, Chx@perm, res.kind = "diag") mkDet(d, logarithm=logarithm) } }) ## setMethod("writeHB", signature(obj = "dsCMatrix"), ## function(obj, file, ...) { ## .Deprecated("writeMM") ## .Call(Matrix_writeHarwellBoeing, ## if (obj@uplo == "U") t(obj) else obj, ## as.character(file), "DSC") ## }) Matrix/R/ngCMatrix.R0000644000175100001440000000314512213574105013757 0ustar hornikusers#### Logical Sparse Matrices in Compressed column-oriented format ### contains = "nsparseMatrix" nC2d <- function(from) .Call(nz_pattern_to_Csparse, from, 0L)## 0 --> "double" nC2l <- function(from) .Call(nz_pattern_to_Csparse, from, 1L)## 1 --> "logical" if(FALSE) { ## nice idea, but needs more method re-definitions --- setAs("nCsparseMatrix", "dMatrix", nC2d) setAs("nCsparseMatrix", "dsparseMatrix", nC2d) setAs("nCsparseMatrix", "dgCMatrix", nC2d) setAs("nCsparseMatrix", "lMatrix", nC2l) setAs("nCsparseMatrix", "lsparseMatrix", nC2l) setAs("nCsparseMatrix", "lgCMatrix", nC2l) } else { setAs("ngCMatrix", "dMatrix", nC2d) setAs("ngCMatrix", "dsparseMatrix", nC2d) setAs("ngCMatrix", "dgCMatrix", nC2d) setAs("ngCMatrix", "lMatrix", nC2l) setAs("ngCMatrix", "lsparseMatrix", nC2l) setAs("ngCMatrix", "lgCMatrix", nC2l) } if(FALSE) ## rather use ("Csparse*, to= "Tsparse*"): setAs("ngCMatrix", "ngTMatrix", function(from) new("ngTMatrix", i = from@i, j = .Call(Matrix_expand_pointers, from@p), Dim = from@Dim, Dimnames = from@Dimnames)) if(FALSE) ## rather use ("Csparse*, to= "dense*"): setAs("ngCMatrix", "ngeMatrix", function(from) new("ngeMatrix", x = c(as(from, "matrix")), # is fast, Dim = from@Dim, Dimnames = from@Dimnames)) setAs("ngCMatrix", "matrix", function(from) .Call(ngC_to_matrix, from)) ## not this: .Call(Csparse_to_matrix, from)), since it goes via dense -> double precision ## TODO (maybe): write matrix_to_lcsc() in ../src/ngCMatrix.c setAs("matrix", "ngCMatrix", function(from) as(as(from, "ngTMatrix"), "ngCMatrix")) Matrix/R/lgCMatrix.R0000644000175100001440000000244512213574105013757 0ustar hornikusers#### Logical Sparse Matrices in Compressed column-oriented format ### contains = "lsparseMatrix" ## Can use CsparseMatrix methods for all of these ## setMethod("t", signature(x = "lgCMatrix"), ## function(x) .Call(lgCMatrix_trans, x), ## valueClass = "lgCMatrix") ## setMethod("diag", signature(x = "lgCMatrix"), ## function(x, nrow, ncol) .Call(lgCMatrix_diag, x)) setAs("lgCMatrix", "dgCMatrix", function(from) new("dgCMatrix", i = from@i, p = from@p, x = as.double(from@x), Dim = from@Dim, Dimnames = from@Dimnames)) setAs("lgCMatrix", "lgTMatrix", function(from) new("lgTMatrix", i = from@i, x = from@x, j = .Call(Matrix_expand_pointers, from@p), Dim = from@Dim, Dimnames = from@Dimnames)) setAs("lgCMatrix", "lgeMatrix", function(from) new("lgeMatrix", x = c(as(from, "matrix")), # is fast, Dim = from@Dim, Dimnames = from@Dimnames)) setAs("lgCMatrix", "matrix", function(from) .Call(lgC_to_matrix, from)) ## not this: .Call(Csparse_to_matrix, from)), since it goes via dense -> double precision ## TODO (maybe): write matrix_to_lcsc() in ../src/lgCMatrix.c setAs("matrix", "lgCMatrix", function(from) as(as(from, "lgTMatrix"), "lgCMatrix")) Matrix/R/Rsparse.R0000644000175100001440000001744412070371667013522 0ustar hornikusers#### Sparse Matrices in Compressed row-oriented format #### --- "R" ### ``mainly for completeness'' --- we *do* favour Csparse ## - - - - - - - - - - - - hence only "minimal" methods here ! ## see also ./SparseM-conv.R ### contains = "dMatrix" ## compressed_to_TMatrix -- fails on 32bit--enable-R-shlib with segfault {Kurt} ## ------------ --> ../src/dgCMatrix.c .R.2.T <- function(from) .Call(compressed_to_TMatrix, from, FALSE) ## slow R-level workaround ## this is cheap; alternative: going there directly, using ## i <- .Call(Matrix_expand_pointers, from@p), if(FALSE) .R.2.T <- function(from) as(.R.2.C(from), "TsparseMatrix") ## R_to_CMatrix ## ------------ --> ../src/dgCMatrix.c .R.2.C <- function(from) .Call(R_to_CMatrix, from) if(FALSE)## "slow" unneeded R-level version .R.2.C <- function(from) { cl <- class(from) valid <- c("dgRMatrix", "dsRMatrix", "dtRMatrix", "lgRMatrix", "lsRMatrix", "ltRMatrix", "ngRMatrix", "nsRMatrix", "ntRMatrix", "zgRMatrix", "zsRMatrix", "ztRMatrix") icl <- match(cl, valid) - 1L if(is.na(icl)) stop(gettextf("invalid class: %s", dQuote(cl)), domain=NA) Ccl <- sub("^(..)R","\\1C", cl) # corresponding Csparse class name r <- new(Ccl) r@Dim <- from@Dim[2:1] if(icl %/% 3 != 2) ## not "n..Matrix" --> has 'x' slot r@x <- from@x if(icl %% 3 != 0) { # symmetric or triangular r@uplo <- from@uplo if(icl %% 3 == 2) # triangular r@diag <- from@diag } r@i <- from@j r@p <- from@p r <- t(r) r@Dimnames <- from@Dimnames r } ## However, a quick way to "treat a t() as corresponding " : .tR.2.C <- function(from) { cl <- class(from) valid <- c("dgRMatrix", "dsRMatrix", "dtRMatrix", "lgRMatrix", "lsRMatrix", "ltRMatrix", "ngRMatrix", "nsRMatrix", "ntRMatrix", "zgRMatrix", "zsRMatrix", "ztRMatrix") icl <- match(cl, valid) - 1L if(is.na(icl)) stop(gettextf("invalid class: %s", dQuote(cl)), domain=NA) Ccl <- sub("^(..)R","\\1C", cl) # corresponding Csparse class name r <- new(Ccl) r@i <- from@j ##- - r@p <- from@p r@Dim <- from@Dim[2:1] r@Dimnames <- from@Dimnames[2:1] if(icl %/% 3 != 2) ## not "n..Matrix" --> has 'x' slot r@x <- from@x if(icl %% 3 != 0) { # symmetric or triangular r@uplo <- from@uplo if(icl %% 3 == 2) # triangular r@diag <- from@diag } r } ## coercion to other virtual classes --- the functionality we want to encourage setAs("RsparseMatrix", "TsparseMatrix", .R.2.T) setAs("RsparseMatrix", "CsparseMatrix", .R.2.C) setAs("RsparseMatrix", "denseMatrix", function(from) as(.R.2.C(from), "denseMatrix")) setAs("RsparseMatrix", "dsparseMatrix", function(from) as(.R.2.C(from), "dsparseMatrix")) setAs("RsparseMatrix", "lsparseMatrix", function(from) as(.R.2.C(from), "lsparseMatrix")) setAs("RsparseMatrix", "nsparseMatrix", function(from) as(.R.2.C(from), "nsparseMatrix")) setAs("RsparseMatrix", "dMatrix", function(from) as(.R.2.C(from), "dMatrix")) setAs("RsparseMatrix", "lMatrix", function(from) as(.R.2.C(from), "lMatrix")) setAs("RsparseMatrix", "nMatrix", function(from) as(.R.2.C(from), "nMatrix")) setAs("RsparseMatrix", "generalMatrix", function(from) as(.R.2.C(from), "generalMatrix")) ## for printing etc: setAs("RsparseMatrix", "dgeMatrix", function(from) as(.R.2.C(from), "dgeMatrix")) setAs("RsparseMatrix", "matrix", function(from) as(.R.2.C(from), "matrix")) ## **VERY** cheap substitute: work via dgC and t(.) .viaC.to.dgR <- function(from) { m <- as(t(from), "dgCMatrix") new("dgRMatrix", Dim = dim(from), Dimnames = .M.DN(from), p = m@p, j = m@i, x = m@x) } ## one of the few coercions "to " {tested in ../tests/Class+Meth.R} setAs("matrix", "dgRMatrix", .viaC.to.dgR) ## *very* cheap substitute: work via t(.) and Csparse .viaC.to.R <- function(from) { m <- as(t(from), "CsparseMatrix")# preserve symmetry/triangular clx <- getClassDef(class(m)) has.x <- !extends(clx, "nsparseMatrix")## <==> has 'x' slot ## instead of "d": .M.kind (m,cl) ## instead of "g": ..M.shape(m,cl) sh <- .M.shapeC(m,clx) r <- new(paste0(.M.kindC(clx), sh, "RMatrix")) r@Dim <- dim(from) r@Dimnames <- .M.DN(from) r@p <- m@p r@j <- m@i if(has.x) r@x <- m@x if(sh != "g") { r@uplo <- if(m@uplo != "U") "U" else "L" if(sh == "t") r@diag <- m@diag } r } setAs("matrix", "RsparseMatrix", .viaC.to.R) setAs("denseMatrix", "RsparseMatrix", .viaC.to.R) setAs("sparseMatrix","RsparseMatrix", .viaC.to.R) ## symmetric: can use same 'p' slot setAs("dsCMatrix", "dsRMatrix", function(from) new("dsRMatrix", Dim = dim(from), Dimnames = .M.DN(from), p = from@p, j = from@i, x = from@x, uplo = if (from@uplo == "U") "L" else "U")) ## FIXME: if this makes sense, do it for "l" and "n" as well as "d" ## setAs("dtCMatrix", "dtRMatrix", .viaC.to.dgR) # should work; can NOT use 'p' ##setAs("dgRMatrix", "dgeMatrix", ## function(from) .Call(csc_to_dgeMatrix, from)) ##setAs("matrix", "dgRMatrix", ## function(from) { ## storage.mode(from) <- "double" ## .Call(matrix_to_csc, from) ## }) ##setMethod("diag", signature(x = "dgRMatrix"), ## function(x = 1, nrow, ncol = n) .Call(csc_getDiag, x)) ## try to define for "Matrix" -- once and for all -- but that fails -- why? __ FIXME __ ## setMethod("dim", signature(x = "dgRMatrix"), ## function(x) x@Dim, valueClass = "integer") ##setMethod("t", signature(x = "dgRMatrix"), ## function(x) .Call(csc_transpose, x), ## valueClass = "dgRMatrix") setMethod("image", "dgRMatrix", function(x, ...) { x <- as(x, "TsparseMatrix") callGeneric() }) setMethod("t", "RsparseMatrix", function(x) as(t(.R.2.T(x)), "RsparseMatrix")) ## Want tril(), triu(), band() --- just as "indexing" --- ## return a "close" class: setMethod("tril", "RsparseMatrix", function(x, k = 0, ...) as(tril(.R.2.C(x), k = k, ...), "RsparseMatrix")) setMethod("triu", "RsparseMatrix", function(x, k = 0, ...) as(triu(.R.2.C(x), k = k, ...), "RsparseMatrix")) setMethod("band", "RsparseMatrix", function(x, k1, k2, ...) as(band(.R.2.C(x), k1 = k1, k2 = k2, ...), "RsparseMatrix")) setReplaceMethod("[", signature(x = "RsparseMatrix", i = "index", j = "missing", value = "replValue"), function (x, i, j, ..., value) replTmat(as(x,"TsparseMatrix"), i=i, value=value)) setReplaceMethod("[", signature(x = "RsparseMatrix", i = "missing", j = "index", value = "replValue"), function (x, i, j, ..., value) replTmat(as(x,"TsparseMatrix"), j=j, value=value)) setReplaceMethod("[", signature(x = "RsparseMatrix", i = "index", j = "index", value = "replValue"), function (x, i, j, ..., value) replTmat(as(x,"TsparseMatrix"), i=i, j=j, value=value)) setReplaceMethod("[", signature(x = "RsparseMatrix", i = "index", j = "missing", value = "sparseVector"), function (x, i, j, ..., value) replTmat(as(x,"TsparseMatrix"), i=i, value=value)) setReplaceMethod("[", signature(x = "RsparseMatrix", i = "missing", j = "index", value = "sparseVector"), function (x, i, j, ..., value) replTmat(as(x,"TsparseMatrix"), j=j, value=value)) setReplaceMethod("[", signature(x = "RsparseMatrix", i = "index", j = "index", value = "sparseVector"), function (x, i, j, ..., value) replTmat(as(x,"TsparseMatrix"), i=i, j=j, value=value)) setReplaceMethod("[", signature(x = "RsparseMatrix", i = "matrix", j = "missing", value = "replValue"), function (x, i, j, ..., value) .TM.repl.i.mat(as(x,"TsparseMatrix"), i=i, value=value)) Matrix/R/symmetricMatrix.R0000644000175100001440000001275512174560321015274 0ustar hornikusers#### symmetricMatrix : virtual class setAs("denseMatrix", "symmetricMatrix", function(from) ## vvvv do *check* symmetry .Call(dense_to_symmetric, from, "U", TRUE)) setAs("matrix", "symmetricMatrix", function(from) .Call(dense_to_symmetric, from, "U", TRUE)) ### ----------- forceSymmetric() ----- *all* methods ------------------------ ## forceSymmetric() coerces to "symmetricMatrix" withOUT testing ## ---------------- contrary to as(M, ) which should only ## work when 'M' is a symmetric matrix __ in the sense of isSymmetric() __ ## i.e., with allowing a little bit of asymmetric numeric fuzz: setMethod("forceSymmetric", signature(x = "matrix", uplo="ANY"), function(x, uplo) .Call(dense_to_symmetric, x, if(missing(uplo)) "U" else uplo, FALSE)) symCls <- names(getClass("symmetricMatrix")@subclasses) for(cls in symCls) { ## When x is symmetric and uplo is missing, we keep 'uplo' from 'x': setMethod("forceSymmetric", signature(x = cls, uplo="missing"), function(x, uplo) x) setMethod("forceSymmetric", signature(x = cls, uplo="character"), function(x, uplo) { if(uplo == x@uplo) x else ## uplo is "wrong" for x t(x) }) } setMethod("forceSymmetric", signature(x = "denseMatrix", uplo="character"), function(x, uplo) .Call(dense_to_symmetric, x, uplo, FALSE)) setMethod("forceSymmetric", signature(x = "denseMatrix", uplo="missing"), function(x, uplo) { uplo <- if(is(x, "triangularMatrix")) x@uplo else "U" ## FIXME? diagU2N() ?? .Call(dense_to_symmetric, x, uplo, FALSE) }) setMethod("forceSymmetric", signature(x="sparseMatrix"), function(x, uplo) { x <- as(x, "CsparseMatrix") callGeneric() }) forceCspSymmetric <- function(x, uplo, isTri = is(x, "triangularMatrix")) { ## isTri ==> effectively *diagonal* if(isTri && x@diag == "U") x <- .Call(Csparse_diagU2N, x) if(missing(uplo)) uplo <- if(isTri) x@uplo else "U" .Call(Csparse_general_to_symmetric, x, uplo) } setMethod("forceSymmetric", signature(x="CsparseMatrix"), function(x, uplo) forceCspSymmetric(x, uplo)) setMethod("symmpart", signature(x = "symmetricMatrix"), function(x) x) setMethod("skewpart", signature(x = "symmetricMatrix"), setZero) ###------- pack() and unpack() --- for *dense* symmetric & triangular matrices: packM <- function(x, Mtype, kind, unpack) { cd <- getClassDef(cx <- class(x)) if(extends(cd, "sparseMatrix")) stop(sprintf("(un)packing only applies to dense matrices, class(x)='%s'", cx)) if(!missing(kind) && kind == "symmetric") { ## use 'unpack' but not 'Mtype' ## special treatment for positive definite ones: as(x, if(unpack) { if(extends(cd, "dppMatrix")) "dpoMatrix" else paste0(.M.kindC(cd), "syMatrix") } else { ## !unpack : "pack" : if(extends(cd, "dpoMatrix")) "dppMatrix" else paste0(.M.kindC(cd), "spMatrix") }) } else as(x, paste0(.M.kindC(cd), Mtype)) } setMethod("unpack", "symmetricMatrix", function(x, ...) packM(x, kind="symmetric", unpack=TRUE)) setMethod("pack", "symmetricMatrix", function(x, ...) packM(x, kind="symmetric", unpack=FALSE)) setMethod("unpack", "triangularMatrix", function(x, ...) packM(x,"trMatrix")) setMethod("pack", "triangularMatrix", function(x, ...) packM(x,"tpMatrix")) ## to produce a nicer error message: pckErr <- function(x, ...) stop(sprintf("(un)packing only applies to dense matrices, class(x)='%s'", class(x))) setMethod("unpack", "sparseMatrix", pckErr) setMethod("pack", "sparseMatrix", pckErr) rm(pckErr) ##' pack () -- smartly: setMethod("pack", signature(x = "matrix"), function(x, symmetric=NA, upperTri = NA, ...) { if(is.na(symmetric)) ## must guess symmetric / triangular symmetric <- isSymmetric.matrix(x) if(symmetric) { pack(.Call(dense_to_symmetric, x, "U", TRUE), ...) } else { # triangular ## isTriMat(..) : should still check fully (speed up ?) .. if(isTr <- isTriMat(x, upper=upperTri)) { uplo <- attr(isTr, "kind") pack(new(paste0(.M.kind(x),"tpMatrix"), x = x[indTri(nrow(x), upper=(uplo == "U"), diag=TRUE)], Dim = dim(x), Dimnames = .M.DN(x), uplo = uplo), ...) } else stop("'x' is not symmetric nor triangular") } }) ## {"traditional"} specific methods setMethod("unpack", signature(x = "dspMatrix"), function(x, ...) as(x, "dsyMatrix"), valueClass = "dsyMatrix") setMethod("unpack", signature(x = "dtpMatrix"), function(x, ...) as(x, "dtrMatrix"), valueClass = "dtrMatrix") ### ## autogenerate coercions ## as(*, "symmetricMatrix") ## ~~~~~~~~~~~~~~~~~~~~~~~~~ ## Basic problem: ## This should work at package install time when package:Matrix does not exist! if(FALSE) local({ allCl <- getClasses("package:Matrix") ## << fails at install time!!!! clss <- allCl[sapply(allCl, extends, class2 = "Matrix")] virt <- sapply(clss, isVirtualClass) ## Now ensure coercions for all non-virtual "Matrix" inheriting classes: for(cl in clss[!virt]) { cld <- getClassDef(cl) if(extends(cld, "symmetricMatrix")) cat("\tsymmetric:\t", cl,"\n") else if(extends(cld, "triangularMatrix")) cat("\ttriangular:\t", cl,"\n") else if(extends(cld, "diagonalMatrix")) cat("\tdiagonal:\t", cl,"\n") else { cat("do ",cl,"\n") ## setAs(cl, "symmetricMatrix", ## function(from) as(from, ".s.Matrix")) } }## for }) Matrix/vignettes/0000755000175100001440000000000012271765426013560 5ustar hornikusersMatrix/vignettes/Design-issues.Rnw0000644000175100001440000001273212070262574016770 0ustar hornikusers\documentclass{article} % \usepackage{myVignette} \usepackage[authoryear,round]{natbib} \bibliographystyle{plainnat} \newcommand{\noFootnote}[1]{{\small (\textit{#1})}} \newcommand{\myOp}[1]{{$\left\langle\ensuremath{#1}\right\rangle$}} %% vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv %%\VignetteIndexEntry{Design Issues in Matrix package Development} %%\VignetteDepends{Matrix} \SweaveOpts{engine=R,eps=FALSE,pdf=TRUE,width=5,height=3,strip.white=true,keep.source=TRUE} % ^^^^^^^^^^^^^^^^ \title{Design Issues in Matrix package Development} \author{Martin Maechler and Douglas Bates\\R Core Development Team \\\email{maechler@stat.math.ethz.ch}, \email{bates@r-project.org}} \date{Spring 2008 ({\tiny typeset on \tiny\today})} % \begin{document} \maketitle \begin{abstract} This is a (\textbf{currently very incomplete}) write-up of the many smaller and larger design decisions we have made in organizing functionalities in the Matrix package. Classes: There's a rich hierarchy of matrix classes, which you can visualize as a set of trees whose inner (and ``upper'') nodes are \emph{virtual} classes and only the leaves are non-virtual ``actual'' classes. Functions and Methods: - setAs() - others \end{abstract} %% Note: These are explained in '?RweaveLatex' : <>= options(width=75) @ \section{The Matrix class structures} \label{sec:classes} Take Martin's DSC 2007 talk to depict class hierarchy. \\ --- --- --- %% \hrule[1pt]{\textwidth} \subsection{Diagonal Matrices} \label{ssec:diagMat} The class of diagonal matrices is worth mentioning for several reasons. First, we have wanted such a class, because \emph{multiplication} methods are particularly simple with diagonal matrices. The typical constructor is \Rfun{Diagonal} whereas the accessor (as for traditional matrices), \Rfun{diag} simply returns the \emph{vector} of diagonal entries: <>= library(Matrix) (D4 <- Diagonal(4, 10*(1:4))) str(D4) diag(D4) @ We can \emph{modify} the diagonal in the traditional way (via method definition for \Rfun{diag<-}): <>= diag(D4) <- diag(D4) + 1:4 D4 @ Note that \textbf{unit-diagonal} matrices (the identity matrices of linear algebra) with slot \code{diag = "U"} can have an empty \code{x} slot, very analogously to the unit-diagonal triangular matrices: <>= str(I3 <- Diagonal(3)) ## empty 'x' slot getClass("diagonalMatrix") ## extending "denseMatrix" @ We have implemented diagonal matrices as \emph{dense} rather than sparse matrices, for the following reasons: \begin{enumerate} \item The \code{diag()}onal (vector) is the basic part of such a matrix, and this is simply the \code{x} slot unless the \code{diag} slot is \code{"U"}, the unit-diagonal case, which is the identity matrix. \item given '1)', it does not make much sense to store \emph{where} the matrix is non-zero. This contrasts with all sparse matrix implementations, and hence we did not want to call a diagonal matrix ``sparse''. \end{enumerate} \section{Matrix Transformations} \label{sec:trafos} \subsection{Coercions between Matrix classes} \label{ssec:coerce} You may need to transform Matrix objects into specific shape (triangular, symmetric), content type (double, logical, \dots) or storage structure (dense or sparse). Every useR should use \code{as(x, )} to this end, where \code{} is a \emph{virtual} Matrix super class, such as \code{"triangularMatrix"} \code{"dMatrix"}, or \code{"sparseMatrix"}. In other words, the user should \emph{not} coerce directly to a specific desired class such as \code{"dtCMatrix"}, even though that may occasionally work as well. Here is a set of rules to which the Matrix developers and the users should typically adhere: \begin{description} \item[Rule~1]: \code{as(M, "matrix")} should work for \textbf{all} Matrix objects \code{M}. \item[Rule~2]: \code{Matrix(x)} should also work for matrix like objects \code{x} and always return a ``classed'' Matrix. Applied to a \code{"matrix"} object \code{m}, \code{M. <- Matrix(m)} can be considered a kind of inverse of \code{m <- as(M, "matrix")}. For sparse matrices however, \code{M.} well be a \code{CsparseMatrix}, and it is often ``more structured'' than \code{M}, e.g., <>= (M <- spMatrix(4,4, i=1:4, j=c(3:1,4), x=c(4,1,4,8))) # dgTMatrix m <- as(M, "matrix") (M. <- Matrix(m)) # dsCMatrix (i.e. *symmetric*) @ \item[Rule~3]: All the following coercions to \emph{virtual} matrix classes should work:\\ \begin{enumerate} \item \code{as(m, "dMatrix")} \item \code{as(m, "lMatrix")} \item \code{as(m, "nMatrix")} \item \code{as(m, "denseMatrix")} \item \code{as(m, "sparseMatrix")} \item \code{as(m, "generalMatrix")} \end{enumerate} whereas the next ones should work under some assumptions: \begin{enumerate} \item \code{as(m1, "triangularMatrix")} \\ should work when \code{m1} is a triangular matrix, i.e. the upper or lower triangle of \code{m1} contains only zeros. \item \code{as(m2, "symmetricMatrix")} should work when \code{m2} is a symmetric matrix in the sense of \code{isSymmetric(m2)} returning \code{TRUE}. Note that this is typically equivalent to something like \code{isTRUE(all.equal(m2, t(m2)))}, i.e., the lower and upper triangle of the matrix have to be equal \emph{up to small numeric fuzz}. \end{enumerate} \end{description} \section{Session Info} <>= toLatex(sessionInfo()) @ %not yet %\bibliography{Matrix} \end{document} Matrix/vignettes/Intro2Matrix.Rnw0000644000175100001440000004453212070262574016613 0ustar hornikusers\documentclass{article} % \usepackage{myVignette} \usepackage{fullpage}% save trees ;-) \usepackage[authoryear,round]{natbib} \bibliographystyle{plainnat} \newcommand{\noFootnote}[1]{{\small (\textit{#1})}} \newcommand{\myOp}[1]{{$\left\langle\ensuremath{#1}\right\rangle$}} % %%\VignetteIndexEntry{2nd Introduction to the Matrix Package} %%\VignetteDepends{Matrix} \SweaveOpts{engine=R,eps=FALSE,pdf=TRUE,width=7,height=4,strip.white=true,keep.source=TRUE} % ^^^^^^^^^^^^^^^^ \title{2nd Introduction to the Matrix package} \author{Martin Maechler and Douglas Bates\\ R Core Development Team \\\email{maechler@stat.math.ethz.ch}, \email{bates@r-project.org}} \date{September 2006 ({\tiny typeset on \tiny\today})} % \begin{document} \maketitle \begin{abstract} % \emph{\Large Why should you want to work with this package and what % does it do for you?} Linear algebra is at the core of many areas of statistical computing and from its inception the \Slang{} has supported numerical linear algebra via a matrix data type and several functions and operators, such as \code{\%*\%}, \code{qr}, \code{chol}, and \code{solve}. However, these data types and functions do not provide direct access to all of the facilities for efficient manipulation of dense matrices, as provided by the Lapack subroutines, and they do not provide for manipulation of sparse matrices. The \pkg{Matrix} package provides a set of S4 classes for dense and sparse matrices that extend the basic matrix data type. Methods for a wide variety of functions and operators applied to objects from these classes provide efficient access to BLAS (Basic Linear Algebra Subroutines), Lapack (dense matrix), CHOLMOD including AMD and COLAMD and \code{Csparse} (sparse matrix) routines. One notable characteristic of the package is that whenever a matrix is factored, the factorization is stored as part of the original matrix so that further operations on the matrix can reuse this factorization. \end{abstract} %% Note: These are explained in '?RweaveLatex' : <>= options(width=75) @ \section{Introduction} \label{sec:Intro} The most automatic way to use the \pkg{Matrix} package is via the \Rfun{Matrix} function which is very similar to the standard \RR\ function \Rfun{matrix}, @ <>= library(Matrix) M <- Matrix(10 + 1:28, 4, 7) M tM <- t(M) @ %def Such a matrix can be appended to (using \Rfun{cBind} or \Rfun{rBind} with capital ``B'') or indexed, <>= (M2 <- cBind(-1, M)) M[2, 1] M[4, ] @ where the last two statements show customary matrix indexing, returning a simple numeric vector each\footnote{because there's an additional default argument to indexing, \code{drop = TRUE}. If you add \hbox{``\code{\ ,\ drop = FALSE}\ ''} you will get submatrices instead of simple vectors.}. We assign 0 to some columns and rows to ``sparsify'' it, and some \code{NA}s (typically ``missing values'' in data analysis) in order to demonstrate how they are dealt with; note how we can \emph{``subassign''} as usual, for classical \RR{} matrices (i.e., single entries or whole slices at once), @ <>= M2[, c(2,4:6)] <- 0 M2[2, ] <- 0 M2 <- rBind(0, M2, 0) M2[1:2,2] <- M2[3,4:5] <- NA @ and then coerce it to a sparse matrix, @ <>= sM <- as(M2, "sparseMatrix") 10 * sM identical(sM * 2, sM + sM) is(sM / 10 + M2 %/% 2, "sparseMatrix") @ %def where the last three calls show that multiplication by a scalar keeps sparcity, as does other arithmetic, but addition to a ``dense'' object does not, as you might have expected after some thought about ``sensible'' behavior: @ <>= sM + 10 @ %def Operations on our classed matrices include (componentwise) arithmetic ($+$, $-$, $*$, $/$, etc) as partly seen above, comparison ($>$, $\le$, etc), e.g., <>= Mg2 <- (sM > 2) Mg2 @ returning a logical sparse matrix. When interested in the internal \textbf{str}ucture, \Rfun{str} comes handy, and we have been using it ourselves more regulary than \Rfun{print}ing (or \Rfun{show}ing as it happens) our matrices; alternatively, \Rfun{summary} gives output similar to Matlab's printing of sparse matrices. @ <>= str(Mg2) summary(Mg2) @ As you see from both of these, \code{Mg2} contains ``extra zero'' (here \code{FALSE}) entries; such sparse matrices may be created for different reasons, and you can use \Rfun{drop0} to remove (``drop'') these extra zeros. This should \emph{never} matter for functionality, and does not even show differently for logical sparse matrices, but the internal structure is more compact: <>= Mg2 <- drop0(Mg2) str(Mg2@x) # length 13, was 16 @ For large sparse matrices, visualization (of the sparsity pattern) is important, and we provide \Rfun{image} methods for that, e.g., <>= data(CAex) print(image(CAex, main = "image(CAex)")) # print(.) needed for Sweave @ \smallskip Further, i.e., in addition to the above implicitly mentioned \code{"Ops"} operators (\code{+}, \code{*},\dots, \code{<=},\code{>},\dots, \code{\&} which all work with our matrices, notably in conjunction with scalars and traditional matrices), the \code{"Math"}-operations (such as \Rfun{exp}, \Rfun{sin} or \Rfun{gamma}) and \code{"Math2"} (\Rfun{round} etc) and the \code{"Summary"} group of functions, \Rfun{min}, \Rfun{range}, \Rfun{sum}, all work on our matrices as they should. Note that all these are implemented via so called \emph{group methods}, see e.g., \code{?Arith} in \RR. The intention is that sparse matrices remain sparse whenever sensible, given the matrix \emph{classes} and operators involved, but not content specifically. E.g., + gives even for the rare cases where it would be advantageous to get a result. These classed matrices can be ``indexed'' (more technically ``subset'') as traditional \Slang{} (and hence \RR) matrices, as partly seen above. This also includes the idiom \code{M [ M \myOp{\mathit{op}} \myOp{\mathrm{num}}~]} which returns simple vectors, @ <>= sM[sM > 2] sml <- sM[sM <= 2] sml @ %def and \emph{``subassign''}ment similarly works in the same generality as for traditional \Slang{} matrices. %% We have seen that already above! %% This was the 2005 - Introduction vignette's first section: \subsection{\pkg{Matrix} package for numerical linear algebra} \label{ssec:intro-linalg} Linear algebra is at the core of many statistical computing techniques and, from its inception, the \Slang{} has supported numerical linear algebra via a matrix data type and several functions and operators, such as \code{\%*\%}, \code{qr}, \code{chol}, and \code{solve}. %% Initially the numerical linear algebra functions in \RR{} called underlying Fortran routines from the Linpack~\citep{Linpack} and Eispack~\citep{Eispack} libraries but over the years most of these functions have been switched to use routines from the Lapack~\citep{Lapack} library which is the state-of-the-art implementation of numerical dense linear algebra. %% Furthermore, \RR{} can be configured to use accelerated BLAS (Basic Linear Algebra Subroutines), such as those from the Atlas~\citep{Atlas} project or other ones, see the \RR~manual ``Installation and Administration''. Lapack provides routines for operating on several special forms of matrices, such as triangular matrices and symmetric matrices. Furthermore, matrix decompositions like the QR decompositions produce multiple output components that should be regarded as parts of a single object. There is some support in \RR{} for operations on special forms of matrices (e.g. the \code{backsolve}, \code{forwardsolve} and \code{chol2inv} functions) and for special structures (e.g. a QR structure is implicitly defined as a list by the \code{qr}, \code{qr.qy}, \code{qr.qty}, and related functions) but it is not as fully developed as it could be. Also there is no direct support for sparse matrices in \RR{} although \citet{koen:ng:2003} have developed the \pkg{SparseM} package for sparse matrices based on SparseKit. The \pkg{Matrix} package provides S4 classes and methods for dense and sparse matrices. The methods for dense matrices use Lapack and BLAS. The sparse matrix methods use CHOLMOD~\citep{Cholmod}, CSparse~\citep{Csparse} and other parts (AMD, COLAMD) of Tim Davis' ``SuiteSparse'' collection of sparse matrix libraries, many of which also use BLAS. \TODO{\Rfun{triu}, \Rfun{tril}, \Rfun{diag}, ... and \command{as(.,.)} , but of course only when they've seen a few different ones.} \TODO{matrix operators include \code{\%*\%}, \Rfun{crossprod}, \Rfun{tcrossprod}, \Rfun{solve}} \TODO{\Rfun{expm} is the matrix exponential ... ...} \TODO{\Rfun{symmpart} and \Rfun{skewpart} compute the symmetric part, \code{(x + t(x))/2} and the skew-symmetric part, \code{(x - t(x))/2} of a matrix \code{x}.} \TODO{factorizations include \Rfun{Cholesky} (or \Rfun{chol}), \Rfun{lu}, \Rfun{qr} (not yet for dense)} \TODO{Although generally the result of an operation on dense matrices is a dgeMatrix, certain operations return matrices of special types.} \TODO{E.g. show the distinction between \code{t(mm) \%*\% mm} and \code{crossprod(mm)}.} % \bigskip % ... ... ... The following is the old \file{Introduction.Rnw} ... FIXME ... ... \bigskip \section{Matrix Classes} The \pkg{Matrix} package provides classes for real (stored as double precision), logical and so-called ``pattern'' (binary) dense and sparse matrices. There are provisions to also provide integer and complex (stored as double precision complex) matrices. Note that in \RR, \code{logical} means entries \code{TRUE}, \code{FALSE}, or \code{NA}. To store just the non-zero pattern for typical sparse matrix algorithms, the pattern matrices are \emph{binary}, i.e., conceptually just \code{TRUE} or \code{FALSE}. In \pkg{Matrix}, the pattern matrices all have class names starting with \code{"n"} (patter\textbf{n}). \subsection{Classes for dense matrices} \label{ssec:DenseClasses} For the sake of brevity, we restrict ourselves to the \emph{real} (\textbf{d}ouble) classes, but they are paralleled by \textbf{l}ogical and patter\textbf{n} matrices for all but the positive definite ones. \begin{description} \item[dgeMatrix] Real matrices in general storage mode \item[dsyMatrix] Symmetric real matrices in non-packed storage \item[dspMatrix] Symmetric real matrices in packed storage (one triangle only) \item[dtrMatrix] Triangular real matrices in non-packed storage \item[dtpMatrix] Triangular real matrices in packed storage (triangle only) \item[dpoMatrix] Positive semi-definite symmetric real matrices in non-packed storage \item[dppMatrix] \ \ ditto \ \ in packed storage \end{description} Methods for these classes include coercion between these classes, when appropriate, and coercion to the \code{matrix} class; methods for matrix multiplication (\code{\%*\%}); cross products (\code{crossprod}), matrix norm (\code{norm}); reciprocal condition number (\code{rcond}); LU factorization (\code{lu}) or, for the \code{poMatrix} class, the Cholesky decomposition (\code{chol}); and solutions of linear systems of equations (\code{solve}). %-- mentioned above already: % Further, group methods have been defined for the \code{Arith} (basic % arithmetic, including with scalar numbers) and the \code{Math} (basic % mathematical functions) group.. Whenever a factorization or a decomposition is calculated it is preserved as a (list) element in the \code{factors} slot of the original object. In this way a sequence of operations, such as determining the condition number of a matrix then solving a linear system based on the matrix, do not require multiple factorizations of the same matrix nor do they require the user to store the intermediate results. \subsection{Classes for sparse matrices} \label{sec:SparseClasses} Used for large matrices in which most of the elements are known to be zero (or \code{FALSE} for logical and binary (``pattern'') matrices). Sparse matrices are automatically built from \Rfun{Matrix} whenever the majority of entries is zero (or \code{FALSE} respectively). Alternatively, \Rfun{sparseMatrix} builds sparse matrices from their non-zero entries and is typically recommended to construct large sparse matrices, rather than direct calls of \Rfun{new}. \TODO{E.g. model matrices created from factors with a large number of levels} \TODO{ or from spline basis functions (e.g. COBS, package \pkg{cobs}), etc.} \TODO{Other uses include representations of graphs. indeed; good you mentioned it! particularly since we still have the interface to the \pkg{graph} package. I think I'd like to draw one graph in that article --- maybe the undirected graph corresponding to a crossprod() result of dimension ca. $50^2$} \TODO{Specialized algorithms can give substantial savings in amount of storage used and execution time of operations.} \TODO{Our implementation is based on the CHOLMOD and CSparse libraries by Tim Davis.} \subsection{Representations of sparse matrices} \label{ssec:SparseReps} \subsubsection{Triplet representation (\class{TsparseMatrix})} Conceptually, the simplest representation of a sparse matrix is as a triplet of an integer vector \code{i} giving the row numbers, an integer vector \code{j} giving the column numbers, and a numeric vector \code{x} giving the non-zero values in the matrix.\footnote{For efficiency reasons, we use ``zero-based'' indexing in the \pkg{Matrix} package, i.e., the row indices \code{i} are in \code{0:(nrow(.)-1)} and the column indices \code{j} accordingly.} In \pkg{Matrix}, the \class{TsparseMatrix} class is the virtual class of all sparse matrices in triplet representation. Its main use is for easy input or transfer to other classes. As for the dense matrices, the class of the \code{x} slot may vary, and the subclasses may be triangular, symmetric or unspecified (``general''), such that the \class{TsparseMatrix} class has several\footnote{the $3 \times 3$ actual subclasses of \class{TsparseMatrix} are the three structural kinds, namely \textbf{t}riangular, \textbf{s}ymmetric and \textbf{g}eneral, times three entry classes, \textbf{d}ouble, \textbf{l}ogical, and patter\textbf{n}.} `actual'' subclasses, the most typical (numeric, general) is \class{dgTMatrix}: <>= getClass("TsparseMatrix") # (i,j, Dim, Dimnames) slots are common to all getClass("dgTMatrix") @ Note that the \emph{order} of the entries in the \code{(i,j,x)} vectors does not matter; consequently, such matrices are not unique in their representation. \footnote{ Furthermore, there can be \emph{repeated} \code{(i,j)} entries with the customary convention that the corresponding \code{x} entries are \emph{added} to form the matrix element $m_{ij}$. } %% The triplet representation is row-oriented if elements in the same row %% were adjacent and column-oriented if elements in the same column were %% adjacent. \subsubsection{Compressed representations: \class{CsparseMatrix} and \class{RsparseMatrix}} For most sparse operations we use the compressed column-oriented representation (virtual class \class{CsparseMatrix}) (also known as ``csc'', ``compressed sparse column''). Here, instead of storing all column indices \code{j}, only the \emph{start} index of every column is stored. Analogously, there is also a compressed sparse row (csr) representation, which e.g. is used in in the \pkg{SparseM} package, and we provide the \class{RsparseMatrix} for compatibility and completeness purposes, in addition to basic coercion (\code({as(., \textit{})} between the classes. %% (column-oriented triplet) except that \code{i} (\code{j}) just stores %% the index of the first element in the row (column). (There are a %% couple of other details but that is the gist of it.) These compressed representations remove the redundant row (column) indices and provide faster access to a given location in the matrix because you only need to check one row (column). There are certain advantages \footnote{routines can make use of high-level (``level-3'') BLAS in certain sparse matrix computations} to csc in systems like \RR{}, Octave and Matlab where dense matrices are stored in column-major order, therefore it is used in sparse matrix libraries such as CHOLMOD or CSparse of which we make use. For this reason, the \class{CsparseMatrix} class and subclasses are the principal classes for sparse matrices in the \pkg{Matrix} package. The Matrix package provides the following classes for sparse matrices \FIXME{many more --- maybe explain naming scheme?} \begin{description} \item[dgTMatrix] general, numeric, sparse matrices in (a possibly redundant) triplet form. This can be a convenient form in which to construct sparse matrices. \item[dgCMatrix] general, numeric, sparse matrices in the (sorted) compressed sparse column format. \item[dsCMatrix] symmetric, real, sparse matrices in the (sorted) compressed sparse column format. Only the upper or the lower triangle is stored. Although there is provision for both forms, the lower triangle form works best with TAUCS. \item[dtCMatrix] triangular, real, sparse matrices in the (sorted) compressed sparse column format. \end{description} \TODO{Can also read and write the Matrix Market and read the Harwell-Boeing representations.} \TODO{Can convert from a dense matrix to a sparse matrix (or use the Matrix function) but going through an intermediate dense matrix may cause problems with the amount of memory required.} \TODO{similar range of operations as for the dense matrix classes.} \section{More detailed examples of ``Matrix'' operations} Have seen \texttt{drop0()} above, %(p.3); only with logical showe a nice double example (where you see ``.'' and ``0''). Show the use of \code{dim<-} for \emph{resizing} a (sparse) matrix. Maybe mention \Rfun{nearPD}. \TODO{Solve a sparse least squares problem and demonstrate memory / speed gain} \TODO{mention \code{lme4} and \Rfun{lmer}, maybe use one example to show the matrix sizes.} \section{Notes about S4 classes and methods implementation} Maybe we could % even here (for R News, not only for JSS) give some glimpses of implementations at least on the \RR{} level ones? \TODO{The class hierarchy: a non-trivial tree where only the leaves are ``actual'' classes.} \TODO{The main advantage of the multi-level hierarchy is that methods can often be defined on a higher (virtual class) level which ensures consistency [and saves from ``cut \& paste'' and forgetting things]} \TODO{Using Group Methods} \section{Session Info} <>= toLatex(sessionInfo()) @ \bibliography{Matrix} \end{document} Matrix/vignettes/sparseModels.Rnw0000644000175100001440000002520212221066570016677 0ustar hornikusers\documentclass{article} % \usepackage{fullpage} \usepackage{myVignette} \usepackage[authoryear,round]{natbib} \bibliographystyle{plainnat} \newcommand{\noFootnote}[1]{{\small (\textit{#1})}} \newcommand{\myOp}[1]{{$\left\langle\ensuremath{#1}\right\rangle$}} %%\VignetteIndexEntry{Sparse Model Matrices} %%\VignetteDepends{Matrix,MASS} \title{Sparse Model Matrices} \author{Martin Maechler\\ R Core Development Team \\\email{maechler@R-project.org}} \date{July 2007, 2008 ({\tiny typeset on \tiny\today})} % \begin{document} \maketitle \SweaveOpts{engine=R, keep.source=TRUE} \SweaveOpts{eps=FALSE, pdf=TRUE, width=8, height=5.5, strip.white=true} \setkeys{Gin}{width=\textwidth} % \begin{abstract} % ............................ FIXME % \end{abstract} %% Note: These are explained in '?RweaveLatex' : <>= options(width=75) @ \section*{Introduction} Model matrices in the very widely used (generalized) linear models of statistics, (typically fit via \Rfun{lm} or \Rfun{glm} in \RR) are often practically sparse --- whenever categorical predictors, \code{factor}s in \RR, are used. %% FIXME: Introduce lm.fit.sparse() or not ? We show for a few classes of such linear models how to construct sparse model matrices using sparse matrix (S4) objects from the \pkg{Matrix} package, and typically \emph{without} using dense matrices in intermediate steps. %% only the latter is really novel, since "SparseM" (and others) %% have used the equivalent of %% as( model.matrix(.....), "sparseMatrix") \section{One factor: \texttt{y $\sim$ f1}} Let's start with an artifical small example: <>= (ff <- factor(strsplit("statistics_is_a_task", "")[[1]], levels=c("_",letters))) factor(ff) # drops the levels that do not occur f1 <- ff[, drop=TRUE] # the same, more transparently @ and now assume a model $$y_i = \mu + \alpha_{j(i)} + E_i,$$ for $i=1,\dots,n =$~\code{length(f1)}$= 20$, and $\alpha_{j(i)}$ with a constraint such as $\sum_j \alpha_j = 0$ (``sum'') or $\alpha_1 = 0$ (``treatment'') and $j(i) =$\code{as.numeric(f1[i])} being the level number of the $i$-th observation. For such a ``design'', the model is only estimable if the levels \code{c} and \code{k} are merged, and <>= levels(f1)[match(c("c","k"), levels(f1))] <- "ck" library(Matrix) Matrix(contrasts(f1)) # "treatment" contrasts by default -- level "_" = baseline Matrix(contrasts(C(f1, sum))) Matrix(contrasts(C(f1, helmert)), sparse=TRUE) # S-plus default; much less sparse @ where \Rfun{contrasts} is (conceptually) just one major ingredient in the well-known \Rfun{model.matrix} function to build the linear model matrix $\mathbf{X}$ of so-called ``dummy variables''. %% Since 2007, the \pkg{Matrix} package has been providing coercion from a \code{factor} object to a \code{sparseMatrix} one to produce the transpose of the model matrix corresponding to a model with that factor as predictor (and no intercept): <>= as(f1, "sparseMatrix") @ which is really almost the transpose of using the above sparsification of \Rfun{contrasts} (and arranging for nice printing), <>= printSpMatrix( t( Matrix(contrasts(f1))[as.character(f1) ,] ), col.names=TRUE) @ and that is the same as the ``sparsification'' of \Rfun{model.matrix}, apart from the column names (here transposed), <>= t( Matrix(model.matrix(~ 0+ f1))) # model with*OUT* intercept @ A more realistic small example is the \code{chickwts} data set, <>= str(chickwts)# a standard R data set, 71 x 2 x.feed <- as(chickwts$feed, "sparseMatrix") x.feed[ , (1:72)[c(TRUE,FALSE,FALSE)]] ## every 3rd column: @ % FIXME: Move this to ../../../MatrixModels/inst/doc/ ??? % ## Provisional (hence unexported) sparse lm.fit(): % Matrix:::lm.fit.sparse(x = t(x.feed), y = chickwts[,1]) %- for emacs: $ \section{One factor, one continuous: \texttt{y $\sim$ f1 + x}} To create the model matrix for the case of one factor and one continuous predictor---called ``analysis of covariance'' in the historical literature--- we can adopt the following simple scheme. %% Possible examples: %% - Puromycin %% - ToothGrowth %--- FIXME --- The final model matrix is the concatenation of: 1) create the sparse 0-1 matrix \code{m1} from the f1 main-effect 2) the single row/column 'x' == 'x' main-effect 3) replacing the values 1 in \code{m1@x} (the x-slot of the factor model matrix), by the values of \code{x} (our continuous predictor). \section{Two (or more) factors, main effects only: \texttt{y $\sim$ f1 + f2}} %% FIXME: 'warpbreaks' is smaller and more natural as fixed effect model! Let us consider the \code{warpbreaks} data set of 54 observations, <>= data(warpbreaks)# a standard R data set str(warpbreaks) # 2 x 3 (x 9) balanced two-way with 9 replicates: xtabs(~ wool + tension, data = warpbreaks) @ %It is \emph{not} statistically sensible to assume that \code{Run} is a %fixed effect, however the example is handy to depict how a model matrix This example depicts how a model matrix would be built for the model \code{breaks ~ wool + tension}. Since this is a main effects model (no interactions), the desired model matrix is simply the concatenation of the model matrices of the main effects. There are two here, but the principle applies to general main effects of factors. The most sparse matrix is reached by \emph{not} using an intercept, (which would give an all-1-column) but rather have one factor fully coded (aka ``swallow'' the intercept), and all others being at \code{"treatment"} contrast, i.e., here, the \emph{transposed} model matrix, \code{tmm}, is <>= tmm <- with(warpbreaks, rBind(as(tension, "sparseMatrix"), as(wool, "sparseMatrix")[-1,,drop=FALSE])) print( image(tmm) ) # print(.) the lattice object @ \\ The matrices are even sparser when the factors have more than just two or three levels, e.g., for the morley data set, <>= data(morley) # a standard R data set morley$Expt <- factor(morley$Expt) morley$Run <- factor(morley$Run) str(morley) t.mm <- with(morley, rBind(as(Expt, "sparseMatrix"), as(Run, "sparseMatrix")[-1,])) print( image(t.mm) ) # print(.) the lattice object @ %% Also see Doug's E-mail to R-help % From: "Douglas Bates" % Subject: Re: [R] Large number of dummy variables % Date: Mon, 21 Jul 2008 18:07:26 -0500 \section{Interactions of two (or more) factors,.....} %% Of course, this is *the* interesting part %% To form interactions, we would have to ``outer-multiply'' %% the single-factor model-matrices (after "[, -1]") In situations with more than one factor, particularly with interactions, the model matrix is currently not directly available via \pkg{Matrix} functions --- but we still show to build them carefully. The easiest---but not at memory resources efficient---way is to go via the dense \Rfun{model.matrix} result: <>= data(npk, package="MASS") npk.mf <- model.frame(yield ~ block + N*P*K, data = npk) ## str(npk.mf) # the data frame + "terms" attribute m.npk <- model.matrix(attr(npk.mf, "terms"), data = npk) class(M.npk <- Matrix(m.npk)) dim(M.npk)# 24 x 13 sparse Matrix t(M.npk) # easier to display, column names readably displayed as row.names(t(.)) @ %% printSpMatrix(M.npk, col.names = "abb1") Another example was reported by a user on R-help (July 15, 2008, {\small \url{https://stat.ethz.ch/pipermail/r-help/2008-July/167772.html}}) about an ``aov error with large data set''. \begin{citation} % RAS: in my PDF, I don't see the first character I I'm looking to analyze a large data set: a within-Ss 2*2*1500 design with 20 Ss. However, aov() gives me an error. %, reproducible as follows: \end{citation} And gave the following code example (slightly edited): <>= id <- factor(1:20) a <- factor(1:2) b <- factor(1:2) d <- factor(1:1500) aDat <- expand.grid(id=id, a=a, b=b, d=d) aDat$y <- rnorm(length(aDat[, 1])) # generate some random DV data dim(aDat) # 120'000 x 5 (120'000 = 2*2*1500 * 20 = 6000 * 20) @ %% ^^^^^^^ MM: "fix" and generate much more interesting data and then continued with \begin{Sinput} m.aov <- aov(y ~ a*b*d + Error(id/(a*b*d)), data=aDat) \end{Sinput} \begin{citation}\sffamily which yields the following error:\\ \ttfamily Error in model.matrix.default(mt, mf, contrasts) :\\ allocMatrix: too many elements specified\\ \end{citation} to which he got the explanation by Peter Dalgaard that the formal model matrix involved was much too large in this case, and that PD assumed, \pkg{lme4} would be able to solve the problem. However, currently there would still be a big problem with using \pkg{lme4}, because of the many levels of \emph{fixed} effects: Specifically\footnote{the following is not run in \RR\ on purpose, rather just displayed here}, \begin{Sinput} dim(model.matrix( ~ a*b*d, data = aDat)) # 120'000 x 6000 \end{Sinput} where we note that $120'000 \times 6000 = 720 \textrm{mio}$, which is $720'000'000 * 8 / 2^{20} \approx 5500$ Megabytes. \emph{Unfortunately} \pkg{lme4} does \emph{not} use a sparse $X$-matrix for the fixed effects (yet), it just uses sparse matrices for the $Z$-matrix of random effects and sparse matrix operations for computations related to $Z$. Let us use a smaller factor \code{d} in order to investigate how sparse the $X$ matrix would be: <>= d2 <- factor(1:150) # 10 times smaller tmp2 <- expand.grid(id=id, a=a, b=b, d=d2) dim(tmp2) dim(mm <- model.matrix( ~ a*b*d, data=tmp2)) ## is 100 times smaller than original example class(smm <- Matrix(mm)) # automatically coerced to sparse round(object.size(mm) / object.size(smm), 1) @ shows that even for the small \code{d} here, the memory reduction would be more than an order of magnitude. \\ %% Reasons to fake here: %% 1) print() is needed for lattice -- but looks ugly, %% 2) the resulting pdf file is too large -- use png instead: <>= image(t(smm), aspect = 1/3, lwd=0, col.regions = "red") <>= png("sparseModels-X-sparse-image.png", width=6, height=3, units='in', res=150) print( <> ) dev.off() @ %%--NB: 'keep.source=FALSE' above is workaround-a-bug-in-R-devel-(2.13.x)--- \par\vspace*{-1ex} \centerline{% \includegraphics[width=1.1\textwidth]{sparseModels-X-sparse-image.png}} and working with the sparse instead of the dense model matrix is considerably faster as well, <>= x <- 1:600 system.time(y <- smm %*% x) ## sparse is much faster system.time(y. <- mm %*% x) ## than dense identical(as.matrix(y), y.) ## TRUE @ <>= toLatex(sessionInfo()) @ \end{document} Matrix/vignettes/myVignette.sty0000644000175100001440000000666512070321331016445 0ustar hornikusers\RequirePackage{hyperref} \RequirePackage{url} \RequirePackage{amsmath} \RequirePackage{bm}%-> \bm (= bold math) \newcommand{\Slang}{\textsf{S} language} \newcommand{\RR}{\textsf{R}} \newcommand{\email}[1]{\href{mailto:#1}{\normalfont\texttt{#1}}} %- R programming markup \newcommand\code{\bgroup\@codex} \def\@codex#1{{\normalfont\ttfamily\hyphenchar\font=-1 #1}\egroup} \let\env=\code \let\command=\code \newcommand*{\Rfun}[1]{\code{#1()}\index{\RR~function #1}} \newcommand*{\class}[1]{\code{#1}\index{class #1}}% \newcommand*{\pkg}[1]{\code{#1}\index{\RR~package #1}} % \newcommand{\kbd}[1]{{\normalfont\texttt{#1}}} \newcommand{\key}[1]{{\normalfont\texttt{\uppercase{#1}}}} \newcommand\samp{`\bgroup\@noligs\@sampx} \def\@sampx#1{{\normalfont\texttt{#1}}\egroup'} \let\option=\samp \newcommand{\var}[1]{{\normalfont\textsl{#1}}} \newcommand{\file}[1]{{`\normalfont\textsf{#1}'}} \newcommand{\dfn}[1]{{\normalfont\textsl{#1}}} \newcommand{\acronym}[1]{{\normalfont\textsc{\lowercase{#1}}}} \newcommand{\strong}[1]{{\normalfont\fontseries{b}\selectfont #1}} \let\pkg=\strong % \RequirePackage{alltt} \newenvironment{example}{\begin{alltt}}{\end{alltt}} \newenvironment{smallexample}{\begin{alltt}\small}{\end{alltt}} \newenvironment{display}{\list{}{}\item\relax}{\endlist} \newenvironment{smallverbatim}{\small\verbatim}{\endverbatim} % This is already in ``Sweave'' -- but withOUT the fontsize=\small part !! %% \RequirePackage{fancyvrb} %% \DefineVerbatimEnvironment{Sinput}{Verbatim}{fontsize=\small,fontshape=sl} %% \DefineVerbatimEnvironment{Soutput}{Verbatim}{fontsize=\small} %% \DefineVerbatimEnvironment{Scode}{Verbatim}{fontsize=\small,fontshape=sl} % \newcommand{\FIXME}[1]{\marginpar{ \dots FIXME \emph{#1} \dots}} \newcommand{\TODO}[1]{\par\noindent\textsc{Todo:} \textit{#1}\par} % %% Matrix stuff : % \newcommand{\trans}{\ensuremath{^\mathsf{T}}} \newcommand{\bA}{\ensuremath{\bm{A}}} \newcommand{\bD}{\ensuremath{\bm{D}}} \newcommand{\bDelta}{\ensuremath{\bm{\Delta}}} \newcommand{\bI}{\ensuremath{\bm{I}}} \newcommand{\bL}{\ensuremath{\bm{L}}} \newcommand{\LXXi}[1]{\ensuremath{\bL_{\mathit{XX}({#1})}}} \newcommand{\LXX}{\ensuremath{\bL_\mathit{XX}}} \newcommand{\LXZi}[1]{\ensuremath{\bL_{\mathit{XZ}({#1})}}} \newcommand{\LXZ}{\ensuremath{\bL_\mathit{XZ}}} \newcommand{\LZZi}[1]{\ensuremath{\bL_{\mathit{ZZ}({#1})}}} \newcommand{\LZZ}{\ensuremath{\bL_\mathit{ZZ}}} \newcommand{\LZZoo}{\ensuremath{\bL_{\mathit{ZZ}11}}} \newcommand{\LZZot}{\ensuremath{\bL_{\mathit{ZZ}12}}} \newcommand{\LZZtt}{\ensuremath{\bL_{\mathit{ZZ}22}}} \newcommand{\bOmega}{\ensuremath{\bm{\Omega}}} \newcommand{\bPhi}{\ensuremath{\bm{\Phi}}} \newcommand{\bR}{\ensuremath{\bm{R}}} \newcommand{\bX}{\ensuremath{\bm{X}}} \newcommand{\bZ}{\ensuremath{\bm{Z}}} \newcommand{\bbeta}{\ensuremath{\bm{\beta}}} \newcommand{\bb}{\ensuremath{\bm{b}}} \newcommand{\beps}{\ensuremath{\bm{\epsilon}}} \newcommand{\dX}{\ensuremath{\bm{d}_{\mathit{X}}}} \newcommand{\dZ}{\ensuremath{\bm{d}_{\mathit{Z}}}} \newcommand{\dy}{\ensuremath{d_{\mathit{y}}}} \newcommand{\lyXi}[1]{\ensuremath{\bm{\ell}_{\mathit{yX}(#1)}}} \newcommand{\lyX}{\ensuremath{\bm{\ell}_\mathit{yX}}} \newcommand{\lyZi}[1]{\ensuremath{\bm{\ell}_{\mathit{yZ}(#1)}}} \newcommand{\lyZ}{\ensuremath{\bm{\ell}_\mathit{yZ}}} \newcommand{\lyyi}[1]{\ensuremath{\bm{\ell}_{\mathit{yy}(#1)}}} \newcommand{\lyy}{\ensuremath{\ell_\mathit{yy}}} \newcommand{\btheta}{\ensuremath{\bm{\theta}}} \newcommand{\by}{\ensuremath{\bm{y}}} \newcommand{\bzer}{\ensuremath{\bm{0}}} Matrix/vignettes/Introduction.Rnw0000644000175100001440000001753412070262574016734 0ustar hornikusers\documentclass{article} \usepackage{myVignette} \usepackage[authoryear,round]{natbib} \bibliographystyle{plainnat} %%\VignetteIndexEntry{Introduction to the Matrix Package} %%\VignetteDepends{Matrix} \SweaveOpts{engine=R,eps=FALSE,pdf=TRUE,width=5,height=3,strip.white=true,keep.source=TRUE} \title{Introduction to the Matrix package --- as of Feb.~2005\footnote{ There's an unfinished ``2nd Introduction to the Matrix package'' which contains partly newer information, but is not at all self-contained. Eventually that will replace this one.}} \author{Douglas Bates\\R Core Development Group\\\email{bates@r-project.org}} \date{\today} \begin{document} \maketitle \begin{abstract} Linear algebra is at the core of many areas of statistical computing and from its inception the \Slang{} has supported numerical linear algebra via a matrix data type and several functions and operators, such as \code{\%*\%}, \code{qr}, \code{chol}, and \code{solve}. However, these data types and functions do not provide direct access to all of the facilities for efficient manipulation of dense matrices, as provided by the Lapack subroutines, and they do not provide for manipulation of sparse matrices. The \code{Matrix} package provides a set of S4 classes for dense and sparse matrices that extend the basic matrix data type. Methods for a wide variety of functions and operators applied to objects from these classes provide efficient access to BLAS (Basic Linear Algebra Subroutines), Lapack (dense matrix), TAUCS (sparse matrix) and UMFPACK (sparse matrix) routines. One notable characteristic of the package is that whenever a matrix is factored, the factorization is stored as part of the original matrix so that further operations on the matrix can reuse this factorization. \end{abstract} <>= options(width=75) @ \section{Introduction} \label{sec:Intro} Linear algebra is at the core of many statistical computing techniques and, from its inception, the \Slang{} has supported numerical linear algebra via a matrix data type and several functions and operators, such as \code{\%*\%}, \code{qr}, \code{chol}, and \code{solve}. Initially the numerical linear algebra functions in \RR{} called underlying Fortran routines from the Linpack~\citep{Linpack} and Eispack~\cite{Eispack} libraries but over the years most of these functions have been switched to use routines from the Lapack~\cite{Lapack} library. Furthermore, \RR{} can be configured to use accelerated BLAS (Basic Linear Algebra Subroutines), such as those from the Atlas~\cite{Atlas} project or Goto's BLAS~\cite{GotosBLAS}. Lapack provides routines for operating on several special forms of matrices, such as triangular matrices and symmetric matrices. Furthermore,matrix decompositions like the QR decompositions produce multiple output components that should be regarded as parts of a single object. There is some support in R for operations on special forms of matrices (e.g. the \code{backsolve}, \code{forwardsolve} and \code{chol2inv} functions) and for special structures (e.g. a QR structure is implicitly defined as a list by the \code{qr}, \code{qr.qy}, \code{qr.qty}, and related functions) but it is not as fully developed as it could be. Also there is no direct support for sparse matrices in R although \citet{koen:ng:2003} have developed a contributed package for sparse matrices based on SparseKit. The \code{Matrix} package provides S4 classes and methods for dense and sparse matrices. The methods for dense matrices use Lapack and BLAS. The sparse matrix methods use TAUCS~\citep{Taucs}, UMFPACK~\citep{Umfpack}, and Metis~\citep{Metis}. \section{Classes for dense matrices} \label{sec:DenseClasses} The \code{Matrix} package will provide classes for real (stored as double precision) and complex (stored as double precision complex) dense matrices. At present only the real classes have been implemented. These classes are \begin{description} \item[dgeMatrix] Real matrices in general storage mode \item[dsyMatrix] Symmetric real matrices in non-packed storage \item[dspMatrix] Symmetric real matrices in packed storage (one triangle only) \item[dtrMatrix] Triangular real matrices in non-packed storage \item[dtpMatrix] Triangular real matrices in packed storage (triangle only) \item[dpoMatrix] Positive semi-definite symmetric real matrices in non-packed storage \item[dppMatrix] \ \ ditto \ \ in packed storage \end{description} Methods for these classes include coercion between these classes, when appropriate, and coercion to the \code{matrix} class; methods for matrix multiplication (\code{\%*\%}); cross products (\code{crossprod}), matrix norm (\code{norm}); reciprocal condition number (\code{rcond}); LU factorization (\code{lu}) or, for the \code{poMatrix} class, the Cholesky decomposition (\code{chol}); and solutions of linear systems of equations (\code{solve}). Further, group methods have been defined for the \code{Arith} (basic arithmetic, including with scalar numbers) and the \code{Math} (basic mathematical functions) group.. Whenever a factorization or a decomposition is calculated it is preserved as a (list) element in the \code{factors} slot of the original object. In this way a sequence of operations, such as determining the condition number of a matrix then solving a linear system based on the matrix, do not require multiple factorizations of the same matrix nor do they require the user to store the intermediate results. \section{Classes for sparse matrices} \label{sec:SparseClasses} \subsection{Representations of sparse matrices} \label{ssec:SparseReps} Conceptually, the simplest representation of a sparse matrix is as a triplet of an integer vector \code{i} giving the row numbers, an integer vector \code{j} giving the column numbers, and a numeric vector \code{x} giving the non-zero values in the matrix. An S4 class definition might be \begin{Schunk} \begin{Sinput} setClass("dgTMatrix", representation(i = "integer", j = "integer", x = "numeric", Dim = "integer")) \end{Sinput} \end{Schunk} The triplet representation is row-oriented if elements in the same row were adjacent and column-oriented if elements in the same column were adjacent. The compressed sparse row (csr) (or compressed sparse column - csc) representation is similar to row-oriented triplet (column-oriented triplet) except that \code{i} (\code{j}) just stores the index of the first element in the row (column). (There are a couple of other details but that is the gist of it.) These compressed representations remove the redundant row (column) indices and provide faster access to a given location in the matrix because you only need to check one row (column). The preferred representation of sparse matrices in the SparseM package is csr. Matlab uses csc. We hope that Octave will also use this representation. There are certain advantages to csc in systems like R and Matlab where dense matrices are stored in column-major order. For example, Sivan Toledo's TAUCS~\cite{Taucs} library and Tim Davis's UMFPACK~\cite{Umfpack} library are both based on csc and can both use level-3 BLAS in certain sparse matrix computations. The Matrix package provides the following classes for sparse matrices \begin{description} \item[dgTMatrix] general, numeric, sparse matrices in (a possibly redundant) triplet form. This can be a convenient form in which to construct sparse matrices. \item[dgCMatrix] general, numeric, sparse matrices in the (sorted) compressed sparse column format. \item[dsCMatrix] symmetric, real, sparse matrices in the (sorted) compressed sparse column format. Only the upper or the lower triangle is stored. Although there is provision for both forms, the lower triangle form works best with TAUCS. \item[dtCMatrix] triangular, real, sparse matrices in the (sorted) compressed sparse column format. \end{description} \bibliography{Matrix} \end{document} Matrix/vignettes/Comparisons.Rnw0000644000175100001440000002150212070262574016536 0ustar hornikusers\documentclass{article} \usepackage{myVignette} \usepackage[authoryear,round]{natbib} \bibliographystyle{plainnat} %%\VignetteIndexEntry{Comparisons of Least Squares calculation speeds} %%\VignetteDepends{Matrix} \begin{document} \SweaveOpts{engine=R,eps=FALSE,pdf=TRUE,width=5,height=3,strip.white=true,keep.source=TRUE} \setkeys{Gin}{width=\textwidth} \title{Comparing Least Squares Calculations} \author{Douglas Bates\\R Development Core Team\\\email{Douglas.Bates@R-project.org}} \date{\today} \maketitle \begin{abstract} Many statistics methods require one or more least squares problems to be solved. There are several ways to perform this calculation, using objects from the base R system and using objects in the classes defined in the \code{Matrix} package. We compare the speed of some of these methods on a very small example and on a example for which the model matrix is large and sparse. \end{abstract} <>= options(width=75) @ \section{Linear least squares calculations} \label{sec:LeastSquares} Many statistical techniques require least squares solutions \begin{equation} \label{eq:LeastSquares} \widehat{\bm{\beta}}= \arg\min_{\bm{\beta}}\left\|\bm{y}-\bX\bm{\beta}\right\|^2 \end{equation} where $\bX$ is an $n\times p$ model matrix ($p\leq n$), $\bm{y}$ is $n$-dimensional and $\bm{\beta}$ is $p$ dimensional. Most statistics texts state that the solution to (\ref{eq:LeastSquares}) is \begin{equation} \label{eq:XPX} \widehat{\bm{\beta}}=\left(\bX\trans\bX\right)^{-1}\bX\trans\bm{y} \end{equation} when $\bX$ has full column rank (i.e. the columns of $\bX$ are linearly independent) and all too frequently it is calculated in exactly this way. \subsection{A small example} \label{sec:smallLSQ} As an example, let's create a model matrix, \code{mm}, and corresponding response vector, \code{y}, for a simple linear regression model using the \code{Formaldehyde} data. <>= data(Formaldehyde) str(Formaldehyde) (m <- cbind(1, Formaldehyde$carb)) (yo <- Formaldehyde$optden) @ Using \code{t} to evaluate the transpose, \code{solve} to take an inverse, and the \code{\%*\%} operator for matrix multiplication, we can translate \ref{eq:XPX} into the \Slang{} as <>= solve(t(m) %*% m) %*% t(m) %*% yo @ On modern computers this calculation is performed so quickly that it cannot be timed accurately in \RR{} \footnote{From R version 2.2.0, \code{system.time()} has default argument \code{gcFirst = TRUE} which is assumed and relevant for all subsequent timings} <>= system.time(solve(t(m) %*% m) %*% t(m) %*% yo) @ and it provides essentially the same results as the standard \code{lm.fit} function that is called by \code{lm}. <>= dput(c(solve(t(m) %*% m) %*% t(m) %*% yo)) dput(unname(lm.fit(m, yo)$coefficients)) @ %$ \subsection{A large example} \label{sec:largeLSQ} For a large, ill-conditioned least squares problem, such as that described in \citet{koen:ng:2003}, the literal translation of (\ref{eq:XPX}) does not perform well. <>= library(Matrix) data(KNex, package = "Matrix") y <- KNex$y mm <- as(KNex$mm, "matrix") # full traditional matrix dim(mm) system.time(naive.sol <- solve(t(mm) %*% mm) %*% t(mm) %*% y) @ Because the calculation of a ``cross-product'' matrix, such as $\bX\trans\bX$ or $\bX\trans\bm{y}$, is a common operation in statistics, the \code{crossprod} function has been provided to do this efficiently. In the single argument form \code{crossprod(mm)} calculates $\bX\trans\bX$, taking advantage of the symmetry of the product. That is, instead of calculating the $712^2=506944$ elements of $\bX\trans\bX$ separately, it only calculates the $(712\cdot 713)/2=253828$ elements in the upper triangle and replicates them in the lower triangle. Furthermore, there is no need to calculate the inverse of a matrix explicitly when solving a linear system of equations. When the two argument form of the \code{solve} function is used the linear system \begin{equation} \label{eq:LSQsol} \left(\bX\trans\bX\right) \widehat{\bm{\beta}} = \bX\trans\by \end{equation} is solved directly. Combining these optimizations we obtain <>= system.time(cpod.sol <- solve(crossprod(mm), crossprod(mm,y))) all.equal(naive.sol, cpod.sol) @ On this computer (2.0 GHz Pentium-4, 1 GB Memory, Goto's BLAS, in Spring 2004) the crossprod form of the calculation is about four times as fast as the naive calculation. In fact, the entire crossprod solution is faster than simply calculating $\bX\trans\bX$ the naive way. <>= system.time(t(mm) %*% mm) @ Note that in newer versions of \RR{} and the BLAS library (as of summer 2007), \RR's \code{\%*\%} is able to detect the many zeros in \code{mm} and shortcut many operations, and is hence much faster for such a sparse matrix than \code{crossprod} which currently does not make use of such optimizations. This is not the case when \RR{} is linked against an optimized BLAS library such as GOTO or ATLAS. %% Also, for fully dense matrices, \code{crossprod()} indeed remains faster (by a factor of two, typically) independently of the BLAS library: <>= fm <- mm set.seed(11) fm[] <- rnorm(length(fm)) system.time(c1 <- t(fm) %*% fm) system.time(c2 <- crossprod(fm)) stopifnot(all.equal(c1, c2, tol = 1e-12)) @ % using stopifnot(.) to save output \subsection{Least squares calculations with Matrix classes} \label{sec:MatrixLSQ} The \code{crossprod} function applied to a single matrix takes advantage of symmetry when calculating the product but does not retain the information that the product is symmetric (and positive semidefinite). As a result the solution of (\ref{eq:LSQsol}) is performed using general linear system solver based on an LU decomposition when it would be faster, and more stable numerically, to use a Cholesky decomposition. The Cholesky decomposition could be used but it is rather awkward <>= system.time(ch <- chol(crossprod(mm))) system.time(chol.sol <- backsolve(ch, forwardsolve(ch, crossprod(mm, y), upper = TRUE, trans = TRUE))) stopifnot(all.equal(chol.sol, naive.sol)) @ The \code{Matrix} package uses the S4 class system \citep{R:Chambers:1998} to retain information on the structure of matrices from the intermediate calculations. A general matrix in dense storage, created by the \code{Matrix} function, has class \code{"dgeMatrix"} but its cross-product has class \code{"dpoMatrix"}. The \code{solve} methods for the \code{"dpoMatrix"} class use the Cholesky decomposition. <>= mm <- as(KNex$mm, "dgeMatrix") class(crossprod(mm)) system.time(Mat.sol <- solve(crossprod(mm), crossprod(mm, y))) stopifnot(all.equal(naive.sol, unname(as(Mat.sol,"matrix")))) @ Furthermore, any method that calculates a decomposition or factorization stores the resulting factorization with the original object so that it can be reused without recalculation. <>= xpx <- crossprod(mm) xpy <- crossprod(mm, y) system.time(solve(xpx, xpy)) system.time(solve(xpx, xpy)) # reusing factorization @ The model matrix \code{mm} is sparse; that is, most of the elements of \code{mm} are zero. The \code{Matrix} package incorporates special methods for sparse matrices, which produce the fastest results of all. <>= mm <- KNex$mm class(mm) system.time(sparse.sol <- solve(crossprod(mm), crossprod(mm, y))) stopifnot(all.equal(naive.sol, unname(as(sparse.sol, "matrix")))) @ As with other classes in the \code{Matrix} package, the \code{dsCMatrix} retains any factorization that has been calculated although, in this case, the decomposition is so fast that it is difficult to determine the difference in the solution times. <>= xpx <- crossprod(mm) xpy <- crossprod(mm, y) system.time(solve(xpx, xpy)) system.time(solve(xpx, xpy)) @ \subsection*{Session Info} <>= toLatex(sessionInfo()) @ <>= if(identical(1L, grep("linux", R.version[["os"]]))) { ##----- Linux - only ---- Sys.procinfo <- function(procfile) { l2 <- strsplit(readLines(procfile),"[ \t]*:[ \t]*") r <- sapply(l2[sapply(l2, length) == 2], function(c2)structure(c2[2], names= c2[1])) attr(r,"Name") <- procfile class(r) <- "simple.list" r } Scpu <- Sys.procinfo("/proc/cpuinfo") Smem <- Sys.procinfo("/proc/meminfo") } # Linux only @ <>= if(identical(1L, grep("linux", R.version[["os"]]))) { ## Linux - only --- Scpu <- sfsmisc::Sys.procinfo("/proc/cpuinfo") Smem <- sfsmisc::Sys.procinfo("/proc/meminfo") print(Scpu[c("model name", "cpu MHz", "cache size", "bogomips")]) print(Smem[c("MemTotal", "SwapTotal")]) } @ <>= if(identical(1L, grep("linux", R.version[["os"]]))) { ## Linux - only --- print(Scpu[c("model name", "cpu MHz", "cache size", "bogomips")]) print(Smem[c("MemTotal", "SwapTotal")]) } @ \bibliography{Matrix} \end{document} Matrix/vignettes/Matrix.bib0000644000175100001440000003410212070321331015456 0ustar hornikusers@BOOK{R:Venables+Ripley:2000, AUTHOR = {William N. Venables and Brian D. Ripley}, TITLE = {S Programming}, PUBLISHER = {Springer}, YEAR = 2000, NOTE = {ISBN 0-387-98966-8}, URL = {http://www.stats.ox.ac.uk/pub/MASS3/Sprog/}, ABSTRACT = {This provides an in-depth guide to writing software in the S language which forms the basis of both the commercial S-PLUS and the Open Source R data analysis software systems.} } @BOOK{R:Chambers+Hastie:1992, AUTHOR = {John M. Chambers and Trevor J. Hastie}, TITLE = {Statistical Models in {S}}, PUBLISHER = {Chapman \& Hall}, YEAR = 1992, ADDRESS = {London}, ISBN = {0-412-83040-X}, ABSTRACT = {This is also called the ``\emph{White Book}'', and introduced S version 3, which added structures to facilitate statistical modeling in S. } } @Article{Rnews:Gentleman+Carey:2002, author = {Robert Gentleman and Vincent Carey}, title = {Bioconductor}, journal = {R News}, year = 2002, volume = 2, number = 1, pages = {11--16}, month = {March}, url = {http://CRAN.R-project.org/doc/Rnews/} } @article{Ke:Wang:2001, author = {Ke, Chunlei and Wang, Yuedong}, title = {Semiparametric nonlinear mixed-effects models and their applications}, year = {2001}, journal = {Journal of the American Statistical Association}, volume = {96}, number = {456}, pages = {1272--1298}, keywords = {NONLINEAR MIXED EFFECTS MODEL; Penalized likelihood; Repeated measures; SELF-MODELING NONLINEAR REGRESSION; Smoothing spline} } @Article{Lind:Bate:1988, author = {Lindstrom, Mary J. and Bates, Douglas M.}, title = {Newton-{R}aphson and {EM} algorithms for linear mixed-effects models for repeated-measures data ({C}orr: 94{V}89 p1572)}, year = {1988}, journal = {Journal of the American Statistical Association}, volume = {83}, pages = {1014--1022}, keywords = {Growth curve; Longitudinal data} } @ARTICLE{Atlas, AUTHOR = "R. Clint Whaley and Antoine Petitet and Jack J. Dongarra", TITLE = "Automated Empirical Optimization of Software and the {ATLAS} Project", JOURNAL = "Parallel Computing", VOLUME = "27", NUMBER = "1--2", PAGES = "3--35", YEAR = 2001, NOTE = "Also available as University of Tennessee LAPACK Working Note \#147, UT-CS-00-448, 2000 ({\tt www.netlib.org/lapack/lawns/lawn147.ps})" } @TechReport{GotosBLAS, author = {Kazushige Goto and Robert van de Geijn}, title = {On Reducing TLB Misses in Matrix Multiplication}, institution = {Department of Computer Sciences, U. of Texas at Austin}, year = 2002, number = {TR02-55} } @Misc{Taucs, author = {Sivan Toledo}, title = {Taucs: A Library of Sparse Linear Solvers}, howpublished = {http://www.tau.ac.il/~stoledo/taucs/}, year = 2003 } @Misc{Umfpack, author = {Tim Davis}, title = {UMFPACK: Unified Multifrontal Package}, howpublished = {http://www.cise.ufl.edu/research/sparse/umfpack}, year = 2003 } @misc{Cholmod, author = {Tim Davis}, title = {{CHOLMOD}: sparse supernodal {Cholesky} factorization and update/downdate}, howpublished = {http://www.cise.ufl.edu/research/sparse/cholmod}, year = 2005 } @Misc{CSparse, author = {Tim Davis}, title = {{CSparse}: a concise sparse matrix package}, howpublished = {http://www.cise.ufl.edu/research/sparse/CSparse}, year = 2005 } @Book{davis06:csparse_book, author = {Timothy A. Davis }, title = {Direct Methods for Sparse Linear Systems}, publisher = {SIAM}, year = 2006, series = {Fundamentals of Algorithms} } @Misc{Metis, author = {George Karapis}, title = {Metis: Family of Multilevel Partioning Algorithms}, howpublished = {http://www-users.cs.umn.edu/~karypis/metis/}, year = 2003 } @Book{Linpack, author = {Jack Dongarra and Cleve Moler and Bunch and G.W. Stewart}, title = {Linpack Users' Guide}, publisher = {SIAM}, year = 1979 } @Book{Lapack, author = {E. Anderson and Z. Bai and C. Bischof and S. Blackford and J. Demmel and J. Dongarra and J. Du Croz and A. Greenbaum and S. Hammarling and A. McKenney and D. Sorensen}, title = {LAPACK Users' Guide}, chapter = {}, publisher = {SIAM}, year = 1999, address = {Philadelphia, PA}, edition = {3rd} } @Book{bryk00:_hlm, author = {A. S. Bryk and S. W. Raudenbush and R. Congdon}, title = {{HLM} version 5}, publisher = {Scientific Software International, Inc.}, year = 2000, address = {Chicago} } @Article{demp:lair:rubi:1977, Journal = JRSSB, Volume = 39, Pages = {1--22}, Keywords = {Posterior mode}, Author = {A. P. Dempster and N. M. Laird and D. B. Rubin}, Title = {Maximum Likelihood From Incomplete Data Via the {EM} Algorithm}, Year = 1977 } @Book{denn:schn:1983, author = {J. E. Dennis and R. B. Schnabel}, title = {Numerical Methods for Unconstrained Optimization and Nonlinear Equations}, publisher = {Prentice-Hall}, year = 1983, address = {Englewood Cliffs, NJ} } @Book{dong:bunc:mole:stew:1979, publisher = "SIAM", address = "Philadelphia", author = "J. J. Dongarra and J. R. Bunch and C. B. Moler and G. W. Stewart", title = "Linpack Users' Guide", year = 1979 } @Book{goldstein98:_mlwin, author = {H. Goldstein and J. Rasbash and I. Plewis and D. Draper and W. Browne and M. Wang}, title = {A user's guide to {MLwiN}}, publisher = {University of London, Institute of Education}, year = 1998, address = {London} } @Book{golu:vanl:1996, author = {Golub, Gene H. and van Loan, Charles F.}, title = {Matrix Computations}, publisher = {Johns Hopkins}, year = 1996, edition = {3rd} } @Article{ harv:1974, author = {Harville, David A.}, title = {Bayesian Inference for Variance Components Using Only Error Contrasts}, journal = {Biometrika}, year = 1974, volume = 61, pages = {383--385}, keywords = {Maximum likelihood} } @Article{ lair:ware:1982, author = {Laird, Nan M. and Ware, James H.}, title = {Random-effects Models for Longitudinal Data}, journal = {Biometrics}, year = 1982, volume = 38, pages = {963--974}, keywords = {Variance components; Repeated measurements; Empirical Bayes; EM algorithm} } @Book{lapack:1992, publisher = "SIAM", address = "Philadelphia", author = "E. Anderson and Z. Bai and C. Bischof and J. Demmel and J. Dongarra and J. Du Croz and A. Greenbaum and S. Hammaring and A. McKenney and S. Ostrouchov and D. Sorensen", title = "Lapack Users' Guide", year = 1992 } @Article{liu:rubi:1994, author = {Liu, Chuanhai and Rubin, Donald B.}, title = {The {ECME} algorithm: {A} simple extension of {EM} and {ECM} with faster monotone convergence}, year = {1994}, journal = {Biometrika}, volume = {81}, pages = {633--648}, keywords = {Markov chain monte carlo; Incomplete data} } @article{patt:thom:1971, Author = {Patterson, H. D. and Thompson, R.}, Title = {Recovery of Interblock Information When Block Sizes Are Unequal}, Year = 1971, Journal = {Biometrika}, Volume = 58, Pages = {545--554}, Keywords = {Incomplete block design; Components of variance; Maximum likelihood; Design of experiments} } @phdthesis{pinh:1994, author = {Jos\'{e} C. Pinheiro}, title = {Topics in Mixed-Effects Models}, school = {University of Wisconsin}, year = 1994, address = {Madison, WI} } @Article{pinh:bate:1995, author = "Jos\'{e} C. Pinheiro and Douglas M. Bates", title = "Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model", year = 1995, journal = "Journal of Computational and Graphical Statistics", volume = 4, number = 1, pages = "12--35" } @Article{ pinh:bate:1996, author = {Jos\'{e} C. Pinheiro and Douglas M. Bates}, title = {Unconstrained Parameterizations for Variance-Covariance Matrices}, journal = {Statistics and Computing}, year = 1996, volume = 6, pages = {289--296} } @Book{pinh:bate:2000, author = {Jos\'{e} C. Pinheiro and Douglas M. Bates}, title = {Mixed-Effects Models in {S} and {S-PLUS}}, year = 2000, pages = {528}, ISBN = {0-387-98957-9}, publisher = {Springer} } @Article{schn:koon:1985, Journal = {ACM Trans. Math. Software}, Volume = 11, Pages = {419--440}, Author = {R. B. Schnabel and J. E. Koontz and B. E. Weiss}, Title = {A modular system of algorithms for unconstrained minimization}, Year = 1985 } @book{snijders99:_multil_analy, author = {Tom Snijders and Roel Bosker}, title = {Multilevel Analysis: An introduction to basic and advanced multilevel analysis}, publisher = {Sage}, year = 1999, address = {London} } @book{this:1988, Author = {Thisted, R. A.}, Title = {Elements of Statistical Computing}, Year = 1988, Publisher = {Chapman \& Hall}, address = {London} } @Article{van:2000, author = {van Dyk, David A.}, title = {Fitting mixed-effects models using efficient {EM}-type algorithms}, year = {2000}, journal = {Journal of Computational and Graphical Statistics}, volume = {9}, number = {1}, pages = {78--98}, keywords = {EM algorithm; ECME algorithm; Gaussian hierarchical models; Posterior inference; PXEM algorithm; random-effects models; Reml; variance-component models; working parameters} } @misc{jfox:2002, author = {Fox, John}, title = {Linear Mixed Models -- Appendix to {An R and S-PLUS Companion to Applied Regression}}, year = 2002, month= {May}, url = {http://www.socsci.mcmaster.ca/jfox/Books/companion/appendix-mixed-models.pdf} } @book{roge:1980, Author = {Rogers, Gerald S.}, Title = {Matrix Derivatives}, Year = 1980, Publisher = {Marcell Dekker, Inc.