gstat/0000755000176200001440000000000014413517710011377 5ustar liggesusersgstat/NAMESPACE0000644000176200001440000000362413777370515012637 0ustar liggesusersuseDynLib(gstat, gstat_debug_level, gstat_exit, gstat_fit_variogram, gstat_get_variogram_models, gstat_init, gstat_load_ev, gstat_load_variogram, gstat_new_data, gstat_new_dummy_data, gstat_predict, gstat_set_merge, gstat_set_method, gstat_set_set, gstat_variogram, gstat_variogram_values ) importFrom(utils, setTxtProgressBar, stack, txtProgressBar, head, tail) importFrom(stats, as.formula, cor, cov2cor, delete.response, .getXlevels, lm, median, model.extract, model.frame, model.matrix, na.exclude, na.fail, na.omit, na.pass, optim, optimise, optimize, predict, residuals, terms, rnorm, fft, numericDeriv, runif, setNames) importFrom(graphics, image.default, lines, locator, text) importFrom(zoo, is.regular) import(methods) import(lattice) importFrom(zoo, zoo, is.regular) import(sp) import(spacetime) import(FNN) export(as.vgm.variomodel, cross.name, fit.lmc, fit.variogram, fit.variogram.reml, fit.variogram.gls, fit.StVariogram, estiStAni, get.contr, get_gstat_progress, gstat, gstat.cv, "[.gstat", hscat, idw0, krigeTg, krige0, krigeST, krigeSTTg, krigeSimCE, krigeSTSimTB, vgmAreaST, map.to.lev, ossfim, show.vgms, spplot.vcov, variogram, variogramST, extractPar, extractParNames, variogramLine, variogramSurface, vgm, vgmArea, vgmST, vgm.panel.xyplot, panel.pointPairs, set_gstat_progress, xyz2img) exportMethods(krige, idw, krige.cv) S3method("[", gstat) S3method(as.data.frame, variogramCloud) S3method(image, data.frame) S3method(plot, pointPairs) S3method(plot, gstatVariogram) S3method(plot, variogramMap) S3method(plot, variogramCloud) S3method(plot, variogramModel) S3method(plot, StVariogram) S3method(predict, gstat) S3method(print, gstat) S3method(print, gstatVariogram) S3method(print, variogramCloud) S3method(print, variogramModel) S3method(print, StVariogramModel) S3method(variogram, default) S3method(variogram, formula) S3method(variogram, gstat) gstat/demo/0000755000176200001440000000000014336470255012331 5ustar liggesusersgstat/demo/gstat3D.R0000644000176200001440000000116413777370515013775 0ustar liggesusers# $Id: gstat3D.R,v 1.5 2007-02-23 13:34:07 edzer Exp $ # simple demo of 3D interpolation of 50 points with random normal values, # randomly located in the unit cube library(sp) library(gstat) n <- 50 data3D <- data.frame(x = runif(n), y = runif(n), z = runif(n), v = rnorm(n)) coordinates(data3D) = ~x+y+z range1D <- seq(from = 0, to = 1, length = 20) grid3D <- expand.grid(x = range1D, y = range1D, z = range1D) gridded(grid3D) = ~x+y+z res3D <- krige(formula = v ~ 1, data3D, grid3D, model = vgm(1, "Exp", .2)) library(lattice) levelplot(var1.pred ~ x + y | z, as.data.frame(res3D)) rm(n, data3D, range1D, grid3D, res3D) gstat/demo/cosimulation.R0000644000176200001440000000427413777370515015177 0ustar liggesusers# $Id: cosimulation.R,v 1.5 2006-02-10 19:05:02 edzer Exp $ library(sp) data(meuse) coordinates(meuse) = ~x+y data(meuse.grid) gridded(meuse.grid) = ~x+y # cosimulation the four heavy metal variables meuse.g <- gstat(id="zn", formula=zinc~1, data=meuse, nmax = 10, set = list(zero = 1e-10)) meuse.g <- gstat(meuse.g, "cu", copper~1, meuse, nmax = 10) meuse.g <- gstat(meuse.g, "cd", cadmium~1, meuse, nmax = 10) meuse.g <- gstat(meuse.g, "pb", lead~1, meuse, nmax = 10) meuse.g <- gstat(meuse.g, model=vgm(1, "Sph", 900, 1), fill.all=T) x <- variogram(meuse.g, cutoff=1000) meuse.fit = fit.lmc(x, meuse.g) plot(x, model = meuse.fit) z <- predict(meuse.fit, newdata = meuse.grid, nsim = 2) library(lattice) pl1 <- spplot(z, c(1,2), main = "zinc simulations") pl2 <- spplot(z, c(3,4), main = "copper simulations") pl3 <- spplot(z, c(5,6), main = "cadmium simulations") pl4 <- spplot(z, c(7,8), main = "lead simulations") print(pl1, split = c(1,1,2,2), more=TRUE) print(pl2, split = c(1,2,2,2), more=TRUE) print(pl3, split = c(2,1,2,2), more=TRUE) print(pl4, split = c(2,2,2,2)) # indicator cosimulation for the 9 deciles of zinc: q <- quantile(meuse$zinc, seq(.1,.9,.1)) meuse.i <- gstat(id = "zn1", formula = I(zinc < q[1])~1, data = meuse, nmax = 7, beta = .1, set = list(order = 4, zero = 1e-5)) meuse.i <- gstat(meuse.i, "zn2", I(zinc < q[2])~1, meuse, nmax = 7, beta=.2) meuse.i <- gstat(meuse.i, "zn3", I(zinc < q[3])~1, meuse, nmax = 7, beta=.3) meuse.i <- gstat(meuse.i, "zn4", I(zinc < q[4])~1, meuse, nmax = 7, beta=.4) meuse.i <- gstat(meuse.i, "zn5", I(zinc < q[5])~1, meuse, nmax = 7, beta=.5) meuse.i <- gstat(meuse.i, "zn6", I(zinc < q[6])~1, meuse, nmax = 7, beta=.6) meuse.i <- gstat(meuse.i, "zn7", I(zinc < q[7])~1, meuse, nmax = 7, beta=.7) meuse.i <- gstat(meuse.i, "zn8", I(zinc < q[8])~1, meuse, nmax = 7, beta=.8) meuse.i <- gstat(meuse.i, "zn9", I(zinc < q[9])~1, meuse, nmax = 7, beta=.9) meuse.i <- gstat(meuse.i, model=vgm(1, "Sph", 900, 1), fill.all=T) x <- variogram(meuse.i, cutoff=1000) meuse.fit = fit.lmc(x, meuse.i) plot(x, model = meuse.fit) z <- predict(meuse.fit, newdata = meuse.grid, nsim = 2, indicators = TRUE) spplot(z, main = "indicator simulations for 9 deciles") gstat/demo/circEmbeddingMeuse.R0000644000176200001440000000625313777370515016206 0ustar liggesusers############################# ## Example: Meuse data set ## ############################# library(sp) library(gstat) data("meuse") coordinates(meuse) <- ~x+y data("meuse.grid") coordinates(meuse.grid) <- ~x+y gridded(meuse.grid) <- TRUE # variography empVgm <- variogram(zinc~1, meuse) modVgm <- fit.variogram(empVgm, vgm(150000, "Sph", 1000, 25000)) # unconditional simulation unconSim <- krigeSimCE(zinc~1, newdata = meuse.grid, model = modVgm, n=100) unconSim@data$zinc.simMean <- apply(unconSim@data[,-c(1:5)], 1, mean) spplot(unconSim[,6:20], main="15 out of 100 unconditional simulations") spplot(unconSim, "zinc.simMean", main="mean of 100 unconditional simulations") # conditional simulation conSim <- krigeSimCE(zinc~1, meuse, meuse.grid, modVgm, n=100) conSim@data$zinc.simMean <- apply(conSim@data[,-c(1:5)], 1, mean) spplot(conSim[,6:20], main="15 out of 100 conditional simulations") # compare with kriging predictor simKrige <- krige(zinc~1, meuse, meuse.grid, modVgm) spplot(simKrige, "var1.pred", main="interpolated zinc concentrations") spplot(conSim, "zinc.simMean", main="mean of 100 conditional simulations") ################################################ ## turning bands simulation in space and time ## ################################################ separableModel <- vgmST("separable", space=vgm(0.85,"Exp", 831, 0.15), time =vgm(0.9,"Exp", 3.25, 0.1), sill=135000) attr(separableModel,"temporal unit") <- "days" library(spacetime) stf <- STF(meuse, Sys.time()-20:0*24*3600) stf_grid <- STF(geometry(meuse.grid), stf@time) ################### ## unconditional ## ################### sTime <- Sys.time() krigedSim <- krigeSTSimTB(newdata = stf_grid, modelList = separableModel, nsim = 100, nLyrs = 100) Sys.time() - sTime # plot one simulation along time stplot(krigedSim[,,"sim1"], main="unconditional siumulation") # plot one simulation along time as time series stplot(krigedSim[1:21,,"sim1"], mode="ts", main="unconditional siumulation") stplot(krigedSim[1:21,,"sim2"], mode="ts", main="unconditional siumulation") stplot(krigedSim[1:21,,"sim3"], mode="ts", main="unconditional siumulation") stplot(krigedSim[1:21,,"sim4"], mode="ts", main="unconditional siumulation") stplot(krigedSim[1:21,,"sim5"], mode="ts", main="unconditional siumulation") stplot(krigedSim[1:21,,"sim6"], mode="ts", main="unconditional siumulation") # plot the ten simulations of the first day spplot(krigedSim[,1], paste0("sim",1:10), as.table=TRUE, main="unconditional siumulation") ################# ## conditional ## ################# sTime <- Sys.time() krigedSim <- krigeSTSimTB(formula= zinc ~ 1, data = STFDF(geometry(meuse), stf@time, data.frame(zinc=rep(meuse$zinc, 21))), newdata = stf_grid[1:500,], modelList = separableModel, nsim = 10, nLyrs = 500) Sys.time() - sTime # plot one simulation along time stplot(krigedSim[,1:12], main="conditinal simulation") # plot one simulation along time as time series stplot(krigedSim[1:12,,"sim1"], mode="ts", main="conditinal simulation") # plot the ten simulations of the first day spplot(krigedSim[,1], paste0("sim",1:10), as.table=TRUE, main="conditinal simulation")gstat/demo/blue.R0000644000176200001440000000154013777370515013411 0ustar liggesusers# how to get the BLUE trend coefficients out of a predict.gstat call? # prepare data library(sp) library(gstat) data(meuse) coordinates(meuse) = ~x+y data(meuse.grid) gridded(meuse.grid) = ~x+y # create a manual, non-automatic intercept meuse$Int = rep(1, length(meuse$zinc)) meuse.grid$Int = rep(1, length(meuse.grid$dist)) # create a gstat object without an automatic intercept: g = gstat(formula = log(zinc)~-1+Int+sqrt(dist), data=meuse, model = vgm(1, "Exp", 300)) newdat = meuse.grid[1:2,c("Int", "dist")] gridded(newdat) = FALSE newdat$dist = c(0,1) newdat$Int = c(1,0) # (in the more general case of n predictors, make sure that the matrix with # predictors, or design matrix, equals the identity matrix.) newdat out = as.data.frame(predict(g, newdat, BLUE = TRUE))[,3:4] rownames(out) = c("Intercept", "slope") colnames(out) = c("BLUE", "Variance") out gstat/demo/depend.R0000644000176200001440000000252713777370515013727 0ustar liggesusersrequire(tools) packages_to_check <- function(dep, which = c("Depends", "Imports", "LinkingTo", "Suggests"), recursive = FALSE){ download.file("https://cran.R-project.org/web/packages/packages.rds", "packages.rds", mode="wb") x <- readRDS("packages.rds") x <- x[!duplicated(x[,1]),] packages <- x[,1] rdeps <- package_dependencies(packages = dep, x, which = which, recursive = recursive, reverse = TRUE) paste(apply(x[x[,1] %in% rdeps[[1]], 1:2], 1, paste, collapse="_"), ".tar.gz", sep="") } #RCheck = function(x, URL = "http://ftp5.gwdg.de/pub/misc/cran/src/contrib/") { RCheck = function(x, URL = "https://cran.r-project.org/src/contrib/") { if (!file.exists(x)) download.file(paste(URL, x, sep=""), x) cmd = paste("R CMD check --as-cran ", x, " > ", x, ".log", sep = "") print(cmd) ret = system(cmd) print(ret) ret } result <- packages_to_check("gstat") result sel = TRUE library(parallel) ncores_to_use = 2 cl <- makeCluster(getOption("cl.cores", ncores_to_use)) clusterExport(cl, c("RCheck", "sel", "result")) out = parLapply(cl, result[sel], function(x) RCheck(x)) succ = unlist(out) x = which(succ != 0) result[x] bla = lapply(result[x], function(y) { cat(paste(y, ":\n")) system(paste("tail -20 ",y,".log", sep="")) } ) #result <- packages_to_check("sp", recursive=TRUE) gstat/demo/lnsim.R0000644000176200001440000000332113777370515013603 0ustar liggesuserslibrary(sp) library(gstat) data(meuse) coordinates(meuse) = ~x+y data(meuse.grid) gridded(meuse.grid) = ~x+y # NLKrige: non-linear kriging (e.g. log-normal kriging), simulation based. # arguments: # formula, data, newdata, vgm: see ?krige # trans: transformation and back-transformation function; # summarize: optional, summarize the simulations, see example below; # nmax, nsim: see ?krige # density: number of points to discretize each block PROVIDED BLOCK SIZES # ARE CONSTANT (note that newdata can also be SpatialPolygons -- if newdata is # a grid, cell size is used as block size) NLKrige = function(formula, data, newdata, vgm, trans = c(log,exp), summarize, nmax = 50, nsim = 100, density = 16, ...) { # transform target: target = as.character(as.list(formula)[[2]]) data[[target]] = trans[[1]](data[[target]]) # conditional simulation sample at finer grid: finegrid = spsample(newdata, n = density * length(newdata), type = "regular", offset = c(.5,.5)) sim = krige(formula, data, finegrid, vgm, nmax = nmax, nsim = nsim) # back transform ALL simulations: sim@data = trans[[2]](sim@data) # spatial aggregation of each simulation, taking block MEAN: aggr = aggregate(sim, newdata, mean) # aggregation to summary: if (!missing(summarize)) { ret = apply(aggr@data, 1, summarize, ...) if (is.matrix(ret)) aggr@data = data.frame(t(ret)) else aggr@data = data.frame(ret) } aggr } aggr = NLKrige(zinc~1, meuse, meuse.grid, vgm(.5, "Sph", 900, .1), nmax = 10, summarize = mean) spplot(aggr, main = "expected value of block means") aggr = NLKrige(zinc~1, meuse, meuse.grid, vgm(.5, "Sph", 900, .1), nmax = 10, summarize = quantile, probs = c(0.025, 0.975)) spplot(aggr, main = "95% CI for block means") gstat/demo/uisim.R0000644000176200001440000000226113777370515013611 0ustar liggesusers# $Id: uisim.R,v 1.5 2008-09-25 10:26:00 edzer Exp $ library(sp) library(gstat) # prediction grid: data(meuse.grid) gridded(meuse.grid) = ~x+y # define variable as dummy data v = vgm(.25, "Sph", 900) g = gstat(NULL, "var1", x~1, beta = .5, nmax = 20, model = v, dummy = TRUE) # simulation of a single variable out = predict(g, meuse.grid, nsim = 20, indicators = TRUE) spplot(out) # simulation of two correlated variables: v = vgm(.1, "Sph", 900) g = gstat(g, "var2", x~1, beta = .25, nmax = 20, model = v, dummy = TRUE) v = vgm(-.1, "Sph", 900) g = gstat(g, c("var1", "var2"), model = v) out = predict(g, meuse.grid, nsim = 10, indicators = TRUE, set = list(order = 2)) spplot(out) # merge all 10 individual simulations into three-group factors: for (i in 1:10) { v1 = paste("var1.sim", i, sep = "") v2 = paste("var2.sim", i, sep = "") m = cbind(out[[v1]], out[[v2]], 1 - (out[[v1]]+out[[v2]])) mout = factor(apply(m, 1, function(x) which(x == 1))) if (i == 1) out2 = SpatialPixelsDataFrame(as(out, "SpatialPixels"), data.frame(mout)) else out2[[i]] = mout } names(out2) = paste("sim", 1:10, sep="") spplot(out2) require(RColorBrewer) spplot(out2, col.regions=brewer.pal(3, "Set2")) gstat/demo/stkrige-crossvalidation.R0000644000176200001440000002456513777370515017350 0ustar liggesusers######################################################## # note that demo(stkrige) and demo(stkrige-prediction) # # need to be run before this one # ######################################################## ## cross-validation crossStat <- function(var1, var2="PM10", STxDF=DE_RB_2005, digits=NA) { diff <- STxDF[,,var1,drop=F]@data[[1]] - STxDF[,,var2,drop=F]@data[[1]] RMSE <- sqrt(mean(diff^2)) MAE <- mean(abs(diff)) ME <- mean(diff) COR <- cor(STxDF[,,var1,drop=F]@data[[1]], STxDF[,,var2,drop=F]@data[[1]]) res <- c(RMSE, MAE, ME, COR) names(res) <- c("RMSE", "MAE", "ME", "COR") if(is.na(digits)) return(res) else return(round(res, digits)) } # purely spatial: DE_RB_2005 <- as(DE_RB_2005, "STSDF") pureSp <- NULL for(i in 1:365) { # i <- 1 pureSp <- c(pureSp, krige.cv(PM10~1,DE_RB_2005[,i,"PM10"], model=spVgmMod, nmax=10)$var1.pred) } DE_RB_2005@data$pureSp10Nghbr <- pureSp pureSp <- NULL for(i in 1:365) { # i <- 1 pureSp <- c(pureSp, krige.cv(PM10~1,DE_RB_2005[,i,"PM10"],model=spVgmMod,nmax=50)$var1.pred) } DE_RB_2005@data$pureSp50Nghbr <- pureSp ## spatio-temporal LOOCV target <- as(DE_RB_2005[,,"PM10"],"STFDF") ## seprable model # 10 neighbours res <- matrix(NA, length(DE_RB_2005@sp), 365) for(loc in 1:length(DE_RB_2005@sp)) { cat("Location", loc, "\n") res[loc,!is.na(target[loc,])[,"PM10"]] <- krigeST(PM10~1, data=DE_RB_2005[(1:length(DE_RB_2005@sp))[-loc],], newdata=DE_RB_2005[loc,,drop=F], fitSepModel, nmax=10, stAni=fitMetricModel$stAni/24/3600)$var1.pred } DE_RB_2005@data$sepModel10Nghbr <- as.vector(res)[!is.na(as.vector(res))] # 50 neighbours res <- matrix(NA, length(DE_RB_2005@sp), 365) for(loc in 1:length(DE_RB_2005@sp)) { # loc <- 1 cat("Location", loc, "\n") res[loc,!is.na(target[loc,])[,"PM10"]] <- krigeST(PM10~1, data=DE_RB_2005[(1:length(DE_RB_2005@sp))[-loc],], newdata=DE_RB_2005[loc,,drop=F], fitSepModel, nmax=50, stAni=fitMetricModel$stAni/24/3600)$var1.pred } DE_RB_2005@data$sepModel50Nghbr <- as.vector(res)[!is.na(as.vector(res))] ## product-sum model # 10 neighbours res <- matrix(NA, length(DE_RB_2005@sp), 365) for(loc in 1:length(DE_RB_2005@sp)) { # loc <- 1 cat("Location", loc, "\n") res[loc,!is.na(target[loc,])[,"PM10"]] <- krigeST(PM10~1, data=DE_RB_2005[(1:length(DE_RB_2005@sp))[-loc],], newdata=DE_RB_2005[loc,,drop=F], fitProdSumModel, nmax=10, stAni=fitMetricModel$stAni/24/3600)$var1.pred } DE_RB_2005@data$psModel10Nghbr <- as.vector(res)[!is.na(as.vector(res))] # 50 neighbours res <- matrix(NA, length(DE_RB_2005@sp), 365) for(loc in 1:length(DE_RB_2005@sp)) { # loc <- 1 cat("Location", loc, "\n") res[loc,!is.na(target[loc,])[,"PM10"]] <- krigeST(PM10~1, data=DE_RB_2005[(1:length(DE_RB_2005@sp))[-loc],], newdata=DE_RB_2005[loc,,drop=F], fitProdSumModel, nmax=50, stAni=fitMetricModel$stAni/24/3600)$var1.pred } DE_RB_2005@data$psModel50Nghbr <- as.vector(res)[!is.na(as.vector(res))] ## metric model # 10 neighbours res <- matrix(NA, length(DE_RB_2005@sp), 365) for(loc in 1:length(DE_RB_2005@sp)) { # loc <- 1 cat("Location", loc, "\n") res[loc,!is.na(target[loc,])[,"PM10"]] <- krigeST(PM10~1, data=DE_RB_2005[(1:length(DE_RB_2005@sp))[-loc],], newdata=DE_RB_2005[loc,,drop=F], fitMetricModel, nmax=10, stAni=fitMetricModel$stAni/24/3600)$var1.pred } DE_RB_2005@data$metricModel10Nghbr <- as.vector(res)[!is.na(as.vector(res))] # 50 neighbours res <- matrix(NA, length(DE_RB_2005@sp), 365) for(loc in 1:length(DE_RB_2005@sp)) { # loc <- 1 cat("Location", loc, "\n") res[loc,!is.na(target[loc,])[,"PM10"]] <- krigeST(PM10~1, data=DE_RB_2005[(1:length(DE_RB_2005@sp))[-loc],], newdata=DE_RB_2005[loc,,drop=F], fitMetricModel, nmax=50, stAni=fitMetricModel$stAni/24/3600)$var1.pred } DE_RB_2005@data$metricModel50Nghbr <- as.vector(res)[!is.na(as.vector(res))] ## sum-metric model # 10 neighbours res <- matrix(NA, length(DE_RB_2005@sp), 365) for(loc in 1:length(DE_RB_2005@sp)) { # loc <- 1 cat("Location", loc, "\n") res[loc,!is.na(target[loc,])[,"PM10"]] <- krigeST(PM10~1, data=DE_RB_2005[(1:length(DE_RB_2005@sp))[-loc],], newdata=DE_RB_2005[loc,,drop=F], fitSumMetricModel, nmax=10, stAni=fitMetricModel$stAni/24/3600)$var1.pred } DE_RB_2005@data$sumMetricModel10Nghbr <- as.vector(res)[!is.na(as.vector(res))] # 50 neighbours res <- array(NA, c(length(DE_RB_2005@sp), 365,2)) for(loc in 1:length(DE_RB_2005@sp)) { # loc <- 38 cat("Location", loc, "\n") res[loc,!is.na(target[loc,])[,"PM10"],] <- as.matrix(krigeST(PM10~1, data=DE_RB_2005[(1:length(DE_RB_2005@sp))[-loc],], newdata=DE_RB_2005[loc,,drop=F], fitSumMetricModel, nmax=50, computeVar=T, stAni=linStAni*1000/24/3600)@data[,c("var1.pred","var1.var")]) } DE_RB_2005@data$sumMetricModel50Nghbr <- as.vector(res[,,1])[!is.na(target@data)] DE_RB_2005@data$sumMetricModel50NghbrVar <- as.vector(res[,,2])[!is.na(target@data)] DE_RB_2005@data$sumMetricModel50Nghbr95u <- apply(DE_RB_2005@data, 1, function(x) { qnorm(0.975, x["sumMetricModel50Nghbr"], sqrt(x["sumMetricModel50NghbrVar"])) }) DE_RB_2005@data$sumMetricModel50Nghbr95l <- apply(DE_RB_2005@data, 1, function(x) { qnorm(0.025, x["sumMetricModel50Nghbr"], sqrt(x["sumMetricModel50NghbrVar"])) }) ## simple sum-metric model # 10 neighbours res <- matrix(NA, length(DE_RB_2005@sp), 365) for(loc in 1:length(DE_RB_2005@sp)) { # loc <- 1 cat("Location", loc, "\n") res[loc,!is.na(target[loc,])[,"PM10"]] <- krigeST(PM10~1, data=DE_RB_2005[(1:length(DE_RB_2005@sp))[-loc],], newdata=DE_RB_2005[loc,,drop=F], fitSimpleSumMetricModel, nmax=10, stAni=fitMetricModel$stAni/24/3600)$var1.pred } DE_RB_2005@data$simpleSumMetricModel10Nghbr <- as.vector(res)[!is.na(as.vector(res))] # 50 neighbours res <- matrix(NA, length(DE_RB_2005@sp), 365) for(loc in 1:length(DE_RB_2005@sp)) { # loc <- 1 cat("Location", loc, "\n") res[loc,!is.na(target[loc,])[,"PM10"]] <- krigeST(PM10~1, data=DE_RB_2005[(1:length(DE_RB_2005@sp))[-loc],], newdata=DE_RB_2005[loc,,drop=F], fitSimpleSumMetricModel, nmax=50, stAni=fitMetricModel$stAni/24/3600)$var1.pred } DE_RB_2005@data$simpleSumMetricModel50Nghbr <- as.vector(res)[!is.na(as.vector(res))] ### # cross-stats rbind( crossStat("pureSp10Nghbr", digits=2), crossStat("pureSp50Nghbr", digits=2), crossStat("sepModel10Nghbr", digits=2), crossStat("sepModel50Nghbr", digits=2), crossStat("psModel10Nghbr", digits=2), crossStat("psModel50Nghbr", digits=2), crossStat("metricModel10Nghbr", digits=2), crossStat("metricModel50Nghbr", digits=2), crossStat("sumMetricModel10Nghbr", digits=2), crossStat("sumMetricModel50Nghbr", digits=2)) if(paper) { texRow <- function(x) { paste(paste(x,collapse=" & ")," \\\\ \n") } cat(apply(round(rbind(crossStat("pureSp10Nghbr"), crossStat("sepModel10Nghbr"), crossStat("psModel10Nghbr"), crossStat("metricModel10Nghbr"), crossStat("sumMetricModel10Nghbr"), crossStat("simpleSumMetricModel50Nghbr"), crossStat("pureSp50Nghbr"), crossStat("sepModel50Nghbr"), crossStat("psModel50Nghbr"), crossStat("metricModel50Nghbr"), crossStat("sumMetricModel50Nghbr"), crossStat("simpleSumMetricModel50Nghbr") ), 2),1,texRow)) loc <- 38 # sample(68,1) # 15 tw <- "2005-01-15/2005-04-15" png("vignettes/figures/singleStationTimeSeries.png", 9, 4, "in", bg="white", res = 149) plot(DE_RB_2005[loc,tw][,"sumMetricModel50Nghbr"], main=paste("Location", DE_RB_2005@sp@data$station_european_code[loc]), ylim=c(0,70)) points(DE_RB_2005[loc,tw][,"PM10"], type="l", col="darkgreen", lty=1) points(DE_RB_2005[loc,tw][,"sumMetricModel50Nghbr95u"], type="l", col="darkgrey", lty=2) points(DE_RB_2005[loc,tw][,"sumMetricModel50Nghbr95l"], type="l", col="darkgrey", lty=2) legend("topright",legend = c("observed","sum-metric","95 % prediction band"), lty=c(1,1,2), col=c("darkgreen", "black", "darkgrey") ) dev.off() DE_RB_2005@data$diffPM10 <- DE_RB_2005@data$sumMetricModel50Nghbr - DE_RB_2005@data$PM10 stpl <- stplot(as(DE_RB_2005[,smplDays, "diffPM10"],"STFDF"), col.regions=bpy.colors(5), sp.layout = list("sp.polygons", DE_NUTS1), scales=list(draw=F), key.space="right", colorkey=T, cuts=c(-25,-15,-5,5,15,25), main=NULL) #expression(paste("daily mean ","PM"[10]," concentration"))) png("vignettes/figures/diffs_daily_means_PM10.png", width=9, height=6, "in", res=150) print(stpl) dev.off() }gstat/demo/fulmar.R0000644000176200001440000000517713777370515013762 0ustar liggesusers# $Id: fulmar.R,v 1.3 2006-02-10 19:05:02 edzer Exp $ library(sp) library(gstat) data(fulmar) data(ncp.grid) glm98 <- glm(formula = fulmar ~ depth + coast, family = quasipoisson, data = fulmar[fulmar$year == 1998, ]) glm99 <- glm(formula = fulmar ~ depth + coast, family = quasipoisson, data = fulmar[fulmar$year == 1999, ]) fulmar98 = data.frame(fulmar[fulmar$year == 1998,], pr98 = predict(glm98, type = "response")) fulmar99 <- data.frame(fulmar[fulmar$year == 1999,], pr99 = predict(glm99, type = "response")) pr98.grd <- predict(glm98, newdata = ncp.grid, type = "response", se.fit=TRUE) pr99.grd <- predict(glm99, newdata = ncp.grid, type = "response", se.fit=TRUE) pr <- data.frame(ncp.grid, pr98=pr98.grd$fit, pr99=pr99.grd$fit, se98 = pr98.grd$se.fit, se99 = pr99.grd$se.fit) # B.3 create gstat object g <- gstat(id = "fulmar98", formula = fulmar~pr98, locations = ~x+y, data = fulmar98, model = vgm(1.89629, "Exp", 50000, 0.852478), beta = c(0,1), variance = "mu") g <- gstat(g, id = "fulmar99", formula = fulmar~pr99, locations = ~x+y, data = fulmar99, model = vgm(2.52259, "Exp", 50000, 1.76474), beta = c(0,1), variance = "mu") h <- g h <- gstat(h, id = c("fulmar98","fulmar99"), model = vgm(2.18, "Exp", 50000, 1.22)) # predict block means for blocks in ncp.grid$area (table 2; cokriging) library(maptools) areas.r = readShapePoly(system.file("external/ncp.shp", package="gstat")) #areas.r <- as.SpatialRings.Shapes(areas.shp$Shapes, areas.shp$att.data$WSVGEB_) coordinates(pr) = ~x+y #pr.df = overlay(pr, areas.r, fn = mean) pr.df = na.omit(as(aggregate(pr, areas.r, FUN = mean), "data.frame")) # match non-empty (and relevant) areas: #areas = SpatialPolygonsDataFrame(areas.r[c(2,3,4,16),"WSVGEB_"], pr.df[c(1,2,3,5),])#,match.ID=F) areas = SpatialPolygonsDataFrame(areas.r[c(1,2,12,7),"WSVGEB_"], pr.df[c(1,2,3,5),], match.ID=F) # areas ID's 0 1 2 14 sk = predict(g, areas) cok = predict(h, areas) spplot(cok, c(3,5), names.attr = c("1998", "1999"), main = "Fulmaris glacialis, density estimates\n(by irregular block cokriging)") sk = as.data.frame(sk) cok = as.data.frame(cok) print(data.frame(area = c(1,2,3,16), SK98 = sk$fulmar98.pred, SE98 = sqrt(sk$fulmar98.var), SK99 = sk$fulmar99.pred, SE99 = sqrt(sk$fulmar99.var), CK98 = cok$fulmar98.pred, SE98 = sqrt(cok$fulmar98.var), CK99 = cok$fulmar99.pred, SE99 = sqrt(cok$fulmar99.var)), digits=3) print(data.frame(area = c(1,2,3,16), dSK = sk$fulmar99.pred - sk$fulmar98.pred, SEdSK = sqrt(sk$fulmar98.var+sk$fulmar99.var), dCOK = cok$fulmar99.pred - cok$fulmar98.pred, SEdCOK = sqrt(cok$fulmar98.var+cok$fulmar99.var - 2*cok$cov.fulmar98.fulmar99)), digits=3) gstat/demo/grass.R0000644000176200001440000000325113777370515013602 0ustar liggesusers# $Id: grass.R,v 1.4 2006-02-10 19:05:02 edzer Exp $ # this demo assumes quite a lot: # a. it assumes GRASS gis is running # b. it assumes that the meuse data zinc variable is available as a site list # c. it assumes that mask_map is present, and contains the mask map values # (i.e., the study area) library(sp) library(GRASS) # load R GRASS interface G = gmeta() # retrieves active data base locations and topology d = sites.get(G, "zinc") # retrieve zinc observations plot(d$east, d$north, asp=1) names(d)[4] = "zinc" # rename attribute mask = rast.get hist(d$zinc) hist(log(d$zinc)) mask = rast.get(G, "mask_map") plot(G, mask$mask.map) points(d$east,d$north, pch="+") library(gstat) # load gstat library bubble(d, zcol = "zinc", col=c(4,5), maxsize=2) # explain S formulae: ~ v = variogram(log(zinc)~1, ~east+north, d) plot(v) v.mod = vgm(.6, "Sph", 900, .1) plot(v, model = v.mod) v.fit = fit.variogram(v, v.mod) plot(v, model = v.fit) zinc.g = gstat(NULL, "lzinc", log(zinc)~1, ~east+north, d, model = v.fit) new.data = data.frame(east = east(G), north = north(G)) new.data[is.na(mask$mask.map), ] = c(NA,NA) zinc.kr = predict(zinc.g, new.data) image(zinc.kr) library(lattice) levelplot(lzinc.pred~east+north, zinc.kr, asp=1.34, col.regions=bpy.colors(100)) # push prediction and variances grids back into GRASS data base: rast.put(G, "lzinc.pred", zinc.kr$lzinc.pred) rast.put(G, "lzinc.var", zinc.kr$lzinc.var) # push cross validation residuals back to GRASS data base: xv = krige.cv(log(zinc)~1, ~east+north, d, v.fit, nmax = 40, verb=F) sites.put2(G, data = xv, dims = c("east", "north", "residual", "zscore"), lname = "lzinc.xv") gstat/demo/a2p.R0000644000176200001440000000167713777370515013157 0ustar liggesusersRprof() # import NC SIDS data: library(sp) library(maptools) fname = system.file("shapes/sids.shp", package="maptools")[1] nc = readShapePoly(fname, proj4string = CRS("+proj=longlat +datum=NAD27 +ellps=clrk66")) # reproject to UTM17, so we can use Euclidian distances: library(rgdal) nc = spTransform(nc, CRS("+proj=utm +zone=17 +datum=WGS84 +ellps=WGS84")) # create a target (newdata) grid, and plot: grd = spsample(nc, "regular", n = 1000) class(grd) plot(nc, axes = TRUE) points(grd, pch = 3) library(gstat) # area-to-point kriging: kr = krige0(SID74 ~ 1, nc, grd, vgmArea, ndiscr = 9, vgm = vgm(1, "Exp", 1e5, 0), # point variogram, verbose = TRUE) out = SpatialPixelsDataFrame(grd, data.frame(pred = kr)) pl0 = spplot(nc["SID74"], main = "areas") pl1 = spplot(out, sp.layout = list("sp.polygons", nc, first=F,col='grey'), main = "points on a grid") print(pl0, split = c(1,1,1,2), more = TRUE) print(pl1, split = c(1,2,1,2), more = FALSE) gstat/demo/stkrige-prediction.R0000644000176200001440000001172613777370515016277 0ustar liggesusers########################################################### # note that demo(stkrige) needs to be run before this one # ########################################################### # libraries library(sp) library(spacetime) library(gstat) library(rgdal) animate <- FALSE # interpolation # build a grid over Germany gridDE <- SpatialGrid(GridTopology(DE_RB_2005@sp@bbox[,1]%/%10000*10000, c(10000,10000), cells.dim=ceiling(apply(DE_RB_2005@sp@bbox,1,diff)/10000))) proj4string(gridDE) <- CRS("+init=epsg:32632") fullgrid(gridDE) <- F ind <- over(gridDE, as(DE_NUTS1,"SpatialPolygons")) gridDE <- gridDE[!is.na(ind)] # back scale vgms: fitSepModel$space$range <- fitSepModel$space$range*1000 fitProdSumModel$space$range <- fitProdSumModel$space$range*1000 fitMetricModel$joint$range <- fitMetricModel$joint$range*1000 fitMetricModel$stAni <- fitMetricModel$stAni*1000 fitSimpleSumMetricModel$space$range <- fitSimpleSumMetricModel$space$range*1000 fitSimpleSumMetricModel$joint$range <- fitSimpleSumMetricModel$joint$range*1000 fitSimpleSumMetricModel$stAni <- fitSimpleSumMetricModel$stAni*1000 fitSumMetricModel$space$range <- fitSumMetricModel$space$range*1000 fitSumMetricModel$joint$range <- fitSumMetricModel$joint$range*1000 fitSumMetricModel$stAni <- fitSumMetricModel$stAni*1000 if(animate) { DE_pred <- STF(gridDE, DE_RB_2005@time) predMat <- matrix(NA,0,2) for (rd in 15:180) { # rd <- 15 predMat <- rbind(predMat, krigeST(PM10~1, data=DE_RB_2005[,rd+(-5:5)], # start: 12:24 newdata=DE_pred[,rd,drop=F], computeVar=T, fitSumMetricModel, # nmax=50, stAni=linStAni*1000/24/3600)@data) } DE_pred_winter <- DE_pred[,15:180] DE_pred_winter <- addAttrToGeom(DE_pred_winter, predMat) for(i in 1:length(DE_pred_winter@time)) { # i <- 1 pnt <- spplot(DE_pred_winter[,i], "var1.pred", col.regions=bpy.colors(160)[-(1:9)], scales=list(draw=F), at=c(-5,0:150), sp.layout = list(list("sp.polygons", DE_NUTS1, first=FALSE, col=gray(0.5)), list("sp.points", DE_RB_2005[,i+14], col=gray(0.25), pch=3, cex=.5)), main=as.character(index(DE_pred_winter[,i,drop=F]@time))) png(file=paste("vignettes/figures/animate/pred",i,".png", sep=""), width=6, height=6, "in", res=150) print(pnt) dev.off() } } DE_pred <- STF(gridDE, DE_RB_2005@time[smplDays]) tIDS <- unique(pmax(1,pmin(as.numeric(outer(-5:5, smplDays, "+")), 365))) sepPred <- krigeST(PM10~1, data=DE_RB_2005[,tIDS], newdata=DE_pred, fitSepModel, nmax=50, stAni=fitMetricModel$stAni/24/3600) psPred <- krigeST(PM10~1, data=DE_RB_2005[,tIDS], newdata=DE_pred, fitProdSumModel, nmax=50, stAni=fitMetricModel$stAni/24/3600) metPred <- krigeST(PM10~1, data=DE_RB_2005[,tIDS], newdata=DE_pred, fitMetricModel, nmax=50, stAni=fitMetricModel$stAni/24/3600) sumPred <- krigeST(PM10~1, data=DE_RB_2005[,tIDS], newdata=DE_pred, fitSumMetricModel, nmax=50, stAni=fitMetricModel$stAni/24/3600) smplSumPred <- krigeST(PM10~1, data=DE_RB_2005[,tIDS], # start: 12:24 newdata=DE_pred, fitSimpleSumMetricModel, nmax=50, stAni=fitMetricModel$stAni/24/3600) # pure spatial prediction pureSpPred <- matrix(NA, nrow=length(gridDE), length(smplDays)) col <- 1 for(i in smplDays) { # i <- 1 pureSpPred[,col] <- krige(PM10~1, as(DE_RB_2005, "STSDF")[,i], gridDE, model=spVgmMod, nmax=50)$var1.pred col <- col+1 } pureSpPred <- STFDF(gridDE, DE_RB_2005@time[smplDays], data.frame(var1.pred = as.numeric(pureSpPred))) DE_RB_2005 <- as(DE_RB_2005, "STFDF") if(paper) { stpl <- stplot(smplSumPred, col.regions=bpy.colors(120)[-(1:20)], scales=list(draw=F), main=NULL, at=0:70, # "spatio-temporal sum-metric model" sp.layout = list(list("sp.polygons", DE_NUTS1, first=FALSE, col=gray(0.5)), list("sp.points", DE_RB_2005@sp, col=gray(0.25), pch=3, cex=.5))) png(file="vignettes/figures/pred_daily_means_PM10.png", width=9, height=6, "in", res=150) print(stpl) dev.off() } else { stplot(pureSpPred, col.regions=bpy.colors, scales=list(draw=F), main="pure spatial daily prediction") stplot(sepPred, col.regions=bpy.colors(), scales=list(draw=F), main="spatio-temporal separable model") stplot(psPred, col.regions=bpy.colors, scales=list(draw=F), main="spatio-temporal product-sum model") stplot(metPred, col.regions=bpy.colors, scales=list(draw=F), main="spatio-temporal metric model") stplot(sumPred, col.regions=bpy.colors, scales=list(draw=F), main="spatio-temporal sum-metric model") stplot(smplSumPred, col.regions=bpy.colors, scales=list(draw=F), main="spatio-temporal simple sum-metric model") }gstat/demo/a2pinST.R0000644000176200001440000000210313777370515013736 0ustar liggesusers## area2point in space and time library(sp) library(gstat) data("meuse") coordinates(meuse) <- ~x+y data("meuse.grid") coordinates(meuse.grid) <- ~x+y gridded(meuse.grid) <- TRUE meuse.coarse.grid <- SpatialGrid(GridTopology(meuse.grid@grid@cellcentre.offset, c(600,600), c(5, 7))) separableModel <- vgmST("separable", space=vgm(0.85,"Exp", 831, 0.15), time =vgm(0.9,"Exp", 3.25, 0.1), sill=135000) attr(separableModel,"temporal unit") <- "days" library(spacetime) stf <- STF(meuse[sample(155, 25),], Sys.time()-2:0*24*3600) stf_grid <- STF(geometry(meuse.coarse.grid), stf@time) krigedSim <- krigeSTSimTB(newdata = stf_grid, modelList = separableModel, nsim = 1, nLyrs = 100) # area-to-point kriging: a2pST = krigeST(sim1 ~ 1, krigedSim, stf, modelList = vgmAreaST, ndiscr = 9, model = separableModel, # point variogram, verbose = TRUE) p1 <- stplot(krigedSim, color.key=F) p2 <- stplot(a2pST, color.key=F) print(p1, position=c(0,0.5,1,1), more=TRUE) print(p2, position=c(0,0,1,0.5)) gstat/demo/zonal.R0000644000176200001440000000063513777370515013611 0ustar liggesusers library(sp) demo(meuse,ask=FALSE,echo=FALSE) library(gstat) v = variogram(log(zinc)~1, meuse, alpha = c(0,45,90,135)) vm = vgm(.25, "Sph", 1000, anis = c(45, 0.5)) plot(v, vm, main = "geometric") zonal = vgm(.5, "Sph", 1e9, anis = c(45, 1/1e6)) # range is 1e9, effectively infinity, in 45 direction; # it is 1e9/1e6 = 1000 in 135 direction. vm = vgm(.25, "Sph", 1000, add.to = zonal) plot(v, vm, main = "zonal") gstat/demo/wind.R0000644000176200001440000000340013777370515013420 0ustar liggesusers#pdf("wind.pdf") # PLEASE read the vignette of package spacetime for a more # clever way to do all this! library(sp) library(gstat) library(rgdal) library(maptools) # load wind data, run test: example(wind) m = map2SpatialLines( map("worldHires", xlim = c(-11,-5.4), ylim = c(51,55.5), plot=F)) proj4string(m) = "+proj=longlat +datum=WGS84 +ellps=WGS84" m = spTransform(m, CRS("+proj=utm +zone=29 +datum=WGS84 +ellps=WGS84")) # model temporal autocorrelation acf(wind[7]) tdiscr = 0:40 lines(tdiscr, exp(- tdiscr/1.5)) # set up data, last year years = 61 months = 1 jday = c(1,6,11,16,21,26) sel = wind[wind$year %in% years & wind$month %in% months & wind$jday %in% jday,] #stations = 4:15 stations = 4:15 sels = stack(sel[stations]) sels$t = rep(sel$jday, length(stations)) sels$x = coordinates(wind.loc)[match(sels$ind, wind.loc$Code),1] sels$y = coordinates(wind.loc)[match(sels$ind, wind.loc$Code),2] summary(sels) coordinates(sels) = ~x+y proj4string(sels) = "+proj=longlat +datum=WGS84 +ellps=WGS84" sels = spTransform(sels, CRS("+proj=utm +zone=29 +datum=WGS84 +ellps=WGS84")) grd = makegrid(m, n = 1000) grd$t = rep(1, nrow(grd)) coordinates(grd) = ~x1+x2 gridded(grd)=TRUE proj4string(grd) = proj4string(sels) #sels = as(sels, "data.frame") # setup grid covfn = function(x, y = x) { u = spDists(coordinates(x), coordinates(y)) t = abs(outer(x$t,y$t,"-")) 0.6 * exp(-u/750000) * exp(-t/1.5) } for (i in 1:120) { grd$t = rep(i/4, nrow(grd)) n = paste("t", i/4, sep="") grd[[n]] = krige0(sqrt(values)~1, sels, grd, covfn) } grd$t = NULL #grd$pr = out$pred #library(lattice) #levelplot(pr~x1+x2|t,grd,col.regions=bpy.colors()) spl = list(list("sp.points", sels,first=F, cex=.5), list("sp.lines", m, col='grey')) spplot(grd, sp.layout = spl, col.regions=bpy.colors()) gstat/demo/rep.R0000644000176200001440000000131113777370515013244 0ustar liggesuserslibrary(sp) library(gstat) data(meuse) coordinates(meuse) = ~x + y data(meuse.grid) coordinates(meuse.grid) = ~x + y # Variogram log Zn lzn.vgm = variogram(log(zinc) ~ 1, meuse) lzn.fit = fit.variogram(lzn.vgm, model = vgm(1, "Sph", 900, 1)) #Conditional simulation nsim = 100 lzn.sim = krige(log(zinc) ~ 1, meuse, meuse.grid, model = lzn.fit, nmax = 30, nsim = nsim) # Variogram of all relizations m = out = list() for (i in 1:nsim) { s = paste("sim", i, sep="") f = as.formula(paste(s, "~1")) v = variogram(f, lzn.sim) v$id = rep(s, nrow(v)) out[[s]] = v m[[s]] = fit.variogram(v, lzn.fit) } plot(do.call(rbind, out), m, layout=c(10,10), skip = FALSE, scales = list(y = list(relation = "same"))) gstat/demo/sftime.R0000644000176200001440000000415114314525261013736 0ustar liggesusers## FNN local prediction ######################## library(sp) library(spacetime) library(gstat) library(lattice) # create n space-time points over [0,1] x [0,1] x [Now, Now+some days] t0 = Sys.time() # now n = 1000 set.seed(13131) # fix outcomes x = runif(n) y = runif(n) t = t0 + 1e6 * runif(n) z = rnorm(n) stidf = STIDF(SpatialPoints(cbind(x,y)), sort(t), data.frame(z=z)) stplot(stidf, number=21, main="random spatio-temporal noise") library(sftime) sft = st_as_sftime(stidf) # create a regular 20 x 20 x 10 grid of prediction locations: grd = as(SpatialGrid(GridTopology(c(0.025,0.025), c(.05, .05), c(20,20))), "SpatialPixels") tgrd = seq(min(t)+10000, max(t)-10000, length.out = 10) stf = STF(grd, tgrd) #stf = STFDF(grd, tgrd, data.frame(x=rep(0,400*10))) library(stars) st = st_as_stars(stf) # define a variogram model sumMetricModel <- vgmST("sumMetric", space=vgm(1/6, "Sph", 0.25, 1/60), time =vgm(2/6, "Exp", 1e5, 1/60), joint=vgm(0.4, "Exp", 0.3, 0.1), stAni=1/1e6) attr(sumMetricModel, "temporal unit") <- "secs" dg <- data.frame(spacelag=rep(c(0.001,1:10)/10,6), timelag=rep(0:5*50e3, each=11)) #wireframe(model~spacelag+timelag, # variogramSurface(sumMetricModel, dist_grid = dg), # scales=list(arrows=F), # drape=T, col.regions=bpy.colors(), # zlim=c(0,1.2), # main="imposed sum-metric model") locKrig_sft <- krigeST(z~1, sft, st, sumMetricModel, nmax=20, computeVar = T) locKrig <- krigeST(z~1, stidf, stf, sumMetricModel, nmax=20, computeVar = T) stplot(locKrig[,,"var1.pred"], col.regions=bpy.colors(), scales=list(draw=T)) plot(locKrig_sft[1], col = sf.colors(), breaks = "equal") stplot(locKrig[,,"var1.var"], col.regions=bpy.colors(), scales=list(draw=T)) plot(locKrig_sft[2], col = sf.colors(), breaks = "equal") st$foo = 0 st_as_sf(st, long = TRUE) |> st_as_sftime() -> st.sftime locKrig_sft <- krigeST(z~1, sft, st.sftime, sumMetricModel, nmax=20, computeVar = T) plot(locKrig_sft["var1.pred"]) gstat/demo/stkrige.R0000644000176200001440000002317013777370515014135 0ustar liggesusers# Ben Graeler, 25 th March, 2016 # # Script reproducing the fit of the vignette "spatio-temporal-kriging # libraries library(sp) library(spacetime) library(gstat) library(rgdal) # load data from package gstat data(DE_RB_2005, package = "gstat") paper <- FALSE set.seed(123) smplDays <- sort(sample(365,8)) # load German boundaries data(air) DE_NUTS1 <- spTransform(DE_NUTS1, CRS("+init=epsg:32632")) if(!paper) plot(DE_NUTS1) # station wise coverage if(!paper) barplot(sort(table(DE_RB_2005@index[,1])), main="reported days per station", ylab="number of days", xaxt="n") # acf if(!paper) { acf(DE_RB_2005[sample(68,1),,drop=F]@data) var(DE_RB_2005@data$PM10) } # a few daily snapshots if(paper) png("vignettes/figures/daily_means_PM10.png", width=9, height=6, "in", res=150) stplot(as(DE_RB_2005[,smplDays],"STFDF"), col.regions=bpy.colors(120)[-(1:20)], sp.layout = list("sp.polygons", DE_NUTS1), scales=list(draw=F), key.space="right", colorkey=T, cuts=0:70, main=NULL) if(paper) dev.off() # number of stations length(DE_RB_2005@sp) # calculate the empirical variogram empVgm <- variogramST(PM10~1, DE_RB_2005, tlags=0:6) if(!paper) { plot(empVgm, wireframe=T, scales=list(arrows=F)) plot(empVgm) } # fit of theoretical purely spatial models # ############################################ spEmpVgm <- empVgm[empVgm$timelag == 0,] class(spEmpVgm) <- c("gstatVariogram", "data.frame") spEmpVgm <- spEmpVgm[-1,1:3] spEmpVgm$dir.hor <- 0 spEmpVgm$dir.ver <- 0 spVgmMod <- fit.variogram(spEmpVgm, vgm(80,"Exp",300000,20)) if(!paper) plot(spEmpVgm, spVgmMod) # fit of theoretical spatio-temporal models # ############################################# linStAni <- estiStAni(empVgm, c(50000,200000)) if(!paper) { plot(gamma~dist, empVgm[empVgm$timelag == 0,], ylim=c(0,100), xlim=c(0,800000)) points(empVgm[empVgm$spacelag == 0,]$timelag*linStAni, empVgm[empVgm$spacelag == 0,]$gamma, col="red") } ## # rescale empVgm and linStAni to km for estimation empVgm$dist <- empVgm$dist/1000 empVgm$avgDist <- empVgm$avgDist/1000 empVgm$spacelag <- empVgm$spacelag/1000 linStAni <- linStAni/1000 # separable separableModel <- vgmST("separable", space=vgm(0.9,"Exp", 200, 0.1), time =vgm(0.9,"Sph", 3.5, 0.1), sill=120) fitSepModel <- fit.StVariogram(empVgm, separableModel, fit.method = 7, stAni = linStAni, method = "L-BFGS-B", control = list(parscale=c(100,1,10,1,100)), lower = c(10,0,.1,0,0.1), upper = c(2000,1,12,1,200)) attr(fitSepModel, "optim.output")$value # Exp+Exp: 9.87, Exp+Sph: 6.82, Sph+Exp: 10.42, Sph+Sph: 7.50 if(!paper) plot(empVgm, fitSepModel, wireframe=T, all=T, scales=list(arrows=F), zlim=c(0,135)) # product-sum prodSumModel <- vgmST("productSum", space=vgm(10, "Exp", 200, 1), time= vgm(10, "Sph", 2, 1), k=2) fitProdSumModel <- fit.StVariogram(empVgm, prodSumModel, fit.method = 7, stAni = linStAni, method = "L-BFGS-B", control = list(parscale = c(1,10,1,1,0.1,1,10)), lower = rep(0.0001,7)) attr(fitProdSumModel, "optim.output")$value # Exp+Exp: 10.09, Exp+Sph: 6.91, Sph+Exp: 10.64, Sph+Sph: 7.59 plot(empVgm, fitProdSumModel, wireframe=T, all=T, scales=list(arrows=F), zlim=c(0,135)) # metric metricModel <- vgmST("metric", joint = vgm(60, "Mat", 150, 10, kappa=0.6), stAni = 60) fitMetricModel <- fit.StVariogram(empVgm, metricModel, fit.method = 7, stAni = linStAni, method = "L-BFGS-B", control = list(parscale = c(10,20,5,10)), lower = c(80,50,5,50), upper = c(200,1500,60,300)) attr(fitMetricModel, "optim.output")$value # Exp: 10.25, Sph: 10.59, # Gau: 21.32, Mat 5: 18.20, Mat 2: 14.43, Mat 1.25: 12.04, # Mat 1: 11.07, Mat 0.75: 10.23, Mat 0.6: 10.05 if(!paper) plot(empVgm, fitMetricModel, wireframe=T, all=T, scales=list(arrows=F), zlim=c(0,135)) # simplified sumMetric model? sumMetricFromsimpleSumMetric <- function(vgm) { vgmST("sumMetric", space=vgm(vgm$space$psill, vgm$space$model, vgm$space$range, vgm$nugget/3), time =vgm(vgm$time$psill, vgm$time$model, vgm$time$range, vgm$nugget/3), joint=vgm(vgm$joint$psill, vgm$joint$model, vgm$joint$range, vgm$nugget/3), stAni=vgm$stAni) } simpleSumMetricModel <- vgmST("simpleSumMetric", space=vgm(120,"Sph", 150), time =vgm(120,"Exp", 10), joint=vgm(120,"Sph", 150), nugget=10, stAni=150) fitSimpleSumMetricModel <- fit.StVariogram(empVgm, simpleSumMetricModel, fit.method = 7, stAni=linStAni, method = "L-BFGS-B", lower = c(sill.s = 0, range.s = 10, sill.t = 0, range.t = 0.1, sill.st= 0, range.st= 10, nugget=0, anis = 40), upper = c(sill.s = 200, range.s = 500, sill.t = 200, range.t = 20, sill.st= 200, range.st = 5000, nugget = 100, anis = 1000), control = list(parscale = c(1,10,1,1,1,100,1,10))) attr(fitSimpleSumMetricModel, "optim.output")$value # Exp+Exp+Exp: 4.10 Exp+Sph+Exp: 3.60 Sph+Exp+Exp: 3.94 Sph+Sph+Exp: 3.32 # Exp+Exp+Sph: 3.74 Exp+Sph+Sph: 3.98 Sph+Exp+Sph: 3.31 Sph+Sph+Sph: 3.56 if(!paper) plot(empVgm,fitSimpleSumMetricModel, wireframe = T, scales = list(arrows = F), all = T , zlim=c(0,130)) # sum-metric # sumMetricModel <- sumMetricFromsimpleSumMetric(fitSimpleSumMetricModel) sumMetricModel <- vgmST("sumMetric", space = vgm(20, "Sph", 150, 1), time = vgm(10, "Exp", 2, 0.5), joint = vgm(80, "Sph", 1500, 2.5), stAni = 120) fitSumMetricModel <- fit.StVariogram(empVgm, sumMetricModel, fit.method = 7, stAni=linStAni, method = "L-BFGS-B", lower = c(sill.s = 0, range.s = 10, nugget.s = 0, sill.t = 0, range.t = 0.1, nugget.t = 0, sill.st= 0, range.st = 10, nugget.st = 0, anis = 40), upper = c(sill.s = 200, range.s = 1E3, nugget.s = 20, sill.t = 200, range.t = 75, nugget.t = 20, sill.st= 200, range.st = 5E3, nugget.st = 20, anis = 500), control = list(parscale = c(1,100,1,1,0.5,1,1,100,1,100), maxit=1e4)) attr(fitSumMetricModel, "optim.output")$value # Exp+Exp+Exp: 4.10 Exp+Sph+Exp: 3.60 Sph+Exp+Exp: 3.89 Sph+Sph+Exp: 3.32 # Exp+Exp+Sph: 3.74 Exp+Sph+Sph: 3.73 Sph+Exp+Sph: 3.31 Sph+Sph+Sph: 3.36 if(!paper) plot(empVgm, fitSumMetricModel, wireframe=T, all=T, scales=list(arrows=F), zlim=c(0,130)) if(!paper) plot(empVgm,fitSumMetricModel, wireframe=T, all=T, scales=list(arrows=F), zlim=c(0,130)) if(paper) png("vignettes/figures/allVgmsWireframe.png", 9, 6, "in", bg="white", res = 150) plot(empVgm, list(fitSepModel, fitProdSumModel, fitMetricModel, fitSumMetricModel, fitSimpleSumMetricModel), wireframe=T, all=T, zlim=c(0,140), ylim=c(0,6.1), xlim=c(0,300), scales=list(arrows = F, cex=.8, x=list(at=0:3*100), y=list(at=0:6, labels=c("0 ","","2 ","","4 ","","6 ")), z=list(at=0:5*25, labels=c("0 ","","50 ","","100 ",""))), at=0:100*1.4, xlab=list("space [km]", rot=27, cex=0.8), ylab=list("time [days]", rot=-40, cex=0.8), zlab=list(NULL, rot=94, cex=0.8)) if(paper) dev.off() if(paper) png("vignettes/figures/allVgmsDiffWireframe.png", 9, 6, "in", bg="white", res = 150) plot(empVgm, list(fitSepModel, fitProdSumModel, fitMetricModel, fitSumMetricModel, fitSimpleSumMetricModel), wireframe=T, all=T, zlim=c(-10,25), ylim=c(0,6.1), xlim=c(0,300), diff=TRUE, scales=list(arrows = F, cex=.8, x=list(at=0:3*100), y=list(at=0:6, labels=c("0 ","","2 ","","4 ","","6 ")), z=list(at=-2:5*5, labels=c("-10 ","","0 ","","10 ","","20 ",""))), xlab=list("space [km]", rot=27, cex=0.8), ylab=list("time [days]", rot=-40, cex=0.8), zlab=list(NULL, rot=94, cex=0.8)) if(paper) dev.off() if(paper) { library(lattice) spacelag <- rep(0:300, 13) timelag <- rep(0:12/2,each=301) cplot <- contourplot(model~spacelag+timelag|type, rbind(cbind(variogramSurface(fitSumMetricModel, data.frame(spacelag=spacelag, timelag=timelag)), data.frame(type = rep("variogram of the sum-metric model", length(spacelag)))), data.frame(spacelag=spacelag, timelag=timelag, gamma=sqrt(spacelag^2+116^2*timelag^2)/10, type="metric distance [10 km]")), at=0:15*10, xlab="space [km]", ylab="timelag [days]") png("vignettes/figures/vgmVsMetricDist.png", 9, 4, "in", bg="white", res = 150) print(cplot) dev.off() }gstat/demo/line.R0000644000176200001440000000302713777370515013413 0ustar liggesuserslibrary(sp) library(gstat) data(meuse.grid) gridded(meuse.grid) = ~x+y data(meuse) coordinates(meuse) = ~x+y # choose arbitrary line over the grid: image(meuse.grid["dist"],axes=T) pp = rbind(c(180000,331000),c(180000,332000),c(181000,333500)) Sl = SpatialLines(list(Lines(list(Line(pp)), "a"))) plot(Sl,add=T,col='green') # use the default spsample arguments of predict.gstat: pts=spsample(Sl,n=500,'regular',offset=c(.5,.5)) plot(pts, pch=3, cex=.2, add=T) v = vgm(.6, "Sph", 900, .06) out1 = krige(log(zinc)~1, meuse, Sl, v) out1 points(180333,332167,pch=3,cex=2) # use the same line as block discretization, and predict for (0,0) # (because the block discretizing points are not centered) out2 = krige(log(zinc)~1, meuse, SpatialPoints(matrix(0,1,2)), v, block=coordinates(pts)) out2 compare.krigingLines = function(formula, data, newdata, model) { out1 = krige(formula, data, newdata, model) pts = spsample(newdata, n=500, 'regular', offset=.5) out2 = krige(formula, data, SpatialPoints(matrix(0,1,2)), model, block = coordinates(pts)) print("difference:") as.data.frame(out1)[3:4]- as.data.frame(out2)[3:4] } compare.krigingLines(log(zinc)~1, meuse, Sl, v) # one line, consisting of two line segments: pp2 = rbind(c(181000,333500),c(181000,332500)) Sl2 = SpatialLines(list(Lines(list(Line(pp),Line(pp2)), "a"))) krige(log(zinc)~1, meuse, Sl2, v) compare.krigingLines(log(zinc)~1, meuse, Sl2, v) # two seperate line segments: Sl3 = SpatialLines(list(Lines(list(Line(pp)), "a"),Lines(list(Line(pp2)),"b"))) krige(log(zinc)~1, meuse, Sl3, v) gstat/demo/lhs.R0000644000176200001440000000217213777370515013252 0ustar liggesuserslibrary(sp) library(gstat) # roughly follows the case presented in: # E.J. Pebesma and G.B.M. Heuvelink, 1999. Latin hypercube sampling # of Gaussian random fields. Technometrics 41 (4), pp. 303-312. data(meuse) data(meuse.grid) coordinates(meuse) = ~x+y gridded(meuse.grid) = ~x+y x <- variogram(log(zinc) ~ 1, meuse) v <- vgm(.5, "Sph", 800, nug = .1) v.fit = fit.variogram(x, model = v) plot(x, model = v.fit) n = 100 ok = krige(log(zinc)~1, meuse, meuse.grid, v.fit, nmax=40) sim = krige(log(zinc)~1, meuse, meuse.grid, v.fit, nsim = n, nmax=40) simo = t(apply(as.data.frame(sim)[1:n], 1, order)) # rank order nr = nrow(simo) # number of prediction locations simo = (simo - 1.0 + matrix(runif(n * nr), nr, n))/n summary(simo) # LHS on uniform [0,1] distribution; back to Gaussian: lhs = t(apply(cbind(ok$var1.pred, sqrt(ok$var1.var), simo), 1, function(x) qnorm(x[-(1:2)], x[1], x[2]))) sim2 = sim sim2@data = data.frame(lhs) spplot(sim2[1:10], main = 'lhs', col.regions=bpy.colors()) # verify that simulated and true mean/var are close: m = apply(lhs, 1, mean) v = apply(lhs, 1, var) summary(m - ok$var1.pred) summary(v - ok$var1.var) gstat/demo/cc.R0000644000176200001440000000100213777370515013040 0ustar liggesuserslibrary(sp) demo(meuse, ask = FALSE, echo = FALSE) library(gstat) # use collocated data: g = gstat(NULL, "lzinc", log(zinc)~1, meuse) g.coll = gstat(g, "dist", dist~1, meuse, nmax = 1, merge = c("lzinc", "dist")) g.fit = fit.lmc(variogram(g.coll), g.coll, vgm(1, "Sph", 900, 1), correct.diagonal = 1.01) g.non_coll = gstat(g, "dist", dist~1, meuse.grid, nmax = 1, merge = c("lzinc", "dist")) g.non_coll$model = g.fit$model # collocated cokriging: pr = predict(g.non_coll, meuse.grid) spplot(pr[c(1,3)]) gstat/demo/block.R0000644000176200001440000000254013777370515013555 0ustar liggesusers# $Id: block.R,v 1.5 2006-02-10 19:05:02 edzer Exp $ library(sp) data(meuse) coordinates(meuse) = ~x+y data(meuse.grid) gridded(meuse.grid) = ~x+y vgm.fit = fit.variogram(variogram(zinc~1, meuse), vgm(1, "Sph", 800, 1)) bl0 = krige(zinc~1, meuse, meuse.grid, model = vgm.fit, block = c(0,0)) bl1 = krige(zinc~1, meuse, meuse.grid, model = vgm.fit, block = c(40,40)) bl2 = krige(zinc~1, meuse, meuse.grid, model = vgm.fit,block = c(100,100)) bl3 = krige(zinc~1, meuse, meuse.grid, model = vgm.fit,block = c(400,400)) bl0$"block=0x0" = bl0$var1.pred bl0$"block=40x40" = bl1$var1.pred bl0$"block=100x100" = bl2$var1.pred bl0$"block=400x400" = bl3$var1.pred plt1 = spplot(bl0, 3:6, layout=c(4,1), col.regions=bpy.colors(), main = "kriging predictions") bl0$"block=0x0" = bl0$var1.var bl0$"block=40x40" = bl1$var1.var bl0$"block=100x100" = bl2$var1.var bl0$"block=400x400" = bl3$var1.var plt2 = spplot(bl0, 3:6, layout=c(4,1), col.regions=bpy.colors(), main = "kriging standard errors") print(plt1, split = c(1, 1, 1, 2), more = T) print(plt2, split = c(1, 2, 1, 2), more = F) # block krige the full area: bl = krige(zinc~1, meuse, newdata = SpatialPoints(data.frame(x=0,y=0)), model = vgm.fit, block = coordinates(meuse.grid)) bl # block kriging standard error: sqrt(bl$var1.var) # classical statistical standard error of mean: sqrt(var(meuse$zinc)/155) gstat/demo/ugsim.R0000644000176200001440000000126713777370515013614 0ustar liggesusers# $Id: ugsim.R,v 1.2 2006-02-10 19:05:02 edzer Exp $ library(sp) library(gstat) # prediction grid: data(meuse.grid) gridded(meuse.grid) = ~x+y # define variable as dummy data (parameters from log-zinc, meuse) v = vgm(.55, "Sph", 900, .05) g = gstat(NULL, "var1", lzn~1, beta = 5.9, nmax = 20, model = v, dummy = TRUE) # simulation of a single variable out = predict(g, meuse.grid, nsim = 20) spplot(out) # simulation of two negatively correlated variables: v = vgm(.55, "Sph", 900, .05) g = gstat(g, "var2", x~1, beta = 5.9, nmax = 20, model = v, dummy = TRUE) v = vgm(-.3, "Sph", 900, 0.00001) g = gstat(g, c("var1", "var2"), model = v) out = predict(g, meuse.grid, nsim = 10) spplot(out) gstat/demo/localKrigeST.R0000644000176200001440000000311513777370515015005 0ustar liggesusers## FNN local prediction ######################## library(sp) library(spacetime) library(gstat) library(lattice) # create n space-time points over [0,1] x [0,1] x [Now, Now+some days] t0 = Sys.time() # now n = 1000 set.seed(13131) # fix outcomes x = runif(n) y = runif(n) t = t0 + 1e6 * runif(n) z = rnorm(n) stidf = STIDF(SpatialPoints(cbind(x,y)), sort(t), data.frame(z=z)) stplot(stidf, number=21, main="random spatio-temporal noise") # create a regular 20 x 20 x 10 grid of prediction locations: grd = as(SpatialGrid(GridTopology(c(0.025,0.025), c(.05, .05), c(20,20))), "SpatialPixels") tgrd = seq(min(t)+10000, max(t)-10000, length.out = 10) stf = STF(grd, tgrd) # define a variogram model sumMetricModel <- vgmST("sumMetric", space=vgm(1/6, "Sph", 0.25, 1/60), time =vgm(2/6, "Exp", 1e5, 1/60), joint=vgm(0.4, "Exp", 0.3, 0.1), stAni=1/1e6) attr(sumMetricModel, "temporal unit") <- "secs" dg <- data.frame(spacelag=rep(c(0.001,1:10)/10,6), timelag=rep(0:5*50e3, each=11)) wireframe(model~spacelag+timelag, variogramSurface(sumMetricModel, dist_grid = dg), scales=list(arrows=F), drape=T, col.regions=bpy.colors(), zlim=c(0,1.2), main="imposed sum-metric model") locKrig <- krigeST(z~1, stidf, stf, sumMetricModel, nmax=50, computeVar = T) stplot(locKrig[,,"var1.pred"], col.regions=bpy.colors(), scales=list(draw=T)) stplot(locKrig[,,"var1.var"], col.regions=bpy.colors(), scales=list(draw=T))gstat/demo/pcb.R0000644000176200001440000001123413777370515013227 0ustar liggesusers# $Id: pcb.R,v 1.9 2008-02-01 22:39:44 edzer Exp $ # FIGURE 1: library(sp) library(gstat) library(maptools) library(lattice) data(pcb) coordinates(pcb) = ~x+y data(ncp.grid) gridded(ncp.grid) = ~x+y wsv = readShapePoly(system.file("external/ncp.shp", package="gstat")) classes = c(.2,1,2,5,10,20) print(xyplot(y ~ x | as.factor(year), groups = sqrt(PCB138)/3, data = as.data.frame(pcb), panel = function(x, y, groups, subscripts, ...) { sp.polygons(wsv, col = grey(.5)) panel.xyplot(x, y, cex = groups[subscripts], ...) }, xlab = "x-coordinate", ylab = "y-coordinate", key = list(corner = c(0,0), x=0.8, y=0.25, points = list(pch = 1, col = 1, cex = sqrt(classes)/3), text = list(as.character(classes))), aspect = "iso", as.table = T, xlim = c(464000, 739000), ylim = c(5696500, 6131500), scales = list(draw = F))) # FIGURE 2: pcb$yf = as.factor(pcb$year) pcb$int = rep(NA, dim(pcb)[1]) c = lm(log(PCB138)~-1+depth+yf,pcb)$coefficients i = 2 for (f in levels(pcb$yf)) { pcb$int[pcb$yf == f] = c[i] i = i+1 } print(xyplot(log(PCB138)~depth | as.factor(year), groups = int, data = as.data.frame(pcb), panel = function(x, y, groups, subscripts, ...) { # panel.grid(h=-1, v= 2) panel.xyplot(x, y) y = c(groups[subscripts][1], groups[subscripts][1] + -0.0641*45) llines(c(0, 45), y, lty = 2) }, scales = list( y = list(at=log(c(.2, .5, 1, 2, 5, 10, 20)), labels=c(".2",".5","1","2","5","10","20"), alternating = F) ), xlab = "water depth", ylab = "PCB138", as.table = T) ) # FIGURE 3: # ps.options(width=2, height=2) pcb$res=residuals(lm(log(PCB138)~year+depth, pcb)) v3 = variogram(res ~ year, pcb, dX=.1, bound=c(0,1000,3000,5000,(1:16)*10000)) print(plot(v3, model = vgm(.224,"Exp",17247,.08), plot.numbers = TRUE)) # FIGURE 4: # next g.pcb = NULL merge = list(c("P1986", 2, "P1991", 2), c("P1986", 2, "P1996", 2), c("P1986", 2, "P2000", 2)) for (f in levels(pcb$yf)[c(1,4,6,7)]) g.pcb= gstat(g.pcb, paste("P", as.character(f), sep = ""), log(PCB138)~depth, pcb[pcb$yf == f,], merge = merge) g.pcb = gstat(g.pcb, model = vgm(.224,"Exp",17247,.08), fill.all=T) v = variogram(g.pcb, cutoff=1e5) #plot(v, model = fit.lmc(v, g)) #plot(v, model = g,plot.numbers = TRUE) PCB.cor = matrix(NA, 4,4) i = 1 for (x in levels(pcb$yf)[c(1,4,6,7)]) { j = 1 for (y in levels(pcb$yf)[c(1,4,6,7)]) { A = log(pcb[pcb$yf == x,]$PCB138) B.tmp = krige(PCB138~1, pcb[pcb$yf == y,], pcb[pcb$yf == x,], nmax = 1, set=list(debug=0)) B = log(B.tmp$var1.pred) # print(paste(x, y, cor(A,B))) PCB.cor[i,j] = cor(A,B) j = j + 1 } i = i + 1 } years=c(1986,1991,1996,2000) dimnames(PCB.cor)=list(years,years) PCB.cor.ns = PCB.cor PCB.cor = 0.5 * (PCB.cor + t(PCB.cor)) i = 1 for (x in levels(pcb$yf)[c(1,4,6,7)]) { j = 1 for (y in levels(pcb$yf)[c(1,4,6,7)]) { if (j > i) { name = paste(paste("P", x, sep=""), paste("P", y, sep=""),sep = ".") print(name) g.pcb$model[[name]]["psill"] = g.pcb$model[[name]]["psill"] * PCB.cor[i,j] } j = j + 1 } i = i + 1 } print(plot(v, model = g.pcb, plot.numbers = FALSE)) print(PCB.cor.ns, digits=3) print(PCB.cor, digits=3) # FIGURE 5: pcb.cok = predict(g.pcb, newdata = ncp.grid, debug.level = 0) levs = c(.1,.2,.5,1,2,5,10,20) spplot(pcb.cok[c(1,3,5,7)], as.table=T, col.regions = bpy.colors(7), at = log(levs), colorkey = list(at = log(levs), labels = as.character(levs), col = bpy.colors(7)), layout = c(4,1) ) spplot(pcb.cok[c(4,11,6,12,13,8,14,15,16,10)-2], skip=c(F,T,T,T,F,F,T,T,F,F,F,T,F,F,F,F), as.table=T, layout=c(4,4), asp="iso", col.regions = bpy.colors()) X = cbind(rep(1,7), c(1986, 1987, 1989, 1991, 1993, 1996, 2000)) X2=X[c(1,4,6,7),] lambda = solve(t(X2) %*% X2) %*% t(X2) dimnames(lambda) = list(NULL, c(1986, 1991, 1996, 2000)) print(lambda[2, ], digits=3) # FIGURE 7: pcb.contr = get.contr(pcb.cok, g.pcb, X=lambda[2, ]) # copy coordinates #pcb.contr$x = pcb.cok$x #pcb.contr$y = pcb.cok$y pl1 = spplot(pcb.contr["beta.1"], main = "log-PCB138: change estimate", col.regions = bpy.colors(100)) pcb.contr$sig = pcb.contr$beta.1 / sqrt(pcb.contr$var.beta.1) pl2 = spplot(pcb.contr["sig"], main = "log-PCB138 change/SE", col.regions = bpy.colors(100)) print(pl1, position=c(0,0,0.5,1), more = TRUE) print(pl2, position=c(0.5,0,1,1), more = FALSE) cat("source:\n\nEdzer J. Pebesma, Richard N.M. Duin (2005) Spatio-temporal mapping of\nsea floor sediment pollution in the North Sea. In: Ph. Renard, and\nR. Froidevaux, eds. Proceedings GeoENV 2004 -- Fifth European Conference\non Geostatistics for Environmental Applications; Springer.\n") gstat/demo/krige.R0000644000176200001440000000203413777370515013562 0ustar liggesusers# $Id: krige.R,v 1.5 2007-02-27 22:09:31 edzer Exp $ library(sp) data(meuse) coordinates(meuse) = ~x+y data(meuse.grid) gridded(meuse.grid) = ~x+y # ordinary kriging v <- variogram(log(zinc)~1, meuse) m <- fit.variogram(v, vgm(1, "Sph", 300, 1)) plot(v, model = m) lzn.kr <- krige(formula = log(zinc)~1, meuse, meuse.grid, model = m) pl1 <- spplot(lzn.kr[1], main = "ordinary kriging prediction of log-zinc") lzn.kr$se = sqrt(lzn.kr$var1.var) pl2 <- spplot(lzn.kr["se"], main = "ordinary kriging prediction error") # universal kriging v <- variogram(log(zinc)~sqrt(dist), meuse) m <- fit.variogram(v, vgm(1, "Exp", 300, 1)) plot(v, model = m) lzn.kr <- krige(log(zinc)~sqrt(dist), meuse, meuse.grid, model = m) pl3 <- spplot(lzn.kr[1], main = "universal kriging prediction of log-zinc") lzn.kr$se = sqrt(lzn.kr$var1.var) pl4 <- spplot(lzn.kr["se"], main = "universal kriging prediction error") print(pl1, split = c(1,1,2,2), more = T) print(pl2, split = c(1,2,2,2), more = T) print(pl3, split = c(2,1,2,2), more = T) print(pl4, split = c(2,2,2,2)) gstat/demo/weight.R0000644000176200001440000000122313777370515013747 0ustar liggesuserskriging.weights = function(x, formula, newdata, model) { weighti = function(x, i, formula,...) { ret =rep(0,nrow(x)) ret[i]=1 x[[1]]=ret krige(formula = formula,locations = x,...) } ret = sapply(1:nrow(x), weighti, x=x, newdata=newdata[1,], model=model,formula=formula) ret = t(sapply(ret, as.data.frame)) unlist(ret[,3]) } # example, at first cell of meuse.grid: require(sp) require(gstat) data(meuse) data(meuse.grid) coordinates(meuse) = ~x+y coordinates(meuse.grid) = ~x+y meuse$wts = kriging.weights(meuse["zinc"], zinc~1, meuse.grid[1,], vgm(1, "Exp", 300)) summary(meuse$wts) spplot(meuse["wts"], col.regions=bpy.colors(), cuts=(0:10)/20) gstat/demo/sic2004.R0000644000176200001440000000776013777370515013560 0ustar liggesusers# $Id: sic2004.R,v 1.4 2006-11-22 12:54:16 edzer Exp $ # compared to the original submission, two errors # were found; one was corrected (dayx~x -> dayx~1), the other not. # read csv files: #sic.pred = read.csv("SIC2004_out.csv", header=F) #names(sic.pred) = c("record", "x", "y") #input = read.csv("SIC2004_input.csv", header=F) #names(input) = c("record", "x", "y", "dayx") #joker = read.csv("SIC2004_joker.csv", header=F) #names(joker) = c("record", "x", "y", "dayx") library(sp) library(gstat) library(lattice) data(sic2004) # load directly from R data base input = sic.test[,1:4] names(input) = c("record", "x", "y", "dayx") joker = sic.test[,c(1,2,3,5)] names(joker) = c("record", "x", "y", "dayx") do.sic = function(sic.input, sic.output) { require(gstat) # calculate omnidirectional sample variogram, cutoff 500000, intervals 20000 sic.input = sic.input[sic.input$record != 838, ] v.sample = variogram(dayx~1, ~x+y, input, width=2e4, cutoff=5e5) # ^^^^^ the error: this should be sic.input # ^ this error has been corrected # initial spherical model for fit: nug=100, p.sill=400,range=4.5e5 initial.model = vgm(400, "Sph", 450000, 100) # fit the nugget, sill and range to the sample variogram: v.fitted = fit.variogram(v.sample, initial.model, fit.method = 2) # function returns the output from the call to krige(): krige(dayx~1, ~x+y, sic.input, sic.output, model = v.fitted, nmax = 125) } # do the spatial interpolations: output = do.sic(input, sic.pred) joker.output = do.sic(joker, sic.pred) # write csv files: #write.table(output, "sic2004_output.csv", # sep=",", col.names=FALSE, row.names=FALSE) #write.table(joker.output, "sic2004_joker_output.csv", # sep=",", col.names=FALSE, row.names=FALSE) # calculate output: # read csv files: sic.stats = function(obs, pred) { print("observed:") x = obs print(c(min=min(x), max=max(x), mean=mean(x), median=median(x), stddev=sqrt(var(x)))) print("predicted:") x = pred print(c(min=min(x), max=max(x), mean=mean(x), median=median(x), stddev=sqrt(var(x)))) print("error:") x = pred - obs print(c(mae=mean(abs(x)), me=mean(x), corr=cor(pred,obs), rmse=sqrt(mean(x^2)))) } options(digits=4) print("input data first") sic.stats(sic.test[,4], output$var1.pred) print("joker with error variogram") sic.stats(sic.test[,4], joker.output$var1.pred) ################## do.sic = function(sic.input, sic.output) { require(gstat) v.sample = variogram(dayx~1, ~x+y, input, width=2e4, cutoff=5e5) initial.model = vgm(400, "Sph", 450000, 100) v.fitted = fit.variogram(v.sample, initial.model, fit.method = 2) krige(dayx~1, ~x+y, sic.input, sic.output, model = v.fitted, nmax = 125) } # do the spatial interpolations on a grid: grid1 = do.sic(input, sic.grid) grid2 = do.sic(joker, sic.grid) grid1$v2 = grid2$var1.pred grid1$v2.var = grid2$var1.var grid1$var1.pred[grid1$var1.pred>200] = 205 # mask larger values! grid1$v2[grid1$v2>200] = 205 # mask larger values! greys = c(255, 247, 240, 228, 217, 203, 189, 169, 150, 132, 115, 99, 82, 60, 37, 0) panel.sic = function(...){ panel.levelplot(...) lpoints(sic.train$x, sic.train$y, pch=22, cex=.5, col=1) lpoints(sic.pred$x, sic.pred$y, pch="+", cex=1, col=1) } cp1 = contourplot(z~x+y|name, map.to.lev(grid1,z=c(3,5), ns=c("data set 1","data set 2")), asp="iso", col.regions=rgb(greys/255,greys/255,greys/255), at=50+(0:16)*10,region=TRUE,labels=FALSE, xlab = "", ylab = "",scales=list(draw=F),panel=panel.sic) cp2 = contourplot(sqrt(z)~x+y|name, map.to.lev(grid1,z=4, ns="standard error"), asp="iso",scales=list(draw=F), col.regions=rgb(greys/255,greys/255,greys/255), region=TRUE,labels=FALSE, xlab = "", ylab = "", panel=panel.sic) print(cp1, c(0,0,0.625,1), more=T) print(cp2, c(0.625,0,1,1), more=F) wireframe(var1.pred~x+y,grid2,asp=c(diff(range(grid2$y))/diff(range(grid2$x)),0.5), xlab="x",ylab="y",zlab="z",drape=T, col.regions=gray(sqrt(seq(from=1.0, to=0.0, length=100)))) gstat/demo/examples.R0000644000176200001440000001616013777370515014304 0ustar liggesusers# $Id: examples.R,v 1.6 2006-02-10 19:05:02 edzer Exp $ ## ex01.cmd, ex02.cmd: ## ## Two variables with (initial estimates of) variograms, ## calcute sample variogram and plot fitted model ## library(sp) par(ask = TRUE) data(meuse) coordinates(meuse)=~x+y x <- variogram(zinc ~ 1, meuse) v <- vgm(140000, "Sph", 800, nug = 10000) plot(x, model = v) plot(x, model = fit.variogram(x, model = v)) x <- variogram(log(zinc) ~ 1, meuse) v <- vgm(.5, "Sph", 800, nug = .1) plot(x, model = v) plot(x, model = fit.variogram(x, model = v)) ## ## ex03.cmd: ## Inverse distance interpolation on a mask map ## data(meuse.grid) gridded(meuse.grid) = ~x+y x <- krige(zinc ~ 1, meuse, meuse.grid, model = NULL) library(lattice) spplot(x[1]) ## ## ex04.cmd ## Local ordinary block kriging at non-gridded locations ## ## the gstat "classic" radius maps into the gstat "S" maxdist argument ## new.locs <- SpatialPoints(cbind(x = c(181170, 180310, 180205, 178673, 178770, 178270), y = c(333250, 332189, 331707, 330066, 330675, 331075))) krige(zinc ~ 1, meuse, new.locs, model = vgm(1.34e5, "Sph", 800, nug = 2.42e4), block = c(40,40), nmax = 40, nmin = 20, maxdist = 1000) ## ## ex05.cmd ## ## Local simple point kriging on a mask map ## v <- vgm(0.581, "Sph", 900, nug = 0.0554) x <- krige(log(zinc) ~ 1, meuse, meuse.grid, model = v, nmax = 40, nmin = 20, maxdist = 1000, beta = 5.9) spplot(x[1], main = "log(zinc) simple kriging prediction") x$se = sqrt(x$var1.var) spplot(x["se"], main = "log(zinc) simple kriging standard errors") ## ## ex06.cmd ## ## Unconditional Gaussian simulation on a mask ## (local neigbourhoods, simple kriging) ## x <- krige(log(zinc) ~ 1, locations = NULL, newdata = meuse.grid, model = v, nmax = 20, beta = c(5.9), nsim = 5, dummy = TRUE) spplot(x, main = "five unconditional realisations of a correlated Gaussian field") ## ## ex07.cmd ## ## Gaussian simulation, conditional upon data ## (local neighbourhoods, simple and ordinary kriging) ## x <- krige(log(zinc) ~ 1, meuse, meuse.grid, model = v, nmax = 20, beta = c(5.9), nsim = 5) spplot(x, main = "five conditional realisations of a correlated Gaussian field") ## ## ex08.cmd ## ## Change of support: local ordinary block kriging on a mask ## x <- krige(log(zinc) ~ 1, meuse, meuse.grid, model = v, nmax = 40, nmin = 20, maxdist = 1000, block = c(40,40)) spplot(x[1], main = "ordinary block kriging predictions") x$se = sqrt(x$var1.var) spplot(x["se"], main = "ordinary block kriging prediction standard errors") ## ## ex09.cmd ## ## Obtain map values at data() locations ## (Point-map overlay) ## # we trick here by using inv.weighted distance interpolation, using the # single nearest observation. It will not fail on points outside the grid. # Note that we reversed meuse.grid and meuse to get these results. x <- krige(part.a ~ 1, meuse.grid, meuse, model = NULL, nmax = 1) meuse$part.a = x$var1.pred x <- krige(part.b ~ 1, meuse.grid, meuse, model = NULL, nmax = 1) meuse$part.b = x$var1.pred ## ## ex10.cmd ## ## Multiple kriging: prediction on more than one variable ## (ordinary kriging of two variables) ## (note that zinc_map.eas wass obtained through ex09.gst) ## x <- variogram(dist~1,meuse) v.dist <- fit.variogram(x, model = vgm(1,"Gau",100)) plot(x, model = v.dist) g <- gstat(id = "ln.zinc", form = log(zinc) ~ 1, data = meuse, nmax = 40, nmin = 20, maxdist = 1000, model = v) g <- gstat(g, id = "dist", form = dist ~ 1, data = meuse, nmax = 40, nmin = 20, maxdist = 1000, model = vgm(.01, "Nug", 0, add.to = v.dist)) # the added nugget variance is necessary to avoid near-singular covariances x <- predict(g, meuse.grid) spplot(x["ln.zinc.pred"], main = "log(zinc) ordinary kriging predictions") x$ln.zinc.se = sqrt(x$ln.zinc.var) spplot(x["ln.zinc.se"], main = "log(zinc) ordinary kriging prediction standard errors") spplot(x["dist.pred"], main = "dist ordinary kriging predictions") x$dist.se = sqrt(x$dist.var) spplot(x["dist.se"], main = "dist ordinary kriging prediction standard errors") ## ## ex11.cmd ## ## Multivariable kriging: ordinary local cokriging of two variables ## For examples of fitting an LMC: see demo(cokriging) ## g <- gstat(id = "ln.zinc", form = log(zinc) ~ 1, data = meuse, nmax = 40, nmin = 20, maxdist = 1000, model = vgm(0.581, "Sph", 900, 0.0554)) g <- gstat(g, id = "sq.dist", form = sqrt(dist) ~ 1, data = meuse, nmax = 40, nmin = 20, maxdist = 1000, model = vgm(0.0631, "Sph", 900, 0.0001)) g <- gstat(g, id = c("ln.zinc", "sq.dist"), model = vgm(-0.156, "Sph", 900, 1e-5)) # small nugget necessary to let gstat recognize LMC x <- predict(g, meuse.grid) spplot(x["ln.zinc.pred"], main = "log(zinc) ordinary cokriging predictions") x$ln.zinc.se = sqrt(x$ln.zinc.var) spplot(x["ln.zinc.se"], main = "log(zinc) ordinary cokriging prediction standard errors") spplot(x["sq.dist.pred"], main = "dist ordinary cokriging predictions") x$sq.dist.se = sqrt(x$sq.dist.var) spplot(x["sq.dist.se"], main = "dist ordinary cokriging prediction standard errors") ## ## ex12.cmd ## ## Stratified ordinary kriging (within-category ordinary kriging) ## # find out in which part the data are: meuse$part.a = krige(part.a~1, meuse.grid, meuse, nmax=1)$var1.pred x1 = krige(log(zinc)~1, meuse[meuse$part.a == 0,], meuse.grid[meuse.grid$part.a == 0,], model = vgm(.548, "Sph", 900, .0654), nmin = 20, nmax = 40, maxdist = 1000) x2 = krige(log(zinc)~1, meuse[meuse$part.a == 1,], meuse.grid[meuse.grid$part.a == 1,], model = vgm(.716, "Sph", 900), nmin = 20, nmax = 40, maxdist = 1000) x = rbind(as.data.frame(x1), as.data.frame(x2)) gridded(x) = ~x+y spplot(x["var1.pred"], main = "stratified kriging predictions") ## ## ex13.cmd ## ## Local universal kriging, using one continuous variable ### ## the variogram should be that of the residual: x <- krige(log(zinc) ~ sqrt(dist), meuse, meuse.grid, model = vgm(.149, "Sph", 700, .0674), nmax = 40, nmin = 20, maxdist = 1000) spplot(x["var1.pred"], main = "universal kriging predictions") x$var1.se = sqrt(x$var1.var) spplot(x["var1.se"], main = "universal kriging prediction standard errors") ## ## ex14.cmd ## ## Universal kriging, using one continuous and ## two binary variables. ## x <- krige(log(zinc) ~ -1 + sqrt(dist)+ part.a + part.b, meuse, meuse.grid, model = vgm(.149, "Sph", 700, .0674)) spplot(meuse.grid["part.a"], main = "the areas defining part.a (1) and part.b (0)") spplot(x["var1.pred"], main = "universal kriging predictions") x$var1.se = sqrt(x$var1.var) spplot(x["var1.se"], main = "universal kriging prediction standard errors") ## ## ex14a.cmd ## ## stratified universal kriging: ## (again: not implemented) ## ## ex15.cmd ## ## Local linear model, using one continuous variable ## x <- krige(log(zinc) ~ sqrt(dist), meuse, meuse.grid, model = NULL, nmax = 40, nmin = 20, maxdist = 1000) spplot(x["var1.pred"], main = "IID local linear model kriging predictions") x$var1.se = sqrt(x$var1.var) spplot(x["var1.se"], main = "IID local linear model prediction standard errors") ## ## ex16.cmd ## ## Multivariable indicator cosimulation ## ==>> see demo(cosimulation) for an extended example how to do this ## ## ## ex17.cmd ## ## global coordinate polynomial trend surfaces ## trend orders 0-3 ==>> better use lm() for this ## gstat/demo/ikr.R0000644000176200001440000000077713777370515013262 0ustar liggesuserslibrary(sp) library(gstat) data(meuse) data(meuse.grid) coordinates(meuse)=~x+y gridded(meuse.grid)=~x+y v = variogram(I(zinc < 500)~1,meuse) plot(v) vm = fit.variogram(v, vgm(1, "Sph", 300, 1)) plot(v,vm) vm # possibly adjust sum of sill to be max. 0.25? ik = krige(I(zinc>500)~1, meuse, meuse.grid, vm) spplot(ik[1],col.regions=bpy.colors()) summary(ik[[1]]) # adjust values outside [0,1] to nearest limit: ik[[1]][ik[[1]]<0] = 0 ik[[1]][ik[[1]]>1] = 1 summary(ik[[1]]) spplot(ik[1],col.regions=bpy.colors()) gstat/demo/snow.R0000644000176200001440000000206513777370515013453 0ustar liggesuserslibrary(sp) library(gstat) data(meuse.grid) gridded(meuse.grid) = ~x+y data(meuse) coordinates(meuse) = ~x+y ncell = 1000000 # sample 1000000 points over meuse.grid: newd = spsample(meuse.grid, ncell, type="regular") ncell = dim(coordinates(newd))[1] v = vgm(0.6, "Sph", 900, 0.05) library(parallel) nclus = detectCores() clus <- c(rep("localhost", nclus)) # set up cluster and data cl <- makeCluster(clus, type = "SOCK") clusterEvalQ(cl, library(gstat)) clusterExport(cl, list("meuse", "meuse.grid", "v")) # split prediction locations: # either at random: splt = sample(1:nclus, nrow(coordinates(newd)), replace = TRUE) # or regular: splt = rep(1:nclus, each = ceiling(ncell/nclus), length.out = ncell) newdlst = lapply(as.list(1:nclus), function(w) newd[splt == w,]) # no cluster: system.time(out.noclus <- krige(log(zinc)~1, meuse, newd, v)) # with cluster: system.time(out.clus <- do.call("rbind", parLapply(cl, newdlst, function(lst) krige(log(zinc)~1, meuse, lst, v) ))) stopCluster(cl) all.equal(out.clus, out.noclus) gridded(out.clus) = TRUE image(out.clus) gstat/demo/00Index0000644000176200001440000000423614322067013013455 0ustar liggesusersa2p area-to-point kriging with krige0 a2pinST area-to-point kriging in space-time with krigeST block block kriging -- effect of block size and irregular blocks blue how to get BLUE coefficients out of a predict.gstat call cc collocated cokriging example circEmbeddingMeuse simulation based in circular embedding allowing fft cokriging fitting a linear model of coregionalization and cokriging comp_geoR compare gstat kriging output with that obtained from geoR cosimulation fitting a linear model of coregionalization and cosimulation depend check gstat package dependencies examples how to do the original gstat example files in S grass example grass/R/gstat run; requires grass meuse data set installed gstat3D example of 3D interpolation of random points ikr example indicator kriging on zinc w. threshold 500 ppm krige sample run of ordinary and universal kriging lhs create latin hypercube sample of Gaussian random field lnsim carry out log-normal kriging, based on conditional simulation sic2004 part of sic2004 excercise; see ?sic2004 sftime demo using package sftime, derived from demo(stkrige) pcb pcb North Sea data analysis as used for geoENV2004 paper; see ?pcb fulmar analysis of Fulmaris glacialis data on Dutch part of the North Sea uisim unconditional indicator simulation, 2 and 3 category examples ugsim unconditional Gaussian simulation snow parallel kriging using package snow (not on Windows) line examples for lines support prediction weight compute (the expensive way) kriging weights for a single prediction location wind space-time kriging with the Irish wind data sets rep 10 x 10 matrix of fitted variograms from 100 simulated fields sftime demonstration for using the classes of sftime, local spatio-temporal kriging stkrige model estimation for Vignette spatio-temporal kriging stkrige-prediction prediction as in Vignette spatio-temporal kriging [!time consuming!] stkrige-crossvalidation crossvalidation as in Vignette spatio-temporal kriging [!very time consuming!] localKrigeST locally krige an irregular spatio-temporal data set to a regular spatio-temporal grid zonal approximate zonal anisotropy with geometrically anistropic model gstat/demo/comp_geoR.R0000644000176200001440000000062413777370515014376 0ustar liggesuserslibrary(sp) library(gstat) library(geoR) xyz = data.frame(x = c(0,0,1), y = c(0, 1, 1), z = c(1,2,3)) coordinates(xyz)=~x+y x0 = SpatialPoints(data.frame(x=0,y=.5)) kr1 = krige(z~1,xyz,x0,vgm(1, "Exp", 1)) kr2 = krige.conv(as.geodata(xyz), locations=coordinates(x0), krige=list(cov.model="exponential", cov.par=c(1,1))) kr1 c(kr2$predict, kr2$krige.var) kr1[[1]] - kr2$predict kr1[[2]] - kr2$krige.var gstat/demo/cokriging.R0000644000176200001440000000367114336470233014433 0ustar liggesusers# $Id: cokriging.R,v 1.4 2006-02-10 19:05:02 edzer Exp $ library(stars) library(gstat) data(meuse, package = "sp") meuse = st_as_sf(meuse, coords = c("x", "y")) data(meuse.grid, package = "sp") meuse.grid = st_as_stars(meuse.grid) # cokriging of the four heavy metal variables # create gstat object, stepwise: gstat(id="zn", formula=log(zinc)~1, data=meuse, nmax = 10) |> gstat("cu", log(copper)~1, meuse, nmax = 10) |> gstat("cd", log(cadmium)~1, meuse, nmax = 10) |> gstat("pb", log(lead)~1, meuse, nmax = 10) |> gstat(model=vgm(1, "Sph", 900, 1), fill.all=T) -> meuse.g x <- variogram(meuse.g, cutoff=1000) meuse.fit = fit.lmc(x, meuse.g) plot(x, model = meuse.fit) z <- predict(meuse.fit, newdata = meuse.grid) z[c(1,3,5,7)] |> merge() |> plot() # compute & plot standard errors: z[c(2,4,6,9)] |> setNames(paste0(c("zn", "cu", "pb", "cd"), ": se")) |> merge() |> sqrt() |> plot() # old-style, with sp: # indicator cokriging for the 9 percentiles of zinc: q <- quantile(meuse$zinc, seq(.1,.9,.1)) gstat(id = "zn1", formula = I(zinc < q[1])~1, data = meuse, nmax = 7, beta = .1, set = list(order = 4, zero = 1e-5)) |> gstat("zn2", I(zinc < q[2])~1, meuse, nmax = 7, beta=.2) |> gstat("zn3", I(zinc < q[3])~1, meuse, nmax = 7, beta=.3) |> gstat("zn4", I(zinc < q[4])~1, meuse, nmax = 7, beta=.4) |> gstat("zn5", I(zinc < q[5])~1, meuse, nmax = 7, beta=.5) |> gstat("zn6", I(zinc < q[6])~1, meuse, nmax = 7, beta=.6) |> gstat("zn7", I(zinc < q[7])~1, meuse, nmax = 7, beta=.7) |> gstat("zn8", I(zinc < q[8])~1, meuse, nmax = 7, beta=.8) |> gstat("zn9", I(zinc < q[9])~1, meuse, nmax = 7, beta=.9) |> gstat(model=vgm(1, "Sph", 900, 1), fill.all=T) -> meuse.i x <- variogram(meuse.i, cutoff=1000) meuse.fit = fit.lmc(x, meuse.i, correct.diagonal = 1.01) plot(x, model = meuse.fit) z <- predict(meuse.fit, newdata = meuse.grid) z[c(1,3,5,7,9,11,13,15,17)] |> setNames(paste("est.Pr(Zn < ", signif(q,4), ")", sep = "")) |> merge() |> plot() gstat/data/0000755000176200001440000000000013777370515012324 5ustar liggesusersgstat/data/sic2004.rda0000644000176200001440000003636414413507477014111 0ustar liggesusers7zXZi"6!XW<])TW"nRʟ$85EҤ fC%#dcj~[AǸY7)]grmŢ{#v!@w7Aal[) HGN~R> >Q <~fHCz8NvYl6ir(|ZڣL \7m,Yߙ Rsu"~4;ˠ^uRta{<dždˉiƤxY]j1y{qOEG&'ߚK/S" NOh<.eKT#q=up{Rfbz%=>HNX{: ,! s0*/Z/Ou+x.ua-* Caok/;)^Q!S!b:+iQJ21ņp eNȡ,KFu65@<0[,zK!=jcNu ~ܴ]7ƧZ>Ǡ&=et56:_ #{ 0=A#ɭvS*Svl58?IZ0b[ܖxvfS ^+/uvYdyS “Kl, K ڃEiN0wyBy#'KS02(7V}8(~ކniJ2D[yJm\!J$Zl/ZS%F:ʵ[A|yIgS>R MhY}Ѝ&֑Ws\gLpǬ=!D`R-7G+OkQz£QTE:9XӒJ+6˃P0(qj%CQ ]t~87I_}w">>fTjoyKzn}3El$IʬA. kW'w)lF*Dӯ j"Ʋ= CY%Y TÓȏͨSNZ(Bz}=n2w[ fCK/ƾ|5QEN^.n0>!V>xQ@Dz@5S$9k;op+Y&UP9kφ ]2ToNv$?>Y="p^_ *pZzI]@Ґb*9~gF*92eՈzHL:%ԚKnA&_,o2:o_˸+ק$F\N8d#f lV _PHZu]E"[0)hq%g{lL*}q)*~5auTXߥ<%Qa@:7 _!|4+aTC/VF3m ~G)* uH]T\^X.jmM|&A^kUŮQnL՗AΫVfJ1wu;*šI'T $A%1wRSu"-͞  Sv ?}7ψ={avv,(uꈰT|8q&_KwY9n˂dnV&5L4Ai婻;6nw`UIm QZ[8^렆56ӂ^" ԵaVgF^uw5Z,*cs3AݶA Qx/\CS4)B-eYM4~9Sͤ> r)I$2*r79 (߶Lp E*N}G( [1=݀O/B =gY 6&49 v^)dLAg{{jnCF؜QgkNwR1胞s:nNz< !CFl.|r(@bMJ$ N<.laҊ.NdhrrB `|xċeDM3V19*M'ۼyݏ;6HaP b jLNsnY$heVt̸8)TN&<4Tz^,OnY2{/oK6rsm }#iק̩ny ؙ`0Փ0?wz͐|G'b噕8f?LR KF,y7Cⴾ#H/e}k=HƨN3g#Dy~\B7}_>[-/O7PNE[P ധŃмW.aA'a^- `n"A:rcīqݢA䠄Ar 8l.sw w,v+VX;|unsr),10Ea8pr/p=Eڣz  }Eg2絎@u1ձO )@,?Sl{]!YfHk&gH` nNf[im֐hf3j"&^\MBJ> @$0H+FëݵYif9g9l'KmQSeN+DU 413hnJ\j" jI'WW嬊%qԜcͽo|ݥq|?hUx΃LP*VfƖPDXI5+rx}P [QJ_߫ 5zr(FaL+Nh'yFO * Nլ _Lrß7H&/H`Zv3gqȴ7c%aiT퓙{n&o"֊*<|I~SlY}mwHh^xv1'B"RD(>FQW+,&ǃ[5߻{q?W$ϨP9\T7If2bf0D ,ݫ\K<]7Lӗ\ya+k l(U0ݜxV_>:(bcc'2am\3?ZEUi! \pʞoG\C6)F[{(ɺm$J/#V }Ib+`?p+GQx Zԣ䰡vqⶫ) <*dà *g˗#$]=W=UZH*9dC 6j̭44Y ?lh1N=?w' ?b$gy$҄P؊% #'wgLm1 :/dM=/ 0ȱN0d24]WwG\yown_HNlkubh4|A#%]_%j@% @!l.D23ca ZYm5Pt Ҷb斱N@x"v:dMExf"obk"C N@dt*!PwHaQdpF=8 Uskxh+%lq.PvM:4ݸoh':P<cUW12%~!YТ jͭ fڑɚ˟/+6`(}a_3`ޝu2^<rq"V o45R7ᄓy9h8NYu}$IN+Cw o;mNbWWN}Ƒv}ͲګDVdHnLqJْms?:!*@~/r'ܒߋ-}`UyxI- Taˇ(eHԸ4Pf|gꌰQ;( k/[-N9W(|N|n7vhIp*0d;Ț͇J5у&OT vT"P~K0N+߼ }+KGLkz]Z# .|-Mg$÷baB.R܊OHy9Dpǯ)ثp9u.+X褔`tVE}NqvuRnۻV۽`V;vYFe3C?WqkżfkzS ݵzγ_t3noܢ p_ #ıe1wfZ1yQAbWPXO{VdRpQ_YH3=J VhG_=u,}1@h>W EdN=G̼`I\Bs'G5vN.E%my =55%-ÔVy#`ܰfoPiVՈGuV 9x:7T~MV˘ $YV} ! 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ÁEedeP ̢] ,BUncR&Y8@U‘Jp@UT HRG庻:\ x:܍`ЉñE5)*xIƴi{U8SQ(?0Q5}ҦPt:є] V/*iZlr8>l%)T(j-=2jy=3ˋy3 qwU7 It6Y&9'mr- #mj?&*7i0\6Kc,UږKPbwsN"ΉmZy qR##%h>)r AmJAd\R;uzKk6MEĄIst/88]p((PP r(%OwY9f>%Ny$I$I$I$I$I$I$I$I$I$I$IBxI$DI$I&nf[PYZi:a" )TER*1(e(nیfU[r˹ۻtw&swn.nMؠ҆ kTR[s\\TEUQmU^VբQQ)}W#dH'L,L6E/,PVР-B(SsWJ a\PP@6';YYyyyyrB t=jիW1 vG{iŨM ]Znݻv۷eUr$I$J5UUUUUT"P'5u~'LZ g{^^u鰌(eU힜]'[g\k }"~߿~e0@($H I&fPI$E3sSR)H0AI$P` ܀sA>>~gŞxz_2Mcu+2Ǚ5sfF<&52/@AޞNL|3S#*(iIMf(hQ(`ifhף*z6C\^%dQm^^7mb+5+{UyQZz]mY]xzwEˇHּP HC BR! bLUdNxcssw(W5˔˖w\IFd sn.](W@\ױjV+xk67X9[x[%j6WjUjɣFTj5I"DdH0P6I\8I%(3HAd;jEZXƊ-%ͻZ",EMjV׸՚@Y$+J Q ZQ*APuv< V /*8CZ] orPL%L2h|Z}-Ǧv\\jqfѮTǿ21pWb&QB#dV@/.*W @738\g~P 8Ne  @PPN'٥;!upeovE}i [~+,Y C~E#c'_KIBohvLL_)T7,U"0l4w6reؕ7w+i%ztyJn{G_ŧAxutniiΟg3YN255vg]a՗j@aUC Eh{pB|8軜4/ORڥK6%RhE)Ȩn$ HR!tDaCWuhXkLeGl'nN39<*Ş :%Y D Ψq,Ñ4"Ӝ4=++]_`;pچ`B>@Z:D: f= 2.10) Imports: utils, stats, graphics, methods, lattice, sp (>= 0.9-72), zoo, sf (>= 0.7-2), sftime, spacetime (>= 1.2-8), stars, FNN Suggests: fields, maps, mapdata, xts, raster, future, future.apply License: GPL (>= 2.0) URL: https://github.com/r-spatial/gstat/ Encoding: UTF-8 BugReports: https://github.com/r-spatial/gstat/issues/ NeedsCompilation: yes RoxygenNote: 6.1.1 Packaged: 2023-04-06 09:22:07 UTC; edzer Author: Edzer Pebesma [aut, cre] (), Benedikt Graeler [aut] Maintainer: Edzer Pebesma Repository: CRAN Date/Publication: 2023-04-06 10:32:40 UTC gstat/build/0000755000176200001440000000000014413507474012504 5ustar liggesusersgstat/build/vignette.rds0000644000176200001440000000054214413507474015044 0ustar liggesusersRMk0 u۴] Av=s.]EIllNn~XS$!c͢vXgDGNDπ 3d^>Wk 9X(!DLS>^"/2S VVj9_H-+HVq 5И5RBA i(|k0 #JS++Cj_pTZ-*[y<-.uNi_<`GnGHS̋dZ 3tca2VP۟25^<㦖)@z.E n?%9(JMt 7\mgstat/tests/0000755000176200001440000000000014413474732012547 5ustar liggesusersgstat/tests/vdist.R0000644000176200001440000000054613777370515014036 0ustar liggesuserslibrary(sp) library(gstat) data(meuse) coordinates(meuse) = ~x+y data(meuse.grid) gridded(meuse.grid) = ~x+y mg = meuse.grid gridded(mg) = FALSE mg= mg[1500,] krige(log(zinc)~1,meuse,mg,vgm(1, "Exp", 300, anis=c(0,0.01)), vdist=FALSE, maxdist=1000,nmax=10) krige(log(zinc)~1,meuse,mg,vgm(1, "Exp", 300, anis=c(0,0.01)), vdist=TRUE, maxdist=1000,nmax=10) gstat/tests/allier.Rout.save0000644000176200001440000003040414314525262015623 0ustar liggesusers R version 4.2.0 (2022-04-22) -- "Vigorous Calisthenics" Copyright (C) 2022 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > # Sytze de Bruin's post to r-sig-geo, Nov 16, 2015: > library(sp) > library(gstat) > > # some data > x <- c(215, 330, 410, 470, 545) > y <- c(230, 310, 330, 340, 365) > fc <- c(0.211, 0.251, 0.281, 0.262, 0.242) > por <- c(0.438, 0.457, 0.419, 0.430, 0.468) > Allier <- data.frame(x, y, fc, por) > coordinates(Allier) = ~x+y > > # gstat object for co-kriging using linear model of co-regionalization > g <- gstat(id=c("fc"), formula=fc~1, data=Allier, + model=vgm(0.00247, "Sph", 480, 0.00166)) > g <- gstat(g, id="por", formula=por~1, data=Allier, + model=vgm(0.00239, "Sph", 480, 0.00118)) > g <- gstat(g, id=c("fc", "por"), + model=vgm(0.00151, "Sph", 480, -0.00124)) > > # predict at single point > g$set = list(choleski = 0) # LDL' > A <- predict(g, SpatialPoints(data.frame(x=450, y=350)), debug = 32) Linear Model of Coregionalization found. Good. [using ordinary cokriging] we're at location X: 450 Y: 350 Z: 0 zero block size we're at point X: 450 Y: 350 Z: 0 # X: #Matrix: 10 by 2 rbind( c( 1.000000, 0.000000), # row 1 c( 1.000000, 0.000000), # row 2 c( 1.000000, 0.000000), # row 3 c( 1.000000, 0.000000), # row 4 c( 1.000000, 0.000000), # row 5 c( 0.000000, 1.000000), # row 6 c( 0.000000, 1.000000), # row 7 c( 0.000000, 1.000000), # row 8 c( 0.000000, 1.000000), # row 9 c( 0.000000, 1.000000) # row 10 ) [using generalized covariances: max_val - semivariance()] # Covariances (x_i, x_j) matrix C (upper triangle): #Matrix: 10 by 10 rbind( c( 0.004130, 0.001419, 0.000896, 0.000566, 0.000224, 0.000270, 0.000868, 0.000548, 0.000346, 0.000137), # row 1 c( 0.001419, 0.004130, 0.001840, 0.001398, 0.000879, 0.000868, 0.000270, 0.001125, 0.000854, 0.000537), # row 2 c( 0.000896, 0.001840, 0.004130, 0.002003, 0.001424, 0.000548, 0.001125, 0.000270, 0.001225, 0.000870), # row 3 c( 0.000566, 0.001398, 0.002003, 0.004130, 0.001865, 0.000346, 0.000854, 0.001225, 0.000270, 0.001140), # row 4 c( 0.000224, 0.000879, 0.001424, 0.001865, 0.004130, 0.000137, 0.000537, 0.000870, 0.001140, 0.000270), # row 5 c( 0.000270, 0.000868, 0.000548, 0.000346, 0.000137, 0.003570, 0.001373, 0.000867, 0.000547, 0.000217), # row 6 c( 0.000868, 0.000270, 0.001125, 0.000854, 0.000537, 0.001373, 0.003570, 0.001780, 0.001352, 0.000851), # row 7 c( 0.000548, 0.001125, 0.000270, 0.001225, 0.000870, 0.000867, 0.001780, 0.003570, 0.001938, 0.001378), # row 8 c( 0.000346, 0.000854, 0.001225, 0.000270, 0.001140, 0.000547, 0.001352, 0.001938, 0.003570, 0.001805), # row 9 c( 0.000137, 0.000537, 0.000870, 0.001140, 0.000270, 0.000217, 0.000851, 0.001378, 0.001805, 0.003570) # row 10 ) # glm->C, LDL' decomposed:: #Matrix: 10 by 10 rbind( c( 0.003399, 0.372269, 0.208612, 0.127967, 0.016746, -0.025847, 0.223862, 0.148767, 0.104047, 0.038371), # row 1 c( 0.000000, 0.002661, 0.483725, 0.327484, 0.153742, 0.233021, -0.125118, 0.262410, 0.219271, 0.150536), # row 2 c( 0.000000, 0.000000, 0.002276, 0.540203, 0.303585, 0.058071, 0.314376, -0.175899, 0.295181, 0.243817), # row 3 c( 0.000000, 0.000000, 0.000000, 0.002484, 0.483068, 0.000301, 0.115816, 0.377362, -0.115338, 0.319418), # row 4 c( 0.000000, 0.000000, 0.000000, 0.000000, 0.003690, -0.038142, 0.000474, 0.120915, 0.377730, 0.075630), # row 5 c( 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.003019, 0.354325, 0.235465, 0.164684, 0.060733), # row 6 c( 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.002623, 0.415337, 0.347059, 0.238266), # row 7 c( 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.002458, 0.467207, 0.385909), # row 8 c( 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.002658, 0.505569), # row 9 c( 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.003570) # row 10 ) # X'C-1 X: #Matrix: 2 by 2 rbind( c(665.433994, -232.313340), # row 1 c(-232.313340, 729.440848) # row 2 ) # beta: #Vector: dim: 2 c( 0.244216, 0.440933) # Cov(beta), (X'C-1 X)-1: #Matrix: 2 by 2 rbind( c( 0.001691, 0.000538), # row 1 c( 0.000538, 0.001542) # row 2 ) # Corr(beta): #Matrix: 2 by 2 rbind( c( 1.000000, 0.333447), # row 1 c( 0.333447, 1.000000) # row 2 ) # X0 (X values at prediction location x0): #Matrix: 2 by 2 rbind( c( 1.000000, 0.000000), # row 1 c( 0.000000, 1.000000) # row 2 ) # BLUE(mu), E(y(x0)) = X0'beta: #Vector: dim: 2 c( 0.244216, 0.440933) # Covariances (x_i, x_0), C0: #Matrix: 10 by 2 rbind( c( 0.000638, 0.000390), # row 1 c( 0.001516, 0.000927), # row 2 c( 0.002126, 0.001300), # row 3 c( 0.002298, 0.001405), # row 4 c( 0.001738, 0.001062), # row 5 c( 0.000390, 0.000618), # row 6 c( 0.000927, 0.001467), # row 7 c( 0.001300, 0.002057), # row 8 c( 0.001405, 0.002223), # row 9 c( 0.001062, 0.001681) # row 10 ) # C-1 C0: #Matrix: 10 by 2 rbind( c( 0.008927, -0.017995), # row 1 c( 0.061935, -0.028550), # row 2 c( 0.225195, 0.078344), # row 3 c( 0.356735, 0.190177), # row 4 c( 0.094128, -0.023136), # row 5 c(-0.021119, 0.004935), # row 6 c(-0.033508, 0.055601), # row 7 c( 0.091947, 0.242576), # row 8 c( 0.223200, 0.398927), # row 9 c(-0.027153, 0.088995) # row 10 ) # [a] Cov_ij(B,B) or Cov_ij(0,0): #Matrix: 2 by 2 rbind( c( 0.004130, 0.000270), # row 1 c( 0.000270, 0.003570) # row 2 ) # [c] (x0-X'C-1 c0)'(X'C-1 X)-1(x0-X'C-1 c0): #Matrix: 2 by 2 rbind( c( 0.000129, -0.000107), # row 1 c(-0.000107, 0.000089) # row 2 ) # [b] c0'C-1 c0: #Matrix: 2 by 2 rbind( c( 0.001926, 0.001532), # row 1 c( 0.001532, 0.001931) # row 2 ) # Best Linear Unbiased Predictor: #Vector: dim: 2 c( 0.253090, 0.441258) # MSPE ([a]-[b]+[c]): #Matrix: 2 by 2 rbind( c( 0.002332, -0.001369), # row 1 c(-0.001369, 0.001729) # row 2 ) # kriging weights: #Matrix: 10 by 2 rbind( c( 0.071177, -0.064988), # row 1 c( 0.108451, -0.066123), # row 2 c( 0.268160, 0.043141), # row 3 c( 0.401959, 0.153312), # row 4 c( 0.150253, -0.065342), # row 5 c(-0.076273, 0.056759), # row 6 c(-0.077605, 0.093781), # row 7 c( 0.050632, 0.277731), # row 8 c( 0.179933, 0.435972), # row 9 c(-0.076688, 0.135756) # row 10 ) > g$set = list(choleski = 1) # Choleski > B <- predict(g, SpatialPoints(data.frame(x=450, y=350)), debug = 32) Linear Model of Coregionalization found. Good. [using ordinary cokriging] we're at location X: 450 Y: 350 Z: 0 zero block size we're at point X: 450 Y: 350 Z: 0 # X: #Matrix: 10 by 2 rbind( c( 1.000000, 0.000000), # row 1 c( 1.000000, 0.000000), # row 2 c( 1.000000, 0.000000), # row 3 c( 1.000000, 0.000000), # row 4 c( 1.000000, 0.000000), # row 5 c( 0.000000, 1.000000), # row 6 c( 0.000000, 1.000000), # row 7 c( 0.000000, 1.000000), # row 8 c( 0.000000, 1.000000), # row 9 c( 0.000000, 1.000000) # row 10 ) [using generalized covariances: max_val - semivariance()] # Covariances (x_i, x_j) matrix C (upper triangle): #Matrix: 10 by 10 rbind( c( 0.004130, 0.001419, 0.000896, 0.000566, 0.000224, 0.000270, 0.000868, 0.000548, 0.000346, 0.000137), # row 1 c( 0.001419, 0.004130, 0.001840, 0.001398, 0.000879, 0.000868, 0.000270, 0.001125, 0.000854, 0.000537), # row 2 c( 0.000896, 0.001840, 0.004130, 0.002003, 0.001424, 0.000548, 0.001125, 0.000270, 0.001225, 0.000870), # row 3 c( 0.000566, 0.001398, 0.002003, 0.004130, 0.001865, 0.000346, 0.000854, 0.001225, 0.000270, 0.001140), # row 4 c( 0.000224, 0.000879, 0.001424, 0.001865, 0.004130, 0.000137, 0.000537, 0.000870, 0.001140, 0.000270), # row 5 c( 0.000270, 0.000868, 0.000548, 0.000346, 0.000137, 0.003570, 0.001373, 0.000867, 0.000547, 0.000217), # row 6 c( 0.000868, 0.000270, 0.001125, 0.000854, 0.000537, 0.001373, 0.003570, 0.001780, 0.001352, 0.000851), # row 7 c( 0.000548, 0.001125, 0.000270, 0.001225, 0.000870, 0.000867, 0.001780, 0.003570, 0.001938, 0.001378), # row 8 c( 0.000346, 0.000854, 0.001225, 0.000270, 0.001140, 0.000547, 0.001352, 0.001938, 0.003570, 0.001805), # row 9 c( 0.000137, 0.000537, 0.000870, 0.001140, 0.000270, 0.000217, 0.000851, 0.001378, 0.001805, 0.003570) # row 10 ) # glm->C, Choleski decomposed:: #Matrix: 10 by 10 rbind( c( 0.064265, 0.022086, 0.013942, 0.008801, 0.003487, 0.004201, 0.013502, 0.008523, 0.005380, 0.002132), # row 1 c( 0.000000, 0.060351, 0.025382, 0.019938, 0.013290, 0.012840, -0.000468, 0.015517, 0.012189, 0.008125), # row 2 c( 0.000000, 0.000000, 0.057370, 0.023954, 0.018091, 0.002846, 0.016530, -0.004230, 0.014644, 0.011059), # row 3 c( 0.000000, 0.000000, 0.000000, 0.055509, 0.020471, -0.000277, 0.006286, 0.016960, -0.006686, 0.012514), # row 4 c( 0.000000, 0.000000, 0.000000, 0.000000, 0.056523, -0.001665, 0.001218, 0.006437, 0.014711, -0.005337), # row 5 c( 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.058108, 0.022018, 0.011347, 0.006008, 0.001147), # row 6 c( 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.050877, 0.027084, 0.018381, 0.010720), # row 7 c( 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.045247, 0.026914, 0.017658), # row 8 c( 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.042645, 0.023811), # row 9 c( 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.046872) # row 10 ) # X'C-1 X: #Matrix: 2 by 2 rbind( c(665.433994, -232.313340), # row 1 c(-232.313340, 729.440848) # row 2 ) # beta: #Vector: dim: 2 c( 0.244216, 0.440933) # Cov(beta), (X'C-1 X)-1: #Matrix: 2 by 2 rbind( c( 0.001691, 0.000538), # row 1 c( 0.000538, 0.001542) # row 2 ) # Corr(beta): #Matrix: 2 by 2 rbind( c( 1.000000, 0.333447), # row 1 c( 0.333447, 1.000000) # row 2 ) # X0 (X values at prediction location x0): #Matrix: 2 by 2 rbind( c( 1.000000, 0.000000), # row 1 c( 0.000000, 1.000000) # row 2 ) # BLUE(mu), E(y(x0)) = X0'beta: #Vector: dim: 2 c( 0.244216, 0.440933) # Covariances (x_i, x_0), C0: #Matrix: 10 by 2 rbind( c( 0.000638, 0.000390), # row 1 c( 0.001516, 0.000927), # row 2 c( 0.002126, 0.001300), # row 3 c( 0.002298, 0.001405), # row 4 c( 0.001738, 0.001062), # row 5 c( 0.000390, 0.000618), # row 6 c( 0.000927, 0.001467), # row 7 c( 0.001300, 0.002057), # row 8 c( 0.001405, 0.002223), # row 9 c( 0.001062, 0.001681) # row 10 ) # C-1 C0: #Matrix: 10 by 2 rbind( c( 0.008927, -0.017995), # row 1 c( 0.061935, -0.028550), # row 2 c( 0.225195, 0.078344), # row 3 c( 0.356735, 0.190177), # row 4 c( 0.094128, -0.023136), # row 5 c(-0.021119, 0.004935), # row 6 c(-0.033508, 0.055601), # row 7 c( 0.091947, 0.242576), # row 8 c( 0.223200, 0.398927), # row 9 c(-0.027153, 0.088995) # row 10 ) # [a] Cov_ij(B,B) or Cov_ij(0,0): #Matrix: 2 by 2 rbind( c( 0.004130, 0.000270), # row 1 c( 0.000270, 0.003570) # row 2 ) # [c] (x0-X'C-1 c0)'(X'C-1 X)-1(x0-X'C-1 c0): #Matrix: 2 by 2 rbind( c( 0.000129, -0.000107), # row 1 c(-0.000107, 0.000089) # row 2 ) # [b] c0'C-1 c0: #Matrix: 2 by 2 rbind( c( 0.001926, 0.001532), # row 1 c( 0.001532, 0.001931) # row 2 ) # Best Linear Unbiased Predictor: #Vector: dim: 2 c( 0.253090, 0.441258) # MSPE ([a]-[b]+[c]): #Matrix: 2 by 2 rbind( c( 0.002332, -0.001369), # row 1 c(-0.001369, 0.001729) # row 2 ) # kriging weights: #Matrix: 10 by 2 rbind( c( 0.071177, -0.064988), # row 1 c( 0.108451, -0.066123), # row 2 c( 0.268160, 0.043141), # row 3 c( 0.401959, 0.153312), # row 4 c( 0.150253, -0.065342), # row 5 c(-0.076273, 0.056759), # row 6 c(-0.077605, 0.093781), # row 7 c( 0.050632, 0.277731), # row 8 c( 0.179933, 0.435972), # row 9 c(-0.076688, 0.135756) # row 10 ) > all.equal(A,B) [1] TRUE > > # TRUE > > proc.time() user system elapsed 0.576 0.056 0.625 gstat/tests/krige0.R0000644000176200001440000000205513777370515014063 0ustar liggesusers# test -- load data: library(sp) data(meuse) coordinates(meuse) = ~x+y data(meuse.grid) gridded(meuse.grid) = ~x+y library(gstat) # test -- idw meuse.grid$idw <- idw0(zinc~1, meuse, meuse.grid)[,1] x <- idw(zinc~1, meuse, meuse.grid) all.equal(x$var1.pred, meuse.grid$idw) spplot(meuse.grid["idw"],col.regions=bpy.colors()) v = vgm(1, "Exp", 500) # test sk: x0 <- krige0(zinc~1, meuse, meuse.grid, v, beta = 500, computeVar = TRUE) rownames(x0$pred)=NULL x <- krige(zinc~1, meuse, meuse.grid, v, beta = 500) all.equal(x$var1.pred, x0$pred[,1]) all.equal(x$var1.var, x0$var) # test ok: x0 <- krige0(zinc~1, meuse, meuse.grid, v, computeVar = TRUE) rownames(x0$pred)=NULL names(x0$var)=NULL x <- krige(zinc~1, meuse, meuse.grid, v) all.equal(x$var1.pred, x0$pred[,1]) all.equal(x$var1.var, x0$var) # test uk: x0 <- krige0(zinc~sqrt(dist), meuse, meuse.grid, v, computeVar = TRUE) rownames(x0$pred)=NULL