}, address = {New York and Basel} } @TechReport{DebRoy:Bates:2003a, author = {Saikat DebRoy and Douglas M. Bates}, title = {Computational Methods for Single Level Linear Mixed-effects Models}, institution = {Department of Statistics, University of Wisconsin-Madison}, number = {1073}, year = 2003 } @TechReport{DebRoy:Bates:2003b, author = {Saikat DebRoy and Douglas M. Bates}, title = {Computational Methods for Multiple Level Linear Mixed-effects Models}, institution = {Department of Statistics, University of Wisconsin-Madison}, number = {1076}, year = 2003 } @Article{RaudenbushYangYosef:2000, author = {Stephen W. Raudenbush and Meng-Li Yang and Matheos Yosef}, title = {Maximum Likelihood for Generalized Linear Models With Nested Random Effects via High-Order, Multivariate {L}aplace Approximation}, journal = {J. Comput. Graph. Statist.}, year = 2000, volume = 9, number = 1, pages = {141--157} } @Book{goldstein87:_multil, author = {Goldstein, Harvey}, title = {Multilevel models in education and social research}, publisher = {Oxford University Press}, year = 1987 } @Book{raudenbush02:_hierar_linear_model, author = {Stephen W. Raudenbush and Anthony S. Bryk}, title = {Hierarchical Linear Models: Applications and Data Analysis Methods}, publisher = {Sage}, year = 2002, edition = {second}, ISBN = {0-7619-1904-X} } @BOOK{R:Chambers:1998, AUTHOR = {John M. Chambers}, TITLE = {Programming with Data}, PUBLISHER = {Springer}, YEAR = 1998, ADDRESS = {New York}, ISBN = {0-387-98503-4}, ABSTRACT = {This ``\emph{Green Book}'' describes version 4 of S, a major revision of S designed by John Chambers to improve its usefulness at every stage of the programming process.} } @article{Rodriguez:Goldman:1995, author = {Germ\'an Rodriguez and Noreen Goldman}, title = {An assessment of estimation procedures for multilevel models with binary responses}, year = {1995}, journal = {Journal of the Royal Statistical Society, Series A, General}, volume = {158}, pages = {73--89}, keywords = {Logistic regression; Random effects model; Software; Variance component} } @Article{koen:ng:2003, author = {Roger Koenker and Pin Ng}, title = {{SparseM}: A Sparse Matrix Package for {R}}, journal = {J. of Statistical Software}, year = 2003, volume = 8, number = 6 } @Book{Eispack, author = {Smith, B. T. and Boyle, J. M. and Dongarra, J. J. and Garbow, B. S. and Ikebe, Y. and Klema, V. C. and Moler, C. B.}, title = {Matrix Eigensystem Routines. EISPACK Guide}, publisher = {Springer-Verlag}, year = 1976, volume = 6, series = {Lecture Notes in Computer Science}, address = {New York} } @Article{bate:debr:2004, author = {Douglas M. Bates and Saikat DebRoy}, title = {Linear Mixed Models and Penalized Least Squares}, journal = {J. of Multivariate Analysis}, year = 2004, note = {to appear} } @Article{Rnews:Lockwood+Doran+Mccaffrey:2003, author = {J.R. Lockwood and Harold Doran and Daniel F. McCaffrey}, title = {Using R for Estimating Longitudinal Student Achievement Models}, journal = {R News}, year = 2003, volume = 3, number = 3, pages = {17--23}, month = {December}, url = {http://CRAN.R-project.org/doc/Rnews/} } @Article{Paterson:1991, author = {L. Paterson}, title = {Socio economic status and educational attainment: a multidimensional and multilevel study}, journal = {Evaluation and Research in Education}, year = 1991, volume = 5, pages = {97--121} } Matrix/vignettes/fullpage.sty0000644000175100001440000000534512070321331016103 0ustar hornikusers%% %% This is file `fullpage.sty', %% generated with the docstrip utility. %% %% The original source files were: %% %% fullpage.dtx (with options: `package') %% ============================================= %% IMPORTANT NOTICE: %% %% This program can be redistributed and/or modified under the terms %% of the LaTeX Project Public License Distributed from CTAN %% archives in directory macros/latex/base/lppl.txt; either %% version 1 of the License, or any later version. %% %% This is a generated file. %% It may not be distributed without the original source file fullpage.dtx. %% %% Full documentation can be obtained by LaTeXing that original file. %% Only a few abbreviated comments remain here to describe the usage. %% ============================================= %% Copyright 1994-1999 Patrick W Daly %% Max-Planck-Institut f\"ur Aeronomie %% Max-Planck-Str. 2 %% D-37191 Katlenburg-Lindau %% Germany %% E-mail: daly@linmpi.mpg.de \NeedsTeXFormat{LaTeX2e}[1994/06/01] \ProvidesPackage{fullpage} [1999/02/23 1.1 (PWD)] % Sets all 4 margins to be either 1 inch or 1.5 cm, and specifies % the page style % Call as \usepackage[options]{fullpage} % Options = in (default) for 1 inch % cm for 1.5 cm % plain (default) sets \pagestyle{plain} % empty sets \pagestyle{empty} % headings sets \pagestyle{headings} % myheadings sets \pagestyle{myheadings} %----------------------------------------------------------- \newlength{\FP@margin} \DeclareOption{in}{\setlength{\FP@margin}{1in}} \DeclareOption{cm}{\setlength{\FP@margin}{1.5cm}} \newif\ifFP@plain \newif\ifFP@empty \DeclareOption{plain}{\FP@plaintrue \FP@emptyfalse \pagestyle{plain}} \DeclareOption{empty}{\FP@plaintrue \FP@emptytrue \pagestyle{empty}} \DeclareOption{headings}{\FP@plainfalse \FP@emptyfalse \pagestyle{headings}} \DeclareOption{myheadings}{\FP@plainfalse \FP@emptyfalse \pagestyle{myheadings}} \ExecuteOptions{in,plain} \ProcessOptions* \ifFP@plain \setlength{\headheight}{0pt} \setlength{\headsep}{0pt} \fi \ifFP@empty \setlength{\footskip}{0pt} \fi \setlength{\textwidth}{\paperwidth} \addtolength{\textwidth}{-2\FP@margin} \setlength{\oddsidemargin}{\FP@margin} \addtolength{\oddsidemargin}{-1in} \setlength{\evensidemargin}{\oddsidemargin} \setlength{\textheight}{\paperheight} \addtolength{\textheight}{-\headheight} \addtolength{\textheight}{-\headsep} \addtolength{\textheight}{-\footskip} \addtolength{\textheight}{-2\FP@margin} \setlength{\topmargin}{\FP@margin} \addtolength{\topmargin}{-1in} %% %% <<<<< End of generated file <<<<<< %% %% End of file `fullpage.sty'. 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c39a26dfe7ccaafd044e88468155b153 *vignettes/Introduction.Rnw e1c318d82820bf0cdda8eaea8708f87e *vignettes/Matrix.bib 05b418f78b224ec872f5b11081138605 *vignettes/fullpage.sty 74ca9e8b3e91ace4ee3f9e85506bcdfa *vignettes/myVignette.sty 491d961ca64f8da569c817b82daa9c58 *vignettes/sparseModels.Rnw Matrix/DESCRIPTION0000644000175100001440000000220412272020333013232 0ustar hornikusersPackage: Matrix Version: 1.1-2 Date: 2014-01-28 Priority: recommended Title: Sparse and Dense Matrix Classes and Methods Author: Douglas Bates and Martin Maechler Maintainer: Martin Maechler Contact: Doug and Martin Description: Classes and methods for dense and sparse matrices and operations on them using LAPACK and SuiteSparse. Depends: R (>= 2.15.2), methods Imports: graphics, grid, stats, utils, lattice Suggests: expm, MASS Enhances: MatrixModels, graph, SparseM, sfsmisc Encoding: UTF-8 LazyData: no LazyDataNote: not possible, since we use data/*.R *and* our classes ByteCompile: yes BuildResaveData: no License: GPL (>= 2) LicenseNote: The Matrix package includes libraries AMD, CHOLMOD, COLAMD, CSparse and SPQR from the SuiteSparse collection of Tim Davis. All sections of that code are covered by the GPL or LGPL licenses. See the directory doc/UFsparse for details. URL: http://Matrix.R-forge.R-project.org/ Packaged: 2014-01-28 17:38:38 UTC; maechler NeedsCompilation: yes Repository: CRAN Date/Publication: 2014-01-28 22:27:55 Matrix/ChangeLog0000644000175100001440000051056012271765277013335 0ustar hornikusers2014-01-28 Martin Maechler * R/products.R: matrix products overhauled; should work with sparseVectors; speedup of crossprod(v, ), thanks to nudge by Niels Richard Hansen. * man/matrix-products.Rd: all matrix products documented in one file. * tests/matprod.R: more extensive testing 2014-01-20 Martin Maechler * DESCRIPTION (Version): 1.1-2 * NAMESPACE: export fast power-user coercion utilities .dsy2mat(), .dxC2mat(), .T2Cmat(), ..2dge(). 2013-12-23 Martin Maechler * R/dgTMatrix.R (image): (xlim, ylim) get a slightly changed default, plus ylim := sort(ylim, "decreasing"). This is strictly not back-compatible but should never harm. 2013-09-26 Martin Maechler * R/spModels.R (fac2sparse, fac2Sparse): newly exported; plus 'giveCsparse' option. 2013-09-16 Martin Maechler * src/scripts/0get-SuiteSparse.sh: new download script, for * src/CHOLMOD/*, src/AMD/*, ...: getting SuiteSparse version 4.2.1 * R/zzz.R (.SuiteSparse_version): new function 2013-09-13 Martin Maechler * R/dsCMatrix.R (solve.dsC.*): finally fix the long-lasting undetected solve() bug (only in case Cholmod fails) [r2908]. * DESCRIPTION (Version): 1.0-15, CRAN-released 2013-09-26 2013-09-12 Martin Maechler * DESCRIPTION (Version): 1.0-14, CRAN-released 2013-09-12 * R/dgCMatrix.R: "stop gap fix" for R 3.0.2: partly revert solve(,*) changes in 1.0-13. 2013-08-27 Fabian Scheipl * man/indMatrix-class.Rd: new "indMatrix" class, a natural superclass of "pMatrix". Many methods moved from "pMatrix" to "indMatrix". 2013-05-09 Martin Maechler * DESCRIPTION (Version): 1.0-13, CRAN-released 2013-09-10 * R/KhatriRao.R: Efficient KhatriRao() by Michael Cysouw 2013-03-26 Martin Maechler * DESCRIPTION (Version): 1.0-12, CRAN-released 2013-03-26 2012-11-10 Martin Maechler * DESCRIPTION (Version): 1.0-11, CRAN-released 2013-02-02 * R/SparseM-conv.R: as(, "dgCMatrix") now works again * tests/other-pkgs.R: test that. * src/Mutils.c: do *not* use '#if R_VERSION < ..' so this also *runs* in older R when installed in R >= 2.15.2. 2012-10-15 Martin Maechler * src/Mutils.c (Mmatrix): new, to be used by .External() in order to replace .Internal(matrix(....)) 2012-10-05 Martin Maechler * R/diagMatrix.R (.sparseDiagonal): new 'unitri' argument; more flexibility; new: solve(, ) 2012-09-10 Martin Maechler * DESCRIPTION (Version): 1.0-10, CRAN-released: 2012-10-16, r2845 2012-09-01 Martin Maechler * R/sparseVector.R (sparseVector): new constructor * inst/test-tools-Matrix.R (rspMat): smarter; also useful for large dimensions. 2012-07-23 Martin Maechler * tests/group-methods.R: now do much more testing, notably of pairs of matrices ... however only when 'doExtras' is true, which it is not by default, e.g., on CRAN. 2012-07-21 Martin Maechler * R/Ops.R, R/diagMatrix.R: many fixes, notably for rare operations that were not triggered before. * R/Auxiliaries.R (allTrueMat): new utility. 2012-07-20 Martin Maechler * R/dsparseMatrix.R, R/sparseVector.R, ...: Newly defined is.finite() and is.infinite() methods for all our *Matrix and *sparseVector. 2012-07-14 Martin Maechler * R/d??Matrix.R (diag<-): many "diag<-" methods, which preserve symmetricity, triangularity (even uni-triangularity sometimes); Partly by also making A[cbind(i,i)] preserve such properties. * src/Mutils.c (SET_packed_setDiag) {and similar}: *_setDiag() C functions implementing "diag<-" R methods. 2012-06-30 Martin Maechler * R/Ops.R (Ops.x.x): now, dense symmetric and triangular matrices are preserved for many arithmetic and logic binary operators. * src/ldense.c (lsyMatrix_as_lspMatrix, ..): more coercions keep the dimnames(). * R/symmetricMatrix.R (pack, unpack): new pack() {"inverse" of unpack(), including pack()}; new unpack() methods. 2012-06-20 Douglas Bates * src/scripts/DEPS.mkf, ... * src/*.c: Update to version 4.0.0 of SuiteSparse 2012-06-19 Martin Maechler * DESCRIPTION (Version): 1.0-8, CRAN-released: 2012-06-20, r2789 * R/CHMfactor.R (update): *DO* allow non-symmetric parent. * man/CHMfactor-class.Rd: be more clear about the two ways. * tests/factorizing.R: more update() testing 2012-06-12 Martin Maechler * tests/matprod.R (chkDnProd): new testing function 2012-06-08 Martin Maechler * R/CHMfactor.R (update): now *warn* when parent is not formally symmetric and coerce it. 2012-06-05 Martin Maechler * R/Auxiliaries.R (chk.s): "check dots" - new utility -- possibly for base R ? 2012-04-16 Martin Maechler * R/sparseMatrix.R (sparseMatrix): now also works for 'symmetric=TRUE' and lower triangular indices. 2012-04-15 Martin Maechler * R/CHMfactor.R (updown): new generic and methods, * man/updown.Rd: provided by Nicholas Nagle. 2012-03-30 Martin Maechler * DESCRIPTION (Version): 1.0-7, CRAN-released: for a few days only. 2012-03-16 Martin Maechler * DESCRIPTION (Version): 1.0-6, CRAN-released: 2012-03-30, r2775 * DESCRIPTION (Depends): R >= 2.15.0 2012-03-15 Martin Maechler * R/spModels.R (sparseInt.r): recursion free (which does not help much). 2012-03-05 Martin Maechler * src/dtCMatrix.c (dtCMatrix_sparse_solve): no longer use Alloca() here. * tests/factorizing.R (checkSchur): check against segfault example. * R/Matrix.R (chol2inv()) new method. 2012-03-01 Martin Maechler * R/spModels.R (sparse.model.matrix, model.spmatrix): add 'verbose' argument in order to show to the user what's going on. * man/sparse.model.matrix.Rd: ditto 2012-02-27 Martin Maechler * R/Ops.R (A.M.n, A.n.M): o now correct, newly via sparseVector. 2012-02-25 Martin Maechler * DESCRIPTION (Version): 1.0-5, CRAN-released: 2012-03-15, r2773 * src/chm_common.c (chm_factor_to_SEXP): in case of failure, * src/dsCMatrix.c (internal_chm_factor): ensure memory cleanup; memory leak reported by Kasper Kristensen at dtu.dk. 2012-02-17 Martin Maechler * DESCRIPTION (Version): 1.0-4, CRAN-released: 2012-02-21, r2765 * R/Ops.R: Fix "-" method for diagonalMatrix types. 2012-01-12 Martin Maechler * DESCRIPTION (Suggests): MASS, as we use a data set in a vignette 2011-12-09 Martin Maechler * DESCRIPTION (Version): 1.0-3, CRAN-released: 2012-01-12, r2749 * R/diagMatrix.R (.bdiag): now works correctly when all blocks are "lMatrix" 2011-11-02 Martin Maechler * R/zzz.R (.onLoad): when R version >= 2.15.0, no longer need to assignInNamespace( ns = "base"), methods provides S4 generic. 2011-10-30 Martin Maechler * DESCRIPTION (Version): 1.0-2, CRAN-released: 2011-11-19, r2739 * tests/other-pkgs.R: print more, don't run SparseM on Solaris for now. * tests/Simple.R: encoding warning should not be promoted to error. 2011-10-22 Martin Maechler * R/rankMatrix.R (rankMatrix): 'method = "qrLINPACK"' now also works for sparse matrices, but using \code{sparseQR()}. * man/sparseQR-class.Rd: document options "Matrix.quiet" (old) and new "Matrix.quiet.qr.R" for suppressiong the permutation warning. * R/sparseQR.R: 2011-10-17 Douglas Bates * src/Csparse.c (Csparse_submatrix): plugging memory leak 2011-10-08 Martin Maechler * R/bind2.R (cbind2Sparse, rbind2Sparse): auxiliaries, used, also in new methods for . * tests/bind.R: testing some of these. * R/Matrix.R, man/Matrix.Rd: optional argument 'doDiag'. * DESCRIPTION (Version): 1.0-1, CRAN-released: 2011-10-18, r2732 2011-09-27 Martin Maechler * DESCRIPTION (Version): 1.0-0 -- to be released for R 2.14.0 2011-09-16 Martin Maechler * R/dsCMatrix.R (solve.dsC.mat): new utility which calls lu() if CHOLMOD'S Cholesky() errors (when matrix is not pos.def.). 2011-09-15 Martin Maechler * R/bandSparse.R (bandSparse): and * R/sparseMatrix.R (sparseMatrix): add 'giveCsparse = TRUE' argument and allow returning Tsparse*, useful e.g. when used in bdiag(). 2011-08-17 Martin Maechler * NAMESPACE: export diagN2U() & diagU2N(). They were "missing" for at least one user (GG). * man/diagU2N.Rd: docu + example. * DESCRIPTION (Version): 0.9996875-4 (*not* yet released) 2011-08-12 Martin Maechler * DESCRIPTION (Version): 0.9996875-3, for CRAN 2011-08-05 Martin Maechler * R/sparseVector.R (head): method; used in a few cases, eliminating two FIXMEs. * DESCRIPTION (Version): 0.9996875-1 * R/ngTMatrix.R: stop() instead of warning() when NA's are coerced. * R/Csparse.R, R/Tsparse.R * src/t_Csparse_subassign.c, src/Csparse.c: [..] <- val now works via .Call(*Csparse_subassign, ...) and no longer suffers from unnecessary memory-blowup. 2011-07-29 Martin Maechler * R/dgTMatrix.R (image): add 'useRaster = FALSE' argument, providing the possibility of using raster (instead of rectangle drawing vector) images. 2011-07-27 Martin Maechler * R/nearPD.R: allow 'ensureSymmetry' argument for speedup. 2011-06-10 Martin Maechler * R/diagMatrix.R (Cspdiagprod, diagCspprod): fixup for symmetric sparse, and non constant-diagonal. 2011-05-20 Martin Maechler * R/dsCMatrix.R (determinant(): fix for Matrix(0, 1) case. 2011-05-18 Martin Maechler * R/sparseMatrix.R (sparseMatrix): add 'symmetric' argument. 2011-04-04 Martin Maechler * src/Csparse.c (Csparse_subassign): unfinished prototype * src/....: Finally no longer hack "UFlong := int", but rather * src/UFconfig/UFconfig.h: use standard CHOLMOD headers * DESCRIPTION (Version): 0.9996875-0 2011-03-31 Martin Maechler * DESCRIPTION (Version): 0.999375-49 2011-03-30 Douglas Bates * Matrix/src/chm_common.c: [r2658] Install symbols first - {preventing seg.fault under -gct} 2011-03-17 Martin Maechler * DESCRIPTION (Version): 0.999375-48 *only* difference to CRAN released *-47, is the work around Sweave bug in inst/doc/sparseModels.Rnw. 2011-02-23 Martin Maechler * src/factorizations.c (LU_expand): now also works for non-square (m x n) * tests/factorizing.R: testing that 2011-02-22 Martin Maechler * R/Auxiliaries.R (t_geMatrix): drop 'factors', as they can be wrong. 2011-02-18 Martin Maechler * R/Tsparse.R (replTmat): fix bug for M[i,j] <- v, when j had duplicated entries. * tests/indexing.R (chkAssign): new function; testing the above. 2011-02-17 Martin Maechler * R/AllClass.R, R/sparseVector.R, man/sparseVector-class.Rd: now require explicitly that i-slot must be sorted for sparseVectors. 2011-02-16 Martin Maechler * R/sparseMatrix.R (formatSparseM): align="right" accidentally did not use zero.print at all. print/format sparse Matrix: fix align="right" and improve docu 2011-02-17 Douglas Bates * DESCRIPTION: Remove Encoding: directive. 2011-02-10 Martin Maechler * inst/doc/sparseModels.Rnw: use png for large graphics (suggestion from Brian) 2011-02-05 Martin Maechler * man/symmpart.Rd: update, thanks to Spencer Graves' prompting. 2011-01-07 Martin Maechler * R/CHMfactor.R (determinant()): no longer warn about incompatible change of 2009-09-01. 2011-01-04 Martin Maechler * R/nearPD.R (nearPD): better error message when all eigenvalues are (at least close to) negative. 2010-12-18 Martin Maechler * DESCRIPTION (Version): 0.999375-47, CRAN-released: 2011-02-23, r2653 * R/spModels.R, NAMESPACE: remove model.Matrix(); we had deprecated it for about four months now. 2010-12-12 Martin Maechler * R/eigen.R,...: use full argument names; * R/*.R: get rid of more from checkUsagePackage("Matrix", suppressPartialMatchArgs = FALSE) 2010-12-11 Martin Maechler * DESCRIPTION (Version): 0.999375-46, CRAN-released: 2010-12-14, r2633 * R/products.R: dimension fixing in some Matrix o vector [t]crossprod()s. * src/Csparse.c (nz2Csparse, nz_pattern_to_Csparse): new utilities, callable from C and R. (Csparse_dense_prod): check pattern matrix and coerce to "d..". * tests/Simple.R: testing %*% * R/ngCMatrix.R, R/nsCMatrix.R, .. : use the new fast coercions. 2010-10-08 Martin Maechler * DESCRIPTION (Version): 0.999375-45, CRAN-released: 2010-11-10, r2624 * R/sparseMatrix.R (graph.wgtMatrix): add 'graph::' in a few places; as 'graph' package is not imported and may well be loaded only. 2010-09-09 Martin Maechler * R/sparseMatrix.R (setAs): graph |-> Matrix: via CsparseMatrix 2010-08-21 Martin Maechler * R/spModels.R (sparse.model.matrix): argument 'drop.unused.levels = FALSE' NB: was *true* implicitly, before. Compatibility with model.matrix(). * R/sparseMatrix.R (formatSpMatrix, formatSparseM): factored out of printSpMatrix(); export as potentially useful for standard matrices, even. 2010-08-11 Martin Maechler * R/eigen.R (Schur): correct setMethod() such that Schur() works. 2010-08-10 Martin Maechler * R/diagMatrix.R, man/bdiag.Rd, NAMESPACE: export .bdiag() as well. 2010-08-09 Martin Maechler * DESCRIPTION (Version): 0.999375-44, CRAN-released: 2010-09-11, r2618 * R/diagMatrix.R (diagCspprod, Cspdiagprod): drop (possibly wrong) @factors * R/Ops.R (.Arith.CM.atom, .Arith.atom.CM, A.M.n, A.n.M): ditto * tests/factorizing.R: check some of the above. 2010-08-04 Douglas Bates * R/spModels.R (fac2sparse): Fix name resolution problem (R-SIG-Mixed-Models post by Florent Duyme). 2010-07-25 Martin Maechler * DESCRIPTION (Depends): require R >= 2.10.0 --> can clean up * R/spModels.R: prepare to move most parts to new package MatrixModels 2010-07-23 Martin Maechler * R/Auxiliaries.R (prMatrix): add " (unitriangular)" as we already have for sparse matrices. 2010-07-22 Martin Maechler * R/Auxiliaries.R (.diagU2N): implement for "dtpMatrix" = old 'FIXME'; (.dense.diagU2N): new utility, called from .diagU2N() 2010-07-19 Martin Maechler * src/dtrMatrix.c (dtrMatrix_dtrMatrix_mm): new for tri %*% tri * R/products.R (%*%): ditto * tests/matprod.R: test it 2010-07-16 Martin Maechler * R/spModels.R (do.defaults): add 'nonMatched.action' with default ensuring that typos are caught. 2010-07-16 Douglas Bates * R/spModels.R (do.defaults): utility function; TODO: move to R 2010-07-16 Martin Maechler * DESCRIPTION (Version): 0.999375-43, CRAN-released: 2010-08-05, r 2599 * R/AllClass.R (Model): as mother class (of "glpModel") * R/spModels.R (IRLS): more options() (updateModel): update() 2010-07-13 Martin Maechler * DESCRIPTION (Version): 0.999375-42, CRAN-released: 2010-07-15, r 2566 * R/spModels.R (glm4, IRLS): glm4 [was 'glm1']; tweaks. 2010-07-12 Martin Maechler * NAMESPACE: rename, export and * man/glpModel-class.Rd: document Doug's new "glpModel" class. 2010-07-08 Douglas Bates * R/AllClass.R: new "lpMod" class (-> later =: "glpModel"), and working function: * R/spModels.R (glm1): using linear pred.Model class, and Bates-Watts convergence criterion. 2010-07-06 Martin Maechler * R/lMatrix.R (whichDense): use arrayInd() * R/zzz.R (arrayInd): provide for older R versions 2010-07-05 Martin Maechler * src/chm_common.c (chm_triplet_to_SEXP): deal more carefully with NAs, needed e.g., on Solaris; thanks to Ruth and Brian Ripley. * R/Ops.R (Compare ): fix bug uncovered by "alongside" the above. 2010-07-02 Martin Maechler * R/sparseMatrix.R (x[] <- 0): fix shortcut code. * tests/indexing.R: and test * R/nearPD.R (nearPD): 'doDykstra = TRUE' and *do* use Dykstra's correction which was *not* used in Jens' code; thanks to Bernhard Spangl for a report 2010-06-26 Martin Maechler * R/Matrix.R: fix mean() method; add sparse one, remaining sparse at least for trim = 0. 2010-06-08 Martin Maechler * DESCRIPTION (Version): 0.999375-41, CRAN-released: 2010-07-03, r 2555 * R/sparseVector.R (spV2M): enable sparseVector -> (sparse)Matrix as(*,.) coercion. 2010-06-07 Martin Maechler * R/Tsparse.R (.TM.repl.i.mat): renamed from .TM.repl.i.2col(). * R/Matrix.R (.repl.i.lSMat): implement logical sparse sub-assignment: M[] <- v; ditto for dense & nsparse. * R/Csparse.R (.CM.repl.i.lSMat, ..): direct logical sparse sub-assignment for "Csparse". 2010-06-04 Martin Maechler * R/sparseMatrix.R (sparseMatrix): re-enable 'dimnames' argument. 2010-06-03 Martin Maechler * R/spModels.R (model.Matrix): tweak for NULL contrasts in dense case. 2010-06-02 Martin Maechler * tests/spModel.matrix.R (Sparse.model.matrix): adapt to the fact, that sparse.model.matrix() returns not just a dgCMatrix. 2010-05-29 Martin Maechler * DESCRIPTION (Version): 0.999375-40, CRAN-released: 2010-06-04, r 2546 * R/AllClass.R: new classes "ModelMatrix", "sparseModelMatrix", etc. * R/spModels.R (sparse.model.matrix): now return "dsparseModelMatrix" object, notably with 'assign' slot. * R/spModels.R (model.spmatrix): faster, using lower level cbind2/rbind2 directly. * R/spModels.R (model.Matrix): new function, returning "ddenseModelMatrix". * NAMESPACE: export new classes. 2010-05-18 Martin Maechler * src/Csparse.c (Csparse_horzcat, Csparse_vertcat): ensure that rBind()/cBind() i.e., rbind2()/cbind2() return logical sparse matrices when the components are. * tests/bind.R: test 2010-05-15 Martin Maechler * R/sparseMatrix.R: A[] <- v ; differentiate dense & sparse * R/pMatrix.R: disallow [] <- v more consequently * tests/indexing.R: test above 2010-05-08 Martin Maechler * R/spModels.R (model.spmatrix): deal with "AsIs" components * tests/spModel.matrix.R: test that 2010-05-01 Martin Maechler * R/condest.R (onenormest, condest): allow to estimate condition number for large sparse matrices. * condest.Rd: docu * R/pMatrix.R (.inv.perm): utility; add [t]crossprod() methods * man/sparseLU-class.Rd: A = P'LUQ; add examples, with "identities" * R/Auxiliaries.R (mmultCheck): new arg. 'kind' 2010-04-28 Martin Maechler * DESCRIPTION (Version): 0.999375-39, CRAN-released: 2010-05-19, r 2540 * R/spModels.R (fac2sparse): using names(formals(new))[[1]] to adapt to a future change in new()'s first argument *name*. 2010-03-31 Martin Maechler * R/spModels.R (lm.fit.sparse): update, allowing weights; also return residuals, notably for "cholesky" case. * man/lm.fit.sparse.Rd: examples; comparing with dense case. * src/dgCMatrix.c (dgCMatrix_cholsol): comments; also compute residuals. 2010-03-30 Martin Maechler * R/spModels.R (sparse.model.matrix, model.spmatrix): border case '~ 1' should also work. Add 'transpose = FALSE' argument. * tests/spModel.matrix.R: test that. 2010-03-27 Martin Maechler * R/sparseMatrix.R (printSpMatrix): ensure returning original argument 2010-03-26 Martin Maechler * R/sparseVector.R (coercion from TsparseMatrix): diagU2N() when needed. * inst/test-tools.R (checkMatrix): explicit which() test for "l" and "nMatrix". New sparseVector (coercion "and back") check. 2010-03-25 Martin Maechler * R/lMatrix.R (which): define methods for which(<[ln]Matrix>). * inst/test-tools.R (Q.eq.symmpart): new utility, now called in checkMatrix(). * R/nearPD.R: use symmpart() for non-symmetric x * man/nearPD.Rd: improve title 2010-03-24 Martin Maechler * R/colSums.R (.diag.Mean): define methods for "diagonalMatrix" * src/Mutils.c (m_encodeInd, do_ii_FILL): coerce ij to integer if necessary; check that ij are within "dim[]" values. Parametrize do_ii_FILL() to be used in m_encodeInd2() as well: * src/Mutils.c (m_encodeInd2): also check bounds (if desired). * tests/indexing.R: test the above. 2010-03-19 Martin Maechler * src/dgeMatrix.c (dgeMatrix_solve): compute the recip.cond.number and also bail out for *computational* singularity {as "base R" does}, from (code) suggestion by Daniel Sabanés Bové. * tests/dg_Matrix.R: "test" the above. 2010-03-01 Martin Maechler * man/rep2abI.Rd: rep2abI() utility is exported now. * R/Csparse.R (subCsp_cols, subCsp_rows, subCsp_ij): dimnames() <- fix for character subsetting. * tests/indexing.R: testing it. 2010-02-26 Martin Maechler * R/spModels.R (model.spmatrix): warn and coerce to sparseMatrix if result would end up dense (e.g., in case of *no* factors in formula). * tests/spModel.matrix.R: test the above. 2010-02-12 Martin Maechler * R/dtrMatrix.R: add solve(, ): e.g., for solve(, ) in lme4. 2010-02-09 Martin Maechler * DESCRIPTION (Version): 0.999375-38, CRAN-released: 2010-03-31, r 2529 * NAMESPACE, R/AllGeneric.R, R/zzz.R: change det() into a regularly exported function (masking base::det) instead of load-time hack. * man/Matrix-class.Rd: \alias, docu 2010-02-05 Martin Maechler * DESCRIPTION (Version): 0.999375-37, CRAN-released: 2010-02-05 * inst/test-tools.R (Qidentical.DN): new (Qidentical): all Qidentical.DN() * R/Csparse.R (subCsp_ij, subCsp_cols, subCsp_rows): use CHOLMOD's submatrix C code, instead of matrix multiplication; now *do* keep dimnames of result, wherever classical matrix subsetting does. 2010-02-04 Martin Maechler * DESCRIPTION (Version): 0.999375-36, CRAN-released: 2010-02-04 * R/Csparse.R (subCsp_ij): Fix [0,0] bug 2010-02-03 Martin Maechler * R/Tsparse.R (.TM.repl.i.2col): [ ] <- FALSE fix * tests/indexing.R, *.Rout.save: test that 2010-01-28 Martin Maechler * src/Csparse.c (Csparse_crossprod): PROTECT() Tsparse_diagU2N() result, from a suggestion by Andrew Runnalls. 2010-01-22 Martin Maechler * R/SparseM-conv.R (setAs(., "matrix.csc")): fix typo in method. 2010-01-20 Martin Maechler * R/AllGeneric.R: nnzero() is now generic, * R/nnzero.R: newly containing all nnzero() methods. * R/zzz.R (det): assign base::det such that it uses S4 generic kronecker. 2010-01-18 Martin Maechler * R/spModels.R (contr.poly): [the back-compatible-only version]: do not use a default for 'scores'; rather rely on stats::contr.poly. * tests/spModel.matrix.R: test that case 2009-12-28 Douglas Bates * DESCRIPTION (Version): 0.999375-35, CRAN-released: 2010-02-03 * src/init.c, inst/include/Matrix_stubs.c: cholmod_band_inplace() exported. 2009-12-23 Martin Maechler * tests/indexing.R: slightly adapt to the very slight [] changes. * inst/test-tools.R (Q.C.identical): + checkClass * R/Tsparse.R ([-methods): for now go via "Csparse" and drop all the sophisticated code dealing with the many cases. * R/Csparse.R (subCsp_cols, etc): faster [i,j] via matrix multiplication, thanks to suggestions by Greg Jorstad. * R/Auxiliaries.R (paste0): more use of paste0() 2009-12-22 Martin Maechler * R/diagMatrix.R (.sparseDiagonal): made more general, allowing to directly build the equivalent of Diagonal(n)[, j] * man/Diagonal.Rd: document .sparseDiagonal() as well. 2009-12-21 Martin Maechler * R/AllClass.R: abIndex@x and rleDiff@first are now "numLike", such that also logical can be converted to "abIndex". * R/abIndex.R (.diff): new utility, used in num2abI() 2009-12-19 Martin Maechler * src/abIndex.c: include new * src/t_Matrix_rle.c (Matrix_RLE_): is template for Matrix_rle_i() and Matrix_rle_d(); now obeys a 'force' argument. * R/abIndex.R: implement methods, at least with scalars. (all.equal.abI): add also all.equal() methods. * tests/abIndex-tsts.R: testing , using all.equal(). * R/AllClass.R: classUnion "numLike" := {"numeric", "logical"} 2009-12-18 Martin Maechler * src/abIndex.c (Matrix_int_rle): UNPROTECT() needed in trivial case. * R/abIndex.R (abIseq1, abIseq): new functions for building "abIndex" vectors. * tests/abIndex-tsts.R (tst.c.abI): test new c("") method. * DESCRIPTION (Version): 0.999375-34, CRAN-released: -never- * R/Ops.R: use prod(d) instead of d[1]*d[2], as the latter may integer overflow; fixes o * tests/Simple.R: test that. 2009-12-11 Martin Maechler * R/sparseVector.R (TsparseM* -> sparseV): symmetricMatrix needs to be expanded. This fixes a bug reported by Yu-Sung Su. * tests/indexing.R: testing the fix. * inst/test-tools.R (all.equalX): new util 2009-12-09 Martin Maechler * R/Ops.R (A.n.M, A.n.M): o : remain sparse also when *majority* (instead of all) of 0 o v is 0. * tests/group-methods.R: test one such case. 2009-12-06 Martin Maechler * DESCRIPTION (Version): 0.999375-33, CRAN-released: 2009-12-11 * R/Ops.R (Compare): fix case with NA x. * R/not.R: fix "typo" in ! * R/Ops.R (Ops.spV.spV): fix thinko 2009-12-05 Martin Maechler * R/sparseVector.R: setAs(nsparseV*, lsparseV*) etc * R/Ops.R (Ops.spM.spV, Ops.spV.spM): sparseVec. o sparseMat. 2009-11-20 Martin Maechler * R/Ops.R (Ops.spV.spV): enable sparseVector operations in more cases. * R/sparseVector.R (is.na): methods defined. * R/sparseVector.R (intIv): also accept "sparseVector"s * tests/Simple.R: check the above 2009-11-19 Martin Maechler * R/sparseVector.R (newSpV, newSpVec): new utility, dropping 0 "on the fly". * R/sparseVector.R (atomic -> sparse*): fix for NA case. * R/Ops.R (): using newSpVec() * R/not.R: fix thinko in ! 2009-11-17 Martin Maechler * tests/other-pkgs.R: detach(*, unload) Rgraphviz too 2009-11-14 Martin Maechler * R/AllClass.R: "abIndex" (and "rleDiff") class * R/abIndex.R: with some methods; commit these finally, even if it's mostly unfinished. * src/abIndex.[ch]: new: currently only for .Call(Matrix_int_rle,*) * tests/abIndex-tsts.R: basic consistency checks for "abIndex". * R/diagMatrix.R (diagOdiag): "exploding" Matrix.msg() only level 2; * tests/indexing.Rout.save: update 2009-11-11 Martin Maechler * DESCRIPTION (Version): 0.999375-32, CRAN-released: 2009-11-20 * src/Csparse.c (Csparse_Csparse_prod, Csparse_Csparse_crossprod): PROTECT(.) the dimnames; thanks to Kaspar Kristensen 2009-10-24 Martin Maechler * R/Ops.R (Logic.lCMat): to be used for lsC* and ltC* as well, effectively replacing previous suboptimal methods. * src/chm_common.c (chm2Ralloc): Fix unidiagonal ntC segfault: assign 'x' only when non-pattern. * src/chm_common.c (as_cholmod_triplet): reallocate now in a way that works; fix documentation about return value in diagU2N case; ditto for * src/chm_common.c (as_cholmod_sparse): * R/sparseMatrix.R (printSpMatrix): add 'cld' argument, typically passed from printSpMatrix2; and indicate "unit-diagonal" 2009-10-22 Martin Maechler * R/lsparseMatrix.R (C2l): fix for case with NA. * R/Csparse.R (replCmat): drop "stale" cached @factors factorizations after sub-assignments. * R/Tsparse.R (replTmat, .TM.repl.i.2col): ditto 2009-10-19 Martin Maechler * src/dgCMatrix.c (dgCMatrix_LU): new boolean argument 'error_on_sing' to allow no error in case of singularity; needed for determinant(), e.g. * R/Auxiliaries.R (detSparseLU): using lu(*, errSing=FALSE) * R/dgCMatrix.R, R/dsparseMatrix.R: lu() methods, using 'errSing' * R/sparseMatrix.R (printSpMatrix): fix bug introduced on *-09-10 * tests/Simple.R: test for that. 2009-10-18 Martin Maechler * src/dgeMatrix.c (dgeMatrix_crossprod): do not fail in 0-column case. * inst/test-tools.R (Q.eq): new utility (checkMatrix): minimally check %*%, crossprod() and tcrossprod() * R/products.R: more '%*%' methods for "[ln]?Matrix", "missing" 2009-10-06 Martin Maechler * DESCRIPTION (Version): 0.999375-31, CRAN-released: 2009-10-06 * inst/include/Matrix_stubs.c (M_R_cholmod_error): revert (2009-09-18), i.e., no longer restore cholmod_common. {{M_cholmod_defaults() still seems not usable from lme4's init.c}} 2009-10-05 Martin Maechler * src/dtrMatrix.c (dtrMatrix_chol2inv): use "dpoMatrix" instead of "dsy" * R/dtrMatrix.R: make use of implicit generic for chol2inv() in newer R versions. 2009-09-30 Martin Maechler * R/CHMfactor.R (solve): fix methods for "ddiMatrix" and "missing" RHS. * tests/factorizing.R: test these * R/Matrix.R (image): fix Matrix method to work for "ddiMatrix" * R/diagMatrix.R: coercion to "dsparse*" * tests/Simple.R: test image() 2009-09-29 Martin Maechler * R/AllGeneric.R: rcond is implicit generic in latest versions of R 2009-09-22 Martin Maechler * R/Ops.R (A.M.n,A.n.M): replace "Ops" methods by explicit "Arith", "Logic", etc, getting rid of ambiguity (notes), and of infinite recursions. * tests/group-methods.R: test these systematically. 2009-09-18 Martin Maechler * inst/include/Matrix_stubs.c (M_R_cholmod_start): print_function = NULL as in src/chm_common.c (2009-07-20) (M_R_cholmod_error): ditto, using new M_cholmod_default(), declared in * inst/include/cholmod.h * R/Tsparse.R (intI): do *not* allow logical subscript (row or column) to be too long, compatibly with traditional matrix indexing. * tests/indexing.R: and assert the error. 2009-09-17 Martin Maechler * R/pMatrix.R: as(sparseMatrix, pMatrix) * R/CHMfactor.R (solve): method for (CHMfactor, missing) * inst/test-tools.R (assertError): use tryCatch() * R/diagMatrix.R (.sparseDiagonal): fix shape "g" case. * R/Auxiliaries.R (isTriC): do not wrongly return TRUE for a *sCMatrix. * man/chol2inv-methods.Rd: document & example 2009-09-16 Douglas Bates * NAMESPACE, R/dtrMatrix.R, src/dtrMatrix.[ch]: add chol2inv() method for dtrMatrix. 2009-09-12 Martin Maechler * R/sparseVector.R ([): allow *indexing* with "lsparseVector" 2009-09-11 Martin Maechler * R/sparseVector.R (prSpVector): using ":" as in printSpMatrix() (Summary): add "Summary" group methods * man/sparseVector-class.Rd: and test a bit 2009-09-10 Martin Maechler * R/sparseMatrix.R (printSpMatrix): visually differentiate non-structural zeros in *logical* sparse matrices, using ":" * R/Auxiliaries.R (setparts): new utility, for * R/Ops.R (Ops.spV.spV): start implementing sparseVector arithmetic etc 2009-09-08 Martin Maechler * R/dgCMatrix.R (qr): for sparseMatrix must coerce to "dgCMatrix". * tests/factorizing.R: test qr() 2009-09-01 Martin Maechler * R/CHMfactor.R (determinant): divide previous log(det(.)) by 2; now returning det(L); and modify the "CHMfactor.warn" message. * man/CHMfactor-class.Rd: modify documentation accordingly. 2009-08-21 Martin Maechler * R/spModels.R (`contrasts<-`): a version that can also work with a "sparseMatrix" value. This is put into R 2.10.0 (devel) as well. * src/Mutils.h: rename any_NA to any_NA_in_x * src/Mutils.c (check_scalar_string): add doxygen doc 2009-08-15 Martin Maechler * R/spModels.R (fac2Sparse): make also work for 'contrasts.arg' = matrix; 2009-07-28 Martin Maechler * R/spModels.R (contr.sum): need also to define contr.*() as long as we document (./man/) them. 2009-07-27 Martin Maechler * DESCRIPTION (Version): 0.999375-30, CRAN-released: 2009-07-28 * R/Matrix.R (all.equal_Mat): add factorsCheck=FALSE argument * R/Auxiliaries.R (attr.all_Mat, attrSlots): ditto 2009-07-25 Martin Maechler * R/Auxiliaries.R (attr.all_Mat): fix checking of non-content slots. * R/Matrix.R (all.equal_Mat): thinko needed s/&&/&/ * R/sparseMatrix.R (all.equal(.) methods): ditto ===> Note: all.equal() is more stringent for "Matrix" arguments now! 2009-07-23 Martin Maechler * R/spModels.R (model.spmatrix, sparse2int): "complete" re-write * tests/spModel.matrix.R: many tests added 2009-07-20 Martin Maechler * src/chm_common.c (R_cholmod_l_start): set print_function to NULL, as we have long suggested ==> get rid of random strings seen in some cholmod warnings. (R_cholmod_error): call cholmod_l_defaults() before error(), so we restore the Cholmod global in case of errors. * R/ldenseMatrix.R (.rcond_via_d): fix thinko 2009-07-18 Martin Maechler * R/CHMfactor.R (isLDL): need a "!" as 'type' is "is_ll" * src/dsCMatrix.c (dsCMatrix_Cholesky): update, notably when caching. * tests/indexing.R: test col.names printing of sparseMatrix 2009-07-16 Martin Maechler * inst/test-tools.R (allCholesky): new testing function 2009-07-15 Martin Maechler * src/dsCMatrix.c (dsCMatrix_Cholesky): add possibility to set each of 'perm', 'LDL', and 'super' to NA (in addition to TRUE / FALSE). in these case, a CHOLMOD-heuristic choses the option "sensibly". * man/Cholesky.Rd: document the new possibility. 2009-07-14 Martin Maechler * R/rankMatrix.R (rankMatrix): diff(sval) <= 0 * R/spModels.R (model.spmatrix): fix case of missing main effect * tests/spModel.matrix.R: new file 2009-07-11 Martin Maechler * R/sparseMatrix.R (show, printSpMatrix2): both print() and show() now use printSpMatrix2(), and that now already prints " x sparse Matrix of class ...". * R/CHMfactor.R (isLDL): fix and * NAMESPACE: export isLDL() 2009-07-10 Martin Maechler * R/spModels.R (model.spmatrix): mf may be simple data.frame 2009-07-09 Martin Maechler * NAMESPACE: export sparse.model.matrix() and * man/sparse.model.matrix.Rd: document it 2009-07-08 Martin Maechler * R/Tsparse.R (intI): also work for integer dimnames (well ..) 2009-07-07 Martin Maechler * R/sparseMatrix.R: "factor out" sparse model things into * R/spModels.R (sparse.model.matrix): new model matrix functions 2009-06-20 Douglas Bates * src/CHMfactor.c: Ensure updated LL stays LL 2009-06-10 Martin Maechler * DESCRIPTION (Version): 0.999375-29, CRAN-released: 2009-06-11 2009-06-10 Douglas Bates * [r2404] src/Mutils.c: Change value of set_factor to be the cached factor * [r2403] src/dgCMatrix.c, src/dgCMatrix.h, src/init.c: Comment out unused dgCMatrix_lusol function * [r2402] R/dgCMatrix.R: R-level implementation of solve("dgCMatrix", "missing") * [r2401] src/dgCMatrix.c: Re-arrange LU factorization to always use the cached value. 2009-06-09 Douglas Bates * [r2399] src/dgCMatrix.c: PROTECT the result from dgCMatrix_LU in dgCMatrix_matrix_solve 2009-06-06 Martin Maechler * R/Tsparse.R: add numeric -> Tsparse* coercion 2009-06-05 Martin Maechler * src/Mutils.h, src/dgeMatrix.c: using dngettext(.) only on future versions of R. 2009-06-04 Martin Maechler * DESCRIPTION (Version): 0.999375-28, CRAN-released: 2009-06-08 * po/de.po, po/R-de.po: German translations from Chris Leick. * inst/po/de/: ditto, via po/update-me.sh 2009-05-28 Martin Maechler * src/chm_common.c, src/cs_utils.c, etc: internationalize more messages; fix some; thanks to feedback from Chris Leick. 2009-05-27 Martin Maechler * man/denseMatrix-class.Rd, etc: 'factors' is *not* a slot in this class; found by the upcoming R 2.10.0 codocClasses(). 2009-05-25 Martin Maechler * po/update-me.sh, Matrix.pot, etc: updated *.pot / *.po files * DESCRIPTION (Version, Date): 0.999375-27, CRAN-released today. * R/sparseVector.R: add as(, "dsparseVector") (spV2M): now works (again!?) for "isparseVector" (-> "dgTMatrix"). * tests/matprod.R: tcrossprod(), sparseVector multiplications, i.e., features of next paragraph. 2009-05-23 Martin Maechler * R/products.R: move almost all %*%, crossprod(), tcrossprod() methods to a new file. tcrossprod() compatibility with *fixed* base-R; enable operations with "sparseVector"s; some extra methods to avoid ambiguity messages. 2009-05-20 Martin Maechler * R/Auxiliaries.R (.M.v, .v.M): slight speedup, and *use* them in * R/Matrix.R (crossprod) 2009-05-18 Martin Maechler * R/sparseVector.R (dim<-): prod(as.integer(.)) may overflow! * R/Matrix.R (Matrix): Matrix(sv, ..) now works for a sparseVector * R/sparseVector.R (spV2M): allow zero nrow or ncol. 2009-05-16 Martin Maechler * R/sparseMatrix.R (dim<-): should also work for diagonalMatrix. * inst/test-tools.R (vec): add test for dim(x) <- c(n, 1) 2009-05-13 Martin Maechler * R/rankMatrix.R (rankMatrix): new function for matrix rank; "to be discussed". 2009-05-07 Doug Bates and Martin Maechler * src/Mutils.c (Matrix_check_class_etc): diverse smallish improvements, stuffing a small leak, adding PROTECT()ion, but, alas, not enough. 2009-05-06 Martin Maechler * R/HBMM.R (readMM): add checkIJ() to produce nicer error messages, on malformed input. * tests/write-read.R: and test that.. 2009-04-18 Martin Maechler * DESCRIPTION (Version, Date): 0.999375-26, CRAN-released on 2009-04-29 * src/Mutils.h (Matrix_check_class_etc): try to ensure it works also when Matrix is loaded but not attached. * src/init.c (R_init_Matrix): get Matrix namespace in C. * R/zzz.R (.onLoad): a *working* fix aka "hack" 2009-04-15 Martin Maechler * DESCRIPTION (Version): 0.999375-25 packaged --> CRAN 2009-04-09 Martin Maechler * R/Auxiliaries.R (Matrix.msg): new utility (.M.vectorSub): ditto, for vector-indexing; in * R/Matrix.R ([): M[i, drop=] should do *vector*-indexing. * R/Tsparse.R ([): ditto; * R/diagMatrix.R ([, subDiag): ditto. * R/Tsparse.R ([): more careful indexing of (triangular) TsparseMatrix. * tests/indexing.R: testing the above * R/Auxiliaries.R (gT2tT, check.gT2tT): consistency and efficiency improvement, using 'do.n' argument. 2009-04-08 Martin Maechler * R/Matrix.R: add as(., "vector") etc * man/Matrix-class.Rd: ditto * inst/test-tools.R (checkMatrix): and check them 2009-04-07 Martin Maechler * DESCRIPTION (Version, Date): 0.999375-24 ... released to CRAN * R/sparseVector.R: fix coercion from xsparse* * tests/Simple.R: and check it. * man/lu.Rd: document 'warnSing' argument * tests/dg_Matrix.R: and test it * src/dgeMatrix.c (dgeMatrix_LU): missing 'return' 2009-04-06 Martin Maechler * DESCRIPTION (Version, Date): 0.999375-24 only for 2.9.0 (and newer) 2009-03-30 Martin Maechler * src/Mutils.h (Matrix_check_class_etc): new version that *computes* the environment to be used. * src/Tsparse.c, src/cs_utils.c, src/chm_common.c, src/dgCMatrix.c: use the above in place of Matrix_check_class_and_super(). 2009-03-26 Martin Maechler * R/Auxiliaries.R (MatrixClass): use cld@package, not packageSlot(.) ! 2009-03-25 Martin Maechler * DESCRIPTION (Version, Date): 0.999375-23 * tests/Class+Meth.R (dotestMat): use getClassDef() for speed; adaptions to also work with "Matrix-extensions". * inst/test-tools.R (checkMatrix): similar adaptions. 2009-03-24 Martin Maechler * R/Auxiliaries.R (MatrixClass, l2d_meth, ...): make use of MatrixClass(): functionality for setClass("foo", contains="dgCMatrix") * src/Mutils.h (Matrix_check_class_and_super): new utility, to be used in lieu of Matrix_check_class() in most cases. * src/Tsparse.c, src/cs_utils.c, src/chm_common.c, src/dgCMatrix.c: use it, currently only with R_GlobalEnv {otherwise: API change} 2009-03-12 Martin Maechler * man/band.Rd: note and example about band() |-> dense * R/ddenseMatrix.R (.bandDense): fix typo in argument check. * R/Csparse.R: ditto * src/dense.c (dense_band): limit index range; thanks to Bill Dunlap. * tests/Simple.R (band): check it 2009-03-11 Martin Maechler * R/dMatrix.R (Summary): (dsparseMatrix): new logic, fixing prod(). * inst/test-tools.R (eqDeterminant): improve after suggestions from Doug * inst/test-tools.R (checkMatrix): message(), not warning(), for differing prod(). * src/dgeMatrix.h, src/init.c: dgeMatrix_LU(x, warn_singularity) * src/dgeMatrix.c (dgeMatrix_LU): allow to suppress singularity warning. (dgeMatrix_determinant, dgeMatrix_rcond): do *not* warn on exact singularity 2009-03-10 Martin Maechler * R/Matrix.R (Summary.l, Summary.np): no conversion to "dMatrix" for all()/any() * tests/Simple.R: do not use memory-expensive all(I.. == Diagonal(n)) for R >= 2.9.0, keep option 'warn = 2', i.e. warnings producing errors ==> * R/Ops.R: small fixes, getting rid of warnings in tests/Simple.R * TODO: think about providing something like allCompare(.,., "==") 2009-03-02 Martin Maechler * DESCRIPTION (Version): 0.999375-22, ready but not submitted 2009-03-01 Martin Maechler * inst/test-tools.R (eqDeterminant): fix for NAs 2009-02-28 Martin Maechler * R/diagMatrix.R (prod, all): fix methods (cut & paste remnant); for NA. * R/Auxiliaries.R (detSparseLU): determinant(<..NA..>) now gives NaN * R/sparseMatrix.R (printSpMatrix): workaround format.info() R bug * tests/Simple.R: test that 2009-02-27 Martin Maechler * R/Matrix.R (Matrix): Matrix(x,*) returns x unaltered when is(x, "diagonalMatrix"); OTOH, Matrix(x,1,1) should typically *not* return a diagonalMatrix. * R/diagMatrix.R (setAs(matrix, *)): fix for NAs. * tests/Simple.R: test things like Matrix(NA, 1,1) 2009-02-25 Martin Maechler * NAMESPACE: add bandSparse() "properly" * man/bandSparse.Rd: doc including examples 2009-02-20 Martin Maechler * R/bandSparse.R (bandSparse): constructor for band(diagonal) sparse matrices. 2009-02-13 Martin Maechler * DESCRIPTION (Version): 0.999375-21, released to CRAN * src/Mutils.h (Matrix_with_SPQR): #define (or #undef), in order to allow easy building "SPQR-free version" of Matrix. 2009-02-11 Martin Maechler * R/Csparse.R (replCmat): another check for 'has.x' * tests/indexing.R: very large (very sparse) sub-indexing. 2009-01-30 Martin Maechler * DESCRIPTION (Version): 0.999375-20 * man/spqr.Rd: disable example on Windows for now * inst/test-tools.R (checkMatrix): simpler for "logical" pMatrix. * R/ngTMatrix.R: fix ngT -> nge / lge coercion, and * tests/Simple.R: adapt test. * R/pMatrix.R: coercion to "matrix": more sensical to coerce to logical instead of 0/1 integer. This a mild back-compatibility breach. * man/pMatrix-class.Rd: adapt, including example * R/sparseMatrix.R (printSpMatrix): print as logical, too. 2009-01-29 Martin Maechler * R/Auxiliaries.R (geClass): define for "pMatrix" * R/pMatrix.R: pMatrix -> ngeMatrix coercion * man/pMatrix-class.Rd: * DESCRIPTION (Version): 0.999375-19 considering release. * R/ngTMatrix.R: coercing correctly to ngeMatrix via lge*. * man/dgTMatrix-class.Rd: remove no-more-existing coercion method; mention a bit less, and note. * R/diagMatrix.R: ensure that * is diagonal even with new method dispatch * R/Matrix.R (.M.sub.i.logical): change comments only, and extend error message which is never called currently. * R/Ops.R (Ops.x.x): fix for new "inherited method" dispatch 2009-01-28 Martin Maechler * R/spqr.R: put spqr() / class "SPQR" related code in one file for now. * NAMESPACE: export "SPQR" class * man/SPQR-class.Rd: document it 2009-01-27 Martin Maechler * R/Auxiliaries.R (is.na_nsp): should produce "nsCMatrix" only when dimnames are symmetric too. * R/sparseQR.R (solve): method for (, ) 2009-01-26 Douglas Bates * src/cs_utils.c (Matrix_as_cs): in diagU2N case: Force sorted columns after expanding unit diagonal. 2009-01-21 Martin Maechler * R/Tsparse.R (intI): for now give intelligible error on NA indices. * R/Matrix.R (subset.ij): should deal correctly with NA indices in the 2-column-matrix index case. * src/Mutils.c (m_encodeInd, m_encodeInd2): prepare to deal better with NA in indices. 2009-01-20 Martin Maechler * inst/doc/Intro2Matrix.Rnw: mention sparseMatrix * man/sparseMatrix.Rd: fix typos found by parse_Rd 2009-01-19 Martin Maechler * DESCRIPTION (Version,Date): release 0.999375-18 (as of yesterday) 2009-01-18 Douglas Bates * [r2319] src/Csparse.c, src/Csparse.h: Added an untested create_Csparse function 2009-01-17 Martin Maechler * R/sparseMatrix.R (sparseMatrix): recycle 'x' if necessary; use 'index1' rather than 'index0' {as proposed by Doug}. * R/dgeMatrix.R: drop two unnecessary (maybe very very slightly faster) methods for %*%. 2009-01-12 Douglas Bates * [r2313] R/sparseMatrix.R, man/sparseMatrix.rd: Use intermediate triplet rep in sparseMatrix. 2009-01-07 Martin Maechler * R/sparseMatrix.R (sparseMatrix): new function to be used in place of new(), notably for CsparseMatrix objects. * man/sparseMatrix.Rd: its doc; plus examples * man/CsparseMatrix-class.Rd: fix long-standing thinko; update the \note{} to reflect the fact that the validity method no longer modifies its argument. * R/Csparse.R (.validateCsparse): new utility accessing * src/Csparse.c (Csparse_validate_, Csparse_validate2): new utilities allowing the "sort-in-place" that used to be part of former Csparse_validate(). 2008-12-10 Douglas Bates * [r2309] DESCRIPTION: Release 0.99375-17 2008-12-05 Douglas Bates * [r2308] inst/include/Matrix_stubs.c, inst/include/cholmod.h: Adding const for picky compilers; Using CHM_FR typedef 2008-11-17 Martin Maechler * [r2307] ChangeLog, tests/validObj.R: update (as of Oct.26) 2008-10-31 Douglas Bates * [r2306] inst/include/Matrix_stubs.c: Consistency with cholmod.h re const qualifier 2008-10-26 Douglas Bates * src/Csparse.c (Csparse_validate): do not sort, but report error on unsorted row-indices within column. * tests/validObj.R: adapt the regression test. 2008-10-17 Douglas Bates * [r2300] inst/include/Matrix_stubs.c: Consistency with SparseSuite names * [r2299] src/AMD/Source/Makefile, src/CHMfactor.c, src/CHOLMOD/Lib/Makefile, src/COLAMD/Source/Makefile, src/Csparse.c, src/Tsparse.c, src/UFconfig/UFconfig.h, src/chm_common.c, src/chm_common.h, src/dense.c, src/dgCMatrix.c, src/dsCMatrix.c, src/init.c, src/t_gCMatrix_colSums.c: Compile only the UF_long version of SparseSuite but setting UF_long to be int 2008-10-17 Martin Maechler * src/Mutils.h: include also for AIX 2008-10-16 Martin Maechler * src/scripts/ : move *.sh, *.mkf and *.mk files from src/ to src/scripts/ * src/*/{Lib|Source}/Makefile: change to non-GNU-make style, and other improvements from Brian Ripley. 2008-10-15 Martin Maechler * src/Makevars, src/Makevars.win: replacing * src/Makefile, src/Makefile.win which are no longer needed 2008-10-14 Martin Maechler * src/Makefile, src/*/Makefile: changes from Brian Ripley enabling parallel make. 2008-10-13 Douglas Bates * [r2285] src/SPQR/Include/spqr.hpp: Include the C string declarations. 2008-10-06 Douglas Bates * [r2284] src/Makefile, src/SPQR/Lib/Makefile_SPQR, src/SPQR/Makefile, src/Win.mk: Modifications for compilation under Windows * [r2283] tests/validObj.R: remove reference to undefined object * [r2282] inst/doc/UFsparse/SPQR.txt: SPQR license information 2008-10-04 Douglas Bates * [r2281] src/Makefile, src/chm_common.c, src/chm_common.h, src/dgCMatrix.c, src/init.c: SparseSuiteQR interface 2008-10-03 Martin Maechler * src/Csparse.c (isValid_Csparse): new utility * src/chm_common.c (as_cholmod_sparse): add validity check early * tests/validObj.R: test the above 2008-10-02 Douglas Bates * [r2277] TODO: Think of a better way of structuring include files * [r2276] src/AMD/Source/Makefile, src/CHOLMOD/Lib/Makefile, src/COLAMD/Source/Makefile, src/Makefile, src/SPQR/Include/SuiteSparseQR_C.h, src/chm_common.h, src/dgCMatrix.c, src/dgCMatrix.h, src/init.c, src/sparseQR.h: Add dgCMatrix_SPQR and modify other code to allow its compilation and linkage 2008-10-02 Martin Maechler * R/sparseMatrix.R (printSpMatrix2): another validObject(.) call * src/Makefile: getting rid of SUBSTAMP etc, thanks to Simon U. 2008-10-01 Douglas Bates * src/Makefile, inst/doc/UFsparse/, inst/include/: Adjustments for SuiteSparse configuration. * src/CHOLMOD, src/UFconfig: update versions of SuiteSparse libraries. * src/SPQR/* add "SPQR", from Tim Davis' "SuiteSparse" collection, not yet with an R interface. 2008-09-25 Martin Maechler * Release 0.999375-15 to CRAN. 2008-09-23 Martin Maechler * src/dsyMatrix.c (dsyMatrix_as_dspMatrix): copy 'factors' slot * tests/dpo-test.R: test for it * R/Tsparse.R (intI): improve one error message. 2008-09-22 Martin Maechler * DESCRIPTION (Version): 0.999375-15 to be released * R/diagMatrix.R (diag o ): explicit setMethods, in order to keep result diagonal in many more cases. (coerce) to denseMatrix now *does* coerce. * man/diagonalMatrix-class.Rd: \alias{} for these. * R/Auxiliaries.R (.dense.prefixes): ".diMatrix" has not been dense anymore! * R/dMatrix.R: as(, ): enable Cholesky/BunchKaufman 2008-09-20 Martin Maechler * R/lsparseMatrix.R (C2l): as(, "lMatrix") should preserve NAs. * R/Ops.R (Arith, Compare): keep diag="U" in more cases when sensible 2008-09-19 Martin Maechler * R/Ops.R (Arith): better o which preserves symmetry / triangularity in "obvious" cases. * R/dpoMatrix.R: setAs(., "lMatrix") and setAs(., "nMatrix") * R/dppMatrix.R: ditto * man/dpoMatrix-class.Rd: * inst/test-tools.R (checkMatrix): add [dln]Matrix <-> [dln]Matrix coercion checks. * tests/indexing.Rout.save: more ambiguity warnings from the new checks. * R/dMatrix.R: dMatrix -> nMatrix: fix dense case. 2008-09-18 Martin Maechler * tests/factorizing.R: test expand() * src/dgCMatrix.c (dgCMatrix_LU): fill @Dim slot correctly. * R/Tsparse.R (replTmat): also optionally warn when sub-assignment loses symmetry of Matrix. 2008-09-17 Martin Maechler * R/Tsparse.R (.TM.repl.i.2col): fix sub-assignment of "dsCMatrix"; bug reported by Jacob van Etten. * tests/indexing.R, tests/indexing.Rout.save: testing it 2008-09-10 Douglas Bates * [r2260] src/Mutils.h, src/chm_common.c, src/cs_utils.c, src/dsCMatrix.c: Update doxygen comments 2008-09-10 Martin Maechler * man/ddiMatrix-class.Rd: docu update : sparse, not dense (see 2008-07-28). * man/ldiMatrix-class.Rd , man/diagonalMatrix-class.Rd: ditto. 2008-09-08 Martin Maechler * DESCRIPTION (Version): 0.999375-14 to be released to CRAN, in order to comply to to pending changes in R-devel (2.8.0). 2008-09-05 Martin Maechler * R/Matrix.R (solve,..): use (Matrix,ANY)... instead of (Matrix,Matrix) * R/Ops.R: ditto; most of these from John Chambers. * man/Matrix-class.Rd * R/Auxiliaries.R (.diagU2N): fix for Rsparse* * tests/Simple.R: test it 2008-09-02 Martin Maechler * man/drop0.Rd: * R/Auxiliaries.R (drop0): new argument 'tol = 0' (and 'is.Csparse'); entails updates in * R/Csparse.R, R/lMatrix.R, R/dMatrix.R 2008-08-30 Martin Maechler * DESCRIPTION (Version): 0.999375-13 released to CRAN 2008-08-29 Martin Maechler * R/Auxiliaries.R (attrSlotNames, attrSlots, attr.all_Mat): new utilities, for now to be used in all.equal() methods. * R/Matrix.R (all.equal_Mat): be more careful (less tolerant) in all.equal() methods. * R/sparseMatrix.R: ditto 2008-08-28 Martin Maechler * DESCRIPTION (Version): 0.999375-12 released to CRAN * R/Ops.R (Compare(,): fix for nsparseMatrix 2008-08-27 Douglas Bates * R/sparseMatrix.R: fac2sparse() for NA's 2008-08-26 Martin Maechler * R/sparseVector.R (all.equal.sparseV): make work for nsparseVector's 2008-08-25 Martin Maechler * src/dgCMatrix.c (dgCMatrix_LU): partially revert change r2175 (2008-04-23) and do give an error for a singular matrix. * man/lu.Rd, R/Auxiliaries.R (detSparseLU): adapt to that. * R/LU.R: expand( ) * NAMESPACE, man/all.equal-methods.Rd: * R/Matrix.R (all.equal): methods for Matrices, * R/sparseMatrix.R, R/sparseVector.R: sparseMatrices and -Vectors 2008-08-23 Douglas Bates * [r2243] R/CHMfactor.R, man/CHMfactor-class.Rd: Added expand method and documentation for CHMfactor class * [r2241] R/CHMfactor.R: Added trivial coercion method for CHMfactor -> pMatrix 2008-08-19 Martin Maechler * R/nsCMatrix.R (setAs(., dgTMatrix))): remove unused method 2008-08-18 Martin Maechler * R/Ops.R (.Ops2dge.via.x, and many others): eliminate never-used variable assignments {from "next version" codetools}. * R/Csparse.R, R/Tsparse.R: ditto 2008-08-17 Martin Maechler * R/sparseVector.R (sp2vec, coerce to sparseVector): make sure no integer overflows happen, and use double precision (n, index) where appropriate. * tests/Simple.R: test "large" sparse vectors. 2008-08-14 Martin Maechler * R/AllClass.R (sparseVector): 'length' and 'i' are "numeric", not just integer (allowing much longer length). 2008-07-28 Martin Maechler * R/AllClass.R (diagonalMatrix): extend "sparseMatrix" instead of "denseMatrix". This renders "scarceMatrix" dispensable and invalidates part of MM's presentations on "space of Matrix classes", but seems cleaner overall. * R/diagMatrix.R, etc: eliminate "scarceMatrix", replacing it by "sparseMatrix" in method signatures; further, instead of coercing to "sparseMatrix", coerce to "TsparseMatrix" now. 2008-07-26 Martin Maechler * src/dgCMatrix.c (dgCMatrix_qrsol): allow third argument 'order' in .Call(.) * R/sparseMatrix.R (lm.fit.sparse), src/dgCMatrix.h, src/init.c: ditto 2008-07-24 Martin Maechler * R/dgeMatrix.R: need solve(, ) against infinite recursion in new test in * tests/matprod.R: testing the above and another solve() case, below * R/sparseMatrix.R (lm.fit.sparse): slightly more efficient for e.g. triangular 'x'. * src/dgCMatrix.c (dgCMatrix_qrsol): use AS_CSP() hence allowing dtC* * src/dgCMatrix.c (dgCMatrix_cholsol): use AS_CHM_SP() to work correctly with unit-triangular x * src/dsCMatrix.c (dsCMatrix_Csparse_solve): use AS_CHM_SP() instead of not checking diagU. * R/diagMatrix.R, R/Auxiliaries.R: tweaks to allow later experiments where diagonalMatrix would extend sparse*. 2008-07-23 Martin Maechler * src/dgCMatrix.c (compressed_non_0_ij): for nnzero(), use "x@p[ncol(x)]" instead of length(x@i). * R/Auxiliaries.R (nnzero): ditto * src/chm_common.c (as_cholmod_sparse): Do not use LENGTH(islot) since that fails for over-allocated i. * tests/validObj.R: more testing of over-allocated (i,x) slots 2008-07-23 Martin Maechler * src/chm_common.c (as_cholmod_sparse): Add 4th argument 'sort_in_place' and set it to TRUE in call from * src/Csparse.c (Csparse_validate): sort in place, making sure that validObject() continues sort the columns if needed. * tests/validObj.R: now tests that more thoroughly, and * man/CsparseMatrix-class.Rd: documents it. 2008-07-22 Douglas Bates * [r2233] src/chm_common.c: sort columns more carefully in as_cholmod_sparse * [r2231] src/chm_common.c: check for sorted columns in as_cholmod_sparse instead of assuming it * [r2228] src/cs_utils.c: Use R_alloc for semi-permanent storage when expanding diagonal 2008-07-21 Martin Maechler * src/cs_utils.c (Matrix_as_cs): add check_Udiag switch * src/cs_utils.h (AS_CSP & AS_CSP__): two versions * src/dtCMatrix.c (dtCMatrix_sparse_solve): no longer needs diagU2N(). * R/diagMatrix.R (.sparseDiagonal): new utility, used in "old" .spDiagonal() and new .trDiagonal(). * R/dtCMatrix.R (solve): make use of .trDiagonal() 2008-07-19 Martin Maechler * R/Auxiliaries.R (dimNamesCheck): fix very long standing buglet, stumbled upon by Michael H. * tests/validObj.R: testing the bug-fix * src/chm_common.h (AS_CHM_SP__, AS_CHM_TR__): the non-diagU2N versions. * src/chm_common.c (as_cholmod_sparse, as_cholmod_triplet): new boolean argument 'check_Udiag' (formerly implicitly was FALSE). * src/Csparse.c (Csparse_Csparse_prod, ...): etc: use the new AS_CHM_SP() which includes diagU2N. * inst/include/Matrix_stubs.c (M_as_cholmod_sparse): similarly adapt to 3 arguments. 2008-07-17 Douglas Bates * [r2220] src/dtCMatrix.c: Correct number of columns for rhs in dtCMatrix_sparse_solve * [r2219] src/cs_utils.c: eye->nz should be -1 for compressed column storage * [r2217] R/dtCMatrix.R, src/dtCMatrix.c, src/dtCMatrix.h, src/init.c: Replace dtCMatrix_solve by more general dtCMatrix_sparse_solve and add new solve method * [r2216] src/cs_utils.c: Utility csp_eye in case we want to fold Csparse_diagU2N functionality into Matrix_as_cs 2008-07-17 Martin Maechler * inst/doc/factor2sparse.Rnw: revive a year-old unfinished vignette 2008-07-16 Douglas Bates * [r2212] R/sparseMatrix.R: fac2sparse gets a drop.unused.levels argument with default TRUE * [r2211] inst/include/Matrix.h, inst/include/Matrix_stubs.c: Export Csparse_diagU2N * [r2210] R/dtCMatrix.R, man/dtCMatrix-class.Rd, src/dtCMatrix.c, src/dtCMatrix.h, src/init.c: Remove vestigial methods based on the parent array; new solve method for signature(a = "dtCMatrix", b = "sparseMatrix") 2008-07-14 Martin Maechler * R/diagMatrix.R (.bdiag): also keep result triangular 2008-07-13 Douglas Bates * [r2208] src/dtCMatrix.c, src/dtTMatrix.c: Revise wording in error messages 2008-07-12 Martin Maechler * R/diagMatrix.R (.bdiag): make more sophisticated, keeping symmetric- or nsparse-Matrix, also fixing the bug introduced with the new version (.999375-10). * tests/Simple.R: regression test for the bugs. 2008-07-07 Martin Maechler * R/sparseVector.R (spV2M): fix for "isparseVector". Further, fix -> coercion (repSpV): add rep(, .) method * R/sparseMatrix.R ([<-): when the RHS is a "scarce"Matrix, do *not* use as.vector(.). * R/Tsparse.R ([<-): & [CR]sparse.R: methods for value = "sparseVector" * R/AllClass.R: new (hidden) class union "scarceMatrix" * R/AllClass.R: sparseVector: add prototype * src/dsCMatrix.c (chk_nm): fix "Cholesky" check, thanks to Kasper Kristensen 2008-06-28 Martin Maechler * tests/other-pkgs.R: add more interesting Matrix -> graph 2008-06-27 Martin Maechler * R/sparseMatrix.R (Tsp2grNEL): add 'need.uniq' argument for speed improvement in "[CR]sparseMatrix" -> "graphNEL" coercion. 2008-06-25 Martin Maechler * DESCRIPTION: release 0.999375-10 to CRAN * R/diagMatrix.R (.bdiag): use more efficient Bates-algorithm for .bdiag(). * man/bdiag.Rd: update, including test. 2008-06-24 Martin Maechler * tests/Simple.R: add minimal bdiag() checks * R/diagMatrix.R (bdiag): fix bdiag(diag(4:5)) case; factor out the Tsparse - internal computation into new .bdiag() 2008-06-14 Martin Maechler * R/nsparseMatrix.R: specific fast all() and any() methods. * src/dgTMatrix.c (MAKE_gTMatrix_to_geMatrix): better error message when trying to produce too large result. * inst/test-tools.R (checkMatrix): add 'do.matrix' with a check for very large matrices. * R/sparseMatrix.R (printSpMatrix2): new function, used by show(). * R/diagMatrix.R (show): print only diagonal entries when nrow(.) >= 50. 2008-06-13 Martin Maechler * src/Mutils.c (m_encodeInd, m_encodeInd2): * R/*.R: .Call(m_encodeInd2?, ..) instead of encodeInd2?(..). * R/Auxiliaries.R (encodeInd2?): care against integer overflow (for big matrices): -> 2nd argument 'di' instead of 'nr' ! 2008-06-09 Martin Maechler * R/dtCMatrix.R: faster dgC* -> dtC* method * tests/Simple.R: (hence removed "FIXME") * R/Auxiliaries.R (copyClass): add 'check = .copyClass.check' which can be be turned off for possible speed gains. 2008-06-02 Martin Maechler * R/dMatrix.R, R/Tsparse.R: get rid of some disambiguation warnings * R/not.R: fix ! implement two old "FIXME"s: ! & ! * R/diagMatrix.R (Ops): fix one-off thinko in o methods * inst/test-tools.R: checkMatrix(): drop0(m12) unconditionally 2008-05-30 Martin Maechler * R/diagMatrix.R (Ops): more o methods * tests/Simple.R: testing the above 2008-05-07 Martin Maechler * NAMESPACE: also import "Ops" {found via new tools:::get_S4_generics_with_methods()} 2008-05-03 Martin Maechler * R/Matrix.R (dimnames<-): dimnames(.) <- NULL works with a message; * NAMESPACE (unname): finally exported 2008-04-28 Martin Maechler * R/Auxiliaries.R (cholMat): possibly keep packed * inst/test-tools.R (checkMatrix): add fixed determinant.matrix() for R < 2.7.0. * R/Tsparse.R ([): for triangularMatrix, check if result may be triangular. * tests/indexing.R: regression test 2008-04-26 Martin Maechler * inst/test-tools.R (checkMatrix): test not only for dMatrix * R/Ops.R: more methods, for lMatrix/nMatrix 2008-04-24 Martin Maechler * R/expm.R: new file for all expm() methods; notably new ones for diagonal*, triangular*, symmetric* and also simple "matrix". 2008-04-23 Martin Maechler * R/dsyMatrix.R: setAs(.) rather than setIs(.) "to dpoMatrix" * inst/test-tools.R (assert.EQ.mat): better message when not equal * src/dgeMatrix.c (dgeMatrix_matrix_crossprod): allow integer RHS. * R/AllClass.R (ddiMatrix,ldiMatrix): extend [dl]Matrix instead of [dl]denseMatrix {identical slots; but more logical method dispatch} 2008-04-23 Martin Maechler * R/sparseMatrix.R (summary): use length() instead of nnzero() * R/diagMatrix.R (determinant): method 2008-04-22 Martin Maechler * src/dsCMatrix.c (dsCMatrix_Cholesky): suppress CHOLMOD printing too * R/Rsparse.R (.viaC.to.R): uplo fix for symmetric & triangular * R/dsCMatrix.R (determinant): switch to use Cholesky( 'LDL' ) and its diagonal 2008-04-21 Martin Maechler * R/dMatrix.R (Summary): short-cut for prod() * R/not.R: fix !<"U"-diag-ltrMatrix> ; drop {R < 2.6.0}-branch * R/Auxiliaries.R (tT2gT): fix for "U"-diag-ltTMatrix * R/AllClass.R: ltTMatrix validity: call (more stringent) tTMatrix_validate 2008-04-19 Martin Maechler * R/Ops.R (Ops.x.x): aux.function, not just for (dMatrix,dMatrix) * R/Ops.R (.do.Logic.lsparse): fix NA case * R/Tsparse.R (replTmat): fix r.sym case, using indTri() * R/Auxiliaries.R (nnzero): fix special cases, using * R/Auxiliaries.R (indDiag): new utility * R/Auxiliaries.R (indTri): new argument 'diag' * R/dMatrix.R: Summmary(): different branch for dsy* 2008-04-18 Martin Maechler * R/diagMatrix.R: "Summary" methods, and more "Arith" / "Ops" * src/Csparse.c (Csparse_drop): preserve (uplo,diag) for ".tCMatrix" triangular matrix. * R/Auxiliaries.R (drop0): use diagU2N(); according to helpfile, 'clx' can be class *or* class representation. (nnzSparse): new. (non0ind): new 'xtendSymm' argument; used in * R/Ops.R: * R/pMatrix.R: more efficient determinant() method 2008-04-17 Martin Maechler * [deactivated] R/Matrix.R (det): det() as base::det(), but with Matrix environment * [deactivated] NAMESPACE: export(det) * R/diagMatrix.R (mkDiag): new substitute for diag() * R/Auxiliaries.R (nnzero): fix for "diagU2N"-case (as0, as1): new utility. * R/Csparse.R (diag, band): need diagU2N() * src/dgeMatrix.c (get_norm): return NA when 'x' slot has NA/NaN. * R/lMatrix.R: coerce(nMatrix |-> lMatrix) fix * R/Ops.R (Compare): fix o case * R/nsparseMatrix.R, R/pMatrix.R: is.na() method 2008-04-16 Martin Maechler * R/Auxiliaries.R (signPerm): new utility for * R/Auxiliaries.R (detSparseLU): determinant() via sparseLU * src/dsCMatrix.c (dsCMatrix_LDL_D): suppress 'CHOLMOD warning'; since we have our own error handler (and can use tryCatch() from R). 2008-04-15 Martin Maechler * R/dgTMatrix.R (image): ha! set col=NA if lwd is small -- very nice! * R/dsCMatrix.R (determinant): use tryCatch() and switch to lu() when not positive definite. * R/Auxiliaries.R (asTri): new auxiliary (non0.i): make *much* faster for Tsparse with many non-zero entries; add 'uniqT = TRUE' argument to be used when sorting is undesired. * tests/Class+Meth.R (dotestMat): now build on checkMatrix() from test-tools.R , see below * R/dMatrix.R: fix "Summary" method: + diagU2N() * NAMESPACE, R/Matrix.R: add mean() method 2008-04-12 Martin Maechler * R/dgTMatrix.R (image): allow to *not* take abs(), and use cold-hot colors; try *changed* default useAbs = FALSE * man/image-methods.Rd: nice examples 2008-04-11 Martin Maechler * inst/test-tools.R (checkMatrix): new function for modularizing part of tstMatrixClass() in tests/Class+Meth.R * R/dsCMatrix.R: coercion from "matrix" * R/ltTMatrix.R, R/ntTMatrix.R: ditto (change it). * tests/Class+Meth.R (tstMatrixClass): some cleanup; add test for as(matrix(,0,0), ) 2008-04-09 Martin Maechler * src/dgeMatrix.c (dgeMatrix_determinant): for n == 0, work as determinant(matrix(,0,0)). * src/dgCMatrix.c (dgCMatrix_LU): return {L,U} as dtCMatrix * man/sparseLU-class.Rd: ditto * R/dgCMatrix.R (determinant): method building on lu() * R/sparseMatrix.R, Matrix.R, ...: ditto * R/Auxiliaries.R (mkDet): auxiliary for determinant() 2008-04-07 Martin Maechler * R/sparseMatrix.R (summary): no 'x' column for pattern matrices. 2008-04-02 Martin Maechler * src/dense.c (dense_to_Csparse): all declarations *before* R_CheckStack(); needed e.g. for ancient gcc 2.96. 2008-03-29 Martin Maechler * DESCRIPTION (Version): 0.999375-9 --- need to release for R-devel (and R 2.7.0 alpha soon). * R/AllClass.R: drop "double" from "atomicVector" class union * R/AllGeneric.R (rcond): check for base::rcond instead of R version * R/dgeMatrix.R: ditto * R/sparseMatrix.R (summary): count NAs * inst/doc/Intro2Matrix.Rnw: changes, aim for *one* introduction. 2008-03-28 Martin Maechler * R/AllGeneric.R: rcond(., norm) instead of rcond(., type), in order to become compatible to new R 2.7.0 base::rcond(). 2008-03-25 Martin Maechler * DESCRIPTION (Version,Date): 0.999375-8 --- released to CRAN * R/diagMatrix.R (Ops): fix newly introduce bug in <.di> o * inst/test-tools.R (isValid): new utility, used much in * tests/simple.R: * man/BunchKaufman-methods.Rd: added too 2008-03-24 Martin Maechler * R/dsyMatrix.R: add BunchKaufman() methods. * R/dspMatrix.R: * src/init.c: add dsyMatrix_trf 2008-03-23 Douglas Bates * DESCRIPTION (Version): release 0.999375-7 * src/CHMfactor.c (CHMfactor_update): fix 2008-03-22 Martin Maechler * src/dsCMatrix.c (dsCMatrix_LDL_D): cleanup, also using internal_chm_factor(). * R/AllGeneric.R: do *not* define a "chol" generic (but rather use the implicit one *without* making pivot part of the signature) * R/*.R: drop the 'pivot' from chol's signature and make 'pivot=FALSE' a default argument of method definitions. * .Rbuildignore: add 'wrld_1deg': I.e. do not put it into released version of Matrix 2008-03-18 Martin Maechler * R/Tsparse.R (.T.2.n): drop 0's before coercion to "nMatrix" * R/sparseMatrix.R (is.na): new simple method * R/denseMatrix.R (is.na): ditto. * R/diagMatrix.R (.symDiagonal): newly exported utility. * R/diagMatrix.R (Ops): * should not become dgeMatrix! * src/UFsparse_download.sh: --> * src/CHOLMOD/: update to CHOLMOD version 1.6 (Nov.2007) 2008-03-17 Martin Maechler * src/dsCMatrix.c (dsCMatrix_LDL_D): even faster utility with same functionality; barely tested in * tests/factorizing.R * src/Csparse.c (diag_tC): new functionality to enable faster determinant(, .) in * R/dsCMatrix.R 2008-03-17 18:53 Douglas Bates * R/CHMfactor.R, inst/include/Matrix.h, inst/include/Matrix_stubs.c, src/CHMfactor.c, src/CHMfactor.h, man/CHMfactor-class.Rd, src/init.c, tests/factorizing.R: Log-determinant of the parent matrix from a CHMfactor object as chm_factor_ldetL2; documentation and support 2008-03-15 Martin Maechler * R/dsCMatrix.R: enable determinant(, .) via chol(.) 2008-03-14 Martin Maechler * R/dsCMatrix.R: setAs(., "dsCMatrix") but with a deprecation warning. 2008-03-13 Martin Maechler * DESCRIPTION (Version, Date): bug-fix release 0.999375-6 * R/diagMatrix.R (diag2tT.u): utility to be smarter in o setAs(., "nMatrix") added. * R/diagMatrix.R (Diagonal): Diagonal(4, x=3) now works too * R/Auxiliaries.R (.diagU2N): more careful coercion in 2 steps new argument 'checkDense = FALSE'. 2008-03-07 Martin Maechler * src/dgeMatrix.c (dgeMatrix_exp): fix the octave-origin bug in the back-permutation of the matrix exponential. * tests/matr-exp.R: test the fix (for an example where expm() was wrong). * DESCRIPTION (Date,Version): ready to release 0.999375-5 * tests/simple.R: testing diagN2U 2008-03-06 Martin Maechler * R/Auxiliaries.R (diagN2U): interface to * src/Csparse.c (Csparse_diagN2U): .Call()able SEXP version of chm_diagN2U() * tests/matprod.R: test for triangularity preserving %*% 2008-03-05 Martin Maechler * src/chm_common.c (chm_diagN2U): new utility. * src/Csparse.c (Csparse_Csparse_crossprod, Csparse_Csparse_prod): make use of chm_diagN2U() and hence now preserve triangularity and unit-triangularity. * DESCRIPTION (LicenseDetails): new; such that 'License:' becomes "canonical" 2008-03-04 Martin Maechler * R/diagMatrix.R (subDiag): fix when x[..] became a vector * src/Tsparse.c (Tsparse_diagU2N): new utility, necessary for e.g. * src/Csparse.c (Csparse_crossprod): use [CT]sparse_diagU2N() !! * R/Auxiliaries.R (.diagU2N): make use of new Tsparse_diagU2N * R/Ops.R ("-" ()): use diagU2N() * src/chm_common.c (AS_CHM_FINISH): add note about problem for triangular (diag = "U"). 2008-02-21 Martin Maechler * R/Auxiliaries.R (as_Csparse2): drop this, replacing by * R/bind.R: .Call(dense_to_Csparse, *) 2008-02-20 Martin Maechler * R/Matrix.R (Matrix): no longer use coercions to specific classes (since we are discouraging them in user code). * tests/*.R: also replaces coercions to specific classes by coercions to super classes. * R/denseMatrix.R (.dense2C): simplified by using forceSymmetric() 2008-02-19 Martin Maechler * man/CAex.Rd: example: coerce to symmetric*, not dsC* * src/dense.c (dense_band): generalized from ddense_band * R/ddenseMatrix.R (.trilDense,.triuDense, .bandDense): now for "denseMatrix" (instead of just "ddense*"); much simplified setMethod()s for these. * src/dense.c (dense_to_symmetric): generalized from ddense_* 2008-02-18 Martin Maechler * R/AllGeneric.R: forceSymmetric() generic: fast no-checking version of as(*, "symmetricMatric"). * src/dense.c (ddense_to_symmetric): add 'symm_test' argument, and * R/symmetricMatrix.R: set it TRUE in coercion to "symmetricMatrix" 2008-02-16 Martin Maechler * R/Matrix.R (subset.ij): utility, as first step to faster M [ ] indexing. * R/Matrix.R (.M.sub.i.logical): M[ ] : try better. * src/dense.c (ddense_symmpart, ddense_skewpart): new functions for more efficient symmpart() and skewpart() methods. * src/Mutils.c (equal_string_vectors): utility * src/dense.c (ddense_to_symmetric): new function used in * R/symmetricMatrix.R: setAs(., "symmetricMatrix") * R/sparseMatrix.R, et_al (isSymmetric): add '...' to formals, in order to match the generic (and evade .local(..)). * R/dsCMatrix.R: dgC -> dsC: use C code! * NAMESPACE, R/AllGeneric.R (symmpart, skewpart): new functions as per TODO * R/Auxiliaries.R (setZero, all0Matrix): new utilities * R/symmetricMatrix.R: obvious symmpart(), skewpart() methods 2008-02-15 Martin Maechler * R/Ops.R (.Arith.Csparse): use diagU2N when needed in triangular * R/Auxiliaries.R (non0.i): take out of non0ind * R/ddenseMatrix.R (.trilDense, .triuDense, .bandDense): make tril(), triu(), band() work for "matrix" and all "dense*" * R/triangularMatrix.R (.tri[lu].tr): need .diagU2N(*) * tests/simple.R: test the fix above * R/sparseMatrix.R ([): simplification: no coerce to before we use as(., )[...] anyway * R/Rsparse.R (.viaC.to.R): mostly instead of .viaC.to.dgR() * R/triangularMatrix.R (isTriangular): methods for all subclasses instead of "triangularMatrix" -- just to disambiguate 2008-02-14 Martin Maechler * tests/Class+Meth.R (dotestMat): add m[FALSE, FALSE] { <-> TODO} * tests/indexing.R: example that fails above 2008-01-26 Martin Maechler * R/Matrix.R (.M.sub.i.2col): fix for logical matrix indexing * R/Tsparse.R (.TM.sub.i.2col, .TM.repl.i.2col): ditto; now, M[lower.tri(M)] and M[lower.tri(M)] <- v work better * src/Tsparse.c (Tsparse_to_tCsparse): new fast utility. * src/Tsparse.h, init.c: ditto * R/Auxiliaries.R (isTriT): new; faster than going via Csparse both isTriC() and isTriT() now return TRUE with "kind" or FALSE. * R/sparseMatrix.R (isTriangular): hence simplified 2008-01-24 Martin Maechler * R/Ops.R (.Arith.Csparse): new utility factored out of former o , extended for triangular and also used in o . 2008-01-23 Martin Maechler * tests/factorizing.R (checkSchur): and more tests for checking Schur() * inst/test-tools.R (isOrthogonal): new function; also file restructured 2008-01-22 Martin Maechler * R/ngTMatrix.R: allow as(, "ngTMatrix") and hence coercion to "nMatrix" and "pMatrix" * R/AllClass.R: "Schur" class; "number" class union * man/number-class.Rd: * man/Schur-class.Rd: * R/eigen.R (.dgeSchur): utility, and return "Schur" class (.simpleSchur): Schur() method for diagonal matrices (.triSchur): Schur() method for triangular matrices (Schur.sym): Schur() for symmetric matrices {building on eigen()}. 2008-01-21 Martin Maechler * src/dgCMatrix.c (dgCMatrix_QR): set @Dim slot (as per doc) 2008-01-15 Martin Maechler * R/CHMfactor.R (solve): method for b="numeric", but also b="ANY" in order to ensure 'system = *' is not lost; formals()$system instead of cut&paste. * tests/factorizing.R: test solve(, ) 2008-01-11 Martin Maechler * DESCRIPTION (Date): make ready for release --> 0.999375-4 * R/dgeMatrix.R: fix rcond() method for "dgeMatrix". 2007-12-08 Martin Maechler * R/pMatrix.R: as(*, "matrix") now returns 0/1 *integer* matrix, and hence does as.vector(.). * man/pMatrix-class.Rd: docs * R/sparseMatrix.R: fix for printing "integer sparse" * tests/Class+Meth.R (tstMatrixClass): test M[FALSE], M[2] etc * R/Matrix.R and others: use "exact" function argument list for both "[" : (x, i,j, ..., drop) and "[<-" : (x, i,j, ..., value) * R/denseMatrix.R: M[i] and M[i] <- v (i vector) now work * R/Tsparse.R (replTmat): ditto * R/diagMatrix.R (replDiag): ditto * R/Csparse.R (replCmat): ditto {was it worth the pain?} * tests/indexing.R: testing the above 2007-12-07 Martin Maechler * R/sparseMatrix.R (cov2cor): method for sparse matrices * R/diagMatrix.R ([<-): fix D[ cbind(i,j) ] <- v * R/bind2.R: fix for Rsparse* and rbind2(dense,dense) * tests/Class+Meth.R: test cbind2, rbind2 and diag<- 2007-12-06 Martin Maechler * R/Matrix.R: "generic" cov2cor() method * R/nearPD.R: new 'only.values', 'keepDiag' arguments; speed up Q %*% D %*% t(Q) * tests/dpoMatrix.R: test nearPD() 2007-12-05 Doug Bates and Martin Maechler * R/sparseMatrix.R: xtabs(*, sparse=.) function; an extention of stats::xtabs() allowing to create sparse matrices. 2007-10-08 Martin Maechler * DESCRIPTION (Version): *-4 (released *-3 two days ago) 2007-10-06 Martin Maechler * R/pMatrix.R: solve(, ) 2007-10-05 Martin Maechler * R/LU.R: solve() method for "denseLU" 2007-10-01 Martin Maechler * DESCRIPTION (Version): 0.999375-3 preparing for release * R/AllGeneric.R: simplify if(.) .. else .. for R <= 2.5.1 * R/Matrix.R (Matrix): .Internal(matrix(..)) different for R >= 2.7.0 2007-09-26 Martin Maechler * R/pMatrix.R (.m.mult.pMat): fix %*% , thanks to Kasper Kristensen. * tests/matprod.R: regression test for that. 2007-09-23 17:32 Douglas Bates * [r4778] R/AllGeneric.R: Check R version before defining generics for primitives 2007-09-13 Martin Maechler * R/denseMatrix.R (rcond): method * R/sparseQR.R (rcond): method, use x or t(x) 2007-09-12 Martin Maechler * R/dgeMatrix.R (rcond): method: work via qr.R() for non-square matrices. * R/sparseMatrix.R: Ditto for all other rcond() method definitions. * man/rcond.Rd: mention the more general definition, and add example for non-square matrices. * man/chol.Rd: new file, for the S4 chol() generic and all methods. 2007-09-11 Martin Maechler * R/sparseQR.R: add qr.R() method [to be used for rcond()] 2007-09-01 Martin Maechler * R/Matrix.R ([<-): add (Matrix,missing,ANY,Matrix) etc * tests/indexing.R: add new regression for the above cases. 2007-08-30 Martin Maechler * src/Mutils.h (__sun): clause for alloca.h on Solaris 2007-08-16 Martin Maechler * DESCRIPTION (Date, Version): 0.999375-2 2007-08-15 Martin Maechler * R/HBMM.R (readMM): make work for pattern matrices as well 2007-08-14 13:07 Douglas Bates * [r4730] src/Mutils.h: declare alloca * [r4734] NAMESPACE, R/AllGeneric.R, R/Csparse.R, R/HBMM.R, R/Tsparse.R, R/dgCMatrix.R, R/dgTMatrix.R, R/dsCMatrix.R, R/dsTMatrix.R, man/externalFormats.Rd, src/Csparse.c, src/Csparse.h, src/DEPS.mkf, src/HBMM.c, src/HBMM.h, src/Mutils.h, src/SOURCES_C.mkf, src/init.c, src/mmio.c, src/mmio.h: Remove deprecated function writeHB and its methods; switch writeMM to use CHOLMOD code; repair readMM 2007-08-14 Martin Maechler * R/nearPD.R, man/nearPD.Rd (nearPD): new function built on Jens Oehlschlaegel's ... result type still to be discussed! 2007-08-10 Martin Maechler * man/image-methods.Rd: new, combining all image() methods 2007-08-09 Martin Maechler * R/dgCMatrix.R: define qr() and lu() methods for "sparseMatrix" to work via dgC... * R/Matrix.R (Matrix): special treatment for "table" (S3) 2007-08-07 Martin Maechler * R/dgTMatrix.R (image): change defaults to aspect = "iso", colorkey = FALSE 2007-08-06 Martin Maechler * src/dsyMatrix.c (dsyMatrix_matrix_mm): 'b' might be matrix; must copy its *expanded* x slot before LAPACK call. * tests/matprod.R: test the last days' changes. 2007-08-06 16:43 Douglas Bates * [r4712] inst/include/Matrix_stubs.c: Change R_cholmod_printf in stubs as well as in sources * [r4713] src/dsyMatrix.c: Duplicate the contents of the RHS before Lapack call 2007-08-03 Martin Maechler * R/Matrix.R (%*%, crossprod, tcrossprod): add method for ("Matrix", "matrix") which is needed in some cases. Ditto for solve(). * R/colSums.R (.as.dge.Fun): need ddenseMatrix methods to avoid infinite recursion in dispatch for some cases. 2007-08-02 08:48 Martin Maechler * [r4693] src/chm_common.c: R_cholmod_printf() instead of Rprintf() just so pointers match 2007-08-02 Martin Maechler * DESCRIPTION (Date): set ready for release -- 0.999375-1 2007-08-01 15:44 Douglas Bates * [r4686] inst/include/Matrix.h, inst/include/Matrix_stubs.c, src/chm_common.c, src/chm_common.h: Change API for numeric_as_chm_dense and N_AS_CHM_DN 2007-08-01 Martin Maechler * src/dtrMatrix.c (dtrMatrix_matrix_mm): fix dimensionality check (!) * tests/matprod.R: regr.test for it 2007-07-20 Martin Maechler * R/dMatrix.R: fix from Brian for Math2(., digits = "missing") * tests/group-methods.R: and regression-test it 2007-07-19 19:45 Douglas Bates * [r4642] inst/include/Matrix.h, inst/include/Matrix_stubs.c, inst/include/cholmod.h, src/chm_common.c, src/init.c: Export triplet_to_sparse, documentation, use typedefs 2007-07-18 Martin Maechler * man/dpoMatrix-class.Rd: added 'corMatrix' example * src/dsyMatrix.[ch] (dsyMatrix_as_matrix): new 'keep_dimnames' arg * src/dtrMatrix.[ch] (dtrMatrix_as_matrix): ditto * src/init.c, R/dsyMatrix.R, R/dtrMatrix.R, R/lgTMatrix.R: ditto * R/lsparseMatrix.R: bug fix in "all" method * R/Ops.R (.do.Logic.lsparse): "|" bug in borderline case * R/dsyMatrix.R (coerce->dsTMatrix): (i,j) slots should *not* have names * R/ngTMatrix.R (coerce->ngTMatrix): ditto; + matrix |-> nMatrix coercion * R/pMatrix.R: + setAs() to dMatrix and from nMatrix * man/pMatrix-class.Rd: ditto * R/Matrix.R (Summary): method for non-dMatrix * tests/Class+Meth.R (extraValid): new check about "dirty" slots * tests/Class+Meth.R (tstMatrixClass): test norm(.); test all Summary methods. 2007-07-16 Martin Maechler * R/dgeMatrix.R (norm, rcond): methods for 'matrix' 2007-07-14 Martin Maechler * R/sparseMatrix.R (norm): simple methods for sparseMatrix * R/pMatrix.R (t?crossprod): methods for pMatrix 2007-07-10 Douglas Bates * src/dgeMatrix.c (dgeMatrix_colsums): Get the logic straight. 2007-07-09 20:45 Douglas Bates * [r4579] src/dgeMatrix.c: Untangle horrible code in dgeMatrix_colsums trying to fix a subtle bug - which has been somewhere else. 2007-07-09 19:43 Martin Maechler * [r4578] src/dgeMatrix.c: "cleaned" dgeMatrix_colsums() - but did not solve the bug 2007-07-08 Martin Maechler * src/dgCMatrix.c (compressed_to_TMatrix): 2007-07-07 Martin Maechler * src/Csparse.c (Rsparse_validate): new, to have some validity checking for RsparseMatrix * src/dgCMatrix.c (xRMatrix_validate): ditto * src/dtCMatrix.c (tRMatrix_validate): ditto 2007-07-07 Douglas Bates * [r4567] R/AllClass.R: Slots already in RsparseMatrix were redefined in lgRMatrix * [r4568] DESCRIPTION: Prepare for bug-fix release * [r4570] src/CHOLMOD/Check/cholmod_write.c: Include cholmod_matrixops.h for declaration of cholmod_symmetry 2007-07-06 Martin Maechler * DESCRIPTION (Version): 0.999375 merged into the trunk; ready for release. 2007-07-06 14:11 Douglas Bates * [r4559] src/iohb.c, src/iohb.h: Remove Harwell-Boeing input/output functions - no longer used * [r4560] src/HBMM.c, src/Mutils.c, src/dgTMatrix.c, src/dgeMatrix.c, src/dspMatrix.c, src/dsyMatrix.c, src/dtCMatrix.c, src/factorizations.c, src/sparseQR.c: Replace most calls to Calloc by Alloca 2007-07-06 13:14 Martin Maechler * [r4558] inst/doc/Comparisons.Rnw, src/CHMfactor.c, src/Csparse.c, src/Tsparse.c, src/chm_common.c, src/chm_common.h, src/dense.c, src/dgCMatrix.c, src/dsCMatrix.c, src/dtTMatrix.c, src/sparseQR.c, src/t_gCMatrix_colSums.c: more R_CheckStack()s 2007-07-05 18:12 Douglas Bates * [r4550] inst/include/Matrix.h: Add the macro N_AS_CHM_DN to "alloca" the required amount of memory then call M_numeric_as_chm_dense. * [r4556] src/Mutils.h, src/dgCMatrix.c: Define and use the Alloca macro (like Calloc but calling alloca) 2007-07-05 Martin Maechler * R/sparseMatrix.R (printSpMatrix): renamed from prSpMatrix() and extended with more sophisticated 'col.names' option. * NAMESPACE: export printSparseMatrix() * man/printSpMatrix.Rd: document, incl. examples 2007-07-04 16:21 Douglas Bates * [r4543] src/cs_utils.c, src/cs_utils.h, src/dgCMatrix.c, src/dtCMatrix.c, src/sparseQR.c: CSP typedef for *cs and macro AS_CSP. API change - pass the empty structure to Matrix_as_cs. 2007-07-04 Martin Maechler * DESCRIPTION (Version): 0.99875-4 * tests/Class+Meth.R (tstMatrixClass): add dimnames, and hence test some dimnames perservation. * R/dsTMatrix.R (t-method): keep dimnames * R/dtTMatrix.R: ditto * R/sparseMatrix.R (prSpMatrix): print colnames when non-trivial and ncol(.) < 10 * src/cs_utils.c: drop check_class() and use Matrix_check_class() from Mutils.h * src/lgCMatrix.c ([ln]csc_to_matrix): no longer lose dimnames, e.g. in as(, "matrix") 2007-07-01 13:27 Douglas Bates * [r4529] .: Create a branch for the API changes from the 0.99875 series to the 0.999375 series * [r4530] DESCRIPTION, inst/include/Matrix.h, inst/include/Matrix_stubs.c, src/CHMfactor.c, src/Csparse.c, src/Mutils.h, src/Tsparse.c, src/chm_common.c, src/chm_common.h, src/dense.c, src/dgCMatrix.c, src/dsCMatrix.c, src/dtTMatrix.c, src/t_gCMatrix_colSums.c: API change - pass the empty structure to the as_cholmod_x functions 2007-06-30 09:05 Martin Maechler * [r4527] trunk/Matrix/DESCRIPTION, trunk/Matrix/NAMESPACE, trunk/Matrix/inst/doc/Comparisons.Rnw: add session- and hardware-info to Comparisons >>>>>>> .merge-right.r4561 2007-06-29 Martin Maechler * DESCRIPTION (Version): 0.99875-3 ready to be released. * R/sparseMatrix.R (spMatrix): make spMatrix(3,4) working * R/AllGeneric.R: set "Math" (and "Math2") group generics in a way that should also work in a future version of R. 2007-06-21 Martin Maechler * NAMESPACE, R/AllClass.R: "xsparseVector" class union. * R/sparseVector.R: more *sparseVector coercions, notably for non - double ones. 2007-06-19 Martin Maechler * R/colSums.R: new file for all (col|row)(Sums|Means) methods, notably the new ones building on the new .Call(.)s: * src/dgCMatrix.c (DEF_gCMatrix_COLSUMS): use to define all 4 of [dlin]gCMatrix_colSums(). 2007-06-18 16:12 Douglas Bates * [r4472] src/Syms.h, src/init.c: Added Matrix_lengthSym * [r4473] src/dgCMatrix.c: Modified dgCMatrix_colSums for sparseVector result 2007-06-16 Martin Maechler * R/kronecker.R: fix typo (could lead to inf.recursion) * test/simple.R: testing that * R/sparseMatrix.R (prSpMatrix): change to be used as print() method as well (which can have arguments, show() can't). 2007-06-16 15:52 Douglas Bates * [r4466] R/dgCMatrix.R, src/dgCMatrix.c, src/dgCMatrix.h, src/init.c: added dgCMatrix_colSums for [col,row][Sums,Means] 2007-06-15 23:15 Douglas Bates * [r4460] R/sparseMatrix.R, man/dgCMatrix-class.Rd, src/dgCMatrix.c, src/dgCMatrix.h, src/init.c: added lm.fit.sparse (unexported), coercion of "factor" to "dgCMatrix" and dgCMatrix_cholsol * [r4461] R/AllClass.R, man/sparseMatrix-class.Rd: draft "indicators" class * [r4463] R/sparseMatrix.R, man/dgCMatrix-class.Rd, man/sparseMatrix-class.Rd: Don't need an "indicators" class - use the row names to store the levels - duh! Added an example. 2007-06-14 Martin Maechler * src/Csparse.c (Csparse_validate): check for *repeated* entries thanks to example from Christian Buchta; with a test here: * tests/simple.R: 2007-06-07 Martin Maechler * R/Auxiliaries.R (callGeneric): another fix, needed for some cases of colSums(*, sparseResult = TRUE) 2007-06-06 Martin Maechler * R/lsparseMatrix.R, R/ldenseMatrix.R (all, any): change default to 'na.rm = FALSE' as "everywhere" else in R. 2007-06-05 Douglas Bates * [r4421] src/CSparse_install.sh: Modify for new organization of CSparse package * [r4425] src/UFsparse_download.sh: Update to version 3.0.0 of SuiteSparse * [r4426] src/Makefile: add ./UFconfig to the include path for compilation * [r4427] src/cs.[ch]: update to CSparse version 2.2.0 * [r4428] inst/doc/UFsparse/* src/{AMD,CHOLMOD,COLAMD}/* src/UFconfig/UFconfig.h: Update to version 3.0.0 of SuiteSparse 2007-06-05 Martin Maechler * R/Auxiliaries.R (emptyColnames): + argument msg.if.not.empty, used in * R/sparseMatrix.R (prSpMatrix): now gives a message about suppressed column names. 2007-06-04 17:13 Douglas Bates * [r4418] src/Csparse.c, src/HBMM.c, src/Mutils.c, src/Mutils.h, src/Tsparse.c, src/chm_common.c, src/chm_common.h, src/dgCMatrix.c, src/dgeMatrix.c, src/dpoMatrix.c, src/dpoMatrix.h, src/dppMatrix.c, src/dppMatrix.h, src/dsCMatrix.c, src/dspMatrix.c, src/dspMatrix.h, src/dsyMatrix.c, src/dsyMatrix.h, src/dtpMatrix.c, src/dtrMatrix.c: Remove warnings after change to const char* CHAR 2007-06-04 17:11 Douglas Bates * [r4417] inst/include/Matrix_stubs.c, inst/include/cholmod.h: Corrected type of M_cholmod_ssmult 2007-06-03 14:42 Douglas Bates * [r4412] inst/include/Matrix_stubs.c, inst/include/cholmod.h, src/init.c: Yet another cholmod export - cholmod_ssmult 2007-05-23 Martin Maechler * NAMESPACE: exported drop0(), since * man/drop0.Rd: I have seen several cases, I really wanted to use it, so our users may want too. 2007-05-22 Martin Maechler * man/colSums.Rd: separately document colSums() etc, since these have the extra argument 'sparseResult'. 2007-05-21 Martin Maechler * R/sparseMatrix.R (spMatrix): utility (T)sparse Matrix constructor; * man/spMatrix.Rd: docu., including examples * R/Auxiliaries.R (sp.colMeans): etc, using a patched callGeneric(), in order to make colMeans() etc fast *and* correct. * R/sparseVector.R (replSPvec): "[<-" functionality for sparseVectors; tested in * tests/simple.R: 2007-05-19 Martin Maechler * R/sparseMatrix.R (print.sparseSummary): and summary() method for (very) sparse Matrices; output similar to Matlab's print(). 2007-05-17 Douglas Bates * src/HBMM.c (Matrix_writeMatrixMarket): Write 1-based, not 0-based, indices (Jose Quesada ). 2007-05-16 Douglas Bates * R/CHMfactor.R: Added solve methods for a CHMfactor object. 2007-05-16 Martin Maechler * R/Auxiliaries.R (sparsapply): new utility, much faster than tapply1() for large sparse matrices. 2007-05-15 Martin Maechler * R/Matrix.R (dim<-): reshape now via sparseVector. * R/sparseVector.R: methods and function for * R/AllClass.R: new "sparseVector" class and daughters. * NAMESPACE: export new classes 2007-05-14 Martin Maechler * DESCRIPTION (Version): 0.99875-1 * src/Makefile.win: also remove Lapack code from here (cf. 04-25). 2007-05-11 Martin Maechler * R/Tsparse.R ([, Tsparse): fix last case: *duplicated*, symmetric indexing * tests/indexing.R: test set for that. 2007-05-08 Martin Maechler * R/Tsparse.R (replTmat): fix the case of *duplicated* index entries. * tests/indexing.R(out): add regression test for it 2007-04-30 Martin Maechler * R/(l(dense|sparse))?Matrix.R (!): use 'x', not 'e1' as argument name for "!" method definitions. 2007-04-26 Martin Maechler * R/Tsparse.R (intI): new utility, used for "[" : Cleanup up there, and fixes for duplicated indices - more TODO! * tests/indexing.R(out): more tests 2007-04-25 Douglas Bates * DESCRIPTION,src/Makefile: require R>= 2.5.0 and remove Lapack code that is now part of the R Lapack library. * src/init.c,inst/include/{Matrix_stubs.c,cholmod.h}:export cholmod_factorize_p (used in lme4 for GLMMs and NLMMs). 2007-04-21 Martin Maechler * R/Matrix.R (image): method for all Matrices, not just sparse ones. 2007-04-17 Martin Maechler * R/Auxiliaries.R (tapply1): unname(.) -> colSums() etc don't end up with extraneous names '0'...'' 2007-04-12 Martin Maechler * R/dgTMatrix.R (mat2dgT): care about NAs 2007-04-11 Martin Maechler * R/kronecker.R: triangularity preserving methods 2007-03-27 Martin Maechler * R/kronecker.R: new file collecting kronecker() methods in one place. Goal: become much faster! 2007-03-23 Martin Maechler * src/dtCMatrix.c (dtCMatrix_solve): use the new code from Kasper Kristensen based cs_spsolve() instead of _lsolve & _usolve which can be much faster. * tests/matprod.R: add regression tests for these (upper & lower). 2007-03-19 Martin Maechler * R/Matrix.R (diff): method for our Matrices. * R/sparseMatrix.R (isDiagonal): check dim()! 2007-03-17 Martin Maechler * R/Matrix.R (dim<-): new method for "reshape()" built on a proposal from Tamas Papp. 2007-03-16 Martin Maechler * R/AllGeneric.R: remove all if(!isGeneric(.)) clauses * R/zzz.R (.onLoad, .onUnload): do *not* leave bind_activation(TRUE); rather define and export cBind() and rBind() only. --> useRs *must* change code that used to have cbind()/rbind() !! * R/bind.R: change tests from cbind() to cBind() and similarly to rBind() * R/bind.Rout.save: ditto 2007-02-16 Douglas Bates * DESCRIPTION (Date, Version): 0.9975-11 with new date * src/dgCMatrix.c (R_to_CMatrix, compressed_to_TMatrix): remove const modifier on declaration of the array 'valid' 2007-02-12 Douglas Bates * R/CHMfactor.R: Add image method (coercion to sparseMatrix). 2007-02-05 Martin Maechler * DESCRIPTION (Date, Version): 0.9975-10 with new date. * R/Ops.R (Arith): make sure Csparse o Csparse also works for e.g. ntCMatrix * tests/simple.R: test the above and some of these coercions: * R/nsparseMatrix.R: coercing "Csparse" to "lsparseMatrix"; be careful to avoid infinite recursion, using new coercions in * R/ngCMatrix.R and nsC... and ntC... * R/lsparseMatrix.R: ditto * R/SparseM-conv.R: more conversion, notably for triplet matrices. * src/dgCMatrix.c (R_to_C_Matrix): port Doug's fix and * R/Rsparse.R: reactivate .Call()s * tests/Class+Meth.R: a bit more on actual classes 2007-02-04 Douglas Bates * src/dgCMatrix.c (compressed_to_TMatrix): fix memory bug using strdup() 2007-02-03 Martin Maechler * DESCRIPTION (Version): 0.9975-10 to upload * tests/Class+Meth.R (tstMatrixClass): require coercions to specific classes less unconditionally. * R/Auxiliaries.R: get rid of as_Tsparse() and as_Rsparse() * R/Tsparse.R (triu): etc, use as(*, "TsparseMatrix") instead of as_Tsparse() * R/Rsparse.R (.R.2.T): R-level workaround using compressed_to_TMatrix. * R/Rsparse.R (.R.2.C): R-level workaround since C-level R_to_CMatrix segfaults on one platform. Eliminate most coercion method to *specific* classes, and replace with virtual classes coercions. 2007-02-01 Martin Maechler * src/init.c: export the CHM...._validate() placeholders, since they *are* called. * tests/Class+Meth.R (classCanCoerce): and starting to test all as(, ) 2007-01-30 Martin Maechler * R/Tsparse.R ([): more care when subsetting triangular Tsparse * tests/indexing.R: tested now * tests/indexing.Rout.save: updated * src/Csparse.c (Csparse_to_dense): use Rkind = -1 for PATTERN to * src/chm_common.c (chm_dense_to_SEXP): return "ngeMatrix" when appropriate. * NAMESPACE: export a trivial * R/Matrix.R: drop() Matrix-method * R/AllClass.R: moved all prototypes to virtual super classes. * R/Rsparse.R: many more coercions to have less exceptions in * tests/Class+Meth.R: * R/Ops.R (Compare): tweak for case with NA * tests/simpl.R: hence another 'FIXME' eliminated 2007-01-29 Martin Maechler * R/diagMatrix.R (solve): the obvious methods for diagonalMatrix objects. * tests/Class+Meth.R (tstMatrixClass): now testing diag(), nnzero(), and more of "!", "&", "|", all, any; coercions * R/Rsparse.R: many coercions (which enable quite a few other methods), thanks to enhancements in * src/dgCMatrix.c (R_to_CMatrix): new, and * src/dgCMatrix.c (compressed_to_TMatrix): now for (d,l,n) , symmetric & triangular and ..RMatrix objects. * src/TMatrix_as.c (Matrix_T_as_DENSE,Matrix_T_as_GENERAL): renamed file from src/dsTMatrix.c; now dealing with symmetric and triangular Tsparse coercions, both to dense and general. 2007-01-27 Martin Maechler * src/dsTMatrix.c: has now "l" and "n" methods besides the "d" ones. * R/Ops.R (Arith): o now remains sparse where sensible when the is of length > 1. 2007-01-26 Martin Maechler * R/Matrix.R ([<-): for M[] <- value: fix length 2007-01-25 Martin Maechler * R/Auxiliaries.R (n2l_Matrix): new, to be used in * R/ndenseMatrix.R: new coercions n* -> l* 2007-01-22 Martin Maechler * R/triangularMatrix.R: new file; simple triu() and tril() methods. * R/Ops.R ("Logic"): and other "Ops", many updates 2007-01-18 Martin Maechler * src/Mutils.h (SET_DimNames): new utility * R/Auxiliaries.R (nnzero): improved and now exported via * NAMESPACE: + nnzero(); length() == prod(dim(.)) method for all "Matrix" objects 2007-01-17 Martin Maechler * R/diagMatrix.R (!): fix typo. 2007-01-16 Martin Maechler * R/Auxiliaries.R (as_Csparse): and quite a few others: allow to pass class definition --> speedup * R/sparseMatrix.R: apply the above * R/Csparse.R: coercion Csparse* to dense* now preserves shape properties. * src/Mutils.h (mMatrix_as_geMatrix): new, based on * src/Mutils.c (dup_mMatrix_as_geMatrix): new; generalization of old dup_mMatrix_as_dgeMatrix), eliminating a long-standing "FIXME". * src/dense.c (dense_to_Csparse): use new mMatrix_as_geMatrix() * R/denseMatrix.R (.dense2C): based on dense_to_Csparse: name it, and use it for "sparse*" as well, since it's faster than the as_Csparse(.) way. 2007-01-15 Martin Maechler * R/Ops.R ("Logic"): more methods, notably an o one. 2007-01-12 Martin Maechler * R/Tsparse.R (.TM.repl.i.2col): new internal function to be used as method for M[ ij ] <- v * R/Csparse.R:: go via Tsparse for "M[ij] <- v" * R/Ops.R: "Compare" for (C|R)sparse: need pointer slot for all FALSE answer * R/Csparse.R (replCmat): fix the "all non-zero" case with reordering * tests/indexing.R: test it, and some of the above 2007-01-05 Martin Maechler * R/Auxiliaries.R (is_duplicatedT): new utility 2007-01-05 Douglas Bates * src/init.c (R_init_Matrix): export cholmod_scale 2006-12-30 Martin Maechler * R/zzz.R (tmp): for R >= 2.5.0, extend formals of our base::as.matrix to (x, ...) 2006-12-28 Martin Maechler * R/Ops.R ("Arith" etc): move almost all "Ops" methods to new R file; start using "Logic", hence * DESCRIPTION (Depends): R >= 2.4.1 (since we want "Logic") * NAMESPACE: import and export "Logic" 2006-12-27 Martin Maechler * src/zpotfr.f and dependencies: use LAPACK 3.1 version only needed previously to R version 2.5.0. 2006-12-26 Martin Maechler * DESCRIPTION (Date, Version): 0.9975-8, ready for release * R/Tsparse.R (replTmat): fix subassignment of triangular * R/Csparse.R (replCmat): ditto * tests/indexing.R: more tests, incl the above fix 2006-12-23 Martin Maechler * R/Auxiliaries.R (drop0): extend for non CSparse * R/Auxiliaries.R (diagU2N): should work for all sparseMatrix * src/Csparse.c (Csparse_to_Tsparse, Csparse_general_to_symmetric): use uplo correctly (!); other places: use uplo_P() macro * R/Csparse.R (replCmat): call diagU2N() when needed * R/Tsparse.R (replTmat): ditto * src/dtCMatrix.c (tCMatrix_validate): new * src/dtTMatrix.c (tTMatrix_validate): new, used in * R/AllClass.R: for validity of dtC, dsC, and dtT, dsT. * R/diagMatrix.R (replDiag): to use in [<- 2006-12-22 Martin Maechler * R/Auxiliaries.R (as_Csparse2, as_geSimpl): new functions; also more general diagU2N(). 2006-12-21 Martin Maechler * R/bind2.R: new file for all cbind2(), rbind() methods moved here from R/Matrix.R files. Better diagonal & improved sparse methods. 2006-12-20 Martin Maechler * tests/bind.R: a few more cases * R/Auxiliaries.R (.M.kind): also work for atomic vectors * R/denseMatrix.R (cbind2/rbind2): moved here (and generalized) from * R/ddenseMatrix.R (cbind2/rbind2) * R/Tsparse.R (replTmat): final(?!) fix for "[<-" .. * tests/indexing.R * tests/indexing.Rout.save: updated 2006-12-18 Martin Maechler * R/Tsparse.R (replTmat): fixed a remaining "[<-" bug in * tests/indexing.R 2006-12-15 Martin Maechler * R/sparseMatrix.R (prSpMatrix): "." alignment much improved: align with proper position of "0", i.e., right for integers. argument 'align' by default is "fancy". 2006-12-14 Martin Maechler * R/sparseMatrix.R: delegate "Compare" to "Csparse.." * R/Csparse.R: and fix "Compare" for more cases. * tests/Class+Meth.R: test some of these (m == m, m != m) 2006-12-13 Martin Maechler * R/lsparseMatrix.R: all() and any() methods * R/ldenseMatrix.R: ditto * NAMESPACE, R/Matrix.R: ditto * man/all-methods.Rd: document them minimally * tests/simple.R: add a few examples for these 2006-12-11 Martin Maechler * R/Tsparse.R ([): fix long standing typo in symmetric case * man/dsCMatrix-class.Rd: add example exhibiting the above case 2006-12-10 Douglas Bates * src/CHMfactor.c (CHMfactor_to_sparse): change LDL factorization to LL before converting to a sparse matrix. (The LDL form can be converted to a sparse matrix but it is implicitly a unit triangular matrix and a diagonal matrix overwritten on the diagonal.) 2006-12-09 Douglas Bates * src/chm_common.c (chm_factor_to_SEXP): allocate and fill the Dim slot. 2006-12-08 Douglas Bates * DESCRIPTION (Version): updated -> release 0.9975-7 * src/{init.c,chm_common.c}, inst/include/*: export cholmod_analyze_p 2006-11-30 Martin Maechler * R/diagMatrix.R (%*%): write a direct [diag o Csparse] method 2006-11-29 Douglas Bates * src/dgeMatrix.c (dgeMatrix_solve): Check error code from dgetri. * tests/dg_Matrix.R: Add Barry Rowlingson's test of a matrix that is exactly singular. 2006-11-07 Martin Maechler * DESCRIPTION (Date): updated -> release 0.9975-6 2006-11-06 Martin Maechler * R/Csparse.R (replCmat): symmetric indexing of symmetric matrix now returns symmetric. * R/zzz.R ("diag<-"): replace "diag<-" in base for R <= 2.4.x * R/Matrix.R (.M.sub.i.2col): new, for M[ cbind(i,j) ] indexing. * R/Matrix.R (.M.repl.i.2col): new, for M[ cbind(i,j) ] <- value * R/Auxiliaries.R (.type.kind): added 2006-11-04 Martin Maechler * src/cs.[ch]: updated to CSparse Version 2.0.3 by simply running src/CSparse_install.sh * R/denseMatrix.R: "[": keep symmetric on symmetric indexing. 2006-11-03 Martin Maechler * src/dsCMatrix.c (dsCMatrix_Csparse_solve): new * R/dsCMatrix.R (solve): "fully-sparse" using the above. * R/AllClass.R: "pMatrix" now also inherits from "generalMatrix" * tests/Class+Meth.R (tstMatrixClass): now assure the (important in method programming) property : ###>> Every "Matrix" is either ###>> "general*", "symmetric*", "triangular*" or "diagonal*" (where "*" stands for "Matrix") * R/Auxiliaries.R (diagU2N): now .Call()s Csparse_diagU2N for * R/dMatrix.R (Compare(,): update and * tests/validObj.R: checks for "comparison" * R/sparseMatrix.R ([): improved indexing for sparse; trying to keep [ n, n] symmmetric * tests/indexing.R: indexing for logical sparse now ok 2006-11-02 Martin Maechler * src/Tsparse.c: use xTsparse_validate() , and hence remove * src/{ltC,lsC,lgT}Matrix.[ch]: removed 2006-11-02 Martin Maechler * R/AllClass.R (Matrix-class): check length of dimnames in validity. * tests/simple.R: validObject() checking the above. * src/dgCMatrix.c (xCMatrix_validate): new, small and simple, replacing both dgCMatrix_validate and lgCM*. * src/Csparse.c (Csparse_dense_prod, etc): do not lose dimnames; fix dimnames setting in other places. * src/chm_common.c (chm_dense_to_SEXP): now can pass dimnames 2006-11-01 Martin Maechler * R/Csparse.R,src/Csparse.c, etc: tcrossprod(,) * R/sparseMatrix.R (isSymmetric): drop 'factors' slot for symmetry test, via * R/Auxiliaries.R (.as.dgC.0.factors): 2006-11-01 Douglas Bates * R/Csparse.R,src/Csparse.c,tests/matprod.R, man/CsparseMatrix-class.Rd: crossprod(, ) added 2006-10-30 Martin Maechler * tests/matprod.R: add a variation of Harri's example * R/dsparseMatrix.R: fix crossprod(, ) to *not* recursive infinitely. * R/dgCMatrix.R: + solve(, ) * tests/indexing.R: add test for the "<" bug fixed 10-27 in R/dMatrix.R 2006-10-28 Martin Maechler * tests/Class+Meth.R (tstMatrixClass): more: use non-trivial matrix if possible; test m+m == 2*m; now test dgRMatrix. * R/dgRMatrix.R (.to.dgR): a few more coercions, in order to satisfy the above test. 2006-10-27 Martin Maechler * R/Matrix.R (Ops): o method added * R/dgCMatrix.R: solve(a, b="missing") based on * src/dgCMatrix.c (dgCMatrix_matrix_solve): extend to work with RHS = NULL. * R/diagMatrix.R (diagdiagprod): extend %*% etc to ldiMatrix; add more (needed) [t]crossprod() methods. * man/ddiMatrix-class.Rd: more info, notably on 'diag' * R/Auxiliaries.R (as_CspClass): cleanup (drop0): internal utility for "Csparse_drop(*, 0)" (.bail.out.2): encourage active feedback 2006-10-26 Martin Maechler * R/dMatrix.R(Compare): new(), then slots [no validity check] * src/Csparse.c (Csparse_validate): fixed (and more efficient in non-valid or 'sorted' case). * R/dsparseMatrix.R: add "chol" method. * R/ddenseMatrix.R: ditto * R/diagMatrix.R (Ops): group methods for o * NAMESPACE (Ops) * R/diagMatrix.R (diag2T): simple utility used "higher level" coercion; deprecating direct lower level coercions. * R/*.R (seq): use seq_len() and seq_along() where possible. 2006-10-23 Martin Maechler * DESCRIPTION (Version): 0.9975-5 ready for release 2006-10-20 Douglas Bates * src/init.c (R_init_Matrix): export more cholmod CCallable functions. 2006-10-20 Martin Maechler * R/AllClass.R (corMatrix): add 'validity' check; comment out unused "LDL" class definition * NAMESPACE: mention, but do not export "LDL" class * R/corMatrix.R: new (simple), needed for R-devel with * tests/Class+Meth.R (tstMatrixClass): 1 exception for corMatrix coerce and t() exceptions for all 5 'Mat.MatFact' classes. 2006-10-19 Douglas Bates * src/chm_common.h: Add R_cholmod_start to initialize cholmod to use Rprintf and R's error handling. 2006-10-17 Martin Maechler * R/diagMatrix.R (%*%): rep(*, each = .) in Matrix %*% diagonal. * tests/matprod.R: add tests for the bug fixed. 2006-10-11 Douglas Bates * src/HBMM.[ch]: remove HarwellBoeing format for writing. * src/SOURCES_C.mkf (SOURCES_C): no longer compile iohb.c 2006-10-06 Douglas Bates * R/d[gs]CMatrix.R: deprecate the writeHB function. Use writeMM instead. 2006-10-06 Martin Maechler * DESCRIPTION (Version): 0.9975-3 * R/diagMatrix.R (bdiag): new function constructing block diagonal (sparse) matrices. * man/bdiag.Rd: docu + examples * R/Csparse.R (replCmat): calling new Csparse_drop() now. * src/Csparse.c (Csparse_general_to_symmetric, Csparse_drop): new functions * R/lsCMatrix.R: three more coercions to lsC (thanks to the above) * R/diagMatrix.R (Diagonal): '[<-' method for diag.matrices such that result is sparse or diagonal (and not dense). * man/Subassign-methods.Rd: fix examples * R/Matrix.R (Matrix): Matrix(0, *) or Matrix(*, sparse=TRUE) should always return a sparse (and not sometimes a diagonal) matrix. 2006-10-05 Martin Maechler * R/Matrix.R ([<-): also for value "Matrix" or "matrix" 2006-10-04 Douglas Bates * DESCRIPTION (Version): 0.9975-2 * inst/include/Matrix_stubs.c (M_cholmod_sparse_to_triplet): export more symbols 2006-10-02 Douglas Bates * tests/dg_Matrix.R: Simplify test taking into account new code. 2006-09-29 Martin Maechler * R/Csparse.R (replCmat): improve for missing i / j in non-simple cases * R/lsTMatrix.R: new files w/ missing methods * R/nsTMatrix.R: " 'for completeness' * tests/Class+Meth.R: a bit less 'not.ok.classes' * R/Tsparse.R (t): generalized "t" method from "dgT*" to "Tsparse*" 2006-09-28 Douglas Bates * src/dppMatrix.h: Ensure definition of dspMatrix_validate is included. * src/init.c, inst/include/{Matrix.h,Matrix_stubs.h,cholmod.h}: Export C-callable functions used in Zt_create in lme4. 2006-09-28 Martin Maechler * DESCRIPTION (Version): 0.9975-1 * tests/simple.R: less checks fail; using NA, found that our kronecker() is not base-compatible with NA's. * R/dMatrix.R: "Compare" method now implemented for all cases * R/Auxiliaries.R (indTri): == which([lower/upper].tri( * )) new utility * man/dtpMatrix-class.Rd: mention length of 'x' slot * src/dtpMatrix.c (dtpMatrix_validate): fix check * src/dspMatrix.c (dspMatrix_validate): ditto * R/dtTMatrix.R (gt2tT): fix ("l" -> "n") including coercion to [nl]tTMatrix. * R/diagMatrix.R (show): print a header line as for other classes. 2006-09-27 Martin Maechler * src/Makefile.win (SUBDIRS): fix typo 2006-09-19 Martin Maechler * DESCRIPTION (Date): ready to release 0.9975-0 to CRAN 2006-09-18 Douglas Bates * R/[CT]sparse.R (crossprod and tcrossprod): Handle the cases for x symmetric and y missing in R code using %*% (cholmod_aat doesn't accept a symmetric matrix). * tests/group-methods.R: Uncomment test of crossprod applied to lsCMatrix objects. 2006-09-18 Martin Maechler * R/AllClass.R (symmetricMatrix): add validity method (available in C for a long time). Many "n..Matrix": drop (wrong) validity arg. * src/lgCMatrix.c (lgCMatrix_validate): check 'x' slot (!) * tests/indexing.Rout.save: * tests/indexing.R: additions, mainly for 'lsparse' * R/diagMatrix.R (Diagonal) & coercion to lgTMatrix: fixes for NA case. * R/Auxiliaries.R (nz.NA): new utility now used in nnzero() 2006-09-16 Martin Maechler * R/sparseMatrix.R (prSpMatrix): print logical NAs "visibly" as 'N' (1-letter - Ok?) * tests/group-methods.R: add test for logical + NAs * R/dMatrix.R ("Compare"): fix to work with NA's * R/AllClass.R: "Cholesky" etc now inherit from MatrixFactorization. * src/lgCMatrix.c (ncsc_to_matrix): renamed from lcsc_to_matrix() which is implemented. 2006-09-15 Martin Maechler * src/chm_common.c: coerce logical <-> double instead of typecasting; needed for "l" matrix handling in cholmod. * tests/other-pkgs.R (graph): small extension in "graph" checks. * R/sparseMatrix.R (graphNEL -> Tsparse): method for weight case. (Tsp2grNEL): other fixes needed 2006-09-11 Martin Maechler * R/AllClass.R ("nMatrix"): and subclasses for "nonzero pattern" Matrices, since "lMatrix", also "lsparseM" can have NA * R/ndenseMatrix.R, etc: new source files * man/nsparseMatrix-classes.Rd, etc: new help files * tests/: adaptions * src/chm_common.c (chm_dense_to_SEXP): and others: new 'Rkind' argument: "l*" and "d*" both use CHOLMOD_REAL * src/Csparse.c, etc: ditto 2006-09-11 Douglas Bates * src/Mutils.[ch],init.c inst/include/*.h: Move the alloc_d**Matrix functions to the lme4 package. 2006-09-09 Douglas Bates * src/dsCMatrix.c (dsCMatrix_Cholesky): igoring LDL = FALSE now fixed 2006-09-09 Martin Maechler * R/lMatrix.R: new * R/sparseMatrix.R (Tsp2grNEL): do not yet use graph::foo() * R/dgeMatrix.R: do not define tcrossprod() methods for "matrix" * man/tcrossprod.Rd: ditto 2006-09-08 Douglas Bates * inst/include/Matrix_stubs.c,Matrix.h: Add declarations and stubs for exported functions * src/Makefile, src/CHOLMOD/Lib/Makefile, src/Metis,CAMD,CCOLAMD: Remove partitioning algorithms for sparse matrix reordering. The copyright on the Metis code was problematic and the methods were rarely used. * src/triplet_to_col.[ch],MMHB.[ch]: Remove triplet_to_col. Such operations are now done entirely in CHOLMOD code. 2006-09-06 Douglas Bates * src/Mutils.h: Remove functions that are no longer used. 2006-09-04 Douglas Bates * src/dtCMatrix.c (dtCMatrix_validate): rename functions. * src/DEPS.mkf: update 2006-09-02 Martin Maechler * created branches/Matrix-for-R-2.3.x; on trunk: do * DESCRIPTION (Version): 0.9975-0 (Depends): R (>= 2.4.0) 2006-09-01 Douglas Bates * R/sparseMatrix.R: Added direct method to CsparseMatrix from graphNEL 2006-09-01 Martin Maechler * R/sparseMatrix.R: add coercion from "ANY" to "sparseMatrix" * R/denseMatrix.R: add coercion from "ANY" to "denseMatrix" * R/Matrix.R ([): use nargs() to disambiguate M[i] and M[i,] 2006-08-31 Martin Maechler * R/sparseMatrix.R (Arith): moved Arith group method one-level up from "dsparse" to "sparse" and now go via "Csparse" instead of "dgC" * R/dsparseMatrix.R: ditto * R/Csparse.R: ditto 2006-08-31 Martin Maechler * R/dMatrix.R (Compare): improve availability of "<", etc * R/Auxiliaries.R (asTuniq): new; also make use of R 2.4.x print(*,max) 2006-08-30 Martin Maechler * R/dgCMatrix.R: aargh: "Arith(, numeric)" was wrong because of a 0-index which was used as 1-index (..hmm) * R/sparseMatrix.R (prSpMatrix): fix printing an all-0 sparse Matrix * R/Auxiliaries.R (all0, is0): for 0-testing in presence of NA's * R/Auxiliaries.R (isTriMat): use all0() for 0-testing. (.is.diagonal): ditto * R/lgTMatrix.R: as("matrix", "lgTMatrix"): warn about NA's * R/Matrix.R (Matrix): also work for NA data 2006-08-28 Martin Maechler * R/Matrix.R (Matrix): + 'forceCheck' argument; dimnames setting in all cases. 2006-08-27 Douglas Bates * src/dense.[ch],init.c, R/ddenseMatrix.R, man/band.Rd (ddense_band): Added triu, tril and band for ddenseMatrix objects. 2006-08-25 Martin Maechler * src/Mutils.c (dup_mMatrix_as_dgeMatrix): added all subclasses of subclasses of "ddenseMatrix" * src/init.c et al: outcomment dtrM*_as_dge* and dsyM*_as_dge*_ * R/ddenseMatrix.R et al: setAs("ddenseMatrix", "dgeMatrix", ..) instead of half dozen specialized ones. 2006-08-25 Douglas Bates * R/lmer.R (qqmath method): Bug fix provided by Emmanuel Tillard - ordering standard errors to match effects. 2006-08-24 Douglas Bates * src/lsCMatrix.c (lsCMatrix_trans): Remove lsCMatrix_chol based on R_ldl. * R/lCholCMatrix.R, src/[dl]CholCMatrix.[ch],R_ldl.[ch],Metis_utils.[ch]: removed * src/dsCMatrix.c (dsCMatrix_to_dgTMatrix): use CHOLMOD * many files in ./R and ./src: Use more general version of dup_mMatrix_as_dgeMatrix to simplify method definitions. * src/Mutils.c (dup_mMatrix_as_dgeMatrix): Add ddiMatrix, dtpMatrix, dspMatrix and dppMatrix conversions. 2006-08-23 Douglas Bates * R/AllClass.R,lCholCMatrix.R,src/SOURCES_C.mkf,init.c,NAMESPACE: Remove classes lCholCMatrix and dCholCMatrix based on R_ldl code. * src/dgeMatrix.c: Ensure 'factors' slot exists in result of dgeMatrix_crossprod (may need to do this in other places). * R/AllGeneric.R,dsCMatrix.R, src/dscMatrix.[ch]: Add Cholesky generic and method for dsCMatrix. Use CHOLMOD for chol(). 2006-08-22 Douglas Bates * src/Mutils.c (dup_mMatrix_as_dgeMatrix): updated for general types of classed Matrices, matrices or numeric or logical vectors. * src/init.c: register dup_mMatrix_as_dgeMatrix for coercions. * src/chm_common.c,Mutils.h (as_cholmod_factor): Move check_class to Mutils.h (as an inline) and change name to Matrix_check_class; fixes in as_cholmod_factor and chm_factor_to_SEXP. * src/dsCMatrix.[ch]: Use CHOLMOD for dsCMatrix_chol and dsCMatrix_matrix_solve. Comment out vestigial functions. * src/Csparse.c: use diag_P and uplo_P macros. 2006-08-21 Douglas Bates * src/lmer.c (internal_mer_RZXinv): Fix memory leak caught by valgrind. * tests/matprod.R: Add tests to verify that 'solve' and '%*%' are inverses. * src/sparseQR.c (sparseQR_validate): add new validation test, fix -Wall warnings. * src/dppMatrix.c,dtrMatrix.c,dgCMatrix.c,dgeMatrix.c,dspMatrix.c: Use dup_mMatrix_as_dgeMatrix. 2006-08-20 Douglas Bates * src/sparseQR.c: Fix thinko in sparseQR_resid_fitted. * tests/sparseQR.R: Added * man/sparseQR-class.Rd: Document methods for qr.* generics * R/sparseQR.R: Return correct # of coefs; fix cut-and-paste errors 2006-08-19 Douglas Bates * NAMESPACE, R/sparseQR.R, src/init.c,sparseQR.[ch],SOURCES_C.mkf: Added methods for sparseQR for qr.qy, qr.qty, qr.coef, qr.resid and qr.fitted. * src/Mutils.[ch]: Added dup_mMatrix_as_dgeMatrix utility * src/dgCMatrix.c: Check for ordering before storing q in dgCMatrix_QR 2006-08-18 Martin Maechler * R/AllGeneric.R: add "qr" and "chol" generics; via 'trick' since the base version has no "..." argument. * R/sparseMatrix.R (prSpMatrix): fix the triangular unit diagonal case. * R/Matrix.R: define and * NAMESPACE: export as.numeric() and as.logical() methods. Let's hope these do not badly slow down something... Finally export the zapsmall() method. 2006-08-17 Douglas Bates * src/dgCMatrix.[ch] (dgCMatrix_matrix_solve), src/init.c, R/dgCMatrix.R: solve methods for dgCMatrix and dense RHS. * src/dtCMatrix.c :Remove code that is no longer used * R/dtCMatrix.R: Use C code for diagU2N in CsparseMatrix classes 2006-08-14 Douglas Bates * src/Csparse.[ch],init.c (Csparse_to_logical): Added utilities Csparse_to_logical and Csparse_symmetric_to_general. * R/dgCMatrix.R,dsCMatrix.R,Csparse.R : Consolidate general coercion methods between CsparseMatrix and TsparseMatrix. 2006-08-14 Douglas Bates * R/dtCMatrix.R,dgCMatrix.R,Csparse.R src/init.c,dgCMatrix.[ch], Csparse.[ch],chm_common.c,dense.c : Use CHOLMOD code and methods for CsparseMatrix, TsparseMatrix, denseMatrix or matrix when possible. 2006-08-12 Douglas Bates * src/chm_common.[ch],Csparse.[ch],Tsparse.[ch],CHMfactor.c,dtTMatrix.c, dgTMatrix.c,dgCMatrix.c,dsCMatrix.c,dtTMatrix.c, R/dsTMatrix.R, Tsparse.R,Csparse.R,dgTMatrix.R,dsCMatrix.R,lsCMatrix.R: generalize conversions between TsparseMatrix, CsparseMatrix, denseMatrix and matrix. Preserve triangularity property and propagate Dimnames in the easy cases. 2006-08-10 Douglas Bates * src/lmer.c: adjust checks in glmer_init for S4SXP * tests/validObj.R: check of all(eq) should be all(eq@x) - worked before S4SXP but for the wrong reasons. 2006-08-08 Douglas Bates * src/Csparse.c (Csparse_crossprod): tcrossprod result has stype = -1. Later modified to return the upper triangle only. * R/dgTMatrix.R: Remove vestigial crossprod and tcrossprod methods. 2006-08-07 Douglas Bates * src/Csparse.c (Csparse_crossprod): Set stype on result to avoid R-level conversion to a sparse symmetric class. * R/Tsparse.R,R/Csparse.R (crossprod and tcrossprod methods): Remove conversion to sparse symmetric classes (now done in C code). 2006-08-07 Martin Maechler * R/dgCMatrix.R: disable old crossprod and tcrossprod methods * man/band.Rd: adapt the \dontshow{} unit test. 2006-08-07 Martin Maechler * DESCRIPTION (Version): 0.995-14 for CRAN * tests/other-pkgs.R: oops: library(Matrix) outside *if* ! * R/sparseMatrix.R (Tsp2grNEL): fixed Tsparse -> graph coercion * tests/other-pkgs.R: more checks, sparseMatrix -> graph * R/Auxiliaries.R (as_Tsparse, as_Rsparse): new * R/Tsparse.R (tril, triu, band): methods * R/dgRMatrix.R (tril, ...): ditto * man/band.Rd: ditto 2006-08-04 Martin Maechler * R/Matrix.R (head, tail): directly use utils:::head.matrix to be up-to-date automatically. 2006-08-03 Martin Maechler * DESCRIPTION (Version): 0.995-13 to be released to CRAN * DESCRIPTION (Lazydata): no, instead of 'yes' because it fails for: * data/CAex.R, inst/external/CAex_slots.rda: replacing data/CAex.rda * data/KNex.R, inst/external/KNex_slots.rda: replacing data/KNex.rda such that the S4 objects are always created by the current version of R and 'Matrix' class definitions. 2006-08-01 Douglas Bates * R/lmer.R (LMEoptimize method), tests/lmer.R, inst/external/test3comp.rda: Added warnings for convergence on boundary and test cases. * src/lmer.c (mer_postVar): Modified to return the variances that are marginal to the fixed effects, not conditional on them (which is what the bVar slot contents represent). 2006-07-31 Douglas Bates * NAMESPACE, src/lmer.c, R/lmer.R (hatTrace): Add the hatTrace function which calls the C function mer_hat_trace2. * man/ranef.Rd: Include description of "postVar" argument and producing a caterpillar plot. 2006-07-31 Martin Maechler * NAMESPACE: change "correlation" to "corMatrix" * R/AllClass.R: to avoid clash with S3 class in 'nlme'. * R/dpoMatrix.R: ditto * R/lmer.R: ditto 2006-07-28 Douglas Bates * src/lmer.c (internal_mer_RZXinv): Split the calculation of the RZXinv slot's contents into a separate internal function that can be used in mer_hat_trace. 2006-07-22 Martin Maechler * R/Matrix.R: Coercions "Matrix" -> (sparse|dense)Matrix via new smart * R/Auxiliaries.R (as_Csparse, as_dense, .M.shapse): new utility functions. 2006-07-21 Martin Maechler * R/Csparse.R (tril, triu, band): do return *triangular* classed matrices when appropriate; band() even symmetric ones. (replCmat): extend to potentially all "CsparseMatrix" * R/Tsparse.R (replTmat): extend to all "TsparseMatrix"; hence allow subassignment for special sparse matrices. * R/Auxiliaries.R (as_geClass): factor out the .M.kind() functionality * src/lmer.c (mer_MCMCsamp, glmer_MCMCsamp): new 'verbose' argument; in glmer_*(): print only if(verbose). speed-optimize a few places by moving REAL(.) out of loops. * src/lmer.h, src/init.h, R/lmer.R: related to above. 2006-07-20 Martin Maechler * R/Matrix.R("["): disable ("Matrix", i = "logical", j = "missing"), since that wrongly triggers also for M[ logi , ] * R/denseMatrix.R: "[" methods now also work e.g. when indexing a symmetric matrix that results in a non-symmetric one. * R/Auxiliaries.R (as_geClass): new function used in "[" above. * R/dMatrix.R: make round(M) work as round(M, 0) * R/dgTMatrix.R (image): coordinate system and axis now use 1-based indices, not 0-based ones. * R/Tsparse.R (.ind.prep for "["): get rid of max() warning. * tests/indexing.R: test it. * NAMESPACE: export isSymmetric(); has been a generic in "base" for a while; * man/isSymmetric-methods.Rd: and document it. * R/SparseM-conv.R: added coercion methods for some 'SparseM' matrices. * man/SparseM-conv.Rd: docu them * tests/other-pkgs.R: renamed from tests/graph.R and add example for 'SparseM' conversions 2006-07-17 Douglas Bates * R/Matrix.R (head): added head() and tail() methods. 2006-07-17 Martin Maechler * DESCRIPTION (Version): 0.995-12 released to CRAN 2006-07-15 Martin Maechler * tests/simple.R: add check for correct dsT -> dgT coercion; add check for correct printing of symmetric sparse matrices. * R/Auxiliaries.R (non0ind): return *all* non-0 entry indices also for sparse symmetric matrices. * src/dsTMatrix.c (dsTMatrix_as_dgTMatrix): do not copy the diagonal twice. 2006-07-11 Douglas Bates * src/dsTMatrix.c (dsTMatrix_as_dgTMatrix): Fix a case of INTEGER being applied to the x slot (detected by Brian Ripley). 2006-07-10 Martin Maechler * src/dgCMatrix.c (dgCMatrix_validate): 'p' slot must have correct length. * R/Auxiliaries.R (isTriC): fix buglet (we were 1-based!) 2006-07-08 Martin Maechler * src/lgCMatrix.c (lgCMatrix_diag): new function * R/lgCMatrix.R (diag): for new method * R/AllClass.R (TsparseMatrix): do use Tsparse_validate ==> construction of illegal "*gTMatrix" via new() should now be much less easy: * tests/Class+Meth.R: assertError() for some illegal "dgT*" * R/Matrix.R (Matrix): Matrix(0, nrow,ncol) now "goes sparse" directly. * man/Matrix.Rd: documents it. 2006-07-06 Douglas Bates * src/pedigree.c (pedigree_inbreeding): Correction in initialization. This function is not currently being used and is not fully tested. * NAMESPACE, R/{AllClass.R,lmer.R}, src/{init.c,lmer.c}: Introduced the glmer class. Added code for mcmcmsamp on glmer objects. Modified validity check on pedigree objects to account for nonparallel patterns of missingness of parents. * man/{lmer-class.Rd,mcmcsamp.Rd}: Update documentation for glmer class. 2006-07-01 Martin Maechler * R/pMatrix.R: coercion pMatrix -> Tsparse 2006-06-12 Douglas Bates * DESCRIPTION (Version): 0.995-11 released to CRAN * R/lmer.R (mcmcsamp method): Corrected arrangments of names on the output from mcmcsamp. 2006-06-10 Douglas Bates * R/lmer.R (simulestimate): added C code for calculating the trace of the hat matrix. 2006-06-09 Martin Maechler * R/diagMatrix.R (setAs): define coercion methods to sparse matrix classes. * R/sparseMatrix.R etc: multiplication of diagonal and sparse 2006-06-08 Martin Maechler * R/dgTMatrix.R (colSums): etc. All four of colSums(), rowSums(), colMeans(), rowMeans() now should work for all "Matrices". 2006-06-01 Douglas Bates * R/lmer.R (panel.ci): Add a reference line at zero and a background grid to the qqmath plot of ranef.lmer. 2006-05-30 Douglas Bates * R/lmer.R (expandSlash): Functions (non-exported) to allow nested grouping factors to be specified in the formula as (1|foo/bar). 2006-05-27 Douglas Bates * R/lmer.R (findbars and others): Change check of is.numeric to !is.language to resolve the bug reported by Jacob Wegelin. * src/pedigree.c (pedigree_inbreeding): Initial implementation of code to evaluate inbreeding coefficients without calculating T, based on code in Sargolzaei and Iwaisaki's paper. 2006-05-27 Douglas Bates * R/{lmer.R,AllGeneric.R}, src/{init.c,lmer.[ch]}: Added local generic and mer methods for isNested and denomDF. This denomDF was an attempt to emulate that in lme but I don't think that makes sense. Use the trace of the hat matrix instead. 2006-05-17 Martin Maechler * R/sparseMatrix.R: Matrix <-> graph methods: can no longer use the C code depending on a slot structure that's no longer valid. * src/dgTMatrix.c: ditto (also: src/init.c src/dgTMatrix.h) 2006-05-17 Douglas Bates * R/{AllGeneric.R,Csparse.R},man/band.Rd,NAMESPACE: changed name of lowerTriMatrix generic and methods to tril (also upper to triu) and added a general band extractor. 2006-05-16 Douglas Bates * R/pedigree.R (pedigree): Replace sire and dam values outside the allowable range with NAs. Added a corresponding check in the validity check for the pedigree class. * R/[CT]sparse.R ([t]crossprod): The result of single-argument crossprod methods now inherits from symmetricMatrix. 2006-05-15 Douglas Bates * R/AllGeneric.R (lowerTriMatrix): Added (but did not export) generics lowerTriMatrix and upperTriMatrix along with methods for the Csparse virtual class. Also added a C function Csparse_band that implements these methods by calling cholmod_band. 2006-05-15 Martin Maechler * R/Tsparse.R ("["): column or row subsetting; @Dimnames[k] got erased when it was NULL. This led to invalid subselections! 2006-04-25 Douglas Bates * R/dtCMatrix.R: avoid coercion of dtCMatrix object to dgCMatrix in method for "t" so as not to lose the unit diagonal property. 2006-04-19 Douglas Bates * R/lmer.R, R/AllGeneric.R, NAMESPACE: Remove the postVar generic and methods. This is now an option to the ranef method for the mer class. * src/cs_utils.c: Ensure that the nz component is -1 for a compressed column-oriented matrix. Minor formatting cleanup. * man/lmer-class.Rd: Document the qqmath method for ranef.lmer objects. 2006-04-19 Martin Maechler * R/Auxiliaries.R (diagU2N): new for the solve() methods in * R/dtCMatrix.R: where dgC -> dgT coercion now preserves diag = "U". 2006-04-15 Douglas Bates * src/cs.[ch],src/cs_utils.[ch] : Added Tim Davis' CSparse library in cs.[ch] and utilities to interface to that code in cs_utils.[ch]. * R/dtCMatrix.R, src/dtCMatrix.[ch] : CSparse-based solve methods for the dtCMatrix class. 2006-04-12 Douglas Bates * R/pedigree.R, R/AllClass.R, NAMESPACE: added a pedigree class and methods for it. 2006-04-12 Martin Maechler * R/dgCMatrix.R: add storage.mode(.) <- "double" for "matrix" arguments, such that M %*% 1:6 now works * Tests/matprod.R: test the above 2006-04-03 Douglas Bates * R/lmer.R (qqmath,ranef.lmer-method): added a qqmath method for the ranef.lmer class. * R/AllClass.R, NAMESPACE, R/lmer.R: Added a postVar generic and methods to extract the posterior variances from the bVar slot. 2006-03-30 Martin Maechler * R/dtCMatrix.R: allow coercion from dgC* to triangular (dtC*) * R/dsCMatrix.R: and symmetric (dsC*) 'Csparse' matrices. * R/Tsparse.R: Tsparse* -> Csparse* coercion now works and is tested in * tests/simple: (extended) * R/sparseMatrix.R (isTriangular): now using much improved * R/Auxiliaries.R (isTriC): new triangularity check for *CMatrix 2006-03-23 Douglas Bates * src/dsyMatrix.c (dsyMatrix_as_dspMatrix): Propagate DimNames (problem report from Franklin Parlamis). This should be done generally. 2006-03-21 Douglas Bates * R/AllClass.R,lmer.R: Change the name of the lmer.ranef class to ranef.lmer (like summary.lmer). Add the coef.lmer class and update the plot methods. 2006-03-20 Douglas Bates * R/lmer.R (resid and ranef methods): Added methods for the "residuals" and "resid" generic but only for linear mixed model fits. Changed the ranef method to return a list of data frames so that the plot methods now work. 2006-03-16 Douglas Bates * src/dpoMatrix.c (dpoMatrix_chol): Require n > 0 in call to dpotrf - otherwise the BLAS on Mac OS X complains and quits. * DESCRIPTION (Date): New release 2006-03-15 Martin Maechler * DESCRIPTION (Version): 0.995-6 -- to be released to CRAN * data/KNex.rda: replacing 'mm' and 'y' by KNex <- list(mm=mm, y=y) * man/KNex.Rd: and other help files * tests/*.R: several ones needed adaption * inst/doc/Comparisons.Rnw: ditto 2006-03-11 Martin Maechler * R/dgCMatrix.R (replCmat): "[<-" methods for dgCMatrix * tests/indexing.R: tests for new [<- methods for sparse matrices. 2006-03-10 Martin Maechler * R/dgTMatrix.R (replTmat): "[<-" methods for dgTMatrix * R/Tsparse.R (.ind.prep): fix out-of-range indexing 2006-03-08 Martin Maechler * R/dMatrix.R: enable things like M [ M < 10 ] * R/dgeMatrix.R: implement it 2006-03-06 Martin Maechler * R/AllClass.R: define "summary.mer" and "*.lmer" * R/lmer.R (summary): summary() computes & returns the above; * R/lmer.R (show): now works with summary() 2006-03-04 Martin Maechler * R/dgCMatrix.R: finally direct "Arith" dgC o dgC * R/Auxiliaries.R (WhichintersectInd): and other utilities to support the above 2006-02-07 Douglas Bates * R/lmer.R (lmer): fix initial values of offset and weights for glm.fit. Use glmFit$prior.weights for weights in a glmm. Allow an option usePQL = FALSE to skip the PQL steps for the Laplace method (and, in time, the AGQ method). * src/lmer.c (mer_factor): Move downdating and factoring of XtX into a separate function internal_mer_Xfactor to be able to call it from internal_bhat. 2006-01-23 Martin Maechler * tests/Class+Meth.R (tstMatrixClass): function for much better testing; now again of all actual classes. * src/Mutils.c (MAKE_TRIANGULAR_BODY, MAKE_SYMMETRIC_BODY): use macros and define make_d_matrix_* and make_i_matrix_* where _i_ is for the ldense routines: * src/ldense.c (ltrMatrix_as_lgeMatrix): provide functions * src/ldense.c (lsyMatrix_as_lgeMatrix): * R/ldenseMatrix.R: use the above in setAs(*,"lgeMatrix") 2006-01-16 Martin Maechler * R/Matrix.R (Matrix): has become much "smarter" now auto-producing many different kinds of matrices. * R/*.R: quite a few new methods were needed for R CMD check with new Matrix(). Very good for users playing around. 2006-01-15 Martin Maechler * src/dgeMatrix.c (dMatrix_validate): new * src/Mutils.c (dense_nonpacked_validate): new * src/dtrMatrix.c (dtrMatrix_validate): improved/fixed 2006-01-14 Douglas Bates * R/AllClass.R (compMatrix), (generalMatrix): new virtual classes 2006-01-07 Douglas Bates * DESCRIPTION (Version): 0.99-6 released to CRAN * src/dgBCMatrix.c (cscb_trcbsm): Fix due to Peter Dalgaard for segfault in cases with multiple non-nested grouping factors. 2006-01-03 Martin Maechler * DESCRIPTION (Version): 0.99-4 to be released to CRAN (Depends): also on 'utils' * R/AllClass.R (diagonalMatrix): new class with "ddi*" and "ldi*" * R/diagMatrix.R (Diagonal): constructor and methods for diagonal matrices * R/ltTMatrix.R: new "minimal methods" 2005-12-12 Martin Maechler * R/AllGeneric.R (tcrossprod): 2-argument version; here, and for all methods (and help files). 2005-12-09 Martin Maechler * R/Auxiliaries.R (dimNamesCheck): fixed thinko -> bug for case (dimn. op no_dimn.) 2005-11-14 Douglas Bates * DESCRIPTION (Version): 0.99-2 released to CRAN 2005-10-21 Douglas Bates * R/lmer.R (simulate method): Fixed a drop=FALSE problem reported by Julian Faraway. 2005-10-06 Martin Maechler * R/Auxiliaries.R (try_as): new utility * R/sparseMatrix.R: use try_as() in coercion to original class 2005-09-30 Martin Maechler * src/dgCMatrix.c (double_to_csc): and dgeMatrix_to_csc() 2005-09-29 Martin Maechler * R/Auxiliaries.R (dimNamesCheck): added * R/Matrix.R (as.array), (as.vector): new 2005-09-28 Martin Maechler * R/Matrix.R (Matrix): get logical argument 'sparse' with a smart default. * R/AllClass.R: move 'factors' slot toplevel "Matrix"; "pMatrix" now contains "sparseMatrix" 2005-09-26 Martin Maechler * tests/Class+Meth.R: new tests; t(t(m)) == m * src/dtCMatrix.c (tsc_transpose): add forgotten "diag" slot * src/dsTMatrix.c (dsTMatrix_as_dsCMatrix): bad typo (segfault!) * src/dtTMatrix.c (dtTMatrix_as_dtCMatrix): new * R/dspMatrix.R: typo in "t" method 2005-09-18 Douglas Bates * R/AllClass.R (TsparseMatrix), CsparseM* and RsparseM* * R/Tsparse.R: instead of R/gTMatrix.R * R/Csparse.R: new * src/Tsparse.c (Tsparse_to_Csparse): new; -> cholmod_() * src/Tsparse.c: new; many trivial methods calling cholmod_() * src/Csparse.c (Csparse_to_Tsparse), transpose, (mat|cross)prod: via cholmod 2005-09-16 Martin Maechler * R/Auxiliaries.R (non0ind): new function using new C code * src/dgCMatrix.c (compressed_non_0_ij): new utility 2005-09-15 Douglas Bates * src/chm_common.h: header file required by all C sources that call CHOLMOD functions. It defines a cholmod_common structure called 'c' whose address is passed as the last argument to (virtually) every CHOLMOD function. * src/Pattern.c: Simple example of the use of CHOLMOD. * src/init.c: initialize and finalize the cholmod_common structure. * src/Makefile: Added source packages CHOLMOD UMFPACK AMD COLAMD LDL and CCOLAMD from the U. of Florida sparse matrix library. 2005-09-08 Martin Maechler * inst/test-tools.R: new file collecting the utility functions used in ./tests/*.R * R/ddenseMatrix.R (cbind2): new methods for "numeric" and "matrix" * R/Matrix.R (cbind2): methods for NULL and missing 2005-08-31 Martin Maechler * R/AllClass.R: new "index" class for "[" and "[<-": First cut at "symmetricMatrix" and "triangularMatrix" * R/gTMatrix.R (.ind.prep): new function; Logical and character indexing now work too. * R/Matrix.R: cheap "[<-" methods for denseMatrix now work * tests/indexing.R: new, including *.Rout.save * tests/dgTMatrix.R: new 2005-08-29 Douglas Bates * src/dgTMatrix.c (graphNEL_as_dgTMatrix): Corrected the position indicator pos not being updated. Also enforced upper triangular for symmetric case. Need to coerce edges component of elements of edge list - grr! (Why don't they define their classes cleanly?) 2005-08-26 Martin Maechler * R/Matrix.R: added first "[<-" methods; not yet functional * R/denseMatrix.R: ditto * man/Subassign-methods.Rd: new help file for these 2005-08-25 Martin Maechler * DESCRIPTION (Version): 0.98-6 * R/denseMatrix.R: new file for "[" fallback methods for all dense matrices. 2005-08-19 Martin Maechler * src/lgCMatrix.c (lcsc_to_matrix): new; need for as( , "matrix") * R/pMatrix.R: coercion to "lgTMatrix" * R/gTMatrix.R: new virtual class to define "[" methods for. * man/gTMatrix-class.Rd: * General slight re-organization of where "[" methods are defined. more to come. 2005-08-18 Douglas Bates * DESCRIPTION (Version): 0.98-5 released to CRAN * src/dgTMatrix.c (graphNEL_as_dgTMatrix): add first graphNEL methods * ..... 2005-08-18 Douglas Bates * R/lmer.R: Corrected naming scheme in mcmcsamp to work with lmer or glmer objects. 2005-08-17 Martin Maechler * DESCRIPTION (Version): 0.98-4 : upload to CRAN 2005-08-16 Douglas Bates * R/HBMM.R: finish re-writing R-only code. 2005-08-15 Douglas Bates * man/externalFormats.Rd: move documentation for writeHB and writeMM here. * src/mmio.c: replace inclusion of by (suggested by Paul Roecker). * tests/validObj.R (assertError): Comment out test that is failing after recent changes in r-devel. 2005-08-11 Martin Maechler * R/AllClass.R: intermediate virtual class "denseMatrix" * man/denseMatrix-class.Rd * NAMESPACE: export it, and also export * man/unused-classes.Rd: "iMatrix", "zMatrix" and "ldenseMatrix" 2005-08-10 Douglas Bates * DESCRIPTION (Version): 0.98-3 to CRAN * src/dtrMatrix.c (dtrMatrix_validate): fixed up validation and matrix_solve code (which was really, really wrong). 2005-08-07 Douglas Bates * DESCRIPTION (Version): 0.98-2 * R/HBMM.R (readHB), (readMM): read Matrix Market formats * R/lmer.R (abbrvNms): new * R/lmer.R (mcmcsamp): allow transformed parameters * src/HBMM.c (Matrix_writeMatrixMarket): Added read/write routines for the Harwell-Boeing and the MatrixMarket formats. 2005-08-04 Martin Maechler * man/dtrMatrix-class.Rd: add examples * man/dtpMatrix-class.Rd: ditto; plus note about PROBLEM * TODO: note the dtpMatrix (docu) bug * R/zzz.R (.onLoad): assignInNamespace("as.matrix", *, "base") in order to ensure that new as.matrix() is used by old functions, e.g., svd(), qr(), eigen(), dist(),..; apply(), also matplot() or pairs(). 2005-08-03 Martin Maechler * R/lmer.R: add 'fixme' comments and move the linear vs glm check; add comments about 'control' / lmerControl() arguments 2005-07-27 Douglas Bates * man/sleepstudy.Rd: Added the sleep data set. * DESCRIPTION (Version): 0.98-1 released to CRAN 2005-07-12 Douglas Bates * man/sleepstudy.Rd: Added the sleep data set. * R/lmer.R (glmmMCMC): Added PACKAGE = "Matrix" in a couple of .Call calls that were producing spurious output. 2005-07-05 Douglas Bates * R/lmer.R (lmer): stored updated variance component estimates in mer object for the generalized model. (Bug reported by Renaud Lancelot). 2005-07-03 Douglas Bates * src/lmer.c (glmer_devAGQ): Added AGQ for single grouping factor, unidimensional case. 2005-06-08 Douglas Bates * DESCRIPTION (Version): 0.96-1 * moved lmer-class' R and C code moved from lme4 to here 2005-06-04 Douglas Bates * R/dgCMatrix.R: Call to csc_matrix_mm used undefined arguments (reported by Guissepe Ragusa ) 2005-06-02 Douglas Bates * src/Makefile.win: Forgot to update this when Makefile changed. 2005-05-11 Douglas Bates * src/dgCMatrix.c (csc_transpose): Simplified function fixing a bug reported by Kurt Hornik and Michael Hahsler. 2005-05-10 Douglas Bates * src/lgCMatrix.c (Matrix_lgClgCmm): Implementation of methods for logical sparse matrices. These will also be used in the symbolic analysis for lmer objects. * src/dsCMatrix.c (dsCMatrix_matrix_solve): Copied the dimensions of b to the result. Fixes bug reported by Jean.Coursol@math.u-psud.fr 2005-05-06 Douglas Bates * src/dgeMatrix.c (dgeMatrix_colsums): Added an implementation of colMeans, colSums, rowMeans and rowSums. 2005-04-18 Douglas Bates * src/lgCMatrix.[ch]: code for _validate method and stub for multiplication operation. * src/dgeMatrix.c (dgeMatrix_matrix_solve): Passing wrong argument to dgetrs. * src/init.c: Fix cut-and-paste error in definition of dgeMatrix_matrix_solve * src/{many files}: Tighten code by using ALLOC_SLOT. 2005-04-15 Douglas Bates * R/AllClass.R: Add lgTMatrix and lgCMatrix classes * DESCRIPTION: Eliminate import of stats. 2005-04-06 Douglas Bates * R/AllClass.R : add logical sparse matrix classes 2005-04-01 Martin Maechler * R/dgTMatrix.R: add "[" method for triplet matrices * R/sparseMatrix.R: and other sparse ones; --> add show() for sparse 2005-03-31 Douglas Bates * DESCRIPTION (Version): release 0.95-5 to CRAN * R/dMatrix.R: add %*%, crossprod and solve "fallback" methods * R/sparseMatrix.R: %*%, crossprod() * R/dgeMatrix.R: more "fallback" methods for numeric/dense matrices * man/*.Rd: move method definitions to 'Matrix' and 'dMatrix' * src/lmer.c (lmer_fitted): fix thinko 2005-03-26 Martin Maechler * R/AllClass.R: add two virtual sparse classes ``on top'' 2005-03-24 Martin Maechler * R/AllClass.R (setClass): use "VIRTUAL" for the virtual classes; correspondingly fix examples and tests/ since new() doesn't work for virtual classes. 2005-03-17 Martin Maechler * R/Matrix.R (as.matrix): method and one for unname() * tests/dpoMatrix.R: tests should now be less platform dependent; also run for R 2.1.0; using as.matrix() 2005-03-15 Douglas Bates * R/pMatrix.R: "pMatrix" class added * .... 2005-03-14 Douglas Bates * R/dtpMatrix.R: Add unpack method and an example. * src/dsyMatrix.c (dsyMatrix_trf): Add BunchKaufman factorization of general symmetric matrices and associated S4 methods. 2005-03-10 Martin Maechler + 2005-03-05 Martin Maechler * R/dgeMatrix.R (setAs): and many other files: more coercion, crossprod() and "%*%" methods added; tests, too. * tests/matprod.R: new, for testing these 2005-03-03 Douglas Bates * src/lmer.c (lmer_fitted): Added. 2005-03-02 Douglas Bates * R/dsTMatrix.R: Conversion from dsTMatrix to dsCMatrix 2005-02-28 Douglas Bates * src/*.c,po/,inst/po: Internationalization and localization of the package. * src/ldl.[ch]: Removed these as their contents are referenced in the R_ldl.c file. * src/flame.[ch]: Removed these source files. * src/dtrMatrix.c (make_array_triangular): Move to Mutils * src/LU.[ch],src/init.c: absorb in factorizations * src/Mutils.h: prepare for internationalization * src/cblas.h: move the enum definitions to Mutils.h and remove this file 2005-02-26 Martin Maechler * R/dgeMatrix.R: provide "dimnames" and "dimnames<-" methods * R/dtrMatrix.R: fix t() method * R/dgeMatrix.R: define group methods "Arith", "Math", "Math2" * NAMESPACE: export them (and import generics from "methods") * tests/group-methods.R : and test them. * src/dtrMatrix.c (dtrMatrix_as_dgeMatrix): prevent seg.fault in border case 2005-02-24 Douglas Bates * DESCRIPTION (Version): 0.95-2 released to CRAN * src/dgBCMatrix.c: * src/lmer.c: many changes * ... 2005-02-04 Martin Maechler * R/Matrix.R: add more sophisticated show() method. 2005-02-02 Douglas Bates * */* : almost complete reorganization of classes. 2005-01-26 Douglas Bates * R/AllGeneric.R: Added matrix exponential generic expm and a method for the geMatrix class. 2005-01-24 Douglas Bates * src/Makefile (clean): Remove *.a and *.so * man/cscBlocked-class.Rd: Remove reference to the lmer-class. 2005-01-23 Douglas Bates * src/lmer.c (Lind): Definition of Lind was backwards. This only had an effect in cases with more than 2 grouping factors. 2005-01-03 Douglas Bates * src/lmeRep.c (lmer_variances): change from lmeRep to lmer 2004-12-23 Douglas Bates * src/init.c (R_init_Matrix): Reorder calls to R_registerRoutines and R_useDynamicSymbols (suggested by B.D.Ripley). 2004-12-14 Douglas Bates * R/sscMatrix.R: Add determinant methods * src/triplet.[ch],src/init.c (triplet_to_matrix): Add a coercion for tripletMatrix to matrix. 2004-12-13 Douglas Bates * R/AllClass.R (.onLoad): Eliminate the bbCrosstab class, which is no longer used. * src/R_ldl.c: Created an R-specific version of the ldl.[ch] files with dynamic allocation of scratch arrays. * src/ssclme.c (ssclme_copy_ctab): Fixed bug in creation of ZtZ for multivariate random effects with multiple grouping factors. Fixes part but not all of #15. 2004-12-03 Douglas Bates * src/lmeRep.c (lmeRep_factor): order of operations for multiple scalar grouping factors corrected. 2004-11-29 Douglas Bates * src/bCrosstab.c: remove diag_update which is no longer used 2004-11-16 Douglas Bates * src/Metis_utils.c: Move metis.h include to C sources so that the .h file can be included. 2004-11-12 Douglas Bates * src/LU.c,geMatrix.c,trMatrix.c, etc.: Complete allocation of slots in NEW_OBJECT. * src/Mutils.h: Moved list of symbols to an include file 2004-11-11 Douglas Bates * src/geMutils.c (Matrix_init): remove unused function 2004-11-10 Douglas Bates * src/cscMatrix.c (csc_to_imagemat): removed unused function 2004-11-05 Douglas Bates * src/Makefile.win (SOURCES_C): Keep consistent with Makefile 2004-10-27 Douglas Bates * R/pdmatrix.R: remove PACKAGE="Matrix" in .Call calls 2004-10-04 Douglas Bates * src/init.c: Created R_init_Matrix and added registration of C routines. 2004-10-02 Douglas Bates * R/tripletMatrix.R: Force a require(lattice) for the image methods. 2004-06-15 Douglas Bates * man/trMatrix-class.Rd: Escape the % chars in .Rd files. 2004-04-20 Douglas Bates * src/Makefile.win ($(SHLIB)): Modifications per Uwe Ligges. 2004-04-19 Douglas Bates * src/ssclme.c (ssclme_update_mm): fix logic error in ssclme_update_mm 2004-04-18 Douglas Bates * src/ssclme.c (ssclme_coef, ssclme_coefGets): Create consistency in the order of unconstrained and constrained parameters. (ssclme_gradient): Added the gradients (not yet correct for multidimensional, unconstrained case). 2004-04-14 Douglas Bates * src/ssclme.c (ssclme_EMsteps): Fix logic in REML update * src/Makefile.win: Remove unneeded ranlib call 2004-04-12 Douglas Bates * DESCRIPTION (Version): New release * src/Makefile.win: Update Makefile.win to umfpack removal. 2004-04-05 Douglas Bates * src/triplet_to_col.c: Create triplet_to_col as a native function, not the version from umfpack. There were problems with the configuration of UMFPACK for 64-bit processors and there was only one umfpack routine being used so I moved it here. 2004-04-04 Douglas Bates * src/ssclme.c (ssclme_variances): New function. 2004-03-28 Douglas Bates * src/ssclme.c (ssclme_fitted): Added function. 2004-03-27 Douglas Bates * src/ssclme.c (ssclme_transfer_dimnames): Add new function to store the dimnames in the XtX and bVar slots (ssclme_update_mm): Change the dimensions of the bVar slot components and the returned value from ssclme_ranef. 2004-03-18 Douglas Bates * R/{pdMat.R,pdIdent.R,pdLogChol.R,pdMatrixLog.R,pdNatural.R}, src/{pdMat.c,pdIdent.c,pdLogChol.c,pdNatural.c}, tests/{pdCompSymm.R,pdDiag.R,pdIdent.R,pdLogChol.R,pdNatural.R}, man/{pdMat-class.Rd,pdmatrix-class.Rd,corrmatrix-class.Rd, pdDiag-class.Rd,pdIdent-class.Rd,pdNatural-class.Rd, pdLogChol-class.Rd,coefGets.Rd,pdCompSymm-class.Rd, pdfactor-class.Rd,pdFactor.Rd,pdMatrix.Rd, pdBlocked-class.Rd},AllClass.R,AllGeneric.R: Moved the pdMat classes from the lme4 package. 2004-03-02 Douglas Bates * man/ssclme-class.Rd: Update definition and documentation of the ssclme class to include the DIsqrt slot. * src/ssclme.c (ssclme_deviance): Modify order of computation (much faster using dsyrk, a level 3 BLAS routine). * src/Makefile (SUBLIBS): Change definition (K. Hornik) 2004-02-28 Douglas Bates * tests/ssclme.R: Modify the test to account for the permutation of the levels of the grouping factors. 2004-02-23 Douglas Bates * R/ssclme.R,src/ssclme.c (ssclme): Move slots of sscCrosstab slot directly into the ssclme class definition. 2004-02-22 Douglas Bates * DESCRIPTION (Date): New release * man/ssclme-class.Rd: new file. * src/ssclme.c (ssclme_loglik): major revisions in design. It works and it's fast! 2004-02-17 Douglas Bates * src/taucs/Makefile.win (lib): Change "ar" to "$(AR)" (B.Ripley) 2004-02-16 Douglas Bates * DESCRIPTION (Date): New release * NAMESPACE: Don't export ssclme. * data/ScotsSec.rda, man/ScotsSec.Rd: Add Scottish secondary school data. 2004-02-11 Douglas Bates * src/sscCrosstab.c (sscCrosstab): Added a row to the incidence to keep track of the fixed-effects and the response. Counts also gets an extra element, which is always one. * src/ldl.c: Include these routines from Tim Davis' LDL package. 2004-02-10 Douglas Bates * src/cscMatrix.c (csc_transpose): new function * src/Mutils.c (csc_sort_columns): perm/iperm confusion corrected (csc_components_transpose): new function 2004-02-06 Douglas Bates * src/triplet.c (triplet_validate): Fix Dim slot on generated triplets 2004-01-30 Douglas Bates * R/sscCrosstab.R (sscCrosstab): Added sscCrosstab generator function. * src/LU.h (MATRIX_LU_H): Add #ifndef #define ... #endif to this and all other .h files in src. * src/Makefile.win: This and other Makefile.win files contributed by Brian Ripley. 2004-01-27 Douglas Bates * R/syMatrix.R: Added methods for "%*%". * R/Hilbert.R (Hilbert): Changed Hilbert function to return a poMatrix object. 2004-01-26 Douglas Bates * man/sscChol-class.Rd,man/mm.Rd,man/y.Rd: Added man pages. 2004-01-25 Douglas Bates * inst/doc/Introduction.Rnw,Comparisons.Rnw: Added vignettes. * R/csc.R: Convert all cscMatrix classes to use Dim slot instead of nrow. 2003-12-31 Douglas Bates * src/taucs/taucs.h: Moved taucs.h, amd.h, and umfpack.h into subdirectories. 2003-12-08 Douglas Bates * src/taucs.h: Accidently referred to global header files instead of local files. 2003-12-04 Douglas Bates * R/AllClass.R: Lots of changes. Removed all the lapack++ code and methods and replaced all classes with S4 classes. 2003-04-19 Douglas Bates * R/det.R,man/det.Rd: Change name of det generic to determinant * src/R_LapackPP.cc: Change method of calculating determinants 2003-02-03 Douglas Bates * DESCRIPTION (Version): removed empty data directory as requested by CRAN maintainers. Changed version number and date. 2002-10-23 Douglas Bates * src/laindex.h: Applied patches from Brian Ripley for compilation under Windows. * Added configure.win and src/Makevars.win as requested by Brian Ripley. 2002-05-03 Douglas Bates * src/lamatrix.h: Removing pre-1.2.0 compatibility code per Kurt Hornik. 2002-04-24 Douglas Bates * configure.ac: Replaced configure.in with configure.ac contributed by Kurt Hornik. * aclocal.m4 (ac_clean_files): Replaced this with Kurt Hornik's version for R-1.5.0 2001-12-10 Douglas Bates * man/eigen.Rd: Removed the .Alias in the example Matrix/man/0000755000175100001440000000000012271765436012324 5ustar hornikusersMatrix/man/nMatrix-class.Rd0000644000175100001440000000703711415621066015334 0ustar hornikusers\name{nMatrix-class} \docType{class} \alias{nMatrix-class} \alias{show,nMatrix-method} \alias{coerce,matrix,nMatrix-method} \alias{coerce,nMatrix,matrix-method} \alias{coerce,nMatrix,dMatrix-method} \alias{coerce,dMatrix,nMatrix-method} \alias{coerce,nMatrix,lMatrix-method} \alias{coerce,lMatrix,nMatrix-method} % %\alias{coerce,dMatrix,dgeMatrix-method} % %% Group methods \alias{Arith,logical,nMatrix-method} \alias{Arith,nMatrix,logical-method} \alias{Arith,nMatrix,numeric-method} \alias{Arith,numeric,nMatrix-method} \alias{Compare,logical,nMatrix-method} \alias{Compare,nMatrix,logical-method} \alias{Compare,nMatrix,nMatrix-method} \alias{Compare,nMatrix,numeric-method} \alias{Compare,numeric,nMatrix-method} \alias{Logic,Matrix,nMatrix-method} \alias{Logic,nMatrix,Matrix-method} \alias{Logic,nMatrix,nMatrix-method} \alias{Logic,nMatrix,logical-method} \alias{Logic,nMatrix,numeric-method} \alias{Logic,logical,nMatrix-method} \alias{Logic,numeric,nMatrix-method} \alias{Ops,lMatrix,nMatrix-method} \alias{Ops,nMatrix,lMatrix-method} \alias{Ops,nMatrix,numeric-method} \alias{Ops,numeric,nMatrix-method} \alias{Summary,nMatrix-method} %\alias{which,nMatrix-method} % \title{Class "nMatrix" of Non-zero Pattern Matrices} \description{ The \code{nMatrix} class is the virtual \dQuote{mother} class of all \emph{\bold{n}on-zero pattern} (or simply \emph{patter\bold{n}}) matrices in the \pkg{Matrix} package. } %\section{Objects from the Class}{A virtual Class: No objects may be % created from it. %} \section{Slots}{ Common to \emph{all} matrix object in the package: \describe{ \item{\code{Dim}:}{Object of class \code{"integer"} - the dimensions of the matrix - must be an integer vector with exactly two non-negative values.} \item{\code{Dimnames}:}{list of length two; each component containing NULL or a \code{\link{character}} vector length equal the corresponding \code{Dim} element.} } } \section{Methods}{ There is a bunch of coercion methods (for \code{\link{as}(..)}), e.g., \describe{ \item{coerce}{\code{signature(from = "nMatrix", to = "matrix")}: ... } \item{coerce}{\code{signature(from = "nMatrix", to = "dMatrix")}: ... } \item{coerce}{\code{signature(from = "nMatrix", to = "lMatrix")}: ... } \item{coerce}{\code{signature(from = "matrix", to = "nMatrix")}: Note that these coercions (must) coerce \code{\link{NA}}s to non-zero, hence conceptually \code{TRUE}. This is particularly important when \code{\linkS4class{sparseMatrix}} objects are coerced to \code{"nMatrix"} and hence to \code{\linkS4class{nsparseMatrix}}. } \item{coerce}{\code{signature(from = "dMatrix", to = "nMatrix")}: ... } \item{coerce}{\code{signature(from = "lMatrix", to = "nMatrix")}: ... } }. Additional methods contain group mehods, such as \describe{ \item{Ops}{\code{signature(e1 = "nMatrix", e2 = "....")}, \dots} \item{Arith}{\code{signature(e1 = "nMatrix", e2 = "....")}, \dots} \item{Compare}{\code{signature(e1 = "nMatrix", e2 = "....")}, \dots} \item{Logic}{\code{signature(e1 = "nMatrix", e2 = "....")}, \dots} \item{Summary}{\code{signature(x = "nMatrix", "....")}, \dots} } } \seealso{ The classes \code{\linkS4class{lMatrix}}, \code{\linkS4class{nsparseMatrix}}, and the mother class, \code{\linkS4class{Matrix}}. } \examples{ getClass("nMatrix") L3 <- Matrix(upper.tri(diag(3))) L3 # an "ltCMatrix" as(L3, "nMatrix") # -> ntC* ## similar, not using Matrix() as(upper.tri(diag(3)), "nMatrix")# currently "ngTMatrix" } \keyword{classes} \keyword{algebra} Matrix/man/MatrixFactorization-class.Rd0000644000175100001440000000364712210462526017714 0ustar hornikusers\name{MatrixFactorization-class} \alias{MatrixFactorization-class} \alias{CholeskyFactorization-class} \docType{class} \title{Class "MatrixFactorization" of Matrix Factorizations} % \alias{dim,MatrixFactorization-method} \alias{expand,MatrixFactorization-method} \alias{show,MatrixFactorization-method} %\alias{solve,MatrixFactorization,ANY-method}--> solve-methods.Rd \description{ The class \code{"MatrixFactorization"} is the virtual (super) class of (potentially) all matrix factorizations of matrices from package \pkg{Matrix}. The class \code{"CholeskyFactorization"} is the virtual class of all Cholesky decompositions from \pkg{Matrix} (and trivial sub class of \code{"MatrixFactorization"}). } \section{Objects from the Class}{A virtual Class: No objects may be created from it.} \section{Slots}{ \describe{ \item{\code{Dim}:}{Object of class \code{"integer"} - the dimensions of the original matrix - must be an integer vector with exactly two non-negative values.} } } \section{Methods}{ \describe{ \item{dim}{\code{(x)} simply returns \code{x@Dim}, see above.} \item{expand}{\code{signature(x = "MatrixFactorization")}: this has not been implemented yet for all matrix factorizations. It should return a list whose components are matrices which when multiplied return the original \code{\linkS4class{Matrix}} object.} \item{show}{\code{signature(object = "MatrixFactorization")}: simple printing, see \code{\link{show}}.} \item{solve}{\code{signature(a = "MatrixFactorization", b= .)}: solve \eqn{A x = b} for \eqn{x}; see \code{\link{solve-methods}}.} } } \seealso{ classes inheriting from \code{"MatrixFactorization"}, such as \code{\linkS4class{LU}}, \code{\linkS4class{Cholesky}}, \code{\linkS4class{CHMfactor}}, and \code{\linkS4class{sparseQR}}. } \examples{ showClass("MatrixFactorization") getClass("CholeskyFactorization") } \keyword{classes} Matrix/man/facmul.Rd0000644000175100001440000000352610027645165014061 0ustar hornikusers\name{facmul} \title{Multiplication by Decomposition Factors} \usage{ facmul(x, factor, y, transpose, left, \dots) } \alias{facmul} \alias{facmul.default} \description{ Performs multiplication by factors for certain decompositions (and allows explicit formation of those factors). } \arguments{ \item{x}{ a matrix decomposition. No missing values or IEEE special values are allowed. } \item{factor}{ an indicator for selecting a particular factor for multiplication. } \item{y}{ a matrix or vector to be multiplied by the factor or its transpose. No missing values or IEEE special values are allowed. } \item{transpose}{ a logical value. When \code{FALSE} (the default) the factor is applied. When \code{TRUE} the transpose of the factor is applied. } \item{left}{ a logical value. When \code{TRUE} (the default) the factor is applied from the left. When \code{FALSE} the factor is applied from the right. } \item{...}{ the method for \code{"qr.Matrix"} has additional arguments. } } \value{ the product of the selected factor (or its transpose) and \code{y} } \section{NOTE}{ Factors for decompositions such as \code{lu} and \code{qr} can be stored in a compact form. The function \code{facmul} allows multiplication without explicit formation of the factors, saving both storage and operations. } \references{ Golub, G., and Van Loan, C. F. (1989). \emph{Matrix Computations,} 2nd edition, Johns Hopkins, Baltimore. } % \seealso{ % \code{\link{facmul.lu.Matrix}}, \code{\link{facmul.lu.Hermitian}}, \code{\link{facmul.qr.Matrix}}, \code{\link{expand}}. % } \examples{ library(Matrix) x <- Matrix(rnorm(9), 3, 3) \dontrun{ qrx <- qr(x) # QR factorization of x y <- rnorm(3) facmul( qr(x), factor = "Q", y) # form Q y } } \keyword{array} \keyword{algebra} Matrix/man/lsparseMatrix-classes.Rd0000644000175100001440000001740612271746775017121 0ustar hornikusers\name{lsparseMatrix-classes} \title{Sparse logical matrices} \docType{class} \alias{lsparseMatrix-class} \alias{lgCMatrix-class} \alias{ltCMatrix-class} \alias{lsCMatrix-class} \alias{lgRMatrix-class} \alias{ltRMatrix-class} \alias{lsRMatrix-class} \alias{lgTMatrix-class} \alias{ltTMatrix-class} \alias{lsTMatrix-class} % Group(like) \alias{Ops,lsparseMatrix,lsparseMatrix-method} \alias{Arith,lsparseMatrix,Matrix-method} \alias{Arith,Matrix,lsparseMatrix-method} \alias{Arith,lgCMatrix,lgCMatrix-method} \alias{Arith,lgTMatrix,lgTMatrix-method} \alias{Compare,lsparseMatrix,lsparseMatrix-method} \alias{Logic,lsparseMatrix,lsparseMatrix-method} \alias{Logic,lgCMatrix,lgCMatrix-method} \alias{Logic,lgTMatrix,lgTMatrix-method} \alias{Logic,lsCMatrix,lsCMatrix-method} \alias{Logic,ltCMatrix,ltCMatrix-method} \alias{-,lsparseMatrix,missing-method} \alias{!,lsparseMatrix-method} % \alias{coerce,lsparseMatrix,matrix-method} \alias{coerce,lsparseMatrix,dsparseMatrix-method} \alias{coerce,lgCMatrix,dgCMatrix-method} \alias{coerce,lgCMatrix,lgTMatrix-method} \alias{coerce,lgCMatrix,lgeMatrix-method} \alias{coerce,lgCMatrix,lsCMatrix-method} \alias{coerce,lgCMatrix,ltCMatrix-method} \alias{coerce,lgCMatrix,matrix-method} \alias{coerce,lgTMatrix,dgTMatrix-method} \alias{coerce,lgTMatrix,lgCMatrix-method} \alias{coerce,lgTMatrix,lgeMatrix-method} \alias{coerce,lgTMatrix,lsCMatrix-method} \alias{coerce,lgTMatrix,triangularMatrix-method} \alias{coerce,lgTMatrix,symmetricMatrix-method} \alias{coerce,lgTMatrix,ltTMatrix-method} \alias{coerce,lgTMatrix,matrix-method} \alias{coerce,lsCMatrix,dgTMatrix-method} \alias{coerce,lsCMatrix,dsCMatrix-method} \alias{coerce,lsCMatrix,generalMatrix-method} \alias{coerce,lsCMatrix,lgCMatrix-method} \alias{coerce,lsCMatrix,lgTMatrix-method} \alias{coerce,lsCMatrix,lsTMatrix-method} \alias{coerce,lsCMatrix,matrix-method} \alias{coerce,lsTMatrix,dsTMatrix-method} \alias{coerce,lsTMatrix,lgCMatrix-method} \alias{coerce,lsTMatrix,lgTMatrix-method} \alias{coerce,lsTMatrix,lsCMatrix-method} \alias{coerce,lsTMatrix,lsyMatrix-method} \alias{coerce,lsTMatrix,matrix-method} \alias{coerce,ltCMatrix,dMatrix-method} \alias{coerce,ltCMatrix,dtCMatrix-method} \alias{coerce,ltCMatrix,lgCMatrix-method} \alias{coerce,ltCMatrix,ltTMatrix-method} \alias{coerce,ltCMatrix,matrix-method} \alias{coerce,ltTMatrix,dtTMatrix-method} \alias{coerce,ltTMatrix,generalMatrix-method} \alias{coerce,ltTMatrix,lgCMatrix-method} \alias{coerce,ltTMatrix,lgTMatrix-method} \alias{coerce,ltTMatrix,ltCMatrix-method} \alias{coerce,ltTMatrix,ltrMatrix-method} \alias{coerce,ltTMatrix,matrix-method} \alias{coerce,matrix,lgCMatrix-method} \alias{coerce,matrix,lgTMatrix-method} \alias{coerce,matrix,lsCMatrix-method} \alias{coerce,matrix,ltCMatrix-method} \alias{coerce,matrix,ltTMatrix-method} % \alias{t,lgCMatrix-method} \alias{t,lgTMatrix-method} \alias{t,lsCMatrix-method} \alias{t,ltCMatrix-method} \alias{t,lsTMatrix-method} \alias{t,ltTMatrix-method} \alias{which,lgTMatrix-method} \alias{which,lsparseMatrix-method} \alias{which,lsparseVector-method} \alias{which,lsTMatrix-method} \alias{which,ltTMatrix-method} % \description{The \code{lsparseMatrix} class is a virtual class of sparse matrices with \code{TRUE}/\code{FALSE} entries. Only the positions of the elements that are \code{TRUE} are stored. These can be stored in the ``triplet'' form (classes \code{lgTMatrix}, \code{lsTMatrix}, and \code{ltTMatrix} which really contain pairs, not triplets) or in compressed column-oriented form (classes \code{lgCMatrix}, \code{lsCMatrix}, and \code{ltCMatrix}) or in compressed row-oriented form (classes \code{lgRMatrix}, \code{lsRMatrix}, and \code{ltRMatrix}). The second letter in the name of these non-virtual classes indicates \code{g}eneral, \code{s}ymmetric, or \code{t}riangular. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("lgCMatrix", ...)} and so on. More frequently objects are created by coercion of a numeric sparse matrix to the logical form for use in the symbolic analysis phase of an algorithm involving sparse matrices. Such algorithms often involve two phases: a symbolic phase wherein the positions of the non-zeros in the result are determined and a numeric phase wherein the actual results are calculated. During the symbolic phase only the positions of the non-zero elements in any operands are of interest, hence any numeric sparse matrices can be treated as logical sparse matrices. } \section{Slots}{ \describe{ \item{\code{x}:}{Object of class \code{"logical"}, i.e., either \code{TRUE}, \code{\link{NA}}, or \code{FALSE}.} \item{\code{uplo}:}{Object of class \code{"character"}. Must be either "U", for upper triangular, and "L", for lower triangular. Present in the triangular and symmetric classes but not in the general class.} \item{\code{diag}:}{Object of class \code{"character"}. Must be either \code{"U"}, for unit triangular (diagonal is all ones), or \code{"N"} for non-unit. The implicit diagonal elements are not explicitly stored when \code{diag} is \code{"U"}. Present in the triangular classes only.} \item{\code{p}:}{Object of class \code{"integer"} of pointers, one for each column (row), to the initial (zero-based) index of elements in the column. Present in compressed column-oriented and compressed row-oriented forms only.} \item{\code{i}:}{Object of class \code{"integer"} of length nnzero (number of non-zero elements). These are the row numbers for each TRUE element in the matrix. All other elements are FALSE. Present in triplet and compressed column-oriented forms only.} \item{\code{j}:}{Object of class \code{"integer"} of length nnzero (number of non-zero elements). These are the column numbers for each TRUE element in the matrix. All other elements are FALSE. Present in triplet and compressed column-oriented forms only.} \item{\code{Dim}:}{Object of class \code{"integer"} - the dimensions of the matrix.} } } \section{Methods}{ \describe{ \item{coerce}{\code{signature(from = "dgCMatrix", to = "lgCMatrix")}} \item{t}{\code{signature(x = "lgCMatrix")}: returns the transpose of \code{x}} \item{which}{\code{signature(x = "lsparseMatrix")}, semantically equivalent to \pkg{base} function \code{\link{which}(x, arr.ind)}; for details, see the \code{\linkS4class{lMatrix}} class documentation.} } } %\references{} %\author{} %\note{} \seealso{ the class \code{\linkS4class{dgCMatrix}} } \examples{ (m <- Matrix(c(0,0,2:0), 3,5, dimnames=list(LETTERS[1:3],NULL))) (lm <- (m > 1)) # lgC !lm # no longer sparse stopifnot(is(lm,"lsparseMatrix"), identical(!lm, m <= 1)) data(KNex) str(mmG.1 <- (KNex $ mm) > 0.1)# "lgC..." table(mmG.1@x)# however with many ``non-structural zeros'' ## from logical to nz_pattern -- okay when there are no NA's : nmG.1 <- as(mmG.1, "nMatrix") # <<< has "TRUE" also where mmG.1 had FALSE ## from logical to "double" dmG.1 <- as(mmG.1, "dMatrix") # has '0' and back: lmG.1 <- as(dmG.1, "lMatrix") # has no extra FALSE, i.e. drop0() included stopifnot(identical(nmG.1, as((KNex $ mm) != 0,"nMatrix")), validObject(lmG.1), all(lmG.1@x), # same "logical" but lmG.1 has no 'FALSE' in x slot: all(lmG.1 == mmG.1)) class(xnx <- crossprod(nmG.1))# "nsC.." class(xlx <- crossprod(mmG.1))# "dsC.." : numeric is0 <- (xlx == 0) mean(as.vector(is0))# 99.3\% zeros: quite sparse, but table(xlx@x == 0)# more than half of the entries are (non-structural!) 0 stopifnot(isSymmetric(xlx), isSymmetric(xnx), ## compare xnx and xlx : have the *same* non-structural 0s : sapply(slotNames(xnx), function(n) identical(slot(xnx, n), slot(xlx, n)))) } \keyword{classes} \keyword{algebra} Matrix/man/dtpMatrix-class.Rd0000644000175100001440000000755012271746775015706 0ustar hornikusers\name{dtpMatrix-class} \title{Packed Triangular Dense Matrices - "dtpMatrix"} \docType{class} \alias{dtpMatrix-class} \alias{coerce,dtpMatrix,dtTMatrix-method} \alias{coerce,dtpMatrix,dtrMatrix-method} \alias{coerce,dtpMatrix,ltpMatrix-method} \alias{coerce,dtpMatrix,matrix-method} \alias{coerce,matrix,dtpMatrix-method} \alias{determinant,dtpMatrix,missing-method} \alias{determinant,dtpMatrix,logical-method} \alias{diag,dtpMatrix-method} \alias{diag<-,dtpMatrix-method} \alias{norm,dtpMatrix,character-method} \alias{norm,dtpMatrix,missing-method} \alias{rcond,dtpMatrix,character-method} \alias{rcond,dtpMatrix,missing-method} %\alias{solve,dtpMatrix,...-method}%--> solve-methods.Rd \alias{t,dtpMatrix-method} \description{The \code{"dtpMatrix"} class is the class of triangular, dense, numeric matrices in packed storage. The \code{"dtrMatrix"} class is the same except in nonpacked storage.} \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("dtpMatrix", ...)} or by coercion from other classes of matrices. } \section{Slots}{ \describe{ \item{\code{uplo}:}{Object of class \code{"character"}. Must be either "U", for upper triangular, and "L", for lower triangular.} \item{\code{diag}:}{Object of class \code{"character"}. Must be either \code{"U"}, for unit triangular (diagonal is all ones), or \code{"N"}; see \code{\linkS4class{triangularMatrix}}.} \item{\code{x}:}{Object of class \code{"numeric"}. The numeric values that constitute the matrix, stored in column-major order. For a packed square matrix of dimension \eqn{d \times d}{d * d}, \code{length(x)} is of length \eqn{d(d+1)/2} (also when \code{diag == "U"}!).} \item{\code{Dim},\code{Dimnames}:}{The dimension (a length-2 \code{"integer"}) and corresponding names (or \code{NULL}), inherited from the \code{\linkS4class{Matrix}}, see there.} } } \section{Extends}{ Class \code{"ddenseMatrix"}, directly. Class \code{"triangularMatrix"}, directly. Class \code{"dMatrix"} and more by class \code{"ddenseMatrix"} etc, see the examples. } \section{Methods}{ \describe{ \item{\%*\%}{\code{signature(x = "dtpMatrix", y = "dgeMatrix")}: Matrix multiplication; ditto for several other signature combinations, see \code{showMethods("\%*\%", class = "dtpMatrix")}.} \item{coerce}{\code{signature(from = "dtpMatrix", to = "dtrMatrix")}} \item{coerce}{\code{signature(from = "dtpMatrix", to = "matrix")}} \item{determinant}{\code{signature(x = "dtpMatrix", logarithm = "logical")}: the \code{\link{determinant}(x)} trivially is \code{prod(diag(x))}, but computed on log scale to prevent over- and underflow.} \item{diag}{\code{signature(x = "dtpMatrix")}: ... } \item{norm}{\code{signature(x = "dtpMatrix", type = "character")}: ... } \item{rcond}{\code{signature(x = "dtpMatrix", norm = "character")}: ... } \item{solve}{\code{signature(a = "dtpMatrix", b = "...")}: efficiently using internal backsolve or forwardsolve, see \code{\link{solve-methods}}.} \item{t}{\code{signature(x = "dtpMatrix")}: \code{t(x)} remains a \code{"dtpMatrix"}, lower triangular if \code{x} is upper triangular, and vice versa.} } } \seealso{ Class \code{\linkS4class{dtrMatrix}} } \examples{ showClass("dtrMatrix") example("dtrMatrix-class", echo=FALSE) (p1 <- as(T2, "dtpMatrix")) str(p1) (pp <- as(T, "dtpMatrix")) ip1 <- solve(p1) stopifnot(length(p1@x) == 3, length(pp@x) == 3, p1 @ uplo == T2 @ uplo, pp @ uplo == T @ uplo, identical(t(pp), p1), identical(t(p1), pp), all((l.d <- p1 - T2) == 0), is(l.d, "dtpMatrix"), all((u.d <- pp - T ) == 0), is(u.d, "dtpMatrix"), l.d@uplo == T2@uplo, u.d@uplo == T@uplo, identical(t(ip1), solve(pp)), is(ip1, "dtpMatrix"), all.equal(as(solve(p1,p1), "diagonalMatrix"), Diagonal(2))) } \keyword{classes} Matrix/man/ldenseMatrix-class.Rd0000644000175100001440000000362312271746775016366 0ustar hornikusers\name{ldenseMatrix-class} \title{Virtual Class "ldenseMatrix" of Dense Logical Matrices} \docType{class} \alias{ldenseMatrix-class} % Group \alias{!,ldenseMatrix-method} \alias{Ops,ldenseMatrix,ldenseMatrix-method} \alias{Logic,ldenseMatrix,lsparseMatrix-method} \alias{Logic,lsparseMatrix,ldenseMatrix-method} % purely "sparse" are in ./lsparseMatrix-classes.Rd %%-- Matrix products: ---> ./matrix-products.Rd \alias{as.logical,ldenseMatrix-method} \alias{as.vector,ldenseMatrix,missing-method} \alias{coerce,matrix,ldenseMatrix-method} \alias{coerce,ldenseMatrix,matrix-method} \alias{diag,ldenseMatrix-method} \alias{norm,ldenseMatrix,character-method} \alias{which,ldenseMatrix-method} \description{ \code{ldenseMatrix} is the virtual class of all dense \bold{l}ogical (S4) matrices. It extends both \code{\linkS4class{denseMatrix}} and \code{\linkS4class{lMatrix}} directly. } \section{Slots}{ \describe{ \item{\code{x}:}{logical vector containing the entries of the matrix.} \item{\code{Dim}, \code{Dimnames}:}{see \code{\linkS4class{Matrix}}.} } } \section{Extends}{ Class \code{"lMatrix"}, directly. Class \code{"denseMatrix"}, directly. Class \code{"Matrix"}, by class \code{"lMatrix"}. Class \code{"Matrix"}, by class \code{"denseMatrix"}. } \section{Methods}{ \describe{ \item{coerce}{\code{signature(from = "matrix", to = "ldenseMatrix")}: ... } \item{coerce}{\code{signature(from = "ldenseMatrix", to = "matrix")}: ... } \item{as.vector}{\code{signature(x = "ldenseMatrix", mode = "missing")}: ...} \item{which}{\code{signature(x = "ndenseMatrix")}, semantically equivalent to \pkg{base} function \code{\link{which}(x, arr.ind)}; for details, see the \code{\linkS4class{lMatrix}} class documentation.} } } \seealso{ Class \code{\linkS4class{lgeMatrix}} and the other subclasses. } \examples{ showClass("ldenseMatrix") as(diag(3) > 0, "ldenseMatrix") } \keyword{classes} Matrix/man/dtCMatrix-class.Rd0000644000175100001440000001232612271746775015626 0ustar hornikusers\name{dtCMatrix-class} \title{Triangular, (compressed) sparse column matrices} \docType{class} \alias{dtCMatrix-class}% C and \alias{dtTMatrix-class}% T % \alias{coerce,dtCMatrix,dgCMatrix-method} \alias{coerce,dtCMatrix,dgeMatrix-method} \alias{coerce,dtCMatrix,dgTMatrix-method} \alias{coerce,dtCMatrix,dsCMatrix-method} \alias{coerce,dtCMatrix,dtTMatrix-method} \alias{coerce,dtCMatrix,dtrMatrix-method} \alias{coerce,dtCMatrix,ltCMatrix-method} \alias{coerce,dtCMatrix,ntCMatrix-method} \alias{coerce,dtCMatrix,TsparseMatrix-method} \alias{coerce,dtCMatrix,matrix-method} \alias{coerce,dtTMatrix,dgTMatrix-method} \alias{coerce,dtTMatrix,dgeMatrix-method} \alias{coerce,dtTMatrix,dtCMatrix-method} \alias{coerce,dtTMatrix,dtrMatrix-method} %no longer\alias{coerce,dtTMatrix,ltTMatrix-method} %no longer\alias{coerce,dtTMatrix,ntTMatrix-method} \alias{coerce,dtTMatrix,generalMatrix-method} \alias{coerce,dtTMatrix,matrix-method} \alias{coerce,matrix,dtCMatrix-method} \alias{coerce,matrix,dtTMatrix-method} %% Group methods \alias{Arith,dtCMatrix,dtCMatrix-method} % %\alias{solve,dtCMatrix,...-method}%--> solve-methods.Rd \alias{t,dtCMatrix-method} \alias{t,dtTMatrix-method} \description{The \code{"dtCMatrix"} class is a class of triangular, sparse matrices in the compressed, column-oriented format. In this implementation the non-zero elements in the columns are sorted into increasing row order. The \code{"dtTMatrix"} class is a class of triangular, sparse matrices in triplet format.} \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("dtCMatrix", ...)} or calls of the form \code{new("dtTMatrix", ...)}, but more typically automatically via \code{\link{Matrix}()} or coercion such as \code{as(x, "dtCMatrix")}. } \section{Slots}{ \describe{ \item{\code{uplo}:}{Object of class \code{"character"}. Must be either "U", for upper triangular, and "L", for lower triangular.} \item{\code{diag}:}{Object of class \code{"character"}. Must be either \code{"U"}, for unit triangular (diagonal is all ones), or \code{"N"}; see \code{\linkS4class{triangularMatrix}}.} \item{\code{p}:}{(only present in \code{"dtCMatrix"}:) an \code{\link{integer}} vector for providing pointers, one for each column, see the detailed description in \code{\linkS4class{CsparseMatrix}}.} \item{\code{i}:}{Object of class \code{"integer"} of length nnzero (number of non-zero elements). These are the row numbers for each non-zero element in the matrix.} \item{\code{j}:}{Object of class \code{"integer"} of length nnzero (number of non-zero elements). These are the column numbers for each non-zero element in the matrix. (Only present in the \code{dtTMatrix} class.)} \item{\code{x}:}{Object of class \code{"numeric"} - the non-zero elements of the matrix.} \item{\code{Dim},\code{Dimnames}:}{The dimension (a length-2 \code{"integer"}) and corresponding names (or \code{NULL}), inherited from the \code{\linkS4class{Matrix}}, see there.} } } \section{Extends}{ Class \code{"dgCMatrix"}, directly. Class \code{"triangularMatrix"}, directly. Class \code{"dMatrix"}, \code{"sparseMatrix"}, and more by class \code{"dgCMatrix"} etc, see the examples. } \section{Methods}{ \describe{ \item{coerce}{\code{signature(from = "dtCMatrix", to = "dgTMatrix")}} \item{coerce}{\code{signature(from = "dtCMatrix", to = "dgeMatrix")}} \item{coerce}{\code{signature(from = "dtTMatrix", to = "dgeMatrix")}} \item{coerce}{\code{signature(from = "dtTMatrix", to = "dtrMatrix")}} \item{coerce}{\code{signature(from = "dtTMatrix", to = "matrix")}} \item{solve}{\code{signature(a = "dtCMatrix", b = "....")}: sparse triangular solve (aka \dQuote{backsolve} or \dQuote{forwardsolve}), see \code{\link{solve-methods}}.} \item{t}{\code{signature(x = "dtCMatrix")}: returns the transpose of \code{x}} \item{t}{\code{signature(x = "dtTMatrix")}: returns the transpose of \code{x}} } } %\references{} %\author{} %\note{} \seealso{ Classes \code{\linkS4class{dgCMatrix}}, \code{\linkS4class{dgTMatrix}}, \code{\linkS4class{dgeMatrix}}, and \code{\linkS4class{dtrMatrix}}. } \examples{ showClass("dtCMatrix") showClass("dtTMatrix") t1 <- new("dtTMatrix", x= c(3,7), i= 0:1, j=3:2, Dim= as.integer(c(4,4))) t1 ## from 0-diagonal to unit-diagonal {low-level step}: tu <- t1 ; tu@diag <- "U" tu (cu <- as(tu, "dtCMatrix")) str(cu)# only two entries in @i and @x stopifnot(cu@i == 1:0, all(2 * symmpart(cu) == Diagonal(4) + forceSymmetric(cu))) t1[1,2:3] <- -1:-2 diag(t1) <- 10*c(1:2,3:2) t1 # still triangular (it1 <- solve(t1)) t1. <- solve(it1) all(abs(t1 - t1.) < 10 * .Machine$double.eps) ## 2nd example U5 <- new("dtCMatrix", i= c(1L, 0:3), p=c(0L,0L,0:2, 5L), Dim = c(5L, 5L), x = rep(1, 5), diag = "U") U5 (iu <- solve(U5)) # contains one '0' validObject(iu2 <- solve(U5, Diagonal(5)))# failed in earlier versions I5 <- iu \%*\% U5 # should equal the identity matrix i5 <- iu2 \%*\% U5 asDiag <- function(M) as(drop0(M), "diagonalMatrix") stopifnot( all.equal(Diagonal(5), asDiag(I5), tolerance=1e-14) , all.equal(Diagonal(5), asDiag(i5), tolerance=1e-14) )} \keyword{classes} \keyword{algebra} Matrix/man/symmetricMatrix-class.Rd0000644000175100001440000000407212213673171017110 0ustar hornikusers\name{symmetricMatrix-class} \docType{class} \alias{symmetricMatrix-class} \alias{coerce,matrix,symmetricMatrix-method} \alias{coerce,denseMatrix,symmetricMatrix-method} \alias{coerce,CsparseMatrix,symmetricMatrix-method} % \title{Virtual Class of Symmetric Matrices in package:Matrix} \description{ The virtual class of symmetric matrices, \code{"symmetricMatrix"}, from the package \pkg{Matrix} contains numeric and logical, dense and sparse matrices, e.g., see the examples. The main use is in methods (and C functions) that can deal with all symmetric matrices. } % \section{Objects from the Class}{A virtual Class: No objects may be created from it.} \section{Slots}{ \describe{ \item{\code{uplo}:}{Object of class \code{"character"}. Must be either "U", for upper triangular, and "L", for lower triangular.} %% below {Dim, Dimnames} work around Slot parsing buglet (< 2.2.0) %% \item{\code{Dim},\code{Dimnames}:}{The dimension (a length-2 \item{\code{Dim, Dimnames}:}{The dimension (a length-2 \code{"integer"}) and corresponding names (or \code{NULL}), inherited from the \code{\linkS4class{Matrix}}, see there.} \item{\code{factors}:}{a list of matrix factorizations, also from the \code{Matrix} class.} } } \section{Extends}{ Class \code{"Matrix"}, directly. } \section{Methods}{ There's a C function \code{symmetricMatrix_validity()} called by the internal validity checking functions. %% Currently: %% No methods defined with class "symmetricMatrix" in the signature. } \seealso{ \code{\link{isSymmetric}} which has efficient methods (\link{isSymmetric-methods}) for the \pkg{Matrix} classes. Classes \code{\linkS4class{triangularMatrix}}, and, e.g., \code{\linkS4class{dsyMatrix}} for numeric \emph{dense} matrices, or \code{\linkS4class{lsCMatrix}} for a logical \emph{sparse} matrix class. } \examples{ showClass("symmetricMatrix") ## The names of direct subclasses: scl <- getClass("symmetricMatrix")@subclasses directly <- sapply(lapply(scl, slot, "by"), length) == 0 names(scl)[directly] } \keyword{classes} Matrix/man/solve-methods.Rd0000644000175100001440000002745312271746775015424 0ustar hornikusers\name{solve-methods} \title{Methods in Package Matrix for Function \code{solve()}} \docType{methods} \alias{solve}%- catch ?solve too (is important enough) \alias{solve-methods} \alias{solve,ANY,Matrix-method} \alias{solve,CHMfactor,ANY-method} \alias{solve,CHMfactor,ddenseMatrix-method} \alias{solve,CHMfactor,diagonalMatrix-method} \alias{solve,CHMfactor,dsparseMatrix-method} \alias{solve,CHMfactor,matrix-method} \alias{solve,CHMfactor,missing-method} \alias{solve,CHMfactor,numeric-method} \alias{solve,ddenseMatrix,ANY-method} \alias{solve,ddenseMatrix,matrix-method} \alias{solve,ddenseMatrix,Matrix-method} \alias{solve,ddenseMatrix,missing-method} \alias{solve,ddenseMatrix,numeric-method} \alias{solve,denseLU,missing-method} \alias{solve,dgCMatrix,ddenseMatrix-method} \alias{solve,dgCMatrix,dsparseMatrix-method} \alias{solve,dgCMatrix,matrix-method} \alias{solve,dgCMatrix,missing-method} \alias{solve,dgeMatrix,ddenseMatrix-method} \alias{solve,dgeMatrix,matrix-method} \alias{solve,dgeMatrix,missing-method} \alias{solve,dgeMatrix,sparseMatrix-method} \alias{solve,diagonalMatrix,matrix-method} \alias{solve,diagonalMatrix,Matrix-method} \alias{solve,diagonalMatrix,missing-method} \alias{solve,dpoMatrix,dgeMatrix-method} \alias{solve,dpoMatrix,matrix-method} \alias{solve,dpoMatrix,missing-method} \alias{solve,dppMatrix,dgeMatrix-method} \alias{solve,dppMatrix,integer-method} \alias{solve,dppMatrix,matrix-method} \alias{solve,dppMatrix,missing-method} \alias{solve,dsCMatrix,ddenseMatrix-method} \alias{solve,dsCMatrix,denseMatrix-method} \alias{solve,dsCMatrix,dsparseMatrix-method} \alias{solve,dsCMatrix,matrix-method} \alias{solve,dsCMatrix,missing-method} \alias{solve,dsCMatrix,numeric-method} \alias{solve,dspMatrix,ddenseMatrix-method} \alias{solve,dspMatrix,matrix-method} \alias{solve,dspMatrix,missing-method} \alias{solve,dsyMatrix,ddenseMatrix-method} \alias{solve,dsyMatrix,denseMatrix-method} \alias{solve,dsyMatrix,matrix-method} \alias{solve,dsyMatrix,missing-method} \alias{solve,dtCMatrix,CsparseMatrix-method} \alias{solve,dtCMatrix,dgeMatrix-method} \alias{solve,dtCMatrix,matrix-method} \alias{solve,dtCMatrix,missing-method} \alias{solve,dtCMatrix,numeric-method} \alias{solve,dtpMatrix,ddenseMatrix-method} \alias{solve,dtpMatrix,matrix-method} \alias{solve,dtpMatrix,missing-method} \alias{solve,dtrMatrix,ddenseMatrix-method} \alias{solve,dtrMatrix,dMatrix-method} \alias{solve,dtrMatrix,matrix-method} \alias{solve,dtrMatrix,Matrix-method} \alias{solve,dtrMatrix,missing-method} \alias{solve,Matrix,ANY-method} \alias{solve,Matrix,diagonalMatrix-method} \alias{solve,matrix,Matrix-method} \alias{solve,Matrix,matrix-method} \alias{solve,Matrix,missing-method} \alias{solve,Matrix,numeric-method} \alias{solve,Matrix,pMatrix-method} \alias{solve,Matrix,sparseVector-method} \alias{solve,MatrixFactorization,ANY-method} \alias{solve,MatrixFactorization,missing-method} \alias{solve,MatrixFactorization,numeric-method} \alias{solve,pMatrix,matrix-method} \alias{solve,pMatrix,Matrix-method} \alias{solve,pMatrix,missing-method} \alias{solve,sparseQR,ANY-method} \alias{solve,TsparseMatrix,ANY-method} \alias{solve,TsparseMatrix,missing-method} \description{ Methods for function \code{\link{solve}} to solve a linear system of equations, or equivalently, solve for \eqn{X} in \deqn{A X = B} where \eqn{A} is a square matrix, and \eqn{X}, \eqn{B} are matrices or vectors (which are treated as 1-column matrices), and the \R syntax is \preformatted{ X <- solve(A,B) } In \code{solve(a,b)} in the \pkg{Matrix} package, \code{a} may also be a \code{\linkS4class{MatrixFactorization}} instead of directly a matrix. } \usage{% usage for those methods which have "surprising arguments" \S4method{solve}{CHMfactor,ddenseMatrix}(a, b, system = c("A", "LDLt", "LD", "DLt", "L", "Lt", "D", "P", "Pt"), \dots) \S4method{solve}{dgCMatrix,matrix}(a, b, sparse = FALSE, tol = .Machine$double.eps, \dots) solve(a, b, ...) ## *the* two-argument version, almost always preferred to # solve(a) ## the *rarely* needed one-argument version % ^ must comment the above; otherwise 'R CMD check' waffles ... } \arguments{ \item{a}{a square numeric matrix, \eqn{A}, typically of one of the classes in \pkg{Matrix}. Logical matrices are coerced to corresponding numeric ones.} \item{b}{numeric vector or matrix (dense or sparse) as RHS of the linear system \eqn{Ax = b}.} \item{system}{only if \code{a} is a \code{\linkS4class{CHMfactor}}: character string indicating the kind of linear system to be solved, see below. Note that the default, \code{"A"}, does \emph{not} solve the triangular system (but \code{"L"} does).} \item{sparse}{only when \code{a} is a \code{\linkS4class{sparseMatrix}}, i.e., typically a \code{\linkS4class{dgCMatrix}}: logical specifying if the result should be a (formally) sparse matrix.}%% FIXME: mention %% pos.definite etc \item{tol}{only used when \code{a} is sparse, in the \code{\link{isSymmetric}(a, tol=*)} test, where that applies.} \item{\dots}{potentially further arguments to the methods.} } \section{Methods}{ \describe{ \item{\code{signature(a = "ANY", b = "ANY")}}{is simply the \pkg{base} package's S3 generic \code{\link{solve}}.} %% This is copy-paste in CHMfactor-class.Rd {FIXME ?} \item{\code{signature(a = "CHMfactor", b = "...."), system= *}}{The \code{solve} methods for a \code{"\linkS4class{CHMfactor}"} object take an optional third argument \code{system} whose value can be one of the character strings \code{"A"}, \code{"LDLt"}, \code{"LD"}, \code{"DLt"}, \code{"L"}, \code{"Lt"}, \code{"D"}, \code{"P"} or \code{"Pt"}. This argument describes the system to be solved. The default, \code{"A"}, is to solve \eqn{Ax = b} for \eqn{x} where \code{A} is sparse, positive-definite matrix that was factored to produce \code{a}. Analogously, \code{system = "L"} returns the solution \eqn{x}, of \eqn{Lx = b}; similarly, for all system codes \bold{but} \code{"P"} and \code{"Pt"} where, e.g., \code{x <- solve(a, b,system="P")} is equivalent to \code{x <- P \%*\% b}. If \code{b} is a \code{\linkS4class{sparseMatrix}}, \code{system} is used as above the corresponding sparse CHOLMOD algorithm is called. } \item{\code{signature(a = "ddenseMatrix", b = "....")}}{(for all \code{b}) work via \code{as(a, "dgeMatrix")}, using the its methods, see below.} \item{\code{signature(a = "denseLU", b = "missing")}}{ basically computes uses triangular forward- and back-solve.} \item{\code{signature(a = "dgCMatrix", b = "matrix")}}{, and} %% -> ../R/dgCMatrix.R \item{\code{signature(a = "dgCMatrix", b = "ddenseMatrix")}}{with extra argument list \code{( sparse = FALSE, tol = .Machine$double.eps ) }: Uses the sparse \code{\link{lu}(a)} decomposition (which is cached in \code{a}'s \code{factor} slot). By default, \code{sparse=FALSE}, returns a \code{\linkS4class{denseMatrix}}, since \eqn{U^{-1} L^{-1} B} may not be sparse at all, even when \eqn{L} and \eqn{U} are. If \code{sparse=TRUE}, returns a \code{\linkS4class{sparseMatrix}} (which may not be very sparse at all, even if \code{a} \emph{was} sparse). } \item{\code{signature(a = "dgCMatrix", b = "dsparseMatrix")}}{, and} \item{\code{signature(a = "dgCMatrix", b = "missing")}}{with extra argument list \code{( sparse=FALSE, tol = .Machine$double.eps ) }: Checks if \code{a} is symmetric, and in that case, coerces it to \code{"\linkS4class{symmetricMatrix}"}, and then computes a \emph{sparse} solution via sparse Cholesky factorization, independently of the \code{sparse} argument. If \code{a} is not symmetric, the sparse \code{\link{lu}} decomposition is used and the result will be sparse or dense, depending on the \code{sparse} argument, exactly as for the above (\code{b = "ddenseMatrix"}) case. } \item{\code{signature(a = "dgeMatrix", b = ".....")}}{ solve the system via internal LU, calling LAPACK routines \code{dgetri} or \code{dgetrs}. } \item{\code{signature(a = "diagonalMatrix", b = "matrix")}}{and other \code{b}s: Of course this is trivially implemented, as \eqn{D^{-1}} is diagonal with entries \eqn{1 / D[i,i]}.} \item{\code{signature(a = "dpoMatrix", b = "....Matrix")}}{, and} \item{\code{signature(a = "dppMatrix", b = "....Matrix")}}{ The Cholesky decomposition of \code{a} is calculated (if needed) while solving the system.} \item{\code{signature(a = "dsCMatrix", b = "....")}}{% ../R/dsCMatrix.R All these methods first try Cholmod's Cholesky factorization; if that works, i.e., typically if \code{a} is positive semi-definite, it is made use of. Otherwise, the sparse LU decomposition is used as for the \dQuote{general} matrices of class \code{"dgCMatrix"}.} \item{\code{signature(a = "dspMatrix", b = "....")}}{, and} \item{\code{signature(a = "dsyMatrix", b = "....")}}{% ../R/dsyMatrix.R all end up calling LAPACK routines \code{dsptri}, \code{dsptrs}, \code{dsytrs} and \code{dsytri}. } \item{\code{signature(a = "dtCMatrix", b = "CsparseMatrix")}}{,} \item{\code{signature(a = "dtCMatrix", b = "dgeMatrix")}}{, etc sparse triangular solve, in traditional S/\R also known as \code{\link{backsolve}}, or \code{\link{forwardsolve}}. \code{solve(a,b)} is a \code{\linkS4class{sparseMatrix}} if \code{b} is, and hence a \code{\linkS4class{denseMatrix}} otherwise. } \item{\code{signature(a = "dtrMatrix", b = "ddenseMatrix")}}{, and} \item{\code{signature(a = "dtpMatrix", b = "matrix")}}{, and% ../R/dtrMatrix.R similar \code{b}, including \code{"missing"}, and \code{"diagonalMatrix"}: all use LAPACK based versions of efficient triangular \code{\link{backsolve}}, or \code{\link{forwardsolve}}. } \item{\code{signature(a = "Matrix", b = "diagonalMatrix")}}{ works via \code{as(b, "CsparseMatrix")}.} \item{\code{signature(a = "sparseQR", b = "ANY")}}{ simply uses \code{\link{qr.coef}(a, b)}.} \item{\code{signature(a = "pMatrix", b = ".....")}}{ these methods typically use \code{\link{crossprod}(a,b)}, as the inverse of a permutation matrix is the same as its transpose.} \item{\code{signature(a = "TsparseMatrix", b = "ANY")}}{ all work via \code{as(a, "CsparseMatrix")}.} } }%{Methods} \seealso{ \code{\link{solve}}, \code{\link{lu}}, and class documentations \code{\linkS4class{CHMfactor}}, \code{\linkS4class{sparseLU}}, and \code{\linkS4class{MatrixFactorization}}. } \examples{ ## A close to symmetric example with "quite sparse" inverse: n1 <- 7; n2 <- 3 dd <- data.frame(a = gl(n1,n2), b = gl(n2,1,n1*n2))# balanced 2-way X <- sparse.model.matrix(~ -1+ a + b, dd)# no intercept --> even sparser XXt <- tcrossprod(X) diag(XXt) <- rep(c(0,0,1,0), length.out = nrow(XXt)) n <- nrow(ZZ <- kronecker(XXt, Diagonal(x=c(4,1)))) image(a <- 2*Diagonal(n) + ZZ \%*\% Diagonal(x=c(10, rep(1, n-1)))) isSymmetric(a) # FALSE image(drop0(skewpart(a))) image(ia0 <- solve(a)) # checker board, dense [but really, a is singular!] try(solve(a, sparse=TRUE))##-> error [ TODO: assertError ] ia. <- solve(a, sparse=TRUE, tol = 1e-19)##-> *no* error if(R.version$arch == "x86_64") ## Fails on 32-bit [Fedora 19, R 3.0.2] from Matrix 1.1-0 on [FIXME ??] only stopifnot(all.equal(as.matrix(ia.), as.matrix(ia0))) a <- a + Diagonal(n) iad <- solve(a) ias <- solve(a, sparse=TRUE) stopifnot(all.equal(as(ias,"denseMatrix"), iad, tolerance=1e-14)) I. <- iad \%*\% a ; image(I.) I0 <- drop0(zapsmall(I.)); image(I0) .I <- a \%*\% iad .I0 <- drop0(zapsmall(.I)) stopifnot( all.equal(as(I0, "diagonalMatrix"), Diagonal(n)), all.equal(as(.I0,"diagonalMatrix"), Diagonal(n)) ) } \keyword{methods} Matrix/man/sparseVector.Rd0000644000175100001440000000242612021056575015265 0ustar hornikusers\name{sparseVector} \alias{sparseVector} \title{Sparse Vector Construction from Nonzero Entries} \description{ User friendly construction sparse vectors, i.e., objects inheriting from \code{\link{class}} \code{\linkS4class{sparseVector}}, from indices and values of its nonzero entries. } \details{ zero entries in \code{x} are dropped automatically, analogously as \code{\link{drop0}()} acts on sparse matrices. } \usage{ sparseVector(x, i, length) } \arguments{ \item{x}{vector of the non zero entries.} \item{i}{integer vector (of the same length as \code{x}) specifying the indices of the non-zero (or non-\code{TRUE}) entries of the sparse vector.} \item{length}{length of the sparse vector.} } \value{ a sparse vector, i.e., inheriting from \code{\link{class}} \code{\linkS4class{sparseVector}}. } \author{Martin Maechler} \seealso{ \code{\link{sparseMatrix}()} constructor for sparse matrices; the class \code{\linkS4class{sparseVector}}. } \examples{ str(sv <- sparseVector(x = 1:10, i = sample(999, 10), length=1000)) sx <- c(0,0,3, 3.2, 0,0,0,-3:1,0,0,2,0,0,5,0,0) ss <- as(sx, "sparseVector") stopifnot(identical(ss, sparseVector(x = c(2, -1, -2, 3, 1, -3, 5, 3.2), i = c(15L, 10:9, 3L,12L,8L,18L, 4L), length = 20L))) } \keyword{array} Matrix/man/chol.Rd0000644000175100001440000000751412271746775013554 0ustar hornikusers\name{chol} \title{Choleski Decomposition - 'Matrix' S4 Generic and Methods} \alias{chol} \alias{chol-methods} \alias{chol,Matrix-method} % dense methods \alias{chol,ddenseMatrix-method} \alias{chol,dgeMatrix-method} \alias{chol,dpoMatrix-method} \alias{chol,dppMatrix-method} % diagonal \alias{chol,ddiMatrix-method} \alias{chol,ldiMatrix-method} % sparse methods \alias{chol,dsparseMatrix-method} \alias{chol,dsCMatrix-method} \alias{chol,dsCMatrix-method} \alias{chol,lsCMatrix-method} \alias{chol,lsCMatrix-method} \alias{chol,nsCMatrix-method} \alias{chol,nsCMatrix-method} % \description{ Compute the Choleski factorization of a real symmetric positive-definite square matrix. } \usage{ chol(x, \dots) \S4method{chol}{dsCMatrix}(x, pivot = FALSE, \dots) } \arguments{ \item{x}{a (sparse or dense) square matrix, here inheriting from class \code{\linkS4class{Matrix}}; if \code{x} is not positive definite, an error is signalled.} \item{pivot}{logical indicating if pivoting is to be used.} \item{\dots}{potentially further arguments passed to methods.} } % \details{ % } \section{Methods}{ Use \code{\link{showMethods}(chol)} to see all; some are worth mentioning here: \describe{ \item{chol}{\code{signature(x = "dgeMatrix")}: works via \code{"dpoMatrix"}, see class \code{\linkS4class{dpoMatrix}}.} \item{chol}{\code{signature(x = "dpoMatrix")}: Returns (and stores) the Cholesky decomposition of \code{x}, via LAPACK routines \code{dlacpy} and \code{dpotrf}.} \item{chol}{\code{signature(x = "dppMatrix")}: Returns (and stores) the Cholesky decomposition via LAPACK routine \code{dpptrf}.} \item{chol}{\code{signature(x = "dsCMatrix", pivot = "logical")}: Returns (and stores) the Cholesky decomposition of \code{x}. If \code{pivot} is \code{TRUE} (the default) the Approximate Minimal Degree (AMD) algorithm is used to create a reordering of the rows and columns of \code{x} so as to reduce fill-in.} } } \value{ a matrix of class \code{\linkS4class{Cholesky}}, i.e., upper triangular: \eqn{R} such that \eqn{R'R = x}. } \references{ Timothy A. Davis (2006) \emph{Direct Methods for Sparse Linear Systems}, SIAM Series \dQuote{Fundamentals of Algorithms}. Tim Davis (1996), An approximate minimal degree ordering algorithm, \emph{SIAM J. Matrix Analysis and Applications}, \bold{17}, 4, 886--905. } \seealso{The default from \pkg{base}, \code{\link[base]{chol}}. } \examples{ showMethods(chol, inherited = FALSE) # show different methods sy2 <- new("dsyMatrix", Dim = as.integer(c(2,2)), x = c(14, NA,32,77)) (c2 <- chol(sy2))#-> "Cholesky" matrix stopifnot(all.equal(c2, chol(as(sy2, "dpoMatrix")), tolerance= 1e-13)) str(c2) ## An example where chol() can't work (sy3 <- new("dsyMatrix", Dim = as.integer(c(2,2)), x = c(14, -1, 2, -7))) try(chol(sy3)) # error, since it is not positive definite ## A sparse example --- exemplifying 'pivot' (mm <- toeplitz(as(c(10, 0, 1, 0, 3), "sparseVector"))) # 5 x 5 (R <- chol(mm)) ## default: pivot = FALSE R2 <- chol(mm, pivot=FALSE) stopifnot( identical(R, R2), all.equal(crossprod(R), mm) ) (R. <- chol(mm, pivot=TRUE))# nice band structure, ## but of course crossprod(R.) is *NOT* equal to mm ## --> see Cholesky() and its examples, for the pivot structure & factorization stopifnot(all.equal(sqrt(det(mm)), det(R)), all.equal(prod(diag(R)), det(R)), all.equal(prod(diag(R.)), det(R))) ## a second, even sparser example: (M2 <- toeplitz(as(c(1,.5, rep(0,12), -.1), "sparseVector"))) c2 <- chol(M2) C2 <- chol(M2, pivot=TRUE) ## check the caching of the factorizations: spd <- as(M2@factors[["spdCholesky"]], "Matrix") sPd <- as(M2@factors[["sPdCholesky"]], "Matrix") stopifnot(identical(t(spd), c2), all.equal(t(sPd), C2, tolerance=0))#%% FIXME -- why not identical()? } \keyword{algebra} \keyword{array} Matrix/man/index-class.Rd0000644000175100001440000000150110435070553015007 0ustar hornikusers\name{index-class} \docType{class} \alias{index-class} %% The "[" and "[<-" methods are %% in ./Xtrct-methods.Rd and ./Subassign-methods.Rd \title{Virtual Class "index" - Simple Class for Matrix Indices} \description{The class \code{"index"} is a virtual class used for indices (in signatures) for matrix indexing and sub-assignment of \pkg{"Matrix"} matrices. In fact, it is currently implemented as a simple class union (\code{\link{setClassUnion}}) of \code{"numeric"}, \code{"logical"} and \code{"character"}. } \section{Objects from the Class}{Since it is a virtual Class, no objects may be created from it.} \seealso{ \code{\link{[-methods}}, and %% FIXME: bug in Rdconv needs '[Matrix]' below: \code{\link[Matrix]{Subassign-methods}}, also for examples. } \examples{ showClass("index") } \keyword{classes} Matrix/man/atomicVector-class.Rd0000644000175100001440000000231211252551775016350 0ustar hornikusers\name{atomicVector-class} \docType{class} \alias{atomicVector-class} \title{Virtual Class "atomicVector" of Atomic Vectors} \description{ The \code{\link{class}} \code{"atomicVector"} is a \emph{virtual} class containing all atomic vector classes of base \R, as also implicitly defined via \code{\link{is.atomic}}. } \section{Objects from the Class}{A virtual Class: No objects may be created from it.} \section{Methods}{ In the \pkg{Matrix} package, the "atomicVector" is used in signatures where typically \dQuote{old-style} "matrix" objects can be used and can be substituted by simple vectors. } \section{Extends}{%% FIXME: promptClass() should show the direct subclasses ! The atomic classes \code{"logical"}, \code{"integer"}, \code{"double"}, \code{"numeric"}, \code{"complex"}, \code{"raw"} and \code{"character"} are extended directly. Note that \code{"numeric"} already contains \code{"integer"} and \code{"double"}, but we want all of them to be direct subclasses of \code{"atomicVector"}. } \author{Martin Maechler} \seealso{ \code{\link{is.atomic}}, \code{\link{integer}}, \code{\link{numeric}}, \code{\link{complex}}, etc. } \examples{ showClass("atomicVector") } \keyword{classes} Matrix/man/rep2abI.Rd0000644000175100001440000000125211352372065014066 0ustar hornikusers\name{rep2abI} \alias{rep2abI} \title{Replicate Vectors into 'abIndex' Result} \description{ \code{rep2abI(x, times)} conceptually computes \code{\link{rep.int}(x, times)} but with an \code{\linkS4class{abIndex}} class result. } \usage{ rep2abI(x, times) } \arguments{ \item{x}{numeric vector} \item{times}{integer (valued) scalar: the number of repetitions} } % \details{ % } \value{ a vector of \code{\link{class}} \code{\linkS4class{abIndex}} } \seealso{ \code{\link{rep.int}()}, the base function; \code{\link{abIseq}}, \code{\linkS4class{abIndex}}. } \examples{ (ab <- rep2abI(2:7, 4)) stopifnot(identical(as(ab, "numeric"), rep(2:7, 4))) } \keyword{manip} Matrix/man/pMatrix-class.Rd0000644000175100001440000001436712271746775015362 0ustar hornikusers\name{pMatrix-class} \docType{class} \alias{pMatrix-class} \alias{-,pMatrix,missing-method} \alias{coerce,integer,pMatrix-method} \alias{coerce,numeric,pMatrix-method} \alias{coerce,matrix,pMatrix-method} \alias{coerce,sparseMatrix,pMatrix-method} \alias{coerce,pMatrix,matrix-method} \alias{coerce,pMatrix,ngeMatrix-method} \alias{coerce,pMatrix,ngTMatrix-method} \alias{coerce,pMatrix,lMatrix-method} \alias{coerce,pMatrix,dMatrix-method} \alias{coerce,pMatrix,nMatrix-method} \alias{coerce,pMatrix,CsparseMatrix-method} \alias{coerce,pMatrix,TsparseMatrix-method} \alias{coerce,pMatrix,dsparseMatrix-method} \alias{coerce,pMatrix,nsparseMatrix-method} \alias{coerce,nMatrix,pMatrix-method} \alias{determinant,pMatrix,logical-method} \alias{Summary,pMatrix-method} %\alias{solve,pMatrix,missing-method}--> solve-methods.Rd \alias{t,pMatrix-method} % \title{Permutation matrices} \description{The \code{"pMatrix"} class is the class of permutation matrices, stored as 1-based integer permutation vectors. Matrix (vector) multiplication with permutation matrices is equivalent to row or column permutation, and is implemented that way in the \pkg{Matrix} package, see the \sQuote{Details} below. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("pMatrix", ...)} or by coercion from an integer permutation vector, see below. } \section{Slots}{ \describe{ \item{\code{perm}:}{An integer, 1-based permutation vector, i.e. an integer vector of length \code{Dim[1]} whose elements form a permutation of \code{1:Dim[1]}.} \item{\code{Dim}:}{Object of class \code{"integer"}. The dimensions of the matrix which must be a two-element vector of equal, non-negative integers.} \item{\code{Dimnames}:}{list of length two; each component containing NULL or a \code{\link{character}} vector length equal the corresponding \code{Dim} element.} } } \section{Extends}{ Class \code{"\linkS4class{indMatrix}"}, directly. } \section{Methods}{ \describe{ \item{\%*\%}{\code{signature(x = "matrix", y = "pMatrix")} and other signatures (use \code{showMethods("\%*\%", class="pMatrix")}): ... } \item{coerce}{\code{signature(from = "integer", to = "pMatrix")}: This is enables typical \code{"pMatrix"} construction, given a permutation vector of \code{1:n}, see the first example.} \item{coerce}{\code{signature(from = "numeric", to = "pMatrix")}: a user convenience, to allow \code{as(perm, "pMatrix")} for numeric \code{perm} with integer values.} \item{coerce}{\code{signature(from = "pMatrix", to = "matrix")}: coercion to a traditional FALSE/TRUE \code{\link{matrix}} of \code{\link{mode}} \code{logical}. (in earlier version of \pkg{Matrix}, it resulted in a 0/1-integer matrix; \code{logical} makes slightly more sense, corresponding better to the \dQuote{natural} sparseMatrix counterpart, \code{"ngTMatrix"}.)} \item{coerce}{\code{signature(from = "pMatrix", to = "ngTMatrix")}: coercion to sparse logical matrix of class \code{\linkS4class{ngTMatrix}}.} \item{determinant}{\code{signature(x = "pMatrix", logarithm="logical")}: Since permutation matrices are orthogonal, the determinant must be +1 or -1. In fact, it is exactly the \emph{sign of the permutation}.} \item{solve}{\code{signature(a = "pMatrix", b = "missing")}: return the inverse permutation matrix; note that \code{solve(P)} is identical to \code{t(P)} for permutation matrices. See \code{\link{solve-methods}} for other methods.} \item{t}{\code{signature(x = "pMatrix")}: return the transpose of the permutation matrix (which is also the inverse of the permutation matrix).} } } \details{ Matrix multiplication with permutation matrices is equivalent to row or column permutation. Here are the four different cases for an arbitrary matrix \eqn{M} and a permutation matrix \eqn{P} (where we assume matching dimensions): %% \describe{ %% \item{\eqn{MP = }}{\code{M \%*\% P} ..} %% \item{\eqn{PM = }}{\code{P \%*\% M} ..} %% \item{\eqn{P'M = }}{\code{crossprod(P,M)} (less efficiently, \code{t(P) \%*\% M}) ..} %% \item{\eqn{MP' = }}{\code{trossprod(M,P)} (less efficiently, \code{M \%*\% t(P)}) ..} %% } \tabular{lclcl}{ \eqn{MP }\tab= \tab\code{M \%*\% P} \tab= \tab\code{M[, i(p)]}\cr \eqn{PM }\tab= \tab\code{P \%*\% M} \tab= \tab\code{M[ p , ]} \cr \eqn{P'M}\tab= \tab\code{crossprod(P,M)} (\eqn{\approx}{~=}\code{t(P) \%*\% M})\tab= \tab\code{M[i(p), ]}\cr \eqn{MP'}\tab= \tab\code{tcrossprod(M,P)} (\eqn{\approx}{~=}\code{M \%*\% t(P)})\tab= \tab\code{M[ , p ]} \cr } where \code{p} is the \dQuote{permutation vector} corresponding to the permutation matrix \code{P} (see first note), and \code{i(p)} is short for \code{\link{invPerm}(p)}. Also one could argue that these are really only two cases if you take into account that inversion (\code{\link{solve}}) and transposition (\code{\link{t}}) are the same for permutation matrices \eqn{P}. } \note{ For every permutation matrix \code{P}, there is a corresponding permutation vector \code{p} (of indices, 1:n), and these are related by \preformatted{ P <- as(p, "pMatrix") p <- P@perm } see also the \sQuote{Examples}. \dQuote{Row-indexing} a permutation matrix typically returns an \code{"indMatrix"}. See \code{"\linkS4class{indMatrix}"} for all other subsetting/indexing and subassignment (\code{A[..] <- v}) operations. } \seealso{\code{\link{invPerm}(p)} computes the inverse permutation of an integer (index) vector \code{p}. } \examples{ (pm1 <- as(as.integer(c(2,3,1)), "pMatrix")) t(pm1) # is the same as solve(pm1) pm1 \%*\% t(pm1) # check that the transpose is the inverse stopifnot(all(diag(3) == as(pm1 \%*\% t(pm1), "matrix")), is.logical(as(pm1, "matrix"))) set.seed(11) ## random permutation matrix : (p10 <- as(sample(10),"pMatrix")) ## Permute rows / columns of a numeric matrix : (mm <- round(array(rnorm(3 * 3), c(3, 3)), 2)) mm \%*\% pm1 pm1 \%*\% mm try(as(as.integer(c(3,3,1)), "pMatrix"))# Error: not a permutation as(pm1, "ngTMatrix") p10[1:7, 1:4] # gives an "ngTMatrix" (most economic!) ## row-indexing of a keeps it as an : p10[1:3, ] } \keyword{classes} Matrix/man/forceSymmetric.Rd0000644000175100001440000000666210757763005015615 0ustar hornikusers\name{forceSymmetric} \alias{forceSymmetric} \alias{forceSymmetric,matrix,ANY-method} \alias{forceSymmetric,Matrix,missing-method} \alias{forceSymmetric,denseMatrix,character-method} \alias{forceSymmetric,denseMatrix,missing-method} \alias{forceSymmetric,sparseMatrix,ANY-method} \alias{forceSymmetric,CsparseMatrix,ANY-method} % all the loop-generated "symmetricMatrix" methods: \alias{forceSymmetric,dsyMatrix,missing-method} \alias{forceSymmetric,dsyMatrix,character-method} \alias{forceSymmetric,dspMatrix,missing-method} \alias{forceSymmetric,dspMatrix,character-method} \alias{forceSymmetric,lsyMatrix,missing-method} \alias{forceSymmetric,lsyMatrix,character-method} \alias{forceSymmetric,lspMatrix,missing-method} \alias{forceSymmetric,lspMatrix,character-method} \alias{forceSymmetric,nsyMatrix,missing-method} \alias{forceSymmetric,nsyMatrix,character-method} \alias{forceSymmetric,nspMatrix,missing-method} \alias{forceSymmetric,nspMatrix,character-method} \alias{forceSymmetric,dsTMatrix,missing-method} \alias{forceSymmetric,dsTMatrix,character-method} \alias{forceSymmetric,dsCMatrix,missing-method} \alias{forceSymmetric,dsCMatrix,character-method} \alias{forceSymmetric,dsRMatrix,missing-method} \alias{forceSymmetric,dsRMatrix,character-method} \alias{forceSymmetric,lsTMatrix,missing-method} \alias{forceSymmetric,lsTMatrix,character-method} \alias{forceSymmetric,lsCMatrix,missing-method} \alias{forceSymmetric,lsCMatrix,character-method} \alias{forceSymmetric,lsRMatrix,missing-method} \alias{forceSymmetric,lsRMatrix,character-method} \alias{forceSymmetric,nsTMatrix,missing-method} \alias{forceSymmetric,nsTMatrix,character-method} \alias{forceSymmetric,nsCMatrix,missing-method} \alias{forceSymmetric,nsCMatrix,character-method} \alias{forceSymmetric,nsRMatrix,missing-method} \alias{forceSymmetric,nsRMatrix,character-method} \alias{forceSymmetric,dpoMatrix,missing-method} \alias{forceSymmetric,dpoMatrix,character-method} \alias{forceSymmetric,corMatrix,missing-method} \alias{forceSymmetric,corMatrix,character-method} \alias{forceSymmetric,dppMatrix,missing-method} \alias{forceSymmetric,dppMatrix,character-method} % \title{Force a Matrix to 'symmetricMatrix' Without Symmetry Checks} \description{ Force \code{x} (inheriting from \code{\linkS4class{Matrix}} class) to \code{\linkS4class{symmetricMatrix}}, \bold{without} a symmetry check (which \emph{is} applied for all \code{as(x, "symmetricMatrix")} alikes). } \usage{ forceSymmetric(x, uplo) } \arguments{ \item{x}{a (classed) square matrix.} \item{uplo}{optional string, \code{"U"} or \code{"L"}. The default is \code{"U"} unless \code{x} already has a \code{uplo} slot (i.e., when it is \code{\linkS4class{symmetricMatrix}}, or \code{\linkS4class{triangularMatrix}}), where the default will be \code{x@uplo}.} } % \details{ % % } \value{ a square matrix inheriting from class \code{\linkS4class{symmetricMatrix}}. } \seealso{\code{\link{symmpart}} for the symmetric part, or the coercions \code{as(x, )}. } \examples{ ## Hilbert matrix i <- 1:6 h6 <- 1/outer(i - 1L, i, "+") sd <- sqrt(diag(h6)) hh <- t(h6/sd)/sd # theoretically symmetric isSymmetric(hh, tol=0) # FALSE; hence try( as(hh, "symmetricMatrix") ) # fails, but this works fine: H6 <- forceSymmetric(hh) ## result can be pretty surprising: (M <- Matrix(1:36, 6)) forceSymmetric(M) # symmetric, hence very different in lower triangle (tm <- tril(M)) forceSymmetric(tm) } \keyword{array} Matrix/man/Xtrct-methods.Rd0000644000175100001440000000566412211567675015372 0ustar hornikusers\name{[-methods} \docType{methods} \alias{[-methods} \title{Methods for "[": Extraction or Subsetting in Package 'Matrix'} % NB: "[<-" are in ./Subassign-methods.Rd % ~~~~~~~~~~~~~~~~~~~~~~ \alias{[,Matrix,missing,missing,ANY-method} \alias{[,Matrix,missing,index,missing-method} \alias{[,Matrix,index,missing,missing-method} \alias{[,Matrix,index,index,missing-method} \alias{[,Matrix,lMatrix,missing,ANY-method} \alias{[,Matrix,logical,missing,ANY-method} \alias{[,Matrix,matrix,missing,ANY-method} \alias{[,Matrix,lMatrix,missing,missing-method} \alias{[,Matrix,logical,missing,missing-method} \alias{[,Matrix,matrix,missing,missing-method} \alias{[,Matrix,ANY,ANY,ANY-method}% bail out if no explicit method % \alias{[,denseMatrix,matrix,missing,ANY-method} \alias{[,denseMatrix,matrix,missing,missing-method} \alias{[,denseMatrix,index,missing,logical-method} \alias{[,denseMatrix,index,index,logical-method} \alias{[,denseMatrix,missing,index,logical-method} \alias{[,diagonalMatrix,index,missing,logical-method} \alias{[,diagonalMatrix,index,index,logical-method} \alias{[,diagonalMatrix,missing,index,logical-method} % \alias{[,CsparseMatrix,missing,index,logical-method} \alias{[,CsparseMatrix,index,missing,logical-method} \alias{[,CsparseMatrix,index,index,logical-method} % \alias{[,TsparseTMatrix,missing,missing,ANY-method} \alias{[,TsparseMatrix,index,missing,logical-method} \alias{[,TsparseMatrix,missing,index,logical-method} \alias{[,TsparseMatrix,index,index,logical-method} % \alias{[,sparseMatrix,missing,index,logical-method} \alias{[,sparseMatrix,index,missing,logical-method} \alias{[,sparseMatrix,index,index,logical-method} % \alias{[,indMatrix,index,missing,logical-method} %------- \description{ Methods for \code{"["}, i.e., extraction or subsetting mostly of matrices, in package \pkg{Matrix}. } \section{Methods}{ There are more than these: \describe{ \item{x = "Matrix", i = "missing", j = "missing", drop= "ANY"}{ ... } \item{x = "Matrix", i = "numeric", j = "missing", drop= "missing"}{ ... } \item{x = "Matrix", i = "missing", j = "numeric", drop= "missing"}{ ... } \item{x = "dsparseMatrix", i = "missing", j = "numeric", drop= "logical"}{ ... } \item{x = "dsparseMatrix", i = "numeric", j = "missing", drop= "logical"}{ ... } \item{x = "dsparseMatrix", i = "numeric", j = "numeric", drop= "logical"}{ ... } } } \seealso{ \code{\link{[<--methods}} for sub\emph{assign}ment to \code{"Matrix"} objects. \code{\link{Extract}} about the standard extraction. } \examples{ % regression tests are in ../tests/indexing.R str(m <- Matrix(round(rnorm(7*4),2), nrow = 7)) stopifnot(identical(m, m[])) m[2, 3] # simple number m[2, 3:4] # simple numeric of length 2 m[2, 3:4, drop=FALSE] # sub matrix of class 'dgeMatrix' ## rows or columns only: m[1,] # first row, as simple numeric vector m[,1:2] # sub matrix of first two columns showMethods("[", inherited = FALSE) } \keyword{methods} \keyword{array} Matrix/man/triangularMatrix-class.Rd0000644000175100001440000000453612213673171017251 0ustar hornikusers\name{triangularMatrix-class} \docType{class} \alias{triangularMatrix-class} \alias{coerce,triangularMatrix,symmetricMatrix-method} \alias{coerce,lgeMatrix,triangularMatrix-method} \alias{coerce,ngeMatrix,triangularMatrix-method} % \title{Virtual Class of Triangular Matrices in package:Matrix} \description{ The virtual class of triangular matrices,\code{"triangularMatrix"}, from the package \pkg{Matrix} contains numeric and logical, dense and sparse matrices, e.g., see the examples. The main use will be in methods (and C functions) that can deal with all triangular matrices. } % \section{Objects from the Class}{A virtual Class: No objects may be created from it.} \section{Slots}{ \describe{ \item{\code{uplo}:}{String (of class \code{"character"}). Must be either "U", for upper triangular, and "L", for lower triangular.} \item{\code{diag}:}{String (of class \code{"character"}). Must be either \code{"U"}, for unit triangular (diagonal is all ones), or \code{"N"} for non-unit. The diagonal elements are not accessed internally when \code{diag} is \code{"U"}. For \code{\linkS4class{denseMatrix}} classes, they need to be allocated though, i.e., the length of the \code{x} slot does not depend on \code{diag}.} \item{\code{Dim}, \code{Dimnames}:}{The dimension (a length-2 \code{"integer"}) and corresponding names (or \code{NULL}), inherited from the \code{\linkS4class{Matrix}}, see there.} } } \section{Extends}{ Class \code{"Matrix"}, directly. } \section{Methods}{ There's a C function \code{triangularMatrix_validity()} called by the internal validity checking functions. Currently, \code{\link{Schur}}, \code{\link{isSymmetric}} and \code{as()} (i.e. \code{\link{coerce}}) have methods with \code{triangularMatrix} in their signature. } \seealso{ \code{\link{isTriangular}()} for testing any matrix for triangularity; classes \code{\linkS4class{symmetricMatrix}}, and, e.g., \code{\linkS4class{dtrMatrix}} for numeric \emph{dense} matrices, or \code{\linkS4class{ltCMatrix}} for a logical \emph{sparse} matrix subclass of \code{"triangularMatrix"}. } \examples{ showClass("triangularMatrix") ## The names of direct subclasses: scl <- getClass("triangularMatrix")@subclasses directly <- sapply(lapply(scl, slot, "by"), length) == 0 names(scl)[directly] } \keyword{classes} Matrix/man/ldiMatrix-class.Rd0000644000175100001440000000312111061674131015633 0ustar hornikusers\name{ldiMatrix-class} \docType{class} \alias{ldiMatrix-class} \alias{!,ldiMatrix-method} %%----> put almost all methods into ./diagonalMatrix-class.Rd % Deprecated: \alias{coerce,ldiMatrix,lgCMatrix-method} \alias{coerce,ldiMatrix,lgTMatrix-method} \title{Class "ldiMatrix" of Diagonal Logical Matrices} \description{The class \code{"ldiMatrix"} of logical diagonal matrices. %% FIXME add more } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("ldiMatrix", ...)} but typically rather via \code{\link{Diagonal}}. } \section{Slots}{ \describe{ \item{\code{x}:}{\code{"logical"} vector.} \item{\code{diag}:}{\code{"character"} string, either "U" or "N", see \code{\linkS4class{ddiMatrix}}.} \item{\code{Dim},\code{Dimnames}:}{matrix dimension and \code{\link{dimnames}}, see the \code{\linkS4class{Matrix}} class description.} } } \section{Extends}{ Class \code{"\linkS4class{diagonalMatrix}"} and class \code{"\linkS4class{lMatrix}"}, directly. Class \code{"\linkS4class{sparseMatrix}"}, by class \code{"diagonalMatrix"}. } % \section{Methods}{ % No methods defined with class "ldiMatrix" in the signature. % } % \references{ ~put references to the literature/web site here ~ } \seealso{ Classes \code{\linkS4class{ddiMatrix}} and \code{\linkS4class{diagonalMatrix}}; function \code{\link{Diagonal}}. } \examples{ (lM <- Diagonal(x = c(TRUE,FALSE,FALSE))) str(lM)#> gory details (slots) crossprod(lM) # numeric (nM <- as(lM, "nMatrix"))# -> sparse (not formally ``diagonal'') crossprod(nM) # logical sparse } \keyword{classes} Matrix/man/lgeMatrix-class.Rd0000644000175100001440000000436312001034107015627 0ustar hornikusers\name{lgeMatrix-class} \docType{class} \title{Class "lgeMatrix" of General Dense Logical Matrices} \alias{lgeMatrix-class} % \alias{!,lgeMatrix-method} \alias{Arith,lgeMatrix,lgeMatrix-method} \alias{Compare,lgeMatrix,lgeMatrix-method} \alias{Logic,lgeMatrix,lgeMatrix-method} \alias{as.vector,lgeMatrix,missing-method} \alias{coerce,matrix,lgeMatrix-method} \alias{coerce,lgeMatrix,dgeMatrix-method} \alias{coerce,lgeMatrix,matrix-method} \alias{coerce,lgeMatrix,lgCMatrix-method} \alias{coerce,lgeMatrix,lgTMatrix-method} \alias{coerce,lgeMatrix,lsyMatrix-method} \alias{coerce,lgeMatrix,ltrMatrix-method} \alias{coerce,lgeMatrix,ltpMatrix-method} \alias{coerce,lgeMatrix,lspMatrix-method} \alias{diag,lgeMatrix-method} \alias{diag<-,lgeMatrix-method} \alias{t,lgeMatrix-method} % \description{This is the class of general dense \code{\link{logical}} matrices. } \section{Slots}{ \describe{ \item{\code{x}:}{Object of class \code{"logical"}. The logical values that constitute the matrix, stored in column-major order.} \item{\code{Dim},\code{Dimnames}:}{The dimension (a length-2 \code{"integer"}) and corresponding names (or \code{NULL}), see the \code{\linkS4class{Matrix}} class.} \item{\code{factors}:}{Object of class \code{"list"}. A named list of factorizations that have been computed for the matrix.} } } \section{Extends}{ Class \code{"ldenseMatrix"}, directly. Class \code{"lMatrix"}, by class \code{"ldenseMatrix"}. Class \code{"denseMatrix"}, by class \code{"ldenseMatrix"}. Class \code{"Matrix"}, by class \code{"ldenseMatrix"}. Class \code{"Matrix"}, by class \code{"ldenseMatrix"}. } \section{Methods}{ Currently, mainly \code{\link{t}()} and coercion methods (for \code{\link{as}(.)}); use, e.g., \code{\link{showMethods}(class="lgeMatrix")} for details. } \seealso{ Non-general logical dense matrix classes such as \code{\linkS4class{ltrMatrix}}, or \code{\linkS4class{lsyMatrix}}; \emph{sparse} logical classes such as \code{\linkS4class{lgCMatrix}}. } \examples{ showClass("lgeMatrix") str(new("lgeMatrix")) set.seed(1) (lM <- Matrix(matrix(rnorm(28), 4,7) > 0))# a simple random lgeMatrix set.seed(11) (lC <- Matrix(matrix(rnorm(28), 4,7) > 0))# a simple random lgCMatrix as(lM, "lgCMatrix") } \keyword{classes} Matrix/man/all-methods.Rd0000644000175100001440000000314010647423674015022 0ustar hornikusers\name{all-methods} \docType{methods} \alias{all-methods} \alias{all,Matrix-method} \alias{any,Matrix-method} % \alias{all,lMatrix-method} \alias{all,ldenseMatrix-method} \alias{all,lsparseMatrix-method} \alias{all,lsyMatrix-method} % \alias{any,lMatrix-method} % \alias{any,ldenseMatrix-method} % \alias{any,lsparseMatrix-method} % \title{"Matrix" Methods for Functions all() and any()} \description{ The basic \R functions \code{\link{all}} and \code{\link{any}} now have methods for \code{\linkS4class{Matrix}} objects and should behave as for \code{\link{matrix}} ones. } \section{Methods}{ %% FIXME: write more \describe{ \item{all}{\code{signature(x = "Matrix", ..., na.rm = FALSE)}: ...} \item{any}{\code{signature(x = "Matrix", ..., na.rm = FALSE)}: ...} \item{all}{\code{signature(x = "ldenseMatrix", ..., na.rm = FALSE)}: ...} \item{all}{\code{signature(x = "lsparseMatrix", ..., na.rm = FALSE)}: ...} } } \keyword{methods} \examples{ M <- Matrix(1:12 +0, 3,4) all(M >= 1) # TRUE any(M < 0 ) # FALSE MN <- M; MN[2,3] <- NA; MN all(MN >= 0) # NA any(MN < 0) # NA any(MN < 0, na.rm = TRUE) # -> FALSE \dontshow{ sM <- as(MN, "sparseMatrix") stopifnot(all(M >= 1), !any(M < 0), all.equal((sM >= 1), as(MN >= 1, "sparseMatrix")), ## MN: any(MN < 2), !all(MN < 5), is.na(all(MN >= 0)), is.na(any(MN < 0)), all(MN >= 0, na.rm=TRUE), !any(MN < 0, na.rm=TRUE), ## same for sM : any(sM < 2), !all(sM < 5), is.na(all(sM >= 0)), is.na(any(sM < 0)), all(sM >= 0, na.rm=TRUE), !any(sM < 0, na.rm=TRUE) ) } } Matrix/man/norm.Rd0000644000175100001440000000324311367111763013561 0ustar hornikusers\name{norm} \title{Matrix Norms} \alias{norm} \alias{norm,ANY,missing-method} \alias{norm,matrix,character-method} \alias{norm,Matrix,character-method} \usage{ norm(x, type, \dots) } \description{ Computes a matrix norm of \code{x}, using Lapack for dense matrices. The norm can be the one norm, the infinity norm, the Frobenius norm, or the maximum modulus among elements of a matrix, as determined by the value of \code{type}. } \arguments{ \item{x}{ a real or complex matrix. } \item{type}{ A character indicating the type of norm desired. \describe{ \item{\code{"O"}, \code{"o"} or \code{"1"}}{specifies the one norm, (maximum absolute column sum);} \item{\code{"I"} or \code{"i"}}{specifies the infinity norm (maximum absolute row sum);} \item{\code{"F"} or \code{"f"}}{specifies the Frobenius norm (the Euclidean norm of \code{x} treated as if it were a vector); and} \item{\code{"M"} or \code{"m"}}{specifies the maximum modulus of all the elements in \code{x}.} } The default is \code{"O"}. Only the first character of \code{type[1]} is used. } \item{\dots}{further arguments passed to or from other methods.} } \value{ A numeric value of class \code{"norm"}, representing the quantity chosen according to \code{type}. } \details{ For dense matrices, the methods eventually call the Lapack functions \code{dlange}, \code{dlansy}, \code{dlantr}, \code{zlange}, \code{zlansy}, and \code{zlantr}. } \references{ Anderson, E., et al. (1994). \emph{LAPACK User's Guide,} 2nd edition, SIAM, Philadelphia. } \examples{ x <- Hilbert(9) norm(x, "1") norm(x, "I") norm(x, "F") norm(x, "M") } \keyword{algebra} Matrix/man/Hilbert.Rd0000644000175100001440000000107010435070553014167 0ustar hornikusers\name{Hilbert} \alias{Hilbert} \title{Generate a Hilbert matrix} \description{ Generate the \code{n} by \code{n} symmetric Hilbert matrix. Because these matrices are ill-conditioned for moderate to large \code{n}, they are often used for testing numerical linear algebra code. } \usage{ Hilbert(n) } \arguments{ \item{n}{a non-negative integer.} } \value{ the \code{n} by \code{n} symmetric Hilbert matrix as a \code{"dpoMatrix"} object. } \seealso{the class \code{\linkS4class{dpoMatrix}}} \examples{ Hilbert(6) } \keyword{array} \keyword{algebra} Matrix/man/nnzero.Rd0000644000175100001440000000606412207615512014120 0ustar hornikusers\name{nnzero} \title{The Number of Non-Zero Values of a Matrix} \alias{nnzero} \alias{nnzero,ANY-method} \alias{nnzero,denseMatrix-method} \alias{nnzero,diagonalMatrix-method} \alias{nnzero,indMatrix-method} \alias{nnzero,sparseMatrix-method} \alias{nnzero,CHMfactor-method} \description{ Returns the number of non-zero values of a numeric-like \R object, and in particular an object \code{x} inheriting from class \code{\linkS4class{Matrix}}. } \usage{ nnzero(x, na.counted = NA) } \arguments{ \item{x}{an \R object, typically inheriting from class \code{\linkS4class{Matrix}} or \code{\link{numeric}}.} \item{na.counted}{a \code{\link{logical}} describing how \code{\link{NA}}s should be counted. There are three possible settings for \code{na.counted}: \describe{ \item{TRUE}{\code{NA}s \emph{are} counted as non-zero (since \dQuote{they are not zero}).} \item{NA}{(default)the result will be \code{NA} if there are \code{NA}'s in \code{x} (since \dQuote{NA's are not known, i.e., \emph{may be} zero}).} \item{FALSE}{\code{NA}s are \emph{omitted} from \code{x} before the non-zero entries are counted.} } For sparse matrices, you may often want to use \code{na.counted = TRUE}. } } % \details{ % } \section{Methods}{ \describe{ \item{\code{signature(x = "ANY")}}{the default method for non-\code{\linkS4class{Matrix}} class objects, simply counts the number \code{0}s in \code{x}, counting \code{NA}'s depending on the \code{na.counted} argument, see above.} \item{\code{signature(x = "denseMatrix")}}{conceptually the same as for traditional \code{\link{matrix}} objects, care has to be taken for \code{"\linkS4class{symmetricMatrix}"} objects.} \item{\code{signature(x = "diagonalMatrix")}, and \code{signature(x = "indMatrix")}}{fast simple methods for these special \code{"sparseMatrix"} classes.} \item{\code{signature(x = "sparseMatrix")}}{typically, the most interesting method, also carefully taking \code{"\linkS4class{symmetricMatrix}"} objects into account.} } } \value{ the number of non zero entries in \code{x} (typically \code{\link{integer}}). Note that for a \emph{symmetric} sparse matrix \code{S} (i.e., inheriting from class \code{\linkS4class{symmetricMatrix}}), \code{nnzero(S)} is typically \emph{twice} the \code{length(S@x)}. } %\author{Martin} \seealso{The \code{\linkS4class{Matrix}} class also has a \code{\link{length}} method; typically, \code{length(M)} is much larger than \code{nnzero(M)} for a sparse matrix M, and the latter is a better indication of the \emph{size} of \code{M}. } \examples{ m <- Matrix(0+1:28, nrow = 4) m[-3,c(2,4:5,7)] <- m[ 3, 1:4] <- m[1:3, 6] <- 0 (mT <- as(m, "dgTMatrix")) nnzero(mT) (S <- crossprod(mT)) nnzero(S) str(S) # slots are smaller than nnzero() stopifnot(nnzero(S) == sum(as.matrix(S) != 0))# failed earlier data(KNex) M <- KNex$mm class(M) dim(M) length(M); stopifnot(length(M) == prod(dim(M))) nnzero(M) # more relevant than length ## the above are also visible from str(M) } \keyword{attribute} Matrix/man/dtrMatrix-class.Rd0000644000175100001440000000667712271746775015721 0ustar hornikusers\name{dtrMatrix-class} \title{Triangular, dense, numeric matrices} \docType{class} \alias{coerce,dgeMatrix,dtrMatrix-method}% or rather setIs? \alias{coerce,dtrMatrix,dtpMatrix-method} \alias{coerce,dtrMatrix,ltrMatrix-method} \alias{coerce,dtrMatrix,matrix-method} \alias{coerce,dtrMatrix,sparseMatrix-method} \alias{coerce,dtrMatrix,CsparseMatrix-method} \alias{coerce,matrix,dtrMatrix-method} \alias{determinant,dtrMatrix,logical-method} \alias{determinant,dtrMatrix,missing-method} \alias{diag,dtrMatrix-method} \alias{diag<-,dtrMatrix-method} \alias{norm,dtrMatrix,character-method} \alias{norm,dtrMatrix,missing-method} \alias{rcond,dtrMatrix,character-method} \alias{rcond,dtrMatrix,missing-method} \alias{show,dtrMatrix-method} %\alias{solve,dtrMatrix,matrix-method}--> solve-methods.Rd \alias{t,dtrMatrix-method} \alias{dtrMatrix-class} \description{ The \code{"dtrMatrix"} class is the class of triangular, dense, numeric matrices in nonpacked storage. The \code{"dtpMatrix"} class is the same except in packed storage. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("dtrMatrix", ...)}. } \section{Slots}{ \describe{ \item{\code{uplo}:}{Object of class \code{"character"}. Must be either "U", for upper triangular, and "L", for lower triangular.} \item{\code{diag}:}{Object of class \code{"character"}. Must be either \code{"U"}, for unit triangular (diagonal is all ones), or \code{"N"}; see \code{\linkS4class{triangularMatrix}}.} \item{\code{x}:}{Object of class \code{"numeric"}. The numeric values that constitute the matrix, stored in column-major order.} \item{\code{Dim}:}{Object of class \code{"integer"}. The dimensions of the matrix which must be a two-element vector of non-negative integers.} } } \section{Extends}{ Class \code{"ddenseMatrix"}, directly. Class \code{"triangularMatrix"}, directly. Class \code{"Matrix"} and others, by class \code{"ddenseMatrix"}. } \section{Methods}{ Among others (such as matrix products, e.g. \code{?\link{crossprod-methods}}), \describe{ \item{coerce}{\code{signature(from = "dgeMatrix", to = "dtrMatrix")}} \item{coerce}{\code{signature(from = "dtrMatrix", to = "matrix")}} \item{coerce}{\code{signature(from = "dtrMatrix", to = "ltrMatrix")}} \item{coerce}{\code{signature(from = "dtrMatrix", to = "matrix")}} \item{coerce}{\code{signature(from = "matrix", to = "dtrMatrix")}} \item{norm}{\code{signature(x = "dtrMatrix", type = "character")}} \item{rcond}{\code{signature(x = "dtrMatrix", norm = "character")}} \item{solve}{\code{signature(a = "dtrMatrix", b = "....")}}{efficientely use a \dQuote{forwardsolve} or \code{backsolve} for a lower or upper triangular matrix, respectively, see also \code{\link{solve-methods}}.} \item{+, -, *, \dots, ==, >=, \dots}{all the \code{\link{Ops}} group methods are available. When applied to two triangular matrices, these return a triangular matrix when easily possible.} } } %\references{} %\author{} \seealso{ Classes \code{\linkS4class{ddenseMatrix}}, \code{\linkS4class{dtpMatrix}}, \code{\linkS4class{triangularMatrix}} } \examples{%% this is used from ./dtpMatrix-class.Rd (change with care!) (m <- rbind(2:3, 0:-1)) (M <- as(m, "dgeMatrix")) (T <- as(M, "dtrMatrix")) ## upper triangular is default (T2 <- as(t(M), "dtrMatrix")) stopifnot(T@uplo == "U", T2@uplo == "L", identical(T2, t(T))) } \keyword{classes} Matrix/man/abIndex-class.Rd0000644000175100001440000001102112003525364015246 0ustar hornikusers\name{abIndex-class} \title{Class "abIndex" of Abstract Index Vectors} \Rdversion{1.1} \docType{class} % \alias{abIndex-class} % \alias{seqMat-class}% unexported for now % hence, we do not yet mention these further below: \alias{coerce,abIndex,seqMat-method} \alias{coerce,numeric,seqMat-method} \alias{coerce,seqMat,abIndex-method} \alias{coerce,seqMat,numeric-method} % \alias{as.integer,abIndex-method} \alias{as.numeric,abIndex-method} \alias{as.vector,abIndex,ANY-method} \alias{as.vector,abIndex,character-method} \alias{[,abIndex,index,ANY,ANY-method} \alias{coerce,logical,abIndex-method} \alias{coerce,numeric,abIndex-method} \alias{coerce,abIndex,integer-method} \alias{coerce,abIndex,numeric-method} \alias{coerce,abIndex,vector-method} \alias{drop,abIndex-method}% not mentioned below {experimental} \alias{length,abIndex-method} \alias{show,abIndex-method} \alias{is.na,abIndex-method} \alias{is.finite,abIndex-method}% not yet mentioned \alias{is.infinite,abIndex-method} % \alias{Ops,numeric,abIndex-method} \alias{Ops,abIndex,abIndex-method} \alias{Ops,abIndex,numeric-method} \alias{Ops,abIndex,ANY-method} \alias{Ops,ANY,abIndex-method} \alias{Arith,abIndex,abIndex-method} \alias{Arith,abIndex,numLike-method}% \alias{Arith,abIndex,numeric-method} \alias{Arith,numLike,abIndex-method}% \alias{Arith,numeric,abIndex-method} % \alias{Summary,abIndex-method} % \description{ The \code{"abIndex"} \code{\link{class}}, short for \dQuote{Abstract Index Vector}, is used for dealing with large index vectors more efficiently, than using integer (or \code{\link{numeric}}) vectors of the kind \code{2:1000000} or \code{c(0:1e5, 1000:1e6)}. Note that the current implementation details are subject to change, and if you consider working with these classes, please contact the package maintainers (\code{packageDescription("Matrix")$Maintainer}). } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("abIndex", ...)}, but more easily and typically either by \code{as(x, "abIndex")} where \code{x} is an integer (valued) vector, or directly by \code{\link{abIseq}()} and combination \code{\link{c}(...)} of such. } \section{Slots}{ \describe{ \item{\code{kind}:}{a \code{\link{character}} string, one of \code{("int32", "double", "rleDiff")}, denoting the internal structure of the abIndex object.} \item{\code{x}:}{Object of class \code{"numLike"}; is used (i.e., not of length \code{0}) only iff the object is \emph{not} compressed, i.e., currently exactly when \code{kind != "rleDiff"}.} \item{\code{rleD}:}{object of class \code{"\linkS4class{rleDiff}"}, used for compression via \code{\link{rle}}.} } } \section{Methods}{ \describe{ \item{as.numeric, as.integer, as.vector}{\code{signature(x = "abIndex")}: ... } \item{[}{\code{signature(x = "abIndex", i = "index", j = "ANY", drop = "ANY")}: ... } \item{coerce}{\code{signature(from = "numeric", to = "abIndex")}: ... } \item{coerce}{\code{signature(from = "abIndex", to = "numeric")}: ... } \item{coerce}{\code{signature(from = "abIndex", to = "integer")}: ... } \item{length}{\code{signature(x = "abIndex")}: ... } \item{Ops}{\code{signature(e1 = "numeric", e2 = "abIndex")}: These and the following arithmetic and logic operations are \bold{not yet implemented}; see \code{\link[methods]{Ops}} for a list of these (S4) group methods.} \item{Ops}{\code{signature(e1 = "abIndex", e2 = "abIndex")}: ... } \item{Ops}{\code{signature(e1 = "abIndex", e2 = "numeric")}: ... } \item{Summary}{\code{signature(x = "abIndex")}: ... } \item{show}{\code{("abIndex")}: simple \code{\link{show}} method, building on \code{show()}.} \item{is.na}{\code{("abIndex")}: works analogously to regular vectors.} \item{is.finite, is.infinite}{\code{("abIndex")}: ditto.} } } \note{ This is currently experimental and not yet used for our own code. Please contact us (\code{packageDescription("Matrix")$Maintainer}), if you plan to make use of this class. Partly builds on ideas and code from Jens Oehlschlaegel, as implemented (around 2008, in the GPL'ed part of) package \pkg{ff}. } %\author{Martin Maechler} \seealso{ \code{\link{rle}} (\pkg{base}) which is used here; \code{\link{numeric}}% ... FIXME } \examples{ showClass("abIndex") ii <- c(-3:40, 20:70) str(ai <- as(ii, "abIndex"))# note ai # -> show() method %% FIXME: add / exchange with ../tests/abIndex-tsts.R stopifnot(identical(-3:20, as(abIseq1(-3,20), "vector"))) } \keyword{classes} Matrix/man/sparseMatrix-class.Rd0000644000175100001440000001520012247126702016364 0ustar hornikusers\name{sparseMatrix-class} \docType{class} \title{Virtual Class "sparseMatrix" --- Mother of Sparse Matrices} \alias{sparseMatrix-class} %% Group methods \alias{Math,sparseMatrix-method} %\alias{Math2,sparseMatrix,numeric-method} \alias{Ops,sparseMatrix,sparseMatrix-method} \alias{Ops,sparseMatrix,numeric-method} \alias{Ops,numeric,sparseMatrix-method} \alias{Ops,diagonalMatrix,sparseMatrix-method} \alias{Ops,sparseMatrix,diagonalMatrix-method} % \alias{cbind2,sparseMatrix,sparseMatrix-method} \alias{cbind2,denseMatrix,sparseMatrix-method} \alias{cbind2,sparseMatrix,denseMatrix-method} \alias{cbind2,sparseMatrix,matrix-method} \alias{cbind2,matrix,sparseMatrix-method} \alias{cbind2,sparseMatrix,numeric-method} \alias{cbind2,numeric,sparseMatrix-method} \alias{rbind2,sparseMatrix,sparseMatrix-method} \alias{rbind2,denseMatrix,sparseMatrix-method} \alias{rbind2,sparseMatrix,denseMatrix-method} \alias{rbind2,sparseMatrix,matrix-method} \alias{rbind2,matrix,sparseMatrix-method} \alias{rbind2,sparseMatrix,numeric-method} \alias{rbind2,numeric,sparseMatrix-method} % \alias{coerce,ANY,sparseMatrix-method} \alias{coerce,table,sparseMatrix-method} \alias{coerce,factor,sparseMatrix-method} \alias{coerce,sparseMatrix,generalMatrix-method} \alias{coerce,sparseMatrix,symmetricMatrix-method} \alias{coerce,sparseMatrix,triangularMatrix-method} \alias{-,sparseMatrix,missing-method} \alias{cov2cor,sparseMatrix-method} \alias{diag,sparseMatrix-method} \alias{dim<-,sparseMatrix-method} \alias{format,sparseMatrix-method} \alias{lu,sparseMatrix-method} \alias{mean,sparseMatrix-method} \alias{print,sparseMatrix-method} \alias{show,sparseMatrix-method} \alias{summary,sparseMatrix-method} \alias{norm,sparseMatrix,character-method} \alias{determinant,dgCMatrix,logical-method} \alias{determinant,dsparseMatrix,logical-method} \alias{determinant,dtCMatrix,logical-method} \alias{determinant,sparseMatrix,missing-method} \alias{determinant,sparseMatrix,logical-method} % "[" are in ./Xtrct-methods.Rd %\alias{colMeans,..} etc are now in ./colSums.Rd % \description{Virtual Mother Class of All Sparse Matrices} \section{Slots}{ \describe{ \item{\code{Dim}:}{Object of class \code{"integer"} - the dimensions of the matrix - must be an integer vector with exactly two non-negative values.} \item{\code{Dimnames}:}{a list of length two - inherited from class \code{Matrix}, see \code{\linkS4class{Matrix}}.} } } \section{Extends}{ Class \code{"Matrix"}, directly. } \section{Methods}{ \describe{ \item{show}{\code{(object = "sparseMatrix")}: The \code{\link{show}} method for sparse matrices prints \emph{\dQuote{structural}} zeroes as \code{"."} using \code{\link{printSpMatrix}()} which allows further customization.} \item{print}{\code{signature(x = "sparseMatrix")}, ....\cr The \code{\link{print}} method for sparse matrices by default is the same as \code{show()} but can be called with extra optional arguments, see \code{\link{printSpMatrix}()}.} \item{format}{\code{signature(x = "sparseMatrix")}, ....\cr The \code{\link{format}} method for sparse matrices, see \code{\link{formatSpMatrix}()} for details such as the extra optional arguments.} \item{summary}{\code{(object = "sparseMatrix")}: Returns an object of S3 class \code{"sparseSummary"} which is basically a \code{\link{data.frame}} with columns \code{(i,j,x)} (or just \code{(i,j)} for \code{\linkS4class{nsparseMatrix}} class objects) with the stored (typically non-zero) entries. The \code{\link{print}} method resembles Matlab's way of printing sparse matrices, and also the MatrixMarket format, see \code{\link{writeMM}}.} \item{cbind2}{\code{(x = *, y = *)}: several methods for binding matrices together, column-wise, see the basic \code{\link{cbind}} and \code{\link{rbind}} functions.\cr Note that the result will typically be sparse, even when one argument is dense and larger than the sparse one. } \item{rbind2}{\code{(x = *, y = *)}: binding matrices together row-wise, see \code{cbind2} above.} \item{determinant}{\code{(x = "sparseMatrix", logarithm=TRUE)}: \code{\link{determinant}()} methods for sparse matrices typically work via \code{\link{Cholesky}} or \code{\link{lu}} decompositions.} \item{diag}{\code{(x = "sparseMatrix")}: extracts the diagonal of a sparse matrix.} \item{dim<-}{\code{signature(x = "sparseMatrix", value = "ANY")}: allows to \emph{reshape} a sparse matrix to a sparse matrix with the same entries but different dimensions. \code{value} must be of length two and fulfill \code{prod(value) == prod(dim(x))}.} \item{coerce}{\code{signature(from = "factor", to = "sparseMatrix")}: Coercion of a factor to \code{"sparseMatrix"} produces the matrix of indicator \bold{rows} stored as an object of class \code{"dgCMatrix"}. To obtain columns representing the interaction of the factor and a numeric covariate, replace the \code{"x"} slot of the result by the numeric covariate then take the transpose. Missing values (\code{\link{NA}}) from the factor are translated to columns of all \code{0}s.} } See also \code{\link{colSums}}, \code{\link{norm}}, ... %% FIXME for methods with separate help pages. } \seealso{ \code{\link{sparseMatrix}}, and its references, such as \code{\link{xtabs}(*, sparse=TRUE)}, or \code{\link{sparse.model.matrix}()}, for constructing sparse matrices. \code{\link{T2graph}} for conversion of \code{"graph"} objects (package \pkg{graph}) to and from sparse matrices. } \note{ In method selection for multiplication operations (i.e. \code{\%*\%} and the two-argument form of \code{\link[base]{crossprod}}) the sparseMatrix class takes precedence in the sense that if one operand is a sparse matrix and the other is any type of dense matrix then the dense matrix is coerced to a \code{dgeMatrix} and the appropriate sparse matrix method is used. } %\author{Martin} \examples{ showClass("sparseMatrix") ## and look at the help() of its subclasses M <- Matrix(0, 10000, 100) M[1,1] <- M[2,3] <- 3.14 M ## show(.) method suppresses printing of the majority of rows data(CAex); dim(CAex) # 72 x 72 matrix determinant(CAex) # works via sparse lu(.) ## factor -> t( ) : (fact <- gl(5, 3, 30, labels = LETTERS[1:5])) (Xt <- as(fact, "sparseMatrix")) # indicator rows ## missing values --> all-0 columns: f.mis <- fact i.mis <- c(3:5, 17) is.na(f.mis) <- i.mis Xt != (X. <- as(f.mis, "sparseMatrix")) # differ only in columns 3:5,17 stopifnot(all(X.[,i.mis] == 0), all(Xt[,-i.mis] == X.[,-i.mis])) } \keyword{classes} Matrix/man/bandSparse.Rd0000644000175100001440000000564611634347144014702 0ustar hornikusers\name{bandSparse} \alias{bandSparse} \title{Construct Sparse Banded Matrix from (Sup-/Super-) Diagonals} \description{ Construct a sparse banded matrix by specifying its non-zero sup- and super-diagonals. } \usage{ bandSparse(n, m = n, k, diagonals, symmetric = FALSE, giveCsparse = TRUE) } \arguments{ \item{n,m}{the matrix dimension \eqn{(n,m) = (nrow, ncol)}.} \item{k}{integer vector of \dQuote{diagonal numbers}, with identical meaning as in \code{\link{band}(*, k)}.