names(x0$var)=NULL x <- krige(zinc~sqrt(dist), meuse, meuse.grid, v) all.equal(x$var1.pred, x0$pred[,1]) all.equal(x$var1.var, x0$var)gstat/tests/variogram.R0000644000176200001440000000056613777370515014676 0ustar liggesuserslibrary(sp) library(gstat) data(meuse) variogram(log(zinc)~1, ~x+y, meuse) coordinates(meuse) <- ~ x + y variogram(log(zinc)~1, meuse) ind=seq(1,155,2) var1= meuse[ind,] var2= meuse[-ind,] g <- gstat(NULL, id = "lead", form = lead ~ 1, data=var1) g <- gstat(g, id = "zinc", form = zinc ~ 1, data=var2) v.cross <- variogram(g) plot(v.cross) gstat/tests/cv3d.R0000644000176200001440000000031513777370515013536 0ustar liggesusersoptions(digits = 4) set.seed(1131) d = data.frame(x=runif(50),y=runif(50),z=runif(50),v=rnorm(50)) library(gstat) xx = krige.cv(v~1,~x+y+z,d,model=vgm(1,"Exp",1), verbose=F, set=list(debug=0)) summary(xx) gstat/tests/cv.R0000644000176200001440000000073413777370515013314 0ustar liggesusers# try bivariate cokriging; cross validate first variable library(sp) data(meuse) library(gstat) g=gstat(NULL, "log-zinc", log(zinc)~1, ~x+y, meuse, nmax=10) g=gstat(g, "log-lead", log(lead)~1, ~x+y, meuse, nmax=10) g=gstat(g, "log-copper", log(copper)~1, ~x+y, meuse, nmax=10) v=variogram(g) g=gstat(g, model=vgm(1, "Sph", 1000), fill.all=T) g=fit.lmc(v, g) g set.seed(13131) summary(gstat.cv(g, remove.all=TRUE, nfold=5)) summary(gstat.cv(g, remove.all=FALSE, nfold=5)) gstat/tests/cv.Rout.save0000644000176200001440000001075713777370515015007 0ustar liggesusers R version 3.6.0 (2019-04-26) -- "Planting of a Tree" Copyright (C) 2019 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > # try bivariate cokriging; cross validate first variable > library(sp) > data(meuse) > library(gstat) > g=gstat(NULL, "log-zinc", log(zinc)~1, ~x+y, meuse, nmax=10) > g=gstat(g, "log-lead", log(lead)~1, ~x+y, meuse, nmax=10) > g=gstat(g, "log-copper", log(copper)~1, ~x+y, meuse, nmax=10) > v=variogram(g) > g=gstat(g, model=vgm(1, "Sph", 1000), fill.all=T) > g=fit.lmc(v, g) > g data: log-zinc : formula = log(zinc)`~`1 ; data dim = 155 x 12 nmax = 10 log-lead : formula = log(lead)`~`1 ; data dim = 155 x 12 nmax = 10 log-copper : formula = log(copper)`~`1 ; data dim = 155 x 12 nmax = 10 variograms: model psill range log-zinc Sph 0.7132435 1000 log-lead Sph 0.6133020 1000 log-copper Sph 0.3634211 1000 log-zinc.log-lead Sph 0.6367012 1000 log-zinc.log-copper Sph 0.4570044 1000 log-lead.log-copper Sph 0.3934910 1000 ~x + y > set.seed(13131) > summary(gstat.cv(g, remove.all=TRUE, nfold=5)) Intrinsic Correlation found. Good. [using ordinary cokriging] Intrinsic Correlation found. Good. [using ordinary cokriging] Intrinsic Correlation found. Good. [using ordinary cokriging] Intrinsic Correlation found. Good. [using ordinary cokriging] Intrinsic Correlation found. Good. [using ordinary cokriging] log.zinc.pred log.zinc.var observed residual Min. :4.779 Min. :0.05426 Min. :4.727 Min. :-1.317697 1st Qu.:5.396 1st Qu.:0.10872 1st Qu.:5.288 1st Qu.:-0.230224 Median :5.858 Median :0.13745 Median :5.787 Median :-0.034374 Mean :5.895 Mean :0.15249 Mean :5.886 Mean :-0.009094 3rd Qu.:6.367 3rd Qu.:0.18303 3rd Qu.:6.514 3rd Qu.: 0.244075 Max. :7.358 Max. :0.60571 Max. :7.517 Max. : 1.414147 zscore fold x y Min. :-3.35764 Min. :1.000 Min. :178605 Min. :329714 1st Qu.:-0.58683 1st Qu.:2.000 1st Qu.:179371 1st Qu.:330762 Median :-0.10755 Median :3.000 Median :179991 Median :331633 Mean :-0.02766 Mean :2.852 Mean :180005 Mean :331635 3rd Qu.: 0.70691 3rd Qu.:4.000 3rd Qu.:180630 3rd Qu.:332463 Max. : 3.43370 Max. :5.000 Max. :181390 Max. :333611 Warning message: In checkNames(value) : attempt to set invalid names: this may lead to problems later on. See ?make.names > summary(gstat.cv(g, remove.all=FALSE, nfold=5)) Intrinsic Correlation found. Good. [using ordinary cokriging] Intrinsic Correlation found. Good. [using ordinary cokriging] Intrinsic Correlation found. Good. [using ordinary cokriging] Intrinsic Correlation found. Good. [using ordinary cokriging] Intrinsic Correlation found. Good. [using ordinary cokriging] log.zinc.pred log.zinc.var observed residual Min. :4.644 Min. :0.002371 Min. :4.727 Min. :-0.4190977 1st Qu.:5.308 1st Qu.:0.004975 1st Qu.:5.288 1st Qu.:-0.0773273 Median :5.777 Median :0.005875 Median :5.787 Median : 0.0006165 Mean :5.883 Mean :0.006609 Mean :5.886 Mean : 0.0026164 3rd Qu.:6.422 3rd Qu.:0.007419 3rd Qu.:6.514 3rd Qu.: 0.0825770 Max. :7.676 Max. :0.027247 Max. :7.517 Max. : 0.4659503 zscore fold x y Min. :-4.793253 Min. :1.000 Min. :178605 Min. :329714 1st Qu.:-1.080725 1st Qu.:2.000 1st Qu.:179371 1st Qu.:330762 Median : 0.007242 Median :3.000 Median :179991 Median :331633 Mean : 0.050487 Mean :2.974 Mean :180005 Mean :331635 3rd Qu.: 1.117469 3rd Qu.:4.000 3rd Qu.:180630 3rd Qu.:332463 Max. : 6.475831 Max. :5.000 Max. :181390 Max. :333611 Warning message: In checkNames(value) : attempt to set invalid names: this may lead to problems later on. See ?make.names > > proc.time() user system elapsed 0.614 0.050 0.655 gstat/tests/unproj.R0000644000176200001440000000406014413474356014211 0ustar liggesusers# DOI 10.1007/s11004-011-9344-7 # http://mypage.iu.edu/~srobeson/Pubs/variogram_sphere_mathgeo_2011.pdf suppressPackageStartupMessages(library(sp)) library(gstat) if (require(sp, quietly = TRUE) && require(fields, quietly = TRUE) && require(sf, quietly = TRUE)) { data(meuse) coordinates(meuse) = ~x+y proj4string(meuse) = CRS("+init=epsg:28992") ll = "+proj=longlat +ellps=WGS84" # meuse.ll = spTransform(meuse, CRS("+proj=longlat +ellps=WGS84")) meuse.ll = as(st_transform(sf::st_as_sf(meuse), sf::st_crs(ll)), "Spatial") meuse.ll[1:10,] variogram(log(zinc)~1, meuse.ll) cloud1 = variogram(log(zinc)~1, meuse, cloud=T, cutoff=6000) cloud2 = variogram(log(zinc)~1, meuse.ll, cloud=T, cutoff=6) plot(cloud1$dist/1000, cloud2$dist, xlab="Amersfoort, km", ylab = "Long/lat") abline(0,1) data(ozone2) oz = SpatialPointsDataFrame(ozone2$lon.lat, data.frame(t(ozone2$y)), proj4string=CRS("+proj=longlat +ellps=WGS84")) variogram(X870731~1,oz[!is.na(oz$X870731),]) utm16 = "+proj=utm +zone=16" # oz.utm = spTransform(oz, utm16) oz.utm = as(sf::st_transform(sf::st_as_sf(oz), utm16) , "Spatial") variogram(X870731~1,oz.utm[!is.na(oz$X870731),]) # Timothy Hilton, r-sig-geo, Sept 14, 2008: foo <- structure(list(z = c(-1.95824831109744, -1.9158901643563, 4.22211761150161, 3.23356929459598, 1.12038389231868, 0.34613850821113, 1.12589932643631, 23.517912251617, 3.0519158690268, 3.20261431141517, -2.10947106854739 ), lon = c(-125.29228, -82.1556, -98.524722, -99.948333, -104.691741, -79.420833, -105.100533, -88.291867, -72.171478, -121.556944, -89.34765), lat = c(49.87217, 48.2167, 55.905833, 56.635833, 53.916264, 39.063333, 48.307883, 40.0061, 42.537756, 44.448889, 46.242017)), .Names = c("z", "lon", "lat"), row.names = c(NA, -11L), class = "data.frame") coordinates(foo) <- ~lon+lat proj4string(foo) <- CRS('+proj=longlat +ellps=WGS84') vg.foo <- variogram(z~1, foo, cloud=TRUE, cutoff=1e10) cat('==========\nvariogram:\n') print(head(vg.foo)) cat('==========\nspDistsN1 Distances:\n') print(spDistsN1(coordinates(foo), coordinates(foo)[1,], longlat=TRUE)) } gstat/tests/stars.R0000644000176200001440000000547214314525262014031 0ustar liggesusersSys.setenv(TZ = "UTC") # 0. using sp: suppressPackageStartupMessages(library(sp)) demo(meuse, ask = FALSE) suppressPackageStartupMessages(library(gstat)) v = variogram(log(zinc)~1, meuse) (v.fit = fit.variogram(v, vgm(1, "Sph", 900, 1))) k_sp = krige(log(zinc)~1, meuse[-(1:5),], meuse[1:5,], v.fit) k_sp_grd = krige(log(zinc)~1, meuse, meuse.grid, v.fit) # 1. using sf: suppressPackageStartupMessages(library(sf)) demo(meuse_sf, ask = FALSE, echo = FALSE) # reloads meuse as data.frame, so demo(meuse, ask = FALSE) v = variogram(log(zinc)~1, meuse_sf) (v.fit = fit.variogram(v, vgm(1, "Sph", 900, 1))) k_sf = krige(log(zinc)~1, meuse_sf[-(1:5),], meuse_sf[1:5,], v.fit) all.equal(k_sp, as(k_sf, "Spatial"), check.attributes = FALSE) all.equal(k_sp, as(k_sf, "Spatial"), check.attributes = TRUE) # 2. using stars for grid: suppressPackageStartupMessages(library(stars)) st = st_as_stars(meuse.grid) st_crs(st) # compare inputs: sp = as(st, "Spatial") fullgrid(meuse.grid) = TRUE all.equal(sp, meuse.grid["dist"], check.attributes = FALSE) all.equal(sp, meuse.grid["dist"], check.attributes = TRUE, use.names = FALSE) # kriging: st_crs(st) = st_crs(meuse_sf) = NA # GDAL roundtrip messes them up! k_st = if (Sys.getenv("USER") == "travis") { try(krige(log(zinc)~1, meuse_sf, st, v.fit)) } else { krige(log(zinc)~1, meuse_sf, st, v.fit) } k_st # handle factors, when going to stars? k_sp_grd$cls = cut(k_sp_grd$var1.pred, c(0, 5, 6, 7, 8, 9)) st_as_stars(k_sp_grd) if (require(raster, quietly = TRUE)) { print(st_as_stars(raster::stack(k_sp_grd))) # check print(all.equal(st_redimension(st_as_stars(k_sp_grd)), st_as_stars(raster::stack(k_sp_grd)), check.attributes=FALSE)) } suppressPackageStartupMessages(library(spacetime)) Sys.setenv(TZ="") tm = as.POSIXct("2019-02-25 15:37:24 CET") n = 4 s = stars:::st_stars(list(foo = array(1:(n^3), rep(n,3))), stars:::create_dimensions(list( x = stars:::create_dimension(from = 1, to = n, offset = 10, delta = 0.5), y = stars:::create_dimension(from = 1, to = n, offset = 0, delta = -0.7), time = stars:::create_dimension(values = tm + 1:n)), raster = stars:::get_raster(dimensions = c("x", "y"))) ) s as.data.frame(s) plot(s, col = sf.colors(), axes = TRUE) (s.stfdf = as(s, "STFDF")) stplot(s.stfdf, scales = list(draw = TRUE)) (s2 = st_as_stars(s.stfdf)) plot(s2, col = sf.colors(), axes = TRUE) all.equal(s, s2, check.attributes = FALSE) # multiple simulations: data(meuse, package = "sp") data(meuse.grid, package = "sp") coordinates(meuse.grid) <- ~x+y gridded(meuse.grid) <- TRUE meuse.grid = st_as_stars(meuse.grid) meuse_sf = st_as_sf(meuse, coords = c("x", "y")) g = gstat(NULL, "zinc", zinc~1, meuse_sf, model = vgm(1, "Exp", 300), nmax = 10) g = gstat(g, "lead", lead~1, meuse_sf, model = vgm(1, "Exp", 300), nmax = 10, fill.cross = TRUE) set.seed(123) (p = predict(g, meuse.grid, nsim = 5)) gstat/tests/na.action.R0000644000176200001440000000156613777370515014562 0ustar liggesuserslibrary(sp) data(meuse) data(meuse.grid) set.seed(13131) # reproduce results # select 10 random rows; # create two missing values in the coordinates: m = meuse.grid[sample(nrow(meuse.grid), 10), ] m[c(2,8), "x"] = NA library(gstat) ## this is not allowed anymore: try(krige(log(zinc)~1,~x+y,meuse,m, na.action = na.pass)) try(krige(log(zinc)~1,~x+y,meuse,m, na.action = na.omit)) try(krige(log(zinc)~1,~x+y,meuse,m, na.action = na.exclude)) try(krige(log(zinc)~1,~x+y,meuse,m, na.action = na.fail)) # select 10 random rows; # create two missing values in the regressor variable: m = meuse.grid[sample(nrow(meuse.grid), 10), ] m[c(3,7), "dist"] = NA krige(log(zinc)~dist,~x+y,meuse,m, na.action = na.pass) krige(log(zinc)~dist,~x+y,meuse,m, na.action = na.omit) krige(log(zinc)~dist,~x+y,meuse,m, na.action = na.exclude) try(krige(log(zinc)~dist,~x+y,meuse,m, na.action = na.fail)) gstat/tests/windst.R0000644000176200001440000000634414413474732014211 0ustar liggesuserssuppressPackageStartupMessages(library(sp)) suppressPackageStartupMessages(library(spacetime)) suppressPackageStartupMessages(library(gstat)) suppressPackageStartupMessages(library(stars)) data(wind) wind.loc$y = as.numeric(char2dms(as.character(wind.loc[["Latitude"]]))) wind.loc$x = as.numeric(char2dms(as.character(wind.loc[["Longitude"]]))) coordinates(wind.loc) = ~x+y proj4string(wind.loc) = "+proj=longlat +datum=WGS84 +ellps=WGS84" wind$time = ISOdate(wind$year+1900, wind$month, wind$day) wind$jday = as.numeric(format(wind$time, '%j')) stations = 4:15 windsqrt = sqrt(0.5148 * wind[stations]) # knots -> m/s Jday = 1:366 daymeans = colMeans( sapply(split(windsqrt - colMeans(windsqrt), wind$jday), colMeans)) meanwind = lowess(daymeans ~ Jday, f = 0.1)$y[wind$jday] velocities = apply(windsqrt, 2, function(x) { x - meanwind }) # match order of columns in wind to Code in wind.loc; # convert to utm zone 29, to be able to do interpolation in # proper Euclidian (projected) space: pts = coordinates(wind.loc[match(names(wind[4:15]), wind.loc$Code),]) pts = SpatialPoints(pts) if (require(sp, quietly = TRUE) && require(maps, quietly = TRUE)) { proj4string(pts) = "+proj=longlat +datum=WGS84 +ellps=WGS84" utm29 = "+proj=utm +zone=29 +datum=WGS84 +ellps=WGS84" pts = as(st_transform(st_as_sfc(pts), utm29), "Spatial") # note the t() in: w = STFDF(pts, wind$time, data.frame(values = as.vector(t(velocities)))) library(mapdata) mp = map("worldHires", xlim = c(-11,-5.4), ylim = c(51,55.5), plot=FALSE) sf = st_transform(st_as_sf(mp, fill = FALSE), utm29) m = as(sf, "Spatial") # setup grid grd = SpatialPixels(SpatialPoints(makegrid(m, n = 300)), proj4string = m@proj4string) # grd$t = rep(1, nrow(grd)) #coordinates(grd) = ~x1+x2 #gridded(grd)=TRUE # select april 1961: w = w[, "1961-04"] covfn = function(x, y = x) { du = spDists(coordinates(x), coordinates(y)) t1 = as.numeric(index(x)) # time in seconds t2 = as.numeric(index(y)) # time in seconds dt = abs(outer(t1, t2, "-")) # separable, product covariance model: 0.6 * exp(-du/750000) * exp(-dt / (1.5 * 3600 * 24)) } n = 10 tgrd = seq(min(index(w)), max(index(w)), length=n) pred = krige0(sqrt(values)~1, w, STF(grd, tgrd), covfn) layout = list(list("sp.points", pts, first=F, cex=.5), list("sp.lines", m, col='grey')) wind.pr0 = STFDF(grd, tgrd, data.frame(var1.pred = pred)) v = vgmST("separable", space = vgm(1, "Exp", 750000), time = vgm(1, "Exp", 1.5 * 3600 * 24), sill = 0.6) wind.ST = krigeST(sqrt(values)~1, w, STF(grd, tgrd), v) all.equal(wind.pr0, wind.ST) # stars: df = data.frame(a = rep(NA, 324*10)) s = STF(grd, tgrd) newd = addAttrToGeom(s, df) wind.sta = krigeST(sqrt(values)~1, st_as_stars(w), st_as_stars(newd), v) # 1 plot(stars::st_as_stars(wind.ST), breaks = "equal", col = sf.colors()) # 2 stplot(wind.ST) # 3 plot(wind.sta, breaks = "equal", col = sf.colors()) st_as_stars(wind.ST)[[1]][1:3,1:3,1] (wind.sta)[[1]][1:3,1:3,1] st_bbox(wind.sta) bbox(wind.ST) all.equal(wind.sta, stars::st_as_stars(wind.ST), check.attributes = FALSE) # 4: roundtrip wind.sta->STFDF->stars rt = stars::st_as_stars(as(wind.sta, "STFDF")) plot(rt, breaks = "equal", col = sf.colors()) # 5: stplot(as(wind.sta, "STFDF")) st_bbox(rt) # 6: stplot(as(st_as_stars(wind.ST), "STFDF")) } gstat/tests/fit.Rout.save0000644000176200001440000000227713777370515015157 0ustar liggesusers R version 3.2.2 (2015-08-14) -- "Fire Safety" Copyright (C) 2015 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(sp) > data(meuse) > library(gstat) > v=variogram(log(zinc)~1,~x+y,meuse,cutoff=500,wi=100) > v$gamma=c(0.5,1,2,3,3) > fit.variogram(v, vgm(1, "Sph", 300, 0),warn.if.neg=TRUE) model psill range 1 Nug 0.000000 0.00 2 Sph 7.878195 1567.77 Warning message: In fit.variogram(v, vgm(1, "Sph", 300, 0), warn.if.neg = TRUE) : partial sill or nugget fixed at zero value > fit.variogram(v, vgm(1, "Sph", 300, 0),warn.if.neg=FALSE) model psill range 1 Nug 0.000000 0.00 2 Sph 7.878195 1567.77 > > proc.time() user system elapsed 0.708 0.244 0.718 gstat/tests/fit.R0000644000176200001440000000034713777370515013466 0ustar liggesuserslibrary(sp) data(meuse) library(gstat) v=variogram(log(zinc)~1,~x+y,meuse,cutoff=500,wi=100) v$gamma=c(0.5,1,2,3,3) fit.variogram(v, vgm(1, "Sph", 300, 0),warn.if.neg=TRUE) fit.variogram(v, vgm(1, "Sph", 300, 0),warn.if.neg=FALSE) gstat/tests/blockkr.Rout.save0000644000176200001440000000513713777370515016022 0ustar liggesusers R version 3.0.1 (2013-05-16) -- "Good Sport" Copyright (C) 2013 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(sp) > data(meuse) > coordinates(meuse) = c("x", "y") > new.locs <- SpatialPoints(data.frame( + x = c(181170, 180310, 180205, 178673, 178770, 178270), + y = c(333250, 332189, 331707, 330066, 330675, 331075))) > library(gstat) > krige(zinc ~ 1, meuse, new.locs, vgm(1.34e5, "Sph", 800, nug = 2.42e4), + block = c(40,40), nmax = 40) [using ordinary kriging] coordinates var1.pred var1.var 1 (181170, 333250) 268.7576 19447.67 2 (180310, 332189) 663.4915 16991.33 3 (180205, 331707) 251.4606 21579.71 4 (178673, 330066) 532.5776 73807.91 5 (178770, 330675) 664.4039 23589.17 6 (178270, 331075) 565.5436 155113.23 > > new.locs <- SpatialPoints(data.frame(x = c(181170), y = c(333250))) > > disc = c(-15,-5,5,15) > block.irreg <- data.frame(expand.grid(x = disc, y = disc)) > block.irreg x y 1 -15 -15 2 -5 -15 3 5 -15 4 15 -15 5 -15 -5 6 -5 -5 7 5 -5 8 15 -5 9 -15 5 10 -5 5 11 5 5 12 15 5 13 -15 15 14 -5 15 15 5 15 16 15 15 > > # first disable default Gaussian quadrature used for block integration, by > # setting nblockdiscr explicitly: > krige(zinc ~ 1, meuse, new.locs, model = vgm(1.34e5, "Sph", 800, nug = 2.42e4), + block = c(40,40), nmax = 40, set = list(nblockdiscr=4)) [using ordinary kriging] coordinates var1.pred var1.var 1 (181170, 333250) 268.7324 19568.76 > # now pass the same block discretization as block.irreg: > krige(zinc ~ 1, meuse, new.locs, vgm(1.34e5, "Sph", 800, nug = 2.42e4), + block = block.irreg, nmax = 40) [using ordinary kriging] coordinates var1.pred var1.var 1 (181170, 333250) 268.7324 19568.76 > # check weights argument: > block.irreg <- data.frame(expand.grid(x = disc, y = disc), weights = rep(1/16, 16)) > krige(zinc ~ 1, meuse, new.locs, vgm(1.34e5, "Sph", 800, nug = 2.42e4), + block = block.irreg, nmax = 40) [using ordinary kriging] coordinates var1.pred var1.var 1 (181170, 333250) 268.7324 19568.76 > > proc.time() user system elapsed 1.080 0.056 1.139 gstat/tests/merge.Rout.save0000644000176200001440000001564514314525262015464 0ustar liggesusers R version 4.2.0 (2022-04-22) -- "Vigorous Calisthenics" Copyright (C) 2022 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(digits=6) > # illustrates the use of merge, for merging parameters accross variables: > # Z1=m+e1(s) > # Z2=m+e2(s) > # Z1 and Z2 each have a different variogram, but share the parameter m > # see documentation of gstat() function > library(gstat) > d1 = data.frame(x=c(0,2),y=c(0,0),z=c(0,1)) > d2 = data.frame(x=c(0,2),y=c(2,2),z=c(4,5)) > g = gstat(NULL,"d1", z~1,~x+y,d1,model=vgm(1, "Exp", 1)) > g = gstat(g,"d2", z~1,~x+y,d2,model=vgm(1, "Exp", 1), merge=c("d1","d2")) > g = gstat(g, c("d1", "d2"), model = vgm(0.5, "Exp", 1)) > predict(g, data.frame(x=1,y=1), debug = 32) Intrinsic Correlation found. Good. [using ordinary cokriging] we're at location X: 1 Y: 1 Z: 0 zero block size we're at point X: 1 Y: 1 Z: 0 # X: #Matrix: 4 by 1 rbind( c( 1.000000), # row 1 c( 1.000000), # row 2 c( 1.000000), # row 3 c( 1.000000) # row 4 ) [using generalized covariances: max_val - semivariance()] # Covariances (x_i, x_j) matrix C (upper triangle): #Matrix: 4 by 4 rbind( c( 1.000000, 0.135335, 0.067668, 0.029553), # row 1 c( 0.135335, 1.000000, 0.029553, 0.067668), # row 2 c( 0.067668, 0.029553, 1.000000, 0.135335), # row 3 c( 0.029553, 0.067668, 0.135335, 1.000000) # row 4 ) # glm->C, Choleski decomposed:: #Matrix: 4 by 4 rbind( c( 1.000000, 0.135335, 0.067668, 0.029553), # row 1 c( 0.000000, 0.990800, 0.020584, 0.064259), # row 2 c( 0.000000, 0.000000, 0.997496, 0.132344), # row 3 c( 0.000000, 0.000000, 0.000000, 0.988677) # row 4 ) # X'C-1 X: #Matrix: 1 by 1 rbind( c( 3.245289) # row 1 ) # beta: #Vector: dim: 1 c( 2.500000) # Cov(beta), (X'C-1 X)-1: #Matrix: 1 by 1 rbind( c( 0.308139) # row 1 ) # Corr(beta): #Matrix: 1 by 1 rbind( c( 1.000000) # row 1 ) # X0 (X values at prediction location x0): #Matrix: 1 by 2 rbind( c( 1.000000, 1.000000) # row 1 ) # BLUE(mu), E(y(x0)) = X0'beta: #Vector: dim: 2 c( 2.500000, 2.500000) # Covariances (x_i, x_0), C0: #Matrix: 4 by 2 rbind( c( 0.243117, 0.121558), # row 1 c( 0.243117, 0.121558), # row 2 c( 0.121558, 0.243117), # row 3 c( 0.121558, 0.243117) # row 4 ) # C-1 C0: #Matrix: 4 by 2 rbind( c( 0.206482, 0.089387), # row 1 c( 0.206482, 0.089387), # row 2 c( 0.089387, 0.206482), # row 3 c( 0.089387, 0.206482) # row 4 ) # [a] Cov_ij(B,B) or Cov_ij(0,0): #Matrix: 2 by 2 rbind( c( 1.000000, 0.500000), # row 1 c( 0.500000, 1.000000) # row 2 ) # [c] (x0-X'C-1 c0)'(X'C-1 X)-1(x0-X'C-1 c0): #Matrix: 2 by 2 rbind( c( 0.051360, 0.051360), # row 1 c( 0.051360, 0.051360) # row 2 ) # [b] c0'C-1 c0: #Matrix: 2 by 2 rbind( c( 0.122130, 0.093662), # row 1 c( 0.093662, 0.122130) # row 2 ) # Best Linear Unbiased Predictor: #Vector: dim: 2 c( 2.031619, 2.968381) # MSPE ([a]-[b]+[c]): #Matrix: 2 by 2 rbind( c( 0.929230, 0.457698), # row 1 c( 0.457698, 0.929230) # row 2 ) # kriging weights: #Matrix: 4 by 2 rbind( c( 0.308548, 0.191452), # row 1 c( 0.308548, 0.191452), # row 2 c( 0.191452, 0.308548), # row 3 c( 0.191452, 0.308548) # row 4 ) x y d1.pred d1.var d2.pred d2.var cov.d1.d2 1 1 1 2.03162 0.92923 2.96838 0.92923 0.457698 > > # Z1 and Z2 share a regression slope: > g = gstat(NULL,"d1", z~x,~x+y,d1,model=vgm(1, "Exp", 1)) > g = gstat(g,"d2", z~x,~x+y,d2,model=vgm(1, "Exp", 1), + merge=list(c("d1",2,"d2",2))) > g = gstat(g, c("d1", "d2"), model = vgm(0.5, "Exp", 1)) > predict(g, data.frame(x=1,y=1), debug = 32) Intrinsic Correlation found. Good. [using universal cokriging] we're at location X: 1 Y: 1 Z: 0 zero block size we're at point X: 1 Y: 1 Z: 0 # X: #Matrix: 4 by 3 rbind( c( 1.000000, 0.000000, 0.000000), # row 1 c( 1.000000, 2.000000, 0.000000), # row 2 c( 0.000000, 0.000000, 1.000000), # row 3 c( 0.000000, 2.000000, 1.000000) # row 4 ) [using generalized covariances: max_val - semivariance()] # Covariances (x_i, x_j) matrix C (upper triangle): #Matrix: 4 by 4 rbind( c( 1.000000, 0.135335, 0.067668, 0.029553), # row 1 c( 0.135335, 1.000000, 0.029553, 0.067668), # row 2 c( 0.067668, 0.029553, 1.000000, 0.135335), # row 3 c( 0.029553, 0.067668, 0.135335, 1.000000) # row 4 ) # glm->C, Choleski decomposed:: #Matrix: 4 by 4 rbind( c( 1.000000, 0.135335, 0.067668, 0.029553), # row 1 c( 0.000000, 0.990800, 0.020584, 0.064259), # row 2 c( 0.000000, 0.000000, 0.997496, 0.132344), # row 3 c( 0.000000, 0.000000, 0.000000, 0.988677) # row 4 ) # X'C-1 X: #Matrix: 3 by 3 rbind( c( 1.774607, 1.622645, -0.151962), # row 1 c( 1.622645, 7.676050, 1.622645), # row 2 c(-0.151962, 1.622645, 1.774607) # row 3 ) # beta: #Vector: dim: 3 c( 0.000000, 0.500000, 4.000000) # Cov(beta), (X'C-1 X)-1: #Matrix: 3 by 3 rbind( c( 0.793363, -0.225695, 0.274305), # row 1 c(-0.225695, 0.225695, -0.225695), # row 2 c( 0.274305, -0.225695, 0.793363) # row 3 ) # Corr(beta): #Matrix: 3 by 3 rbind( c( 1.000000, -0.533366, 0.345750), # row 1 c(-0.533366, 1.000000, -0.533366), # row 2 c( 0.345750, -0.533366, 1.000000) # row 3 ) # X0 (X values at prediction location x0): #Matrix: 3 by 2 rbind( c( 1.000000, 0.000000), # row 1 c( 1.000000, 1.000000), # row 2 c( 0.000000, 1.000000) # row 3 ) # BLUE(mu), E(y(x0)) = X0'beta: #Vector: dim: 2 c( 0.500000, 4.500000) # Covariances (x_i, x_0), C0: #Matrix: 4 by 2 rbind( c( 0.243117, 0.121558), # row 1 c( 0.243117, 0.121558), # row 2 c( 0.121558, 0.243117), # row 3 c( 0.121558, 0.243117) # row 4 ) # C-1 C0: #Matrix: 4 by 2 rbind( c( 0.206482, 0.089387), # row 1 c( 0.206482, 0.089387), # row 2 c( 0.089387, 0.206482), # row 3 c( 0.089387, 0.206482) # row 4 ) # [a] Cov_ij(B,B) or Cov_ij(0,0): #Matrix: 2 by 2 rbind( c( 1.000000, 0.500000), # row 1 c( 0.500000, 1.000000) # row 2 ) # [c] (x0-X'C-1 c0)'(X'C-1 X)-1(x0-X'C-1 c0): #Matrix: 2 by 2 rbind( c( 0.203564, -0.100844), # row 1 c(-0.100844, 0.203564) # row 2 ) # [b] c0'C-1 c0: #Matrix: 2 by 2 rbind( c( 0.122130, 0.093662), # row 1 c( 0.093662, 0.122130) # row 2 ) # Best