} \item{diagonals}{optional list of sub-/super- diagonals; if missing, the result will be a patter\bold{n} matrix, i.e., inheriting from class \code{\linkS4class{nMatrix}}. \code{diagonals} can also be \eqn{n' \times d}{n' x d} matrix, where \code{d <- length(k)} and \eqn{n' >= min(n,m)}. In that case, the sub-/super- diagonals are taken from the columns of \code{diagonals}, where only the first several rows will be used (typically) for off-diagonals. } \item{symmetric}{logical; if true the result will be symmetric (inheriting from class \code{\linkS4class{symmetricMatrix}}) and only the upper or lower triangle must be specified (via \code{k} and \code{diagonals}).} \item{giveCsparse}{logical indicating if the result should be a \code{\linkS4class{CsparseMatrix}} or a \code{\linkS4class{TsparseMatrix}}. The default, \code{TRUE} is very often more efficient subsequently, but not always.} } % \details{ __needed ?__ % % } \value{ a sparse matrix (of \code{\link{class}} \code{\linkS4class{CsparseMatrix}}) of dimension \eqn{n \times m}{n x m} with diagonal \dQuote{bands} as specified. } %\author{Martin Maechler} \seealso{ \code{\link{band}}, for \emph{extraction} of matrix bands; \code{\link{bdiag}}, \code{\link{diag}}, \code{\link{sparseMatrix}}, \code{\link{Matrix}}. } \examples{ diags <- list(1:30, 10*(1:20), 100*(1:20)) s1 <- bandSparse(13, k = -c(0:2, 6), diag = c(diags, diags[2]), symm=TRUE) s1 s2 <- bandSparse(13, k = c(0:2, 6), diag = c(diags, diags[2]), symm=TRUE) stopifnot(identical(s1, t(s2)), is(s1,"dsCMatrix")) ## a pattern Matrix of *full* (sub-)diagonals: bk <- c(0:4, 7,9) (s3 <- bandSparse(30, k = bk, symm = TRUE)) ## If you want a pattern matrix, but with "sparse"-diagonals, ## you currently need to go via logical sparse: lLis <- lapply(list(rpois(20, 2), rpois(20,1), rpois(20,3))[c(1:3,2:3,3:2)], as.logical) (s4 <- bandSparse(20, k = bk, symm = TRUE, diag = lLis)) (s4. <- as(drop0(s4), "nsparseMatrix")) n <- 1e4 bk <- c(0:5, 7,11) bMat <- matrix(1:8, n, 8, byrow=TRUE) bLis <- as.data.frame(bMat) B <- bandSparse(n, k = bk, diag = bLis) Bs <- bandSparse(n, k = bk, diag = bLis, symmetric=TRUE) B [1:15, 1:30] Bs[1:15, 1:30] ## can use a list *or* a matrix for specifying the diagonals: stopifnot(identical(B, bandSparse(n, k = bk, diag = bMat)), identical(Bs, bandSparse(n, k = bk, diag = bMat, symmetric=TRUE))) } \keyword{array} \keyword{algebra} Matrix/man/graph2T.Rd0000644000175100001440000000735412254575000014116 0ustar hornikusers\name{graph-sparseMatrix} \title{Conversions "graph" <--> (sparse) Matrix} \alias{graph2T} \alias{T2graph} % graph stuff \alias{coerce,graph,Matrix-method} \alias{coerce,graph,sparseMatrix-method} \alias{coerce,graph,CsparseMatrix-method} \alias{coerce,graphAM,sparseMatrix-method} \alias{coerce,graphNEL,CsparseMatrix-method} \alias{coerce,graphNEL,TsparseMatrix-method} \alias{coerce,sparseMatrix,graph-method} \alias{coerce,sparseMatrix,graphNEL-method} \alias{coerce,TsparseMatrix,graphNEL-method} \alias{coerce,dgTMatrix,graphNEL-method} \description{ The \pkg{Matrix} package has supported conversion from and to \code{"\link[graph:graph-class]{graph}"} objects from (Bioconductor) package \pkg{graph} since summer 2005, via the usual \code{as(., "")} coercion, \preformatted{ as(from, Class) } Since 2013, this functionality is further exposed as the \code{graph2T()} and \code{T2graph()} functions (with further arguments than just \code{from}), which convert graphs to and from the triplet form of sparse matrices (of class \code{"\linkS4class{TsparseMatrix}"}) . } \usage{ graph2T(from, use.weights = ) T2graph(from, need.uniq = is_not_uniqT(from), edgemode = NULL) } \arguments{ \item{from}{for \code{graph2T()}, an \R object of class \code{"graph"}; \cr for \code{T2graph()}, a sparse matrix inheriting from \code{"\linkS4class{TsparseMatrix}"}.} \item{use.weights}{logical indicating if weights should be used, i.e., equivalently the result will be numeric, i.e. of class \code{\linkS4class{dgTMatrix}}; otherwise the result will be \code{\linkS4class{ngTMatrix}} or \code{\linkS4class{nsTMatrix}}, the latter if the graph is undirected. The default looks if there are weights in the graph, and if any differ from \code{1}, weights are used.} \item{need.uniq}{a logical indicating if \code{from} may need to be internally \dQuote{uniqified}; do not set this and hence rather use the default, unless you know what you are doing!} \item{edgemode}{one of \code{NULL}, \code{"directed"}, or \code{"undirected"}. The default \code{NULL} looks if the matrix is symmetric and assumes \code{"undirected"} in that case.} } \value{ For \code{graph2T()}, a sparse matrix inheriting from \code{"\linkS4class{TsparseMatrix}"}. For \code{T2graph()} an \R object of class \code{"graph"}. } \seealso{ Note that the CRAN package \pkg{igraph} also provides conversions from and to sparse matrices (of package \pkg{Matrix}) via its \code{\link[igraph]{graph.adjacency}()} and \code{\link[igraph]{get.adjacency}()}. } \examples{ if(isTRUE(try(require(graph)))) { ## super careful .. for "checking reasons" n4 <- LETTERS[1:4]; dns <- list(n4,n4) show(a1 <- sparseMatrix(i= c(1:4), j=c(2:4,1), x = 2, dimnames=dns)) show(g1 <- as(a1, "graph")) # directed unlist(edgeWeights(g1)) # all '2' show(a2 <- sparseMatrix(i= c(1:4,4), j=c(2:4,1:2), x = TRUE, dimnames=dns)) show(g2 <- as(a2, "graph")) # directed # now if you want it undirected: show(g3 <- T2graph(as(a2,"TsparseMatrix"), edgemode="undirected")) show(m3 <- as(g3,"Matrix")) show( graph2T(g3) ) # a "pattern Matrix" (nsTMatrix) \dontshow{ stopifnot( identical(as(g3,"Matrix"), as(as(a2 + t(a2), "nMatrix"),"symmetricMatrix")) , identical(tg3 <- graph2T(g3), graph2T(g3, use.weights=FALSE)) , identical(as(m3,"TsparseMatrix"), Matrix:::uniqTsparse(tg3)) ) } a. <- sparseMatrix(i= 4:1, j=1:4, dimnames=list(n4,n4), giveC=FALSE) # no 'x' show(a.) # "ngTMatrix" show(g. <- as(a., "graph")) \dontshow{ stopifnot(edgemode(g.) == "undirected", numEdges(g.) == 2, all.equal(as(g., "TsparseMatrix"), as(a., "symmetricMatrix")) ) } }% only if( graph ) } \keyword{graph} \keyword{utilities} Matrix/man/TsparseMatrix-class.Rd0000644000175100001440000000656112271746775016541 0ustar hornikusers\name{TsparseMatrix-class} \title{Class "TsparseMatrix" of Sparse Matrices in Triplet Form} \docType{class} \alias{TsparseMatrix-class} %% Methods: \alias{coerce,TsparseMatrix,CsparseMatrix-method} \alias{coerce,TsparseMatrix,lsparseMatrix-method} \alias{coerce,TsparseMatrix,lMatrix-method} \alias{coerce,TsparseMatrix,nsparseMatrix-method} \alias{coerce,TsparseMatrix,nMatrix-method} \alias{coerce,TsparseMatrix,matrix-method} \alias{coerce,Matrix,TsparseMatrix-method} \alias{coerce,matrix,TsparseMatrix-method} \alias{coerce,numeric,TsparseMatrix-method} % \alias{Ops,TsparseMatrix,TsparseMatrix-method} % \alias{Ops,TsparseMatrix,CsparseMatrix-method} % \alias{Ops,CsparseMatrix,TsparseMatrix-method} % % "[" are in ./Xtrct-methods.Rd; "[<-" in ./Subassign-methods.Rd %\alias{solve,...} --> solve-methods.Rd %\alias{\%*%,... } --> matrix-products.Rd \alias{t,TsparseMatrix-method} % \description{The \code{"TsparseMatrix"} class is the virtual class of all sparse matrices coded in triplet form. Since it is a virtual class, no objects may be created from it. See \code{showClass("TsparseMatrix")} for its subclasses. } \section{Slots}{ \describe{ \item{\code{Dim}, \code{Dimnames}:}{from the \code{"\linkS4class{Matrix}"} class,} \item{\code{i}:}{Object of class \code{"integer"} - the row indices of non-zero entries \emph{in 0-base}, i.e., must be in \code{0:(nrow(.)-1)}.} \item{\code{j}:}{Object of class \code{"integer"} - the column indices of non-zero entries. Must be the same length as slot \code{i} and \emph{0-based} as well, i.e., in \code{0:(ncol(.)-1)}. For numeric Tsparse matrices, \code{(i,j)} pairs can occur more than once, see \code{\linkS4class{dgTMatrix}}. } } } \section{Extends}{ Class \code{"sparseMatrix"}, directly. Class \code{"Matrix"}, by class \code{"sparseMatrix"}. } \section{Methods}{ Extraction (\code{"["}) methods, see \code{\link{[-methods}}.%-> ./Xtrct-methods.Rd } \note{ Most operations with sparse matrices are performed using the compressed, column-oriented or \code{\linkS4class{CsparseMatrix}} representation. The triplet representation is convenient for creating a sparse matrix or for reading and writing such matrices. Once it is created, however, the matrix is generally coerced to a \code{\linkS4class{CsparseMatrix}} for further operations. Note that all \code{new(.)}, \code{\link{spMatrix}} and \code{\link{sparseMatrix}(*, giveCsparse=FALSE)} constructors for \code{"TsparseMatrix"} classes implicitly add \eqn{x_k}'s that belong to identical \eqn{(i_k, j_k)} pairs, see, the example below, or also \code{"\linkS4class{dgTMatrix}"}. For convenience, methods for some operations such as \code{\%*\%} and \code{crossprod} are defined for \code{\linkS4class{TsparseMatrix}} objects. These methods simply coerce the \code{\linkS4class{TsparseMatrix}} object to a \code{\linkS4class{CsparseMatrix}} object then perform the operation. } % \author{Martin Maechler} \seealso{ its superclass, \code{\linkS4class{sparseMatrix}}, and the \code{\linkS4class{dgTMatrix}} class, for the links to other classes. } \examples{ showClass("TsparseMatrix") ## or just the subclasses' names names(getClass("TsparseMatrix")@subclasses) T3 <- spMatrix(3,4, i=c(1,3:1), j=c(2,4:2), x=1:4) T3 # only 3 non-zero entries, 5 = 1+4 ! \dontshow{stopifnot(nnzero(T3) == 3)} } \keyword{classes} Matrix/man/colSums.Rd0000644000175100001440000000754611353363473014247 0ustar hornikusers\name{colSums} \alias{colSums} \alias{colMeans} \alias{rowSums} \alias{rowMeans} \alias{colMeans,diagonalMatrix-method} \alias{colSums,diagonalMatrix-method} \alias{rowMeans,diagonalMatrix-method} \alias{rowSums,diagonalMatrix-method} \alias{colMeans,CsparseMatrix-method} \alias{colSums,CsparseMatrix-method} \alias{rowMeans,CsparseMatrix-method} \alias{rowSums,CsparseMatrix-method} \alias{colMeans,TsparseMatrix-method} \alias{colSums,TsparseMatrix-method} \alias{rowMeans,TsparseMatrix-method} \alias{rowSums,TsparseMatrix-method} \alias{colMeans,RsparseMatrix-method} \alias{colSums,RsparseMatrix-method} \alias{rowMeans,RsparseMatrix-method} \alias{rowSums,RsparseMatrix-method} \alias{colMeans,dgCMatrix-method} \alias{colSums,dgCMatrix-method} \alias{rowMeans,dgCMatrix-method} \alias{rowSums,dgCMatrix-method} \alias{colMeans,igCMatrix-method} \alias{colSums,igCMatrix-method} \alias{rowMeans,igCMatrix-method} \alias{rowSums,igCMatrix-method} \alias{colMeans,lgCMatrix-method} \alias{colSums,lgCMatrix-method} \alias{rowMeans,lgCMatrix-method} \alias{rowSums,lgCMatrix-method} \alias{colMeans,ngCMatrix-method} \alias{colSums,ngCMatrix-method} \alias{rowMeans,ngCMatrix-method} \alias{rowSums,ngCMatrix-method} % dense ones \alias{colMeans,denseMatrix-method} \alias{colSums,denseMatrix-method} \alias{rowMeans,denseMatrix-method} \alias{rowSums,denseMatrix-method} \alias{colMeans,ddenseMatrix-method} \alias{colSums,ddenseMatrix-method} \alias{rowMeans,ddenseMatrix-method} \alias{rowSums,ddenseMatrix-method} % NB: kept those documented in ./dgeMatrix-class.Rd % \title{Form Row and Column Sums and Means} % see also ~/R/D/r-devel/R/src/library/base/man/colSums.Rd \description{ Form row and column sums and means for \code{\linkS4class{Matrix}} objects. } \usage{ colSums (x, na.rm = FALSE, dims = 1, \dots) rowSums (x, na.rm = FALSE, dims = 1, \dots) colMeans(x, na.rm = FALSE, dims = 1, \dots) rowMeans(x, na.rm = FALSE, dims = 1, \dots) \S4method{colSums}{CsparseMatrix}(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) \S4method{rowSums}{CsparseMatrix}(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) \S4method{colMeans}{CsparseMatrix}(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) \S4method{rowMeans}{CsparseMatrix}(x, na.rm = FALSE, dims = 1, sparseResult = FALSE) } \arguments{ \item{x}{a Matrix, i.e., inheriting from \code{\linkS4class{Matrix}}.} \item{na.rm}{logical. Should missing values (including \code{NaN}) be omitted from the calculations?} \item{dims}{completely ignored by the \code{Matrix} methods.} \item{\dots}{potentially further arguments, for method \code{<->} generic compatibility.} \item{sparseResult}{logical indicating if the result should be sparse, i.e., inheriting from class \code{\linkS4class{sparseVector}}.} } % \details{ % ~~ If necessary, more details than the description above ~~ % } \value{ returns a numeric vector if \code{sparseResult} is \code{FALSE} as per default. Otherwise, returns a \code{\linkS4class{sparseVector}}. } %\author{Martin} \seealso{\code{\link[base]{colSums}} and the \code{\linkS4class{sparseVector}} classes. } \examples{ (M <- bdiag(Diagonal(2), matrix(1:3, 3,4), diag(3:2))) # 7 x 8 colSums(M) d <- Diagonal(10, c(0,0,10,0,2,rep(0,5))) MM <- kronecker(d, M) dim(MM) # 70 80 length(MM@x) # 160, but many are '0' ; drop those: MM <- drop0(MM) length(MM@x) # 32 cm <- colSums(MM) (scm <- colSums(MM, sparseResult = TRUE)) stopifnot(is(scm, "sparseVector"), identical(cm, as.numeric(scm))) rowSums(MM, sparseResult = TRUE) # 16 of 70 are not zero colMeans(MM, sparseResult = TRUE) ## Since we have no 'NA's, these two are equivalent : stopifnot(identical(rowMeans(MM, sparseResult = TRUE), rowMeans(MM, sparseResult = TRUE, na.rm = TRUE)), rowMeans(Diagonal(16)) == 1/16, colSums(Diagonal(7)) == 1) } \keyword{array} \keyword{algebra} \keyword{arith} Matrix/man/formatSparseM.Rd0000644000175100001440000000624611530442451015370 0ustar hornikusers\name{formatSparseM} \alias{formatSparseM} \alias{.formatSparseSimple} \title{Formatting Sparse Numeric Matrices Utilities} \description{ Utilities for formatting sparse numeric matrices in a flexible way. These functions are used by the \code{\link{format}} and \code{print} methods for sparse matrices and can be applied as well to standard \R matrices. Note that \emph{all} arguments but the first are optional. \code{formatSparseM()} is the main \dQuote{workhorse} of \code{\link{formatSpMatrix}}, the \code{format} method for sparse matrices. \code{.formatSparseSimple()} is a simple helper function, also dealing with (short/empty) column names construction. } \usage{ formatSparseM(x, zero.print = ".", align = c("fancy", "right"), m = as(x,"matrix"), asLogical=NULL, digits=NULL, cx, iN0, dn = dimnames(m)) .formatSparseSimple(m, asLogical=FALSE, digits=NULL, col.names, note.dropping.colnames = TRUE, dn=dimnames(m)) } \arguments{ \item{x}{an \R object inheriting from class \code{\linkS4class{sparseMatrix}}.} \item{zero.print}{character which should be used for \emph{structural} zeroes. The default \code{"."} may occasionally be replaced by \code{" "} (blank); using \code{"0"} would look almost like \code{print()}ing of non-sparse matrices.} \item{align}{a string specifying how the \code{zero.print} codes should be aligned, see \code{\link{formatSpMatrix}}.} \item{m}{(optional) a (standard \R) \code{\link{matrix}} version of \code{x}.} \item{asLogical}{should the matrix be formatted as a logical matrix (or rather as a numeric one); mostly for \code{formatSparseM()}.} \item{digits}{significant digits to use for printing, see \code{\link{print.default}}.} \item{cx}{(optional) character matrix; a formatted version of \code{x}, still with strings such as \code{"0.00"} for the zeros.} \item{iN0}{(optional) integer vector, specifying the location of the \emph{non}-zeroes of \code{x}.} \item{col.names, note.dropping.colnames}{see \code{\link{formatSpMatrix}}.} \item{dn}{\code{\link{dimnames}} to be used; a list (of length two) with row and column names (or \code{\link{NULL}}).} } \seealso{ \code{\link{formatSpMatrix}} which calls \code{formatSparseM()} and is the \code{\link{format}} method for sparse matrices.\cr \code{\link{printSpMatrix}} which is used by the (typically implicitly called) \code{\link{show}} and \code{\link{print}} methods for sparse matrices. } \value{ a character matrix like \code{cx}, where the zeros have been replaced with (padded versions of) \code{zero.print}. As this is a \emph{dense} matrix, do not use these functions for really large (really) sparse matrices! } \author{Martin Maechler} \examples{ m <- suppressWarnings(matrix(c(0, 3.2, 0,0, 11,0,0,0,0,-7,0), 4,9)) fm <- formatSparseM(m) noquote(fm) ## nice, but this is nicer : print(fm, quote=FALSE, right=TRUE) ## and "the same" as : Matrix(m) ## align = "right" is cheaper --> the "." are not aligned: noquote(f2 <- formatSparseM(m,align="r")) stopifnot(f2 == fm | m == 0, dim(f2) == dim(m), (f2 == ".") == (m == 0)) } \keyword{utilities} \keyword{print} Matrix/man/dsyMatrix-class.Rd0000644000175100001440000001124612271746775015713 0ustar hornikusers\name{dsyMatrix-class} \docType{class} \alias{dspMatrix-class} \alias{dsyMatrix-class} % % \alias{solve, ..} --> solve-methods.Rd % \alias{\%*%, ..} --> matrix-products.Rd \alias{coerce,dspMatrix,dsyMatrix-method} \alias{coerce,dspMatrix,lspMatrix-method} \alias{coerce,dspMatrix,matrix-method} \alias{coerce,dspMatrix,CsparseMatrix-method} \alias{coerce,dspMatrix,sparseMatrix-method} \alias{coerce,dgeMatrix,dspMatrix-method} \alias{coerce,matrix,dspMatrix-method} \alias{coerce,dgeMatrix,dsyMatrix-method}% or rather setIs? \alias{coerce,dsyMatrix,corMatrix-method} \alias{coerce,dsyMatrix,dpoMatrix-method}% instead of setIs \alias{coerce,dsyMatrix,dspMatrix-method} \alias{coerce,dsyMatrix,lsyMatrix-method} \alias{.dsy2mat}% hidden but exported \alias{coerce,dsyMatrix,matrix-method} \alias{coerce,matrix,dsyMatrix-method} \alias{diag,dspMatrix-method} \alias{diag,dsyMatrix-method} \alias{diag<-,dspMatrix-method} \alias{diag<-,dsyMatrix-method} % \alias{show,dsyMatrix-method} \alias{norm,dspMatrix,character-method} \alias{norm,dspMatrix,missing-method} \alias{norm,dsyMatrix,character-method} \alias{norm,dsyMatrix,missing-method} \alias{rcond,dspMatrix,character-method} \alias{rcond,dspMatrix,missing-method} \alias{rcond,dsyMatrix,character-method} \alias{rcond,dsyMatrix,missing-method} \alias{t,dspMatrix-method} \alias{t,dsyMatrix-method} \title{Symmetric Dense Numeric Matrices} \description{ The \code{"dsyMatrix"} class is the class of symmetric, dense matrices in non-packed storage and \code{"dspMatrix"} is the class of symmetric dense matrices in packed storage. Only the upper triangle or the lower triangle is stored. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("dsyMatrix", ...)}. } \section{Slots}{ \describe{ \item{\code{uplo}:}{Object of class \code{"character"}. Must be either "U", for upper triangular, and "L", for lower triangular.} \item{\code{x}:}{Object of class \code{"numeric"}. The numeric values that constitute the matrix, stored in column-major order.} \item{\code{Dim},\code{Dimnames}:}{The dimension (a length-2 \code{"integer"}) and corresponding names (or \code{NULL}), see the \code{\linkS4class{Matrix}}.} \item{\code{factors}:}{Object of class \code{"list"}. A named list of factorizations that have been computed for the matrix.} } } \section{Extends}{ \code{"dsyMatrix"} extends class \code{"dgeMatrix"}, directly, whereas\cr \code{"dspMatrix"} extends class \code{"ddenseMatrix"}, directly. Both extend class \code{"symmetricMatrix"}, directly, and class \code{"Matrix"} and others, \emph{in}directly, use \code{\link{showClass}("dsyMatrix")}, e.g., for details. } \section{Methods}{ \describe{ \item{coerce}{\code{signature(from = "ddenseMatrix", to = "dgeMatrix")}} % \item{coerce}{\code{signature(from = "dspMatrix", to = "matrix")}} \item{coerce}{\code{signature(from = "dsyMatrix", to = "matrix")}} \item{coerce}{\code{signature(from = "dsyMatrix", to = "dspMatrix")}} \item{coerce}{\code{signature(from = "dspMatrix", to = "dsyMatrix")}} \item{norm}{\code{signature(x = "dspMatrix", type = "character")}} \item{norm}{\code{signature(x = "dsyMatrix", type = "character")}} \item{norm}{\code{signature(x = "dspMatrix", type = "missing")}} \item{norm}{\code{signature(x = "dsyMatrix", type = "missing")}} \item{solve}{\code{signature(a = "dspMatrix", b = "....")}, and} \item{solve}{\code{signature(a = "dsyMatrix", b = "....")}: \code{x <- solve(a,b)} solves \eqn{A x = b} for \eqn{x}; see \code{\link{solve-methods}}.} \item{t}{\code{signature(x = "dsyMatrix")}: Transpose; swaps from upper triangular to lower triangular storage, i.e., the uplo slot from \code{"U"} to \code{"L"} or vice versa, the same as for all symmetric matrices.} } } %\references{} %\author{} \seealso{ Classes \code{\linkS4class{dgeMatrix}} and \code{\linkS4class{Matrix}}; \code{\link[base]{solve}}, \code{\link{norm}}, \code{\link{rcond}}, \code{\link[base]{t}} } \examples{ ## Only upper triangular part matters (when uplo == "U" as per default) (sy2 <- new("dsyMatrix", Dim = as.integer(c(2,2)), x = c(14, NA,32,77))) str(t(sy2)) # uplo = "L", and the lower tri. (i.e. NA is replaced). chol(sy2) #-> "Cholesky" matrix (sp2 <- pack(sy2)) # a "dspMatrix" ## Coercing to dpoMatrix gives invalid object: sy3 <- new("dsyMatrix", Dim = as.integer(c(2,2)), x = c(14, -1, 2, -7)) try(as(sy3, "dpoMatrix")) # -> error: not positive definite \dontshow{ tr <- try(as(sy3, "dpoMatrix"), silent=TRUE) stopifnot(1 == grep("not a positive definite matrix", as.character(tr)), is(sp2, "dspMatrix")) } } \keyword{classes} Matrix/man/chol2inv-methods.Rd0000644000175100001440000000362212023457647016000 0ustar hornikusers\name{chol2inv-methods} \docType{methods} % \alias{chol2inv}% needed, if we want \usage{} \alias{chol2inv-methods} \alias{chol2inv,ANY-method} \alias{chol2inv,dtrMatrix-method} \alias{chol2inv,CHMfactor-method} \alias{chol2inv,denseMatrix-method} \alias{chol2inv,sparseMatrix-method} \title{Inverse from Choleski or QR Decomposition -- Matrix Methods} \description{ Invert a symmetric, positive definite square matrix from its Choleski decomposition. Equivalently, compute \eqn{(X'X)^{-1}}{(X'X)^(-1)} from the (\eqn{R} part) of the QR decomposition of \eqn{X}. \cr Even more generally, given an upper triangular matrix \eqn{R}, compute \eqn{(R'R)^{-1}}{(R'R)^(-1)}. } % \usage{ % chol2inv(x, \dots) % } % \arguments{ % \item{x}{a matrix(-like) object; see below.} % \item{\dots}{not used here; for compatibility with other methods.} % } \section{Methods}{ \describe{ \item{x = "ANY"}{the default method from \pkg{base}, see \code{\link[base]{chol2inv}}, for traditional matrices.} \item{x = "dtrMatrix"}{method for the numeric triangular matrices, built on the same LAPACK \command{DPOTRI} function as the base method.} \item{x = "denseMatrix"}{if \code{x} is coercable to a \code{\linkS4class{triangularMatrix}}, call the \code{"dtrMatrix"} method above.} \item{x = "sparseMatrix"}{if \code{x} is coercable to a \code{\linkS4class{triangularMatrix}}, use \code{\link{solve}()} currently.} %% better algorithms are welcome! } } \seealso{ \code{\link{chol}} (for \code{\linkS4class{Matrix}} objects); further, \code{\link[base]{chol2inv}} (from the \pkg{base} package), \code{\link{solve}}. } \examples{ (M <- Matrix(cbind(1, 1:3, c(1,3,7)))) (cM <- chol(M)) # a "Cholesky" object, inheriting from "dtrMatrix" chol2inv(cM) \%*\% M # the identity stopifnot(all(chol2inv(cM) \%*\% M - Diagonal(nrow(M))) < 1e-10) } \keyword{methods} \keyword{algebra} Matrix/man/number-class.Rd0000644000175100001440000000111510746336135015177 0ustar hornikusers\name{number-class} \docType{class} \alias{number-class} \title{Class "number" of Possibly Complex Numbers} \description{The class \code{"number"} is a virtual class, currently used for vectors of eigen values which can be \code{"numeric"} or \code{"complex"}. It is a simple class union (\code{\link{setClassUnion}}) of \code{"numeric"} and \code{"complex"}. } \section{Objects from the Class}{Since it is a virtual Class, no objects may be created from it.} \examples{ showClass("number") stopifnot( is(1i, "number"), is(pi, "number"), is(1:3, "number") ) } \keyword{classes} Matrix/man/nsyMatrix-class.Rd0000644000175100001440000000475712001034107015700 0ustar hornikusers\name{nsyMatrix-class} \title{Symmetric Dense Nonzero-Pattern Matrices} \docType{class} \alias{nspMatrix-class} \alias{nsyMatrix-class} % \alias{coerce,nspMatrix,dspMatrix-method} \alias{coerce,nspMatrix,nsyMatrix-method} \alias{coerce,nspMatrix,ngeMatrix-method} \alias{coerce,nsyMatrix,dsyMatrix-method} \alias{coerce,nsyMatrix,ngeMatrix-method} \alias{coerce,nsyMatrix,nspMatrix-method} \alias{coerce,matrix,nsyMatrix-method} \alias{coerce,matrix,nspMatrix-method} \alias{diag<-,nspMatrix-method} \alias{diag<-,nsyMatrix-method} \alias{t,nspMatrix-method} \alias{t,nsyMatrix-method} % \description{ The \code{"nsyMatrix"} class is the class of symmetric, dense nonzero-pattern matrices in non-packed storage and \code{"nspMatrix"} is the class of of these in packed storage. Only the upper triangle or the lower triangle is stored. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("nsyMatrix", ...)}. } \section{Slots}{ \describe{ \item{\code{uplo}:}{Object of class \code{"character"}. Must be either "U", for upper triangular, and "L", for lower triangular.} \item{\code{x}:}{Object of class \code{"logical"}. The logical values that constitute the matrix, stored in column-major order.} \item{\code{Dim},\code{Dimnames}:}{The dimension (a length-2 \code{"integer"}) and corresponding names (or \code{NULL}), see the \code{\linkS4class{Matrix}} class.} \item{\code{factors}:}{Object of class \code{"list"}. A named list of factorizations that have been computed for the matrix.} } } \section{Extends}{ \code{"nsyMatrix"} extends class \code{"ngeMatrix"}, directly, whereas\cr \code{"nspMatrix"} extends class \code{"ndenseMatrix"}, directly. Both extend class \code{"symmetricMatrix"}, directly, and class \code{"Matrix"} and others, \emph{in}directly, use \code{\link{showClass}("nsyMatrix")}, e.g., for details. } \section{Methods}{ Currently, mainly \code{\link{t}()} and coercion methods (for \code{\link{as}(.)}; use, e.g., \code{\link{showMethods}(class="dsyMatrix")} for details. } %\references{} %\author{} \seealso{ \code{\linkS4class{ngeMatrix}}, \code{\linkS4class{Matrix}}, \code{\link[base]{t}} } \examples{ (s0 <- new("nsyMatrix")) (M2 <- Matrix(c(TRUE, NA,FALSE,FALSE), 2,2)) # logical dense (ltr) (sM <- M2 & t(M2)) # "lge" class(sM <- as(sM, "nMatrix")) # -> "nge" (sM <- as(sM, "nsyMatrix")) # -> "nsy" str ( sM <- as(sM, "nspMatrix")) # -> "nsp": packed symmetric } \keyword{classes} Matrix/man/indMatrix-class.Rd0000644000175100001440000001646512271746775015676 0ustar hornikusers\name{indMatrix-class} \docType{class} \alias{indMatrix-class} \alias{-,indMatrix,missing-method} \alias{coerce,integer,indMatrix-method} \alias{coerce,numeric,indMatrix-method} \alias{coerce,list,indMatrix-method} \alias{coerce,matrix,indMatrix-method} \alias{coerce,sparseMatrix,indMatrix-method} \alias{coerce,indMatrix,matrix-method} \alias{coerce,indMatrix,ngeMatrix-method} \alias{coerce,indMatrix,ngTMatrix-method} \alias{coerce,indMatrix,dMatrix-method} \alias{coerce,indMatrix,lMatrix-method} \alias{coerce,indMatrix,nMatrix-method} \alias{coerce,indMatrix,CsparseMatrix-method} \alias{coerce,indMatrix,TsparseMatrix-method} \alias{coerce,indMatrix,dsparseMatrix-method} \alias{coerce,indMatrix,lsparseMatrix-method} \alias{coerce,indMatrix,nsparseMatrix-method} \alias{coerce,nMatrix,indMatrix-method} \alias{determinant,indMatrix,logical-method} \alias{Summary,indMatrix-method} % \alias{rbind2,indMatrix,indMatrix-method} \alias{t,indMatrix-method} \alias{colSums,indMatrix-method} \alias{colMeans,indMatrix-method} \alias{rowSums,indMatrix-method} \alias{rowMeans,indMatrix-method} % \title{Index matrices} \description{The \code{"indMatrix"} class is the class of index matrices, stored as 1-based integer index vectors. An index matrix is a matrix with exactly one non-zero entry per row. Index matrices are useful for mapping observations to unique covariate values, for example. Matrix (vector) multiplication with index matrices is equivalent to replicating and permuting rows, or \dQuote{sampling rows with replacement}, and is implemented that way in the \pkg{Matrix} package, see the \sQuote{Details} below. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("indMatrix", ...)} or by coercion from an integer index vector, see below. } \section{Slots}{ \describe{ \item{\code{perm}:}{An integer, 1-based index vector, i.e. an integer vector of length \code{Dim[1]} whose elements are taken from \code{1:Dim[2]}.} \item{\code{Dim}:}{Object of class \code{"integer"}. The dimensions of the matrix which must skinny, i.e., the first dimension has to be at least as large as the second.} \item{\code{Dimnames}:}{list of length two; each component containing NULL or a \code{\link{character}} vector length equal the corresponding \code{Dim} element.} } } \section{Extends}{ Class \code{"\linkS4class{sparseMatrix}"} and \code{"\linkS4class{generalMatrix}"}, directly. } \section{Methods}{ \describe{ \item{\%*\%}{\code{signature(x = "matrix", y = "indMatrix")} and other signatures (use \code{showMethods("\%*\%", class="indMatrix")}): ... } \item{coerce}{\code{signature(from = "integer", to = "indMatrix")}: This enables typical \code{"indMatrix"} construction, given an index vector from elements in \code{1:Dim[2]}, see the first example.} \item{coerce}{\code{signature(from = "numeric", to = "indMatrix")}: a user convenience, to allow \code{as(perm, "indMatrix")} for numeric \code{perm} with integer values.} \item{coerce}{\code{signature(from = "list", to = "indMatrix")}: The list must have two (integer-valued) entries: the first giving the index vector with elements in \code{1:Dim[2]}, the second giving \code{Dim[2]}. This allows \code{"indMatrix"} construction for cases in which the values represented by the rightmost column(s) are not associated with any observations, i.e., in which the index does not contain values \code{Dim[2], Dim[2]-1, Dim[2]-2, ...}} \item{coerce}{\code{signature(from = "indMatrix", to = "matrix")}: coercion to a traditional FALSE/TRUE \code{\link{matrix}} of \code{\link{mode}} \code{logical}.} \item{coerce}{\code{signature(from = "indMatrix", to = "ngTMatrix")}: coercion to sparse logical matrix of class \code{\linkS4class{ngTMatrix}}.} \item{t}{\code{signature(x = "indMatrix")}: return the transpose of the index matrix (which is no longer an \code{indMatrix}, but of class \code{\linkS4class{ngTMatrix}}.} \item{colSums, colMeans, rowSums, rowMeans}{\code{signature(x = "indMatrix")}: return the column or row sums or means.} \item{rbind2}{\code{signature(x = "indMatrix", y = "indMatrix")}: a fast method for rowwise catenation of two index matrices (with the same number of columns).} \item{kronecker}{\code{signature(X = "indMatrix", Y = "indMatrix")}: return the kronecker product of two index matrices, which corresponds to the index matrix of the interaction of the two.} } } \author{Fabian Scheipl \email{....@uni-muenchen.de} building on existing "pMatrix", after a nice hike's conversation with Martin Maechler and tweaks by the latter. } \details{ Matrix (vector) multiplication with index matrices from the left is equivalent to replicating and permuting rows of the matrix on the right hand side. (Similarly, matrix multiplication with the transpose of an index matrix from the right corresponds to selecting \emph{columns}.) The crossproduct of an index matrix \eqn{M} with itself is a diagonal matrix with the number of entries in each column of \eqn{M} on the diagonal, i.e., \eqn{M'M=}\code{Diagonal(x=table(M@perm))}. Permutation matrices (of class \code{\linkS4class{pMatrix}}) are special cases of index matrices: They are square, of dimension, say, \eqn{n \times n}{n * n}, and their index vectors contain exactly all of \code{1:n}. While \dQuote{row-indexing} (of more than one row \emph{or} using \code{drop=FALSE}) stays within the \code{"indMatrix"} class, all other subsetting/indexing operations (\dQuote{column-indexing}, including, \code{\link{diag}}) on \code{"indMatrix"} objects treats them as nonzero-pattern matrices (\code{"\linkS4class{ngTMatrix}"} specifically), such that non-matrix subsetting results in \code{\link{logical}} vectors. Sub-assignment (\code{M[i,j] <- v}) is not sensible and hence an error for these matrices. } \seealso{ The permutation matrices \code{\linkS4class{pMatrix}} are special index matrices. The \dQuote{pattern} matrices, \code{\linkS4class{nMatrix}} and its subclasses. } \examples{ p1 <- as(c(2,3,1), "pMatrix") (sm1 <- as(rep(c(2,3,1), e=3), "indMatrix")) stopifnot(all(sm1 == p1[rep(1:3, each=3),])) ## row-indexing of a turns it into an : class(p1[rep(1:3, each=3),]) set.seed(12) # so we know '10' is in sample ## random index matrix for 30 observations and 10 unique values: (s10 <- as(sample(10, 30, replace=TRUE),"indMatrix")) ## Sample rows of a numeric matrix : (mm <- matrix(1:10, nrow=10, ncol=3)) s10 \%*\% mm set.seed(27) IM1 <- as(sample(1:20, 100, replace=TRUE), "indMatrix") IM2 <- as(sample(1:18, 100, replace=TRUE), "indMatrix") (c12 <- crossprod(IM1,IM2)) ## same as cross-tabulation of the two index vectors: stopifnot(all(c12 - unclass(table(IM1@perm, IM2@perm)) == 0)) # 3 observations, 4 implied values, first does not occur in sample: as(2:4, "indMatrix") # 3 observations, 5 values, first and last do not occur in sample: as(list(2:4, 5), "indMatrix") as(sm1, "ngTMatrix") s10[1:7, 1:4] # gives an "ngTMatrix" (most economic!) s10[1:4, ] # preserves "indMatrix"-class I1 <- as(c(5:1,6:4,7:3), "indMatrix") I2 <- as(7:1, "pMatrix") (I12 <- rBind(I1, I2)) stopifnot(is(I12, "indMatrix"), colSums(I12) == c(2L,2:4,4:2)) } \keyword{classes} Matrix/man/lsyMatrix-class.Rd0000644000175100001440000000457612001034107015675 0ustar hornikusers\name{lsyMatrix-class} \title{Symmetric Dense Logical Matrices} \docType{class} \alias{lspMatrix-class} \alias{lsyMatrix-class} % \alias{coerce,lspMatrix,dspMatrix-method} \alias{coerce,lspMatrix,lsyMatrix-method} \alias{coerce,lspMatrix,lgeMatrix-method} \alias{coerce,lsyMatrix,dsyMatrix-method} \alias{coerce,lsyMatrix,lgeMatrix-method} \alias{coerce,lsyMatrix,lspMatrix-method} \alias{coerce,matrix,lsyMatrix-method} \alias{coerce,matrix,lspMatrix-method} \alias{diag,lspMatrix-method} \alias{diag,lsyMatrix-method} \alias{diag<-,lspMatrix-method} \alias{diag<-,lsyMatrix-method} \alias{t,lspMatrix-method} \alias{t,lsyMatrix-method} % \description{ The \code{"lsyMatrix"} class is the class of symmetric, dense logical matrices in non-packed storage and \code{"lspMatrix"} is the class of of these in packed storage. In the packed form, only the upper triangle or the lower triangle is stored. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("lsyMatrix", ...)}. } \section{Slots}{ \describe{ \item{\code{uplo}:}{Object of class \code{"character"}. Must be either "U", for upper triangular, and "L", for lower triangular.} \item{\code{x}:}{Object of class \code{"logical"}. The logical values that constitute the matrix, stored in column-major order.} \item{\code{Dim},\code{Dimnames}:}{The dimension (a length-2 \code{"integer"}) and corresponding names (or \code{NULL}), see the \code{\linkS4class{Matrix}} class.} \item{\code{factors}:}{Object of class \code{"list"}. A named list of factorizations that have been computed for the matrix.} } } \section{Extends}{ Both extend classes \code{"\linkS4class{ldenseMatrix}"} and \code{"\linkS4class{symmetricMatrix}"}, directly; further, class \code{"Matrix"} and others, \emph{in}directly. Use \code{\link{showClass}("lsyMatrix")}, e.g., for details. } \section{Methods}{ Currently, mainly \code{\link{t}()} and coercion methods (for \code{\link{as}(.)}; use, e.g., \code{\link{showMethods}(class="dsyMatrix")} for details. } %\references{} %\author{} \seealso{ \code{\linkS4class{lgeMatrix}}, \code{\linkS4class{Matrix}}, \code{\link[base]{t}} } \examples{ (M2 <- Matrix(c(TRUE, NA,FALSE,FALSE), 2,2)) # logical dense (ltr) str(M2) # can (sM <- M2 | t(M2)) # "lge" as(sM, "lsyMatrix") str(sM <- as(sM, "lspMatrix")) # packed symmetric } \keyword{classes} Matrix/man/rankMatrix.Rd0000644000175100001440000001501612257570015014725 0ustar hornikusers\name{rankMatrix} \alias{rankMatrix} \title{Rank of a Matrix} \description{ Compute \sQuote{the} matrix rank, a well-defined functional in theory, somewhat ambigous in practice. We provide several methods, the default corresponding to Matlab's definition. } \usage{ rankMatrix(x, tol = NULL, method = c("tolNorm2", "qr.R", "qrLINPACK", "qr", "useGrad", "maybeGrad"), sval = svd(x, 0, 0)$d, warn.t = TRUE) } \arguments{ \item{x}{numeric matrix, of dimension \eqn{n \times m}{n x m}, say.} \item{tol}{nonnegative number specifying a (relative, \dQuote{scalefree}) tolerance for testing of \dQuote{practically zero} with specific meaning depending on \code{method}; by default, \code{max(dim(x)) * \link{.Machine}$double.eps} is according to Matlab's default (for its only method which is our \code{method="tolNorm2"}).} \item{method}{a character string specifying the computational method for the rank, can be abbreviated: \describe{ \item{\code{"tolNorm2"}:}{the number of singular values \code{>= tol * max(sval)};} \item{\code{"qrLINPACK"}:}{for a dense matrix, this is the rank of \code{\link[base]{qr}(x, tol, LAPACK=FALSE)} (which is \code{qr(...)$rank}); \cr This ("qr*", dense) version used to be \emph{the} recommended way to compute a matrix rank for a while in the past. For sparse \code{x}, this is equivalent to \code{"qr.R"}. } \item{\code{"qr.R"}:}{this is the rank of triangular matrix \eqn{R}, where \code{qr()} uses LAPACK or a "sparseQR" method (see \code{\link{qr-methods}}) to compute the decomposition \eqn{QR}. The rank of \eqn{R} is then defined as the number of \dQuote{non-zero} diagonal entries \eqn{d_i} of \eqn{R}, and \dQuote{non-zero}s fulfill \eqn{|d_i| \ge \mathrm{tol}\cdot\max(|d_i|)}{|d_i| >= tol * max(|d_i|)}. } \item{\code{"qr"}:}{is for back compatibility; for dense \code{x}, it corresponds to \code{"qrLINPACK"}, whereas for sparse \code{x}, it uses \code{"qr.R"}. For all the "qr*" methods, singular values \code{sval} are not used, which may be crucially important for a large sparse matrix \code{x}, as in that case, when \code{sval} is not specified, the default, computing \code{\link{svd}()} currently coerces \code{x} to a dense matrix. } \item{\code{"useGrad"}:}{considering the \dQuote{gradient} of the (decreasing) singular values, the index of the \emph{smallest} gap.} \item{\code{"maybeGrad"}:}{choosing method \code{"useGrad"} only when that seems \emph{reasonable}; otherwise using \code{"tolNorm2"}.} %% FIXME say more } } \item{sval}{numeric vector of non-increasing singular values of \code{x}; typically unspecified and computed from \code{x} when needed, i.e., unless \code{method = "qr"}.} \item{warn.t}{logical indicating if \code{rankMatrix()} should warn when it needs \code{\link{t}(x)} instead of \code{x}. Currently, for \code{method = "qr"} only, gives a warning by default because the caller often could have passed \code{t(x)} directly, more efficiently.} } % \details{ % FIXME % } \note{For large sparse matrices \code{x}, unless you can specify \code{sval} yourself, currently \code{method = "qr"} may be the only feasible one, as the others need \code{sval} and call \code{\link{svd}()} which currently coerces \code{x} to a \code{\linkS4class{denseMatrix}} which may be very slow or impossible, depending on the matrix dimensions. Note that in the case of sparse \code{x}, \code{method = "qr"}, all non-strictly zero diagonal entries \eqn{d_i} where counted, up to including \pkg{Matrix} version 1.1-0, i.e., that method implicitly used \code{tol = 0}, see also the seed(42) example below. } \value{ positive integer in \code{1:min(dim(x))}, with attributes detailing the method used. } % \references{ % %% ~put references to the literature/web site here ~ % } \author{Martin Maechler; for the "*Grad" methods, building on suggestions by Ravi Varadhan. } \seealso{ \code{\link{qr}}, \code{\link{svd}}. } \examples{ rankMatrix(cbind(1, 0, 1:3)) # 2 (meths <- eval(formals(rankMatrix)$method)) ## a "border" case: H12 <- Hilbert(12) rankMatrix(H12, tol = 1e-20) # 12; but 11 with default method & tol. sapply(meths, function(.m.) rankMatrix(H12, method = .m.)) ## tolNorm2 qr qr.R qrLINPACK useGrad maybeGrad ## 11 12 11 12 11 11 ## The meaning of 'tol' for method="qrLINPACK" and *dense* x is not entirely "scale free" rMQL <- function(ex, M) rankMatrix(M, method="qrLINPACK",tol = 10^-ex) rMQR <- function(ex, M) rankMatrix(M, method="qr.R", tol = 10^-ex) sapply(5:15, rMQL, M = H12) # result is platform dependent ## 7 7 8 10 10 11 11 11 12 12 12 {x86_64} sapply(5:15, rMQL, M = 1000 * H12) # not identical unfortunately ## 7 7 8 10 11 11 12 12 12 12 12 sapply(5:15, rMQR, M = H12) ## 5 6 7 8 8 9 9 10 10 11 11 sapply(5:15, rMQR, M = 1000 * H12) # the *same* \dontshow{ (r12 <- sapply(5:15, rMQR, M = H12)) stopifnot(identical(r12, sapply(5:15, rMQR, M = H12 / 100)), identical(r12, sapply(5:15, rMQR, M = H12 * 1e5))) rM1 <- function(ex, M) rankMatrix(M, tol = 10^-ex) (r12 <- sapply(5:15, rM1, M = H12)) stopifnot(identical(r12, sapply(5:15, rM1, M = H12 / 100)), identical(r12, sapply(5:15, rM1, M = H12 * 1e5))) } ## "sparse" case: M15 <- kronecker(diag(x=c(100,1,10)), Hilbert(5)) sapply(meths, function(.m.) rankMatrix(M15, method = .m.)) #--> all 15, but 'useGrad' has 14. ## "large" sparse n <- 250000; p <- 33; nnz <- 10000 L <- sparseMatrix(i = sample.int(n, nnz, replace=TRUE), j = sample.int(p, nnz, replace=TRUE), x = rnorm(nnz)) (st1 <- system.time(r1 <- rankMatrix(L))) # warning + ~1.5 sec (st2 <- system.time(r2 <- rankMatrix(L, method = "qr"))) # considerably faster! r1[[1]] == print(r2[[1]]) ## --> ( 33 TRUE ) \dontshow{ stopifnot(r1[[1]] == 33, 33 == r2[[1]]) if(doExtras <- interactive() || identical("true", unname(Sys.getenv("R_PKG_CHECKING_doExtras")))) stopifnot(st2[[1]] < 0.2) # seeing 0.03 (on ~ 2010-hardware; R 3.0.2) } ## another sparse-"qr" one, which ``failed'' till 2013-11-23: set.seed(42) f1 <- factor(sample(50, 1000, replace=TRUE)) f2 <- factor(sample(50, 1000, replace=TRUE)) f3 <- factor(sample(50, 1000, replace=TRUE)) D <- t(do.call('rBind', lapply(list(f1,f2,f3), as, 'sparseMatrix'))) dim(D); nnzero(D) ## 1000 x 150 // 3000 non-zeros (= 2\%) stopifnot(rankMatrix(D, method='qr') == 148, rankMatrix(crossprod(D),method='qr') == 148) } \keyword{algebra} \keyword{array} Matrix/man/ntrMatrix-class.Rd0000644000175100001440000000515512001034107015663 0ustar hornikusers\name{ntrMatrix-class} \docType{class} \alias{ntpMatrix-class} \alias{ntrMatrix-class} % \alias{!,ntpMatrix-method} \alias{!,ntrMatrix-method} \alias{coerce,ntpMatrix,dtpMatrix-method} \alias{coerce,ntpMatrix,ngeMatrix-method} \alias{coerce,ntpMatrix,ntrMatrix-method} \alias{coerce,ntrMatrix,dtrMatrix-method} \alias{coerce,ntrMatrix,ngeMatrix-method} \alias{coerce,ntrMatrix,ntpMatrix-method} \alias{coerce,matrix,ntrMatrix-method} \alias{coerce,matrix,ntpMatrix-method} \alias{diag<-,ntpMatrix-method} \alias{diag<-,ntrMatrix-method} \alias{t,ntpMatrix-method} \alias{t,ntrMatrix-method} % \title{Triangular Dense Logical Matrices} \description{ The \code{"ntrMatrix"} class is the class of triangular, dense, logical matrices in nonpacked storage. The \code{"ntpMatrix"} class is the same except in packed storage. } \section{Slots}{ \describe{ \item{\code{x}:}{Object of class \code{"logical"}. The logical values that constitute the matrix, stored in column-major order.} \item{\code{uplo}:}{Object of class \code{"character"}. Must be either "U", for upper triangular, and "L", for lower triangular.} \item{\code{diag}:}{Object of class \code{"character"}. Must be either \code{"U"}, for unit triangular (diagonal is all ones), or \code{"N"}; see \code{\linkS4class{triangularMatrix}}.} \item{\code{Dim},\code{Dimnames}:}{The dimension (a length-2 \code{"integer"}) and corresponding names (or \code{NULL}), see the \code{\linkS4class{Matrix}} class.} \item{\code{factors}:}{Object of class \code{"list"}. A named list of factorizations that have been computed for the matrix.} } } \section{Extends}{ \code{"ntrMatrix"} extends class \code{"ngeMatrix"}, directly, whereas\cr \code{"ntpMatrix"} extends class \code{"ndenseMatrix"}, directly. Both extend Class \code{"triangularMatrix"}, directly, and class \code{"denseMatrix"}, \code{"lMatrix"} and others, \emph{in}directly, use \code{\link{showClass}("nsyMatrix")}, e.g., for details. } \section{Methods}{ Currently, mainly \code{\link{t}()} and coercion methods (for \code{\link{as}(.)}; use, e.g., \code{\link{showMethods}(class="nsyMatrix")} for details. } \seealso{ Classes \code{\linkS4class{ngeMatrix}}, \code{\linkS4class{Matrix}}; function \code{\link[base]{t}} } \examples{ showClass("ntrMatrix") str(new("ntpMatrix")) (nutr <- as(upper.tri(matrix(,4,4)), "ntrMatrix")) str(nutp <- as(nutr, "ntpMatrix"))# packed matrix: only 10 = (4+1)*4/2 entries !nutp ## the logical negation (is *not* logical triangular !) ## but this one is: stopifnot(all.equal(nutp, as(!!nutp, "ntpMatrix"))) } \keyword{classes} Matrix/man/CsparseMatrix-class.Rd0000644000175100001440000001257712271746775016524 0ustar hornikusers\name{CsparseMatrix-class} \docType{class} \alias{CsparseMatrix-class} \alias{coerce,CsparseMatrix,lsparseMatrix-method} \alias{coerce,CsparseMatrix,lMatrix-method} \alias{coerce,CsparseMatrix,nsparseMatrix-method} \alias{coerce,CsparseMatrix,nMatrix-method} \alias{coerce,CsparseMatrix,TsparseMatrix-method} \alias{coerce,CsparseMatrix,denseMatrix-method} \alias{coerce,matrix,CsparseMatrix-method} \alias{coerce,numeric,CsparseMatrix-method} \alias{diag,CsparseMatrix-method} \alias{t,CsparseMatrix-method} % "[" are in ./Xtrct-methods.Rd; "[<-" in ./Subassign-methods.Rd %% Group methods --------- FIXME: not tested yet (or documented) \alias{Compare,CsparseMatrix,CsparseMatrix-method} \alias{Arith,CsparseMatrix,CsparseMatrix-method} \alias{Arith,CsparseMatrix,numeric-method} \alias{Arith,numeric,CsparseMatrix-method} \alias{Logic,CsparseMatrix,CsparseMatrix-method} \alias{Math,CsparseMatrix-method} % \alias{.validateCsparse} % \title{Class "CsparseMatrix" of Sparse Matrices in Column-compressed Form} \description{The \code{"CsparseMatrix"} class is the virtual class of all sparse matrices coded in sorted compressed column-oriented form. Since it is a virtual class, no objects may be created from it. See \code{showClass("CsparseMatrix")} for its subclasses. } \section{Slots}{ \describe{ \item{\code{i}:}{Object of class \code{"integer"} of length nnzero (number of non-zero elements). These are the \emph{0-based} row numbers for each non-zero element in the matrix, i.e., \code{i} must be in \code{0:(nrow(.)-1)}.} \item{\code{p}:}{\code{\link{integer}} vector for providing pointers, one for each column, to the initial (zero-based) index of elements in the column. \code{.@p} is of length \code{ncol(.) + 1}, with \code{p[1] == 0} and \code{p[length(p)] == nnzero}, such that in fact, \code{diff(.@p)} are the number of non-zero elements for each column. In other words, \code{m@p[1:ncol(m)]} contains the indices of those elements in \code{m@x} that are the first elements in the respective column of \code{m}. } \item{\code{Dim}, \code{Dimnames}:}{inherited from the superclass, see the \code{\linkS4class{sparseMatrix}} class.} } } \section{Extends}{ Class \code{"sparseMatrix"}, directly. Class \code{"Matrix"}, by class \code{"sparseMatrix"}. } \section{Methods}{ \describe{ matrix products \code{\link[=crossprod-methods]{\%*\%}}, \code{\link[=crossprod-methods]{crossprod}()} and \code{tcrossprod()}, several \code{\link{solve}} methods, and other matrix methods available: %% The following is generated by promptClass(..) -- %% FIXME: write a script that update all the *-class.Rd files \item{Arith}{\code{signature(e1 = "CsparseMatrix", e2 = "numeric")}: ... } \item{Arith}{\code{signature(e1 = "numeric", e2 = "CsparseMatrix")}: ... } \item{Math}{\code{signature(x = "CsparseMatrix")}: ... } \item{band}{\code{signature(x = "CsparseMatrix")}: ... } \item{-}{\code{signature(e1 = "CsparseMatrix", e2 = "numeric")}: ... } \item{-}{\code{signature(e1 = "numeric", e2 = "CsparseMatrix")}: ... } \item{+}{\code{signature(e1 = "CsparseMatrix", e2 = "numeric")}: ... } \item{+}{\code{signature(e1 = "numeric", e2 = "CsparseMatrix")}: ... } \item{coerce}{\code{signature(from = "CsparseMatrix", to = "TsparseMatrix")}: ... } \item{coerce}{\code{signature(from = "CsparseMatrix", to = "denseMatrix")}: ... } \item{coerce}{\code{signature(from = "CsparseMatrix", to = "matrix")}: ... } \item{coerce}{\code{signature(from = "CsparseMatrix", to = "lsparseMatrix")}: ... } \item{coerce}{\code{signature(from = "CsparseMatrix", to = "nsparseMatrix")}: ... } \item{coerce}{\code{signature(from = "TsparseMatrix", to = "CsparseMatrix")}: ... } \item{coerce}{\code{signature(from = "denseMatrix", to = "CsparseMatrix")}: ... } \item{diag}{\code{signature(x = "CsparseMatrix")}: ... } \item{gamma}{\code{signature(x = "CsparseMatrix")}: ... } \item{lgamma}{\code{signature(x = "CsparseMatrix")}: ... } \item{log}{\code{signature(x = "CsparseMatrix")}: ... } \item{t}{\code{signature(x = "CsparseMatrix")}: ... } \item{tril}{\code{signature(x = "CsparseMatrix")}: ... } \item{triu}{\code{signature(x = "CsparseMatrix")}: ... } } } \note{ All classes extending \code{CsparseMatrix} have a common validity (see \code{\link{validObject}}) check function. That function additionally checks the \code{i} slot for each column to contain increasing row numbers. \cr In earlier versions of \pkg{Matrix} (\code{<= 0.999375-16}), \code{\link{validObject}} automatically re-sorted the entries when necessary, and hence \code{new()} calls with somewhat permuted \code{i} and \code{x} slots worked, as \code{\link{new}(...)} (\emph{with} slot arguments) automatically checks the validity. Now, you have to use \code{\link{sparseMatrix}} to achieve the same functionality or know how to use \code{.validateCsparse()} to do so. } \seealso{ \code{\link{colSums}}, \code{\link{kronecker}}, and other such methods with own help pages. Further, the super class of \code{CsparseMatrix}, \code{\linkS4class{sparseMatrix}}, and, e.g., class \code{\linkS4class{dgCMatrix}} for the links to other classes. } \examples{ getClass("CsparseMatrix") ## The common validity check function (based on C code): getValidity(getClass("CsparseMatrix")) } \keyword{classes} Matrix/man/LU-class.Rd0000644000175100001440000000634012210462526014224 0ustar hornikusers\name{LU-class} \docType{class} \alias{LU-class} \alias{denseLU-class} \alias{expand,denseLU-method} %% \alias{solve,denseLU,missing-method} \title{LU (dense) Matrix Decompositions} \description{ The \code{"LU"} class is the \emph{virtual} class of LU decompositions of real matrices. \code{"denseLU"} the class of LU decompositions of dense real matrices. } \details{ The decomposition is of the form \deqn{A = P L U}{A = P L U} where typically all matrices are of size \eqn{n\times n}{n by n}, and the matrix \eqn{P} is a permutation matrix, \eqn{L} is lower triangular and \eqn{U} is upper triangular (both of class \code{\linkS4class{dtrMatrix}}). Note that the \emph{dense} decomposition is also implemented for a \eqn{m\times n}{m by n} matrix \eqn{A}, when \eqn{m \ne n}{m != n}. If \eqn{m < n} (\dQuote{wide case}), \eqn{U} is \eqn{m\times n}{m by n}, and hence not triangular.\cr If \eqn{m > n} (\dQuote{long case}), \eqn{L} is \eqn{m\times n}{m by n}, and hence not triangular. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("denseLU", ...)}. More commonly the objects are created explicitly from calls of the form \code{\link{lu}(mm)} where \code{mm} is an object that inherits from the \code{"dgeMatrix"} class or as a side-effect of other functions applied to \code{"dgeMatrix"} objects. } \section{Extends}{ \code{"LU"} directly extends the virtual class \code{"\linkS4class{MatrixFactorization}"}. \code{"denseLU"} directly extends \code{"LU"}. } \section{Slots}{ \describe{ \item{\code{x}:}{object of class \code{"numeric"}. The \code{"L"} (unit lower triangular) and \code{"U"} (upper triangular) factors of the original matrix. These are stored in a packed format described in the Lapack manual, and can retrieved by the \code{expand()} method, see below.} \item{\code{perm}:}{Object of class \code{"integer"} - a vector of length \code{min(Dim)} that describes the permutation applied to the rows of the original matrix. The contents of this vector are described in the Lapack manual.} \item{\code{Dim}:}{the dimension of the original matrix; inherited from class \code{\linkS4class{MatrixFactorization}} .} } } \section{Methods}{ \describe{ \item{expand}{\code{signature(x = "denseLU")}: Produce the \code{"L"} and \code{"U"} (and \code{"P"}) factors as a named list of matrices, see also the example below.} \item{solve}{\code{signature(a = "denseLU", b = "missing")}: Compute the inverse of A, \eqn{A^{-1}}{A^(-1)}, \code{solve(A)} using the LU decomposition, see also \code{\link{solve-methods}}.} } } % \references{} \seealso{ class \code{\linkS4class{sparseLU}} for LU decompositions of \emph{sparse} matrices; further, class \code{\linkS4class{dgeMatrix}} and functions \code{\link{lu}}, \code{\link{expand}}. } \examples{ set.seed(1) mm <- Matrix(round(rnorm(9),2), nrow = 3) mm str(lum <- lu(mm)) elu <- expand(lum) elu # three components: "L", "U", and "P", the permutation elu$L \%*\% elu$U (m2 <- with(elu, P \%*\% L \%*\% U)) # the same as 'mm' stopifnot(all.equal(as(mm, "matrix"), as(m2, "matrix"))) } \keyword{classes} \keyword{algebra} Matrix/man/all.equal-methods.Rd0000644000175100001440000000321711314233025016112 0ustar hornikusers\name{all.equal-methods} \title{Matrix Package Methods for Function all.equal()} \docType{methods} \alias{all.equal-methods} % \alias{all.equal,Matrix,Matrix-method} \alias{all.equal,Matrix,ANY-method} \alias{all.equal,ANY,Matrix-method} \alias{all.equal,sparseMatrix,sparseMatrix-method} \alias{all.equal,sparseMatrix,ANY-method} \alias{all.equal,ANY,sparseMatrix-method} \alias{all.equal,sparseVector,sparseVector-method} \alias{all.equal,sparseMatrix,sparseVector-method} \alias{all.equal,sparseVector,sparseMatrix-method} \alias{all.equal,sparseVector,ANY-method} \alias{all.equal,ANY,sparseVector-method} \alias{all.equal,abIndex,abIndex-method} \alias{all.equal,abIndex,numLike-method} \alias{all.equal,numLike,abIndex-method} % \description{ Methods for function \code{\link{all.equal}()} (from \R package \pkg{base}) are defined for all \code{\linkS4class{Matrix}} classes. } \section{Methods}{ \describe{ \item{target = "Matrix", current = "Matrix"}{\ } \item{target = "ANY", current = "Matrix"}{\ } \item{target = "Matrix", current = "ANY"}{these three methods are simply using \code{\link{all.equal.numeric}} directly and work via \code{\link{as.vector}()}.} } } \examples{ (A <- spMatrix(3,3, i= c(1:3,2:1), j=c(3:1,1:2), x = 1:5)) ex <- expand(lu. <- lu(A)) stopifnot( all.equal(as(A[lu.@p + 1L, lu.@q + 1L], "CsparseMatrix"), lu.@L \%*\% lu.@U), with(ex, all.equal(as(P \%*\% A \%*\% Q, "CsparseMatrix"), L \%*\% U)), with(ex, all.equal(as(A, "CsparseMatrix"), t(P) \%*\% L \%*\% U \%*\% t(Q)))) } \keyword{methods} \keyword{arith} Matrix/man/KNex.Rd0000644000175100001440000000210012271746775013456 0ustar hornikusers\name{KNex} \alias{KNex} \docType{data} \title{Koenker-Ng Example Sparse Model Matrix and Response Vector} \description{ A model matrix \code{mm} and corresponding response vector \code{y} used in an example by Koenker and Ng. The matrix \code{mm} is a sparse matrix with 1850 rows and 712 columns but only 8758 non-zero entries. It is a \code{"dgCMatrix"} object. The vector \code{y} is just \code{\link{numeric}} of length 1850. } \usage{data(KNex)} %\details{} %\source{} \references{ Roger Koenker and Pin Ng (2003). SparseM: A sparse matrix package for R; \emph{J. of Statistical Software}, \bold{8} (6), \url{http://www.jstatsoft.org/} } \examples{ data(KNex) class(KNex$mm) dim(KNex$mm) image(KNex$mm) str(KNex) system.time( # a fraction of a second sparse.sol <- with(KNex, solve(crossprod(mm), crossprod(mm, y)))) head(round(sparse.sol,3)) ## Compare with QR-based solution ("more accurate, but slightly slower"): system.time( sp.sol2 <- with(KNex, qr.coef(qr(mm), y) )) all.equal(sparse.sol, sp.sol2, tolerance = 1e-13) # TRUE } \keyword{datasets} Matrix/man/is.na-methods.Rd0000644000175100001440000000471112207615512015253 0ustar hornikusers\name{is.na-methods} \title{is.na(), is.{in}finite() Methods for 'Matrix' Objects} \docType{methods} \alias{is.finite,ddenseMatrix-method} \alias{is.finite,dgeMatrix-method} \alias{is.finite,dsparseMatrix-method} \alias{is.finite,diagonalMatrix-method} \alias{is.finite,lMatrix-method} \alias{is.finite,nMatrix-method} \alias{is.finite,indMatrix-method} \alias{is.infinite,ddenseMatrix-method} \alias{is.infinite,dsparseMatrix-method} \alias{is.infinite,diagonalMatrix-method} \alias{is.infinite,lMatrix-method} \alias{is.infinite,nMatrix-method} \alias{is.infinite,indMatrix-method} \alias{is.na,denseMatrix-method} \alias{is.na,indMatrix-method} \alias{is.na,sparseMatrix-method} \alias{anyNA,nsparseMatrix-method} \alias{anyNA,nsparseVector-method} \alias{anyNA,sparseVector-method} \alias{anyNA,xMatrix-method} \alias{is.na-methods} \description{ Methods for function \code{\link{is.na}()}, \code{\link{is.finite}()}, and \code{\link{is.infinite}()} for all Matrices (objects extending the \code{\linkS4class{Matrix}} class): \describe{ \item{x = "denseMatrix"}{returns a \code{"nMatrix"} object of same dimension as \code{x}, with TRUE's whenever \code{x} is \code{\link{NA}}, finite, or infinite, respectively.} \item{x = "sparseMatrix"}{ditto.} } } \usage{ \S4method{is.na}{sparseMatrix}(x) \S4method{is.finite}{dsparseMatrix}(x) \S4method{is.infinite}{ddenseMatrix}(x) ## ... ## and for other classes \S4method{anyNA}{xMatrix}(x) \S4method{anyNA}{nsparseMatrix}(x) \S4method{anyNA}{sparseVector}(x) \S4method{anyNA}{nsparseVector}(x) } \arguments{ \item{x}{sparse or dense matrix or sparse vector (here; any \R object in general).} } \seealso{ \code{\link{NA}}, \code{\link{is.na}}; \code{\link{is.finite}}, \code{\link{is.infinite}}; \code{\linkS4class{nMatrix}}, \code{\linkS4class{denseMatrix}}, \code{\linkS4class{sparseMatrix}}. The \code{\linkS4class{sparseVector}} class. } \examples{ M <- Matrix(1:6, nrow=4, ncol=3, dimnames = list(c("a", "b", "c", "d"), c("A", "B", "C"))) stopifnot(all(!is.na(M))) M[2:3,2] <- NA is.na(M) if(exists("anyNA", mode="function")) anyNA(M) A <- spMatrix(10,20, i = c(1,3:8), j = c(2,9,6:10), x = 7 * (1:7)) stopifnot(all(!is.na(A))) %TODO stopifnot(all(!is.na(A)), !anyNA(A)) A[2,3] <- A[1,2] <- A[5, 5:9] <- NA inA <- is.na(A) stopifnot(sum(inA) == 1+1+5) \dontshow{ if(exists("anyNA", mode="function")) stopifnot(anyNA(M), anyNA(A)) }% dont.. } \keyword{methods} Matrix/man/nearPD.Rd0000644000175100001440000001713012271746775013773 0ustar hornikusers\name{nearPD} \alias{nearPD} \title{Nearest Positive Definite Matrix} \description{ Compute the nearest positive definite matrix to an approximate one, typically a correlation or variance-covariance matrix. } \usage{ nearPD(x, corr = FALSE, keepDiag = FALSE, do2eigen = TRUE, doSym = FALSE, doDykstra = TRUE, only.values = FALSE, ensureSymmetry = !isSymmetric(x), eig.tol = 1e-06, conv.tol = 1e-07, posd.tol = 1e-08, maxit = 100, conv.norm.type = "I", trace = FALSE) } \arguments{ \item{x}{numeric \eqn{n \times n}{n * n} approximately positive definite matrix, typically an approximation to a correlation or covariance matrix. If \code{x} is not symmetric (and \code{ensureSymmetry} is not false), \code{\link{symmpart}(x)} is used.} \item{corr}{logical indicating if the matrix should be a \emph{correlation} matrix.} \item{keepDiag}{logical, generalizing \code{corr}: if \code{TRUE}, the resulting matrix should have the same diagonal (\code{\link{diag}(x)}) as the input matrix.} \item{do2eigen}{logical indicating if a \code{\link[sfsmisc]{posdefify}()} eigen step should be applied to the result of the Higham algorithm.} \item{doSym}{logical indicating if \code{X <- (X + t(X))/2} should be done, after \code{X <- tcrossprod(Qd, Q)}; some doubt if this is necessary.} \item{doDykstra}{logical indicating if Dykstra's correction should be used; true by default. If false, the algorithm is basically the direct fixpoint iteration \eqn{Y_k = P_U(P_S(Y_{k-1}))}{Y(k) = P_U(P_S(Y(k-1)))}.} \item{only.values}{logical; if \code{TRUE}, the result is just the vector of eigen values of the approximating matrix.} \item{ensureSymmetry}{logical; by default, \code{\link{symmpart}(x)} is used whenever \code{\link{isSymmetric}(x)} is not true. The user can explicitly set this to \code{TRUE} or \code{FALSE}, saving the symmetry test. \emph{Beware} however that setting it \code{FALSE} for an \bold{a}symmetric input \code{x}, is typically nonsense!} \item{eig.tol}{defines relative positiveness of eigenvalues compared to largest one, \eqn{\lambda_1}. Eigen values \eqn{\lambda_k} are treated as if zero when \eqn{\lambda_k / \lambda_1 \le eig.tol}.} \item{conv.tol}{convergence tolerance for Higham algorithm.} \item{posd.tol}{tolerance for enforcing positive definiteness (in the final \code{posdefify} step when \code{do2eigen} is \code{TRUE}).} \item{maxit}{maximum number of iterations allowed.} \item{conv.norm.type}{convergence norm type (\code{\link{norm}(*, type)}) used for Higham algorithm. The default is \code{"I"} (infinity), for reasons of speed (and back compatibility); using \code{"F"} is more in line with Higham's proposal.} \item{trace}{logical or integer specifying if convergence monitoring should be traced.} } \details{ This implements the algorithm of Higham (2002), and then (if \code{do2eigen} is true) forces positive definiteness using code from \code{\link[sfsmisc]{posdefify}}. The algorithm of Knol DL and ten Berge (1989) (not implemented here) is more general in (1) that it allows constraints to fix some rows (and columns) of the matrix and (2) to force the smallest eigenvalue to have a certain value. Note that setting \code{corr = TRUE} just sets \code{diag(.) <- 1} within the algorithm. Higham (2002) uses Dykstra's correction, but the version by Jens Oehlschlaegel did not use it (accidentally), and has still lead to good results; this simplification, now only via \code{doDykstra = FALSE}, was active in \code{nearPD()} upto Matrix version 0.999375-40. } \value{ If \code{only.values = TRUE}, a numeric vector of eigen values of the approximating matrix; Otherwise, as by default, an S3 object of \code{\link{class}} \code{"nearPD"}, basically a list with components \item{mat}{a matrix of class \code{\linkS4class{dpoMatrix}}, the computed positive-definite matrix.} \item{eigenvalues}{numeric vector of eigen values of \code{mat}.} \item{corr}{logical, just the argument \code{corr}.} \item{normF}{the Frobenius norm (\code{\link{norm}(x-X, "F")}) of the difference between the original and the resulting matrix.} \item{iterations}{number of iterations needed.} \item{converged}{logical indicating if iterations converged.} } \references{%% more in /u/maechler/R/Pkgs/sfsmisc/man/posdefify.Rd Cheng, Sheung Hun and Higham, Nick (1998) A Modified Cholesky Algorithm Based on a Symmetric Indefinite Factorization; \emph{SIAM J. Matrix Anal.\ Appl.}, \bold{19}, 1097--1110. Knol DL, ten Berge JMF (1989) Least-squares approximation of an improper correlation matrix by a proper one. \emph{Psychometrika} \bold{54}, 53--61. Higham, Nick (2002) Computing the nearest correlation matrix - a problem from finance; \emph{IMA Journal of Numerical Analysis} \bold{22}, 329--343. } \author{Jens Oehlschlaegel donated a first version. Subsequent changes by the Matrix package authors. } \seealso{A first version of this (with non-optional \code{corr=TRUE}) has been available as \code{\link[sfsmisc]{nearcor}()}; and more simple versions with a similar purpose \code{\link[sfsmisc]{posdefify}()}, both from package \pkg{sfsmisc}. } \examples{ ## Higham(2002), p.334f - simple example A <- matrix(1, 3,3); A[1,3] <- A[3,1] <- 0 n.A <- nearPD(A, corr=TRUE, do2eigen=FALSE) n.A[c("mat", "normF")] stopifnot(all.equal(n.A$mat[1,2], 0.760689917), all.equal(n.A$normF, 0.52779033, tolerance=1e-9) ) set.seed(27) m <- matrix(round(rnorm(25),2), 5, 5) m <- m + t(m) diag(m) <- pmax(0, diag(m)) + 1 (m <- round(cov2cor(m), 2)) str(near.m <- nearPD(m, trace = TRUE)) round(near.m$mat, 2) norm(m - near.m$mat) # 1.102 / 1.08 if(require("sfsmisc")) { m2 <- posdefify(m) # a simpler approach norm(m - m2) # 1.185, i.e., slightly "less near" } round(nearPD(m, only.values=TRUE), 9) ## A longer example, extended from Jens' original, ## showing the effects of some of the options: pr <- Matrix(c(1, 0.477, 0.644, 0.478, 0.651, 0.826, 0.477, 1, 0.516, 0.233, 0.682, 0.75, 0.644, 0.516, 1, 0.599, 0.581, 0.742, 0.478, 0.233, 0.599, 1, 0.741, 0.8, 0.651, 0.682, 0.581, 0.741, 1, 0.798, 0.826, 0.75, 0.742, 0.8, 0.798, 1), nrow = 6, ncol = 6) nc. <- nearPD(pr, conv.tol = 1e-7) # default nc.$iterations # 2 nc.1 <- nearPD(pr, conv.tol = 1e-7, corr = TRUE) nc.1$iterations # 11 / 12 (!) ncr <- nearPD(pr, conv.tol = 1e-15) str(ncr)# still 2 iterations ncr.1 <- nearPD(pr, conv.tol = 1e-15, corr = TRUE) ncr.1 $ iterations # 27 / 30 ! ncF <- nearPD(pr, conv.tol = 1e-15, conv.norm = "F") stopifnot(all.equal(ncr, ncF))# norm type does not matter at all in this example ## But indeed, the 'corr = TRUE' constraint did ensure a better solution; ## cov2cor() does not just fix it up equivalently : norm(pr - cov2cor(ncr$mat)) # = 0.09994 norm(pr - ncr.1$mat) # = 0.08746 / 0.08805 ### 3) a real data example from a 'systemfit' model (3 eq.): (load(system.file("external", "symW.rda", package="Matrix"))) # "symW" dim(symW) # 24 x 24 class(symW)# "dsCMatrix": sparse symmetric if(dev.interactive()) image(symW) EV <- eigen(symW, only=TRUE)$values summary(EV) ## looking more closely {EV sorted decreasingly}: tail(EV)# all 6 are negative EV2 <- eigen(sWpos <- nearPD(symW)$mat, only=TRUE)$values stopifnot(EV2 > 0) if(require("sfsmisc")) { plot(pmax(1e-3,EV), EV2, type="o", log="xy", xaxt="n",yaxt="n") eaxis(1); eaxis(2) } else plot(pmax(1e-3,EV), EV2, type="o", log="xy") abline(0,1, col="red3",lty=2) } \keyword{algebra} \keyword{array} Matrix/man/dsCMatrix-class.Rd0000644000175100001440000001465212254023541015605 0ustar hornikusers\name{dsCMatrix-class} \title{Numeric Symmetric Sparse (column compressed) Matrices} \docType{class} \alias{dsCMatrix-class} \alias{dsTMatrix-class} % %\alias{solve,dsCMatrix,...-method}--> solve-methods.Rd \alias{t,dsCMatrix-method} \alias{t,dsTMatrix-method} \alias{as.vector,dsCMatrix,missing-method} \alias{coerce,dgeMatrix,dsCMatrix-method} \alias{coerce,dgeMatrix,dsTMatrix-method} \alias{coerce,dsCMatrix,dgCMatrix-method} \alias{coerce,dsCMatrix,dgTMatrix-method} \alias{coerce,dsCMatrix,dgeMatrix-method} \alias{coerce,dsCMatrix,dsRMatrix-method} \alias{coerce,dsCMatrix,dsTMatrix-method} \alias{coerce,dsCMatrix,dsyMatrix-method} \alias{coerce,dsCMatrix,lsCMatrix-method} \alias{coerce,dsCMatrix,generalMatrix-method} \alias{coerce,dsCMatrix,matrix-method} \alias{coerce,dsCMatrix,vector-method} \alias{coerce,dsCMatrix,nsCMatrix-method} \alias{coerce,dsTMatrix,dgTMatrix-method} \alias{coerce,dsTMatrix,dgeMatrix-method} \alias{coerce,dsTMatrix,dsCMatrix-method} \alias{coerce,dsTMatrix,dsyMatrix-method} \alias{coerce,dsTMatrix,lsTMatrix-method} \alias{coerce,dsTMatrix,matrix-method} \alias{coerce,dsyMatrix,dsCMatrix-method} \alias{coerce,dsyMatrix,dsTMatrix-method} \alias{coerce,dtCMatrix,dtRMatrix-method} \alias{coerce,matrix,dsCMatrix-method} \alias{coerce,matrix,dsTMatrix-method} \alias{coerce,graphNEL,dsCMatrix-method} %% Group methods \alias{Arith,dsCMatrix,dsCMatrix-method} \alias{determinant,dsCMatrix,missing-method} \alias{determinant,dsCMatrix,logical-method} \description{The \code{dsCMatrix} class is a class of symmetric, sparse numeric matrices in the compressed, column-oriented format. In this implementation the non-zero elements in the columns are sorted into increasing row order.\cr The \code{dsTMatrix} class is the class of symmetric, sparse numeric matrices in triplet format. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("dsCMatrix", ...)} or \code{new("dsTMatrix", ...)}, or automatically via e.g., \code{as(*, "symmetricMatrix")}, or (for \code{dsCMatrix}) also from \code{\link{Matrix}(.)}. Creation \dQuote{from scratch} most efficiently happens via \code{\link{sparseMatrix}(*, symmetric=TRUE)}. } \section{Slots}{ \describe{ \item{\code{uplo}:}{A character object indicating if the upper triangle (\code{"U"}) or the lower triangle (\code{"L"}) is stored.} \item{\code{i}:}{Object of class \code{"integer"} of length nnZ (\emph{half} number of non-zero elements). These are the row numbers for each non-zero element in the lower triangle of the matrix.} \item{\code{p}:}{(only in class \code{"dsCMatrix"}:) an \code{\link{integer}} vector for providing pointers, one for each column, see the detailed description in \code{\linkS4class{CsparseMatrix}}.} \item{\code{j}:}{(only in class \code{"dsTMatrix"}:) Object of class \code{"integer"} of length nnZ (as \code{i}). These are the column numbers for each non-zero element in the lower triangle of the matrix.} \item{\code{x}:}{Object of class \code{"numeric"} of length nnZ -- the non-zero elements of the matrix (to be duplicated for full matrix).} \item{\code{factors}:}{Object of class \code{"list"} - a list of factorizations of the matrix. } \item{\code{Dim}:}{Object of class \code{"integer"} - the dimensions of the matrix - must be an integer vector with exactly two non-negative values.} } } \section{Extends}{ Both classes extend classes and \code{\linkS4class{symmetricMatrix}} \code{\linkS4class{dsparseMatrix}} directly; \code{dsCMatrix} further directly extends \code{\linkS4class{CsparseMatrix}}, where \code{dsTMatrix} does \code{\linkS4class{TsparseMatrix}}. } \section{Methods}{ \describe{ \item{solve}{\code{signature(a = "dsCMatrix", b = "....")}: \code{x <- solve(a,b)} solves \eqn{A x = b} for \eqn{x}; see \code{\link{solve-methods}}.} \item{chol}{\code{signature(x = "dsCMatrix", pivot = "logical")}: Returns (and stores) the Cholesky decomposition of \code{x}, see \code{\link{chol}}.} \item{Cholesky}{\code{signature(A = "dsCMatrix",...)}: Computes more flexibly Cholesky decompositions, see \code{\link{Cholesky}}.} \item{determinant}{\code{signature(x = "dsCMatrix", logarithm = "missing")}: Evaluate the determinant of \code{x} on the logarithm scale. This creates and stores the Cholesky factorization.} \item{determinant}{\code{signature(x = "dsCMatrix", logarithm = "logical")}: Evaluate the determinant of \code{x} on the logarithm scale or not, according to the \code{logarithm} argument. This creates and stores the Cholesky factorization.} \item{t}{\code{signature(x = "dsCMatrix")}: Transpose. As for all symmetric matrices, a matrix for which the upper triangle is stored produces a matrix for which the lower triangle is stored and vice versa, i.e., the \code{uplo} slot is swapped, and the row and column indices are interchanged.} \item{t}{\code{signature(x = "dsTMatrix")}: Transpose. The \code{uplo} slot is swapped from \code{"U"} to \code{"L"} or vice versa, as for a \code{"dsCMatrix"}, see above.} \item{coerce}{\code{signature(from = "dsCMatrix", to = "dgTMatrix")}} \item{coerce}{\code{signature(from = "dsCMatrix", to = "dgeMatrix")}} \item{coerce}{\code{signature(from = "dsCMatrix", to = "matrix")}} \item{coerce}{\code{signature(from = "dsTMatrix", to = "dgeMatrix")}} \item{coerce}{\code{signature(from = "dsTMatrix", to = "dsCMatrix")}} \item{coerce}{\code{signature(from = "dsTMatrix", to = "dsyMatrix")}} \item{coerce}{\code{signature(from = "dsTMatrix", to = "matrix")}} } } %\references{} %\author{} %\note{} \seealso{ Classes \code{\linkS4class{dgCMatrix}}, \code{\linkS4class{dgTMatrix}}, \code{\linkS4class{dgeMatrix}} and those mentioned above. } \examples{ mm <- Matrix(toeplitz(c(10, 0, 1, 0, 3)), sparse = TRUE) mm # automatically dsCMatrix str(mm) ## how would we go from a manually constructed Tsparse* : mT <- as(mm, "dgTMatrix") ## Either (symM <- as(mT, "symmetricMatrix"))# dsT (symC <- as(symM, "CsparseMatrix"))# dsC ## or sC <- Matrix(mT, sparse=TRUE, forceCheck=TRUE) sym2 <- as(symC, "TsparseMatrix") ## --> the same as 'symM', a "dsTMatrix" \dontshow{ stopifnot(identical(symC, sC), identical(sym2, symM), class(sym2) == "dsTMatrix", identical(sym2[1,], sC[1,]), identical(sym2[,2], sC[,2])) } } \keyword{classes} \keyword{algebra} Matrix/man/BunchKaufman-methods.Rd0000644000175100001440000000376411635064643016623 0ustar hornikusers\name{BunchKaufman-methods} \docType{methods} \alias{BunchKaufman} \alias{BunchKaufman-methods} \alias{BunchKaufman,dspMatrix-method} \alias{BunchKaufman,dsyMatrix-method} \title{Bunch-Kaufman Decomposition Methods} \description{ The Bunch-Kaufman Decomposition of a square symmetric matrix \eqn{A} is \eqn{A = P LDL' P'} where \eqn{P} is a permutation matrix, \eqn{L} is \emph{unit}-lower triangular and \eqn{D} is \emph{block}-diagonal with blocks of dimension \eqn{1\times 1}{1 x 1} or \eqn{2\times2}{2 x 2}. } \usage{ BunchKaufman(x, \dots) } \arguments{ \item{x}{a symmetric square matrix.} \item{\dots}{potentially further arguments passed to methods.} } \section{Methods}{ Currently, only methods for \bold{dense} numeric symmetric matrices are implemented. \describe{ \item{\code{x = "dspMatrix"}}{uses Lapack routine \code{dsptrf},} \item{\code{x = "dsyMatrix"}}{uses Lapack routine \code{dsytrf}, computing the Bunch-Kaufman decomposition.} } } \value{ an object of class \code{\linkS4class{BunchKaufman}}, which can also be used as a (triangular) matrix directly. %% FIXME: Really need an expand() method, in order to *work* with the result! } \references{ The original LAPACK source code, including documentation; \url{http://www.netlib.org/lapack/double/dsytrf.f} and \url{http://www.netlib.org/lapack/double/dsptrf.f} } \seealso{ The resulting class, \code{\linkS4class{BunchKaufman}}. Related decompositions are the LU, \code{\link{lu}}, and the Cholesky, \code{\link{chol}} (and for \emph{sparse} matrices, \code{\link{Cholesky}}). } \examples{ data(CAex) dim(CAex) isSymmetric(CAex)# TRUE CAs <- as(CAex, "symmetricMatrix") if(FALSE) # no method defined yet for *sparse* : bk. <- BunchKaufman(CAs) ## does apply to *dense* symmetric matrices: bkCA <- BunchKaufman(as(CAs, "denseMatrix")) bkCA image(bkCA)# shows how sparse it is, too str(R.CA <- as(bkCA, "sparseMatrix")) ## an upper triangular 72x72 matrix with only 144 non-zero entries } \keyword{methods} Matrix/man/replValue-class.Rd0000644000175100001440000000141010460463631015637 0ustar hornikusers\name{replValue-class} \docType{class} \alias{replValue-class} %% >>>>>>> The "[<-" methods are in ./Subassign-methods.Rd \title{Virtual Class "replValue" - Simple Class for subassignment Values} \description{The class \code{"replValue"} is a virtual class used for values in signatures for sub-assignment of \pkg{"Matrix"} matrices. In fact, it is a simple class union (\code{\link{setClassUnion}}) of \code{"numeric"} and \code{"logical"} (and maybe \code{"complex"} in the future). } \section{Objects from the Class}{Since it is a virtual Class, no objects may be created from it.} \seealso{ %% FIXME: bug in Rdconv needs '[Matrix]' below: \code{\link[Matrix]{Subassign-methods}}, also for examples. } \examples{ showClass("replValue") } \keyword{classes} Matrix/man/dgCMatrix-class.Rd0000644000175100001440000000713612271746775015614 0ustar hornikusers\name{dgCMatrix-class} \docType{class} \title{Compressed, sparse, column-oriented numeric matrices} \alias{dgCMatrix-class} \alias{as.vector,dgCMatrix,missing-method} \alias{coerce,matrix,dgCMatrix-method} \alias{coerce,dgeMatrix,dgCMatrix-method} \alias{coerce,dgCMatrix,dgTMatrix-method} \alias{coerce,dgCMatrix,dsCMatrix-method}% deprecated \alias{coerce,dgCMatrix,dtCMatrix-method} \alias{coerce,dgCMatrix,lgCMatrix-method} \alias{coerce,dgCMatrix,ngCMatrix-method} \alias{coerce,dgCMatrix,dgeMatrix-method} \alias{coerce,dgCMatrix,matrix-method} \alias{coerce,dgCMatrix,vector-method} \alias{coerce,factor,dgCMatrix-method} \alias{diag,dgCMatrix-method} \alias{dim,dgCMatrix-method} %\alias{lu,dgCMatrix-method}-> ./lu.Rd \alias{isSymmetric,dgCMatrix-method} \alias{t,dgCMatrix-method} %\alias{solve,dgCMatrix,matrix-method}--> solve-methods.Rd %% Group methods --------- FIXME: These are not tested yet (or documented) \alias{Arith,logical,dgCMatrix-method} \alias{Arith,numeric,dgCMatrix-method} \alias{Arith,dgCMatrix,logical-method} \alias{Arith,dgCMatrix,numeric-method} \alias{Arith,dgCMatrix,dgCMatrix-method} %\alias{Math2,dgCMatrix,numeric-method} \alias{Math,dgCMatrix-method} % for silly reasons, need these 2+3 as well: \alias{round,dgCMatrix,numeric-method} \alias{signif,dgCMatrix,numeric-method} \alias{log,dgCMatrix-method} \alias{gamma,dgCMatrix-method} \alias{lgamma,dgCMatrix-method} % \description{The \code{dgCMatrix} class is a class of sparse numeric matrices in the compressed, sparse, column-oriented format. In this implementation the non-zero elements in the columns are sorted into increasing row order. \code{dgCMatrix} is the \emph{\dQuote{standard}} class for sparse numeric matrices in the \pkg{Matrix} package. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("dgCMatrix", ...)}, more typically via \code{as(*, "CsparseMatrix")} or similar. Often however, more easily via \code{\link{Matrix}(*, sparse = TRUE)}, or most efficiently via \code{\link{sparseMatrix}()}. } \section{Slots}{ \describe{ \item{\code{x}:}{Object of class \code{"numeric"} - the non-zero elements of the matrix.} \item{\dots}{all other slots are inherited from the superclass \code{"\linkS4class{CsparseMatrix}"}. } } } \section{Methods}{ Matrix products (e.g., \link{crossprod-methods}), and (among other) \describe{ \item{coerce}{\code{signature(from = "matrix", to = "dgCMatrix")}} \item{coerce}{\code{signature(from = "dgCMatrix", to = "matrix")}} \item{coerce}{\code{signature(from = "dgCMatrix", to = "dgTMatrix")}} \item{diag}{\code{signature(x = "dgCMatrix")}: returns the diagonal of \code{x}} \item{dim}{\code{signature(x = "dgCMatrix")}: returns the dimensions of \code{x}} \item{image}{\code{signature(x = "dgCMatrix")}: plots an image of \code{x} using the \code{\link[lattice]{levelplot}} function} \item{solve}{\code{signature(a = "dgCMatrix", b = "...")}: see \code{\link{solve-methods}}, notably the extra argument \code{sparse}.} \item{lu}{\code{signature(x = "dgCMatrix")}: computes the LU decomposition of a square \code{dgCMatrix} object} } } %\references{} %\author{} %\note{} \seealso{ Classes \code{\linkS4class{dsCMatrix}}, \code{\linkS4class{dtCMatrix}}, \code{\link{lu}} } \examples{ (m <- Matrix(c(0,0,2:0), 3,5)) str(m) m[,1] \dontshow{## regression test: this must give a validity-check error: stopifnot(inherits(try(new("dgCMatrix", i = 0:1, p = 0:2, x = c(2,3), Dim = 3:4)), "try-error")) } } \keyword{classes} \keyword{algebra} Matrix/man/Schur.Rd0000644000175100001440000000656112271746775013714 0ustar hornikusers\name{Schur} \title{Schur Decomposition of a Matrix} \usage{ Schur(x, vectors, \dots) } \alias{Schur} \alias{Schur,dgeMatrix,logical-method} \alias{Schur,dgeMatrix,missing-method} \alias{Schur,diagonalMatrix,logical-method} \alias{Schur,diagonalMatrix,missing-method} \alias{Schur,triangularMatrix,logical-method} \alias{Schur,triangularMatrix,missing-method} \alias{Schur,dsyMatrix,ANY-method} \alias{Schur,generalMatrix,logical-method} \alias{Schur,generalMatrix,missing-method} \alias{Schur,symmetricMatrix,logical-method} \alias{Schur,symmetricMatrix,missing-method} % \alias{Schur,matrix,logical-method} \alias{Schur,matrix,missing-method} \description{ Computes the Schur decomposition and eigenvalues of a square matrix; see the BACKGROUND information below. } \arguments{ \item{x}{ numeric %(or complex, in future) square Matrix (inheriting from class \code{"Matrix"}) or traditional \code{\link{matrix}}. Missing values (NAs) are not allowed. } \item{vectors}{logical. When \code{TRUE} (the default), the Schur vectors are computed, and the result is a proper \code{\linkS4class{MatrixFactorization}} of class \code{\linkS4class{Schur}}. } \item{\dots}{further arguments passed to or from other methods.