Linear Unbiased Predictor: #Vector: dim: 2 c( 0.500000, 4.500000) # MSPE ([a]-[b]+[c]): #Matrix: 2 by 2 rbind( c( 1.081434, 0.305494), # row 1 c( 0.305494, 1.081434) # row 2 ) # kriging weights: #Matrix: 4 by 2 rbind( c( 0.500000, 0.000000), # row 1 c( 0.500000, 0.000000), # row 2 c( 0.000000, 0.500000), # row 3 c( 0.000000, 0.500000) # row 4 ) x y d1.pred d1.var d2.pred d2.var cov.d1.d2 1 1 1 0.5 1.08143 4.5 1.08143 0.305494 > > proc.time() user system elapsed 0.551 0.044 0.588 gstat/tests/cv3d.Rout.save0000644000176200001440000000371613777370515015233 0ustar liggesusers R version 3.6.2 (2019-12-12) -- "Dark and Stormy Night" Copyright (C) 2019 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(digits = 4) > set.seed(1131) > d = data.frame(x=runif(50),y=runif(50),z=runif(50),v=rnorm(50)) > library(gstat) > xx = krige.cv(v~1,~x+y+z,d,model=vgm(1,"Exp",1), verbose=F, set=list(debug=0)) > summary(xx) var1.pred var1.var observed residual Min. :-1.163 Min. :0.116 Min. :-2.240 Min. :-2.1755 1st Qu.:-0.571 1st Qu.:0.175 1st Qu.:-0.876 1st Qu.:-0.7881 Median :-0.201 Median :0.192 Median :-0.219 Median : 0.1175 Mean :-0.165 Mean :0.208 Mean :-0.142 Mean : 0.0233 3rd Qu.: 0.161 3rd Qu.:0.240 3rd Qu.: 0.500 3rd Qu.: 0.8508 Max. : 1.085 Max. :0.426 Max. : 1.857 Max. : 2.5224 zscore fold x y Min. :-5.168 Min. : 1.0 Min. :0.0068 Min. :0.0034 1st Qu.:-1.875 1st Qu.:13.2 1st Qu.:0.2397 1st Qu.:0.2466 Median : 0.245 Median :25.5 Median :0.4867 Median :0.4525 Mean : 0.017 Mean :25.5 Mean :0.4997 Mean :0.4969 3rd Qu.: 2.020 3rd Qu.:37.8 3rd Qu.:0.7473 3rd Qu.:0.7394 Max. : 7.354 Max. :50.0 Max. :0.9875 Max. :0.9872 z Min. :0.0016 1st Qu.:0.1865 Median :0.4485 Mean :0.4714 3rd Qu.:0.7240 Max. :0.9942 > > proc.time() user system elapsed 0.776 0.050 0.815 gstat/tests/line.R0000644000176200001440000000305113777370515013626 0ustar liggesusersoptions(digits=5) library(sp) data(meuse.grid) gridded(meuse.grid) = ~x+y data(meuse) coordinates(meuse) = ~x+y # choose arbitrary line over the grid: image(meuse.grid["dist"],axes=T) pp = rbind(c(180000,331000),c(180000,332000),c(181000,333500)) Sl = SpatialLines(list(Lines(list(Line(pp)), "a"))) plot(Sl,add=T,col='green') # use the default spsample arguments of predict.gstat: pts=spsample(Sl,n=500,'regular',offset=c(.5,.5)) plot(pts, pch=3, cex=.2, add=T) library(gstat) v = vgm(.6, "Sph", 900, .06) out1 = krige(log(zinc)~1, meuse, Sl, v) out1 points(180333,332167,pch=3,cex=2) # use the same line as block discretization, and predict for (0,0) # (because the block discretizing points are not centered) out2 = krige(log(zinc)~1, meuse, SpatialPoints(matrix(0,1,2)), v, block=coordinates(pts)) out2 compare.krigingLines = function(formula, data, newdata, model) { out1 = krige(formula, data, newdata, model) pts = spsample(newdata, n=500, 'regular', offset=.5) out2 = krige(formula, data, SpatialPoints(matrix(0,1,2)), model, block = coordinates(pts)) print("difference:") as.data.frame(out1)[3:4]- as.data.frame(out2)[3:4] } compare.krigingLines(log(zinc)~1, meuse, Sl, v) # one line, consisting of two line segments: pp2 = rbind(c(181000,333500),c(181000,332500)) Sl2 = SpatialLines(list(Lines(list(Line(pp),Line(pp2)), "a"))) krige(log(zinc)~1, meuse, Sl2, v) compare.krigingLines(log(zinc)~1, meuse, Sl2, v) # two seperate line segments: Sl3 = SpatialLines(list(Lines(list(Line(pp)), "a"),Lines(list(Line(pp2)),"b"))) krige(log(zinc)~1, meuse, Sl3, v) gstat/tests/unproj.Rout.save0000644000176200001440000001002114413507432015660 0ustar liggesusers R version 4.2.3 (2023-03-15) -- "Shortstop Beagle" Copyright (C) 2023 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > # DOI 10.1007/s11004-011-9344-7 > # http://mypage.iu.edu/~srobeson/Pubs/variogram_sphere_mathgeo_2011.pdf > > suppressPackageStartupMessages(library(sp)) > library(gstat) > > if (require(sp, quietly = TRUE) && require(fields, quietly = TRUE) && require(sf, quietly = TRUE)) { + data(meuse) + coordinates(meuse) = ~x+y + proj4string(meuse) = CRS("+init=epsg:28992") + ll = "+proj=longlat +ellps=WGS84" + # meuse.ll = spTransform(meuse, CRS("+proj=longlat +ellps=WGS84")) + meuse.ll = as(st_transform(sf::st_as_sf(meuse), sf::st_crs(ll)), "Spatial") + meuse.ll[1:10,] + variogram(log(zinc)~1, meuse.ll) + + cloud1 = variogram(log(zinc)~1, meuse, cloud=T, cutoff=6000) + cloud2 = variogram(log(zinc)~1, meuse.ll, cloud=T, cutoff=6) + + plot(cloud1$dist/1000, cloud2$dist, xlab="Amersfoort, km", ylab = "Long/lat") + abline(0,1) + + data(ozone2) + oz = SpatialPointsDataFrame(ozone2$lon.lat, + data.frame(t(ozone2$y)), + proj4string=CRS("+proj=longlat +ellps=WGS84")) + variogram(X870731~1,oz[!is.na(oz$X870731),]) + utm16 = "+proj=utm +zone=16" + # oz.utm = spTransform(oz, utm16) + oz.utm = as(sf::st_transform(sf::st_as_sf(oz), utm16) , "Spatial") + variogram(X870731~1,oz.utm[!is.na(oz$X870731),]) + + # Timothy Hilton, r-sig-geo, Sept 14, 2008: + + foo <- + structure(list(z = c(-1.95824831109744, -1.9158901643563, 4.22211761150161, + 3.23356929459598, 1.12038389231868, 0.34613850821113, 1.12589932643631, + 23.517912251617, 3.0519158690268, 3.20261431141517, -2.10947106854739 + ), lon = c(-125.29228, -82.1556, -98.524722, -99.948333, -104.691741, + -79.420833, -105.100533, -88.291867, -72.171478, -121.556944, + -89.34765), lat = c(49.87217, 48.2167, 55.905833, 56.635833, + 53.916264, 39.063333, 48.307883, 40.0061, 42.537756, 44.448889, + 46.242017)), .Names = c("z", "lon", "lat"), row.names = c(NA, + -11L), class = "data.frame") + + coordinates(foo) <- ~lon+lat + + proj4string(foo) <- CRS('+proj=longlat +ellps=WGS84') + + vg.foo <- variogram(z~1, foo, cloud=TRUE, cutoff=1e10) + + cat('==========\nvariogram:\n') + print(head(vg.foo)) + + cat('==========\nspDistsN1 Distances:\n') + print(spDistsN1(coordinates(foo), coordinates(foo)[1,], longlat=TRUE)) + } Spam version 2.9-1 (2022-08-07) is loaded. Type 'help( Spam)' or 'demo( spam)' for a short introduction and overview of this package. Help for individual functions is also obtained by adding the suffix '.spam' to the function name, e.g. 'help( chol.spam)'. Attaching package: 'spam' The following objects are masked from 'package:base': backsolve, forwardsolve Try help(fields) to get started. Linking to GEOS 3.11.1, GDAL 3.6.2, PROJ 9.1.1; sf_use_s2() is TRUE ========== variogram: dist gamma dir.hor dir.ver id left right 1 3115.1190 8.971063e-04 0 0 var1 2 1 2 1908.0468 1.909846e+01 0 0 var1 3 1 3 1405.6211 1.883757e+01 0 0 var1 3 2 4 1837.5667 1.347749e+01 0 0 var1 4 1 5 1522.8765 1.325847e+01 0 0 var1 4 2 6 119.9386 4.886139e-01 0 0 var1 4 3 ========== spDistsN1 Distances: [1] 0.0000 3115.1190 1908.0468 1837.5667 1481.6293 3775.6751 1480.4477 [8] 3081.7541 4090.4022 665.9348 2683.1516 Warning message: In CPL_crs_from_input(x) : GDAL Message 1: +init=epsg:XXXX syntax is deprecated. It might return a CRS with a non-EPSG compliant axis order. > > proc.time() user system elapsed 2.028 0.818 1.946 gstat/tests/krige0.Rout.save0000644000176200001440000000367513777370515015561 0ustar liggesusers R version 3.0.2 (2013-09-25) -- "Frisbee Sailing" Copyright (C) 2013 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > # test -- load data: > library(sp) > data(meuse) > coordinates(meuse) = ~x+y > data(meuse.grid) > gridded(meuse.grid) = ~x+y > > library(gstat) > # test -- idw > meuse.grid$idw <- idw0(zinc~1, meuse, meuse.grid)[,1] > x <- idw(zinc~1, meuse, meuse.grid) [inverse distance weighted interpolation] > all.equal(x$var1.pred, meuse.grid$idw) [1] TRUE > spplot(meuse.grid["idw"],col.regions=bpy.colors()) > v = vgm(1, "Exp", 500) > # test sk: > x0 <- krige0(zinc~1, meuse, meuse.grid, v, beta = 500, computeVar = TRUE) > rownames(x0$pred)=NULL > x <- krige(zinc~1, meuse, meuse.grid, v, beta = 500) [using simple kriging] > all.equal(x$var1.pred, x0$pred[,1]) [1] TRUE > all.equal(x$var1.var, x0$var) [1] TRUE > # test ok: > x0 <- krige0(zinc~1, meuse, meuse.grid, v, computeVar = TRUE) > rownames(x0$pred)=NULL > names(x0$var)=NULL > x <- krige(zinc~1, meuse, meuse.grid, v) [using ordinary kriging] > all.equal(x$var1.pred, x0$pred[,1]) [1] TRUE > all.equal(x$var1.var, x0$var) [1] TRUE > # test uk: > x0 <- krige0(zinc~sqrt(dist), meuse, meuse.grid, v, computeVar = TRUE) > rownames(x0$pred)=NULL > names(x0$var)=NULL > x <- krige(zinc~sqrt(dist), meuse, meuse.grid, v) [using universal kriging] > all.equal(x$var1.pred, x0$pred[,1]) [1] TRUE > all.equal(x$var1.var, x0$var) [1] TRUE > > proc.time() user system elapsed 3.424 0.064 3.490 gstat/tests/sim.R0000644000176200001440000000054413777370515013473 0ustar liggesusersoptions(digits=6) library(sp) data(meuse) set.seed(158229572) new.locs <- data.frame(x = c(181170, 180310, 180205, 178673, 178770, 178270), y = c(333250, 332189, 331707, 330066, 330675, 331075)) library(gstat) krige(zinc ~ 1, ~ x + y, meuse, newdata = new.locs, model = vgm(1.34e5, "Sph", 800, nug = 2.42e4), block = c(40,40), nmax = 40, nsim = 10) gstat/tests/windst.Rout.save0000644000176200001440000001133214413506706015664 0ustar liggesusers R version 4.2.3 (2023-03-15) -- "Shortstop Beagle" Copyright (C) 2023 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > suppressPackageStartupMessages(library(sp)) > suppressPackageStartupMessages(library(spacetime)) > suppressPackageStartupMessages(library(gstat)) > suppressPackageStartupMessages(library(stars)) > > data(wind) > wind.loc$y = as.numeric(char2dms(as.character(wind.loc[["Latitude"]]))) > wind.loc$x = as.numeric(char2dms(as.character(wind.loc[["Longitude"]]))) > coordinates(wind.loc) = ~x+y > proj4string(wind.loc) = "+proj=longlat +datum=WGS84 +ellps=WGS84" > > wind$time = ISOdate(wind$year+1900, wind$month, wind$day) > wind$jday = as.numeric(format(wind$time, '%j')) > stations = 4:15 > windsqrt = sqrt(0.5148 * wind[stations]) # knots -> m/s > Jday = 1:366 > daymeans = colMeans( + sapply(split(windsqrt - colMeans(windsqrt), wind$jday), colMeans)) > meanwind = lowess(daymeans ~ Jday, f = 0.1)$y[wind$jday] > velocities = apply(windsqrt, 2, function(x) { x - meanwind }) > # match order of columns in wind to Code in wind.loc; > # convert to utm zone 29, to be able to do interpolation in > # proper Euclidian (projected) space: > pts = coordinates(wind.loc[match(names(wind[4:15]), wind.loc$Code),]) > pts = SpatialPoints(pts) > if (require(sp, quietly = TRUE) && require(maps, quietly = TRUE)) { + proj4string(pts) = "+proj=longlat +datum=WGS84 +ellps=WGS84" + utm29 = "+proj=utm +zone=29 +datum=WGS84 +ellps=WGS84" + pts = as(st_transform(st_as_sfc(pts), utm29), "Spatial") + # note the t() in: + w = STFDF(pts, wind$time, data.frame(values = as.vector(t(velocities)))) + + library(mapdata) + mp = map("worldHires", xlim = c(-11,-5.4), ylim = c(51,55.5), plot=FALSE) + sf = st_transform(st_as_sf(mp, fill = FALSE), utm29) + m = as(sf, "Spatial") + + # setup grid + grd = SpatialPixels(SpatialPoints(makegrid(m, n = 300)), + proj4string = m@proj4string) + # grd$t = rep(1, nrow(grd)) + #coordinates(grd) = ~x1+x2 + #gridded(grd)=TRUE + + # select april 1961: + w = w[, "1961-04"] + + covfn = function(x, y = x) { + du = spDists(coordinates(x), coordinates(y)) + t1 = as.numeric(index(x)) # time in seconds + t2 = as.numeric(index(y)) # time in seconds + dt = abs(outer(t1, t2, "-")) + # separable, product covariance model: + 0.6 * exp(-du/750000) * exp(-dt / (1.5 * 3600 * 24)) + } + + n = 10 + tgrd = seq(min(index(w)), max(index(w)), length=n) + pred = krige0(sqrt(values)~1, w, STF(grd, tgrd), covfn) + layout = list(list("sp.points", pts, first=F, cex=.5), + list("sp.lines", m, col='grey')) + wind.pr0 = STFDF(grd, tgrd, data.frame(var1.pred = pred)) + + v = vgmST("separable", + space = vgm(1, "Exp", 750000), + time = vgm(1, "Exp", 1.5 * 3600 * 24), + sill = 0.6) + wind.ST = krigeST(sqrt(values)~1, w, STF(grd, tgrd), v) + + all.equal(wind.pr0, wind.ST) + + # stars: + df = data.frame(a = rep(NA, 324*10)) + s = STF(grd, tgrd) + newd = addAttrToGeom(s, df) + wind.sta = krigeST(sqrt(values)~1, st_as_stars(w), st_as_stars(newd), v) + # 1 + plot(stars::st_as_stars(wind.ST), breaks = "equal", col = sf.colors()) + # 2 + stplot(wind.ST) + # 3 + plot(wind.sta, breaks = "equal", col = sf.colors()) + st_as_stars(wind.ST)[[1]][1:3,1:3,1] + (wind.sta)[[1]][1:3,1:3,1] + st_bbox(wind.sta) + bbox(wind.ST) + all.equal(wind.sta, stars::st_as_stars(wind.ST), check.attributes = FALSE) + + # 4: roundtrip wind.sta->STFDF->stars + rt = stars::st_as_stars(as(wind.sta, "STFDF")) + plot(rt, breaks = "equal", col = sf.colors()) + # 5: + stplot(as(wind.sta, "STFDF")) + st_bbox(rt) + + # 6: + stplot(as(st_as_stars(wind.ST), "STFDF")) + } Warning messages: 1: In krigeST(sqrt(values) ~ 1, w, STF(grd, tgrd), v) : The spatio-temporal variogram model does not carry the strongly recommended attribute 'temporal unit'. The unit 'secs' has been assumed. krigeST could not check whether the temporal distances between locations and in the variogram coincide. 2: In krigeST(sqrt(values) ~ 1, st_as_stars(w), st_as_stars(newd), : The spatio-temporal variogram model does not carry the strongly recommended attribute 'temporal unit'. The unit 'secs' has been assumed. krigeST could not check whether the temporal distances between locations and in the variogram coincide. > > proc.time() user system elapsed 4.489 3.497 3.766 gstat/tests/rings.R0000644000176200001440000000624413777370515014030 0ustar liggesuserslibrary(sp) library(gstat) set.seed(13331) x = runif(10) y = runif(10) z = rnorm(10) d = data.frame(x=x,y=y,z=z) bl = c(1,1) nd = data.frame(x=.5, y=.5) # single block: library(sp) coordinates(d) = ~x+y nd = SpatialPoints(nd) xx = krige(z~1, d, nd, model=vgm(1, "Exp", 1), block = bl, set = list(nb=4)) ring = cbind(c(0,bl[1],bl[1],0,0), c(0,0,bl[2],bl[2],0)) r1 = SpatialPolygons(list(Polygons(list(Polygon(ring)), ID = "xx"))) a = data.frame(a = 1, b = 2) rownames(a) = "xx" r1df = SpatialPolygonsDataFrame(r1, a) g = gstat(formula=z~1, data=d, model=vgm(1, "Exp", 1)) args = list(type = "regular", n=16, offset=c(0.5,0.5)) yy = predict(g, r1df, block = bl, sps.args = args) xx = as.data.frame(xx) yy = as.data.frame(yy) row.names(xx) = row.names(yy) print(all.equal(xx,yy)) ## multiple blocks of equal size: nd = data.frame(x= 0:4 + .5, y=rep(.5,5)) nd = SpatialPoints(nd) xx = krige(z~1, d, nd, model=vgm(1, "Exp", 1), block = bl, set = list(nb=4)) ring0 = cbind(c(0,bl[1],bl[1],0,0), c(0,0,bl[2],bl[2],0)) ring1 = cbind(c(1+0,1+bl[1],1+bl[1],1+0,1+0), c(0,0,bl[2],bl[2],0)) ring2 = cbind(c(2+0,2+bl[1],2+bl[1],2+0,2+0), c(0,0,bl[2],bl[2],0)) ring3 = cbind(c(3+0,3+bl[1],3+bl[1],3+0,3+0), c(0,0,bl[2],bl[2],0)) ring4 = cbind(c(4+0,4+bl[1],4+bl[1],4+0,4+0), c(0,0,bl[2],bl[2],0)) r1 = SpatialPolygons(list( Polygons(list(Polygon(ring0)), ID = "x0"), Polygons(list(Polygon(ring1)), ID = "x1"), Polygons(list(Polygon(ring2)), ID = "x2"), Polygons(list(Polygon(ring3)), ID = "x3"), Polygons(list(Polygon(ring4)), ID = "x4") )) df = data.frame(a=rep(1,5), b= rep(1,5)) rownames(df) = c("x0", "x1", "x2", "x3", "x4") r1df = SpatialPolygonsDataFrame(r1, df) yy = predict(g, r1, block = bl, sps.args = args) xx = as.data.frame(xx) yy = as.data.frame(yy) row.names(xx) = row.names(yy) all.equal(xx, yy) ## multiple blocks of equal size: args = list(type = "regular", cellsize=.25, offset=c(0.5,0.5), n=16) yy = predict(g, r1, block = bl, sps.args = args) xx = as.data.frame(xx) yy = as.data.frame(yy) row.names(xx) = row.names(yy) print(all.equal(xx, yy)) ## multiple blocks of varying size: nd = data.frame(x=c(0.5, 2, 4.5), y=c(0.5, 1, 1.5)) nd = SpatialPoints(nd) bl = c(1,1) ring0 = cbind(c(0,bl[1],bl[1],0,0), c(0,0,bl[2],bl[2],0)) xx1 = krige(z~1, d, nd[1], model=vgm(1, "Exp", 1), block = bl, set = list(nb=4)) bl = c(2,2) ring1 = cbind(c(1+0,1+bl[1],1+bl[1],1+0,1+0), c(0,0,bl[2],bl[2],0)) xx2 = krige(z~1, d, nd[2], model=vgm(1, "Exp", 1), block = bl, set = list(nb=4)) bl = c(3,3) ring2 = cbind(c(3+0,3+bl[1],3+bl[1],3+0,3+0), c(0,0,bl[2],bl[2],0)) xx3 = krige(z~1, d, nd[3], model=vgm(1, "Exp", 1), block = bl, set = list(nb=4)) r1 = SpatialPolygons(list( Polygons(list(Polygon(ring0)), ID = "x0"), Polygons(list(Polygon(ring1)), ID = "x1"), Polygons(list(Polygon(ring2)), ID = "x2") )) df = data.frame(a = rep(1,3), b = rep(1,3)) rownames(df) = c("x0", "x1", "x2") r1df = SpatialPolygonsDataFrame(r1, df) args = list(type = "regular", n=16, offset=c(0.5,0.5)) yy = predict(g, r1df, block = bl, sps.args = args) xx = rbind(as.data.frame(xx1), as.data.frame(xx2), as.data.frame(xx3)) row.names(xx) = 1:3 xx = as.data.frame(xx) yy = as.data.frame(yy) row.names(xx) = row.names(yy) print(all.equal(xx, yy)) gstat/tests/variogram.Rout.save0000644000176200001440000000515213777370515016357 0ustar liggesusers R version 3.0.1 (2013-05-16) -- "Good Sport" Copyright (C) 2013 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(sp) > library(gstat) > data(meuse) > variogram(log(zinc)~1, ~x+y, meuse) np dist gamma dir.hor dir.ver id 1 57 79.29244 0.1234479 0 0 var1 2 299 163.97367 0.2162185 0 0 var1 3 419 267.36483 0.3027859 0 0 var1 4 457 372.73542 0.4121448 0 0 var1 5 547 478.47670 0.4634128 0 0 var1 6 533 585.34058 0.5646933 0 0 var1 7 574 693.14526 0.5689683 0 0 var1 8 564 796.18365 0.6186769 0 0 var1 9 589 903.14650 0.6471479 0 0 var1 10 543 1011.29177 0.6915705 0 0 var1 11 500 1117.86235 0.7033984 0 0 var1 12 477 1221.32810 0.6038770 0 0 var1 13 452 1329.16407 0.6517158 0 0 var1 14 457 1437.25620 0.5665318 0 0 var1 15 415 1543.20248 0.5748227 0 0 var1 > > coordinates(meuse) <- ~ x + y > variogram(log(zinc)~1, meuse) np dist gamma dir.hor dir.ver id 1 57 79.29244 0.1234479 0 0 var1 2 299 163.97367 0.2162185 0 0 var1 3 419 267.36483 0.3027859 0 0 var1 4 457 372.73542 0.4121448 0 0 var1 5 547 478.47670 0.4634128 0 0 var1 6 533 585.34058 0.5646933 0 0 var1 7 574 693.14526 0.5689683 0 0 var1 8 564 796.18365 0.6186769 0 0 var1 9 589 903.14650 0.6471479 0 0 var1 10 543 1011.29177 0.6915705 0 0 var1 11 500 1117.86235 0.7033984 0 0 var1 12 477 1221.32810 0.6038770 0 0 var1 13 452 1329.16407 0.6517158 0 0 var1 14 457 1437.25620 0.5665318 0 0 var1 15 415 1543.20248 0.5748227 0 0 var1 > > ind=seq(1,155,2) > var1= meuse[ind,] > var2= meuse[-ind,] > g <- gstat(NULL, id = "lead", form = lead ~ 1, data=var1) > g <- gstat(g, id = "zinc", form = zinc ~ 1, data=var2) > v.cross <- variogram(g) > plot(v.cross) > > > proc.time() user system elapsed 1.528 0.076 1.612 gstat/tests/covtable.Rout.save0000644000176200001440000000276513777370515016176 0ustar liggesusers R version 3.2.3 (2015-12-10) -- "Wooden Christmas-Tree" Copyright (C) 2015 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(gstat) > d=expand.grid(x=c(-.5,.5), y=c(-.5,.5)) > d$z=1:4 > vv=vgm(model = "Tab", covtable = + variogramLine(vgm(1, "Sph", 1), 1, n=1e4,min = 0, covariance = TRUE)) > vv model psill maxdist 1 Tab NA 1 covariance table: [1] 1.0000000 0.7039712 0.4319496 0.2080384 0.0560108 0.0000000 > krige(z~1,~x+y,d,data.frame(x=0,y=0),vgm(1, "Sph", 1)) [using ordinary kriging] x y var1.pred var1.var 1 0 0 2.5 1.017767 > krige(z~1,~x+y,d,data.frame(x=0,y=0),vv) [using ordinary kriging] x y var1.pred var1.var 1 0 0 2.5 1.017863 > krige(z~1,~x+y,d[1:2,],data.frame(x=0,y=0),vgm(1, "Sph", 1)) [using ordinary kriging] x y var1.pred var1.var 1 0 0 1.5 1.267767 > krige(z~1,~x+y,d[1:2,],data.frame(x=0,y=0),vv) [using ordinary kriging] x y var1.pred var1.var 1 0 0 1.5 1.267863 > > proc.time() user system elapsed 0.704 0.276 0.670 gstat/tests/line.Rout.save0000644000176200001440000001066514413346074015313 0ustar liggesusers R version 4.2.3 (2023-03-15) -- "Shortstop Beagle" Copyright (C) 2023 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(digits=5) > library(sp) > data(meuse.grid) > gridded(meuse.grid) = ~x+y > data(meuse) > coordinates(meuse) = ~x+y > > # choose arbitrary line over the grid: > image(meuse.grid["dist"],axes=T) > pp = rbind(c(180000,331000),c(180000,332000),c(181000,333500)) > Sl = SpatialLines(list(Lines(list(Line(pp)), "a"))) > plot(Sl,add=T,col='green') > > # use the default spsample arguments of predict.gstat: > pts=spsample(Sl,n=500,'regular',offset=c(.5,.5)) > plot(pts, pch=3, cex=.2, add=T) > > library(gstat) > v = vgm(.6, "Sph", 900, .06) > out1 = krige(log(zinc)~1, meuse, Sl, v) [using ordinary kriging] > out1 An object of class "SpatialLinesDataFrame" Slot "data": x y var1.pred var1.var a 180333 332167 6.1618 0.008025 Slot "lines": [[1]] An object of class "Lines" Slot "Lines": [[1]] An object of class "Line" Slot "coords": [,1] [,2] [1,] 180000 331000 [2,] 180000 332000 [3,] 181000 333500 Slot "ID": [1] "a" Slot "bbox": min max x 180000 181000 y 331000 333500 Slot "proj4string": Coordinate Reference System: Deprecated Proj.4 representation: NA > > points(180333,332167,pch=3,cex=2) > > # use the same line as block discretization, and predict for (0,0) > # (because the block discretizing points are not centered) > out2 = krige(log(zinc)~1, meuse, SpatialPoints(matrix(0,1,2)), v, block=coordinates(pts)) [using ordinary kriging] > out2 coordinates var1.pred var1.var 1 (0, 0) 6.1618 0.008025 > > compare.krigingLines = function(formula, data, newdata, model) { + out1 = krige(formula, data, newdata, model) + pts = spsample(newdata, n=500, 'regular', offset=.5) + out2 = krige(formula, data, SpatialPoints(matrix(0,1,2)), model, block = coordinates(pts)) + print("difference:") + as.data.frame(out1)[3:4]- as.data.frame(out2)[3:4] + } > > compare.krigingLines(log(zinc)~1, meuse, Sl, v) [using ordinary kriging] [using ordinary kriging] [1] "difference:" var1.pred var1.var a 0 0 > > # one line, consisting of two line segments: > pp2 = rbind(c(181000,333500),c(181000,332500)) > Sl2 = SpatialLines(list(Lines(list(Line(pp),Line(pp2)), "a"))) > krige(log(zinc)~1, meuse, Sl2, v) [using ordinary kriging] An object of class "SpatialLinesDataFrame" Slot "data": x y var1.pred var1.var a 180667 332583 6.0424 0.0053191 Slot "lines": [[1]] An object of class "Lines" Slot "Lines": [[1]] An object of class "Line" Slot "coords": [,1] [,2] [1,] 180000 331000 [2,] 180000 332000 [3,] 181000 333500 [[2]] An object of class "Line" Slot "coords": [,1] [,2] [1,] 181000 333500 [2,] 181000 332500 Slot "ID": [1] "a" Slot "bbox": min max x 180000 181000 y 331000 333500 Slot "proj4string": Coordinate Reference System: Deprecated Proj.4 representation: NA > compare.krigingLines(log(zinc)~1, meuse, Sl2, v) [using ordinary kriging] [using ordinary kriging] [1] "difference:" var1.pred var1.var a 0 0 > > # two seperate line segments: > Sl3 = SpatialLines(list(Lines(list(Line(pp)), "a"),Lines(list(Line(pp2)),"b"))) > krige(log(zinc)~1, meuse, Sl3, v) [using ordinary kriging] An object of class "SpatialLinesDataFrame" Slot "data": x y var1.pred var1.var a 180333 332167 6.1618 0.008025 b 181000 333000 5.7060 0.011043 Slot "lines": [[1]] An object of class "Lines" Slot "Lines": [[1]] An object of class "Line" Slot "coords": [,1] [,2] [1,] 180000 331000 [2,] 180000 332000 [3,] 181000 333500 Slot "ID": [1] "a" [[2]] An object of class "Lines" Slot "Lines": [[1]] An object of class "Line" Slot "coords": [,1] [,2] [1,] 181000 333500 [2,] 181000 332500 Slot "ID": [1] "b" Slot "bbox": min max x 180000 181000 y 331000 333500 Slot "proj4string": Coordinate Reference System: Deprecated Proj.4 representation: NA > > proc.time() user system elapsed 1.703 2.198 1.248 gstat/tests/covtable.R0000644000176200001440000000057013777370515014501 0ustar liggesuserslibrary(gstat) d=expand.grid(x=c(-.5,.5), y=c(-.5,.5)) d$z=1:4 vv=vgm(model = "Tab", covtable = variogramLine(vgm(1, "Sph", 1), 1, n=1e4,min = 0, covariance = TRUE)) vv