} } \value{ If \code{vectors} are \code{TRUE}, as per default: If \code{x} is a \code{\linkS4class{Matrix}} an object of class \code{\linkS4class{Schur}}, otherwise, for a traditional \code{\link{matrix}} \code{x}, a \code{\link{list}} with components \code{T}, \code{Q}, and \code{EValues}. If \code{vectors} are \code{FALSE}, a list with components \item{T}{the upper quasi-triangular (square) matrix of the Schur decomposition.} \item{EValues}{the vector of \code{\link{numeric}} or \code{\link{complex}} eigen values of \eqn{T} or \eqn{A}.} } \details{ Based on the Lapack subroutine \code{dgees}. } \section{BACKGROUND}{ If \code{A} is a square matrix, then \code{A = Q T t(Q)}, where \code{Q} is orthogonal, and \code{T} is upper block-triangular (nearly triangular with either 1 by 1 or 2 by 2 blocks on the diagonal) where the 2 by 2 blocks correspond to (non-real) complex eigenvalues. The eigenvalues of \code{A} are the same as those of \code{T}, which are easy to compute. The Schur form is used most often for computing non-symmetric eigenvalue decompositions, and for computing functions of matrices such as matrix exponentials. } \references{ Anderson, E., et al. (1994). \emph{LAPACK User's Guide,} 2nd edition, SIAM, Philadelphia. } \examples{ Schur(Hilbert(9)) # Schur factorization (real eigenvalues) (A <- Matrix(round(rnorm(5*5, sd = 100)), nrow = 5)) (Sch.A <- Schur(A)) eTA <- eigen(Sch.A@T) str(SchA <- Schur(A, vectors=FALSE))# no 'T' ==> simple list stopifnot(all.equal(eTA$values, eigen(A)$values, tolerance = 1e-13), all.equal(eTA$values, local({z <- Sch.A@EValues z[order(Mod(z), decreasing=TRUE)]}), tolerance = 1e-13), identical(SchA$T, Sch.A@T), identical(SchA$EValues, Sch.A@EValues)) ## For the faint of heart, we provide Schur() also for traditional matrices: a.m <- function(M) unname(as(M, "matrix")) a <- a.m(A) Sch.a <- Schur(a) stopifnot(identical(Sch.a, list(Q = a.m(Sch.A @ Q), T = a.m(Sch.A @ T), EValues = Sch.A@EValues)), all.equal(a, with(Sch.a, Q \%*\% T \%*\% t(Q))) ) } \keyword{algebra} Matrix/man/condest.Rd0000644000175100001440000000626611635064643014257 0ustar hornikusers\name{condest} \alias{condest} \alias{onenormest} \title{Compute Approximate CONDition number and 1-Norm of (Large) Matrices} \description{ \dQuote{Estimate}, i.e. compute approximately the CONDition number of a (potentially large, often sparse) matrix \code{A}. It works by apply a fast approximation of the 1-norm, \code{norm(A,"1")}, through \code{onenormest(.)}. } \usage{ condest(A, t = min(n, 5), normA = norm(A, "1"), silent = FALSE, quiet = TRUE) onenormest(A, t = min(n, 5), A.x, At.x, n, silent = FALSE, quiet = silent, iter.max = 10, eps = 4 * .Machine$double.eps) } \arguments{ \item{A}{a square matrix, optional for \code{onenormest()}, where instead of \code{A}, \code{A.x} and \code{At.x} can be specified, see there.} \item{t}{number of columns to use in the iterations.} \item{normA}{number; (an estimate of) the 1-norm of \code{A}, by default \code{\link{norm}(A, "1")}; may be replaced by an estimate.} \item{silent}{logical indicating if warning and (by default) convergence messages should be displayed.} \item{quiet}{logical indicating if convergence messages should be displayed.} \item{A.x, At.x}{when \code{A} is missing, these two must be given as functions which compute \code{A \%\% x}, or \code{t(A) \%\% x}, respectively.} \item{n}{\code{ == nrow(A)}, only needed when \code{A} is not specified.} \item{iter.max}{maximal number of iterations for the 1-norm estimator.} \item{eps}{the relaive change that is deemed irrelevant.} } % \details{ % %% ~~ If necessary, more details than the description above ~~ % } \value{Both functions return a \code{\link{list}}; \code{onenormest()} with components, \item{est}{a number \eqn{> 0}, the estimated \code{norm(A, "1")}.} \item{v}{the maximal \eqn{A X} column.} The function \code{condest()} returns a list with components, \item{est}{a number \eqn{> 0}, the estimated condition number \eqn{\hat\kappa}{k.}; when \eqn{r :=}\code{rcond(A)}, \eqn{1/\hat\kappa \approx r}{1/k. ~= r}.} \item{v}{integer vector length \code{n}, with an \code{1} at the index \code{j} with maximal column \code{A[,j]} in \eqn{A}.} \item{w}{numeric vector, the largest \eqn{A x} found.} \item{iter}{the number of iterations used.} } \references{ %% See also Tim Davis(2006, p.96): Nicholas J. Higham and Françoise Tisseur (2000). A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra. \emph{SIAM J. Matrix Anal. Appl.} \bold{21}, 4, 1185--1201. \url{http://dx.doi.org/10.1137/S0895479899356080} %% and \url{http://citeseer.ist.psu.edu/223007.html} William W. Hager (1984). Condition Estimates. \emph{SIAM J. Sci. Stat. Comput.} \bold{5}, 311--316. } \author{This is based on octave's \code{condest()} and \code{onenormest()} implementations with original author Jason Riedy, U Berkeley; translation to \R and adaption by Martin Maechler. } \seealso{ \code{\link{norm}}, \code{\link{rcond}}. } \examples{ data(KNex) mtm <- with(KNex, crossprod(mm)) system.time(ce <- condest(mtm)) ## reciprocal 1 / ce$est system.time(rc <- rcond(mtm)) # takes ca 3 x longer rc all.equal(rc, 1/ce$est) # TRUE -- the approxmation was good } Matrix/man/SparseM-conv.Rd0000644000175100001440000000434712247126702015126 0ustar hornikusers\name{SparseM-conversions} \docType{methods} \alias{SparseM-coerce-methods} % \alias{coerce,matrix.coo,CsparseMatrix-method} \alias{coerce,matrix.coo,TsparseMatrix-method} \alias{coerce,matrix.csc,CsparseMatrix-method} \alias{coerce,matrix.csc,TsparseMatrix-method} \alias{coerce,matrix.csr,CsparseMatrix-method} \alias{coerce,matrix.csr,RsparseMatrix-method} \alias{coerce,matrix.csr,TsparseMatrix-method} % \alias{coerce,CsparseMatrix,matrix.csr-method} \alias{coerce,CsparseMatrix,matrix.coo-method} \alias{coerce,CsparseMatrix,matrix.csc-method} \alias{coerce,dsparseMatrix,matrix.csr-method} \alias{coerce,dgRMatrix,matrix.csr-method} \alias{coerce,dgCMatrix,matrix.csc-method} \alias{coerce,dgTMatrix,matrix.coo-method} \alias{coerce,matrix.csr,dgRMatrix-method} \alias{coerce,matrix.csc,dgCMatrix-method} \alias{coerce,matrix.coo,dgTMatrix-method} \alias{coerce,matrix.csr,dgCMatrix-method} \alias{coerce,matrix.coo,dgCMatrix-method} % \alias{coerce,matrix.csr,Matrix-method} \alias{coerce,matrix.coo,Matrix-method} \alias{coerce,matrix.csc,Matrix-method} % \title{Sparse Matrix Coercion from and to those from package "SparseM"} \description{ Methods for coercion from and to sparse matrices from package \pkg{SparseM} are provided here, for ease of porting functionality to the \pkg{Matrix} package, and comparing functionality of the two packages. } \section{Methods}{ \describe{ \item{from = "matrix.csr", to = "dgRMatrix"}{ ... } \item{from = "matrix.csc", to = "dgCMatrix"}{ ... } \item{from = "matrix.coo", to = "dgTMatrix"}{ ... } \item{from = "dgRMatrix", to = "matrix.csr"}{ ... } \item{from = "dgCMatrix", to = "matrix.csc"}{ ... } \item{from = "dgTMatrix", to = "matrix.coo"}{ ... } \item{from = "sparseMatrix", to = "matrix.csr"}{ ... } \item{from = "matrix.csr", to = "dgCMatrix"}{ ... } \item{from = "matrix.coo", to = "dgCMatrix"}{ ... } \item{from = "matrix.csr", to = "Matrix"}{ ... } \item{from = "matrix.csc", to = "Matrix"}{ ... } \item{from = "matrix.coo", to = "Matrix"}{ ... } } } \seealso{ The documentation in package \pkg{SparseM}, such as \code{\link[SparseM]{SparseM.ontology}}, and one important class, \code{\link[SparseM:matrix.csr-class]{matrix.csr}}. } \keyword{methods} Matrix/man/qr-methods.Rd0000644000175100001440000000474212053355101014663 0ustar hornikusers\name{qr-methods} \docType{methods} \alias{qr} \alias{qrR} \alias{qr-methods} \alias{qr,dgCMatrix-method} \alias{qr,sparseMatrix-method} \title{QR Decomposition -- S4 Methods and Generic} \description{ The \code{"Matrix"} package provides methods for the QR decomposition of special classes of matrices. There is a generic function which uses \code{\link[base]{qr}} as default, but methods defined in this package can take extra arguments. In particular there is an option for determining a fill-reducing permutation of the columns of a sparse, rectangular matrix. } \usage{ qr(x, \dots) qrR(qr, complete=FALSE, backPermute=TRUE) } \arguments{ \item{x}{a numeric or complex matrix whose QR decomposition is to be computed. Logical matrices are coerced to numeric.} \item{qr}{a QR decomposition of the type computed by \code{qr}.} \item{complete}{logical indicating whether the \eqn{\bold{R}} matrix is to be completed by binding zero-value rows beneath the square upper triangle.} \item{backPermute}{logical indicating if the rows of the \eqn{\bold{R}} matrix should be back permuted such that \code{qrR()}'s result can be used directly to reconstruct the original matrix \eqn{\bold{X}}.} \item{\dots}{further arguments passed to or from other methods} } \section{Methods}{ \describe{ \item{x = "dgCMatrix"}{QR decomposition of a general sparse double-precision matrix with \code{nrow(x) >= ncol(x)}. Returns an object of class \code{"\linkS4class{sparseQR}"}.} \item{x = "sparseMatrix"}{works via \code{"dgCMatrix"}.} } } \seealso{\code{\link[base]{qr}}; then, the class documentations, mainly \code{\linkS4class{sparseQR}}, and also \code{\linkS4class{dgCMatrix}}. } \examples{ ##------------- example of pivoting -- from base' qraux.Rd ------------- X <- Matrix(cbind(int = 1, b1=rep(1:0, each=3), b2=rep(0:1, each=3), c1=rep(c(1,0,0), 2), c2=rep(c(0,1,0), 2), c3=rep(c(0,0,1),2)), sparse=TRUE) X # is singular, columns "b2" and "c3" are "extra" (qx <- qr(X)) # both @p and @q are non-trivial permutations drop0(R. <- qr.R(qx), tol=1e-15) # columns are int b1 c1 c2 b2 c3 Q. <- qr.Q(qx) qI <- sort.list(qx@q) # the inverse 'q' permutation (X. <- drop0(Q. \%*\% R.[, qI], tol=1e-15))## just = X stopifnot(all(X - X.) < 8*.Machine$double.eps, ## qR(.) returns R already "back permuted" (as with qI): identical(R.[, qI], qrR(qx)) ) } \keyword{methods} \keyword{algebra} \keyword{array} Matrix/man/ddiMatrix-class.Rd0000644000175100001440000000346311140343613015630 0ustar hornikusers\name{ddiMatrix-class} \title{Class "ddiMatrix" of Diagonal Numeric Matrices} \docType{class} \alias{ddiMatrix-class} %%----> put all methods into ./diagonalMatrix-class.Rd % \description{The class \code{"ddiMatrix"} of numerical diagonal matrices. %% FIXME add more Note that diagonal matrices now extend \emph{\code{sparseMatrix}}, whereas they did extend dense matrices earlier.% up to early summer 2008. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("ddiMatrix", ...)} but typically rather via \code{\link{Diagonal}}. } \section{Slots}{ \describe{ \item{\code{x}:}{numeric vector. For an \eqn{n \times n}{n * n} matrix, the \code{x} slot is of length \eqn{n} or \code{0}, depending on the \code{diag} slot:} \item{\code{diag}:}{\code{"character"} string, either \code{"U"} or \code{"N"} where \code{"U"} denotes unit-diagonal, i.e., identity matrices.} \item{\code{Dim},\code{Dimnames}:}{matrix dimension and \code{\link{dimnames}}, see the \code{\linkS4class{Matrix}} class description.} } } \section{Extends}{ Class \code{"\linkS4class{diagonalMatrix}"}, directly. Class \code{"\linkS4class{dMatrix}"}, directly. Class \code{"\linkS4class{sparseMatrix}"}, indirectly, see \code{\link{showClass}("ddiMatrix")}. } \section{Methods}{ \describe{ \item{\%*\%}{\code{signature(x = "ddiMatrix", y = "ddiMatrix")}: ... } } } \seealso{ Class \code{\linkS4class{diagonalMatrix}} and function \code{\link{Diagonal}}. } \examples{ (d2 <- Diagonal(x = c(10,1))) str(d2) ## slightly larger in internal size: str(as(d2, "sparseMatrix")) M <- Matrix(cbind(1,2:4)) M \%*\% d2 #> `fast' multiplication chol(d2) # trivial stopifnot(is(cd2 <- chol(d2), "ddiMatrix"), all.equal(cd2@x, c(sqrt(10),1))) } \keyword{classes} Matrix/man/RsparseMatrix-class.Rd0000644000175100001440000000514411006011151016473 0ustar hornikusers\name{RsparseMatrix-class} \docType{class} \alias{RsparseMatrix-class} % \alias{coerce,RsparseMatrix,CsparseMatrix-method} \alias{coerce,RsparseMatrix,TsparseMatrix-method} \alias{coerce,RsparseMatrix,denseMatrix-method} \alias{coerce,RsparseMatrix,dgeMatrix-method} \alias{coerce,RsparseMatrix,generalMatrix-method} \alias{coerce,RsparseMatrix,matrix-method} \alias{coerce,RsparseMatrix,dsparseMatrix-method} \alias{coerce,RsparseMatrix,lsparseMatrix-method} \alias{coerce,RsparseMatrix,nsparseMatrix-method} \alias{coerce,RsparseMatrix,dMatrix-method} \alias{coerce,RsparseMatrix,lMatrix-method} \alias{coerce,RsparseMatrix,nMatrix-method} \alias{coerce,matrix,RsparseMatrix-method} \alias{coerce,denseMatrix,RsparseMatrix-method} \alias{coerce,sparseMatrix,RsparseMatrix-method} % all other ..RMatrix coercions -- here as well for now -- \alias{coerce,matrix,dgRMatrix-method} % \alias{t,RsparseMatrix-method} % \title{Class "RsparseMatrix" of Sparse Matrices in Column-compressed Form} \description{The \code{"RsparseMatrix"} class is the virtual class of all sparse matrices coded in sorted compressed row-oriented form. Since it is a virtual class, no objects may be created from it. See \code{showClass("RsparseMatrix")} for its subclasses. } \section{Slots}{ \describe{ \item{\code{j}:}{Object of class \code{"integer"} of length \code{nnzero} (number of non-zero elements). These are the row numbers for each non-zero element in the matrix.} \item{\code{p}:}{Object of class \code{"integer"} of pointers, one for each row, to the initial (zero-based) index of elements in the row.} \item{\code{Dim}, \code{Dimnames}:}{inherited from the superclass, see \code{\linkS4class{sparseMatrix}}.} } } \section{Extends}{ Class \code{"sparseMatrix"}, directly. Class \code{"Matrix"}, by class \code{"sparseMatrix"}. } \section{Methods}{ Only \bold{few} methods are defined currently on purpose, since we rather use the \code{\linkS4class{CsparseMatrix}} in \pkg{Matrix}. Recently, more methods were added but \emph{beware} that these typically do \emph{not} return \code{"RsparseMatrix"} results, but rather Csparse* or Tsparse* ones. \describe{ \item{t}{\code{signature(x = "RsparseMatrix")}: ... } \item{coerce}{\code{signature(from = "RsparseMatrix", to = "CsparseMatrix")}: ... } \item{coerce}{\code{signature(from = "RsparseMatrix", to = "TsparseMatrix")}: ... } } } \seealso{ its superclass, \code{\linkS4class{sparseMatrix}}, and, e.g., class \code{\linkS4class{dgRMatrix}} for the links to other classes. } \examples{ showClass("RsparseMatrix") } \keyword{classes} Matrix/man/generalMatrix-class.Rd0000644000175100001440000000206010435070553016503 0ustar hornikusers\name{generalMatrix-class} \docType{class} \alias{generalMatrix-class} \title{Class "generalMatrix" of General Matrices} \description{ Virtual class of \dQuote{general} matrices; i.e., matrices that do not have a known property such as symmetric, triangular, or diagonal. } \section{Objects from the Class}{A virtual Class: No objects may be created from it.} \section{Slots}{ \describe{ \item{\code{factors}}{,} \item{\code{Dim}}{,} \item{\code{Dimnames}:}{all slots inherited from \code{\linkS4class{compMatrix}}; see its description.} } } \section{Extends}{ Class \code{"compMatrix"}, directly. Class \code{"Matrix"}, by class \code{"compMatrix"}. } % \section{Methods}{ % No methods defined with class "generalMatrix" in the signature. % } \seealso{ Classes \code{\linkS4class{compMatrix}}, and the non-general virtual classes: \code{\linkS4class{symmetricMatrix}}, \code{\linkS4class{triangularMatrix}}, \code{\linkS4class{diagonalMatrix}}. } % \examples{ % ##---- Should be DIRECTLY executable !! ---- % } \keyword{classes} Matrix/man/CHMfactor-class.Rd0000644000175100001440000002276312271746775015543 0ustar hornikusers\name{CHMfactor-class} \title{CHOLMOD-based Cholesky Factorizations} \docType{class} \alias{CHMfactor-class}% "mother" virtual \alias{CHMsimpl-class}% virtual \alias{CHMsuper-class}% virtual \alias{dCHMsimpl-class} \alias{nCHMsimpl-class} \alias{dCHMsuper-class} \alias{nCHMsuper-class} \alias{isLDL} % \alias{coerce,CHMfactor,Matrix-method} \alias{coerce,CHMfactor,sparseMatrix-method} \alias{coerce,CHMfactor,pMatrix-method} \alias{expand,CHMfactor-method} %\alias{solve,CHMfactor,...}%--> solve-methods.Rd \alias{determinant,CHMfactor,missing-method} \alias{determinant,CHMfactor,logical-method} \alias{update,CHMfactor-method} \alias{.updateCHMfactor} % \description{The virtual class \code{"CHMfactor"} is a class of CHOLMOD-based Cholesky factorizations of symmetric, sparse, compressed, column-oriented matrices. Such a factorization is simplicial (virtual class \code{"CHMsimpl"}) or supernodal (virtual class \code{"CHMsuper"}). Objects that inherit from these classes are either numeric factorizations (classes \code{"dCHMsimpl"} and \code{"dCHMsuper"}) or symbolic factorizations (classes \code{"nCHMsimpl"} and \code{"nCHMsuper"}). } \usage{% want usage for the update method which has "surprising arguments" isLDL(x) \S4method{update}{CHMfactor}(object, parent, mult = 0, \dots) .updateCHMfactor(object, parent, mult)% otherwise don't mention; for experts ## and many more methods, notably, ## solve(a, b, system = c("A","LDLt","LD","DLt","L","Lt","D","P","Pt"), ...) ## ----- see below } \arguments{ \item{x,object,a}{a \code{"CHMfactor"} object (almost always the result of \code{\link{Cholesky}()}).} \item{parent}{a \code{"\linkS4class{dsCMatrix}"} or \code{"\linkS4class{dgCMatrix}"} matrix object with the same nonzero pattern as the matrix that generated \code{object}. If \code{parent} is symmetric, of class \code{"\linkS4class{dsCMatrix}"}, then \code{object} should be a decomposition of a matrix with the same nonzero pattern as \code{parent}. If \code{parent} is not symmetric then \code{object} should be the decomposition of a matrix with the same nonzero pattern as \code{tcrossprod(parent)}. Since Matrix version 1.0-8, other \code{"\linkS4class{sparseMatrix}"} matrices are coerced to \code{\linkS4class{dsparseMatrix}} and \code{\linkS4class{CsparseMatrix}} if needed.} \item{mult}{a numeric scalar (default 0). \code{mult} times the identity matrix is (implicitly) added to \code{parent} or \code{tcrossprod(parent)} before updating the decomposition \code{object}.} \item{\dots}{potentially further arguments to the methods.} } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("dCHMsuper", ...)} but are more commonly created via \code{\link{Cholesky}()}, applied to \code{\linkS4class{dsCMatrix}} or \code{\linkS4class{lsCMatrix}} objects. For an introduction, it may be helpful to look at the \code{expand()} method and examples below. } \section{Slots}{ of \code{"CHMfactor"} and all classes inheriting from it: \describe{ \item{\code{perm}:}{An integer vector giving the 0-based permutation of the rows and columns chosen to reduce fill-in and for post-ordering.} \item{\code{colcount}:}{Object of class \code{"integer"} .... }%% FIXME \item{\code{type}:}{Object of class \code{"integer"} .... } } Slots of the non virtual classes \dQuote{[dl]CHM(super|simpl)}: \describe{ \item{\code{p}:}{Object of class \code{"integer"} of pointers, one for each column, to the initial (zero-based) index of elements in the column. Only present in classes that contain \code{"CHMsimpl"}.} \item{\code{i}:}{Object of class \code{"integer"} of length nnzero (number of non-zero elements). These are the row numbers for each non-zero element in the matrix. Only present in classes that contain \code{"CHMsimpl"}.} \item{\code{x}:}{For the \code{"d*"} classes: \code{"numeric"} - the non-zero elements of the matrix.} } } \section{Methods}{ \describe{ \item{isLDL}{\code{(x)} returns a \code{\link{logical}} indicating if \code{x} is an \eqn{LDL'} decomposition or (when \code{FALSE}) an \eqn{LL'} one.} \item{coerce}{\code{signature(from = "CHMfactor", to = "sparseMatrix")} Returns the lower triangular factor \eqn{L} from the \eqn{LL'} form of the Cholesky factorization. Note that (currently) the factor from the \eqn{LL'} form is always returned, even if the \code{"CHMfactor"} object represents an \eqn{LDL'} decomposition. Furthermore, this is the factor after any fill-reducing permutation has been applied. See the \code{expand} method for obtaining both the permutation matrix, \eqn{P}, and the lower Cholesky factor, \eqn{L}.} \item{coerce}{\code{signature(from = "CHMfactor", to = "pMatrix")} Returns the permutation matrix, \eqn{P}, representing the fill-reducing permutation used in the decomposition.} \item{expand}{\code{signature(x = "CHMfactor")} Returns a list with components \code{P}, the matrix representing the fill-reducing permutation, and \code{L}, the lower triangular Cholesky factor. The original positive-definite matrix \eqn{A} corresponds to the product \eqn{A = P'LL'P}. Because of fill-in during the decomposition the product may apparently have more non-zeros than the original matrix, even after applying \code{\link{drop0}} to it. However, the extra "non-zeros" should be very small in magnitude.} \item{image}{\code{signature(x = "CHMfactor")} Plot the image of the lower triangular factor, \eqn{L}, from the decomposition. This method is equivalent to \code{image(as(x, "sparseMatrix"))} so the comments in the above description of the \code{coerce} method apply here too.} \item{solve}{\code{signature(a = "CHMfactor", b = "ddenseMatrix"), system= *}: %% This is copy-paste from solve-methods.Rd {FIXME ?} The \code{solve} methods for a \code{"CHMfactor"} object take an optional third argument \code{system} whose value can be one of the character strings \code{"A"}, \code{"LDLt"}, \code{"LD"}, \code{"DLt"}, \code{"L"}, \code{"Lt"}, \code{"D"}, \code{"P"} or \code{"Pt"}. This argument describes the system to be solved. The default, \code{"A"}, is to solve \eqn{Ax = b} for \eqn{x} where \code{A} is the sparse, positive-definite matrix that was factored to produce \code{a}. Analogously, \code{system = "L"} returns the solution \eqn{x}, of \eqn{Lx = b}. Similarly, for all system codes \bold{but} \code{"P"} and \code{"Pt"} where, e.g., \code{x <- solve(a, b,system="P")} is equivalent to \code{x <- P \%*\% b}. See also \code{\link{solve-methods}}. } \item{determinant}{\code{signature(x = "CHMfactor", logarithm = "logical")} returns the determinant (or the logarithm of the determinant, if \code{logarithm = TRUE}, the default) of the factor \eqn{L} from the \eqn{LL'} decomposition (even if the decomposition represented by \code{x} is of the \eqn{LDL'} form (!)). This is the square root of the determinant (half the logarithm of the determinant when \code{logarithm = TRUE}) of the positive-definite matrix that was decomposed.} %% since 0.999375-8 (2008-03-25): \item{update}{\code{signature(object = "CHMfactor"), parent}. The \code{\link{update}} method requires an additional argument \code{parent}, which is \emph{either} a \code{"\linkS4class{dsCMatrix}"} object, say \eqn{A}, (with the same structure of nonzeros as the matrix that was decomposed to produce \code{object}) or a general \code{"\linkS4class{dgCMatrix}"}, say \eqn{M}, where \eqn{A := M M'} (\code{== tcrossprod(parent)}) is used for \eqn{A}. Further it provides an optional argument \code{mult}, a numeric scalar. This method updates the numeric values in \code{object} to the decomposition of \eqn{A+mI} where \eqn{A} is the matrix above (either the \code{parent} or \eqn{M M'}) and \eqn{m} is the scalar \code{mult}. Because only the numeric values are updated this method should be faster than creating and decomposing \eqn{A+mI}. It is not uncommon to want, say, the determinant of \eqn{A+mI} for many different values of \eqn{m}. This method would be the preferred approach in such cases.} } } %\references{} %\author{} %\note{} \seealso{ \code{\link{Cholesky}}, also for examples; class \code{\linkS4class{dgCMatrix}}. } \examples{% most are in ./Cholesky.Rd ## An example for the expand() method n <- 1000; m <- 200; nnz <- 2000 set.seed(1) M1 <- spMatrix(n, m, i = sample(n, nnz, replace = TRUE), j = sample(m, nnz, replace = TRUE), x = round(rnorm(nnz),1)) XX <- crossprod(M1) ## = M1'M1 = M M' where M <- t(M1) CX <- Cholesky(XX) isLDL(CX) str(CX) ## a "dCHMsimpl" object r <- expand(CX) L.P <- with(r, crossprod(L,P)) ## == L'P PLLP <- crossprod(L.P) ## == (L'P)' L'P == P'LL'P b <- sample(m) stopifnot(all.equal(PLLP, XX), % not needed: factorsCheck is off: check.attributes=FALSE), all(as.vector(solve(CX, b, system="P" )) == r$P \%*\% b), all(as.vector(solve(CX, b, system="Pt")) == t(r$P) \%*\% b) ) u1 <- update(CX, XX, mult=pi) if(FALSE) ## fails ___ FIXME ? ___ u2 <- update(CX, t(M1), mult=pi) ## [ See help(Cholesky) for more examples ] ## ------------- } \keyword{classes} \keyword{algebra} Matrix/man/CAex.Rd0000644000175100001440000000230410757763005013427 0ustar hornikusers\name{CAex} \alias{CAex} \docType{data} \title{Albers' example Matrix with "Difficult" Eigen Factorization} \description{ An example of a sparse matrix for which \code{\link{eigen}()} seemed to be difficult, an unscaled version of this has been posted to the web, accompanying an E-mail to R-help (\url{https://stat.ethz.ch/mailman/listinfo/r-help}), by Casper J Albers, Open University, UK. } \usage{data(CAex)} \format{ This is a \eqn{72 \times 72}{72 * 72} symmetric matrix with 216 non-zero entries in five bands, stored as sparse matrix of class \code{\linkS4class{dgCMatrix}}. } \details{ In some versions of \R, \code{\link{eigen}(CAex)} fell into an infinite loop (whereas \code{\link{eigen}(CAex, EISPACK=TRUE)} has been okay). } % \source{ see above % } \examples{ data(CAex) str(CAex) # of class "dgCMatrix" image(CAex)# -> it's a simple band matrix with 5 bands ## and the eigen values are basically 1 (42 times) and 0 (30 x): zapsmall(ev <- eigen(CAex, EISPACK=TRUE, only.values=TRUE)$values) ## i.e., the matrix is symmetric, hence sCA <- as(CAex, "symmetricMatrix") ## and stopifnot(class(sCA) == "dsCMatrix", as(sCA, "matrix") == as(CAex, "matrix")) } \keyword{datasets} Matrix/man/image-methods.Rd0000644000175100001440000001247412256042001015321 0ustar hornikusers\name{image-methods} \title{Methods for image() in Package 'Matrix'} \docType{methods} %\alias{image}% <- needed for \usage{.} \alias{image-methods} \alias{image,ANY-method} \alias{image,CHMfactor-method} \alias{image,Matrix-method} \alias{image,dgRMatrix-method} \alias{image,dgCMatrix-method} \alias{image,dgTMatrix-method} \alias{image,dsparseMatrix-method} \alias{image,lsparseMatrix-method} \alias{image,nsparseMatrix-method} \description{ Methods for function \code{\link[graphics]{image}} in package \pkg{Matrix}. An image of a matrix simply color codes all matrix entries and draws the \eqn{n\times m}{n x m} matrix using an \eqn{n\times m}{n x m} grid of (colored) rectangles. } \usage{% want \usage{} since we have many "surprising arguments" \S4method{image}{dgTMatrix}(x, xlim = c(1, di[2]), ylim = c(di[1], 1), aspect = "iso", sub = sprintf("Dimensions: \%d x \%d", di[1], di[2]), xlab = "Column", ylab = "Row", cuts = 15, useRaster = FALSE, useAbs = NULL, colorkey = !useAbs, col.regions = NULL, lwd = NULL, \dots) } \arguments{ \item{x}{a Matrix object, i.e., fulfilling \code{\link{is}(x, "Matrix")}.} \item{xlim, ylim}{x- and y-axis limits; may be used to \dQuote{zoom into} matrix. Note that \eqn{x,y} \dQuote{feel reversed}: \code{ylim} is for the rows (= 1st index) and \code{xlim} for the columns (= 2nd index). For convenience, when the limits are integer valued, they are both extended by \code{0.5}; also, \code{ylim} is always used decreasingly.} \item{aspect}{aspect ratio specified as number (y/x) or string; see \code{\link[lattice]{levelplot}}.} \item{sub, xlab, ylab}{axis annotation with sensible defaults; see \code{\link{plot.default}}.} \item{cuts}{number of levels the range of matrix values would be divided into.} \item{useRaster}{logical indicating if raster graphics should be used (instead of the tradition rectangle vector drawing). If true, \code{\link[lattice]{panel.levelplot.raster}} (from \pkg{lattice} package) is used, and the colorkey is also done via rasters, see also \code{\link[lattice]{levelplot}} and possibly \code{\link[grid]{grid.raster}}. Note that using raster graphics may often be faster, but can be slower, depending on the matrix dimensions and the graphics device (dimensions).} \item{useAbs}{logical indicating if \code{\link{abs}(x)} should be shown; if \code{TRUE}, the former (implicit) default, the default \code{col.regions} will be \code{\link{grey}} colors (and no \code{colorkey} drawn). The default is \code{FALSE} unless the matrix has no negative entries.} \item{colorkey}{logical indicating if a color key aka \sQuote{legend} should be produced. Default is to draw one, unless \code{useAbs} is true. You can also specify a \code{\link{list}}, see \code{\link[lattice]{levelplot}}, such as\code{list(raster=TRUE)} in the case of rastering.} \item{col.regions}{vector of gradually varying colors; see \code{\link[lattice]{levelplot}}.} \item{lwd}{non-negative number or \code{NULL} (default), specifying the line-width of the rectangles of each non-zero matrix entry (drawn by \code{\link[grid]{grid.rect}}). The default depends on the matrix dimension and the device size.} \item{\dots}{further arguments passed to methods and \code{\link[lattice]{levelplot}}, notably \code{at} for specifying (possibly non equidistant) cut values for dividing the matrix values (superseding \code{cuts} above).}% FIXME? example *using* at=.. } \section{Methods}{ All methods currently end up calling the method for the \code{\linkS4class{dgTMatrix}} class. Use \code{showMethods(image)} to list them all. } \examples{ showMethods(image) ## If you want to see all the methods' implementations: showMethods(image, incl=TRUE, inherit=FALSE) data(CAex) image(CAex, main = "image(CAex)") image(CAex, useAbs=TRUE, main = "image(CAex, useAbs=TRUE)") cCA <- Cholesky(crossprod(CAex), Imult = .01) image(cCA, main="Cholesky(crossprod(CAex), Imult = .01)") image(cCA, useAbs=TRUE) data(USCounties) image(USCounties)# huge image(sign(USCounties))## just the pattern # how the result looks, may depend heavily on # the device, screen resolution, antialiasing etc # e.g. x11(type="Xlib") may show very differently than cairo-based ## Drawing borders around each rectangle; # again, viewing depends very much on the device: image(USCounties[1:400,1:200], lwd=.1) ## Using (xlim,ylim) has advantage : matrix dimension and (col/row) indices: image(USCounties, c(1,200), c(1,400), lwd=.1) image(USCounties, c(1,300), c(1,200), lwd=.5 ) image(USCounties, c(1,300), c(1,200), lwd=.01) if(doExtras <- interactive() || nzchar(Sys.getenv("R_MATRIX_CHECK_EXTRA")) || identical("true", unname(Sys.getenv("R_PKG_CHECKING_doExtras")))) { ## Using raster graphics: For PDF this would give a 77 MB file, ## however, for such a large matrix, this is typically considerably ## *slower* (than vector graphics rectangles) in most cases : if(doPNG <- !dev.interactive()) png("image-USCounties-raster.png", width=3200, height=3200) image(USCounties, useRaster = TRUE) # should not suffer from anti-aliasing if(doPNG) dev.off() ## and now look at the *.png image in a viewer you can easily zoom in and out }#only if(doExtras) } \keyword{methods} \keyword{hplot} Matrix/man/Subassign-methods.Rd0000644000175100001440000001511112254575000016174 0ustar hornikusers\name{[<--methods} \docType{methods} \alias{[<--methods} \alias{Subassign-methods}% <- nicer to use in \link{.} % \title{Methods for "[<-" - Assigning to Subsets for 'Matrix'} % in ../R/Matrix.R \alias{[<-,Matrix,ANY,ANY,ANY-method} \alias{[<-,Matrix,ANY,ANY,Matrix-method} \alias{[<-,Matrix,ANY,missing,Matrix-method} \alias{[<-,Matrix,missing,ANY,Matrix-method} \alias{[<-,Matrix,ANY,ANY,matrix-method} \alias{[<-,Matrix,ANY,missing,matrix-method} \alias{[<-,Matrix,missing,ANY,matrix-method} \alias{[<-,Matrix,matrix,missing,replValue-method} \alias{[<-,Matrix,lsparseMatrix,missing,replValue-method} \alias{[<-,Matrix,nsparseMatrix,missing,replValue-method} \alias{[<-,Matrix,ldenseMatrix,missing,replValue-method} \alias{[<-,Matrix,ndenseMatrix,missing,replValue-method} % \alias{[<-,Matrix,missing,numeric,missing-method} % \alias{[<-,Matrix,numeric,missing,missing-method} % \alias{[<-,Matrix,numeric,numeric,missing-method} % in ../R/denseMatrix.R \alias{[<-,denseMatrix,index,missing,replValue-method} \alias{[<-,denseMatrix,index,index,replValue-method} \alias{[<-,denseMatrix,matrix,missing,replValue-method} \alias{[<-,denseMatrix,missing,index,replValue-method} \alias{[<-,denseMatrix,missing,missing,ANY-method} % in ../R/diagMatrix.R \alias{[<-,diagonalMatrix,index,index,replValue-method} \alias{[<-,diagonalMatrix,index,missing,replValue-method} \alias{[<-,diagonalMatrix,matrix,missing,replValue-method} \alias{[<-,diagonalMatrix,missing,index,replValue-method} \alias{[<-,diagonalMatrix,missing,missing,ANY-method} % \alias{[<-,diagonalMatrix,index,index,sparseMatrix-method} \alias{[<-,diagonalMatrix,index,missing,sparseMatrix-method} \alias{[<-,diagonalMatrix,missing,index,sparseMatrix-method} % \alias{[<-,diagonalMatrix,index,index,sparseVector-method} \alias{[<-,diagonalMatrix,index,missing,sparseVector-method} \alias{[<-,diagonalMatrix,missing,index,sparseVector-method} % % -> ../R/sparseMatrix.R : \alias{[<-,sparseMatrix,ANY,ANY,sparseMatrix-method} \alias{[<-,sparseMatrix,ANY,missing,sparseMatrix-method} \alias{[<-,sparseMatrix,missing,ANY,sparseMatrix-method} \alias{[<-,sparseMatrix,missing,missing,ANY-method} % -> ../R/indMatrix.R : -- these give errors \alias{[<-,indMatrix,index,ANY,ANY-method} \alias{[<-,indMatrix,missing,index,ANY-method} \alias{[<-,indMatrix,missing,missing,ANY-method} % -> ../R/Tsparse.R : replValue = { numeric, logical } \alias{[<-,TsparseMatrix,index,index,replValue-method} \alias{[<-,TsparseMatrix,index,missing,replValue-method} \alias{[<-,TsparseMatrix,matrix,missing,replValue-method} \alias{[<-,TsparseMatrix,Matrix,missing,replValue-method} \alias{[<-,TsparseMatrix,lMatrix,missing,replValue-method} \alias{[<-,TsparseMatrix,nMatrix,missing,replValue-method} \alias{[<-,TsparseMatrix,missing,index,replValue-method} \alias{[<-,TsparseMatrix,missing,index,sparseVector-method} \alias{[<-,TsparseMatrix,index,missing,sparseVector-method} \alias{[<-,TsparseMatrix,index,index,sparseVector-method} % \alias{[<-,dgTMatrix,missing,missing,numeric-method} % -> ../R/Csparse.R : \alias{[<-,CsparseMatrix,index,index,replValue-method} \alias{[<-,CsparseMatrix,index,missing,replValue-method} \alias{[<-,CsparseMatrix,Matrix,missing,replValue-method} \alias{[<-,CsparseMatrix,matrix,missing,replValue-method} \alias{[<-,CsparseMatrix,lsparseMatrix,missing,replValue-method} \alias{[<-,CsparseMatrix,nsparseMatrix,missing,replValue-method} \alias{[<-,CsparseMatrix,ldenseMatrix,missing,replValue-method} \alias{[<-,CsparseMatrix,ndenseMatrix,missing,replValue-method} \alias{[<-,CsparseMatrix,missing,index,replValue-method} \alias{[<-,CsparseMatrix,missing,index,sparseVector-method} \alias{[<-,CsparseMatrix,index,missing,sparseVector-method} \alias{[<-,CsparseMatrix,index,index,sparseVector-method} % % \alias{[<-,RsparseMatrix,index,index,replValue-method} \alias{[<-,RsparseMatrix,index,missing,replValue-method} \alias{[<-,RsparseMatrix,matrix,missing,replValue-method} \alias{[<-,RsparseMatrix,missing,index,replValue-method} \alias{[<-,RsparseMatrix,missing,index,sparseVector-method} \alias{[<-,RsparseMatrix,index,missing,sparseVector-method} \alias{[<-,RsparseMatrix,index,index,sparseVector-method} % % % \alias{[<-,dsparseMatrix,missing,index,numeric-method} % \alias{[<-,dsparseMatrix,index,missing,numeric-method} % \alias{[<-,dsparseMatrix,index,index,numeric-method} % % % \alias{[<-,lsparseMatrix,missing,numeric,logical-method} % \alias{[<-,lsparseMatrix,numeric,missing,logical-method} % \alias{[<-,lsparseMatrix,numeric,numeric,logical-method} %------- \description{ Methods for \code{"[<-"}, i.e., extraction or subsetting mostly of matrices, in package \pkg{Matrix}. \bold{Note}: Contrary to standard \code{\link{matrix}} assignment in base \R, in \code{x[..] <- val} it is typically an \bold{error} (see \code{\link{stop}}) when the \link{type} or \code{\link{class}} of \code{val} would require the class of \code{x} to be changed, e.g., when \code{x} is logical, say \code{"lsparseMatrix"}, and \code{val} is numeric. In other cases, e.g., when \code{x} is a \code{"nsparseMatrix"} and \code{val} is not \code{TRUE} or \code{FALSE}, a warning is signalled, and \code{val} is \dQuote{interpreted} as \code{\link{logical}}, and (logical) \code{\link{NA}} is interpreted as \code{TRUE}. } \section{Methods}{ There are \emph{many many} more than these: \describe{ \item{x = "Matrix", i = "missing", j = "missing", value= "ANY"}{ is currently a simple fallback method implementation which ensures \dQuote{readable} error messages.} \item{x = "Matrix", i = "ANY", j = "ANY", value= "ANY"}{ currently gives an error } \item{x = "denseMatrix", i = "index", j = "missing", value= "numeric"}{ ... } \item{x = "denseMatrix", i = "index", j = "index", value= "numeric"}{ ... } \item{x = "denseMatrix", i = "missing", j = "index", value= "numeric"}{ ... } } } \seealso{ %% ./Xtrct-methods.Rd: \code{\link{[-methods}} for subsetting \code{"Matrix"} objects; the \code{\linkS4class{index}} class; \code{\link{Extract}} about the standard subset assignment (and extraction). } \examples{ %% Note that ./Xtrct-methods.Rd has the indexing ones set.seed(101) (a <- m <- Matrix(round(rnorm(7*4),2), nrow = 7)) a[] <- 2.2 # <<- replaces **every** entry a ## as do these: a[,] <- 3 ; a[TRUE,] <- 4 m[2, 3] <- 3.14 # simple number m[3, 3:4]<- 3:4 # simple numeric of length 2 ## sub matrix assignment: m[-(4:7), 3:4] <- cbind(1,2:4) #-> upper right corner of 'm' m[3:5, 2:3] <- 0 m[6:7, 1:2] <- Diagonal(2) m ## rows or columns only: m[1,] <- 10 m[,2] <- 1:7 m[-(1:6), ] <- 3:0 # not the first 6 rows, i.e. only the 7th as(m, "sparseMatrix") } \keyword{methods} \keyword{array} Matrix/man/sparseLU-class.Rd0000644000175100001440000000604012271746775015461 0ustar hornikusers\name{sparseLU-class} \docType{class} \alias{sparseLU-class} \alias{expand,sparseLU-method} \title{Sparse LU decomposition of a square sparse matrix} \description{Objects of this class contain the components of the LU decomposition of a sparse square matrix.} \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("sparseLU", ...)} but are more commonly created by function \code{\link{lu}()} applied to a sparse matrix, such as a matrix of class \code{\linkS4class{dgCMatrix}}. } \section{Slots}{ \describe{ \item{\code{L}:}{Object of class \code{"\linkS4class{dtCMatrix}"}, the lower triangular factor from the left.} \item{\code{U}:}{Object of class \code{"\linkS4class{dtCMatrix}"}, the upper triangular factor from the right.} \item{\code{p}:}{Object of class \code{"integer"}, permutation applied from the left. } \item{\code{q}:}{Object of class \code{"integer"}, permutation applied from the right.} \item{\code{Dim}:}{the dimension of the original matrix; inherited from class \code{\linkS4class{MatrixFactorization}}.} } } \section{Extends}{ Class \code{"\linkS4class{LU}"}, directly. Class \code{"\linkS4class{MatrixFactorization}"}, by class \code{"LU"}. } \section{Methods}{ \describe{ \item{expand}{\code{signature(x = "sparseLU")} Returns a list with components \code{P}, \code{L}, \code{U}, and \code{Q}, where \eqn{P} and \eqn{Q} represent fill-reducing permutations, and \eqn{L}, and \eqn{U} the lower and upper triangular matrices of the decomposition. The original matrix corresponds to the product \eqn{PLUQ}.} } } %\references{} \note{ The decomposition is of the form \deqn{A = P'LUQ,} %% --------- or equivalently \eqn{PAQ' = LU}, where all matrices are sparse and of size \eqn{n\times n}{n by n}. The matrices \eqn{P} and \eqn{Q}, and their transposes \eqn{P'} and \eqn{Q'} are permutation matrices, \eqn{L} is lower triangular and \eqn{U} is upper triangular. } \seealso{ \code{\link{lu}}, \code{\link[base]{solve}}, \code{\linkS4class{dgCMatrix}} } \examples{ ## Extending the one in examples(lu), calling the matrix A, ## and confirming the factorization identities : A <- as(readMM(system.file("external/pores_1.mtx", package = "Matrix")), "CsparseMatrix") str(luA <- lu(A)) # p is a 0-based permutation of the rows # q is a 0-based permutation of the columns xA <- expand(luA) ## which is simply doing stopifnot(identical(xA$ L, luA@L), identical(xA$ U, luA@U), identical(xA$ P, as(luA@p +1L, "pMatrix")), identical(xA$ Q, as(luA@q +1L, "pMatrix"))) P.LUQ <- with(xA, t(P) \%*\% L \%*\% U \%*\% Q) stopifnot(all.equal(A, P.LUQ, tolerance = 1e-12)) ## permute rows and columns of original matrix pA <- A[luA@p + 1L, luA@q + 1L] stopifnot(identical(pA, with(xA, P \%*\% A \%*\% t(Q)))) pLU <- drop0(luA@L \%*\% luA@U) # L \%*\% U -- dropping extra zeros stopifnot(all.equal(pA, pLU)) } \keyword{classes} Matrix/man/dgeMatrix-class.Rd0000644000175100001440000001132612271746775015652 0ustar hornikusers\name{dgeMatrix-class} \title{Class "dgeMatrix" of Dense Numeric (S4 Class) Matrices} \docType{class} \alias{dgeMatrix-class} % METHODS: %\alias{solve,....-method}--> solve-methods.Rd %\alias{\%*\%,....-method} --> matrix-products.Rd %\alias{crossprod,...-method}--> matrix-products.Rd %\alias{tcrossprod,..-method}--> " " % Group ones \alias{Arith,dgeMatrix,dgeMatrix-method} \alias{Arith,dgeMatrix,logical-method} \alias{Arith,dgeMatrix,numeric-method} \alias{Arith,logical,dgeMatrix-method} \alias{Arith,numeric,dgeMatrix-method} \alias{Math,dgeMatrix-method} %\alias{Math2,dgeMatrix,numeric-method} % Others % \alias{as.vector,dgeMatrix,missing-method} \alias{coerce,dgeMatrix,matrix-method} \alias{coerce,dgeMatrix,triangularMatrix-method} \alias{coerce,dgeMatrix,lgeMatrix-method} \alias{coerce,numLike,dgeMatrix-method} \alias{coerce,matrix,dgeMatrix-method} \alias{colMeans,dgeMatrix-method} \alias{colSums,dgeMatrix-method} \alias{determinant,dgeMatrix,logical-method} \alias{determinant,dgeMatrix,missing-method} \alias{diag,dgeMatrix-method} \alias{diag<-,dgeMatrix-method} \alias{dim,dgeMatrix-method} \alias{dimnames,dgeMatrix-method} \alias{eigen,dgeMatrix,missing-method} \alias{eigen,dgeMatrix,logical-method} \alias{norm,dgeMatrix,missing-method} \alias{norm,dgeMatrix,character-method} \alias{rcond,dgeMatrix,missing-method} \alias{rcond,dgeMatrix,character-method} \alias{rowMeans,dgeMatrix-method} \alias{rowSums,dgeMatrix-method} \alias{t,dgeMatrix-method} % \description{A general numeric dense matrix in the S4 Matrix representation. \code{dgeMatrix} is the \emph{\dQuote{standard}} class for dense numeric matrices in the \pkg{Matrix} package. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("dgeMatrix", ...)} or, more commonly, by coercion from the \code{Matrix} class (see \linkS4class{Matrix}) or by \code{\link{Matrix}(..)}. } \section{Slots}{ \describe{ \item{\code{x}:}{Object of class \code{"numeric"} - the numeric values contained in the matrix, in column-major order.} \item{\code{Dim}:}{Object of class \code{"integer"} - the dimensions of the matrix - must be an integer vector with exactly two non-negative values.} \item{\code{Dimnames}:}{a list of length two - inherited from class \code{\linkS4class{Matrix}}.} \item{\code{factors}:}{Object of class \code{"list"} - a list of factorizations of the matrix.} } } \section{Methods}{ The are group methods (see, e.g., \code{\link{Arith}}) \describe{ \item{Arith}{\code{signature(e1 = "dgeMatrix", e2 = "dgeMatrix")}: ... } \item{Arith}{\code{signature(e1 = "dgeMatrix", e2 = "numeric")}: ... } \item{Arith}{\code{signature(e1 = "numeric", e2 = "dgeMatrix")}: ... } \item{Math}{\code{signature(x = "dgeMatrix")}: ... } \item{Math2}{\code{signature(x = "dgeMatrix", digits = "numeric")}: ...} } matrix products \code{\link[=crossprod-methods]{\%*\%}}, \code{\link[=crossprod-methods]{crossprod}()} and \code{tcrossprod()}, several \code{\link{solve}} methods, and other matrix methods available: \describe{ \item{Schur}{\code{signature(x = "dgeMatrix", vectors = "logical")}: ... } \item{Schur}{\code{signature(x = "dgeMatrix", vectors = "missing")}: ... } \item{chol}{\code{signature(x = "dgeMatrix")}: see \code{\link{chol}}.} \item{coerce}{\code{signature(from = "dgeMatrix", to = "lgeMatrix")}: ... } \item{coerce}{\code{signature(from = "dgeMatrix", to = "matrix")}: ... } \item{coerce}{\code{signature(from = "matrix", to = "dgeMatrix")}: ... } \item{colMeans}{\code{signature(x = "dgeMatrix")}: columnwise means (averages)} \item{colSums}{\code{signature(x = "dgeMatrix")}: columnwise sums} \item{diag}{\code{signature(x = "dgeMatrix")}: ... } \item{dim}{\code{signature(x = "dgeMatrix")}: ... } \item{dimnames}{\code{signature(x = "dgeMatrix")}: ... } \item{eigen}{\code{signature(x = "dgeMatrix", only.values= "logical")}: ...} \item{eigen}{\code{signature(x = "dgeMatrix", only.values= "missing")}: ...} \item{norm}{\code{signature(x = "dgeMatrix", type = "character")}: ... } \item{norm}{\code{signature(x = "dgeMatrix", type = "missing")}: ... } \item{rcond}{\code{signature(x = "dgeMatrix", norm = "character")}: ... } \item{rcond}{\code{signature(x = "dgeMatrix", norm = "missing")}: ... } \item{rowMeans}{\code{signature(x = "dgeMatrix")}: rowwise means (averages)} \item{rowSums}{\code{signature(x = "dgeMatrix")}: rowwise sums} \item{t}{\code{signature(x = "dgeMatrix")}: ... } } } %\references{} %\author{} %\note{} \seealso{ Classes \code{\linkS4class{Matrix}}, \code{\linkS4class{dtrMatrix}}, and \code{\linkS4class{dsyMatrix}}. } %\examples{} \keyword{classes} \keyword{algebra} Matrix/man/sparseVector-class.Rd0000644000175100001440000002503512271746775016410 0ustar hornikusers%%----- Docu for *all* sparse vector classes ---------- \name{sparseVector-class} \docType{class} \title{Sparse Vector Classes} \alias{sparseVector-class} % sub classes \alias{dsparseVector-class} \alias{isparseVector-class} \alias{lsparseVector-class} \alias{nsparseVector-class} \alias{zsparseVector-class} \alias{xsparseVector-class}% the class union %% Group methods % \alias{Math,sparseVector-method} % %\alias{Math2,sparseVector,numeric-method} \alias{Arith,sparseVector,sparseVector-method} \alias{Arith,dsparseVector,dsparseVector-method} \alias{-,dsparseVector,missing-method} \alias{!,sparseVector-method} \alias{Logic,sparseVector,sparseVector-method} \alias{Logic,lsparseVector,lsparseVector-method} \alias{Logic,nsparseVector,nsparseVector-method} \alias{Ops,ANY,sparseVector-method} \alias{Ops,sparseVector,ANY-method} \alias{Ops,sparseVector,sparseVector-method} \alias{Ops,sparseVector,atomicVector-method} \alias{Ops,atomicVector,sparseVector-method} \alias{Ops,Matrix,sparseVector-method} \alias{Ops,sparseVector,Matrix-method} \alias{Arith,ddenseMatrix,sparseVector-method} \alias{Arith,dgeMatrix,sparseVector-method} \alias{Arith,sparseVector,ddenseMatrix-method} \alias{Arith,sparseVector,dgeMatrix-method} \alias{Logic,dMatrix,sparseVector-method} \alias{Logic,lMatrix,sparseVector-method} \alias{Logic,nMatrix,sparseVector-method} \alias{Logic,sparseVector,dMatrix-method} \alias{Logic,sparseVector,lMatrix-method} \alias{Logic,sparseVector,nMatrix-method} \alias{Summary,sparseVector-method} \alias{Summary,nsparseVector-method} %% non-group : %\alias{solve,..} --> solve-methods.Rd %\alias{\%*\%,..} --> matrix-products.Rd \alias{coerce,ANY,sparseVector-method} \alias{coerce,ANY,nsparseVector-method} \alias{coerce,CsparseMatrix,sparseVector-method} \alias{coerce,TsparseMatrix,sparseVector-method} \alias{coerce,sparseMatrix,sparseVector-method} \alias{coerce,diagonalMatrix,sparseVector-method} \alias{coerce,atomicVector,sparseVector-method} \alias{coerce,atomicVector,dsparseVector-method} \alias{coerce,sparseVector,integer-method} \alias{coerce,sparseVector,logical-method} \alias{coerce,sparseVector,numeric-method} \alias{coerce,sparseVector,vector-method} \alias{coerce,sparseVector,Matrix-method} \alias{coerce,sparseVector,sparseMatrix-method} \alias{coerce,sparseVector,CsparseMatrix-method} \alias{coerce,sparseVector,TsparseMatrix-method} \alias{coerce,nsparseVector,lsparseVector-method} \alias{coerce,nsparseVector,dsparseVector-method} \alias{coerce,nsparseVector,isparseVector-method} \alias{coerce,nsparseVector,zsparseVector-method} \alias{coerce,xsparseVector,dsparseVector-method} \alias{coerce,xsparseVector,isparseVector-method} \alias{coerce,xsparseVector,lsparseVector-method} \alias{coerce,xsparseVector,zsparseVector-method} \alias{coerce,xsparseVector,nsparseVector-method} % \alias{as.logical,sparseVector-method} \alias{as.numeric,sparseVector-method} \alias{as.vector,sparseVector,missing-method} \alias{as.vector,sparseVector,character-method} \alias{dim<-,sparseVector-method} \alias{is.na,nsparseVector-method} \alias{is.na,sparseVector-method} \alias{is.finite,nsparseVector-method} \alias{is.finite,sparseVector-method} \alias{is.infinite,nsparseVector-method} \alias{is.infinite,sparseVector-method} \alias{length,sparseVector-method} \alias{mean,sparseVector-method} \alias{rep,sparseVector-method} \alias{show,sparseVector-method} \alias{toeplitz}% only needed if(as.numeric(R.version$`svn rev`) < 60620) \alias{toeplitz,sparseVector-method} % \alias{head,sparseVector-method} \alias{tail,sparseVector-method} \alias{[,sparseVector,index,ANY,ANY-method} \alias{[,sparseVector,lsparseVector,ANY,ANY-method} \alias{[,sparseVector,nsparseVector,ANY,ANY-method} \alias{[<-,sparseVector,index,missing,replValue-method} \alias{[<-,sparseVector,sparseVector,missing,replValue-method} % also indexing in "traditional" vectors: %R_FIXME \alias{[<-,atomicVector,sparseVector,missing,replValue-method} %R_FIXME \alias{[,atomicVector,lsparseVector,ANY,ANY-method} %R_FIXME \alias{[,atomicVector,nsparseVector,ANY,ANY-method} % \description{Sparse Vector Classes: The virtual mother class \code{"sparseVector"} has the five actual daughter classes \code{"dsparseVector"}, \code{"isparseVector"}, \code{"lsparseVector"}, \code{"nsparseVector"}, and \code{"zsparseVector"}, where we've mainly implemented methods for the \code{d*}, \code{l*} and \code{n*} ones. } \section{Slots}{ \describe{ \item{\code{length}:}{class \code{"numeric"} - the \code{\link{length}} of the sparse vector. Note that \code{"numeric"} can be considerably larger than the maximal \code{"integer"}, \code{\link{.Machine}$integer.max}, on purpose.} \item{\code{i}:}{class \code{"numeric"} - the (1-based) indices of the non-zero entries. Must \emph{not} be \code{NA} and strictly sorted increasingly. Note that \code{"integer"} is \dQuote{part of} \code{"numeric"}, and can (and often will) be used for non-huge sparseVectors.} \item{\code{x}:}{(for all but \code{"nsparseVector"}): the non-zero entries. This is of class \code{"numeric"} for class \code{"dsparseVector"}, \code{"logical"} for class \code{"lsparseVector"}, etc. Note that \code{"nsparseVector"}s have no \code{x} slot. Further, mainly for ease of method definitions, we've defined the class union (see \code{\link{setClassUnion}}) of all sparse vector classes which \emph{have} an \code{x} slot, as class \code{"xsparseVector"}. } } } \section{Methods}{ \describe{ \item{length}{\code{signature(x = "sparseVector")}: simply extracts the \code{length} slot.} \item{show}{\code{signature(object = "sparseVector")}: The \code{\link{show}} method for sparse vectors prints \emph{\dQuote{structural}} zeroes as \code{"."} using the non-exported \code{prSpVector} function which allows further customization such as replacing \code{"."} by \code{" "} (blank). Note that \code{\link{options}(max.print)} will influence how many entries of large sparse vectors are printed at all.} \item{as.vector}{\code{signature(x = "sparseVector", mode = "character")} coerces sparse vectors to \dQuote{regular}, i.e., atomic vectors. This is the same as \code{as(x, "vector")}.} \item{as}{..: see \code{coerce} below} \item{coerce}{\code{signature(from = "sparseVector", to = "sparseMatrix")}, and} \item{coerce}{\code{signature(from = "sparseMatrix", to = "sparseVector")}, etc: coercions to and from sparse matrices (\code{\linkS4class{sparseMatrix}}) are provided and work analogously as in standard \R, i.e., a vector is coerced to a 1-column matrix.} \item{dim<-}{\code{signature(x = "sparseVector", value = "integer")} coerces a sparse vector to a sparse Matrix, i.e., an object inheriting from \code{\linkS4class{sparseMatrix}}, of the appropriate dimension.} \item{head}{\code{signature(x = "sparseVector")}: as with \R's (package \pkg{util}) \code{\link{head}}, \code{head(x,n)} (for \eqn{n >= 1}) is equivalent to \code{x[1:n]}, but here can be much more efficient, see the example.} \item{tail}{\code{signature(x = "sparseVector")}: analogous to \code{\link{head}}, see above.} \item{toeplitz}{\code{signature(x = "sparseVector")}: as \code{\link[stats]{toeplitz}(x)}, produce the \eqn{n \times n} Toeplitz matrix from \code{x}, where \code{n = length(x)}.} \item{rep}{\code{signature(x = "sparseVector")} repeat \code{x}, with the same argument list \code{(x, times, length.out, each, ...)} as the default method for rep().} \item{Ops}{\code{signature(e1 = "sparseVector", e2 = "*")}: define arithmetic, compare and logic operations, (see \code{\link[=S4groupGeneric]{Ops}}).} \item{Summary}{\code{signature(x = "sparseVector")}: define all the \code{\link[=S4groupGeneric]{Summary}} methods.} \item{[}{\code{signature(x = "atomicVector", i = ...)}: not only can you subset (aka \emph{\dQuote{index into}}) sparseVectors \code{x[i]} using sparseVectors \code{i}, but we also support efficient subsetting of traditional vectors \code{x} by logical sparse vectors (i.e., \code{i} of class \code{"nsparseVector"} or \code{"lsparseVector"}).} \item{is.na, is.finite, is.infinite}{\code{(x = "sparseVector")}, and} \item{is.na, is.finite, is.infinite}{\code{(x = "nsparseVector")}: return \code{\link{logical}} or \code{"nsparseVector"} of the same length as \code{x}, indicating if/where \code{x} is \code{\link{NA}} (or \code{NaN}), finite or infinite, entirely analogously to the corresponding base \R functions.} } } \seealso{ \code{\link{sparseVector}()} for friendly construction of sparse vectors (apart from \code{as(*, "sparseVector")}). } %\author{Martin} \examples{ getClass("sparseVector") getClass("dsparseVector") getClass("xsparseVector")# those with an 'x' slot sx <- c(0,0,3, 3.2, 0,0,0,-3:1,0,0,2,0,0,5,0,0) (ss <- as(sx, "sparseVector")) ix <- as.integer(round(sx)) (is <- as(ix, "sparseVector")) ## an "isparseVector" (!) ## rep() works too: (ri <- rep(is, length.out= 25)) ## Using `dim<-` as in base R : r <- ss dim(r) <- c(4,5) # becomes a sparse Matrix: r ## or coercion (as as.matrix() in base R): as(ss, "Matrix") stopifnot(all(ss == print(as(ss, "CsparseMatrix")))) ## currently has "non-structural" FALSE -- printing as ":" (lis <- is & FALSE) (nn <- is[is == 0]) # all "structural" FALSE ## NA-case sN <- sx; sN[4] <- NA (svN <- as(sN, "sparseVector")) v <- as(c(0,0,3, 3.2, rep(0,9),-3,0,-1, rep(0,20),5,0), "sparseVector") v <- rep(rep(v, 50), 5000) set.seed(1); v[sample(v@i, 1e6)] <- 0 str(v) % Formal class 'dsparseVector' [package "Matrix"] with 3 slots % ..@ x : num [1:250000] 3.2 -1 -3 3 5 3.2 -3 3 -1 5 ... % ..@ length: int 9500000 % ..@ i : int [1:250000] 4 16 52 155 189 194 204 231 244 265 ... system.time(for(i in 1:4) hv <- head(v, 1e6)) ## user system elapsed ## 0.033 0.000 0.032 system.time(for(i in 1:4) h2 <- v[1:1e6]) ## user system elapsed ## 1.317 0.000 1.319 stopifnot(identical(hv, h2), identical(is | FALSE, is != 0), validObject(svN), validObject(lis), as.logical(is.na(svN[4])), identical(is^2 > 0, is & TRUE), all(!lis), !any(lis), length(nn@i) == 0, !any(nn), all(!nn), sum(lis) == 0, !prod(lis), range(lis) == c(0,0)) x20 <- sparseVector(c(9,3:1), i=c(1:2,4,7), length=20) (T20 <- toeplitz(x20)) stopifnot(is(T20, "symmetricMatrix"), is(T20, "sparseMatrix"), identical(unname(as.matrix(T20)), toeplitz(as.vector(x20)))) } \keyword{classes} Matrix/man/externalFormats.Rd0000644000175100001440000000622712271746775016005 0ustar hornikusers\name{externalFormats} \alias{readHB} \alias{readMM} % \alias{writeHB} \alias{writeMM} \alias{writeMM,CsparseMatrix-method} \alias{writeMM,sparseMatrix-method} \title{Read and write external matrix formats} \description{ Read matrices stored in the Harwell-Boeing or MatrixMarket formats or write \code{\linkS4class{sparseMatrix}} objects to one of these formats. } \usage{ readHB(file) readMM(file) writeMM(obj, file, \dots) } \arguments{ \item{obj}{a real sparse matrix} \item{file}{for \code{writeMM} - the name of the file to be written. For \code{readHB} and \code{readMM} the name of the file to read, as a character scalar. The names of files storing matrices in the Harwell-Boeing format usually end in \code{".rua"} or \code{".rsa"}. Those storing matrices in the MatrixMarket format usually end in \code{".mtx"}. Alternatively, \code{readHB} and \code{readMM} accept connection objects.} \item{\dots}{optional additional arguments. Currently none are used in any methods.} } \value{ The \code{readHB} and \code{readMM} functions return an object that inherits from the \code{"\linkS4class{Matrix}"} class. Methods for the \code{writeMM} generic functions usually return \code{\link{NULL}} and, as a side effect, the matrix \code{obj} is written to \code{file} in the MatrixMarket format (writeMM). } \note{ The Harwell-Boeing format is older and less flexible than the MatrixMarket format. The function \code{writeHB} was deprecated and has now been removed. Please use \code{writeMM} instead. A very simple way to export small sparse matrices \code{S}, is to use \code{summary(S)} which returns a \code{\link{data.frame}} with columns \code{i}, \code{j}, and possibly \code{x}, see \code{summary} in \code{\link{sparseMatrix-class}}, and an example below. } \references{ \url{http://math.nist.gov/MatrixMarket} \url{http://www.cise.ufl.edu/research/sparse/matrices} } \examples{ str(pores <- readMM(system.file("external/pores_1.mtx", package = "Matrix"))) str(utm <- readHB(system.file("external/utm300.rua", package = "Matrix"))) str(lundA <- readMM(system.file("external/lund_a.mtx", package = "Matrix"))) str(lundA <- readHB(system.file("external/lund_a.rsa", package = "Matrix"))) \dontrun{ ## NOTE: The following examples take quite some time ## ---- even on a fast internet connection: if(FALSE) # the URL has been corrected, but we need an un-tar step! str(sm <- readHB(gzcon(url("http://www.cise.ufl.edu/research/sparse/RB/Boeing/msc00726.tar.gz")))) str(jgl009 <- readMM(gzcon(url("ftp://math.nist.gov/pub/MatrixMarket2/Harwell-Boeing/counterx/jgl009.mtx.gz")))) } data(KNex) writeMM(KNex$mm, "mmMM.mtx") ## very simple export - in triplet format - to text file: data(CAex) s.CA <- summary(CAex) message("writing to ", outf <- tempfile()) write.table(s.CA, file = outf, row.names=FALSE) ## and read it back -- showing off sparseMatrix(): dd <- read.table(outf, header=TRUE) mm <- do.call(sparseMatrix, dd) stopifnot(all.equal(mm, CAex, tolerance=1e-15)) } \keyword{IO} \keyword{array} \keyword{algebra} Matrix/man/ddenseMatrix-class.Rd0000644000175100001440000000416612271746775016361 0ustar hornikusers\name{ddenseMatrix-class} \docType{class} \alias{ddenseMatrix-class} \title{Virtual Class "ddenseMatrix" of Numeric Dense Matrices} % now separated from ./dgeMatrix-class.Rd - on purpose % METHODS: % undocu (FIXME) \alias{show,ddenseMatrix-method} \alias{coerce,ddenseMatrix,matrix-method} \alias{coerce,ddenseMatrix,dgeMatrix-method} %\alias{coerce,ddenseMatrix,CsparseMatrix-method} % % Group \alias{Arith,ddenseMatrix,ddenseMatrix-method} \alias{Arith,ddenseMatrix,logical-method} \alias{Arith,ddenseMatrix,numeric-method} \alias{Arith,logical,ddenseMatrix-method} \alias{Arith,numeric,ddenseMatrix-method} \alias{Math,ddenseMatrix-method} \alias{Summary,ddenseMatrix-method} % \alias{as.numeric,ddenseMatrix-method} \alias{diag,ddenseMatrix-method} \alias{determinant,ddenseMatrix,missing-method} \alias{determinant,ddenseMatrix,logical-method} \alias{lu,ddenseMatrix-method} \alias{norm,ddenseMatrix,missing-method} \alias{norm,ddenseMatrix,character-method} \alias{rcond,ddenseMatrix,missing-method} \alias{rcond,ddenseMatrix,character-method} %% \alias{solve,ddenseMatrix,ANY-method}--> solve-methods.Rd \alias{t,ddenseMatrix-method} % \description{This is the virtual class of all dense numeric (i.e., \bold{d}ouble, hence \emph{\dQuote{ddense}}) S4 matrices. Its most important subclass is the \code{\linkS4class{dgeMatrix}} class. %% and now say what the difference is ! __ FIXME __ } \section{Extends}{ Class \code{"dMatrix"} directly; class \code{"Matrix"}, by the above. } \section{Slots}{ the same slots at its subclass \code{\linkS4class{dgeMatrix}}, see there. } \section{Methods}{ Most methods are implemented via \code{as(*, "dgeMatrix")} and are mainly used as \dQuote{fallbacks} when the subclass doesn't need its own specialized method. Use \code{\link{showMethods}(class = "ddenseMatrix", where = "package:Matrix")} for an overview. } %\references{} %\note{} \seealso{ The virtual classes \code{\linkS4class{Matrix}}, \code{\linkS4class{dMatrix}}, and \code{\linkS4class{dsparseMatrix}}. } \examples{ showClass("ddenseMatrix") showMethods(class = "ddenseMatrix", where = "package:Matrix") } \keyword{classes} Matrix/man/Matrix.Rd0000644000175100001440000001047711644124434014056 0ustar hornikusers\name{Matrix} \alias{Matrix} \title{Construct a Classed Matrix} \usage{ Matrix(data=NA, nrow=1, ncol=1, byrow=FALSE, dimnames=NULL, sparse = NULL, doDiag = TRUE, forceCheck = FALSE) } \description{ Construct a Matrix of a class that inherits from \code{Matrix}. } \arguments{ \item{data}{an optional numeric data vector or matrix.} \item{nrow}{when \code{data} is not a matrix, the desired number of rows} \item{ncol}{when \code{data} is not a matrix, the desired number of columns} \item{byrow}{logical. If \code{FALSE} (the default) the matrix is filled by columns, otherwise the matrix is filled by rows.} \item{dimnames}{a \code{\link{dimnames}} attribute for the matrix: a \code{list} of two character components. They are set if not \code{\link{NULL}} (as per default).} \item{sparse}{logical or \code{NULL}, specifying if the result should be sparse or not. By default, it is made sparse when more than half of the entries are 0. Note that when the resulting matrix is diagonal (\dQuote{mathematically}), \code{sparse=FALSE} results in a \code{\linkS4class{diagonalMatrix}}, unless \code{doDiag=FALSE} as well, see the first examples.} \item{doDiag}{only when \code{sparse = FALSE}, logical indicating if a \code{\linkS4class{diagonalMatrix}} object should be considered (default). Otherwise, in such a case, a dense (symmetric) matrix will be returned.} \item{forceCheck}{logical indicating if the checks for structure should even happen when \code{data} is already a \code{"Matrix"} object.} } \value{ Returns matrix of a class that inherits from \code{"Matrix"}. Only if \code{data} is not a \code{\link{matrix}} and does not already inherit from class \code{\linkS4class{Matrix}} are the arguments \code{nrow}, \code{ncol} and \code{byrow} made use of. } \details{ If either of \code{nrow} or \code{ncol} is not given, an attempt is made to infer it from the length of \code{data} and the other parameter. Further, \code{Matrix()} makes efforts to keep \code{\link{logical}} matrices logical, i.e., inheriting from class \code{\linkS4class{lMatrix}}, and to determine specially structured matrices such as symmetric, triangular or diagonal ones. Note that a \emph{symmetric} matrix also needs symmetric \code{\link{dimnames}}, e.g., by specifying \code{dimnames = list(NULL,NULL)}, see the examples. Most of the time, the function works via a traditional (\emph{full}) \code{\link{matrix}}. However, \code{Matrix(0, nrow,ncol)} directly constructs an \dQuote{empty} \linkS4class{sparseMatrix}, as does \code{Matrix(FALSE, *)}. Although it is sometime possible to mix unclassed matrices (created with \code{matrix}) with ones of class \code{"Matrix"}, it is much safer to always use carefully constructed ones of class \code{"Matrix"}. } \seealso{ The classes \code{\linkS4class{Matrix}}, \code{\linkS4class{symmetricMatrix}}, \code{\linkS4class{triangularMatrix}}, and \code{\linkS4class{diagonalMatrix}}; further, \code{\link{matrix}}. Special matrices can be constructed, e.g., via \code{\link{sparseMatrix}} (sparse), \code{\link{bdiag}} (block-diagonal), \code{\link{bandSparse}} (banded sparse), or \code{\link{Diagonal}}. } \examples{ Matrix(0, 3, 2) # 3 by 2 matrix of zeros -> sparse Matrix(0, 3, 2, sparse=FALSE)# -> 'dense' Matrix(0, 2, 2, sparse=FALSE)# diagonal ! Matrix(0, 2, 2, sparse=FALSE, doDiag=FALSE)# -> dense Matrix(1:6, 3, 2) # a 3 by 2 matrix (+ integer warning) Matrix(1:6 + 1, nrow=3) ## logical ones: Matrix(diag(4) > 0)# -> "ldiMatrix" with diag = "U" Matrix(diag(4) > 0, sparse=TRUE)# -> sparse... Matrix(diag(4) >= 0)# -> "lsyMatrix" (of all 'TRUE') ## triangular l3 <- upper.tri(matrix(,3,3)) (M <- Matrix(l3)) # -> "ltCMatrix" Matrix(! l3)# -> "ltrMatrix" as(l3, "CsparseMatrix") Matrix(1:9, nrow=3, dimnames = list(c("a", "b", "c"), c("A", "B", "C"))) (I3 <- Matrix(diag(3)))# identity, i.e., unit "diagonalMatrix" str(I3) # note the empty 'x' slot (A <- cbind(a=c(2,1), b=1:2))# symmetric *apart* from dimnames Matrix(A) # hence 'dgeMatrix' (As <- Matrix(A, dimnames = list(NULL,NULL)))# -> symmetric stopifnot(is(As, "symmetricMatrix"), is(Matrix(0, 3,3), "sparseMatrix"), is(Matrix(FALSE, 1,1), "sparseMatrix")) } \keyword{array} \keyword{algebra} Matrix/man/isTriangular.Rd0000644000175100001440000000555712253551634015264 0ustar hornikusers\name{isTriangular} \title{isTriangular() and isDiagonal() Methods} %\docType{methods} both generic *and* methods \alias{isDiagonal} \alias{isDiagonal-methods} \alias{isDiagonal,symmetricMatrix-method} \alias{isDiagonal,triangularMatrix-method} \alias{isDiagonal,denseMatrix-method} \alias{isDiagonal,diagonalMatrix-method} \alias{isDiagonal,sparseMatrix-method} \alias{isDiagonal,matrix-method} % \alias{isTriangular} \alias{isTriangular-methods} \alias{isTriangular,triangularMatrix-method} \alias{isTriangular,denseMatrix-method} \alias{isTriangular,diagonalMatrix-method} \alias{isTriangular,BunchKaufman-method} \alias{isTriangular,Cholesky-method} \alias{isTriangular,CsparseMatrix-method} \alias{isTriangular,TsparseMatrix-method} \alias{isTriangular,dtCMatrix-method} \alias{isTriangular,dtRMatrix-method} \alias{isTriangular,dtTMatrix-method} \alias{isTriangular,dtpMatrix-method} \alias{isTriangular,dtrMatrix-method} \alias{isTriangular,ltCMatrix-method} \alias{isTriangular,ltRMatrix-method} \alias{isTriangular,ltTMatrix-method} \alias{isTriangular,ltpMatrix-method} \alias{isTriangular,ltrMatrix-method} \alias{isTriangular,ntCMatrix-method} \alias{isTriangular,ntRMatrix-method} \alias{isTriangular,ntTMatrix-method} \alias{isTriangular,ntpMatrix-method} \alias{isTriangular,ntrMatrix-method} \alias{isTriangular,pBunchKaufman-method} \alias{isTriangular,pCholesky-method} \alias{isTriangular,matrix-method} % \description{ \code{isTriangular(M)} returns a \code{\link{logical}} indicating \code{M} is a triangular matrix. Analogously, \code{isDiagonal(M)} is true iff \code{M} is a diagonal matrix. Contrary to \code{\link{isSymmetric}()}, these two functions are generically from \pkg{Matrix} package, and hence also define methods for traditional (\code{\link{class}} \code{"matrix"}) matrices. } \usage{ isDiagonal(object) isTriangular(object, ...) \S4method{isTriangular}{CsparseMatrix}(object, upper = NA) } \arguments{ \item{object}{any \R object, typically a matrix (traditional or Matrix package).} \item{upper}{logical, one of \code{NA} (default), \code{FALSE}, or \code{TRUE} where the last two cases require a lower or upper triangular \code{object} to result in \code{TRUE}.} \item{\dots}{potentially further arguments for other methods.} } \value{ a (\dQuote{scalar}) logical, \code{TRUE} or \code{FALSE}, never \code{\link{NA}}. } \seealso{ \code{\link{isSymmetric}}; formal class (and subclasses) \code{"\linkS4class{triangularMatrix}"} and \code{"\linkS4class{diagonalMatrix}"}. } \examples{ isTriangular(Diagonal(4)) ## is TRUE: a diagonl matrix is also (both upper and lower) triangular (M <- Matrix(c(1,2,0,1), 2,2)) isTriangular(M) # TRUE (*and* of formal class "dtrMatrix") isTriangular(as(M, "dgeMatrix")) # still triangular, even if not "formally" isTriangular(crossprod(M)) # FALSE isDiagonal(matrix(c(2,0,0,1), 2,2)) # TRUE } \keyword{methods} Matrix/man/band.Rd0000644000175100001440000001176411156163642013520 0ustar hornikusers\name{band} \docType{methods} \alias{band-methods} \alias{tril-methods} \alias{triu-methods} \alias{band,CsparseMatrix-method} \alias{tril,CsparseMatrix-method} \alias{triu,CsparseMatrix-method} \alias{band,RsparseMatrix-method} \alias{tril,RsparseMatrix-method} \alias{triu,RsparseMatrix-method} \alias{band,TsparseMatrix-method} \alias{tril,TsparseMatrix-method} \alias{triu,TsparseMatrix-method} \alias{tril,dsCMatrix-method} \alias{tril,lsCMatrix-method} \alias{tril,nsCMatrix-method} \alias{triu,dsCMatrix-method} \alias{triu,lsCMatrix-method} \alias{triu,nsCMatrix-method} \alias{band,ddenseMatrix-method} \alias{tril,ddenseMatrix-method} \alias{triu,ddenseMatrix-method} \alias{band,denseMatrix-method} \alias{tril,denseMatrix-method} \alias{triu,denseMatrix-method} \alias{band,matrix-method} \alias{tril,matrix-method} \alias{triu,matrix-method} % Begin{UGLY-disAMBIGUATION-hack} -- in ../R/triangularMatrix.R % we would want to define 'triangularMatrix' methods, but they ambiguate with the above! % \alias{tril,triangularMatrix-method} % \alias{triu,triangularMatrix-method} \alias{tril,dtCMatrix-method} \alias{tril,dtRMatrix-method} \alias{tril,dtTMatrix-method} \alias{tril,dtpMatrix-method} \alias{tril,dtrMatrix-method} \alias{tril,ltCMatrix-method} \alias{tril,ltRMatrix-method} \alias{tril,ltTMatrix-method} \alias{tril,ltpMatrix-method} \alias{tril,ltrMatrix-method} \alias{tril,ntCMatrix-method} \alias{tril,ntRMatrix-method} \alias{tril,ntTMatrix-method} \alias{tril,ntpMatrix-method} \alias{tril,ntrMatrix-method} \alias{tril,itTMatrix-method} \alias{tril,itCMatrix-method} \alias{tril,itRMatrix-method} \alias{triu,dtCMatrix-method} \alias{triu,dtRMatrix-method} \alias{triu,dtTMatrix-method} \alias{triu,dtpMatrix-method} \alias{triu,dtrMatrix-method} \alias{triu,ltCMatrix-method} \alias{triu,ltRMatrix-method} \alias{triu,ltTMatrix-method} \alias{triu,ltpMatrix-method} \alias{triu,ltrMatrix-method} \alias{triu,ntCMatrix-method} \alias{triu,ntRMatrix-method} \alias{triu,ntTMatrix-method} \alias{triu,ntpMatrix-method} \alias{triu,ntrMatrix-method} \alias{triu,itTMatrix-method} \alias{triu,itCMatrix-method} \alias{triu,itRMatrix-method} % End{UGLY-disAMBIGUATION-hack} % \alias{band} \alias{tril} \alias{triu} \title{Extract bands of a matrix} \description{ Returns a new matrix formed by extracting the lower triangle (\code{tril}) or the upper triangle (\code{triu}) or a general band relative to the diagonal (\code{band}), and setting other elements to zero. The general forms of these functions include integer arguments to specify how many diagonal bands above or below the main diagonal are not set to zero. } \usage{ band(x, k1, k2, \dots) tril(x, k = 0, \dots) triu(x, k = 0, \dots) } \arguments{ \item{x}{a matrix-like object} \item{k,k1,k2}{integers specifying the diagonal bands that will not be set to zero. These are given relative to the main diagonal, which is \code{k=0}. A negative value of \code{k} indicates a diagonal below the main diagonal and a positive value indicates a diagonal above the main diagonal.} \item{\dots}{Optional arguments used by specific methods. (None used at present.)} } \value{ An object of an appropriate matrix class. The class of the value of \code{tril} or \code{triu} inherits from \code{\linkS4class{triangularMatrix}} when appropriate. Note that the result is of class \code{\linkS4class{sparseMatrix}} only if \code{x} is. } \section{Methods}{ \describe{ \item{x = "CsparseMatrix"}{method for compressed, sparse, column-oriented matrices.} \item{x = "TsparseMatrix"}{method for sparse matrices in triplet format.} \item{x = "RsparseMatrix"}{method for compressed, sparse, row-oriented matrices.} \item{x = "ddenseMatrix"}{method for dense numeric matrices, including packed numeric matrices.} } } \seealso{ \code{\link{bandSparse}} for the \emph{construction} of a banded sparse matrix directly from its non-zero diagonals. } \examples{ ## A random sparse matrix : set.seed(7) m <- matrix(0, 5, 5) m[sample(length(m), size = 14)] <- rep(1:9, length=14) (mm <- as(m, "CsparseMatrix")) tril(mm) # lower triangle tril(mm, -1) # strict lower triangle triu(mm, 1) # strict upper triangle band(mm, -1, 2) # general band (m5 <- Matrix(rnorm(25), nc = 5)) tril(m5) # lower triangle tril(m5, -1) # strict lower triangle triu(m5, 1) # strict upper triangle band(m5, -1, 2) # general band (m65 <- Matrix(rnorm(30), nc = 5)) # not square triu(m65) # result in not dtrMatrix unless square (sm5 <- crossprod(m65)) # symmetric band(sm5, -1, 1)# symmetric band preserves symmetry property as(band(sm5, -1, 1), "sparseMatrix")# often preferable %% \dontshow{ ## this uses special methods (x.x <- crossprod(mm)) tril(x.x) xx <- tril(x.x) + triu(x.x, 1) ## the same as x.x (but stored differently): txx <- t(as(xx, "symmetricMatrix")) stopifnot(identical(triu(x.x), t(tril(x.x))), identical(class(x.x), class(txx)), identical(as(x.x, "generalMatrix"), as(txx, "generalMatrix"))) } } \keyword{methods} \keyword{algebra} Matrix/man/rleDiff-class.Rd0000644000175100001440000000265111314233025015252 0ustar hornikusers\name{rleDiff-class} \docType{class} \Rdversion{1.1} \title{Class "rleDiff" of rle(diff(.)) Stored Vectors} \alias{rleDiff-class} \alias{show,rleDiff-method} \description{ Class \code{"rleDiff"} is for compactly storing long vectors which mainly consist of \emph{linear} stretches. For such a vector \code{x}, \code{\link{diff}(x)} consists of \emph{constant} stretches and is hence well compressable via \code{\link{rle}()}. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("rleDiff", ...)}. Currently experimental, see below. } \section{Slots}{ \describe{ \item{\code{first}:}{A single number (of class \code{"numLike"}, a class union of \code{"numeric"} and \code{"logical"}).} \item{\code{rle}:}{Object of class \code{"rle"}, basically a \code{\link{list}} with components \code{"lengths"} and \code{"values"}, see \code{\link{rle}()}. As this is used to encode potentially huge index vectors, \code{lengths} may be of type \code{\link{double}} here.} } } \section{Methods}{ There is a simple \code{\link{show}} method only.% currently } \note{ This is currently an \emph{experimental} auxiliary class for the class \code{\linkS4class{abIndex}}, see there. } \seealso{ \code{\link{rle}}, \code{\linkS4class{abIndex}}. } \examples{ showClass("rleDiff") ab <- c(abIseq(2, 100), abIseq(20, -2)) ab@rleD # is "rleDiff" } \keyword{classes} Matrix/man/symmpart.Rd0000644000175100001440000000420511523240150014444 0ustar hornikusers\name{symmpart} \title{Symmetric Part and Skew(symmetric) Part of a Matrix} %% Hmm, want the generic and methods all in this file ... %% \docType{methods} \alias{symmpart} \alias{skewpart} % \alias{symmpart-methods} \alias{skewpart-methods} \alias{symmpart,Matrix-method} \alias{skewpart,Matrix-method} \alias{symmpart,diagonalMatrix-method} \alias{skewpart,diagonalMatrix-method} \alias{symmpart,ddenseMatrix-method} \alias{skewpart,ddenseMatrix-method} \alias{symmpart,denseMatrix-method} \alias{skewpart,denseMatrix-method} \alias{symmpart,symmetricMatrix-method} \alias{skewpart,symmetricMatrix-method} \alias{symmpart,matrix-method} \alias{skewpart,matrix-method} % \description{ \code{symmpart(x)} computes the symmetric part \code{(x + t(x))/2} and \code{skewpart(x)} the skew symmetric part \code{(x - t(x))/2} of a square matrix \code{x}, more efficiently for specific Matrix classes. Note that \code{x == symmpart(x) + skewpart(x)} for all square matrices -- apart from extraneous \code{\link{NA}} values in the RHS. } \usage{ symmpart(x) skewpart(x) } \arguments{ \item{x}{a \emph{square} matrix; either \dQuote{traditional} of class \code{"matrix"}, or typically, inheriting from the \code{\linkS4class{Matrix}} class.} } % \section{Methods}{ % \describe{ % \item{x = "Matrix"}{ ~~describe this method here } % }} \details{ These are generic functions with several methods for different matrix classes, use e.g., \code{\link{showMethods}(symmpart)} to see them. } \value{ \code{symmpart()} returns a symmetric matrix, inheriting from \code{\linkS4class{symmetricMatrix}} iff \code{x} inherited from \code{Matrix}. \code{skewpart()} returns a skew-symmetric matrix, typically of the same class as \code{x} (or the closest \dQuote{general} one, see \code{\linkS4class{generalMatrix}}). } %\references{ ~put references to the literature/web site here ~ } %\seealso{ ~~objects to See Also as \code{\link{help}}, ~~~ } \examples{ m <- Matrix(1:4, 2,2) symmpart(m) skewpart(m) stopifnot(all(m == symmpart(m) + skewpart(m))) ## investigate the current methods: showMethods(skewpart, include = TRUE) } \keyword{array} \keyword{arith} Matrix/man/ngeMatrix-class.Rd0000644000175100001440000000412112001034107015621 0ustar hornikusers\name{ngeMatrix-class} \docType{class} \title{Class "ngeMatrix" of General Dense Nonzero-pattern Matrices} \alias{ngeMatrix-class} % \alias{!,ngeMatrix-method} \alias{Arith,ngeMatrix,ngeMatrix-method} \alias{Compare,ngeMatrix,ngeMatrix-method} \alias{Logic,ngeMatrix,ngeMatrix-method} \alias{as.vector,ngeMatrix,missing-method} \alias{coerce,matrix,ngeMatrix-method} \alias{coerce,ngeMatrix,dgeMatrix-method} \alias{coerce,ngeMatrix,matrix-method} \alias{coerce,ngeMatrix,ngCMatrix-method} \alias{coerce,ngeMatrix,ngTMatrix-method} \alias{coerce,ngeMatrix,nsyMatrix-method} \alias{coerce,ngeMatrix,ntrMatrix-method} \alias{coerce,ngeMatrix,ntpMatrix-method} \alias{coerce,ngeMatrix,nspMatrix-method} \alias{diag<-,ngeMatrix-method} \alias{t,ngeMatrix-method} % \description{This is the class of general dense nonzero-pattern matrices, see \code{\linkS4class{nMatrix}}. } \section{Slots}{ \describe{ \item{\code{x}:}{Object of class \code{"logical"}. The logical values that constitute the matrix, stored in column-major order.} \item{\code{Dim},\code{Dimnames}:}{The dimension (a length-2 \code{"integer"}) and corresponding names (or \code{NULL}), see the \code{\linkS4class{Matrix}} class.} \item{\code{factors}:}{Object of class \code{"list"}. A named list of factorizations that have been computed for the matrix.} } } \section{Extends}{ Class \code{"ndenseMatrix"}, directly. Class \code{"lMatrix"}, by class \code{"ndenseMatrix"}. Class \code{"denseMatrix"}, by class \code{"ndenseMatrix"}. Class \code{"Matrix"}, by class \code{"ndenseMatrix"}. Class \code{"Matrix"}, by class \code{"ndenseMatrix"}. } \section{Methods}{ Currently, mainly \code{\link{t}()} and coercion methods (for \code{\link{as}(.)}); use, e.g., \code{\link{showMethods}(class="ngeMatrix")} for details. } \seealso{ Non-general logical dense matrix classes such as \code{\linkS4class{ntrMatrix}}, or \code{\linkS4class{nsyMatrix}}; \emph{sparse} logical classes such as \code{\linkS4class{ngCMatrix}}. } \examples{ showClass("ngeMatrix") ## "lgeMatrix" is really more relevant } \keyword{classes} Matrix/man/Matrix-class.Rd0000644000175100001440000001670212271746775015175 0ustar hornikusers\name{Matrix-class} \docType{class} \alias{Matrix-class} \alias{!,Matrix-method} %% Group methods: \alias{-,Matrix,missing-method} \alias{+,Matrix,missing-method} \alias{Arith,Matrix,Matrix-method} \alias{Ops,Matrix,Matrix-method} \alias{Ops,Matrix,ANY-method} \alias{Ops,ANY,Matrix-method} \alias{Ops,Matrix,matrix-method} \alias{Ops,matrix,Matrix-method} \alias{Ops,logical,Matrix-method} \alias{Ops,Matrix,logical-method} \alias{Logic,logical,Matrix-method} \alias{Logic,Matrix,logical-method} \alias{Logic,Matrix,ANY-method} \alias{Logic,ANY,Matrix-method} \alias{Summary,Matrix-method} \alias{mean,Matrix-method} % "[" ---> Xtrct-methods.Rd % "[<-" ---> Subassign-methods.Rd %\alias{solve,...} --> solve-methods.Rd %\alias{\%*%,... } --> matrix-products.Rd \alias{cbind2,ANY,Matrix-method} \alias{cbind2,Matrix,ANY-method} \alias{cbind2,Matrix,Matrix-method} \alias{cbind2,Matrix,NULL-method} \alias{cbind2,Matrix,atomicVector-method} \alias{cbind2,Matrix,missing-method} \alias{cbind2,NULL,Matrix-method} \alias{cbind2,atomicVector,Matrix-method} \alias{rbind2,ANY,Matrix-method} \alias{rbind2,Matrix,ANY-method} \alias{rbind2,Matrix,Matrix-method} \alias{rbind2,Matrix,NULL-method} \alias{rbind2,Matrix,atomicVector-method} \alias{rbind2,Matrix,missing-method} \alias{rbind2,NULL,Matrix-method} \alias{rbind2,atomicVector,Matrix-method} % \alias{cov2cor,Matrix-method} \alias{det}% "the function" (our copy of base::det) \alias{determinant,Matrix,missing-method} \alias{determinant,Matrix,logical-method} \alias{diag,Matrix-method} \alias{drop,Matrix-method} \alias{head,Matrix-method} \alias{tail,Matrix-method} \alias{diff,Matrix-method} \alias{dim,Matrix-method} \alias{dim<-,Matrix-method} \alias{dimnames,Matrix-method} \alias{dimnames<-,Matrix,list-method} \alias{dimnames<-,Matrix,NULL-method} \alias{length,Matrix-method} \alias{show,Matrix-method} \alias{as.array,Matrix-method} \alias{as.matrix,Matrix-method} \alias{as.vector,Matrix,missing-method} \alias{as.numeric,Matrix-method} \alias{as.logical,Matrix-method} \alias{t,Matrix-method} \alias{unname,Matrix-method} \alias{coerce,Matrix,vector-method} \alias{coerce,Matrix,numeric-method} \alias{coerce,Matrix,logical-method} \alias{coerce,Matrix,integer-method} \alias{coerce,Matrix,complex-method} % \alias{coerce,Matrix,matrix-method}% \alias{coerce,matrix,Matrix-method} \alias{coerce,Matrix,denseMatrix-method} \alias{coerce,Matrix,CsparseMatrix-method} \alias{coerce,Matrix,sparseMatrix-method} %\alias{solve,Matrix,....-method}--> ./solve-methods.Rd %\alias{unname,Matrix-method} \alias{unname,Matrix,missing-method} % \title{Virtual Class "Matrix" Class of Matrices} \description{ The \code{Matrix} class is a class contained by all actual classes in the \pkg{Matrix} package. It is a \dQuote{virtual} class. } \section{Slots}{ Common to \emph{all} matrix objects in the package: \describe{ \item{\code{Dim}:}{Object of class \code{"integer"} - the dimensions of the matrix - must be an integer vector with exactly two non-negative values.} \item{\code{Dimnames}:}{list of length two; each component containing NULL or a \code{\link{character}} vector length equal the corresponding \code{Dim} element.} } } \section{Methods}{ \describe{ \item{determinant}{\code{signature(x = "Matrix", logarithm = "missing")}: and} \item{determinant}{\code{signature(x = "Matrix", logarithm = "logical")}: compute the (\eqn{\log}) determinant of \code{x}. The method chosen depends on the actual Matrix class of \code{x}. Note that \code{\link[base]{det}} also works for all our matrices, calling the appropriate \code{determinant()} method. The \code{Matrix::det} is an exact copy of \code{base::det}, but in the correct namespace, and hence calling the S4-aware version of \code{determinant()}.).} \item{diff}{\code{signature(x = "Matrix")}: As \code{\link{diff}()} for traditional matrices, i.e., applying \code{diff()} to each column.} \item{dim}{\code{signature(x = "Matrix")}: extract matrix dimensions \code{\link{dim}}.} \item{dim<-}{\code{signature(x = "Matrix", value = "ANY")}: where \code{value} is integer of length 2. Allows to \emph{reshape} Matrix objects, but only when \code{prod(value) == prod(dim(x))}.} \item{dimnames}{\code{signature(x = "Matrix")}: extract \code{\link{dimnames}}.} \item{dimnames<-}{\code{signature(x = "Matrix", value = "list")}: set the \code{dimnames} to a \code{\link{list}} of length 2, see \code{\link{dimnames<-}}.} \item{length}{\code{signature(x = "Matrix")}: simply defined as \code{prod(dim(x))} (and hence of mode \code{"double"}).} \item{show}{\code{signature(object = "Matrix")}: \code{\link{show}} method for \code{\link{print}}ing.} \item{image}{\code{signature(object = "Matrix")}: draws an \code{\link{image}} of the matrix entries, using \code{\link[lattice]{levelplot}()} from package \pkg{lattice}.} \item{head}{\code{signature(object = "Matrix")}: return only the \emph{\dQuote{head}}, i.e., the first few rows.} \item{tail}{\code{signature(object = "Matrix")}: return only the \emph{\dQuote{tail}}, i.e., the last few rows of the respective matrix.} \cr %------------------------------------ \item{as.matrix, as.array}{\code{signature(x = "Matrix")}: the same as \code{as(x, "matrix")}; see also the note below.} \item{as.vector}{\code{signature(x = "Matrix", mode = "missing")}: \code{as.vector(m)} should be identical to \code{as.vector(as(m, "matrix"))}, implemented more efficiently for some subclasses.} \item{as(x, "vector"), as(x, "numeric")}{etc, similarly.} } There are many more methods that (conceptually should) work for all \code{"Matrix"} objects, e.g., \code{\link{colSums}}, \code{\link{rowMeans}}. Even \pkg{base} functions may work automagically (if they first call \code{\link{as.matrix}()} on their principal argument), e.g., \code{\link{apply}}, \code{\link{eigen}}, \code{\link{svd}} or \code{\link{kappa}} all do work via coercion to a \dQuote{traditional} (dense) \code{\link{matrix}}. %% --> ../tests/base-matrix-fun.R } \note{ Loading the \code{Matrix} namespace \dQuote{overloads} \code{\link{as.matrix}} and \code{\link{as.array}} in the \pkg{base} namespace by the equivalent of \code{function(x) as(x, "matrix")}. Consequently, \code{as.matrix(m)} or \code{as.array(m)} will properly work when \code{m} inherits from the \code{"Matrix"} class --- \emph{also} for functions in package \pkg{base} and other packages. E.g., \code{\link{apply}} or \code{\link{outer}} can therefore be applied to \code{"Matrix"} matrices. } %\references{} \author{Douglas Bates \email{bates@stat.wisc.edu} and Martin Maechler} \seealso{ the classes \code{\linkS4class{dgeMatrix}}, \code{\linkS4class{dgCMatrix}}, and function \code{\link{Matrix}} for construction (and examples). Methods, e.g., for \code{\link[=kronecker-methods]{kronecker}}. } \examples{ slotNames("Matrix") cl <- getClass("Matrix") names(cl@subclasses) # more than 40 .. showClass("Matrix")#> output with slots and all subclasses (M <- Matrix(c(0,1,0,0), 6, 4)) dim(M) diag(M) cm <- M[1:4,] + 10*Diagonal(4) diff(M) ## can reshape it even : dim(M) <- c(2, 12) M stopifnot(identical(M, Matrix(c(0,1,0,0), 2,12)), all.equal(det(cm), determinant(as(cm,"matrix"), log=FALSE)$modulus, check.attributes=FALSE)) } \keyword{classes} \keyword{algebra} Matrix/man/matrix-products.Rd0000644000175100001440000003522112271746775015770 0ustar hornikusers\name{matrix-products} \docType{methods} \title{Matrix (Cross) Products (of Transpose)} \alias{\%*\%-methods} \alias{crossprod-methods} \alias{tcrossprod-methods} %%-- %*% ------------------------------------- \alias{\%*\%,dgeMatrix,dgeMatrix-method} \alias{\%*\%,dgeMatrix,matrix-method} \alias{\%*\%,dgeMatrix,numeric-method} \alias{\%*\%,matrix,dgeMatrix-method} \alias{\%*\%,numeric,dgeMatrix-method} \alias{\%*\%,numLike,CsparseMatrix-method} \alias{\%*\%,CsparseMatrix,CsparseMatrix-method} \alias{\%*\%,CsparseMatrix,ddenseMatrix-method} \alias{\%*\%,CsparseMatrix,matrix-method} \alias{\%*\%,CsparseMatrix,numeric-method} \alias{\%*\%,ddenseMatrix,CsparseMatrix-method} \alias{\%*\%,matrix,CsparseMatrix-method} \alias{\%*\%,numeric,CsparseMatrix-method} \alias{\%*\%,ddenseMatrix,ddenseMatrix-method} \alias{\%*\%,dgCMatrix,dgeMatrix-method} \alias{\%*\%,dgCMatrix,matrix-method} \alias{\%*\%,numeric,dgCMatrix-method} \alias{\%*\%,ddenseMatrix,dgCMatrix-method} \alias{\%*\%,dgeMatrix,dgCMatrix-method} \alias{\%*\%,matrix,dgCMatrix-method} \alias{\%*\%,dgeMatrix,diagonalMatrix-method} \alias{\%*\%,matrix,diagonalMatrix-method} \alias{\%*\%,diagonalMatrix,dgeMatrix-method} \alias{\%*\%,diagonalMatrix,diagonalMatrix-method} \alias{\%*\%,diagonalMatrix,matrix-method} \alias{\%*\%,diagonalMatrix,CsparseMatrix-method} \alias{\%*\%,diagonalMatrix,sparseMatrix-method} \alias{\%*\%,CsparseMatrix,diagonalMatrix-method} \alias{\%*\%,sparseMatrix,diagonalMatrix-method} \alias{\%*\%,denseMatrix,diagonalMatrix-method} \alias{\%*\%,diagonalMatrix,denseMatrix-method} \alias{\%*\%,diagonalMatrix,lgeMatrix-method} \alias{\%*\%,lgeMatrix,diagonalMatrix-method} \alias{\%*\%,nMatrix,lMatrix-method} \alias{\%*\%,lMatrix,nMatrix-method} \alias{\%*\%,lMatrix,lMatrix-method} \alias{\%*\%,nMatrix,nMatrix-method} \alias{\%*\%,dMatrix,lMatrix-method} \alias{\%*\%,dMatrix,nMatrix-method} \alias{\%*\%,lMatrix,dMatrix-method} \alias{\%*\%,nMatrix,dMatrix-method} \alias{\%*\%,dMatrix,integer-method} \alias{\%*\%,integer,dMatrix-method} \alias{\%*\%,Matrix,numLike-method} \alias{\%*\%,numLike,Matrix-method} \alias{\%*\%,Matrix,ANY-method} \alias{\%*\%,ANY,Matrix-method} \alias{\%*\%,Matrix,matrix-method} \alias{\%*\%,matrix,Matrix-method} \alias{\%*\%,ddenseMatrix,dsparseMatrix-method} \alias{\%*\%,dgeMatrix,dsparseMatrix-method} \alias{\%*\%,dsparseMatrix,ddenseMatrix-method} \alias{\%*\%,dsparseMatrix,dgeMatrix-method} \alias{\%*\%,ddenseMatrix,dsyMatrix-method} \alias{\%*\%,matrix,dsyMatrix-method} \alias{\%*\%,dsyMatrix,dsyMatrix-method} \alias{\%*\%,dspMatrix,ddenseMatrix-method} \alias{\%*\%,dspMatrix,matrix-method} \alias{\%*\%,dsyMatrix,ddenseMatrix-method} \alias{\%*\%,dsyMatrix,matrix-method} \alias{\%*\%,dtpMatrix,ddenseMatrix-method} \alias{\%*\%,dgeMatrix,dtpMatrix-method} \alias{\%*\%,dtpMatrix,matrix-method} \alias{\%*\%,matrix,dtpMatrix-method} \alias{\%*\%,dtrMatrix,dtrMatrix-method} \alias{\%*\%,ddenseMatrix,dtrMatrix-method} \alias{\%*\%,dtrMatrix,ddenseMatrix-method} \alias{\%*\%,dtrMatrix,matrix-method} \alias{\%*\%,matrix,dtrMatrix-method} \alias{\%*\%,matrix,indMatrix-method} \alias{\%*\%,indMatrix,matrix-method} \alias{\%*\%,indMatrix,indMatrix-method} \alias{\%*\%,Matrix,indMatrix-method} \alias{\%*\%,indMatrix,Matrix-method} \alias{\%*\%,lgCMatrix,lgCMatrix-method} \alias{\%*\%,lsparseMatrix,lsparseMatrix-method} \alias{\%*\%,lsparseMatrix,ldenseMatrix-method} \alias{\%*\%,ldenseMatrix,lsparseMatrix-method} \alias{\%*\%,ngCMatrix,ngCMatrix-method} \alias{\%*\%,nsparseMatrix,nsparseMatrix-method} \alias{\%*\%,nsparseMatrix,ndenseMatrix-method} \alias{\%*\%,ndenseMatrix,nsparseMatrix-method} \alias{\%*\%,matrix,pMatrix-method} \alias{\%*\%,pMatrix,matrix-method} \alias{\%*\%,pMatrix,pMatrix-method} \alias{\%*\%,Matrix,pMatrix-method} \alias{\%*\%,pMatrix,Matrix-method} \alias{\%*\%,Matrix,sparseVector-method} \alias{\%*\%,sparseVector,Matrix-method} \alias{\%*\%,sparseVector,sparseVector-method} \alias{\%*\%,TsparseMatrix,ANY-method} \alias{\%*\%,ANY,TsparseMatrix-method} \alias{\%*\%,TsparseMatrix,Matrix-method} \alias{\%*\%,Matrix,TsparseMatrix-method} \alias{\%*\%,TsparseMatrix,TsparseMatrix-method} %%-- crossprod ------------------------------- \alias{crossprod-methods} \alias{crossprod,dgeMatrix,dgeMatrix-method} \alias{crossprod,dgeMatrix,matrix-method} \alias{crossprod,dgeMatrix,numeric-method} \alias{crossprod,dgeMatrix,missing-method} \alias{crossprod,matrix,dgeMatrix-method} \alias{crossprod,numLike,dgeMatrix-method} \alias{crossprod,numLike,dgeMatrix-method} \alias{crossprod,numeric,CsparseMatrix-method} \alias{crossprod,CsparseMatrix,missing-method} \alias{crossprod,CsparseMatrix,CsparseMatrix-method} \alias{crossprod,CsparseMatrix,ddenseMatrix-method} \alias{crossprod,CsparseMatrix,matrix-method} \alias{crossprod,CsparseMatrix,numeric-method} \alias{crossprod,ddenseMatrix,CsparseMatrix-method} \alias{crossprod,matrix,CsparseMatrix-method} \alias{crossprod,ddenseMatrix,missing-method} \alias{crossprod,ddenseMatrix,dgCMatrix-method} \alias{crossprod,dgCMatrix,missing-method} \alias{crossprod,dgCMatrix,matrix-method} \alias{crossprod,dgCMatrix,dgeMatrix-method} \alias{crossprod,CsparseMatrix,diagonalMatrix-method} \alias{crossprod,diagonalMatrix,CsparseMatrix-method} \alias{crossprod,diagonalMatrix,dgeMatrix-method} \alias{crossprod,diagonalMatrix,diagonalMatrix-method} \alias{crossprod,diagonalMatrix,lgeMatrix-method} \alias{crossprod,diagonalMatrix,matrix-method} \alias{crossprod,diagonalMatrix,missing-method} \alias{crossprod,diagonalMatrix,sparseMatrix-method} \alias{crossprod,sparseMatrix,diagonalMatrix-method} \alias{crossprod,ANY,Matrix-method} \alias{crossprod,Matrix,numLike-method} \alias{crossprod,numLike,Matrix-method} \alias{crossprod,Matrix,ANY-method} \alias{crossprod,Matrix,missing-method} \alias{crossprod,Matrix,Matrix-method} \alias{crossprod,Matrix,matrix-method} \alias{crossprod,matrix,Matrix-method} \alias{crossprod,ddenseMatrix,dsparseMatrix-method} \alias{crossprod,dgeMatrix,dsparseMatrix-method} \alias{crossprod,dsparseMatrix,ddenseMatrix-method} \alias{crossprod,dsparseMatrix,dgeMatrix-method} \alias{crossprod,dtpMatrix,ddenseMatrix-method} \alias{crossprod,dtpMatrix,matrix-method} \alias{crossprod,dtrMatrix,ddenseMatrix-method} \alias{crossprod,dtrMatrix,dtrMatrix-method} \alias{crossprod,dtrMatrix,matrix-method} \alias{crossprod,dtrMatrix,missing-method} \alias{crossprod,indMatrix,matrix-method} \alias{crossprod,indMatrix,Matrix-method} \alias{crossprod,indMatrix,indMatrix-method} \alias{crossprod,indMatrix,missing-method} \alias{crossprod,lgCMatrix,missing-method} \alias{crossprod,lgTMatrix,missing-method} \alias{crossprod,lsparseMatrix-method} \alias{crossprod,lsparseMatrix,missing-method} \alias{crossprod,lsparseMatrix,lsparseMatrix-method} \alias{crossprod,lsparseMatrix,ldenseMatrix-method} \alias{crossprod,ldenseMatrix,lsparseMatrix-method} \alias{crossprod,ngCMatrix,missing-method} \alias{crossprod,ngTMatrix,missing-method} \alias{crossprod,nsparseMatrix-method} \alias{crossprod,nsparseMatrix,missing-method} \alias{crossprod,nsparseMatrix,nsparseMatrix-method} \alias{crossprod,nsparseMatrix,ndenseMatrix-method} \alias{crossprod,ndenseMatrix,nsparseMatrix-method} \alias{crossprod,pMatrix,matrix-method} \alias{crossprod,pMatrix,Matrix-method} \alias{crossprod,pMatrix,pMatrix-method} \alias{crossprod,pMatrix,missing-method} \alias{crossprod,Matrix,sparseVector-method} \alias{crossprod,sparseVector,Matrix-method} \alias{crossprod,sparseVector,missing-method} \alias{crossprod,sparseVector,sparseVector-method} \alias{crossprod,TsparseMatrix,ANY-method} \alias{crossprod,ANY,TsparseMatrix-method} \alias{crossprod,TsparseMatrix,Matrix-method} \alias{crossprod,Matrix,TsparseMatrix-method} \alias{crossprod,TsparseMatrix,TsparseMatrix-method} \alias{crossprod,TsparseMatrix,missing-method} \alias{crossprod,dgTMatrix,missing-method} \alias{crossprod,dgTMatrix,matrix-method} \alias{crossprod,dgTMatrix,numeric-method} %%-- tcrossprod ------------------------------ \alias{tcrossprod-methods} \alias{tcrossprod,dgeMatrix,missing-method} \alias{tcrossprod,dgeMatrix,dgeMatrix-method} \alias{tcrossprod,dgeMatrix,matrix-method} \alias{tcrossprod,dgeMatrix,numLike-method} \alias{tcrossprod,matrix,dgeMatrix-method} \alias{tcrossprod,numLike,dgeMatrix-method} \alias{tcrossprod,dgCMatrix,missing-method} \alias{tcrossprod,dgTMatrix,missing-method} \alias{tcrossprod,CsparseMatrix,ddenseMatrix-method} \alias{tcrossprod,CsparseMatrix,matrix-method} \alias{tcrossprod,CsparseMatrix,numLike-method} \alias{tcrossprod,Matrix,numLike-method} \alias{tcrossprod,ddenseMatrix,CsparseMatrix-method} \alias{tcrossprod,dgeMatrix,numLike-method} \alias{tcrossprod,matrix,CsparseMatrix-method} \alias{tcrossprod,numLike,CsparseMatrix-method} \alias{tcrossprod,numLike,Matrix-method} \alias{tcrossprod,numLike,dgeMatrix-method} \alias{tcrossprod,CsparseMatrix,CsparseMatrix-method} \alias{tcrossprod,CsparseMatrix,missing-method} \alias{tcrossprod,ddenseMatrix,missing-method} \alias{tcrossprod,CsparseMatrix,diagonalMatrix-method} \alias{tcrossprod,dgeMatrix,diagonalMatrix-method} \alias{tcrossprod,diagonalMatrix,CsparseMatrix-method} \alias{tcrossprod,diagonalMatrix,diagonalMatrix-method} \alias{tcrossprod,diagonalMatrix,matrix-method} \alias{tcrossprod,diagonalMatrix,missing-method} \alias{tcrossprod,diagonalMatrix,sparseMatrix-method} \alias{tcrossprod,lgeMatrix,diagonalMatrix-method} \alias{tcrossprod,matrix,diagonalMatrix-method} \alias{tcrossprod,sparseMatrix,diagonalMatrix-method} \alias{tcrossprod,ANY,Matrix-method} \alias{tcrossprod,Matrix,numeric-method} \alias{tcrossprod,Matrix,ANY-method} \alias{tcrossprod,Matrix,missing-method} \alias{tcrossprod,Matrix,Matrix-method} \alias{tcrossprod,Matrix,matrix-method} \alias{tcrossprod,matrix,Matrix-method} \alias{tcrossprod,numeric,Matrix-method} \alias{tcrossprod,ddenseMatrix,dtrMatrix-method} \alias{tcrossprod,dtrMatrix,dtrMatrix-method} \alias{tcrossprod,matrix,dtrMatrix-method} \alias{tcrossprod,matrix,indMatrix-method} \alias{tcrossprod,Matrix,indMatrix-method} \alias{tcrossprod,indMatrix,indMatrix-method} \alias{tcrossprod,indMatrix,missing-method} \alias{tcrossprod,lgCMatrix,missing-method} \alias{tcrossprod,lgTMatrix,missing-method} \alias{tcrossprod,lsparseMatrix,missing-method} \alias{tcrossprod,ngCMatrix,missing-method} \alias{tcrossprod,ngTMatrix,missing-method} \alias{tcrossprod,nsparseMatrix,missing-method} \alias{tcrossprod,matrix,pMatrix-method} \alias{tcrossprod,Matrix,pMatrix-method} \alias{tcrossprod,pMatrix,pMatrix-method} \alias{tcrossprod,pMatrix,missing-method} \alias{tcrossprod,Matrix,sparseVector-method} \alias{tcrossprod,sparseMatrix,sparseVector-method} \alias{tcrossprod,sparseVector,Matrix-method} \alias{tcrossprod,sparseVector,missing-method} \alias{tcrossprod,sparseVector,sparseMatrix-method} \alias{tcrossprod,sparseVector,sparseVector-method} \alias{tcrossprod,TsparseMatrix,ANY-method} \alias{tcrossprod,ANY,TsparseMatrix-method} \alias{tcrossprod,TsparseMatrix,Matrix-method} \alias{tcrossprod,Matrix,TsparseMatrix-method} \alias{tcrossprod,TsparseMatrix,TsparseMatrix-method} \alias{tcrossprod,TsparseMatrix,missing-method} %%--------------- %- these three are needed for R CMD check: \alias{\%*\%} \alias{crossprod} \alias{tcrossprod} %% no longer (don't want to mask 'base' functionality): % \alias{tcrossprod,matrix,missing-method} % \alias{tcrossprod,numeric,missing-method} \description{ The basic matrix product, \code{\%*\%} is implemented for all our \code{\linkS4class{Matrix}} and also for \code{\linkS4class{sparseVector}} classes, fully analogously to \R's base \code{matrix} and vector objects. The functions \code{\link{crossprod}} and \code{\link{tcrossprod}} are matrix products or \dQuote{cross products}, ideally implemented efficiently without computing \code{\link{t}(.)}'s unnecessarily. They also return \code{\linkS4class{symmetricMatrix}} classed matrices when easily detectable, e.g., in \code{crossprod(m)}, the one argument case. \code{tcrossprod()} takes the cross-product of the transpose of a matrix. \code{tcrossprod(x)} is formally equivalent to, but faster than, the call \code{x \%*\% t(x)}, and so is \code{tcrossprod(x, y)} instead of \code{x \%*\% t(y)}. } \usage{ \S4method{\%*\%}{CsparseMatrix,diagonalMatrix}(x, y) ## .... and many more \S4method{crossprod}{dgeMatrix,missing}(x, y = NULL) ## .... and many more \S4method{tcrossprod}{CsparseMatrix,ddenseMatrix}(x, y = NULL) ## .... and many more } \arguments{ \item{x}{a matrix-like object} \item{y}{a matrix-like object, or for \code{[t]crossprod()} \code{NULL} (by default); the latter case is formally equivalent to \code{y = x}.} } \details{ For some classes in the \code{Matrix} package, such as \code{\linkS4class{dgCMatrix}}, it is much faster to calculate the cross-product of the transpose directly instead of calculating the transpose first and then its cross-product. } \value{ A \code{\linkS4class{Matrix}} object, in the one argument case of an appropriate symmetric matrix class. } \section{Methods}{ \describe{ \item{\%*\%}{\code{signature(x = "dgeMatrix", y = "dgeMatrix")}: Matrix multiplication; ditto for several other signature combinations, see \code{showMethods("\%*\%", class = "dgeMatrix")}.} \item{\%*\%}{\code{signature(x = "dtrMatrix", y = "matrix")} and other signatures (use \code{showMethods("\%*\%", class="dtrMatrix")}): matrix multiplication. Multiplication of (matching) triangular matrices now should remain triangular (in the sense of class \linkS4class{triangularMatrix}).} \item{crossprod}{\code{signature(x = "dgeMatrix", y = "dgeMatrix")}: ditto for several other signatures, use \code{showMethods("crossprod", class = "dgeMatrix")}, matrix crossproduct, an efficient version of \code{t(x) \%*\% y}.} \item{crossprod}{\code{signature(x = "dgCMatrix", y = "missing")} returns \code{t(x) \%*\% x} as an \code{dsCMatrix} object.} \item{crossprod}{\code{signature(x = "dgTMatrix", y = "missing")} returns \code{t(x) \%*\% x} as an \code{dsCMatrix} object.} \item{crossprod,tcrossprod}{\code{signature(x = "dtrMatrix", y = "matrix")} and other signatures, see \code{"\%*\%"} above.} }%{describe} } \seealso{\code{\link[base]{tcrossprod}} in \R's base, \code{\link{crossprod}} and \code{\link{\%*\%}}.} \examples{ ## A random sparse "incidence" matrix : m <- matrix(0, 400, 500) set.seed(12) m[runif(314, 0, length(m))] <- 1 mm <- as(m, "dgCMatrix") object.size(m) / object.size(mm) # smaller by a factor of > 200 ## tcrossprod() is very fast: system.time(tCmm <- tcrossprod(mm))# 0 (PIII, 933 MHz) system.time(cm <- crossprod(t(m))) # 0.16 system.time(cm. <- tcrossprod(m)) # 0.02 stopifnot(cm == as(tCmm, "matrix")) ## show sparse sub matrix tCmm[1:16, 1:30] } \keyword{methods} \keyword{algebra} Matrix/man/dsparseMatrix-class.Rd0000644000175100001440000000241112271746775016547 0ustar hornikusers\name{dsparseMatrix-class} \docType{class} \alias{dsparseMatrix-class} % Group \alias{Summary,dsparseMatrix-method} \alias{Arith,dsparseMatrix,logical-method} \alias{Arith,dsparseMatrix,numeric-method} \alias{Arith,logical,dsparseMatrix-method} \alias{Arith,numeric,dsparseMatrix-method} % \alias{lu,dsparseMatrix-method} % \title{Virtual Class "dsparseMatrix" of Numeric Sparse Matrices} \description{The Class \code{"dsparseMatrix"} is the virtual (super) class of all numeric sparse matrices. } \section{Slots}{ \describe{ \item{\code{Dim}:}{the matrix dimension, see class \code{"\linkS4class{Matrix}"}.} \item{\code{Dimnames}:}{see the \code{"Matrix"} class.} \item{\code{x}:}{a \code{\link{numeric}} vector containing the (non-zero) matrix entries.} } } \section{Extends}{ Class \code{"dMatrix"} and \code{"sparseMatrix"}, directly.\cr Class \code{"Matrix"}, by the above classes. } % \section{Methods}{ % No methods defined with class "dsparseMatrix" in the signature. % } %%\author{Martin} \seealso{ the documentation of the (non virtual) sub classes, see \code{showClass("dsparseMatrix")}; in particular, \linkS4class{dgTMatrix}, \linkS4class{dgCMatrix}, and \linkS4class{dgRMatrix}. } \examples{ showClass("dsparseMatrix") } \keyword{classes} Matrix/man/dMatrix-class.Rd0000644000175100001440000001242212271746775015334 0ustar hornikusers\name{dMatrix-class} \docType{class} \title{(Virtual) Class "dMatrix" of "double" Matrices} \alias{dMatrix-class} \alias{lMatrix-class} % \alias{show,dMatrix-method} %\alias{coerce,dMatrix,matrix-method} \alias{coerce,dMatrix,lMatrix-method} \alias{coerce,lMatrix,dMatrix-method} \alias{coerce,lMatrix,dgCMatrix-method} \alias{coerce,matrix,lMatrix-method} %\alias{coerce,dMatrix,dgeMatrix-method} \alias{[,dMatrix,lMatrix,missing,ANY-method} \alias{[,dMatrix,logical,missing,ANY-method} % Group methods \alias{Ops,dMatrix,dMatrix-method} \alias{Ops,dMatrix,lMatrix-method} \alias{Ops,dMatrix,nMatrix-method} \alias{Ops,lMatrix,dMatrix-method} \alias{Ops,lMatrix,lMatrix-method} \alias{Ops,lMatrix,numeric-method} \alias{Ops,nMatrix,dMatrix-method} \alias{Ops,numeric,lMatrix-method} \alias{Arith,dMatrix,dMatrix-method} \alias{Arith,lMatrix,logical-method} \alias{Arith,lMatrix,numeric-method} \alias{Arith,logical,lMatrix-method} \alias{Arith,numeric,lMatrix-method} \alias{Compare,dMatrix,logical-method} \alias{Compare,dMatrix,numeric-method} \alias{Compare,lMatrix,logical-method} \alias{Compare,lMatrix,numeric-method} \alias{Compare,logical,dMatrix-method} \alias{Compare,logical,lMatrix-method} \alias{Compare,numeric,dMatrix-method} \alias{Compare,numeric,lMatrix-method} \alias{Logic,dMatrix,logical-method} \alias{Logic,dMatrix,numeric-method} \alias{Logic,lMatrix,logical-method} \alias{Logic,lMatrix,numeric-method} \alias{Logic,logical,dMatrix-method} \alias{Logic,logical,lMatrix-method} \alias{Logic,numeric,dMatrix-method} \alias{Logic,numeric,lMatrix-method} \alias{Summary,lMatrix-method} %% R <= 2.5.x : % \alias{Math2,dMatrix,ANY-method}% Math2 = round + signif,.., but % \alias{Math2,dMatrix,missing-method} % % for silly reasons, need these 2+3 as well: % \alias{round,dMatrix,numeric-method} % \alias{signif,dMatrix,numeric-method} %% R-2.6.0 - maybe \alias{Math2,dMatrix-method} \alias{log,dMatrix-method} \alias{gamma,dMatrix-method} \alias{lgamma,dMatrix-method} % \alias{zapsmall,dMatrix-method} %\alias{which,lMatrix-method} % %\alias{solve,...} --> solve-methods.Rd \description{ The \code{dMatrix} class is a virtual class contained by all actual classes of numeric matrices in the \pkg{Matrix} package. Similarly, all the actual classes of logical matrices inherit from the \code{lMatrix} class. } %\section{Objects from the Class}{A virtual Class: No objects may be % created from it. %} \section{Slots}{ Common to \emph{all} matrix object in the package: \describe{ \item{\code{Dim}:}{Object of class \code{"integer"} - the dimensions of the matrix - must be an integer vector with exactly two non-negative values.} \item{\code{Dimnames}:}{list of length two; each component containing NULL or a \code{\link{character}} vector length equal the corresponding \code{Dim} element.} } } \section{Methods}{ There are (relatively simple) group methods (see, e.g., \code{\link{Arith}}) \describe{ \item{Arith}{\code{signature(e1 = "dMatrix", e2 = "dMatrix")}: ... } \item{Arith}{\code{signature(e1 = "dMatrix", e2 = "numeric")}: ... } \item{Arith}{\code{signature(e1 = "numeric", e2 = "dMatrix")}: ... } \item{Math}{\code{signature(x = "dMatrix")}: ... } \item{Math2}{\code{signature(x = "dMatrix", digits = "numeric")}: this group contains \code{\link{round}()} and \code{\link{signif}()}.} \item{Compare}{\code{signature(e1 = "numeric", e2 = "dMatrix")}: ... } \item{Compare}{\code{signature(e1 = "dMatrix", e2 = "numeric")}: ... } \item{Compare}{\code{signature(e1 = "dMatrix", e2 = "dMatrix")}: ... } \item{Summary}{\code{signature(x = "dMatrix")}: The \code{"Summary"} group contains the seven functions \code{\link{max}()}, \code{\link{min}()}, \code{\link{range}()}, \code{\link{prod}()}, \code{\link{sum}()}, \code{\link{any}()}, and \code{\link{all}()}.} } The following methods are also defined for all double matrices: \describe{ \item{coerce}{\code{signature(from = "dMatrix", to = "matrix")}: ... } % \item{expm}{\code{signature(x = "dMatrix")}: computes the \emph{\dQuote{Matrix Exponential}}, see \code{\link{expm}}.} \item{zapsmall}{\code{signature(x = "dMatrix")}: ... } } The following methods are defined for all logical matrices: \describe{ \item{which}{\code{signature(x = "lsparseMatrix")} and many other subclasses of \code{"lMatrix"}: as the \pkg{base} function \code{\link{which}(x, arr.ind)} returns the indices of the \code{\link{TRUE}} entries in \code{x}; if \code{arr.ind} is true, as a 2-column matrix of row and column indices.} } } %\references{} % Martin + Doug\author{Douglas Bates \email{bates@stat.wisc.edu}} \seealso{ The nonzero-pattern matrix class \code{\linkS4class{nMatrix}}, which can be used to store non-\code{\link{NA}} \code{\link{logical}} matrices even more compactly. The numeric matrix classes \code{\linkS4class{dgeMatrix}}, \code{\linkS4class{dgCMatrix}}, and \code{\linkS4class{Matrix}}. \code{\link{drop0}(x, tol=1e-10)} is sometimes preferable to (and more efficient than) \code{zapsmall(x, digits=10)}. } \examples{ showClass("dMatrix") set.seed(101) round(Matrix(rnorm(28), 4,7), 2) M <- Matrix(rlnorm(56, sd=10), 4,14) (M. <- zapsmall(M)) table(as.logical(M. == 0)) } \keyword{classes} \keyword{algebra} Matrix/man/kronecker-methods.Rd0000644000175100001440000000446112207615512016230 0ustar hornikusers\name{kronecker-methods} \docType{methods} \title{Methods for Function 'kronecker()' in Package 'Matrix'} \alias{kronecker-methods} % \alias{kronecker,ANY,Matrix-method} \alias{kronecker,ANY,diagonalMatrix-method} \alias{kronecker,ANY,sparseMatrix-method} \alias{kronecker,Matrix,ANY-method} \alias{kronecker,Matrix,diagonalMatrix-method} \alias{kronecker,diagonalMatrix,ANY-method} \alias{kronecker,diagonalMatrix,Matrix-method} \alias{kronecker,indMatrix,indMatrix-method} \alias{kronecker,sparseMatrix,ANY-method} \alias{kronecker,sparseMatrix,TsparseMatrix-method} % \alias{kronecker,TsparseMatrix,sparseMatrix-method} \alias{kronecker,TsparseMatrix,TsparseMatrix-method} \alias{kronecker,dgTMatrix,dgTMatrix-method} \alias{kronecker,dgTMatrix,dtTMatrix-method} \alias{kronecker,dtTMatrix,dgTMatrix-method} \alias{kronecker,dtTMatrix,dtTMatrix-method} \alias{kronecker,dsparseMatrix,dsparseMatrix-method} % \description{ Computes Kronecker products for objects inheriting from \code{"\linkS4class{Matrix}"}. In order to preserver sparseness, we treat \code{0 * NA} as \code{0}, not as \code{\link{NA}} as usually in \R (and as used for the \pkg{base} function \code{\link[base]{kronecker}}). } \section{Methods}{ \describe{ \item{kronecker}{\code{signature(X = "Matrix", Y = "ANY")} .......} \item{kronecker}{\code{signature(X = "ANY", Y = "Matrix")} .......} \item{kronecker}{\code{signature(X = "diagonalMatrix", Y = "ANY")} .......} \item{kronecker}{\code{signature(X = "sparseMatrix", Y = "ANY")} .......} \item{kronecker}{\code{signature(X = "TsparseMatrix", Y = "TsparseMatrix")} .......} \item{kronecker}{\code{signature(X = "dgTMatrix", Y = "dgTMatrix")} .......} \item{kronecker}{\code{signature(X = "dtTMatrix", Y = "dtTMatrix")} .......} \item{kronecker}{\code{signature(X = "indMatrix", Y = "indMatrix")} .......} } } \examples{ (t1 <- spMatrix(5,4, x= c(3,2,-7,11), i= 1:4, j=4:1)) # 5 x 4 (t2 <- kronecker(Diagonal(3, 2:4), t1)) # 15 x 12 ## should also work with special-cased logical matrices l3 <- upper.tri(matrix(,3,3)) M <- Matrix(l3) (N <- as(M, "nsparseMatrix")) N2 <- as(N, "generalMatrix") MM <- kronecker(M,M) NN <- kronecker(N,N) NN2 <- kronecker(N2,N2) stopifnot(identical(NN,MM), is(NN, "triangularMatrix")) } \keyword{methods} \keyword{array} Matrix/man/abIseq.Rd0000644000175100001440000000360111617257315014012 0ustar hornikusers\name{abIseq} \title{Sequence Generation of "abIndex", Abstract Index Vectors} \Rdversion{1.1} % \alias{abIseq} \alias{abIseq1} \alias{c.abIndex} % \description{ Generation of abstract index vectors, i.e., objects of class \code{"\linkS4class{abIndex}"}. \code{abIseq()} is designed to work entirely like \code{\link{seq}}, but producing \code{"abIndex"} vectors.\cr \code{abIseq1()} is its basic building block, where \code{abIseq1(n,m)} corresponds to \code{n:m}. \code{c(x, ...)} will return an \code{"abIndex"} vector, when \code{x} is one. } \usage{ abIseq1(from = 1, to = 1) abIseq (from = 1, to = 1, by = ((to - from)/(length.out - 1)), length.out = NULL, along.with = NULL) \method{c}{abIndex}(\dots) } \arguments{ \item{from, to}{the starting and (maximal) end value of the sequence.} \item{by}{number: increment of the sequence.} \item{length.out}{desired length of the sequence. A non-negative number, which for \code{seq} and \code{seq.int} will be rounded up if fractional.} \item{along.with}{take the length from the length of this argument.} \item{\dots}{in general an arbitrary number of \R objects; here, when the first is an \code{"\linkS4class{abIndex}"} vector, these arguments will be concatenated to a new \code{"abIndex"} object.} } %\author{Martin Maechler} % \details{ % } \value{ An abstract index vector, i.e., object of class \code{"\linkS4class{abIndex}"}. } % \references{ % %% ~put references to the literature/web site here ~ % } \seealso{ the class \code{\linkS4class{abIndex}} documentation; \code{\link{rep2abI}()} for another constructor; \code{\link{rle}} (\pkg{base}). } \examples{ stopifnot(identical(-3:20, as(abIseq1(-3,20), "vector"))) try( ## (arithmetic) not yet implemented abIseq(1, 50, by = 3) ) %% FIXME: add / exchange with ../tests/abIndex-tsts.R } \keyword{manip} \keyword{classes} Matrix/man/nsparseMatrix-classes.Rd0000644000175100001440000002015712271746775017120 0ustar hornikusers\name{nsparseMatrix-classes} \title{Sparse "pattern" Matrices} \docType{class} \alias{nsparseMatrix-class} %not yet \alias{nCsparseMatrix-class} \alias{ngCMatrix-class} \alias{ntCMatrix-class} \alias{nsCMatrix-class} \alias{ngRMatrix-class} \alias{ntRMatrix-class} \alias{nsRMatrix-class} \alias{ngTMatrix-class} \alias{ntTMatrix-class} \alias{nsTMatrix-class} % \alias{all,nsparseMatrix-method} \alias{any,nsparseMatrix-method} \alias{-,nsparseMatrix,missing-method} \alias{!,nsparseMatrix-method} \alias{coerce,nsparseMatrix,dsparseMatrix-method} \alias{coerce,matrix,ngCMatrix-method} \alias{coerce,matrix,ngTMatrix-method} \alias{coerce,matrix,ntCMatrix-method} \alias{coerce,matrix,ntTMatrix-method} \alias{coerce,ngCMatrix,dMatrix-method} \alias{coerce,ngCMatrix,dgCMatrix-method} \alias{coerce,ngCMatrix,dsparseMatrix-method} \alias{coerce,ngCMatrix,lMatrix-method} \alias{coerce,ngCMatrix,lgCMatrix-method} \alias{coerce,ngCMatrix,lsparseMatrix-method} \alias{coerce,ngCMatrix,matrix-method} \alias{coerce,ngCMatrix,ngTMatrix-method} \alias{coerce,ngCMatrix,ngeMatrix-method} \alias{coerce,ngCMatrix,ntCMatrix-method} \alias{coerce,ngTMatrix,dMatrix-method} \alias{coerce,ngTMatrix,dgTMatrix-method} \alias{coerce,ngTMatrix,dsparseMatrix-method} \alias{coerce,ngTMatrix,generalMatrix-method} \alias{coerce,ngTMatrix,lMatrix-method} \alias{coerce,ngTMatrix,lgTMatrix-method} \alias{coerce,ngTMatrix,matrix-method} \alias{coerce,ngTMatrix,ngCMatrix-method} \alias{coerce,ngTMatrix,lgeMatrix-method} \alias{coerce,ngTMatrix,ngeMatrix-method} \alias{coerce,ngTMatrix,ntTMatrix-method} \alias{coerce,ngTMatrix,symmetricMatrix-method} \alias{coerce,ngTMatrix,triangularMatrix-method} \alias{coerce,nsCMatrix,dMatrix-method} \alias{coerce,nsCMatrix,dsCMatrix-method} \alias{coerce,nsCMatrix,dsparseMatrix-method} \alias{coerce,nsCMatrix,generalMatrix-method} \alias{coerce,nsCMatrix,lMatrix-method} \alias{coerce,nsCMatrix,lsCMatrix-method} \alias{coerce,nsCMatrix,lsparseMatrix-method} \alias{coerce,nsCMatrix,matrix-method} \alias{coerce,nsCMatrix,ngCMatrix-method} \alias{coerce,nsCMatrix,nsTMatrix-method} \alias{coerce,nsTMatrix,dsTMatrix-method} \alias{coerce,nsTMatrix,matrix-method} \alias{coerce,nsTMatrix,ngCMatrix-method} \alias{coerce,nsTMatrix,ngTMatrix-method} \alias{coerce,nsTMatrix,nsCMatrix-method} \alias{coerce,nsTMatrix,nsyMatrix-method} \alias{coerce,ntCMatrix,dMatrix-method} \alias{coerce,ntCMatrix,dsparseMatrix-method} \alias{coerce,ntCMatrix,dtCMatrix-method} \alias{coerce,ntCMatrix,lMatrix-method} \alias{coerce,ntCMatrix,lsparseMatrix-method} \alias{coerce,ntCMatrix,ltCMatrix-method} \alias{coerce,ntCMatrix,matrix-method} \alias{coerce,ntCMatrix,ngCMatrix-method} \alias{coerce,ntCMatrix,TsparseMatrix-method} \alias{coerce,ntTMatrix,dtTMatrix-method} \alias{coerce,ntTMatrix,generalMatrix-method} \alias{coerce,ntTMatrix,matrix-method} \alias{coerce,ntTMatrix,ngCMatrix-method} \alias{coerce,ntTMatrix,ngTMatrix-method} \alias{coerce,ntTMatrix,ntCMatrix-method} \alias{coerce,ntTMatrix,ntrMatrix-method} % \alias{t,ngCMatrix-method} \alias{t,ngTMatrix-method} \alias{t,nsCMatrix-method} \alias{t,ntCMatrix-method} \alias{t,nsTMatrix-method} \alias{t,ntTMatrix-method} \alias{is.na,nsparseMatrix-method} \alias{which,ngTMatrix-method} \alias{which,nsparseMatrix-method} \alias{which,nsparseVector-method} \alias{which,nsTMatrix-method} \alias{which,ntTMatrix-method} % Group \alias{Ops,dsparseMatrix,nsparseMatrix-method} \alias{Ops,nsparseMatrix,dsparseMatrix-method} \alias{Ops,lsparseMatrix,nsparseMatrix-method} \alias{Ops,nsparseMatrix,lsparseMatrix-method} \alias{Ops,sparseMatrix,nsparseMatrix-method} \alias{Ops,nsparseMatrix,sparseMatrix-method} \alias{Arith,nsparseMatrix,Matrix-method} \alias{Arith,Matrix,nsparseMatrix-method} % \description{The \code{nsparseMatrix} class is a virtual class of sparse \emph{\dQuote{pattern}} matrices, i.e., binary matrices conceptually with \code{TRUE}/\code{FALSE} entries. Only the positions of the elements that are \code{TRUE} are stored. These can be stored in the ``triplet'' form (classes \code{ngTMatrix}, \code{nsTMatrix}, and \code{ntTMatrix} which really contain pairs, not triplets) or in compressed column-oriented form (classes \code{ngCMatrix}, \code{nsCMatrix}, and \code{ntCMatrix}) or in compressed row-oriented form (classes \code{ngRMatrix}, \code{nsRMatrix}, and \code{ntRMatrix}). The second letter in the name of these non-virtual classes indicates \code{g}eneral, \code{s}ymmetric, or \code{t}riangular. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("ngCMatrix", ...)} and so on. More frequently objects are created by coercion of a numeric sparse matrix to the pattern form for use in the symbolic analysis phase of an algorithm involving sparse matrices. Such algorithms often involve two phases: a symbolic phase wherein the positions of the non-zeros in the result are determined and a numeric phase wherein the actual results are calculated. During the symbolic phase only the positions of the non-zero elements in any operands are of interest, hence numeric sparse matrices can be treated as sparse pattern matrices. } \section{Slots}{ \describe{ \item{\code{uplo}:}{Object of class \code{"character"}. Must be either "U", for upper triangular, and "L", for lower triangular. Present in the triangular and symmetric classes but not in the general class.} \item{\code{diag}:}{Object of class \code{"character"}. Must be either \code{"U"}, for unit triangular (diagonal is all ones), or \code{"N"} for non-unit. The implicit diagonal elements are not explicitly stored when \code{diag} is \code{"U"}. Present in the triangular classes only.} \item{\code{p}:}{Object of class \code{"integer"} of pointers, one for each column (row), to the initial (zero-based) index of elements in the column. Present in compressed column-oriented and compressed row-oriented forms only.} \item{\code{i}:}{Object of class \code{"integer"} of length nnzero (number of non-zero elements). These are the row numbers for each TRUE element in the matrix. All other elements are FALSE. Present in triplet and compressed column-oriented forms only.} \item{\code{j}:}{Object of class \code{"integer"} of length nnzero (number of non-zero elements). These are the column numbers for each TRUE element in the matrix. All other elements are FALSE. Present in triplet and compressed column-oriented forms only.} \item{\code{Dim}:}{Object of class \code{"integer"} - the dimensions of the matrix.} } } \section{Methods}{ \describe{ \item{coerce}{\code{signature(from = "dgCMatrix", to = "ngCMatrix")}, and many similar ones; typically you should coerce to \code{"nsparseMatrix"} (or \code{"nMatrix"}). Note that coercion to a sparse pattern matrix records all the potential non-zero entries, i.e., explicit (\dQuote{non-structural}) zeroes are coerced to \code{TRUE}, not \code{FALSE}, see the example. } \item{t}{\code{signature(x = "ngCMatrix")}: returns the transpose of \code{x}} \item{which}{\code{signature(x = "lsparseMatrix")}, semantically equivalent to \pkg{base} function \code{\link{which}(x, arr.ind)}; for details, see the \code{\linkS4class{lMatrix}} class documentation.} } } %\references{} %\author{} %\note{} \seealso{ the class \code{\linkS4class{dgCMatrix}} } \examples{ (m <- Matrix(c(0,0,2:0), 3,5, dimnames=list(LETTERS[1:3],NULL))) ## ``extract the nonzero-pattern of (m) into an nMatrix'': nm <- as(m, "nsparseMatrix") ## -> will be a "ngCMatrix" str(nm) # no 'x' slot nnm <- !nm # no longer sparse (nnm <- as(nnm, "sparseMatrix"))# "lgCMatrix" ## consistency check: stopifnot(xor(as( nm, "matrix"), as(nnm, "matrix"))) ## low-level way of adding "non-structural zeros" : nnm@x[2:4] <- c(FALSE,NA,NA) nnm as(nnm, "nMatrix") # NAs *and* non-structural 0 |---> 'TRUE' data(KNex) nmm <- as(KNex $ mm, "ngCMatrix") str(xlx <- crossprod(nmm))# "nsCMatrix" stopifnot(isSymmetric(xlx)) image(xlx, main=paste("crossprod(nmm) : Sparse", class(xlx))) } \keyword{classes} \keyword{algebra} Matrix/man/sparseMatrix.Rd0000644000175100001440000002146012254023262015261 0ustar hornikusers\name{sparseMatrix} \alias{sparseMatrix} \title{General Sparse Matrix Construction from Nonzero Entries} \description{ User friendly construction of a compressed, column-oriented, sparse matrix, inheriting from \code{\link{class}} \code{\linkS4class{CsparseMatrix}} (or \code{\linkS4class{TsparseMatrix}} if \code{giveCsparse} is false), from locations (and values) of its nonzero entries. This is the recommended user interface rather than direct \code{\link{new}("***Matrix", ....)} calls. } \usage{ sparseMatrix(i = ep, j = ep, p, x, dims, dimnames, symmetric = FALSE, index1 = TRUE, giveCsparse = TRUE, check = TRUE, use.last.ij = FALSE) } \arguments{ \item{i,j}{integer vectors of the same length specifying the locations (row and column indices) of the non-zero (or non-\code{TRUE}) entries of the matrix. Note that for \emph{repeated} pairs \eqn{(i_k,j_k)}, when \code{x} is not missing, the corresponding \eqn{x_k} are \emph{added}, in consistency with the definition of the \code{"\linkS4class{TsparseMatrix}"} class, unless \code{use.last.ij} is true, in which case only the \emph{last} of the corresponding \eqn{(i_k, j_k, x_k)} triplet is used.} \item{p}{numeric (integer valued) vector of pointers, one for each column (or row), to the initial (zero-based) index of elements in the column (or row). Exactly one of \code{i}, \code{j} or \code{p} must be missing.} \item{x}{ optional values of the matrix entries. If specified, must be of the same length as \code{i} / \code{j}, or of length one where it will be recycled to full length. If missing, the resulting matrix will be a 0/1 patter\bold{n} matrix, i.e., extending class \code{\linkS4class{nsparseMatrix}}. } \item{dims}{optional, non-negative, integer, dimensions vector of length 2. Defaults to \code{c(max(i), max(j))}.} \item{dimnames}{optional list of \code{\link{dimnames}}; if not specified, none, i.e., \code{\link{NULL}} ones, are used.} \item{symmetric}{logical indicating if the resulting matrix should be symmetric. In that case, only the lower or upper triangle needs to be specified via \eqn{(i/j/p)}.} \item{index1}{logical scalar. If \code{TRUE}, the default, the index vectors \code{i} and/or \code{j} are 1-based, as is the convention in \R. That is, counting of rows and columns starts at 1. If \code{FALSE} the index vectors are 0-based so counting of rows and columns starts at 0; this corresponds to the internal representation.} \item{giveCsparse}{logical indicating if the result should be a \code{\linkS4class{CsparseMatrix}} or a \code{\linkS4class{TsparseMatrix}}. The default, \code{TRUE} is very often more efficient subsequently, but not always.} \item{check}{logical indicating if a validity check is performed; do not set to \code{FALSE} unless you know what you're doing!} \item{use.last.ij}{logical indicating if in the case of repeated, i.e., duplicated pairs \eqn{(i_k, j_k)} only the last one should be used. The default, \code{FALSE}, corresponds to the \code{"\linkS4class{TsparseMatrix}"} definition.} } \value{ A sparse matrix, by default (see \code{giveCsparse}) in compressed, column-oriented form, as an \R object inheriting from both \code{\linkS4class{CsparseMatrix}} and \code{\linkS4class{generalMatrix}}. } \details{ Exactly one of the arguments \code{i}, \code{j} and \code{p} must be missing. In typical usage, \code{p} is missing, \code{i} and \code{j} are vectors of positive integers and \code{x} is a numeric vector. These three vectors, which must have the same length, form the triplet representation of the sparse matrix. If \code{i} or \code{j} is missing then \code{p} must be a non-decreasing integer vector whose first element is zero. It provides the compressed, or \dQuote{pointer} representation of the row or column indices, whichever is missing. The expanded form of \code{p}, \code{rep(seq_along(dp),dp)} where \code{dp <- diff(p)}, is used as the (1-based) row or column indices. The values of \code{i}, \code{j}, \code{p} and \code{index1} are used to create 1-based index vectors \code{i} and \code{j} from which a \code{\linkS4class{TsparseMatrix}} is constructed, with numerical values given by \code{x}, if non-missing. Note that in that case, when some pairs \eqn{(i_k,j_k)} are repeated (aka \dQuote{duplicated}), the corresponding \eqn{x_k} are \emph{added}, in consistency with the definition of the \code{"\linkS4class{TsparseMatrix}"} class, unless \code{use.last.ij} is set to true. %% By default, when \code{giveCsparse} is true, the \code{\linkS4class{CsparseMatrix}} derived from this triplet form is returned. The reason for returning a \code{\linkS4class{CsparseMatrix}} object instead of the triplet format by default is that the compressed column form is easier to work with when performing matrix operations. In particular, if there are no zeros in \code{x} then a \code{\linkS4class{CsparseMatrix}} is a unique representation of the sparse matrix. } \seealso{\code{\link{Matrix}(*, sparse=TRUE)} for the more usual constructor of such matrices; further \code{\link{bdiag}} and \code{\link{Diagonal}} for (block-)diagonal and \code{\link{bandSparse}} for banded sparse matrix constructors. The standard \R \code{\link{xtabs}(*, sparse=TRUE)}, for sparse tables and \code{\link{sparse.model.matrix}()} for building sparse model matrices. Consider \code{\linkS4class{CsparseMatrix}} and similar class definition help files. } \examples{ ## simple example i <- c(1,3:8); j <- c(2,9,6:10); x <- 7 * (1:7) (A <- sparseMatrix(i, j, x = x)) summary(A) str(A) # note that *internally* 0-based row indices are used ## dims can be larger than the maximum row or column indices (AA <- sparseMatrix(c(1,3:8), c(2,9,6:10), x = 7 * (1:7), dims = c(10,20))) summary(AA) ## i, j and x can be in an arbitrary order, as long as they are consistent set.seed(1); (perm <- sample(1:7)) (A1 <- sparseMatrix(i[perm], j[perm], x = x[perm])) stopifnot(identical(A, A1)) ## the (i,j) pairs can be repeated, in which case the x's are summed (args <- data.frame(i = c(i, 1), j = c(j, 2), x = c(x, 2))) (Aa <- do.call(sparseMatrix, args)) ## explicitly ask for elimination of such duplicates, so ## that the last one is used: (A. <- do.call(sparseMatrix, c(args, list(use.last.ij = TRUE)))) stopifnot(Aa[1,2] == 9, # 2+7 == 9 A.[1,2] == 2) # 2 was *after* 7 ## for a pattern matrix, of course there is no "summing": (nA <- do.call(sparseMatrix, args[c("i","j")])) dn <- list(LETTERS[1:3], letters[1:5]) ## pointer vectors can be used, and the (i,x) slots are sorted if necessary: m <- sparseMatrix(i = c(3,1, 3:2, 2:1), p= c(0:2, 4,4,6), x = 1:6, dimnames = dn) m str(m) stopifnot(identical(dimnames(m), dn)) sparseMatrix(x = 2.72, i=1:3, j=2:4) # recycling x sparseMatrix(x = TRUE, i=1:3, j=2:4) # recycling x, |--> "lgCMatrix" ## no 'x' --> patter*n* matrix: (n <- sparseMatrix(i=1:6, j=rev(2:7)))# -> ngCMatrix ## an empty sparse matrix: (e <- sparseMatrix(dims = c(4,6), i={}, j={})) ## a symmetric one: (sy <- sparseMatrix(i= c(2,4,3:5), j= c(4,7:5,5), x = 1:5, dims = c(7,7), symmetric=TRUE)) stopifnot(isSymmetric(sy), identical(sy, ## switch i <-> j {and transpose } t( sparseMatrix(j= c(2,4,3:5), i= c(4,7:5,5), x = 1:5, dims = c(7,7), symmetric=TRUE)))) ##' @title Random Sparse Matrix ##' @param nrow, ##' @param ncol number of rows and columns, i.e., the matrix dimension ##' @param nnz number of non-zero entries ##' @param rand.x random number generator for 'x' slot ##' @param ... optionally further arguments passed to sparseMatrix() ##' @return a sparseMatrix of dimension (nrow, ncol) ##' @author Martin Maechler rSparseMatrix <- function(nrow, ncol, nnz, rand.x = function(n) round(rnorm(nnz), 2), ...) { stopifnot((nnz <- as.integer(nnz)) >= 0, nrow >= 0, ncol >= 0, nnz <= nrow * ncol) sparseMatrix(i = sample(nrow, nnz, replace = TRUE), j = sample(ncol, nnz, replace = TRUE), x = rand.x(nnz), dims = c(nrow, ncol), ...) } M1 <- rSparseMatrix(1000, 20, nnz = 200) summary(M1) \donttest{% as SparseM is "outside" ## pointers example in converting from other sparse matrix representations. if(require(SparseM) && packageVersion("SparseM") >= 0.87 && nzchar(dfil <- system.file("textdata", "rua_32_ax.rua", package = "SparseM"))) { X <- model.matrix(read.matrix.hb(dfil)) XX <- sparseMatrix(j = X@ja, p = X@ia - 1L, x = X@ra, dims = X@dimension) validObject(XX) ## Alternatively, and even more user friendly : X. <- as(X, "Matrix") # or also X2 <- as(X, "sparseMatrix") stopifnot(identical(XX, X.), identical(X., X2)) }% if }% donttest }% example \keyword{array} Matrix/man/ndenseMatrix-class.Rd0000644000175100001440000000510212271746775016362 0ustar hornikusers\name{ndenseMatrix-class} \docType{class} \alias{ndenseMatrix-class} \alias{!,ndenseMatrix-method} \alias{Ops,ndenseMatrix,ndenseMatrix-method} \alias{as.logical,ndenseMatrix-method} \alias{coerce,matrix,ndenseMatrix-method} \alias{coerce,ndenseMatrix,matrix-method} \alias{coerce,ndenseMatrix,CsparseMatrix-method} \alias{coerce,ndenseMatrix,TsparseMatrix-method} \alias{coerce,ndenseMatrix,ldenseMatrix-method} \alias{coerce,ndenseMatrix,sparseMatrix-method} \alias{coerce,ngeMatrix,lgeMatrix-method} \alias{coerce,nspMatrix,lspMatrix-method} \alias{coerce,nsyMatrix,lsyMatrix-method} \alias{coerce,ntpMatrix,ltpMatrix-method} \alias{coerce,ntrMatrix,ltrMatrix-method} \alias{as.vector,ndenseMatrix,missing-method} \alias{diag,ndenseMatrix-method} \alias{norm,ndenseMatrix,character-method} \alias{which,ndenseMatrix-method} % \title{Virtual Class "ndenseMatrix" of Dense Logical Matrices} \description{ \code{ndenseMatrix} is the virtual class of all dense \bold{l}ogical (S4) matrices. It extends both \code{\linkS4class{denseMatrix}} and \code{\linkS4class{lMatrix}} directly. } \section{Slots}{ \describe{ \item{\code{x}:}{logical vector containing the entries of the matrix.} \item{\code{Dim}, \code{Dimnames}:}{see \code{\linkS4class{Matrix}}.} } } \section{Extends}{ Class \code{"nMatrix"}, directly. Class \code{"denseMatrix"}, directly. Class \code{"Matrix"}, by class \code{"nMatrix"}. Class \code{"Matrix"}, by class \code{"denseMatrix"}. } \section{Methods}{ \describe{ \item{\%*\%}{\code{signature(x = "nsparseMatrix", y = "ndenseMatrix")}: ... } \item{\%*\%}{\code{signature(x = "ndenseMatrix", y = "nsparseMatrix")}: ... } \item{coerce}{\code{signature(from = "matrix", to = "ndenseMatrix")}: ... } \item{coerce}{\code{signature(from = "ndenseMatrix", to = "matrix")}: ... } \item{crossprod}{\code{signature(x = "nsparseMatrix", y = "ndenseMatrix")}: ... } \item{crossprod}{\code{signature(x = "ndenseMatrix", y = "nsparseMatrix")}: ... } \item{as.vector}{\code{signature(x = "ndenseMatrix", mode = "missing")}: ...} \item{diag}{\code{signature(x = "ndenseMatrix")}: extracts the diagonal as for all matrices, see the generic \code{\link{diag}()}.} \item{which}{\code{signature(x = "ndenseMatrix")}, semantically equivalent to \pkg{base} function \code{\link{which}(x, arr.ind)}; for details, see the \code{\linkS4class{lMatrix}} class documentation.} } } \seealso{ Class \code{\linkS4class{ngeMatrix}} and the other subclasses. } \examples{ showClass("ndenseMatrix") as(diag(3) > 0, "ndenseMatrix")# -> "nge" } \keyword{classes} Matrix/man/Schur-class.Rd0000644000175100001440000000270610773452776015014 0ustar hornikusers\name{Schur-class} \docType{class} \alias{Schur-class} % \title{Class "Schur" of Schur Matrix Factorizations} \description{Class \code{"Schur"} is the class of Schur matrix factorizations. These are a generalization of eigen value (or \dQuote{spectral}) decompositions for general (possibly asymmmetric) square matrices, see the \code{\link{Schur}()} function. } \section{Objects from the Class}{ Objects of class \code{"Schur"} are typically created by \code{\link{Schur}()}. } \section{Slots}{ \code{"Schur"} has slots \describe{ \item{\code{T}:}{Upper Block-triangular \code{\linkS4class{Matrix}} object.} \item{\code{Q}:}{Square \emph{orthogonal} \code{"Matrix"}.} \item{\code{EValues}:}{numeric or complex vector of eigenvalues of \code{T}.} \item{\code{Dim}:}{the matrix dimension: equal to \code{c(n,n)} of class \code{"integer"}.} } } \section{Extends}{ Class \code{"\linkS4class{MatrixFactorization}"}, directly. } % \section{Methods}{ % are all inherited from the MatrixFactorization class % } % \note{There's not yet a class for \emph{sparse} Schur decompositions; % mainly because there's no \code{\link{Schur}()} method for those neither. % } \seealso{ \code{\link{Schur}()} for object creation; \code{\linkS4class{MatrixFactorization}}. } \examples{ showClass("Schur") Schur(M <- Matrix(c(1:7, 10:2), 4,4)) ## Trivial, of course: str(Schur(Diagonal(5))) ## for more examples, see Schur() } \keyword{classes} Matrix/man/lu.Rd0000644000175100001440000000747512201004116013216 0ustar hornikusers\name{lu} \title{(Generalized) Triangular Decomposition of a Matrix} \alias{lu} \alias{lu,matrix-method} \alias{lu,dgeMatrix-method} \alias{lu,dgCMatrix-method} \usage{ lu(x, \dots) \S4method{lu}{matrix}(x, warnSing = TRUE, \dots) \S4method{lu}{dgeMatrix}(x, warnSing = TRUE, \dots) \S4method{lu}{dgCMatrix}(x, errSing = TRUE, order = TRUE, tol = 1, \dots) } \description{ Computes (generalized) triangular decompositions of square (sparse or dense) and non-square dense matrices. } \arguments{ \item{x}{a dense or sparse matrix, in the latter case of square dimension. No missing values or IEEE special values are allowed.} \item{warnSing}{(when \code{x} is a \code{"\linkS4class{denseMatrix}"}) logical specifying if a \code{\link{warning}} should be signalled when \code{x} is singular.} \item{errSing}{(when \code{x} is a \code{"\linkS4class{sparseMatrix}"}) logical specifying if an error (see \code{\link{stop}}) should be signalled when \code{x} is singular. When \code{x} is singular, \code{lu(x, errSing=FALSE)} returns \code{\link{NA}} instead of an LU decomposition. No warning is signalled and the useR should be careful in that case. } \item{order}{logical or integer, used to chose which will-reducing permutation technique will be used internally. Do not change unless you know what you are doing.} \item{tol}{positive number indicating the pivoting tolerance used in \code{cs_lu}. Do only change with much care.} \item{\dots}{further arguments passed to or from other methods.} } \value{ An object of class \code{"LU"}, i.e., \code{"\linkS4class{denseLU}"}%% ./LU-class.Rd (see its separate help page), or \code{"sparseLU"}, see \code{\linkS4class{sparseLU}}; this is a representation of a triangular decomposition of \code{x}. } \details{ \code{lu()} is a generic function with special methods for different types of matrices. Use \code{\link{showMethods}("lu")} to list all the methods for the \code{\link{lu}} generic. The method for class \code{\linkS4class{dgeMatrix}} (and all dense matrices) is based on LAPACK's \code{"dgetrf"} subroutine. It returns a decomposition also for singular and non-square matrices. The method for class \code{\linkS4class{dgCMatrix}} (and all sparse matrices) is based on functions from the CSparse library. It signals an error (or returns \code{NA}, when \code{errSing = FALSE}, see above) when the decomposition algorithm fails, as when \code{x} is (too close to) singular.% yes, it would be nice if we could have it % behave more similar to the dense method: still give an LU, % and an optional warning. } \references{ Golub, G., and Van Loan, C. F. (1989). \emph{Matrix Computations,} 2nd edition, Johns Hopkins, Baltimore. Tim Davis (2005) \url{http://www.cise.ufl.edu/research/sparse/CSparse/} Timothy A. Davis (2006) \emph{Direct Methods for Sparse Linear Systems}, SIAM Series \dQuote{Fundamentals of Algorithms}. } \seealso{ Class definitions \code{\linkS4class{LU}} and \code{\linkS4class{sparseLU}} and function \code{\link{expand}}; \code{\link{qr}}, \code{\link{chol}}. } \examples{ ##--- Dense ------------------------- x <- Matrix(rnorm(9), 3, 3) lu(x) dim(x2 <- round(10 * x[,-3]))# non-square expand(lu2 <- lu(x2)) ##--- Sparse (see more in ?"sparseLU-class")----- % ./sparseLU-class.Rd pm <- as(readMM(system.file("external/pores_1.mtx", package = "Matrix")), "CsparseMatrix") str(pmLU <- lu(pm)) # p is a 0-based permutation of the rows # q is a 0-based permutation of the columns ## permute rows and columns of original matrix ppm <- pm[pmLU@p + 1L, pmLU@q + 1L] pLU <- drop0(pmLU@L \%*\% pmLU@U) # L \%*\% U -- dropping extra zeros ## equal up to "rounding" ppm[1:14, 1:5] pLU[1:14, 1:5] } \keyword{array} \keyword{algebra} Matrix/man/compMatrix-class.Rd0000644000175100001440000000205210435070553016025 0ustar hornikusers\name{compMatrix-class} \docType{class} \alias{compMatrix-class} \title{Class "compMatrix" of Composite (Factorizable) Matrices} \description{ Virtual class of \emph{composite} matrices; i.e., matrices that can be \emph{factorized}, typically as a product of simpler matrices. } \section{Objects from the Class}{A virtual Class: No objects may be created from it.} \section{Slots}{ \describe{ \item{\code{factors}:}{Object of class \code{"list"} - a list of factorizations of the matrix. Note that this is typically empty, i.e. \code{list()}, initially and is updated automagically whenever a matrix factorization is computed.} \item{\code{Dim}}{,} \item{\code{Dimnames}:}{inherited from the \code{\linkS4class{Matrix}} class, see there.} } } \section{Extends}{ Class \code{"Matrix"}, directly. } % \section{Methods}{ % No methods defined with class "compMatrix" in the signature. % } %% FIXME: add stuff here: % \seealso{ % % } % \examples{ % ##---- Should be DIRECTLY executable !! ---- % } \keyword{classes} Matrix/man/dgTMatrix-class.Rd0000644000175100001440000001010412271746775015622 0ustar hornikusers\name{dgTMatrix-class} \title{Sparse matrices in triplet form} \docType{class} \alias{dgTMatrix-class} \alias{+,dgTMatrix,dgTMatrix-method} \alias{coerce,dgTMatrix,dgCMatrix-method} \alias{coerce,dgTMatrix,dgeMatrix-method} \alias{coerce,dgTMatrix,matrix-method} \alias{coerce,dgTMatrix,dtCMatrix-method} \alias{coerce,dgTMatrix,dsTMatrix-method} \alias{coerce,dgTMatrix,dtTMatrix-method} \alias{coerce,dgTMatrix,symmetricMatrix-method} \alias{coerce,dgTMatrix,triangularMatrix-method} \alias{coerce,dgeMatrix,dgTMatrix-method} \alias{coerce,matrix,dgTMatrix-method} \description{The \code{"dgTMatrix"} class is the class of sparse matrices stored as (possibly redundant) triplets. The internal representation is not at all unique, contrary to the one for class \code{\linkS4class{dgCMatrix}}. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("dgTMatrix", ...)}, but more typically via \code{as(*, "dgTMatrix")}, \code{\link{spMatrix}()}, or \code{\link{sparseMatrix}(*, giveCsparse=FALSE)}. } \section{Slots}{ \describe{ \item{\code{i}:}{Object of class \code{"integer"} - the row indices of non-zero entries \emph{in 0-base}, i.e., must be in \code{0:(nrow(.)-1)}.} \item{\code{j}:}{Object of class \code{"integer"} - the column indices of non-zero entries. Must be the same length as slot \code{i} and \emph{0-based} as well, i.e., in \code{0:(ncol(.)-1)}.} \item{\code{x}:}{Object of class \code{"numeric"} - the (non-zero) entry at position \code{(i,j)}. Must be the same length as slot \code{i}. If an index pair occurs more than once the corresponding values of slot \code{x} are added to form the element of the matrix.} \item{\code{Dim}:}{Object of class \code{"integer"} of length 2 - the dimensions of the matrix.} } } \section{Methods}{ \describe{ \item{+}{\code{signature(e1 = "dgTMatrix", e2 = "dgTMatrix")}} \item{coerce}{\code{signature(from = "dgTMatrix", to = "dgCMatrix")}} \item{coerce}{\code{signature(from = "dgTMatrix", to = "dgeMatrix")}} \item{coerce}{\code{signature(from = "dgTMatrix", to = "matrix")}, and typically coercion methods for more specific signatures, we are not mentioning here. Note that these are not guaranteed to continue to exist, but rather you should use calls like \code{as(x, "CsparseMatrix")}, \code{as(x, "generalMatrix")}, \code{as(x, "dMatrix")}, i.e. coercion to higher level virtual classes.} \item{coerce}{\code{signature(from = "matrix", to = "dgTMatrix")}, (direct coercion from tradition matrix).} \item{image}{\code{signature(x = "dgTMatrix")}: plots an image of \code{x} using the \code{\link[lattice]{levelplot}} function} \item{t}{\code{signature(x = "dgTMatrix")}: returns the transpose of \code{x}} } } %\references{} %\author{} \note{Triplet matrices are a convenient form in which to construct sparse matrices after which they can be coerced to \code{\linkS4class{dgCMatrix}} objects. Note that both \code{new(.)} and \code{\link{spMatrix}} constructors for \code{"dgTMatrix"} (and other \code{"linkS4class{TsparseMatrix}"} classes) implicitly add \eqn{x_k}'s that belong to identical \eqn{(i_k, j_k)} pairs. } \seealso{ Class \code{\linkS4class{dgCMatrix}} or the superclasses \code{\linkS4class{dsparseMatrix}} and \code{\linkS4class{TsparseMatrix}}; } \examples{ m <- Matrix(0+1:28, nrow = 4) m[-3,c(2,4:5,7)] <- m[ 3, 1:4] <- m[1:3, 6] <- 0 (mT <- as(m, "dgTMatrix")) str(mT) mT[1,] mT[4, drop = FALSE] stopifnot(identical(mT[lower.tri(mT)], m [lower.tri(m) ])) mT[lower.tri(mT,diag=TRUE)] <- 0 mT ## Triplet representation with repeated (i,j) entries ## *adds* the corresponding x's: T2 <- new("dgTMatrix", i = as.integer(c(1,1,0,3,3)), j = as.integer(c(2,2,4,0,0)), x=10*1:5, Dim=4:5) str(T2) # contains (i,j,x) slots exactly as above, but T2 ## has only three non-zero entries, as for repeated (i,j)'s, ## the corresponding x's are "implicitly" added stopifnot(nnzero(T2) == 3) } \keyword{classes} \keyword{algebra} Matrix/man/is.null.DN.Rd0000644000175100001440000000321012102200250014436 0ustar hornikusers\name{is.null.DN} \alias{is.null.DN} \title{Are the Dimnames \code{dn} NULL-like ?} \description{ Are the \code{\link{dimnames}} \code{dn} \code{\link{NULL}}-like? \code{is.null.DN(dn)} is less strict than \code{\link{is.null}(dn)}, because it is also true (\code{\link{TRUE}}) when the dimnames \code{dn} are \dQuote{like} \code{NULL}, or \code{list(NULL,NULL)}, as they can easily be for the traditional \R matrices (\code{\link{matrix}}) which have no formal \code{\link{class}} definition, and hence much freedom in how their \code{\link{dimnames}} look like. } \usage{ is.null.DN(dn) } \arguments{ \item{dn}{\code{\link{dimnames}()} of a \code{\link{matrix}}-like \R object. } } \note{ This function is really to be used on \dQuote{traditional} matrices rather than those inheriting from \code{\linkS4class{Matrix}}, as the latter will always have dimnames \code{list(NULL,NULL)} exactly, in such a case. } \value{ \code{\link{logical}} \code{\link{TRUE}} or \code{\link{FALSE}}. } %% \details{ %% } \author{Martin Maechler} \seealso{ \code{\link{is.null}}, \code{\link{dimnames}}, \code{\link{matrix}}. } \examples{ m <- matrix(round(100 * rnorm(6)), 2,3); m1 <- m2 <- m3 <- m4 <- m dimnames(m1) <- list(NULL, NULL) dimnames(m2) <- list(NULL, character()) dimnames(m3) <- rev(dimnames(m2)) dimnames(m4) <- rep(list(character()),2) m4 ## prints absolutely identically to m stopifnot(m == m1, m1 == m2, m2 == m3, m3 == m4, identical(capture.output(m) -> cm, capture.output(m1)), identical(cm, capture.output(m2)), identical(cm, capture.output(m3)), identical(cm, capture.output(m4))) } \keyword{utilities} Matrix/man/cBind.Rd0000644000175100001440000000445111644124434013624 0ustar hornikusers\name{cBind} \alias{cBind} \alias{rBind} %no \alias{cbind} %no \alias{rbind} % \title{Versions of 'cbind' and 'rbind' recursively built on cbind2/rbind2} \description{ The base functions \code{\link{cbind}} and \code{\link{rbind}} are defined for an arbitrary number of arguments and hence have the first formal argument \code{...}. For that reason, S4 methods cannot easily be defined for binding together matrices inheriting from \code{\link{Matrix}}. For that reason, \code{\link{cbind2}} and \code{\link{rbind2}} have been provided for binding together \emph{two} matrices, and we have defined methods for these and the \code{'Matrix'}-matrices. As a substitute for \emph{S4-enabled} versions of \code{cbind} and \code{rbind}, you can use \code{cBind} and \code{rBind} with identical syntax and semantic in order to bind together multiple matrices (\code{"matrix"} or \code{"Matrix"} and vectors. } \usage{ %no cbind(..., deparse.level = 1) %no rbind(..., deparse.level = 1) cBind(..., deparse.level = 1) rBind(..., deparse.level = 1) } \arguments{ \item{\dots}{matrix-like \R objects to be bound together, see \code{\link{cbind}} and \code{\link{rbind}}.} \item{deparse.level}{integer determining under which circumstances column and row names are built from the actual arguments' \sQuote{expression}, see \code{\link{cbind}}.} } \details{ The implementation of these is \emph{recursive}, calling \code{\link{cbind2}} or \code{\link{rbind2}} respectively, where these have methods defined and so should dispatch appropriately. } \value{ typically a \sQuote{matrix-like} object of a similar \code{\link{class}} as the first argument in \code{\dots}. Note that sometimes by default, the result is a \code{\linkS4class{sparseMatrix}} if one of the arguments is (even in the case where this is not efficient). In other cases, the result is chosen to be sparse when there are more zero entries is than non-zero ones (as the default \code{sparse} in \code{\link{Matrix}()}). } \author{Martin Maechler} \seealso{\code{\link{cbind2}}, \code{\link{cbind}}, \code{\link[methods]{Methods}}. } \examples{ (a <- matrix(c(2:1,1:2), 2,2)) cbind(0, rBind(a, 7)) # remains traditional matrix D <- Diagonal(2) cBind(4, a, D, -1, D, 0) # a sparse Matrix } \keyword{array} \keyword{manip} Matrix/man/Cholesky.Rd0000644000175100001440000001413612215610444014363 0ustar hornikusers\name{Cholesky} \alias{Cholesky} \alias{Cholesky,dsCMatrix-method}% -> ../R/dsCMatrix.R \alias{Cholesky,CsparseMatrix-method}% coerce \alias{Cholesky,sparseMatrix-method}% coerce \alias{Cholesky,nsparseMatrix-method}% error for now; todo in the future \alias{Cholesky,Matrix-method}% <- "good" error message \alias{.SuiteSparse_version} \title{Cholesky Decomposition of a Sparse Matrix} \usage{ Cholesky(A, perm = TRUE, LDL = !super, super = FALSE, Imult = 0, \dots) } \description{ Computes the Cholesky decomposition of a sparse, symmetric, positive-definite matrix. However, typically \code{\link{chol}()} should rather be used unless you are interested in the different kinds of sparse Cholesky decompositions. } \arguments{ \item{A}{sparse symmetric matrix. No missing values or IEEE special values are allowed.} \item{perm}{logical scalar indicating if a fill-reducing permutation should be computed and applied to the rows and columns of \code{A}. Default is \code{TRUE}.}% NA not available here \item{LDL}{logical scalar indicating if the decomposition should be computed as LDL' where \code{L} is a unit lower triangular matrix. The alternative is LL' where \code{L} is lower triangular with arbitrary diagonal elements. Default is \code{TRUE}. Setting it to \code{\link{NA}} leaves the choice to a CHOLMOD-internal heuristic.} \item{super}{logical scalar indicating is a supernodal decomposition should be created. The alternative is a simplicial decomposition. Default is \code{FALSE}. Setting it to \code{\link{NA}} leaves the choice to a CHOLMOD-internal heuristic.} \item{Imult}{numeric scalar which defaults to zero. The matrix that is decomposed is \eqn{A+m*I} where \eqn{m} is the value of \code{Imult} and \code{I} is the identity matrix of order \code{ncol(A)}.} \item{\dots}{further arguments passed to or from other methods.} } \value{ an object inheriting from either \code{"\linkS4class{CHMsuper}"}, or \code{"\linkS4class{CHMsimpl}"}, depending on the \code{super} argument; both classes extend \code{"\linkS4class{CHMfactor}"} which extends \code{"\linkS4class{MatrixFactorization}"}. In other words, the result of \code{Cholesky()} is \emph{not} a matrix, and if you want one, you should probably rather use \code{\link{chol}()}. } \details{ This is a generic function with special methods for different types of matrices. Use \code{\link{showMethods}("Cholesky")} to list all the methods for the \code{\link{Cholesky}} generic. The method for class \code{\linkS4class{dsCMatrix}} of sparse matrices --- the only one available currently --- is based on functions from the CHOLMOD library. Again: If you just want the Cholesky decomposition of a matrix, you should probably rather use \code{\link{chol}(.)}. } \references{ Tim Davis (2005) \emph{{CHOLMOD}: sparse supernodal {Cholesky} factorization and update/downdate} \url{http://www.cise.ufl.edu/research/sparse/cholmod/} Timothy A. Davis (2006) \emph{Direct Methods for Sparse Linear Systems}, SIAM Series \dQuote{Fundamentals of Algorithms}. } \seealso{ Class definitions \code{\linkS4class{CHMfactor}} and \code{\linkS4class{dsCMatrix}} and function \code{\link{expand}}. Note the extra \code{\link{solve}(*, system = . )} options in \code{\linkS4class{CHMfactor}}. Note that \code{\link{chol}()} returns matrices (inheriting from \code{"\linkS4class{Matrix}"}) whereas \code{Cholesky()} returns a \code{"\linkS4class{CHMfactor}"} object, and hence a typical user will rather use \code{chol(A)}. } \examples{ data(KNex) mtm <- with(KNex, crossprod(mm)) str(mtm@factors) # empty list() (C1 <- Cholesky(mtm)) # uses show() str(mtm@factors) # 'sPDCholesky' (simpl) (Cm <- Cholesky(mtm, super = TRUE)) c(C1 = isLDL(C1), Cm = isLDL(Cm)) str(mtm@factors) # 'sPDCholesky' *and* 'SPdCholesky' str(cm1 <- as(C1, "sparseMatrix")) str(cmat <- as(Cm, "sparseMatrix"))# hmm: super is *less* sparse here cm1[1:20, 1:20] b <- matrix(c(rep(0, 711), 1), nc = 1) ## solve(Cm, b) by default solves Ax = b, where A = Cm'Cm (= mtm)! ## hence, the identical() check *should* work, but fails on some GOTOblas: x <- solve(Cm, b) stopifnot(identical(x, solve(Cm, b, system = "A")), all.equal(x, solve(mtm, b))) Cn <- Cholesky(mtm, perm = FALSE)# no permutation -- much worse: sizes <- c(simple = object.size(C1), super = object.size(Cm), noPerm = object.size(Cn)) ## simple is 100, super= 137, noPerm= 812 : noquote(cbind(format(100 * sizes / sizes[1], digits=4))) ## Visualize the sparseness: dq <- function(ch) paste('"',ch,'"', sep="") ## dQuote() gives bad plots image(mtm, main=paste("crossprod(mm) : Sparse", dq(class(mtm)))) image(cm1, main= paste("as(Cholesky(crossprod(mm)),\"sparseMatrix\"):", dq(class(cm1)))) \dontshow{% FIXME-- move to ../tests/factorizing.R : expand(C1) ## to check printing } ## Smaller example, with same matrix as in help(chol) : (mm <- Matrix(toeplitz(c(10, 0, 1, 0, 3)), sparse = TRUE)) # 5 x 5 (opts <- expand.grid(perm = c(TRUE,FALSE), LDL = c(TRUE,FALSE), super = c(FALSE,TRUE))) rr <- lapply(seq_len(nrow(opts)), function(i) do.call(Cholesky, c(list(A = mm), opts[i,]))) nn <- do.call(expand.grid, c(attr(opts, "out.attr")$dimnames, stringsAsFactors=FALSE,KEEP.OUT.ATTRS=FALSE)) names(rr) <- apply(nn, 1, function(r) paste(sub("(=.).*","\\\\1", r), collapse=","))% extra '\\' in Rd str(rr, max=1) str(re <- lapply(rr, expand), max=2) ## each has a 'P' and a 'L' matrix %% FIXME !! --- "check" them __unfinished__ R0 <- chol(mm, pivot=FALSE) R1 <- chol(mm, pivot=TRUE ) stopifnot(all.equal(t(R1), re[[1]]$L), all.equal(t(R0), re[[2]]$L), identical(as(1:5, "pMatrix"), re[[2]]$P), # no pivoting TRUE) %% --> ../TODO : .diag.dsC() should be renamed, documented, tested,... \dontshow{ str(dd <- .diag.dsC(mtm)) dc <- .diag.dsC(Chx=C1) # <- directly from the Cholesky stopifnot(all.equal(dd,dc)) }%dont # Version of the underlying SuiteSparse library by Tim Davis : .SuiteSparse_version() } \keyword{array} \keyword{algebra} Matrix/man/Diagonal.Rd0000644000175100001440000000731112033656275014327 0ustar hornikusers\name{Diagonal} \title{Create Diagonal Matrix Object} \alias{Diagonal} \alias{.sparseDiagonal} \alias{.symDiagonal} \description{ Create a diagonal matrix object, i.e., an object inheriting from \code{\linkS4class{diagonalMatrix}}. } \usage{ Diagonal(n, x = NULL) .symDiagonal(n, x = rep.int(1,n), uplo = "U") .sparseDiagonal(n, x = 1, uplo = "U", shape = if(missing(cols)) "t" else "g", unitri, kind, cols = if(n) 0:(n - 1L) else integer(0)) } \arguments{ \item{n}{integer specifying the dimension of the (square) matrix. If missing, \code{length(x)} is used.} \item{x}{numeric or logical; if missing, a \emph{unit} diagonal \eqn{n \times n}{n x n} matrix is created.} \item{uplo}{for \code{.symDiagonal}, the resulting sparse \code{\linkS4class{symmetricMatrix}} will have slot \code{uplo} set from this argument, either \code{"U"} or \code{"L"}. Only rarely will it make sense to change this from the default.} \item{shape}{string of 1 character, one of \code{c("t","s","g")}, to chose a triangular, symmetric or general result matrix.} \item{unitri}{optional logical indicating if a triangular result should be \dQuote{unit-triangular}, i.e., with \code{diag = "U"} slot, if possible. The default, \code{\link{missing}}, is the same as \code{\link{TRUE}}.} \item{kind}{string of 1 character, one of \code{c("d","l","n")}, to chose the storage mode of the result, from classes \code{\linkS4class{dsparseMatrix}}, \code{\linkS4class{lsparseMatrix}}, or \code{\linkS4class{nsparseMatrix}}, respectively.} \item{cols}{integer vector with values from \code{0:(n-1)}, denoting the \emph{columns} to subselect conceptually, i.e., get the equivalent of \code{Diagonal(n,*)[, cols + 1]}.} } \value{ \code{Diagonal()} returns an object of class \code{\linkS4class{ddiMatrix}} or \code{\linkS4class{ldiMatrix}} (with \dQuote{superclass} \code{\linkS4class{diagonalMatrix}}). \code{.symDiagonal()} returns an object of class \code{\linkS4class{dsCMatrix}} or \code{\linkS4class{lsCMatrix}}, i.e., a \emph{sparse} \emph{symmetric} matrix. This can be more efficient than \code{Diagonal(n)} when the result is combined with further symmetric (sparse) matrices, however \emph{not} for matrix multiplications where \code{Diagonal()} is clearly preferred. \code{.sparseDiagonal()}, the workhorse of \code{.symDiagonal} returns a \code{\linkS4class{CsparseMatrix}} (the resulting class depending on \code{shape} and \code{kind}) representation of \code{Diagonal(n)}, or, when \code{cols} are specified, of \code{Diagonal(n)[, cols+1]}. } \author{Martin Maechler} \seealso{the generic function \code{\link{diag}} for \emph{extraction} of the diagonal from a matrix works for all \dQuote{Matrices}. \code{\link{bandSparse}} constructs a \emph{banded} sparse matrix from its non-zero sub-/super - diagonals. \code{\link{band}(A)} returns a band matrix containing some sub-/super - diagonals of \code{A}. \code{\link{Matrix}} for general matrix construction; further, class \code{\linkS4class{diagonalMatrix}}. } \examples{ Diagonal(3) Diagonal(x = 10^(3:1)) Diagonal(x = (1:4) >= 2)#-> "ldiMatrix" ## Use Diagonal() + kronecker() for "repeated-block" matrices: M1 <- Matrix(0+0:5, 2,3) (M <- kronecker(Diagonal(3), M1)) (S <- crossprod(Matrix(rbinom(60, size=1, prob=0.1), 10,6))) (SI <- S + 10*.symDiagonal(6)) # sparse symmetric still stopifnot(is(SI, "dsCMatrix")) (I4 <- .sparseDiagonal(4, shape="t"))# now (2012-10) unitriangular stopifnot(I4@diag == "U", all(I4 == diag(4))) \dontshow{% checking some "unit-diagonality": L <- Diagonal(5, TRUE) stopifnot(L@diag == "U", identical(L, Diagonal(5) > 0)) } } \keyword{array} \keyword{algebra} Matrix/man/dpoMatrix-class.Rd0000644000175100001440000001300212271746775015666 0ustar hornikusers\name{dpoMatrix-class} \title{Positive Semi-definite Dense Numeric Matrices} \docType{class} \alias{dpoMatrix-class} \alias{dppMatrix-class} \alias{corMatrix-class} % --- \alias{coerce,dpoMatrix,corMatrix-method} \alias{coerce,dpoMatrix,dppMatrix-method} \alias{coerce,dpoMatrix,lMatrix-method} \alias{coerce,dpoMatrix,nMatrix-method} \alias{coerce,dppMatrix,lMatrix-method} \alias{coerce,dppMatrix,nMatrix-method} \alias{coerce,dppMatrix,sparseMatrix-method} \alias{coerce,dppMatrix,CsparseMatrix-method} \alias{coerce,dppMatrix,dpoMatrix-method} \alias{coerce,dspMatrix,dpoMatrix-method} \alias{coerce,dspMatrix,dppMatrix-method} \alias{coerce,matrix,corMatrix-method} \alias{coerce,Matrix,corMatrix-method} \alias{coerce,matrix,dpoMatrix-method} \alias{coerce,Matrix,dpoMatrix-method} \alias{coerce,matrix,dppMatrix-method} \alias{coerce,Matrix,dppMatrix-method} %\alias{coerce,corMatrix,lMatrix-method} \alias{Ops,dpoMatrix,logical-method} \alias{Ops,dpoMatrix,numeric-method} \alias{Ops,dppMatrix,logical-method} \alias{Ops,dppMatrix,numeric-method} \alias{Ops,logical,dpoMatrix-method} \alias{Ops,logical,dppMatrix-method} \alias{Ops,numeric,dpoMatrix-method} \alias{Ops,numeric,dppMatrix-method} \alias{Arith,dpoMatrix,logical-method} \alias{Arith,dpoMatrix,numeric-method} \alias{Arith,dppMatrix,logical-method} \alias{Arith,dppMatrix,numeric-method} \alias{Arith,logical,dpoMatrix-method} \alias{Arith,logical,dppMatrix-method} \alias{Arith,numeric,dpoMatrix-method} \alias{Arith,numeric,dppMatrix-method} % \alias{rcond,dpoMatrix,character-method} \alias{rcond,dppMatrix,character-method} \alias{rcond,dpoMatrix,missing-method} \alias{rcond,dppMatrix,missing-method} \alias{determinant,dpoMatrix,logical-method} \alias{determinant,dppMatrix,logical-method} \alias{determinant,dpoMatrix,missing-method} \alias{determinant,dppMatrix,missing-method} %\alias{solve,dpoMatrix,...