krige(z~1,~x+y,d,data.frame(x=0,y=0),vgm(1, "Sph", 1)) krige(z~1,~x+y,d,data.frame(x=0,y=0),vv) krige(z~1,~x+y,d[1:2,],data.frame(x=0,y=0),vgm(1, "Sph", 1)) krige(z~1,~x+y,d[1:2,],data.frame(x=0,y=0),vv) gstat/tests/allier.R0000644000176200001440000000164213777370515014153 0ustar liggesusers# Sytze de Bruin's post to r-sig-geo, Nov 16, 2015: library(sp) library(gstat) # some data x <- c(215, 330, 410, 470, 545) y <- c(230, 310, 330, 340, 365) fc <- c(0.211, 0.251, 0.281, 0.262, 0.242) por <- c(0.438, 0.457, 0.419, 0.430, 0.468) Allier <- data.frame(x, y, fc, por) coordinates(Allier) = ~x+y # gstat object for co-kriging using linear model of co-regionalization g <- gstat(id=c("fc"), formula=fc~1, data=Allier, model=vgm(0.00247, "Sph", 480, 0.00166)) g <- gstat(g, id="por", formula=por~1, data=Allier, model=vgm(0.00239, "Sph", 480, 0.00118)) g <- gstat(g, id=c("fc", "por"), model=vgm(0.00151, "Sph", 480, -0.00124)) # predict at single point g$set = list(choleski = 0) # LDL' A <- predict(g, SpatialPoints(data.frame(x=450, y=350)), debug = 32) g$set = list(choleski = 1) # Choleski B <- predict(g, SpatialPoints(data.frame(x=450, y=350)), debug = 32) all.equal(A,B) # TRUE gstat/tests/blockkr.R0000644000176200001440000000214113777370515014325 0ustar liggesuserslibrary(sp) data(meuse) coordinates(meuse) = c("x", "y") new.locs <- SpatialPoints(data.frame( x = c(181170, 180310, 180205, 178673, 178770, 178270), y = c(333250, 332189, 331707, 330066, 330675, 331075))) library(gstat) krige(zinc ~ 1, meuse, new.locs, vgm(1.34e5, "Sph", 800, nug = 2.42e4), block = c(40,40), nmax = 40) new.locs <- SpatialPoints(data.frame(x = c(181170), y = c(333250))) disc = c(-15,-5,5,15) block.irreg <- data.frame(expand.grid(x = disc, y = disc)) block.irreg # first disable default Gaussian quadrature used for block integration, by # setting nblockdiscr explicitly: krige(zinc ~ 1, meuse, new.locs, model = vgm(1.34e5, "Sph", 800, nug = 2.42e4), block = c(40,40), nmax = 40, set = list(nblockdiscr=4)) # now pass the same block discretization as block.irreg: krige(zinc ~ 1, meuse, new.locs, vgm(1.34e5, "Sph", 800, nug = 2.42e4), block = block.irreg, nmax = 40) # check weights argument: block.irreg <- data.frame(expand.grid(x = disc, y = disc), weights = rep(1/16, 16)) krige(zinc ~ 1, meuse, new.locs, vgm(1.34e5, "Sph", 800, nug = 2.42e4), block = block.irreg, nmax = 40) gstat/tests/na.action.Rout.save0000644000176200001440000000652713777370515016251 0ustar liggesusers R version 3.6.0 (2019-04-26) -- "Planting of a Tree" Copyright (C) 2019 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(sp) > > data(meuse) > data(meuse.grid) > > set.seed(13131) # reproduce results > > # select 10 random rows; > # create two missing values in the coordinates: > m = meuse.grid[sample(nrow(meuse.grid), 10), ] > m[c(2,8), "x"] = NA > > library(gstat) > ## this is not allowed anymore: > try(krige(log(zinc)~1,~x+y,meuse,m, na.action = na.pass)) Error in na.fail.default(structure(list(x = c(179220, NA, 178740, 179300, : missing values in object > try(krige(log(zinc)~1,~x+y,meuse,m, na.action = na.omit)) Error in na.fail.default(structure(list(x = c(179220, NA, 178740, 179300, : missing values in object > try(krige(log(zinc)~1,~x+y,meuse,m, na.action = na.exclude)) Error in na.fail.default(structure(list(x = c(179220, NA, 178740, 179300, : missing values in object > try(krige(log(zinc)~1,~x+y,meuse,m, na.action = na.fail)) Error in na.fail.default(structure(list(x = c(179220, NA, 178740, 179300, : missing values in object > > # select 10 random rows; > # create two missing values in the regressor variable: > m = meuse.grid[sample(nrow(meuse.grid), 10), ] > m[c(3,7), "dist"] = NA > krige(log(zinc)~dist,~x+y,meuse,m, na.action = na.pass) [ordinary or weighted least squares prediction] x y var1.pred var1.var 1 178860 330860 6.530134 0.2415196 2 180260 331860 5.389567 0.2406041 3 180100 331860 NA NA 4 180460 331820 5.213370 0.2417197 5 179660 330580 5.550859 0.2398778 6 179740 330300 6.108648 0.2395392 7 180220 330660 NA NA 8 178580 329820 6.533801 0.2415453 9 180100 331900 5.580264 0.2397758 10 180780 331900 5.095967 0.2426499 > krige(log(zinc)~dist,~x+y,meuse,m, na.action = na.omit) [ordinary or weighted least squares prediction] x y var1.pred var1.var 1877 178860 330860 6.530134 0.2415196 1015 180260 331860 5.389567 0.2406041 1056 180460 331820 5.213370 0.2417197 2199 179660 330580 5.550859 0.2398778 2556 179740 330300 6.108648 0.2395392 2985 178580 329820 6.533801 0.2415453 975 180100 331900 5.580264 0.2397758 992 180780 331900 5.095967 0.2426499 > krige(log(zinc)~dist,~x+y,meuse,m, na.action = na.exclude) [ordinary or weighted least squares prediction] x y var1.pred var1.var 1877 178860 330860 6.530134 0.2415196 1015 180260 331860 5.389567 0.2406041 1056 180460 331820 5.213370 0.2417197 2199 179660 330580 5.550859 0.2398778 2556 179740 330300 6.108648 0.2395392 2985 178580 329820 6.533801 0.2415453 975 180100 331900 5.580264 0.2397758 992 180780 331900 5.095967 0.2426499 > try(krige(log(zinc)~dist,~x+y,meuse,m, na.action = na.fail)) Error in na.fail.default(structure(list(dist = c(0.00135803, 0.423804, : missing values in object > > proc.time() user system elapsed 0.490 0.047 0.528 gstat/tests/stars.Rout.save0000644000176200001440000003615314413506715015520 0ustar liggesusers R version 4.2.3 (2023-03-15) -- "Shortstop Beagle" Copyright (C) 2023 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > Sys.setenv(TZ = "UTC") > > # 0. using sp: > > suppressPackageStartupMessages(library(sp)) > demo(meuse, ask = FALSE) demo(meuse) ---- ~~~~~ > require(sp) > crs = CRS("+init=epsg:28992") > data("meuse") > coordinates(meuse) <- ~x+y > proj4string(meuse) <- crs > data("meuse.grid") > coordinates(meuse.grid) <- ~x+y > gridded(meuse.grid) <- TRUE > proj4string(meuse.grid) <- crs > data("meuse.riv") > meuse.riv <- SpatialPolygons(list(Polygons(list(Polygon(meuse.riv)),"meuse.riv"))) > proj4string(meuse.riv) <- crs > data("meuse.area") > meuse.area = SpatialPolygons(list(Polygons(list(Polygon(meuse.area)), "area"))) > proj4string(meuse.area) <- crs > suppressPackageStartupMessages(library(gstat)) > v = variogram(log(zinc)~1, meuse) > (v.fit = fit.variogram(v, vgm(1, "Sph", 900, 1))) model psill range 1 Nug 0.05066243 0.0000 2 Sph 0.59060780 897.0209 > k_sp = krige(log(zinc)~1, meuse[-(1:5),], meuse[1:5,], v.fit) [using ordinary kriging] > k_sp_grd = krige(log(zinc)~1, meuse, meuse.grid, v.fit) [using ordinary kriging] > > # 1. using sf: > suppressPackageStartupMessages(library(sf)) > demo(meuse_sf, ask = FALSE, echo = FALSE) > # reloads meuse as data.frame, so > demo(meuse, ask = FALSE) demo(meuse) ---- ~~~~~ > require(sp) > crs = CRS("+init=epsg:28992") > data("meuse") > coordinates(meuse) <- ~x+y > proj4string(meuse) <- crs > data("meuse.grid") > coordinates(meuse.grid) <- ~x+y > gridded(meuse.grid) <- TRUE > proj4string(meuse.grid) <- crs > data("meuse.riv") > meuse.riv <- SpatialPolygons(list(Polygons(list(Polygon(meuse.riv)),"meuse.riv"))) > proj4string(meuse.riv) <- crs > data("meuse.area") > meuse.area = SpatialPolygons(list(Polygons(list(Polygon(meuse.area)), "area"))) > proj4string(meuse.area) <- crs > > v = variogram(log(zinc)~1, meuse_sf) > (v.fit = fit.variogram(v, vgm(1, "Sph", 900, 1))) model psill range 1 Nug 0.05066243 0.0000 2 Sph 0.59060780 897.0209 > k_sf = krige(log(zinc)~1, meuse_sf[-(1:5),], meuse_sf[1:5,], v.fit) [using ordinary kriging] > > all.equal(k_sp, as(k_sf, "Spatial"), check.attributes = FALSE) [1] TRUE > all.equal(k_sp, as(k_sf, "Spatial"), check.attributes = TRUE) [1] "Attributes: < Component \"bbox\": Attributes: < Component \"dimnames\": Component 1: 2 string mismatches > >" [2] "Attributes: < Component \"coords\": Attributes: < Component \"dimnames\": Component 2: 2 string mismatches > >" [3] "Attributes: < Component \"coords.nrs\": Numeric: lengths (2, 0) differ >" [4] "Attributes: < Component \"proj4string\": Attributes: < Names: 1 string mismatch > >" [5] "Attributes: < Component \"proj4string\": Attributes: < Length mismatch: comparison on first 2 components > >" [6] "Attributes: < Component \"proj4string\": Attributes: < Component 2: 1 string mismatch > >" > > # 2. using stars for grid: > > suppressPackageStartupMessages(library(stars)) > st = st_as_stars(meuse.grid) Warning message: In CPL_crs_from_input(x) : GDAL Message 1: +init=epsg:XXXX syntax is deprecated. It might return a CRS with a non-EPSG compliant axis order. > st_crs(st) Coordinate Reference System: User input: +init=epsg:28992 wkt: PROJCRS["Amersfoort / RD New", BASEGEOGCRS["Amersfoort", DATUM["Amersfoort", ELLIPSOID["Bessel 1841",6377397.155,299.1528128, LENGTHUNIT["metre",1]]], PRIMEM["Greenwich",0, ANGLEUNIT["degree",0.0174532925199433]], ID["EPSG",4289]], CONVERSION["RD New", METHOD["Oblique Stereographic", ID["EPSG",9809]], PARAMETER["Latitude of natural origin",52.1561605555556, ANGLEUNIT["degree",0.0174532925199433], ID["EPSG",8801]], PARAMETER["Longitude of natural origin",5.38763888888889, ANGLEUNIT["degree",0.0174532925199433], ID["EPSG",8802]], PARAMETER["Scale factor at natural origin",0.9999079, SCALEUNIT["unity",1], ID["EPSG",8805]], PARAMETER["False easting",155000, LENGTHUNIT["metre",1], ID["EPSG",8806]], PARAMETER["False northing",463000, LENGTHUNIT["metre",1], ID["EPSG",8807]], ID["EPSG",19914]], CS[Cartesian,2], AXIS["(E)",east, ORDER[1], LENGTHUNIT["metre",1, ID["EPSG",9001]]], AXIS["(N)",north, ORDER[2], LENGTHUNIT["metre",1, ID["EPSG",9001]]], USAGE[ SCOPE["unknown"], AREA["Netherlands - onshore, including Waddenzee, Dutch Wadden Islands and 12-mile offshore coastal zone."], BBOX[50.75,3.2,53.7,7.22]]] > > # compare inputs: > sp = as(st, "Spatial") > fullgrid(meuse.grid) = TRUE > all.equal(sp, meuse.grid["dist"], check.attributes = FALSE) [1] "Names: Lengths (5, 1) differ (string compare on first 1)" [2] "Names: 1 string mismatch" > all.equal(sp, meuse.grid["dist"], check.attributes = TRUE, use.names = FALSE) [1] "Names: Lengths (5, 1) differ (string compare on first 1)" [2] "Names: 1 string mismatch" [3] "Attributes: < Component 3: Names: 1 string mismatch >" [4] "Attributes: < Component 3: Length mismatch: comparison on first 1 components >" [5] "Attributes: < Component 3: Component 1: Mean relative difference: 1.08298 >" [6] "Attributes: < Component 4: Attributes: < Component 2: names for current but not for target > >" [7] "Attributes: < Component 4: Attributes: < Component 3: names for current but not for target > >" [8] "Attributes: < Component 5: Attributes: < Names: 1 string mismatch > >" [9] "Attributes: < Component 5: Attributes: < Length mismatch: comparison on first 2 components > >" [10] "Attributes: < Component 5: Attributes: < Component 2: 1 string mismatch > >" > > # kriging: > st_crs(st) = st_crs(meuse_sf) = NA # GDAL roundtrip messes them up! > k_st = if (Sys.getenv("USER") == "travis") { + try(krige(log(zinc)~1, meuse_sf, st, v.fit)) + } else { + krige(log(zinc)~1, meuse_sf, st, v.fit) + } [using ordinary kriging] > k_st stars object with 2 dimensions and 2 attributes attribute(s): Min. 1st Qu. Median Mean 3rd Qu. Max. NA's var1.pred 4.7765547 5.2376293 5.5728839 5.7072287 6.1717619 7.4399911 5009 var1.var 0.0854949 0.1372864 0.1621838 0.1853319 0.2116152 0.5002756 5009 dimension(s): from to offset delta x/y x 1 78 178440 40 [x] y 1 104 333760 -40 [y] > > # handle factors, when going to stars? > k_sp_grd$cls = cut(k_sp_grd$var1.pred, c(0, 5, 6, 7, 8, 9)) > st_as_stars(k_sp_grd) stars object with 2 dimensions and 3 attributes attribute(s): var1.pred var1.var cls Min. :4.777 Min. :0.085 (0,5]: 316 1st Qu.:5.238 1st Qu.:0.137 (5,6]:1778 Median :5.573 Median :0.162 (6,7]: 962 Mean :5.707 Mean :0.185 (7,8]: 47 3rd Qu.:6.172 3rd Qu.:0.212 (8,9]: 0 Max. :7.440 Max. :0.500 NA's :5009 NA's :5009 NA's :5009 dimension(s): from to offset delta refsys x/y x 1 78 178440 40 Amersfoort / RD New [x] y 1 104 333760 -40 Amersfoort / RD New [y] > if (require(raster, quietly = TRUE)) { + print(st_as_stars(raster::stack(k_sp_grd))) # check + print(all.equal(st_redimension(st_as_stars(k_sp_grd)), st_as_stars(raster::stack(k_sp_grd)), check.attributes=FALSE)) + } stars object with 3 dimensions and 1 attribute attribute(s): Min. 1st Qu. Median Mean 3rd Qu. Max. NA's var1.pred 0.0854949 0.2116778 2 2.710347 5.237542 7.439991 15027 dimension(s): from to offset delta refsys values x 1 78 178440 40 Amersfoort / RD New NULL y 1 104 333760 -40 Amersfoort / RD New NULL band 1 3 NA NA NA var1.pred, var1.var , cls x/y x [x] y [y] band [1] TRUE > > suppressPackageStartupMessages(library(spacetime)) > > Sys.setenv(TZ="") > tm = as.POSIXct("2019-02-25 15:37:24 CET") > n = 4 > s = stars:::st_stars(list(foo = array(1:(n^3), rep(n,3))), + stars:::create_dimensions(list( + x = stars:::create_dimension(from = 1, to = n, offset = 10, delta = 0.5), + y = stars:::create_dimension(from = 1, to = n, offset = 0, delta = -0.7), + time = stars:::create_dimension(values = tm + 1:n)), + raster = stars:::get_raster(dimensions = c("x", "y"))) + ) > s stars object with 3 dimensions and 1 attribute attribute(s): Min. 1st Qu. Median Mean 3rd Qu. Max. foo 1 16.75 32.5 32.5 48.25 64 dimension(s): from to offset delta refsys x/y x 1 4 10 0.5 NA [x] y 1 4 0 -0.7 NA [y] time 1 4 2019-02-25 15:37:25 UTC 1 secs POSIXct > > as.data.frame(s) x y time foo 1 10.25 -0.35 2019-02-25 15:37:25 1 2 10.75 -0.35 2019-02-25 15:37:25 2 3 11.25 -0.35 2019-02-25 15:37:25 3 4 11.75 -0.35 2019-02-25 15:37:25 4 5 10.25 -1.05 2019-02-25 15:37:25 5 6 10.75 -1.05 2019-02-25 15:37:25 6 7 11.25 -1.05 2019-02-25 15:37:25 7 8 11.75 -1.05 2019-02-25 15:37:25 8 9 10.25 -1.75 2019-02-25 15:37:25 9 10 10.75 -1.75 2019-02-25 15:37:25 10 11 11.25 -1.75 2019-02-25 15:37:25 11 12 11.75 -1.75 2019-02-25 15:37:25 12 13 10.25 -2.45 2019-02-25 15:37:25 13 14 10.75 -2.45 2019-02-25 15:37:25 14 15 11.25 -2.45 2019-02-25 15:37:25 15 16 11.75 -2.45 2019-02-25 15:37:25 16 17 10.25 -0.35 2019-02-25 15:37:26 17 18 10.75 -0.35 2019-02-25 15:37:26 18 19 11.25 -0.35 2019-02-25 15:37:26 19 20 11.75 -0.35 2019-02-25 15:37:26 20 21 10.25 -1.05 2019-02-25 15:37:26 21 22 10.75 -1.05 2019-02-25 15:37:26 22 23 11.25 -1.05 2019-02-25 15:37:26 23 24 11.75 -1.05 2019-02-25 15:37:26 24 25 10.25 -1.75 2019-02-25 15:37:26 25 26 10.75 -1.75 2019-02-25 15:37:26 26 27 11.25 -1.75 2019-02-25 15:37:26 27 28 11.75 -1.75 2019-02-25 15:37:26 28 29 10.25 -2.45 2019-02-25 15:37:26 29 30 10.75 -2.45 2019-02-25 15:37:26 30 31 11.25 -2.45 2019-02-25 15:37:26 31 32 11.75 -2.45 2019-02-25 15:37:26 32 33 10.25 -0.35 2019-02-25 15:37:27 33 34 10.75 -0.35 2019-02-25 15:37:27 34 35 11.25 -0.35 2019-02-25 15:37:27 35 36 11.75 -0.35 2019-02-25 15:37:27 36 37 10.25 -1.05 2019-02-25 15:37:27 37 38 10.75 -1.05 2019-02-25 15:37:27 38 39 11.25 -1.05 2019-02-25 15:37:27 39 40 11.75 -1.05 2019-02-25 15:37:27 40 41 10.25 -1.75 2019-02-25 15:37:27 41 42 10.75 -1.75 2019-02-25 15:37:27 42 43 11.25 -1.75 2019-02-25 15:37:27 43 44 11.75 -1.75 2019-02-25 15:37:27 44 45 10.25 -2.45 2019-02-25 15:37:27 45 46 10.75 -2.45 2019-02-25 15:37:27 46 47 11.25 -2.45 2019-02-25 15:37:27 47 48 11.75 -2.45 2019-02-25 15:37:27 48 49 10.25 -0.35 2019-02-25 15:37:28 49 50 10.75 -0.35 2019-02-25 15:37:28 50 51 11.25 -0.35 2019-02-25 15:37:28 51 52 11.75 -0.35 2019-02-25 15:37:28 52 53 10.25 -1.05 2019-02-25 15:37:28 53 54 10.75 -1.05 2019-02-25 15:37:28 54 55 11.25 -1.05 2019-02-25 15:37:28 55 56 11.75 -1.05 2019-02-25 15:37:28 56 57 10.25 -1.75 2019-02-25 15:37:28 57 58 10.75 -1.75 2019-02-25 15:37:28 58 59 11.25 -1.75 2019-02-25 15:37:28 59 60 11.75 -1.75 2019-02-25 15:37:28 60 61 10.25 -2.45 2019-02-25 15:37:28 61 62 10.75 -2.45 2019-02-25 15:37:28 62 63 11.25 -2.45 2019-02-25 15:37:28 63 64 11.75 -2.45 2019-02-25 15:37:28 64 > plot(s, col = sf.colors(), axes = TRUE) > (s.stfdf = as(s, "STFDF")) An object of class "STFDF" Slot "data": foo 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40 40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 Slot "sp": Object of class SpatialPixels Grid topology: cellcentre.offset cellsize cells.dim x 10.25 0.5 4 y -2.45 0.7 4 SpatialPoints: x y [1,] 10.25 -0.35 [2,] 10.75 -0.35 [3,] 11.25 -0.35 [4,] 11.75 -0.35 [5,] 10.25 -1.05 [6,] 10.75 -1.05 [7,] 11.25 -1.05 [8,] 11.75 -1.05 [9,] 10.25 -1.75 [10,] 10.75 -1.75 [11,] 11.25 -1.75 [12,] 11.75 -1.75 [13,] 10.25 -2.45 [14,] 10.75 -2.45 [15,] 11.25 -2.45 [16,] 11.75 -2.45 Coordinate Reference System (CRS) arguments: NA Slot "time": timeIndex 2019-02-25 15:37:25 1 2019-02-25 15:37:26 2 2019-02-25 15:37:27 3 2019-02-25 15:37:28 4 Slot "endTime": [1] "2019-02-25 15:37:26 UTC" "2019-02-25 15:37:27 UTC" [3] "2019-02-25 15:37:28 UTC" "2019-02-25 15:37:29 UTC" > stplot(s.stfdf, scales = list(draw = TRUE)) > > (s2 = st_as_stars(s.stfdf)) stars object with 3 dimensions and 1 attribute attribute(s): Min. 1st Qu. Median Mean 3rd Qu. Max. foo 1 16.75 32.5 32.5 48.25 64 dimension(s): from to offset delta refsys x/y x 1 4 10 0.5 NA [x] y 1 4 -1.11022e-16 -0.7 NA [y] time 1 4 2019-02-25 15:37:25 UTC 1 secs POSIXct > plot(s2, col = sf.colors(), axes = TRUE) > all.equal(s, s2, check.attributes = FALSE) [1] TRUE > > # multiple simulations: > data(meuse, package = "sp") > data(meuse.grid, package = "sp") > coordinates(meuse.grid) <- ~x+y > gridded(meuse.grid) <- TRUE > meuse.grid = st_as_stars(meuse.grid) > meuse_sf = st_as_sf(meuse, coords = c("x", "y")) > g = gstat(NULL, "zinc", zinc~1, meuse_sf, model = vgm(1, "Exp", 300), nmax = 10) > g = gstat(g, "lead", lead~1, meuse_sf, model = vgm(1, "Exp", 300), nmax = 10, fill.cross = TRUE) > set.seed(123) > (p = predict(g, meuse.grid, nsim = 5)) drawing 5 multivariate GLS realisations of beta... [using conditional Gaussian simulation] stars object with 3 dimensions and 2 attributes attribute(s): Min. 1st Qu. Median Mean 3rd Qu. Max. NA's zinc 101.7643 199.59256 300.2140 399.8017 544.0327 1817.2057 25045 lead 32.7799 73.03151 107.9339 133.1725 178.8162 638.9396 25045 dimension(s): from to offset delta values x/y x 1 78 178440 40 NULL [x] y 1 104 333760 -40 NULL [y] sample 1 5 NA NA sim1,...,sim5 > > proc.time() user system elapsed 6.827 3.845 6.117 gstat/tests/rings.Rout.save0000644000176200001440000001044713777370515015515 0ustar liggesusers R version 3.0.1 (2013-05-16) -- "Good Sport" Copyright (C) 2013 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(sp) > library(gstat) > set.seed(13331) > > x = runif(10) > y = runif(10) > z = rnorm(10) > d = data.frame(x=x,y=y,z=z) > bl = c(1,1) > > nd = data.frame(x=.5, y=.5) > > # single block: > library(sp) > coordinates(d) = ~x+y > nd = SpatialPoints(nd) > xx = krige(z~1, d, nd, model=vgm(1, "Exp", 1), block = bl, + set = list(nb=4)) [using ordinary kriging] > > ring = cbind(c(0,bl[1],bl[1],0,0), c(0,0,bl[2],bl[2],0)) > r1 = SpatialPolygons(list(Polygons(list(Polygon(ring)), ID = "xx"))) > a = data.frame(a = 1, b = 2) > rownames(a) = "xx" > r1df = SpatialPolygonsDataFrame(r1, a) > > g = gstat(formula=z~1, data=d, model=vgm(1, "Exp", 1)) > args = list(type = "regular", n=16, offset=c(0.5,0.5)) > yy = predict(g, r1df, block = bl, sps.args = args) [using ordinary kriging] > > xx = as.data.frame(xx) > yy = as.data.frame(yy) > row.names(xx) = row.names(yy) > print(all.equal(xx,yy)) [1] TRUE > > ## multiple blocks of equal size: > nd = data.frame(x= 0:4 + .5, y=rep(.5,5)) > nd = SpatialPoints(nd) > xx = krige(z~1, d, nd, model=vgm(1, "Exp", 1), block = bl, + set = list(nb=4)) [using ordinary kriging] > ring0 = cbind(c(0,bl[1],bl[1],0,0), c(0,0,bl[2],bl[2],0)) > ring1 = cbind(c(1+0,1+bl[1],1+bl[1],1+0,1+0), c(0,0,bl[2],bl[2],0)) > ring2 = cbind(c(2+0,2+bl[1],2+bl[1],2+0,2+0), c(0,0,bl[2],bl[2],0)) > ring3 = cbind(c(3+0,3+bl[1],3+bl[1],3+0,3+0), c(0,0,bl[2],bl[2],0)) > ring4 = cbind(c(4+0,4+bl[1],4+bl[1],4+0,4+0), c(0,0,bl[2],bl[2],0)) > r1 = SpatialPolygons(list( + Polygons(list(Polygon(ring0)), ID = "x0"), + Polygons(list(Polygon(ring1)), ID = "x1"), + Polygons(list(Polygon(ring2)), ID = "x2"), + Polygons(list(Polygon(ring3)), ID = "x3"), + Polygons(list(Polygon(ring4)), ID = "x4") + )) > df = data.frame(a=rep(1,5), b= rep(1,5)) > rownames(df) = c("x0", "x1", "x2", "x3", "x4") > r1df = SpatialPolygonsDataFrame(r1, df) > > yy = predict(g, r1, block = bl, sps.args = args) [using ordinary kriging] > xx = as.data.frame(xx) > yy = as.data.frame(yy) > row.names(xx) = row.names(yy) > all.equal(xx, yy) [1] TRUE > > ## multiple blocks of equal size: > args = list(type = "regular", cellsize=.25, offset=c(0.5,0.5), n=16) > yy = predict(g, r1, block = bl, sps.args = args) [using ordinary kriging] > xx = as.data.frame(xx) > yy = as.data.frame(yy) > row.names(xx) = row.names(yy) > print(all.equal(xx, yy)) [1] TRUE > > ## multiple blocks of varying size: > nd = data.frame(x=c(0.5, 2, 4.5), y=c(0.5, 1, 1.5)) > nd = SpatialPoints(nd) > bl = c(1,1) > ring0 = cbind(c(0,bl[1],bl[1],0,0), c(0,0,bl[2],bl[2],0)) > xx1 = krige(z~1, d, nd[1], model=vgm(1, "Exp", 1), block = bl, + set = list(nb=4)) [using ordinary kriging] > bl = c(2,2) > ring1 = cbind(c(1+0,1+bl[1],1+bl[1],1+0,1+0), c(0,0,bl[2],bl[2],0)) > xx2 = krige(z~1, d, nd[2], model=vgm(1, "Exp", 1), block = bl, + set = list(nb=4)) [using ordinary kriging] > bl = c(3,3) > ring2 = cbind(c(3+0,3+bl[1],3+bl[1],3+0,3+0), c(0,0,bl[2],bl[2],0)) > xx3 = krige(z~1, d, nd[3], model=vgm(1, "Exp", 1), block = bl, + set = list(nb=4)) [using ordinary kriging] > r1 = SpatialPolygons(list( + Polygons(list(Polygon(ring0)), ID = "x0"), + Polygons(list(Polygon(ring1)), ID = "x1"), + Polygons(list(Polygon(ring2)), ID = "x2") + )) > df = data.frame(a = rep(1,3), b = rep(1,3)) > rownames(df) = c("x0", "x1", "x2") > r1df = SpatialPolygonsDataFrame(r1, df) > > args = list(type = "regular", n=16, offset=c(0.5,0.5)) > yy = predict(g, r1df, block = bl, sps.args = args) [using ordinary kriging] > xx = rbind(as.data.frame(xx1), as.data.frame(xx2), as.data.frame(xx3)) > row.names(xx) = 1:3 > xx = as.data.frame(xx) > yy = as.data.frame(yy) > row.names(xx) = row.names(yy) > print(all.equal(xx, yy)) [1] TRUE > > proc.time() user system elapsed 1.260 0.024 1.288 gstat/tests/merge.R0000644000176200001440000000151513777370515014001 0ustar liggesusersoptions(digits=6) # illustrates the use of merge, for merging parameters accross variables: # Z1=m+e1(s) # Z2=m+e2(s) # Z1 and Z2 each have a different variogram, but share the parameter m # see documentation of gstat() function library(gstat) d1 = data.frame(x=c(0,2),y=c(0,0),z=c(0,1)) d2 = data.frame(x=c(0,2),y=c(2,2),z=c(4,5)) g = gstat(NULL,"d1", z~1,~x+y,d1,model=vgm(1, "Exp", 1)) g = gstat(g,"d2", z~1,~x+y,d2,model=vgm(1, "Exp", 1), merge=c("d1","d2")) g = gstat(g, c("d1", "d2"), model = vgm(0.5, "Exp", 1)) predict(g, data.frame(x=1,y=1), debug = 32) # Z1 and Z2 share a regression slope: g = gstat(NULL,"d1", z~x,~x+y,d1,model=vgm(1, "Exp", 1)) g = gstat(g,"d2", z~x,~x+y,d2,model=vgm(1, "Exp", 1), merge=list(c("d1",2,"d2",2))) g = gstat(g, c("d1", "d2"), model = vgm(0.5, "Exp", 1)) predict(g, data.frame(x=1,y=1), debug = 32) gstat/tests/vdist.Rout.save0000644000176200001440000000241613777370515015521 0ustar liggesusers R version 3.0.1 (2013-05-16) -- "Good Sport" Copyright (C) 2013 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(sp) > library(gstat) > > data(meuse) > coordinates(meuse) = ~x+y > data(meuse.grid) > gridded(meuse.grid) = ~x+y > > mg = meuse.grid > gridded(mg) = FALSE > mg= mg[1500,] > krige(log(zinc)~1,meuse,mg,vgm(1, "Exp", 300, anis=c(0,0.01)), + vdist=FALSE, maxdist=1000,nmax=10) [using ordinary kriging] coordinates var1.pred var1.var 1500 (180260, 331300) 