-method}--> solve-methods.Rd \alias{t,dppMatrix-method} \description{ The \code{"dpoMatrix"} class is the class of positive-semidefinite symmetric matrices in nonpacked storage. The \code{"dppMatrix"} class is the same except in packed storage. Only the upper triangle or the lower triangle is required to be available. The \code{"corMatrix"} class extends \code{"dpoMatrix"} with a slot \code{sd}. } \section{Objects from the Class}{Objects can be created by calls of the form \code{new("dpoMatrix", ...)} or from \code{crossprod} applied to an \code{"dgeMatrix"} object.} \section{Slots}{ \describe{ \item{\code{uplo}:}{Object of class \code{"character"}. Must be either "U", for upper triangular, and "L", for lower triangular.} \item{\code{x}:}{Object of class \code{"numeric"}. The numeric values that constitute the matrix, stored in column-major order.} \item{\code{Dim}:}{Object of class \code{"integer"}. The dimensions of the matrix which must be a two-element vector of non-negative integers.} \item{\code{Dimnames}:}{inherited from class \code{"Matrix"}} \item{\code{factors}:}{Object of class \code{"list"}. A named list of factorizations that have been computed for the matrix.} \item{\code{sd}:}{(for \code{"corMatrix"}) a \code{\link{numeric}} vector of length \code{n} containing the (original) \eqn{\sqrt{var(.)}}{sqrt(var(.))} entries which allow reconstruction of a covariance matrix from the correlation matrix.} } } \section{Extends}{ Class \code{"dsyMatrix"}, directly.\cr Classes \code{"dgeMatrix"}, \code{"symmetricMatrix"}, and many more by class \code{"dsyMatrix"}. } \section{Methods}{ \describe{ \item{chol}{\code{signature(x = "dpoMatrix")}: Returns (and stores) the Cholesky decomposition of \code{x}, see \code{\link{chol}}.} \item{determinant}{\code{signature(x = "dpoMatrix")}: Returns the \code{\link{determinant}} of \code{x}, via \code{chol(x)}, see above.} \item{rcond}{\code{signature(x = "dpoMatrix", norm = "character")}: Returns (and stores) the reciprocal of the condition number of \code{x}. The \code{norm} can be \code{"O"} for the one-norm (the default) or \code{"I"} for the infinity-norm. For symmetric matrices the result does not depend on the norm.} \item{solve}{\code{signature(a = "dpoMatrix", b = "....")}}{, and} \item{solve}{\code{signature(a = "dppMatrix", b = "....")}}{work via the Cholesky composition, see also the Matrix \code{\link{solve-methods}}.} \item{Arith}{\code{signature(e1 = "dpoMatrix", e2 = "numeric")} (and quite a few other signatures): The result of (\dQuote{elementwise} defined) arithmetic operations is typically \emph{not} positive-definite anymore. The only exceptions, currently, are multiplications, divisions or additions with \emph{positive} \code{length(.) == 1} numbers (or \code{\link{logical}}s).} } } %\references{} %\author{} \seealso{ Classes \code{\linkS4class{dsyMatrix}} and \code{\linkS4class{dgeMatrix}}; further, \code{\link{Matrix}}, \code{\link{rcond}}, \code{\link[base]{chol}}, \code{\link[base]{solve}}, \code{\link{crossprod}}. } \examples{ h6 <- Hilbert(6) rcond(h6) str(h6) h6 * 27720 # is ``integer'' solve(h6) str(hp6 <- as(h6, "dppMatrix")) ### Note that as(*, "corMatrix") *scales* the matrix (ch6 <- as(h6, "corMatrix")) stopifnot(all.equal(h6 * 27720, round(27720 * h6), tolerance = 1e-14), all.equal(ch6@sd^(-2), 2*(1:6)-1, tolerance= 1e-12)) chch <- chol(ch6) stopifnot(identical(chch, ch6@factors$Cholesky), all(abs(crossprod(chch) - ch6) < 1e-10)) } \keyword{classes} \keyword{algebra} Matrix/man/isSymmetric-methods.Rd0000644000175100001440000000263612213673171016561 0ustar hornikusers\name{isSymmetric-methods} \docType{methods} \alias{isSymmetric-methods} \alias{isSymmetric,symmetricMatrix-method} \alias{isSymmetric,triangularMatrix-method} \alias{isSymmetric,denseMatrix-method} \alias{isSymmetric,diagonalMatrix-method} \alias{isSymmetric,sparseMatrix-method} \title{Methods for Function isSymmetric in Package 'Matrix'} \description{ \code{isSymmetric(M)} returns a \code{\link{logical}} indicating if \code{M} is a symmetric matrix. This is a \pkg{base} function with a default method for the traditional matrices of \code{\link{class}} \code{"matrix"}. Methods here are defined for virtual Matrix classes such that it works for all objects inheriting from class \code{\linkS4class{Matrix}}. } \seealso{\code{\link{forceSymmetric}}, \code{\link{symmpart}}, and the formal class (and subclasses) \code{"\linkS4class{symmetricMatrix}"}. } %% \usage{ %% } %% \section{Methods}{ %% \describe{ %% \item{object = "symmetricMatrix"}{ ... } %% \item{object = "triangularMatrix"}{ ... } %% \item{object = "denseMatrix"}{ ... } %% \item{object = "diagonalMatrix"}{ ... } %% \item{object = "sparseMatrix"}{ ... } %% } %% } \examples{ isSymmetric(Diagonal(4)) # TRUE of course M <- Matrix(c(1,2,2,1), 2,2) isSymmetric(M) # TRUE (*and* of formal class "dsyMatrix") isSymmetric(as(M, "dgeMatrix")) # still symmetric, even if not "formally" isSymmetric(triu(M)) # FALSE } \keyword{methods} Matrix/man/diagonalMatrix-class.Rd0000644000175100001440000002626012271746775016674 0ustar hornikusers\name{diagonalMatrix-class} \title{Class "diagonalMatrix" of Diagonal Matrices} \docType{class} \alias{diagonalMatrix-class} % \alias{as.vector,diagonalMatrix,missing-method} \alias{coerce,matrix,diagonalMatrix-method} \alias{coerce,diagonalMatrix,denseMatrix-method} \alias{coerce,diagonalMatrix,generalMatrix-method} \alias{coerce,diagonalMatrix,matrix-method} \alias{coerce,diagonalMatrix,nMatrix-method} \alias{coerce,diagonalMatrix,nsparseMatrix-method} \alias{coerce,Matrix,diagonalMatrix-method} \alias{cbind2,sparseMatrix,diagonalMatrix-method} \alias{cbind2,diagonalMatrix,sparseMatrix-method} \alias{rbind2,sparseMatrix,diagonalMatrix-method} \alias{rbind2,diagonalMatrix,sparseMatrix-method} \alias{determinant,diagonalMatrix,logical-method} \alias{norm,diagonalMatrix,character-method} % \alias{coerce,ddiMatrix,dgeMatrix-method} \alias{coerce,ddiMatrix,ddenseMatrix-method} \alias{coerce,ldiMatrix,ldenseMatrix-method} % Mainly against ambiguity warnings: % Horrible-Hack: currently define for "all subclasses of diagonalMatrix" % ------------- in ../R/diagMatrix.R \alias{coerce,ddiMatrix,symmetricMatrix-method} \alias{coerce,ldiMatrix,symmetricMatrix-method} \alias{coerce,ddiMatrix,triangularMatrix-method} \alias{coerce,ldiMatrix,triangularMatrix-method} %_no_longer_ \alias{coerce,ddiMatrix,sparseMatrix-method} %_no_longer_ \alias{coerce,ldiMatrix,sparseMatrix-method} \alias{coerce,ddiMatrix,CsparseMatrix-method} \alias{coerce,ldiMatrix,CsparseMatrix-method} \alias{coerce,ddiMatrix,TsparseMatrix-method} \alias{coerce,ddiMatrix,dsparseMatrix-method} \alias{coerce,ldiMatrix,TsparseMatrix-method} \alias{coerce,ldiMatrix,lsparseMatrix-method} % \alias{cbind2,ddiMatrix,matrix-method} \alias{cbind2,ldiMatrix,matrix-method} \alias{cbind2,matrix,ddiMatrix-method} \alias{cbind2,matrix,ldiMatrix-method} \alias{rbind2,ddiMatrix,matrix-method} \alias{rbind2,ldiMatrix,matrix-method} \alias{rbind2,matrix,ddiMatrix-method} \alias{rbind2,matrix,ldiMatrix-method} % \alias{cbind2,ddiMatrix,atomicVector-method} \alias{cbind2,ldiMatrix,atomicVector-method} \alias{cbind2,atomicVector,ddiMatrix-method} \alias{cbind2,atomicVector,ldiMatrix-method} \alias{rbind2,ddiMatrix,atomicVector-method} \alias{rbind2,ldiMatrix,atomicVector-method} \alias{rbind2,atomicVector,ddiMatrix-method} \alias{rbind2,atomicVector,ldiMatrix-method} \alias{diag,diagonalMatrix-method} % \alias{diag,ddiMatrix-method} % \alias{diag,ldiMatrix-method} \alias{which,ldiMatrix-method} % \alias{Ops,diagonalMatrix,triangularMatrix-method} \alias{Ops,ddiMatrix,sparseMatrix-method} \alias{Ops,sparseMatrix,ddiMatrix-method} \alias{Ops,ldiMatrix,sparseMatrix-method} \alias{Ops,sparseMatrix,ldiMatrix-method} \alias{Ops,ddiMatrix,numeric-method} \alias{Ops,numeric,ddiMatrix-method} \alias{Ops,ldiMatrix,numeric-method} \alias{Ops,numeric,ldiMatrix-method} \alias{Ops,ddiMatrix,logical-method} \alias{Ops,logical,ddiMatrix-method} \alias{Ops,ldiMatrix,logical-method} \alias{Ops,logical,ldiMatrix-method} % \alias{Ops,ddiMatrix,ANY-method} \alias{Ops,ANY,ddiMatrix-method} \alias{Ops,ldiMatrix,ANY-method} \alias{Ops,ANY,ldiMatrix-method} \alias{Ops,ddiMatrix,Matrix-method} \alias{Ops,Matrix,ddiMatrix-method} \alias{Ops,ldiMatrix,Matrix-method} \alias{Ops,Matrix,ldiMatrix-method} \alias{Ops,ddiMatrix,dMatrix-method} \alias{Ops,dMatrix,ddiMatrix-method} \alias{Ops,ldiMatrix,dMatrix-method} \alias{Ops,dMatrix,ldiMatrix-method} % \alias{Ops,ddiMatrix,ddiMatrix-method} \alias{Ops,ddiMatrix,ldiMatrix-method} \alias{Ops,ldiMatrix,ddiMatrix-method} \alias{Ops,ldiMatrix,ldiMatrix-method} \alias{Arith,triangularMatrix,diagonalMatrix-method} \alias{Compare,triangularMatrix,diagonalMatrix-method} \alias{Logic,triangularMatrix,diagonalMatrix-method} \alias{Arith,numeric,ddiMatrix-method} \alias{Arith,numeric,ldiMatrix-method} \alias{Arith,ddiMatrix,numeric-method} \alias{Arith,ldiMatrix,numeric-method} \alias{Arith,logical,ddiMatrix-method} \alias{Arith,logical,ldiMatrix-method} \alias{Arith,ddiMatrix,logical-method} \alias{Arith,ldiMatrix,logical-method} \alias{-,ddiMatrix,missing-method} \alias{-,ldiMatrix,missing-method} \alias{all,ddiMatrix-method} \alias{all,ldiMatrix-method} \alias{any,ddiMatrix-method} \alias{any,ldiMatrix-method} \alias{prod,ddiMatrix-method} \alias{prod,ldiMatrix-method} \alias{sum,ddiMatrix-method} \alias{sum,ldiMatrix-method} %%--"hack"-- for all these signatures explicitly (in loop in ../R/diagMatrix.R ): %% <[dln]denseMatrix o [dl]diMatrix : \alias{^,ddenseMatrix,ddiMatrix-method} \alias{^,ddenseMatrix,ldiMatrix-method} \alias{^,ddiMatrix,ddenseMatrix-method} \alias{^,ddiMatrix,ldenseMatrix-method} \alias{^,ddiMatrix,ndenseMatrix-method} \alias{^,ldenseMatrix,ddiMatrix-method} \alias{^,ldenseMatrix,ldiMatrix-method} \alias{^,ldiMatrix,ddenseMatrix-method} \alias{^,ldiMatrix,ldenseMatrix-method} \alias{^,ldiMatrix,ndenseMatrix-method} \alias{^,ndenseMatrix,ddiMatrix-method} \alias{^,ndenseMatrix,ldiMatrix-method} \alias{/,ddiMatrix,ddenseMatrix-method} \alias{/,ddiMatrix,ldenseMatrix-method} \alias{/,ddiMatrix,ndenseMatrix-method} \alias{/,ldiMatrix,ddenseMatrix-method} \alias{/,ldiMatrix,ldenseMatrix-method} \alias{/,ldiMatrix,ndenseMatrix-method} \alias{*,ddenseMatrix,ddiMatrix-method} \alias{*,ddenseMatrix,ldiMatrix-method} \alias{*,ddiMatrix,ddenseMatrix-method} \alias{*,ddiMatrix,ldenseMatrix-method} \alias{*,ddiMatrix,ndenseMatrix-method} \alias{*,ldenseMatrix,ddiMatrix-method} \alias{*,ldenseMatrix,ldiMatrix-method} \alias{*,ldiMatrix,ddenseMatrix-method} \alias{*,ldiMatrix,ldenseMatrix-method} \alias{*,ldiMatrix,ndenseMatrix-method} \alias{*,ndenseMatrix,ddiMatrix-method} \alias{*,ndenseMatrix,ldiMatrix-method} \alias{&,ddenseMatrix,ddiMatrix-method} \alias{&,ddenseMatrix,ldiMatrix-method} \alias{&,ddiMatrix,ddenseMatrix-method} \alias{&,ddiMatrix,ldenseMatrix-method} \alias{&,ddiMatrix,ndenseMatrix-method} \alias{&,ldenseMatrix,ddiMatrix-method} \alias{&,ldenseMatrix,ldiMatrix-method} \alias{&,ldiMatrix,ddenseMatrix-method} \alias{&,ldiMatrix,ldenseMatrix-method} \alias{&,ldiMatrix,ndenseMatrix-method} \alias{&,ndenseMatrix,ddiMatrix-method} \alias{&,ndenseMatrix,ldiMatrix-method} \alias{\%/\%,ddiMatrix,ddenseMatrix-method} \alias{\%/\%,ddiMatrix,ldenseMatrix-method} \alias{\%/\%,ddiMatrix,ndenseMatrix-method} \alias{\%/\%,ldiMatrix,ddenseMatrix-method} \alias{\%/\%,ldiMatrix,ldenseMatrix-method} \alias{\%/\%,ldiMatrix,ndenseMatrix-method} \alias{\%\%,ddiMatrix,ddenseMatrix-method} \alias{\%\%,ddiMatrix,ldenseMatrix-method} \alias{\%\%,ddiMatrix,ndenseMatrix-method} \alias{\%\%,ldiMatrix,ddenseMatrix-method} \alias{\%\%,ldiMatrix,ldenseMatrix-method} \alias{\%\%,ldiMatrix,ndenseMatrix-method} %% Matrix o [dl]diMatrix : \alias{^,Matrix,ddiMatrix-method} \alias{^,Matrix,ldiMatrix-method} \alias{^,ddiMatrix,Matrix-method} \alias{^,ldiMatrix,Matrix-method} \alias{/,ddiMatrix,Matrix-method} \alias{/,ldiMatrix,Matrix-method} \alias{*,Matrix,ddiMatrix-method} \alias{*,Matrix,ldiMatrix-method} \alias{*,ddiMatrix,Matrix-method} \alias{*,ldiMatrix,Matrix-method} \alias{&,Matrix,ddiMatrix-method} \alias{&,Matrix,ldiMatrix-method} \alias{&,ddiMatrix,Matrix-method} \alias{&,ldiMatrix,Matrix-method} \alias{\%/\%,ddiMatrix,Matrix-method} \alias{\%/\%,ldiMatrix,Matrix-method} \alias{\%\%,ddiMatrix,Matrix-method} \alias{\%\%,ldiMatrix,Matrix-method} %> %-end{H.Hack} \alias{Ops,diagonalMatrix,diagonalMatrix-method} \alias{Ops,diagonalMatrix,ddiMatrix-method} \alias{Ops,ddiMatrix,diagonalMatrix-method} \alias{Summary,ddiMatrix-method} \alias{Summary,ldiMatrix-method} % \alias{chol2inv,diagonalMatrix-method} \alias{t,diagonalMatrix-method} \alias{print,diagonalMatrix-method} \alias{show,diagonalMatrix-method} %\alias{solve,...} --> solve-methods.Rd %\alias{\%*%,... } --> matrix-products.Rd \alias{summary,diagonalMatrix-method} \description{ Class "diagonalMatrix" is the virtual class of all diagonal matrices. } \section{Objects from the Class}{A virtual Class: No objects may be created from it.} \section{Slots}{ \describe{ \item{\code{diag}:}{code{"character"} string, either \code{"U"} or \code{"N"}, where \code{"U"} means \sQuote{unit-diagonal}.} \item{\code{Dim}:}{matrix dimension, and} \item{\code{Dimnames}:}{the \code{\link{dimnames}}, a \code{\link{list}}, see the \code{\linkS4class{Matrix}} class description. Typically \code{list(NULL,NULL)} for diagonal matrices.} } } \section{Extends}{ Class \code{"\linkS4class{sparseMatrix}"}, directly. } \section{Methods}{ These are just a subset of the signature for which defined methods. Currently, there are (too) many explicit methods defined in order to ensure efficient methods for diagonal matrices. \describe{ \item{coerce}{\code{signature(from = "matrix", to = "diagonalMatrix")}: ... } \item{coerce}{\code{signature(from = "Matrix", to = "diagonalMatrix")}: ... } \item{coerce}{\code{signature(from = "diagonalMatrix", to = "generalMatrix")}: ... } \item{coerce}{\code{signature(from = "diagonalMatrix", to = "triangularMatrix")}: ... } \item{coerce}{\code{signature(from = "diagonalMatrix", to = "nMatrix")}: ... } \item{coerce}{\code{signature(from = "diagonalMatrix", to = "matrix")}: ... } \item{coerce}{\code{signature(from = "diagonalMatrix", to = "sparseVector")}: ... } \item{t}{\code{signature(x = "diagonalMatrix")}: ... } \cr and many more methods \item{solve}{\code{signature(a = "diagonalMatrix", b, ...)}: is trivially implemented, of course; see also \code{\link{solve-methods}}.} \item{which}{\code{signature(x = "nMatrix")}, semantically equivalent to \pkg{base} function \code{\link{which}(x, arr.ind)}.} \item{*}{\code{signature(e1 = "ddiMatrix", e2="denseMatrix")}: arithmetic and other operators from the \code{\link[=S4groupGeneric]{Ops}} group have a few dozen explicit method definitions, in order to keep the results \emph{diagonal} in many cases, including the following:} \item{/}{\code{signature(e1 = "ddiMatrix", e2="denseMatrix")}: the result is from class \code{\linkS4class{ddiMatrix}} which is typically very desirable. Note that when \code{e2} contains off-diagonal zeros or \code{\link{NA}}s, we implicitly use \eqn{0 / x = 0}, hence differing from traditional \R arithmetic (where \eqn{0 / 0 \mapsto \mbox{NaN}}{0/0 |-> NaN}), in order to preserve sparsity.} \item{summary}{\code{(object = "diagonalMatrix")}: Returns an object of S3 class \code{"diagSummary"} which is the summary of the vector \code{object@x} plus a simple heading, and an appropriate \code{\link{print}} method.} } } \seealso{ \code{\link{Diagonal}()} as constructor of these matrices, and \code{\link{isDiagonal}}. \code{\linkS4class{ddiMatrix}} and \code{\linkS4class{ldiMatrix}} are \dQuote{actual} classes extending \code{"diagonalMatrix"}. } \examples{ I5 <- Diagonal(5) D5 <- Diagonal(x = 10*(1:5)) ## trivial (but explicitly defined) methods: stopifnot(identical(crossprod(I5), I5), identical(tcrossprod(I5), I5), identical(crossprod(I5, D5), D5), identical(tcrossprod(D5, I5), D5), identical(solve(D5), solve(D5, I5)), all.equal(D5, solve(solve(D5)), tolerance = 1e-12) ) solve(D5)# efficient as is diagonal # an unusual way to construct a band matrix: rbind2(cbind2(I5, D5), cbind2(D5, I5)) } \keyword{classes} Matrix/man/bdiag.Rd0000644000175100001440000000374511670362473013666 0ustar hornikusers\name{bdiag} \alias{bdiag} \alias{.bdiag} \title{Construct a Block Diagonal Matrix} \description{ Build a block diagonal matrix given several building block matrices. } \usage{ bdiag(\dots) .bdiag(lst) } \arguments{ \item{\dots}{individual matrices or a \code{\link{list}} of matrices.} \item{lst}{non-empty \code{\link{list}} of matrices.} } \details{ For non-trivial argument list, \code{bdiag()} calls \code{.bdiag()}. The latter maybe useful to programmers } \value{ A \emph{sparse} matrix obtained by combining the arguments into a block diagonal matrix. The value of \code{bdiag()} inheris from class \code{\linkS4class{CsparseMatrix}}, whereas \code{.bdiag()} returns a \code{\linkS4class{TsparseMatrix}}. } \author{Martin Maechler, built on a version posted by Berton Gunter to R-help; earlier versions have been posted by other authors, notably Scott Chasalow to S-news. Doug Bates's faster implementation builds on \code{\linkS4class{TsparseMatrix}} objects. } \seealso{\code{\link{Diagonal}} for constructing matrices of class \code{\linkS4class{diagonalMatrix}}, or \code{\link{kronecker}} which also works for \code{"Matrix"} inheriting matrices. \code{\link{bandSparse}} constructs a \emph{banded} sparse matrix from its non-zero sub-/super - diagonals. Note that other CRAN \R packages have own versions of \code{bdiag()} which return traditional matrices. } \examples{ bdiag(matrix(1:4, 2), diag(3)) ## combine "Matrix" class and traditional matrices: bdiag(Diagonal(2), matrix(1:3, 3,4), diag(3:2)) mlist <- list(1, 2:3, diag(x=5:3), 27, cbind(1,3:6), 100:101) bdiag(mlist) stopifnot(identical(bdiag(mlist), % <- used to fail in earlier versions bdiag(lapply(mlist, as.matrix)))) ml <- c(as(matrix((1:24)\%\% 11 == 0, 6,4),"nMatrix"), rep(list(Diagonal(2, x=TRUE)), 3)) mln <- c(ml, Diagonal(x = 1:3)) stopifnot(is(bdiag(ml), "lsparseMatrix"),% failed in Matrix <= 1.0-2 is(bdiag(mln),"dsparseMatrix") ) } \keyword{array} Matrix/man/updown.Rd0000644000175100001440000000346111745552731014130 0ustar hornikusers\name{updown} \alias{updown} \alias{updown-methods} \alias{updown,ANY,ANY,ANY-method} \alias{updown,character,mMatrix,CHMfactor-method} \alias{updown,logical,mMatrix,CHMfactor-method} \title{Up- and Down-Dating a Cholesky Decomposition} \description{ Compute the up- or down-dated Cholesky decomposition } \usage{ updown(update, C, L) } \arguments{ \item{update}{logical (\code{TRUE} or \code{FALSE}) or \code{"+"} or \code{"-"} indicating if an up- or a down-date is to be computed.} \item{C}{any \R object, coercable to a sparse matrix (i.e., of subclass of \code{\linkS4class{sparseMatrix}}).} \item{L}{a Cholesky factor, specifically, of class \code{"\linkS4class{CHMfactor}"}.} } % \details{ % } \value{ an updated Cholesky factor, of the same dimension as \code{L}. Typically of class \code{"\linkS4class{dCHMsimpl}"} (a sub class of \code{"\linkS4class{CHMfactor}"}). } \references{ CHOLMOD manual, currently beginning of chapter~18. ... %% FIXME } \author{Contributed by Nicholas Nagle, University of Tennessee, Knoxville, USA} \section{Methods}{ \describe{ \item{\code{signature(update = "character", C = "mMatrix", L = "CHMfactor")}}{..} \item{\code{signature(update = "logical", C = "mMatrix", L = "CHMfactor")}}{ .. } } } \seealso{ \code{\link{Cholesky}}, } \examples{ dn <- list(LETTERS[1:3], letters[1:5]) ## pointer vectors can be used, and the (i,x) slots are sorted if necessary: m <- sparseMatrix(i = c(3,1, 3:2, 2:1), p= c(0:2, 4,4,6), x = 1:6, dimnames = dn) cA <- Cholesky(A <- crossprod(m) + Diagonal(5)) 166 * as(cA,"Matrix") ^ 2 uc1 <- updown("+", Diagonal(5), cA) ## Hmm: this loses positive definiteness: uc2 <- updown("-", 2*Diagonal(5), cA) image(show(as(cA, "Matrix"))) image(show(c2 <- as(uc2,"Matrix")))# severely negative entries ##--> Warning } \keyword{methods} Matrix/man/invPerm.Rd0000644000175100001440000000240712053354650014224 0ustar hornikusers\name{invPerm} \alias{invPerm} \title{Inverse Permutation Vector} \description{ From a permutation vector \code{p}, compute its \emph{inverse} permutation vector. } \usage{ invPerm(p, zero.p = FALSE, zero.res = FALSE) } \arguments{ \item{p}{an integer vector of length, say, \code{n}.} \item{zero.p}{logical indicating if \code{p} contains values \code{0:(n-1)} or rather (by default, \code{zero.p = FALSE}) \code{1:n}.} \item{zero.res}{logical indicating if the result should contain values \code{0:(n-1)} or rather (by default, \code{zero.res = FALSE}) \code{1:n}.} } \value{ an integer vector of the same length (\code{n}) as \code{p}. By default, (\code{zero.p = FALSE, zero.res = FALSE}), \code{invPerm(p)} is the same as \code{\link{order}(p)} or \code{\link{sort.list}(p)} and for that case, the function is equivalent to \code{invPerm. <- function(p) { p[p] <- seq_along(p) ; p }}. } \author{Martin Maechler} \seealso{the class of permutation matrices, \code{\linkS4class{pMatrix}}. } \examples{ p <- sample(10) # a random permutation vector ip <- invPerm(p) p[ip] # == 1:10 ## they are indeed inverse of each other: stopifnot( identical(p[ip], 1:10), identical(ip[p], 1:10), identical(invPerm(ip), p) ) } \keyword{arithmetic} Matrix/man/rcond.Rd0000644000175100001440000001137212271746775013731 0ustar hornikusers\name{rcond} \title{Estimate the Reciprocal Condition Number} \alias{rcond} % most methods are documented in Matrix-class.Rd \alias{rcond,ANY,missing-method} \alias{rcond,matrix,character-method}%<- no longer for R >= 2.7.0 \alias{rcond,Matrix,character-method} \alias{rcond,ldenseMatrix,character-method} \alias{rcond,ndenseMatrix,character-method} \alias{rcond,sparseMatrix,character-method} % \usage{ rcond(x, norm, \dots) \S4method{rcond}{sparseMatrix,character}(x, norm, useInv=FALSE, \dots) } \description{ Estimate the reciprocal of the condition number of a matrix. This is a generic function with several methods, as seen by \code{\link{showMethods}(rcond)}. } \arguments{ \item{x}{an \R object that inherits from the \code{Matrix} class.} \item{norm}{ Character indicating the type of norm to be used in the estimate. The default is \code{"O"} for the 1-norm (\code{"O"} is equivalent to \code{"1"}). The other possible value is \code{"I"} for the infinity norm, see also \code{\link{norm}}. } \item{useInv}{logical (or \code{"Matrix"} containing \code{\link{solve}(x)}). If not false, compute the reciprocal condition number as \eqn{1/(\|x\| \cdot \|x^{-1}\|)}{1/(||x|| * ||x^(-1)||)}, where \eqn{x^{-1}}{x^(-1)} is the inverse of \eqn{x}, \code{solve(x)}. This may be an efficient alternative (only) in situations where \code{solve(x)} is fast (or known), e.g., for (very) sparse or triangular matrices. Note that the \emph{result} may differ depending on \code{useInv}, as per default, when it is false, an \emph{approximation} is computed. } \item{\dots}{further arguments passed to or from other methods.} } \value{ An estimate of the reciprocal condition number of \code{x}. } \section{BACKGROUND}{ The condition number of a regular (square) matrix is the product of the \code{\link{norm}} of the matrix and the norm of its inverse (or pseudo-inverse). More generally, the condition number is defined (also for non-square matrices \eqn{A}) as \deqn{\kappa(A) = \frac{\max_{\|v\| = 1} \|A v\|}{\min_{\|v\| = 1} \|A v\|}.}{% kappa(A) = (max_(||v|| = 1; || Av ||)) /(min_(||v|| = 1; || Av ||)).} Whenever \code{x} is \emph{not} a square matrix, in our method definitions, this is typically computed via \code{rcond(qr.R(qr(X)), ...)} where \code{X} is \code{x} or \code{t(x)}. The condition number takes on values between 1 and infinity, inclusive, and can be viewed as a factor by which errors in solving linear systems with this matrix as coefficient matrix could be magnified. \code{rcond()} computes the \emph{reciprocal} condition number \eqn{1/\kappa} with values in \eqn{[0,1]} and can be viewed as a scaled measure of how close a matrix is to being rank deficient (aka \dQuote{singular}). Condition numbers are usually estimated, since exact computation is costly in terms of floating-point operations. An (over) estimate of reciprocal condition number is given, since by doing so overflow is avoided. Matrices are well-conditioned if the reciprocal condition number is near 1 and ill-conditioned if it is near zero. } \seealso{ \code{\link{norm}}, \code{\link[base]{kappa}()} from package \pkg{base} computes an \emph{approximate} condition number of a \dQuote{traditional} matrix, even non-square ones, with respect to the \eqn{p=2} (Euclidean) \code{\link{norm}}. \code{\link[base]{solve}}. \code{\link{condest}}, a newer approximate estimate of the (1-norm) condition number, particularly efficient for large sparse matrices. } \references{ Golub, G., and Van Loan, C. F. (1989). \emph{Matrix Computations,} 2nd edition, Johns Hopkins, Baltimore. } \examples{ x <- Matrix(rnorm(9), 3, 3) rcond(x) ## typically "the same" (with more computational effort): 1 / (norm(x) * norm(solve(x))) rcond(Hilbert(9)) # should be about 9.1e-13 ## For non-square matrices: rcond(x1 <- cbind(1,1:10))# 0.05278 rcond(x2 <- cbind(x1, 2:11))# practically 0, since x2 does not have full rank ## sparse (S1 <- Matrix(rbind(0:1,0, diag(3:-2)))) rcond(S1) m1 <- as(S1, "denseMatrix") all.equal(rcond(S1), rcond(m1)) ## wide and sparse rcond(Matrix(cbind(0, diag(2:-1)))) ## Large sparse example ---------- m <- Matrix(c(3,0:2), 2,2) M <- bdiag(kronecker(Diagonal(2), m), kronecker(m,m)) 36*(iM <- solve(M)) # still sparse MM <- kronecker(Diagonal(10), kronecker(Diagonal(5),kronecker(m,M))) dim(M3 <- kronecker(bdiag(M,M),MM)) # 12'800 ^ 2 if(interactive()) ## takes about 2 seconds system.time(r <- rcond(M3)) ## whereas this is *fast* even though it computes solve(M3) system.time(r. <- rcond(M3, useInv=TRUE)) if(interactive()) ## the values are not the same c(r, r.) # 0.05555 0.013888 \dontshow{stopifnot(all.equal(r., 1/72, tolerance=1e-12))} } \keyword{array} \keyword{algebra} Matrix/man/sparse.model.matrix.Rd0000644000175100001440000001351712271746775016526 0ustar hornikusers\name{sparse.model.matrix} \title{Construct Sparse Design / Model Matrices} \alias{sparse.model.matrix} \alias{fac2sparse} \alias{fac2Sparse} \description{Construct a sparse model or \dQuote{design} matrix, form a formula and data frame (\code{sparse.model.matrix}) or a single factor (\code{fac2sparse}). The \code{fac2[Ss]parse()} functions are utilities, also used internally in the principal user level function \code{sparse.model.matrix()}. } \usage{ sparse.model.matrix(object, data = environment(object), contrasts.arg = NULL, xlev = NULL, transpose = FALSE, drop.unused.levels = FALSE, row.names = TRUE, verbose = FALSE, \dots) fac2sparse(from, to = c("d", "i", "l", "n", "z"), drop.unused.levels = TRUE, giveCsparse = TRUE) fac2Sparse(from, to = c("d", "i", "l", "n", "z"), drop.unused.levels = TRUE, giveCsparse = TRUE, factorPatt12, contrasts.arg = NULL) } \arguments{ \item{object}{an object of an appropriate class. For the default method, a model formula or terms object.} \item{data}{a data frame created with \code{\link{model.frame}}. If another sort of object, \code{model.frame} is called first.} \item{contrasts.arg}{\describe{ \item{for \code{sparse.model.matrix()}:}{A list, whose entries are contrasts suitable for input to the \code{\link{contrasts}} replacement function and whose names are the names of columns of \code{data} containing \code{\link{factor}}s.} \item{for \code{fac2Sparse()}:}{character string or \code{NULL} or (coercable to) \code{"\linkS4class{sparseMatrix}"}, specifying the contrasts to be applied to the factor levels.} }} \item{xlev}{to be used as argument of \code{\link{model.frame}} if \code{data} has no \code{"terms"} attribute.} \item{transpose}{logical indicating if the \emph{transpose} should be returned; if the transposed is used anyway, setting \code{transpose = TRUE} is more efficient.} \item{drop.unused.levels}{should factors have unused levels dropped? The default for \code{sparse.model.matrix} has been changed to \code{FALSE}, 2010-07, for compatibility with \R's standard (dense) \code{\link{model.matrix}()}.} \item{row.names}{logical indicating if row names should be used.} \item{verbose}{logical or integer indicating if (and how much) progress output should be printed.} \item{\dots}{further arguments passed to or from other methods.} \item{from}{(for \code{fac2sparse()}:) a \code{\link{factor}}.} \item{to}{a character indicating the \dQuote{kind} of sparse matrix to be returned. The default, \code{"d"} is for \code{\link{double}}.} \item{giveCsparse}{(for \code{fac2sparse()}:) logical indicating if the result must be a \code{\linkS4class{CsparseMatrix}}.} \item{factorPatt12}{logical vector, say \code{fp}, of length two; when \code{fp[1]} is true, return \dQuote{contrasted} \code{t(X)}; when \code{fp[2]} is true, the original (\dQuote{dummy}) \code{t(X)}, i.e, the result of \code{\link{fac2sparse}()}.} } \value{ a sparse matrix, extending \code{\linkS4class{CsparseMatrix}} (for \code{fac2sparse()} if \code{giveCsparse} is true as per default; a \code{\linkS4class{TsparseMatrix}}, otherwise). For \code{fac2Sparse()}, a \code{\link{list}} of length two, both components with the corresponding transposed model matrix, where the corresponding \code{factorPatt12} is true. Note that \code{\link[MatrixModels]{model.Matrix}(*, sparse=TRUE)} from package \pkg{MatrixModels} may be often be preferable to \code{sparse.model.matrix()} nowadays, as \code{model.Matrix()} returns \code{\link[MatrixModels:modelMatrix-class]{modelMatrix}} objects with additional slots \code{assign} and \code{contrasts} which relate back to the variables used. \code{fac2sparse()}, the basic workhorse of \code{sparse.model.matrix()}, returns the \emph{transpose} (\code{\link{t}}) of the model matrix. } \author{Doug Bates and Martin Maechler, with initial suggestions from Tim Hesterberg. } \seealso{ \code{\link{model.matrix}} in standard \R's package \pkg{stats}.\cr \code{\link[MatrixModels]{model.Matrix}} which calls \code{sparse.model.matrix} or \code{model.matrix} depending on its \code{sparse} argument may be preferred to \code{sparse.model.matrix}. \code{as(f, "sparseMatrix")} (see \code{coerce(from = "factor", ..)} in the class doc \linkS4class{sparseMatrix}) produces the \emph{transposed} sparse model matrix for a single factor \code{f} (and \emph{no} contrasts). } \examples{ dd <- data.frame(a = gl(3,4), b = gl(4,1,12))# balanced 2-way options("contrasts") # the default: "contr.treatment" sparse.model.matrix(~ a + b, dd) sparse.model.matrix(~ -1+ a + b, dd)# no intercept --> even sparser sparse.model.matrix(~ a + b, dd, contrasts = list(a="contr.sum")) sparse.model.matrix(~ a + b, dd, contrasts = list(b="contr.SAS")) ## Sparse method is equivalent to the traditional one : stopifnot(all(sparse.model.matrix(~ a + b, dd) == Matrix(model.matrix(~ a + b, dd), sparse=TRUE)), all(sparse.model.matrix(~ 0+ a + b, dd) == Matrix(model.matrix(~ 0+ a + b, dd), sparse=TRUE))) %% many more and tougher examples ---> ../tests/spModel.matrix.R (ff <- gl(3,4,, c("X","Y", "Z"))) fac2sparse(ff) # 3 x 12 sparse Matrix of class "dgCMatrix" ## ## X 1 1 1 1 . . . . . . . . ## Y . . . . 1 1 1 1 . . . . ## Z . . . . . . . . 1 1 1 1 ## can also be computed via sparse.model.matrix(): f30 <- gl(3,0 ) f12 <- gl(3,0, 12) stopifnot( all.equal(t( fac2sparse(ff) ), sparse.model.matrix(~ 0+ff), tolerance = 0, check.attributes=FALSE), is(M <- fac2sparse(f30, drop= TRUE),"CsparseMatrix"), dim(M) == c(0, 0), is(M <- fac2sparse(f30, drop=FALSE),"CsparseMatrix"), dim(M) == c(3, 0), is(M <- fac2sparse(f12, drop= TRUE),"CsparseMatrix"), dim(M) == c(0,12), is(M <- fac2sparse(f12, drop=FALSE),"CsparseMatrix"), dim(M) == c(3,12) ) } \keyword{models} Matrix/man/expand.Rd0000644000175100001440000000166711763577200014077 0ustar hornikusers\name{expand} \title{Expand a Decomposition into Factors} \usage{ expand(x, \dots) } \alias{expand} \description{ Expands decompositions stored in compact form into factors. } \arguments{ \item{x}{a matrix decomposition.} \item{\dots}{further arguments passed to or from other methods.} } \value{ The expanded decomposition, typically a list of matrix factors. } \details{ This is a generic function with special methods for different types of decompositions, see \code{\link{showMethods}(expand)} to list them all. } \note{ Factors for decompositions such as \code{lu} and \code{qr} can be stored in a compact form. The function \code{expand} allows all factors to be fully expanded. } \seealso{ The LU \code{\link{lu}}, and the \code{\link{Cholesky}} decompositions which have \code{expand} methods; \code{\link{facmul}}. } \examples{ (x <- Matrix(round(rnorm(9),2), 3, 3)) (ex <- expand(lux <- lu(x))) } \keyword{algebra} Matrix/man/KhatriRao.Rd0000644000175100001440000000537112210462526014470 0ustar hornikusers\name{KhatriRao} \title{Khatri-Rao Matrix Product} \alias{KhatriRao} \description{ Computes Khatri-Rao products for any kind of matrices. The Khatri-Rao product is a column-wise Kronecker product. Originally introduced by Khatri and Rao (1968), it has many different applications, see Liu and Trenkler (2008) for a survey. Notably, it is used in higher-dimensional tensor decompositions, see Bader and Kolda (2008). } \usage{ KhatriRao(X, Y = X, FUN = "*", make.dimnames = FALSE) } \arguments{ \item{X,Y}{matrices of with the same number of columns.} \item{FUN}{the (name of the) \code{\link{function}} to be used for the column-wise Kronecker products, see \code{\link{kronecker}}, defaulting to the usual multiplication.} \item{make.dimnames}{logical indicating if the result should inherit \code{\link{dimnames}} from \code{X} and \code{Y} in a simple way.} } %\details{ %} \value{ a \code{"\linkS4class{CsparseMatrix}"}, say \code{R}, the Khatri-Rao product of \code{X} (\eqn{n \times k}{n x k}) and \code{Y} (\eqn{m \times k}{m x k}), is of dimension \eqn{(n\cdot m) \times k}{(n*m) x k}, where the j-th column, \code{R[,j]} is the kronecker product \code{\link{kronecker}(X[,j], Y[,j])}. } \note{%% TODO? Could make it generic, and have dense and sparse methods The current implementation is efficient for large sparse matrices. } \references{ Khatri, C. G., and Rao, C. Radhakrishna (1968) Solutions to Some Functional Equations and Their Applications to Characterization of Probability Distributions. \emph{Sankhya: Indian J. Statistics, Series A} \bold{30}, 167--180. Liu, Shuangzhe, and G\enc{õ}{oe}tz Trenkler (2008) Hadamard, Khatri-Rao, Kronecker and Other Matrix Products. \emph{International J. Information and Systems Sciences} \bold{4}, 160--177. Bader, Brett W, and Tamara G Kolda (2008) Efficient MATLAB Computations with Sparse and Factored Tensors. \emph{SIAM J. Scientific Computing} \bold{30}, 205--231. } \author{ Michael Cysouw, Univ. Marburg; minor tweaks by Martin Maechler. } \seealso{ \code{\link{kronecker}}. } \examples{ ## Example with very small matrices: m <- matrix(1:12,3,4) d <- diag(1:4) KhatriRao(m,d) KhatriRao(d,m) dimnames(m) <- list(LETTERS[1:3], letters[1:4]) KhatriRao(m,d, make.dimnames=TRUE) KhatriRao(d,m, make.dimnames=TRUE) dimnames(d) <- list(NULL, paste0("D", 1:4)) KhatriRao(m,d, make.dimnames=TRUE) KhatriRao(d,m, make.dimnames=TRUE) dimnames(d) <- list(paste0("d", 10*1:4), paste0("D", 1:4)) KhatriRao(m,d, make.dimnames=TRUE) KhatriRao(d,m, make.dimnames=TRUE) nm <- as(m,"nMatrix") nd <- as(d,"nMatrix") KhatriRao(nm,nd, make.dimnames=TRUE) KhatriRao(nd,nm, make.dimnames=TRUE) stopifnot(dim(KhatriRao(m,d)) == c(nrow(m)*nrow(d), ncol(d))) } \keyword{methods} \keyword{array} Matrix/man/expm.Rd0000644000175100001440000000431312271746775013572 0ustar hornikusers\name{expm} \title{Matrix Exponential} \alias{expm} \alias{expm,Matrix-method} \alias{expm,dMatrix-method} \alias{expm,dgeMatrix-method} \alias{expm,triangularMatrix-method} \alias{expm,symmetricMatrix-method} \alias{expm,ddiMatrix-method} \alias{expm,matrix-method}% < for now \description{ Compute the exponential of a matrix. } \usage{ expm(x) } \arguments{ \item{x}{a matrix, typically inheriting from the \code{\linkS4class{dMatrix}} class.} } \details{ The exponential of a matrix is defined as the infinite Taylor series \code{expm(A) = I + A + A^2/2! + A^3/3! + ...} (although this is definitely not the way to compute it). The method for the \code{dgeMatrix} class uses Ward's diagonal Pade' approximation with three step preconditioning. %% which used to be the state-of-the-art of the original %% Moler & Van Loan (1978) "Nineteen dubious ..." } \value{ The matrix exponential of \code{x}. } \references{ \url{http://en.wikipedia.org/wiki/Matrix_exponential} Cleve Moler and Charles Van Loan (2003) Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. \emph{SIAM Review} \bold{45}, 1, 3--49. %% MM: Till we have something better, this is quite good: Eric W. Weisstein et al. (1999) \emph{Matrix Exponential}. From MathWorld, \url{http://mathworld.wolfram.com/MatrixExponential.html} } \author{This is a translation of the implementation of the corresponding Octave function contributed to the Octave project by A. Scottedward Hodel \email{A.S.Hodel@Eng.Auburn.EDU}. A bug in there has been fixed by Martin Maechler. } %\note{} \seealso{\code{\link{Schur}}; additionally, \code{\link[expm]{expm}}, \code{\link[expm]{logm}}, etc in package \pkg{expm}. } \note{The \pkg{expm} package contains newer (partly faster and more accurate) algorithms for \code{expm()} and includes \code{\link[expm]{logm}} and \code{\link[expm]{sqrtm}}. } \examples{ (m1 <- Matrix(c(1,0,1,1), nc = 2)) (e1 <- expm(m1)) ; e <- exp(1) stopifnot(all.equal(e1@x, c(e,0,e,e), tolerance = 1e-15)) (m2 <- Matrix(c(-49, -64, 24, 31), nc = 2)) (e2 <- expm(m2)) (m3 <- Matrix(cbind(0,rbind(6*diag(3),0))))# sparse! (e3 <- expm(m3)) # upper triangular } \keyword{algebra} \keyword{math} Matrix/man/denseMatrix-class.Rd0000644000175100001440000000343611717530545016202 0ustar hornikusers\name{denseMatrix-class} \docType{class} \title{Virtual Class "denseMatrix" of All Dense Matrices} \alias{denseMatrix-class} %% Group methods \alias{Math,denseMatrix-method} \alias{-,denseMatrix,missing-method} % \alias{show,denseMatrix-method} \alias{coerce,ANY,denseMatrix-method} \alias{coerce,denseMatrix,CsparseMatrix-method} \alias{coerce,denseMatrix,TsparseMatrix-method} \alias{coerce,denseMatrix,generalMatrix-method} \alias{coerce,denseMatrix,sparseMatrix-method} \alias{cbind2,denseMatrix,denseMatrix-method} \alias{cbind2,denseMatrix,matrix-method} \alias{cbind2,matrix,denseMatrix-method} \alias{cbind2,denseMatrix,numeric-method} \alias{cbind2,numeric,denseMatrix-method} \alias{rbind2,denseMatrix,denseMatrix-method} \alias{rbind2,denseMatrix,matrix-method} \alias{rbind2,matrix,denseMatrix-method} \alias{rbind2,denseMatrix,numeric-method} \alias{rbind2,numeric,denseMatrix-method} \alias{dim<-,denseMatrix-method} \alias{rcond,denseMatrix,character-method} % \description{This is the virtual class of all dense (S4) matrices. It is the direct superclass of \code{\linkS4class{ddenseMatrix}}, \code{\linkS4class{ldenseMatrix}} } \section{Extends}{ class \code{"Matrix"} directly. } \section{Slots}{ exactly those of its superclass \code{"\linkS4class{Matrix}"}. } % \section{Methods}{ Use \code{\link{showMethods}(class = "denseMatrix", where = "package:Matrix")} for an overview of methods. Extraction (\code{"["}) methods, see \code{\link{[-methods}}.%-> ./Xtrct-methods.Rd } \seealso{ \code{\link{colSums}}, \code{\link{kronecker}}, and other such methods with own help pages. Its superclass \code{\linkS4class{Matrix}}, and main subclasses, \code{\linkS4class{ddenseMatrix}} and \code{\linkS4class{sparseMatrix}}. } \examples{ showClass("denseMatrix") } \keyword{classes} Matrix/man/diagU2N.Rd0000644000175100001440000000450112001034107014013 0ustar hornikusers\name{diagU2N} \title{Transform Triangular Matrices from Unit Triangular to General and back} \alias{diagN2U} \alias{diagU2N} \alias{.diagU2N} \description{ Transform a triangular matrix \code{x}, i.e., of \code{\link{class}} \code{"\linkS4class{triangularMatrix}"}, from (internally!) unit triangular (\dQuote{unitriangular}) to \dQuote{general} (\code{diagU2N(x)}) or back (\code{diagN2U(x)}). Note that the latter, \code{diagN2U(x)}, also sets the diagonal to one in cases where \code{diag(x)} was not all one. \code{.diagU2N(x)} assumes but does \emph{not} check that \code{x} is a \code{\linkS4class{triangularMatrix}} with \code{diag} slot \code{"U"}, and should hence be used with care. } \usage{ diagN2U(x, cl = getClassDef(class(x)), checkDense = FALSE) diagU2N(x, cl = getClassDef(class(x)), checkDense = FALSE) .diagU2N(x, cl, checkDense = FALSE) } \arguments{ \item{x}{a \code{\linkS4class{triangularMatrix}}, often sparse.} \item{cl}{(optional, for speedup only:) class (definition) of \code{x}.} \item{checkDense}{logical indicating if dense (see \code{\linkS4class{denseMatrix}}) matrices should be considered at all; i.e., when false, as per default, the result will be sparse even when \code{x} is dense.} } \details{ The concept of unit triangular matrices with a \code{diag} slot of \code{"U"} stems from LAPACK. } \note{Such internal storage details should rarely be of relevance to the user. Hence, these functions really are rather \emph{internal} utilities. } \value{ a triangular matrix of the same \code{\link{class}} and (semantically) with identical entries as \code{x}, but with a different \code{diag} slot. } \seealso{ \code{"\linkS4class{triangularMatrix}"}, \code{"\linkS4class{dtCMatrix}"}. } \examples{ (T <- Diagonal(7) + triu(Matrix(rpois(49, 1/4), 7,7), k = 1)) (uT <- diagN2U(T)) # "unitriangular" (t.u <- diagN2U(10*T))# changes the diagonal! stopifnot(all(T == uT), diag(t.u) == 1, identical(T, diagU2N(uT))) T[upper.tri(T)] <- 5 T <- diagN2U(as(T,"triangularMatrix")) stopifnot(T@diag == "U") dT <- as(T, "denseMatrix") dt. <- diagN2U(dT) dtU <- diagN2U(dT, checkDense=TRUE) stopifnot(is(dtU, "denseMatrix"), is(dt., "sparseMatrix"), all(dT == dt.), all(dT == dtU), dt.@diag == "U", dtU@diag == "U") } \keyword{utilities} \keyword{classes} Matrix/man/USCounties.Rd0000644000175100001440000000402512164774464014657 0ustar hornikusers\name{USCounties} \alias{USCounties} \docType{data} \title{USCounties Contiguity Matrix} \description{ This matrix represents the contiguities of 3111 US counties using the Queen criterion of at least a single shared boundary point. The representation is as a row standardised spatial weights matrix transformed to a symmetric matrix (see Ord (1975), p. 125). } \usage{data(USCounties)} \format{ A \eqn{3111 ^2} symmetric sparse matrix of class \code{\linkS4class{dsCMatrix}} with 9101 non-zero entries. } \details{ The data were read into \R using \code{\link[spdep]{read.gal}}, and row-standardised and transformed to symmetry using \code{\link[spdep]{nb2listw}} and \code{\link[spdep]{similar.listw}}. This spatial weights object was converted to class \code{\linkS4class{dsCMatrix}} using \code{\link[spdep]{as_dsTMatrix_listw}} and coercion. } \source{ The data were retrieved from \url{http://sal.uiuc.edu/weights/zips/usc.zip}, files \dQuote{usc.txt} and \dQuote{usc\_q.GAL}, with permission for use and distribution from Luc Anselin. } \references{ Ord, J. K. (1975) Estimation methods for models of spatial interaction; \emph{Journal of the American Statistical Association} \bold{70}, 120--126. } \examples{ data(USCounties) (n <- ncol(USCounties)) IM <- .symDiagonal(n) nn <- 50 set.seed(1) rho <- runif(nn, 0, 1) system.time(MJ <- sapply(rho, function(x) determinant(IM - x * USCounties, logarithm = TRUE)$modulus)) nWC <- -USCounties C1 <- Cholesky(nWC, Imult = 2) system.time(MJ1 <- n * log(rho) + sapply(rho, function(x) c(determinant(update(C1, nWC, 1/x))$modulus))) all.equal(MJ, MJ1) C2 <- Cholesky(nWC, super = TRUE, Imult = 2) system.time(MJ2 <- n * log(rho) + sapply(rho, function(x) c(determinant(update(C2, nWC, 1/x))$modulus))) all.equal(MJ, MJ2) system.time(MJ3 <- n * log(rho) + Matrix:::ldetL2up(C1, nWC, 1/rho)) all.equal(MJ, MJ3) system.time(MJ4 <- n * log(rho) + Matrix:::ldetL2up(C2, nWC, 1/rho)) all.equal(MJ, MJ4) } \keyword{datasets} Matrix/man/spMatrix.Rd0000644000175100001440000000526611245765545014434 0ustar hornikusers\name{spMatrix} \alias{spMatrix} \title{Sparse Matrix Constructor From Triplet} \description{ User friendly construction of a sparse matrix (inheriting from class \code{\linkS4class{TsparseMatrix}}) from the triplet representation. } \usage{ spMatrix(nrow, ncol, i = integer(), j = integer(), x = numeric()) } \arguments{ \item{nrow, ncol}{integers specifying the desired number of rows and columns.} \item{i,j}{integer vectors of the same length specifying the locations of the non-zero (or non-\code{TRUE}) entries of the matrix.} \item{x}{atomic vector of the same length as \code{i} and \code{j}, specifying the values of the non-zero entries.} } \value{ A sparse matrix in triplet form, as an \R object inheriting from both \code{\linkS4class{TsparseMatrix}} and \code{\linkS4class{generalMatrix}}. The matrix \eqn{M} will have \code{M[i[k], j[k]] == x[k]}, for \eqn{k = 1,2,\ldots, n}, where \code{n = length(i)} and \code{M[ i', j' ] == 0} for all other pairs \eqn{(i',j')}. } \seealso{\code{\link{Matrix}(*, sparse=TRUE)} for the more usual constructor of such matrices; similarly, \code{\link{sparseMatrix}} which is a bit more general than \code{spMatrix()} and returns a \code{\linkS4class{CsparseMatrix}} which is often slightly more desirable. Further, \code{\link{bdiag}} and \code{\link{Diagonal}} for (block-)diagonal matrix constructors. Consider \code{\linkS4class{TsparseMatrix}} and similar class definition help files. } \examples{ ## simple example A <- spMatrix(10,20, i = c(1,3:8), j = c(2,9,6:10), x = 7 * (1:7)) A # a "dgTMatrix" summary(A) str(A) # note that *internally* 0-based indices (i,j) are used L <- spMatrix(9, 30, i = rep(1:9, 3), 1:27, (1:27) \%\% 4 != 1) L # an "lgTMatrix" ### This is a useful utility, to be used for experiments : rSpMatrix <- function(nrow, ncol, nnz, rand.x = function(n) round(rnorm(nnz), 2)) { ## Purpose: random sparse matrix ## -------------------------------------------------------------- ## Arguments: (nrow,ncol): dimension ## nnz : number of non-zero entries ## rand.x: random number generator for 'x' slot ## -------------------------------------------------------------- ## Author: Martin Maechler, Date: 14.-16. May 2007 stopifnot((nnz <- as.integer(nnz)) >= 0, nrow >= 0, ncol >= 0, nnz <= nrow * ncol) spMatrix(nrow, ncol, i = sample(nrow, nnz, replace = TRUE), j = sample(ncol, nnz, replace = TRUE), x = rand.x(nnz)) } M1 <- rSpMatrix(100000, 20, nnz = 200) summary(M1) } \keyword{array} Matrix/man/printSpMatrix.Rd0000644000175100001440000001331111530442451015420 0ustar hornikusers\name{printSpMatrix} \alias{formatSpMatrix} \alias{printSpMatrix} \alias{printSpMatrix2} \title{Format and Print Sparse Matrices Flexibly} \description{ Format and print sparse matrices flexibly. These are the \dQuote{workhorses} used by the \code{\link{format}}, \code{\link{show}} and \code{\link{print}} methods for sparse matrices. If \code{x} is large, \code{printSpMatrix2(x)} calls \code{printSpMatrix()} twice, namely, for the first and the last few rows, suppressing those in between, and also suppresses columns when \code{x} is too wide. \code{printSpMatrix()} basically prints the result of \code{formatSpMatrix()}. } \usage{ formatSpMatrix(x, digits = NULL, maxp = 1e9, cld = getClassDef(class(x)), zero.print = ".", col.names, note.dropping.colnames = TRUE, align = c("fancy", "right")) printSpMatrix(x, digits = NULL, maxp = getOption("max.print"), cld = getClassDef(class(x)), zero.print = ".", col.names, note.dropping.colnames = TRUE, col.trailer = "", align = c("fancy", "right")) printSpMatrix2(x, digits = NULL, maxp = getOption("max.print"), zero.print = ".", col.names, note.dropping.colnames = TRUE, suppRows = NULL, suppCols = NULL, col.trailer = if(suppCols) "......" else "", align = c("fancy", "right")) } \arguments{ \item{x}{an \R object inheriting from class \code{\linkS4class{sparseMatrix}}.} \item{digits}{significant digits to use for printing, see \code{\link{print.default}}, the default, \code{\link{NULL}}, corresponds to using \code{\link{getOption}("digits")}.} \item{maxp}{integer, default from \code{\link{options}(max.print)}, influences how many entries of large matrices are printed at all.} \item{cld}{the class definition of \code{x}; must be equivalent to \code{\link{getClassDef}(class(x))} and exists mainly for possible speedup.} \item{zero.print}{character which should be printed for \emph{structural} zeroes. The default \code{"."} may occasionally be replaced by \code{" "} (blank); using \code{"0"} would look almost like \code{print()}ing of non-sparse matrices.} \item{col.names}{logical or string specifying if and how column names of \code{x} should be printed, possibly abbreviated. The default is taken from \code{\link{options}("sparse.colnames")} if that is set, otherwise \code{FALSE} unless there are less than ten columns. When \code{TRUE} the full column names are printed.\cr When \code{col.names} is a string beginning with \code{"abb"} or \code{"sub"} and ending with an integer \code{n} (i.e., of the form \code{"abb... "}), the column names are \code{\link{abbreviate}()}d or \code{\link{substring}()}ed to (target) length \code{n}, see the examples. } \item{note.dropping.colnames}{logical specifying, when \code{col.names} is \code{FALSE} if the dropping of the column names should be noted, \code{TRUE} by default.} \item{col.trailer}{a string to be appended to the right of each column; this is typically made use of by \code{\link{show}()} only, when suppressing columns.} \item{suppRows, suppCols}{logicals or \code{NULL}, for \code{printSpMatrix2()} specifying if rows or columns should be suppressed in printing. If \code{NULL}, sensible defaults are determined from \code{\link{dim}(x)} and \code{\link{options}(c("width", "max.print"))}. Setting both to \code{FALSE} may be a very bad idea.} \item{align}{a string specifying how the \code{zero.print} codes should be aligned, i.e., padded as strings. The default, \code{"fancy"}, takes some effort to align the typical \code{zero.print = "."} with the position of \code{0}, i.e., the first decimal (one left of decimal point) of the numbers printed, whereas \code{align = "right"} just makes use of \code{\link{print}(*, right = TRUE)}. } } \details{ \describe{ \item{formatSpMatrix:}{ If \code{x} is large, only the first rows making up the approximately first \code{maxp} entries is used, otherwise all of \code{x}. \code{\link{.formatSparseSimple}()} is applied to (a dense version of) the matrix. Then, \code{\link{formatSparseM}} is used, unless in trivial cases or for sparse matrices without \code{x} slot.} } } \value{ \item{formatSpMatrix()}{returns a character matrix with possibly empty column names, depending on \code{col.names} etc, see above.} \item{printSpMatrix*()}{return \code{x} \emph{invisibly}, see \code{\link{invisible}}.} } \author{Martin Maechler} \seealso{the virtual class \code{\linkS4class{sparseMatrix}} and the classes extending it; maybe \code{\link{sparseMatrix}} or \code{\link{spMatrix}} as simple constructors of such matrices. The underlying utilities \code{\link{formatSparseM}} and \code{.formatSparseSimple()} (on the same page). } \examples{ f1 <- gl(5, 3, labels = LETTERS[1:5]) X <- as(f1, "sparseMatrix") X ## <==> show(X) <==> print(X) t(X) ## shows column names, since only 5 columns X2 <- as(gl(12, 3, labels = paste(LETTERS[1:12],"c",sep=".")), "sparseMatrix") X2 ## less nice, but possible: print(X2, col.names = TRUE) # use [,1] [,2] .. => does not fit t(X2) # suppressing column names print(t(X2), col.names=TRUE) print(t(X2), zero.print = "", col.names="abbr. 1") print(t(X2), zero.print = "-", col.names="substring 2") \dontshow{% show() was slow in 0.9975-8 because of slow adjust="fancy" op <- options(max.print = 25000, width = 80) sink(print(tempfile())) M <- Matrix(0, 10000, 100) M[1,1] <- M[2,3] <- 3.14 stopifnot((st <- system.time(show(M)))[1] < 1.0) # only 0.09 on cmath-3 sink() st options(op) } } \keyword{print} Matrix/man/drop0.Rd0000644000175100001440000000404412210462526013624 0ustar hornikusers\name{drop0} \alias{drop0} \title{Drop "Explicit Zeroes" from a Sparse Matrix} \description{ Returns a sparse matrix with no \dQuote{explicit zeroes}, i.e., all zero or \code{FALSE} entries are dropped from the explicitly indexed matrix entries. } \usage{ drop0(x, tol = 0, is.Csparse = NA) } \arguments{ \item{x}{a Matrix, typically sparse, i.e., inheriting from \code{\linkS4class{sparseMatrix}}.} % \item{clx}{[optional:] the \code{\link{class}} or \dQuote{class % definition} (see \code{\link{getClassDef}}; it is of class % \code{\linkS4class{classRepresentation}}) of \code{x}.\cr % This argument just exists for the possibility of speedup.} \item{tol}{non-negative number to be used as tolerance for checking if an entry \eqn{x_{i,j}}{x[i,j]} should be considered to be zero.} \item{is.Csparse}{logical indicating prior knowledge about the \dQuote{Csparseness} of \code{x}. This exists for possible speedup reasons only.} } % \details{ % ~~ If necessary, more details than the description above ~~ % } \value{ a Matrix like \code{x} but with no explicit zeros, i.e., \code{!any(x@x == 0)}, always inheriting from \code{\linkS4class{CsparseMatrix}}. } % \author{Martin} \note{When a sparse matrix is the result of matrix multiplications, you may want to consider combining \code{drop0()} with \code{\link{zapsmall}()}, see the example. } \seealso{\code{\link{spMatrix}}, class \code{\linkS4class{sparseMatrix}} } \examples{ m <- spMatrix(10,20, i= 1:8, j=2:9, x = c(0:2,3:-1)) m drop0(m) ## A larger example: t5 <- new("dtCMatrix", Dim = c(5L, 5L), uplo = "L", x = c(10, 1, 3, 10, 1, 10, 1, 10, 10), i = c(0L,2L,4L, 1L, 3L,2L,4L, 3L, 4L), p = c(0L, 3L, 5L, 7:9)) TT <- kronecker(t5, kronecker(kronecker(t5,t5), t5)) IT <- solve(TT) I. <- TT \%*\% IT ; nnzero(I.) # 697 ( = 625 + 72 ) I.0 <- drop0(zapsmall(I.)) ## which actually can be more efficiently achieved by I.. <- drop0(I., tol = 1e-15) stopifnot(all(I.0 == Diagonal(625)), nnzero(I..) == 625) } \keyword{utilities} \keyword{array} Matrix/man/Cholesky-class.Rd0000644000175100001440000001044012271746775015503 0ustar hornikusers\name{Cholesky-class} \docType{class} \alias{Cholesky-class} \alias{pCholesky-class} \alias{BunchKaufman-class} \alias{pBunchKaufman-class} % \alias{coerce,pCholesky,lMatrix-method} \alias{coerce,pBunchKaufman,lMatrix-method} \alias{coerce,Cholesky,lMatrix-method} \alias{coerce,BunchKaufman,lMatrix-method} \alias{show,BunchKaufman-method} \alias{show,pBunchKaufman-method} % \title{Cholesky and Bunch-Kaufman Decompositions} \description{The \code{"Cholesky"} class is the class of Cholesky decompositions of positive-semidefinite, real dense matrices. The \code{"BunchKaufman"} class is the class of Bunch-Kaufman decompositions of symmetric, real matrices. The \code{"pCholesky"} and \code{"pBunchKaufman"} classes are their \emph{\bold{p}acked} storage versions. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("Cholesky", ...)} or \code{new("BunchKaufman", ...)}, etc, or rather by calls of the form \code{\link{chol}(pm)} or \code{\link{BunchKaufman}(pm)} where \code{pm} inherits from the \code{"\linkS4class{dpoMatrix}"} or \code{"\linkS4class{dsyMatrix}"} class or as a side-effect of other functions applied to \code{"dpoMatrix"} objects (see \code{\linkS4class{dpoMatrix}}). } \note{ \enumerate{ \item Objects of class \code{"Cholesky"} typically stem from \code{\link{chol}(D)}, applied to a \emph{dense} matrix \code{D}. On the other hand, the \emph{function} \code{\link{Cholesky}(S)} applies to a \emph{sparse} matrix \code{S}, and results in objects inheriting from class \code{\linkS4class{CHMfactor}}. \item For traditional matrices \code{m}, \code{chol(m)} is a traditional matrix as well, triangular, but simply an \eqn{n\times n}{n * n} numeric \code{\link{matrix}}. Hence, for compatibility, the \code{"Cholesky"} and \code{"BunchKaufman"} classes (and their \code{"p*"} packed versions) also extend triangular Matrix classes (such as "dtrMatrix"). Consequently, \code{\link{determinant}(R)} for \code{R <- chol(A)} returns the determinant of \code{R}, not of \code{A}. This is in contrast to class \code{\linkS4class{CHMfactor}} objects \code{C}, where \code{determinant(C)} gives the determinant of the \emph{original} matrix \code{A}, for \code{C <- Cholesky(A)}, see also the \code{determinant} method documentation on the class \code{\linkS4class{CHMfactor}} page. } } \section{Slots}{ A Cholesky decomposition extends class \code{\linkS4class{MatrixFactorization}} but is basically a triangular matrix extending the \code{"\linkS4class{dtrMatrix}"} class. \describe{ \item{\code{uplo}:}{inherited from the \code{"dtrMatrix"} class.} \item{\code{diag}:}{inherited from the \code{"dtrMatrix"} class.} \item{\code{x}:}{inherited from the \code{"dtrMatrix"} class.} \item{\code{Dim}:}{inherited from the \code{"dtrMatrix"} class.} \item{\code{Dimnames}:}{inherited from the \code{"dtrMatrix"} class.} } A Bunch-Kaufman decomposition also extends the \code{"dtrMatrix"} class and has a \code{perm} slot representing a permutation matrix. The packed versions extend the \code{"dtpMatrix"} class. } \section{Extends}{ Class \code{"MatrixFactorization"} and \code{"dtrMatrix"}, directly. Class \code{"dgeMatrix"}, by class \code{"dtrMatrix"}. Class \code{"Matrix"}, by class \code{"dtrMatrix"}. } \section{Methods}{ Both these factorizations can \emph{directly} be treated as (triangular) matrices, as they extend \code{"dtrMatrix"}, see above. There are currently no further explicit methods defined with class \code{"Cholesky"} or \code{"BunchKaufman"} in the signature. } \seealso{ Classes \code{\linkS4class{dtrMatrix}}, \code{\linkS4class{dpoMatrix}}; function \code{\link{chol}}. Function \code{\link{Cholesky}} resulting in class \code{\linkS4class{CHMfactor}} objects, \emph{not} class "Cholesky" ones, see the section \sQuote{Note}. } \examples{ (sm <- as(as(Matrix(diag(5) + 1), "dsyMatrix"), "dspMatrix")) signif(csm <- chol(sm), 4) (pm <- crossprod(Matrix(rnorm(18), nrow = 6, ncol = 3))) (ch <- chol(pm)) if (toupper(ch@uplo) == "U") # which is TRUE crossprod(ch) stopifnot(all.equal(as(crossprod(ch), "matrix"), as(pm, "matrix"), tolerance=1e-14)) } \keyword{classes} \keyword{algebra} Matrix/man/dgRMatrix-class.Rd0000644000175100001440000000424411705754605015620 0ustar hornikusers\name{dgRMatrix-class} \docType{class} \title{Sparse Compressed, Row-oriented Numeric Matrices} \alias{dgRMatrix-class} % all alias{coerce,...} are currently in ./RsparseMatrix-class.Rd \alias{diag,dgRMatrix-method} \alias{dim,dgRMatrix-method} \alias{t,dgRMatrix-method} \description{The \code{dgRMatrix} class is a class of sparse numeric matrices in the compressed, sparse, row-oriented format. In this implementation the non-zero elements in the rows are sorted into increasing column order. \bold{Note:} The column-oriented sparse classes, e.g., \code{\linkS4class{dgCMatrix}}, are preferred and better supported in the \pkg{Matrix} package. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("dgRMatrix", ...)}. } \section{Slots}{ \describe{ \item{\code{j}:}{Object of class \code{"integer"} of length nnzero (number of non-zero elements). These are the column numbers for each non-zero element in the matrix.} \item{\code{p}:}{Object of class \code{"integer"} of pointers, one for each row, to the initial (zero-based) index of elements in the row.} \item{\code{x}:}{Object of class \code{"numeric"} - the non-zero elements of the matrix.} \item{\code{Dim}:}{Object of class \code{"integer"} - the dimensions of the matrix.} } } \section{Methods}{ \describe{ \item{coerce}{\code{signature(from = "matrix", to = "dgRMatrix")}} \item{coerce}{\code{signature(from = "dgRMatrix", to = "matrix")}} \item{coerce}{\code{signature(from = "dgRMatrix", to = "dgTMatrix")}} \item{diag}{\code{signature(x = "dgRMatrix")}: returns the diagonal of \code{x}} \item{dim}{\code{signature(x = "dgRMatrix")}: returns the dimensions of \code{x}} \item{image}{\code{signature(x = "dgRMatrix")}: plots an image of \code{x} using the \code{\link[lattice]{levelplot}} function} } } \seealso{ the \code{\linkS4class{RsparseMatrix}} class, the virtual class of all sparse compressed \bold{r}ow-oriented matrices, with its methods. The \code{\linkS4class{dgCMatrix}} class (\bold{c}olumn compressed sparse) is really preferred. } \keyword{classes} \keyword{algebra} Matrix/man/unpack.Rd0000644000175100001440000000515311773633512014073 0ustar hornikusers\name{unpack} \title{Representation of Packed and Unpacked (Dense) Matrices} \usage{ pack(x, \dots) \S4method{pack}{matrix}(x, symmetric = NA, upperTri = NA, \dots) unpack(x, \dots) } \alias{pack} \alias{pack,symmetricMatrix-method} \alias{pack,triangularMatrix-method} \alias{pack,matrix-method} \alias{pack,sparseMatrix-method} \alias{unpack} \alias{unpack,dtpMatrix-method} \alias{unpack,dspMatrix-method} \alias{unpack,symmetricMatrix-method} \alias{unpack,triangularMatrix-method} \alias{unpack,sparseMatrix-method} \description{ \dQuote{Packed} matrix storage here applies to dense matrices (\code{\linkS4class{denseMatrix}}) only, and there is available only for symmetric (\code{\linkS4class{symmetricMatrix}}) or triangular (\code{\linkS4class{triangularMatrix}}) matrices, where only one triangle of the matrix needs to be stored. \code{unpack()} unpacks \dQuote{packed} matrices, where \cr \code{pack()} produces \dQuote{packed} matrices. } \arguments{ \item{x}{ \describe{ \item{for \code{unpack()}:}{a matrix stored in packed form, e.g., of class \code{"d?pMatrix"} where "?" is "t" for triangular or "s" for symmetric.} \item{for \code{pack()}:}{a (symmetric or triangular) matrix stored in full storage.} } } \item{symmetric}{logical (including \code{NA}) for optionally specifying if \code{x} is symmetric (or rather triangular).} \item{upperTri}{(for the triangular case only) logical (incl. \code{NA}) indicating if \code{x} is upper (or lower) triangular.} \item{\dots}{further arguments passed to or from other methods.} } \value{ \describe{ \item{for \code{unpack()}:}{A \code{\linkS4class{Matrix}} object containing the full-storage representation of \code{x}.} \item{for \code{pack()}:}{ A packed \code{Matrix} (i.e. of class \code{"..pMatrix"}) representation of \code{x}.} } } \details{ These are generic functions with special methods for different types of packed (or non-packed) symmetric or triangular dense matrices. Use \code{\link{showMethods}("unpack")} to list the methods for \code{unpack()}, and similarly for \code{pack()}. } \examples{ showMethods("unpack") (cp4 <- chol(Hilbert(4))) # is triangular tp4 <- as(cp4,"dtpMatrix")# [t]riangular [p]acked str(tp4) (unpack(tp4)) stopifnot(identical(tp4, pack(unpack(tp4)))) (s <- crossprod(matrix(sample(15), 5,3))) # traditional symmetric matrix (sp <- pack(s)) mt <- as.matrix(tt <- tril(s)) (pt <- pack(mt)) stopifnot(identical(pt, pack(tt)), dim(s ) == dim(sp), all(s == sp), dim(mt) == dim(pt), all(mt == pt), all(mt == tt)) showMethods("pack") } \keyword{array} \keyword{algebra} Matrix/man/dsRMatrix-class.Rd0000644000175100001440000000541410757763005015634 0ustar hornikusers\name{dsRMatrix-class} \title{Symmetric Sparse Compressed Row Matrices} \docType{class} \alias{dsRMatrix-class} % \description{The \code{dsRMatrix} class is a class of symmetric, sparse matrices in the compressed, row-oriented format. In this implementation the non-zero elements in the rows are sorted into increasing column order. } \section{Objects from the Class}{ These \code{"..RMatrix"} classes are currently still mostly unimplemented! Objects can be created by calls of the form \code{new("dsRMatrix", ...)}. } \section{Slots}{ \describe{ \item{\code{uplo}:}{A character object indicating if the upper triangle (\code{"U"}) or the lower triangle (\code{"L"}) is stored. At present only the lower triangle form is allowed.} \item{\code{j}:}{Object of class \code{"integer"} of length \code{nnzero} (number of non-zero elements). These are the row numbers for each non-zero element in the matrix.} \item{\code{p}:}{Object of class \code{"integer"} of pointers, one for each row, to the initial (zero-based) index of elements in the row.} \item{\code{factors}:}{Object of class \code{"list"} - a list of factorizations of the matrix.} \item{\code{x}:}{Object of class \code{"numeric"} - the non-zero elements of the matrix.} \item{\code{Dim}:}{Object of class \code{"integer"} - the dimensions of the matrix - must be an integer vector with exactly two non-negative values.} \item{\code{Dimnames}:}{List of length two, see \code{\link{Matrix}}.} } } \section{Extends}{ Classes \code{\linkS4class{RsparseMatrix}}, \code{\linkS4class{dsparseMatrix}} and \code{\linkS4class{symmetricMatrix}}, directly. Class \code{"dMatrix"}, by class \code{"dsparseMatrix"}, class \code{"sparseMatrix"}, by class \code{"dsparseMatrix"} or \code{"RsparseMatrix"}; class \code{"compMatrix"} by class \code{"symmetricMatrix"} and of course, class \code{"Matrix"}. } \section{Methods}{ \describe{ \item{forceSymmetric}{\code{signature(x = "dsRMatrix", uplo = "missing")}: a trivial method just returning \code{x}} \item{forceSymmetric}{\code{signature(x = "dsRMatrix", uplo = "character")}: if \code{uplo == x@uplo}, this trivially returns \code{x}; otherwise \code{t(x)}.} \item{coerce}{\code{signature(from = "dsCMatrix", to = "dsRMatrix")}} } } \seealso{ the classes \code{\linkS4class{dgCMatrix}}, \code{\linkS4class{dgTMatrix}}, and \code{\linkS4class{dgeMatrix}}. } \examples{ (m0 <- new("dsRMatrix")) m2 <- new("dsRMatrix", Dim = c(2L,2L), x = c(3,1), j = c(1L,1L), p = 0:2) m2 stopifnot(colSums(as(m2, "TsparseMatrix")) == 3:4) str(m2) (ds2 <- forceSymmetric(diag(2))) # dsy* dR <- as(ds2, "RsparseMatrix") dR # dsRMatrix } \keyword{classes} \keyword{algebra} Matrix/man/sparseQR-class.Rd0000644000175100001440000001520012271746775015461 0ustar hornikusers\name{sparseQR-class} \docType{class} \title{Sparse QR decomposition of a sparse matrix} \alias{sparseQR-class} \alias{qr.R,sparseQR-method} \alias{qr.Q}% the generic \alias{qr.Q,sparseQR-method} \alias{qr.coef,sparseQR,ddenseMatrix-method} \alias{qr.coef,sparseQR,matrix-method} \alias{qr.coef,sparseQR,Matrix-method} \alias{qr.coef,sparseQR,numeric-method} \alias{qr.fitted,sparseQR,ddenseMatrix-method} \alias{qr.fitted,sparseQR,matrix-method} \alias{qr.fitted,sparseQR,Matrix-method} \alias{qr.fitted,sparseQR,numeric-method} \alias{qr.qty,sparseQR,ddenseMatrix-method} \alias{qr.qty,sparseQR,matrix-method} \alias{qr.qty,sparseQR,numeric-method} \alias{qr.qty,sparseQR,Matrix-method} \alias{qr.qy,sparseQR,ddenseMatrix-method} \alias{qr.qy,sparseQR,matrix-method} \alias{qr.qy,sparseQR,numeric-method} \alias{qr.qy,sparseQR,Matrix-method} \alias{qr.resid,sparseQR,ddenseMatrix-method} \alias{qr.resid,sparseQR,matrix-method} \alias{qr.resid,sparseQR,Matrix-method} \alias{qr.resid,sparseQR,numeric-method} %\alias{solve,sparseQR,ANY-method}--> solve-methods.Rd % \description{Objects class \code{"sparseQR"} represent a QR decomposition of a sparse \eqn{n \times p}{n x p} rectangular matrix \eqn{X}, typically resulting from \code{\link{qr}()} } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("sparseQR", ...)} but are more commonly created by function \code{\link[base]{qr}} applied to a sparse matrix such as a matrix of class \code{\linkS4class{dgCMatrix}}. } \section{Slots}{ \describe{ \item{\code{V}:}{Object of class \code{"dgCMatrix"}. The columns of \code{V} are the vectors that generate the Householder transformations of which the matrix Q is composed.} \item{\code{beta}:}{Object of class \code{"numeric"}, the normalizing factors for the Householder transformations.} \item{\code{p}:}{Object of class \code{"integer"}: Permutation (of \code{0:(n-1)}) applied to the rows of the original matrix.} \item{\code{R}:}{Object of class \code{"dgCMatrix"}: An upper triangular matrix of dimension \ } % << FIXME \item{\code{q}:}{Object of class \code{"integer"}: Permutation applied from the right. Can be of length 0 which implies no permutation.} } } \section{Methods}{ \describe{ \item{qr.R}{\code{signature(qr = "sparseQR")}: compute the upper triangular \eqn{R} matrix of the QR decomposition. Note that this currently warns because of possible permutation mismatch with the classical \code{qr.R()} result, \emph{and} you can suppress these warnings by setting \code{\link{options}()} either \code{"Matrix.quiet.qr.R"} or (the more general) either \code{"Matrix.quiet"} to \code{\link{TRUE}}.} \item{qr.Q}{\code{signature(qr = "sparseQR")}: compute the orthogonal \eqn{Q} matrix of the QR decomposition.} \item{qr.coef}{\code{signature(qr = "sparseQR", y = "ddenseMatrix")}: ... } \item{qr.coef}{\code{signature(qr = "sparseQR", y = "matrix")}: ... } \item{qr.coef}{\code{signature(qr = "sparseQR", y = "numeric")}: ... } \item{qr.fitted}{\code{signature(qr = "sparseQR", y = "ddenseMatrix")}: ... } \item{qr.fitted}{\code{signature(qr = "sparseQR", y = "matrix")}: ... } \item{qr.fitted}{\code{signature(qr = "sparseQR", y = "numeric")}: ... } \item{qr.qty}{\code{signature(qr = "sparseQR", y = "ddenseMatrix")}: ... } \item{qr.qty}{\code{signature(qr = "sparseQR", y = "matrix")}: ... } \item{qr.qty}{\code{signature(qr = "sparseQR", y = "numeric")}: ... } \item{qr.qy}{\code{signature(qr = "sparseQR", y = "ddenseMatrix")}: ... } \item{qr.qy}{\code{signature(qr = "sparseQR", y = "matrix")}: ... } \item{qr.qy}{\code{signature(qr = "sparseQR", y = "numeric")}: ... } \item{qr.resid}{\code{signature(qr = "sparseQR", y = "ddenseMatrix")}: ... } \item{qr.resid}{\code{signature(qr = "sparseQR", y = "matrix")}: ... } \item{qr.resid}{\code{signature(qr = "sparseQR", y = "numeric")}: ... } \item{solve}{\code{signature(a = "sparseQR", b = "ANY")}: For \code{solve(a,b)}, simply uses \code{qr.coef(a,b)}.} } } %\references{} %\author{} \details{ The decomposition is of the form \code{A[p+1,] == Q \%*\% R}, if the \code{q} slot is of length 0 or \code{A[p+1,q+1] == Q \%*\% R} where A is a sparse \eqn{m\times n}{m by n} matrix (\eqn{m\ge n}{m >= n}), \eqn{R} is an \eqn{m\times n}{m by n} matrix that is zero below the main diagonal. The \code{p} slot is a 0-based permutation of \code{1:m} applied to the rows of the original matrix. If the \code{q} slot has length \code{n} it is a 0-based permutation of \code{1:n} applied to the columns of the original matrix to reduce the amount of \dQuote{fill-in} in the matrix \eqn{R}. The matrix \eqn{Q} is a "virtual matrix". It is the product of \eqn{n} Householder transformations. The information to generate these Householder transformations is stored in the \code{V} and \code{beta} slots. The \code{"sparseQR"} methods for the \code{qr.*} functions return objects of class \code{"dgeMatrix"} (see \code{\linkS4class{dgeMatrix}}). Results from \code{qr.coef}, \code{qr.resid} and \code{qr.fitted} (when \code{k == ncol(R)}) are well-defined and should match those from the corresponding dense matrix calculations. However, because the matrix \code{Q} is not uniquely defined, the results of \code{qr.qy} and \code{qr.qty} do not necessarily match those from the corresponding dense matrix calculations. Also, the results of \code{qr.qy} and \code{qr.qty} apply to the permuted column order when the \code{q} slot has length \code{n}. } \seealso{ \code{\link[base]{qr}}, \code{\link{qr.Q}}, \code{\link{qr.R}}, \code{\link{qr.fitted}}, \code{\link{qr.resid}}, \code{\link{qr.coef}}, \code{\link{qr.qty}}, \code{\link{qr.qy}}, \code{\linkS4class{dgCMatrix}}, \code{\linkS4class{dgeMatrix}}. %%% not (yet) in CRAN-released version of Matrix: %% \code{\linkS4class{SPQR}} an alternative QR decomposition resulting %% from \code{\link{spqr}()}. } \examples{ data(KNex) mm <- KNex $ mm y <- KNex $ y y. <- as(as.matrix(y), "dgCMatrix") str(qrm <- qr(mm)) qc <- qr.coef (qrm, y); qc. <- qr.coef (qrm, y.) # 2nd failed in Matrix <= 1.1-0 qf <- qr.fitted(qrm, y); qf. <- qr.fitted(qrm, y.) qs <- qr.resid (qrm, y); qs. <- qr.resid (qrm, y.) stopifnot(all.equal(qc, as.numeric(qc.), tolerance=1e-12), all.equal(qf, as.numeric(qf.), tolerance=1e-12), all.equal(qs, as.numeric(qs.), tolerance=1e-12), all.equal(qf+qs, y, tolerance=1e-12)) %% FIXME: add more similarly to ./lu.Rd, see also ./qr-methods.Rd } \keyword{classes} \keyword{algebra} \keyword{array} Matrix/man/unused-classes.Rd0000644000175100001440000000111611055522413015531 0ustar hornikusers\name{Unused-classes} %% This is just a stub, not yet used really: -- move to own page when used \docType{class} \alias{iMatrix-class} \alias{zMatrix-class} \title{Virtual Classes Not Yet Really Implemented and Used} \description{ \code{iMatrix} is the virtual class of all \bold{i}nteger (S4) matrices. It extends the \code{\linkS4class{Matrix}} class directly. \code{zMatrix} is the virtual class of all \code{\link{complex}} (S4) matrices. It extends the \code{\linkS4class{Matrix}} class directly. } \examples{ showClass("iMatrix") showClass("zMatrix") } \keyword{classes} Matrix/man/dtRMatrix-class-def.Rd0000644000175100001440000000531511004024375016353 0ustar hornikusers\name{dtRMatrix-class} \title{Triangular Sparse Compressed Row Matrices} \docType{class} \alias{dtRMatrix-class} %%--- No methods currently --- see ./dtCMatrix-class.Rd for more \description{The \code{dtRMatrix} class is a class of triangular, sparse matrices in the compressed, row-oriented format. In this implementation the non-zero elements in the rows are sorted into increasing columnd order. } \section{Objects from the Class}{ This class is currently still mostly unimplemented! Objects can be created by calls of the form \code{new("dtRMatrix", ...)}. } \section{Slots}{ \describe{ \item{\code{uplo}:}{Object of class \code{"character"}. Must be either "U", for upper triangular, and "L", for lower triangular. At present only the lower triangle form is allowed.} \item{\code{diag}:}{Object of class \code{"character"}. Must be either \code{"U"}, for unit triangular (diagonal is all ones), or \code{"N"}; see \code{\linkS4class{triangularMatrix}}.} \item{\code{j}:}{Object of class \code{"integer"} of length \code{\link{nnzero}(.)} (number of non-zero elements). These are the row numbers for each non-zero element in the matrix.} \item{\code{p}:}{Object of class \code{"integer"} of pointers, one for each row, to the initial (zero-based) index of elements in the row. (Only present in the \code{dsRMatrix} class.)} \item{\code{x}:}{Object of class \code{"numeric"} - the non-zero elements of the matrix.} \item{\code{Dim}:}{The dimension (a length-2 \code{"integer"})} \item{\code{Dimnames}:}{corresponding names (or \code{NULL}), inherited from the \code{\linkS4class{Matrix}}, see there.} } } \section{Extends}{ Class \code{"dgRMatrix"}, directly. Class \code{"dsparseMatrix"}, by class \code{"dgRMatrix"}. Class \code{"dMatrix"}, by class \code{"dgRMatrix"}. Class \code{"sparseMatrix"}, by class \code{"dgRMatrix"}. Class \code{"Matrix"}, by class \code{"dgRMatrix"}. } \section{Methods}{ No methods currently with class "dsRMatrix" in the signature. % \describe{ % \item{solve}{\code{signature(a = "dsRMatrix", b = "matrix")}: Solve % a linear system of equations defined by \code{x} using a Cholesky % decomposition.} % ...... % \item{coerce}{\code{signature(from = "dsRMatrix", to = "dgTMatrix")}} % ...... % } } %\references{} %\author{} %\note{} \seealso{ Classes \code{\linkS4class{dgCMatrix}}, \code{\linkS4class{dgTMatrix}}, \code{\linkS4class{dgeMatrix}} } \examples{ (m0 <- new("dtRMatrix")) (m2 <- new("dtRMatrix", Dim = c(2L,2L), x = c(5, 1:2), p = c(0L,2:3), j= c(0:1,1L))) str(m2) (m3 <- as(Diagonal(2), "RsparseMatrix"))# --> dtRMatrix } \keyword{classes} \keyword{algebra} Matrix/man/ltrMatrix-class.Rd0000644000175100001440000000514112001034107015654 0ustar hornikusers\name{ltrMatrix-class} \docType{class} \alias{ltpMatrix-class} \alias{ltrMatrix-class} % \alias{!,ltpMatrix-method} \alias{!,ltrMatrix-method} \alias{coerce,ltpMatrix,dtpMatrix-method} \alias{coerce,ltpMatrix,lgeMatrix-method} \alias{coerce,ltpMatrix,ltrMatrix-method} \alias{coerce,ltrMatrix,dtrMatrix-method} \alias{coerce,ltrMatrix,lgeMatrix-method} \alias{coerce,ltrMatrix,ltpMatrix-method} \alias{coerce,matrix,ltrMatrix-method} \alias{coerce,matrix,ltpMatrix-method} \alias{diag,ltrMatrix-method} \alias{diag,ltpMatrix-method} \alias{diag<-,ltpMatrix-method} \alias{diag<-,ltrMatrix-method} \alias{t,ltpMatrix-method} \alias{t,ltrMatrix-method} % \title{Triangular Dense Logical Matrices} \description{ The \code{"ltrMatrix"} class is the class of triangular, dense, logical matrices in nonpacked storage. The \code{"ltpMatrix"} class is the same except in packed storage. } \section{Slots}{ \describe{ \item{\code{x}:}{Object of class \code{"logical"}. The logical values that constitute the matrix, stored in column-major order.} \item{\code{uplo}:}{Object of class \code{"character"}. Must be either "U", for upper triangular, and "L", for lower triangular.} \item{\code{diag}:}{Object of class \code{"character"}. Must be either \code{"U"}, for unit triangular (diagonal is all ones), or \code{"N"}; see \code{\linkS4class{triangularMatrix}}.} \item{\code{Dim},\code{Dimnames}:}{The dimension (a length-2 \code{"integer"}) and corresponding names (or \code{NULL}), see the \code{\linkS4class{Matrix}} class.} \item{\code{factors}:}{Object of class \code{"list"}. A named list of factorizations that have been computed for the matrix.} } } \section{Extends}{ Both extend classes \code{"\linkS4class{ldenseMatrix}"} and \code{"\linkS4class{triangularMatrix}"}, directly; further, class \code{"Matrix"}, \code{"\linkS4class{lMatrix}"} and others, \emph{in}directly. Use \code{\link{showClass}("ltrMatrix")}, e.g., for details. } \section{Methods}{ Currently, mainly \code{\link{t}()} and coercion methods (for \code{\link{as}(.)}; use, e.g., \code{\link{showMethods}(class="ltpMatrix")} for details. } \seealso{ Classes \code{\linkS4class{lgeMatrix}}, \code{\linkS4class{Matrix}}; function \code{\link[base]{t}} } \examples{ showClass("ltrMatrix") str(new("ltpMatrix")) (lutr <- as(upper.tri(matrix(,4,4)), "ltrMatrix")) str(lutp <- as(lutr, "ltpMatrix"))# packed matrix: only 10 = (4+1)*4/2 entries !lutp ## the logical negation (is *not* logical triangular !) ## but this one is: stopifnot(all.equal(lutp, as(!!lutp, "ltpMatrix"))) } \keyword{classes} Matrix/cleanup0000755000175100001440000000075511422721046013117 0ustar hornikusers#!/bin/sh # Cleans up after the auxiliary files that were created when installing # the Matrix package (shamelessly taken from the XML source pkg) # echo " Cleaning up after installing the Matrix package" ## No configure currently --> empty for now: not yet really needed for f in config.log config.status config.cache ; do if test -w $f ; then rm -f $f fi done for D in `sed -n '/^SUBDIRS *= */s///p' src/Makevars` do if test -d src/$D then (cd src/$D ; make clean ) fi done Matrix/.Rinstignore0000644000175100001440000000001411704374013014033 0ustar hornikusersdoc/.*\.sty