5.007376 1.102622 > krige(log(zinc)~1,meuse,mg,vgm(1, "Exp", 300, anis=c(0,0.01)), + vdist=TRUE, maxdist=1000,nmax=10) [using ordinary kriging] coordinates var1.pred var1.var 1500 (180260, 331300) 5.50671 1.100095 > > proc.time() user system elapsed 1.308 0.052 1.370 gstat/tests/sim.Rout.save0000644000176200001440000000352413777370515015161 0ustar liggesusers R version 3.6.0 (2019-04-26) -- "Planting of a Tree" Copyright (C) 2019 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(digits=6) > library(sp) > data(meuse) > set.seed(158229572) > new.locs <- data.frame(x = c(181170, 180310, 180205, 178673, 178770, 178270), + y = c(333250, 332189, 331707, 330066, 330675, 331075)) > library(gstat) > krige(zinc ~ 1, ~ x + y, meuse, newdata = new.locs, + model = vgm(1.34e5, "Sph", 800, nug = 2.42e4), + block = c(40,40), nmax = 40, nsim = 10) drawing 10 GLS realisations of beta... [using conditional Gaussian simulation] x y sim1 sim2 sim3 sim4 sim5 sim6 sim7 1 181170 333250 267.385 27.5686 428.144 381.576 151.119 175.890 293.273 2 180310 332189 429.437 659.6579 564.023 611.666 612.756 619.791 771.961 3 180205 331707 205.978 412.7276 271.827 380.349 169.488 369.822 266.026 4 178673 330066 117.479 684.0663 399.148 585.096 606.396 867.866 807.634 5 178770 330675 780.072 837.4628 682.690 911.052 600.984 783.019 749.476 6 178270 331075 1025.778 1582.0269 614.235 332.377 660.228 589.447 972.018 sim8 sim9 sim10 1 294.107 113.347 279.991 2 776.498 724.160 901.692 3 338.021 630.244 140.272 4 127.301 957.242 444.007 5 533.773 748.144 623.960 6 1084.170 537.604 -214.972 > > proc.time() user system elapsed 0.467 0.020 0.479 gstat/src/0000755000176200001440000000000014413507477012177 5ustar liggesusersgstat/src/sem.h0000644000176200001440000000125613777370515013143 0ustar liggesusers/* sem.c */ #ifndef SEM_H # define SEM_H /* avoid multiple inclusion */ #if defined(__cplusplus) extern "C" { #endif int calc_variogram(VARIOGRAM *v, const char *fname); void fill_cutoff_width(DATA *data, VARIOGRAM *v); int is_directional(VARIOGRAM *v); void fprint_header_vgm(FILE *f, const DATA *d1, const DATA *d2, const SAMPLE_VGM *ev); void fprint_sample_vgm(const SAMPLE_VGM *ev); #if defined(__cplusplus) } #endif #define LONGSIZE (sizeof(unsigned long)) #define MAX_NH (1UL << (4 * LONGSIZE)) #define TO_NH(x,y) (x + ((unsigned long)y << (4 * LONGSIZE))) #define HIGH_NH(x) (x / (1UL << (4 * LONGSIZE))) #define LOW_NH(x) (x % (1UL << (4 * LONGSIZE))) #endif /* SEM_H */ gstat/src/data.c0000644000176200001440000006131214127263756013260 0ustar liggesusers/* * data.c: basic i/o routines on DATA structure */ #include /* sqrt */ #include /* memcpy */ #include "defs.h" #include "data.h" #include "mapio.h" #include "userio.h" #include "utils.h" #include "block.h" #include "debug.h" #include "glvars.h" #include "defaults.h" #include "mtrx.h" #include "lm.h" /* free_lm() */ #include "gls.h" /* free_glm() */ #include "nsearch.h" #include "gcdist.h" const DATA_TYPE data_types[] = { { DATA_UNKNOWN, "Unknown file type"}, { DATA_ASCII_TABLE, "Ascii table file"}, { DATA_EAS, "GeoEAS file"}, { DATA_IDRISI_VEC, "Idrisi ascii .vec"}, { DATA_IDRISI32_VEC, "Idrisi binary .vct"}, { DATA_IDRISI_BIN, "Idrisi binary .img"}, { DATA_IDRISI_ASCII, "Idrisi ascii .img"}, { DATA_IDRISI32_BIN, "Idrisi binary .rst"}, { DATA_IDRISI32_ASCII, "Idrisi ascii .rst"}, { DATA_GRIDASCII, "ArcInfo gridascii"}, { DATA_GRIDFLOAT, "ArcInfo gridfloat"}, { DATA_CSF, "PCRaster map"}, { DATA_T2, "T2 map"}, { DATA_ERMAPPER, "ER-Mapper file"}, { DATA_GNUPLOT, "Gnuplot binary"}, { DATA_GMT, "GMT netCDF format" }, { DATA_SURFER_DSAA, "Surfer DSAA ascii grid" }, { DATA_GSLIB, "GSLIB grid" }, { DATA_GRASS, "GRASS site list" }, { DATA_GRASS_GRID, "GRASS raster" }, { DATA_GDAL, "GDAL raster map" } }; static void calc_data_mean_std(DATA *d); static void grid_push_point(DATA *d, DPOINT *p, int adjust_to_gridcentrs); static double point_norm_1D(const DPOINT *p); static double point_norm_2D(const DPOINT *p); static double point_norm_3D(const DPOINT *p); static double pp_norm_1D(const DPOINT *a, const DPOINT *b); static double pp_norm_2D(const DPOINT *a, const DPOINT *b); static double pp_norm_3D(const DPOINT *a, const DPOINT *b); /* great circle distances: */ static double point_norm_gc(const DPOINT *p); static double pp_norm_gc2(const DPOINT *a, const DPOINT *b); static double pb_norm_gc2(const DPOINT *where, BBOX bbox); static void logprint_data_header(const DATA *d); static DPOINT min, max; static int fix_minmax = 0; const POLY_NM polynomial[N_POLY] = {{ POLY_X, "x", 1, X_BIT_SET}, { POLY_Y, "y", 1, Y_BIT_SET}, { POLY_Z, "z", 1, Z_BIT_SET}, { POLY_X2, "x2", 2, X_BIT_SET}, { POLY_Y2, "y2", 2, Y_BIT_SET}, { POLY_Z2, "z2", 2, Z_BIT_SET}, { POLY_XY, "xy", 2, Y_BIT_SET}, { POLY_XZ, "xz", 2, Z_BIT_SET}, { POLY_YZ, "yz", 2, Z_BIT_SET}, { POLY_X3, "x3", 3, X_BIT_SET}, { POLY_Y3, "y3", 3, Y_BIT_SET}, { POLY_Z3, "z3", 3, Z_BIT_SET}, { POLY_X2Y, "x2y", 3, Y_BIT_SET}, { POLY_XY2, "xy2", 3, Y_BIT_SET}, { POLY_X2Z, "x2z", 3, Z_BIT_SET}, { POLY_XZ2, "xz2", 3, Z_BIT_SET}, { POLY_Y2Z, "y2z", 3, Z_BIT_SET}, { POLY_YZ2, "yz2", 3, Z_BIT_SET}}; void set_norm_fns(DATA *d) { if (d->mode & Z_BIT_SET) { d->point_norm = point_norm_3D; d->pp_norm2 = pp_norm_3D; d->pb_norm2 = pb_norm_3D; } else if (d->mode & Y_BIT_SET) { if (gl_longlat) { d->point_norm = point_norm_gc; d->pp_norm2 = pp_norm_gc2; d->pb_norm2 = pb_norm_gc2; /* if (gl_split != DEF_split) pr_warning("longlat data cannot do quadtree, setting split to %d", INT_MAX); */ gl_split = INT_MAX; } else { d->point_norm = point_norm_2D; d->pp_norm2 = pp_norm_2D; d->pb_norm2 = pb_norm_2D; } } else { d->point_norm = point_norm_1D; d->pp_norm2 = pp_norm_1D; d->pb_norm2 = pb_norm_1D; } } void init_data_minmax(void) { fix_minmax = 0; set_mv_double(&(min.x)); set_mv_double(&(min.y)); set_mv_double(&(min.z)); set_mv_double(&(max.x)); set_mv_double(&(max.y)); set_mv_double(&(max.z)); } void setup_data_minmax(DATA *d) { if (fix_minmax) ErrMsg(ER_NULL, "min and max should be fixed"); if (d->id == 0) { min.x = d->minX; min.y = d->minY; min.z = d->minZ; max.x = d->maxX; max.y = d->maxY; max.z = d->maxZ; } else { min.x = MIN(min.x, d->minX); min.y = MIN(min.y, d->minY); min.z = MIN(min.z, d->minZ); max.x = MAX(max.x, d->maxX); max.y = MAX(max.y, d->maxY); max.z = MAX(max.z, d->maxZ); } } DATA *get_area_centre(DATA *area, DATA *d) { int i, j; DPOINT p; d->n_list = d->n_max = 0; d->variable = area->variable; d->x_coord = area->x_coord; d->y_coord = area->y_coord; d->z_coord = area->z_coord; d->type = data_types[area->type.type]; d->fname = ""; p.x = p.y = p.z = 0.0; p.u.stratum = 0; d->n_X = area->n_X; if (area->n_X > 0) { p.X = (double *) emalloc(area->n_X * sizeof(double)); d->colX = (int *) emalloc(area->n_X * sizeof(int)); for (j = 0; j < area->n_X; j++) { p.X[j] = 0.0; d->colX[j] = area->colX[j]; } } else { p.X = NULL; d->colX = NULL; } for (i = 0; i < area->n_list; i++) { p.x += area->list[i]->x; p.y += area->list[i]->y; p.z += area->list[i]->z; for (j = 0; j < area->n_X; j++) p.X[j] += area->list[i]->X[j]; } p.x /= area->n_list; p.y /= area->n_list; p.z /= area->n_list; for (j = 0; j < area->n_X; j++) p.X[j] /= area->n_list; p.attr = 0.0; printlog("prediction centre at x=%g, y=%g, z=%g",p.x,p.y,p.z); if (d->n_X) { printlog(" where x0 averages ["); for (j = 0; j < area->n_X; j++) printlog("%g%s", p.X[j], jn_X-1?",":""); printlog("]\n"); } else printlog("\n"); push_point(d, &p); d->minX = d->maxX = p.x; d->minY = d->maxY = p.y; d->minZ = d->maxZ = p.z; d->mode = area->mode; d->n_X = area->n_X; calc_data_mean_std(d); return d; } void centre_area(DATA *area) { int i; DPOINT p; p.x = p.y = p.z = 0.0; for (i = 0; i < area->n_list; i++) { p.x += area->list[i]->x; p.y += area->list[i]->y; p.z += area->list[i]->z; } p.x /= area->n_list; p.y /= area->n_list; p.z /= area->n_list; for (i = 0; i < area->n_list; i++) { area->list[i]->x -= p.x; area->list[i]->y -= p.y; area->list[i]->z -= p.z; } area->minX -= p.x; area->maxX -= p.x; area->minY -= p.y; area->maxY -= p.y; area->minZ -= p.z; area->maxZ -= p.z; } static void calc_data_mean_std(DATA *d) { /* * Calculates fields mean and std of d with mean and standard dev. (/(n-1)) */ int i; if (d->standard == 2) { /* we did this already.. */ for (i = 0; i < d->n_list; i++) d->list[i]->attr *= d->std; } d->mean = 0.0; d->std = 0.0; if (d->n_list <= 0) { pr_warning("calc_data_mean_std: n_list <= 0: %d", d->n_list); return; } for (i = 0; i < d->n_list; i++) d->mean += d->list[i]->attr; d->mean /= d->n_list; if (d->n_list == 1) return; for (i = 0; i < d->n_list; i++) d->std += SQR(d->list[i]->attr - d->mean); d->std = sqrt((d->std)/(d->n_list - 1)); if (d->standard > 0) { for (i = 0; i < d->n_list; i++) d->list[i]->attr /= d->std; d->standard = 2; } return; } void setup_polynomial_X(DATA *d) { int i, j, degree; degree = d->polynomial_degree; if (degree < 0 || degree > 3) ErrMsg(ER_SYNTAX, "polynomial degree n, `d=n', should be in [0..3]"); for (i = 1; i <= degree; i++) for (j = 0; j < N_POLY; j++) if (polynomial[j].degree == i && (d->mode & polynomial[j].mode)) data_add_X(d, polynomial[j].poly_nr); } void data_add_X(DATA *d, int col) { int i; for (i = 0; d->id != ID_OF_VALDATA && i < d->n_X; i++) if (d->colX[i] == col) ErrMsg(ER_IMPOSVAL, "X-variable: column appears twice"); d->n_X++; d->colX = (int *) erealloc(d->colX, d->n_X * sizeof(int)); d->colX[d->n_X - 1] = col; } void calc_polynomials(DATA *d) { int i, j, do_block; #define CHECK_BITX if(!(d->mode & X_BIT_SET)) ErrMsg(ER_VARNOTSET,"x coordinate not set") #define CHECK_BITY if(!(d->mode & Y_BIT_SET)) ErrMsg(ER_VARNOTSET,"y coordinate not set") #define CHECK_BITZ if(!(d->mode & Z_BIT_SET)) ErrMsg(ER_VARNOTSET,"z coordinate not set") for (j = 0; j < d->n_X; j++) { if (d->colX[j] < -1) { switch(d->colX[j]) { case POLY_X: case POLY_X2: case POLY_X3: CHECK_BITX; break; case POLY_Y: case POLY_Y2: case POLY_Y3: CHECK_BITY; break; case POLY_Z: case POLY_Z2: case POLY_Z3: CHECK_BITZ; break; case POLY_XY: CHECK_BITX; CHECK_BITY; break; case POLY_XZ: CHECK_BITX; CHECK_BITZ; break; case POLY_YZ: CHECK_BITY; CHECK_BITZ; break; case POLY_X2Y: CHECK_BITX; CHECK_BITY; break; case POLY_XY2: CHECK_BITX; CHECK_BITY; break; case POLY_X2Z: CHECK_BITX; CHECK_BITZ; break; case POLY_XZ2: CHECK_BITX; CHECK_BITZ; break; case POLY_Y2Z: CHECK_BITY; CHECK_BITZ; break; case POLY_YZ2: CHECK_BITY; CHECK_BITZ; break; default: ErrMsg(ER_IMPOSVAL, "unknown polynomial number"); break; } } } for (j = do_block = 0; !do_block && j < d->n_X; j++) do_block = (d->colX[j] < -1); for (i = 0; do_block && i < d->n_list; i++) /* bl is a single point-list if IS_POINT(d->list[i]) */ calc_polynomial_point(d, d->list[i]); } void calc_polynomial_point(DATA *d, DPOINT *pt) { static DATA *bl = NULL; int j, k; bl = block_discr(bl, get_block_p(), pt); for (j = 0; j < d->n_X; j++) { if (d->colX[j] < -1) /* do eventual block averaging here: */ for (k = 0, pt->X[j] = 0.0; k < bl->n_list; k++) pt->X[j] += bl->list[k]->u.weight * calc_polynomial(bl->list[k], d->colX[j]); } } double calc_polynomial(DPOINT *p, int colX) { /* * fills polynomial field (x, y, z, x2, y2, z2, xy, xz, yz) * with standardized values * * Counting on the following behaviour: * first, all data + valdata are passed through setup_data_minmax(), in * order to get the right values into min and max; * then, the routines calc_polynomial* are called. * changing min or max inbetween would result in rubbish. */ double x, y, z; if (fix_minmax == 0) fix_minmax = 1; /* stop touching it */ x = ((min.x==max.x) ? p->x : (p->x - min.x)/(max.x - min.x)); y = ((min.y==max.y) ? p->y : (p->y - min.y)/(max.y - min.y)); z = ((min.z==max.z) ? p->z : (p->z - min.z)/(max.z - min.z)); switch(colX) { case POLY_X: return (x); case POLY_X2: return (x * x); case POLY_X3: return (x * x * x); case POLY_Y: return (y); case POLY_Y2: return (y * y); case POLY_Y3: return (y * y * y); case POLY_Z: return (z); case POLY_Z2: return (z * z); case POLY_Z3: return (z * z * z); case POLY_XY: return (x * y); case POLY_XZ: return (x * z); case POLY_YZ: return (y * z); case POLY_X2Y: return (x * x * y); case POLY_XY2: return (x * y * y); case POLY_X2Z: return (x * x * z); case POLY_XZ2: return (x * z * z); case POLY_Y2Z: return (y * y * z); case POLY_YZ2: return (y * z * z); default: ErrMsg(ER_IMPOSVAL, "unknown polynomial number"); break; } return 1.0; /* will never happen */ } void free_data(DATA *d) { int i; assert(d); if (DEBUG_FORCE) /* let atexit(qtree_print) do it's job... */ return; if (d->P_base) { /* segmented: */ efree(d->P_base); if (d->n_X && d->X_base) efree(d->X_base); } else { /* non-segmented */ if (d->list) /* CW at all MV on output both P_base and d_list are 0 */ for (i = d->n_list - 1; i >= 0; i--) pop_point(d, i); } if (d->sel != NULL && d->sel != d->list) efree(d->sel); if (d->list) efree(d->list); if (d->colX) efree(d->colX); if (d->qtree_root != NULL) qtree_free(d->qtree_root); if (d->lm) free_lm(d->lm); if (d->glm) free_glm(d->glm); if (d->grid) free_data_gridmap(d->grid); if (d->point_ids != NULL) { for (i = d->n_list - 1; i >= 0; i--) efree(d->point_ids[i]); } if (d->beta != NULL) efree(d->beta); efree(d); return; } DATA *init_one_data(DATA *data) { if (data == NULL) data = (DATA *) emalloc(sizeof(DATA)); data->colnvalue = 0; data->colnx = 0; data->colny = 0; data->colnz = 0; data->colns = 0; data->coln_id = 0; data->colnvariance = 0; data->n_list = -1; data->n_max = -1; data->nsim_at_data = 0; data->init_max = 0; data->n_sel = -1; data->n_sel_max = 0; data->id = -1; data->log = 0; data->standard = 0; data->what_is_u = U_UNKNOWN; data->centre = 0; data->region = 0; data->mode = 0; data->dummy = 0; data->force = 0; data->vdist = 0; data->square = 0; data->average = 0; data->every = 1; data->offset = 0; data->prob = 1.0; data->skip = 0; data->lambda = 1.0; data->calc_residuals = 1; data->is_residual = 0; data->polynomial_degree = 0; data->n_averaged = 0; data->fname = NULL; data->type = data_types[DATA_UNKNOWN]; data->variable = NULL; data->x_coord = NULL; data->y_coord = NULL; data->z_coord = NULL; data->s_coord = NULL; data->V_coord = NULL; data->point_ids = NULL; data->id_name = NULL; data->mean = 0.0; data->std = 0.0; data->sel_rad = DBL_MAX; data->dX = DBL_MAX; data->sel_max = INT_MAX; data->sel_min = 0; data->oct_max = 0; /* default: don't use octant search */ data->oct_filled = 1; /* in case of no octants */ data->list = NULL; data->sel = NULL; data->P_base = NULL; data->X_base = NULL; data->lm = NULL; data->glm = NULL; data->n_merge = 0; data->mtbl = NULL; data->n_X = 0; data->colX = NULL; data_add_X(data, 0); /* add intercept -->> UK, defaulting to ordinary kriging */ data->qtree_root = NULL; data->grid = NULL; data->togrid = 0; data->point_norm = NULL; data->pp_norm2 = NULL; data->pb_norm2 = NULL; data->beta = NULL; data->Category = NULL; data->var_fn_str = NULL; data->nscore_table = NULL; data->variance_fn = NULL; set_mv_double(&(data->Icutoff)); set_mv_double(&(data->mv)); return data; } void print_data(const DATA *d, int list) { int i; printlog("\ndata id: %d\n", d->id); if (! is_mv_double(&(d->Icutoff))) printlog("ind. cutoff: %g\n", d->Icutoff); if (d->Category) printlog("category: %s\n", d->Category); if (! is_mv_double(&(d->mv))) printlog("missing value: %g\n", d->mv); if (d->beta) { printlog("beta: ["); for (i = 0; i < d->beta->size; i++) printlog(" %g", d->beta->val[i]); printlog("]\n"); } printlog("sel_radius %g sel_max %d sel_min %d\n", d->sel_rad, d->sel_max, d->sel_min); if (d->n_X > 0) { for (i = 0; i < d->n_X; i++) { printlog("X[%d]: ", i); if (d->colX[i] == 0) printlog("intercept "); if (d->colX[i] < 0) printlog("%s ", POLY_NAME(d->colX[i])); if (d->colX[i] > 0) printlog("%d ", d->colX[i]); } printlog("\n"); } printlog("n_list %d n_max %d n_sel %d\n", d->n_list, d->n_max, d->n_sel); if (list) { printlog("current list:\n"); logprint_data_header(d); if (d->n_list) { for (i = 0; i < d->n_list; i++) logprint_point(d->list[i], d); } else printlog("\n"); } else { printlog("current selection:\n"); logprint_data_header(d); if (d->n_sel) { for (i = 0; i < d->n_sel; i++) logprint_point(d->sel[i], d); } else printlog("\n"); } } static void logprint_data_header(const DATA *d) { printlog("\nidx x:%s;", d->x_coord); printlog("y:%s;", d->y_coord); printlog("z:%s;", d->z_coord); printlog("v:%s;\n", d->variable); } void logprint_point(const DPOINT *p, const DATA *d) { /* * print contents of p (non zero: use d) to log device */ int j; printlog("%3d ", GET_INDEX(p)); if (d->mode & X_BIT_SET) printlog("x: %4g ", p->x); if (d->mode & Y_BIT_SET) printlog("y: %4g ", p->y); if (d->mode & Z_BIT_SET) printlog("z: %4g ", p->z); if (d->mode & V_BIT_SET) printlog("v: %4g ", p->attr); switch (d->what_is_u) { case U_UNKNOWN: break; case U_ISDIST: printlog("dist: %4g ", sqrt(p->u.dist2)); break; case U_ISWEIGHT: printlog("weight: %4g ", p->u.weight); break; case U_ISSTRATUM: printlog("stratum: %d ", p->u.stratum); break; } for (j = 0; j < d->n_X; j++) printlog("X[%d]: %6g ", j, p->X[j]); if (d->point_ids) { printlog("ID: %s ", d->point_ids[GET_INDEX(p)]); } printlog("\n"); } void push_point(DATA *d, const DPOINT *p) { int i; /* * add one point p to the data structure d * [counts on the fact that erealloc(NULL,size) calls malloc(size)] */ if (d->prob < 1.0) { ErrMsg(ER_IMPOSVAL, "sample in R, not in gstat"); } else if (d->every > 1) { /* EJP: WAS if ((d->n_list + d->offset) % d->every != 0) */ if ((d->n_list + d->skip + 1 - d->offset) % d->every != 0) { d->skip++; return; } } if (d->n_list < 0) { message("push_point: n_list < 0: %d (%s)\n", d->n_list, d->fname); ErrMsg(ER_NULL, "push_point(): n_list < 0"); } if (d->n_max < 0) { message("push_point: n_max < 0: %d (%s)\n", d->n_max, d->fname); ErrMsg(ER_NULL, "push_point(): n_max < 0"); } /* * use rather large blocks of memory for points: */ if (d->n_list == d->n_max) { /* increase memory: */ /* resize d->n_max: */ if (d->list == NULL) { if (d->init_max > 0) d->n_max = d->init_max; else d->n_max = MAX_DATA; } else { d->n_max += MAX_DATA; /* or else: d->n_max *= 2; */ if (d->init_max > 0 && DEBUG_DUMP) pr_warning("exceeding nmax, now %d", d->n_max); } /* resize blocked memory bases P_base and X_base, and list: */ d->P_base = (DPOINT *) erealloc(d->P_base, d->n_max * sizeof(DPOINT)); if (d->n_X > 0) { if (intercept_only(d)) { /* create a single instance of the X row: */ if (d->X_base == NULL) { /* first time */ d->X_base = (double *) emalloc(sizeof(double)); d->X_base[0] = 1.0; } } else /* each point needs it's own X row: */ d->X_base = (double *) erealloc(d->X_base, d->n_max * d->n_X * sizeof(double)); } d->list = (DPOINT **) erealloc(d->list, d->n_max * sizeof(DPOINT *)); /* * realloc'ing may have moved P_base or X_base, so reset all pointers: */ for (i = 0; i < d->n_list; i++) { d->list[i] = &(d->P_base[i]); if (d->n_X) { if (intercept_only(d)) /* d->P_base[i].X = d->X_base; */ d->list[i]->X = d->X_base; else /* d->P_base[i].X = &(d->X_base[d->n_X * i]); */ d->list[i]->X = &(d->X_base[d->n_X * i]); } else /* d->P_base[i].X = NULL; */ d->list[i]->X = NULL; } for (i = d->n_list; i < d->n_max; i++) d->list[i] = NULL; /* for savety */ /* rebuild qtree_root: this is avoided by setting nmax */ qtree_rebuild(d); datagrid_rebuild(d, 0); } /* * copy information on current point into P_base and X_base arrays: */ #ifdef SLOW d->P_base[d->n_list] = *p; #else memcpy(&(d->P_base[d->n_list]), p, sizeof(DPOINT)); #endif if (d->n_X > 0 && !intercept_only(d)) { #define SLOW 1 #ifdef SLOW /* slow... copy X row */ for (i = 0; i < d->n_X; i++) d->X_base[d->n_X * d->n_list + i] = p->X[i]; #else memcpy(&(d->X_base[d->n_X * d->n_list]), p->X, d->n_X * sizeof(double)); #endif } /* * adjust list and X pointer to this copy: */ d->list[d->n_list] = &(d->P_base[d->n_list]); if (intercept_only(d)) d->list[d->n_list]->X = d->X_base; else d->list[d->n_list]->X = &(d->X_base[d->n_X * d->n_list]); SET_INDEX(d->list[d->n_list], d->n_list); qtree_push_point(d, d->list[d->n_list]); grid_push_point(d, d->list[d->n_list], 0); /* * this will be ignored during read_gstat_data(), the tree structure will * be filled only during the first call to qtree_quick_select(). * Later on, it does have effect if simulated points are pushed. */ d->n_list++; return; } void pop_point(DATA *d, int list_nr) /* * removes DPOINT list_nr, and makes it point to the last DPOINT * also changes d->n_list */ { if (list_nr >= d->n_list) { message("pop_point: list_nr >= n_list: %d %d\n", list_nr, d->n_list); ErrMsg(ER_NULL, "pop_point():"); } qtree_pop_point(d->list[list_nr], d); if (d->P_base == NULL) { /* * free this one: */ if (d->n_X > 0 && !(intercept_only(d))) efree(d->list[list_nr]->X); efree(d->list[list_nr]); } /* * change the last pointer to this: */ if (list_nr != d->n_list - 1) /* we didn't pop the last: */ d->list[list_nr] = d->list[d->n_list - 1]; d->list[d->n_list - 1] = NULL; d->n_list--; } static double point_norm_1D(const DPOINT *p) { /* calculate norm of vector (p->x) */ return fabs(p->x); } static double point_norm_2D(const DPOINT *p) { /* calculate norm of vector (p->x, p->y, p->z) */ return sqrt(p->x * p->x + p->y * p->y); } static double point_norm_3D(const DPOINT *p) { /* calculate norm of vector (p->x, p->y, p->z) */ return sqrt(p->x * p->x + p->y * p->y + p->z * p->z); } static double pp_norm_1D(const DPOINT *a, const DPOINT *b) { /* calculate 2-norm of vector (p->x) */ double dx; dx = a->x - b->x; return dx * dx; } static double pp_norm_2D(const DPOINT *a, const DPOINT *b) { /* calculate 2-norm of vector (p->x, p->y) */ double dx, dy; dx = a->x - b->x; dy = a->y - b->y; return dx * dx + dy * dy; } static double pp_norm_3D(const DPOINT *a, const DPOINT *b) { /* calculate 2-norm of vector (p->x, p->y, p->z) */ double dx, dy, dz; dx = a->x - b->x; dy = a->y - b->y; dz = a->z - b->z; return dx * dx + dy * dy + dz * dz; } static double point_norm_gc(const DPOINT *p) { /* calculate norm of vector (p->x, p->y, p->z) */ ErrMsg(ER_IMPOSVAL, "long/lat: this function should never be called?"); return gstat_gcdist(p->x, 0.0, p->y, 0.0); } double pp_norm_gc(const DPOINT *a, const DPOINT *b) { return gstat_gcdist(a->x, b->x, a->y, b->y); /* dist */ } static double pp_norm_gc2(const DPOINT *a, const DPOINT *b) { return pow(gstat_gcdist(a->x, b->x, a->y, b->y), 2.0); /* squared dist */ } static double pb_norm_gc2(const DPOINT *where, BBOX bbox) { /* ErrMsg(ER_IMPOSVAL, "great circle distances cannot be combined with quadtree"); */ return 0.0; /* always inside, no quadtree */ } int coordinates_are_equal(const DATA *a, const DATA *b) { int i, equal = 1 /* try to disprove equality */; if (a->n_list != b->n_list) return 0; i = 0; while (equal && i < a->n_list) { equal = ((a->list[i]->x == b->list[i]->x) && (a->list[i]->y == b->list[i]->y) && (a->list[i]->z == b->list[i]->z)); i++; } return equal; } int push_to_merge_table(DATA *d, int to_var, int col_this_X, int col_other_X) { int i; DATA **data; data = get_gstat_data(); if (to_var >= d->id) { /* should not occur by construction */ pr_warning("use push_to_merge_table only backwards (%d >= %d)", to_var, d->id); return 1; } if (col_this_X >= d->n_X || col_other_X >= data[to_var]->n_X) { pr_warning("merge error: variable out of range"); return 1; } if (d->beta || data[to_var]->beta) { pr_warning("cannot merge to or from fixed (known) parameters"); return 1; } for (i = 0; i < d->n_merge; i++) { if (col_this_X == d->mtbl[i].col_this_X) { pr_warning("merge error: cannot merge column twice"); return 1; } } d->n_merge++; d->mtbl = (MERGE_TABLE *) erealloc(d->mtbl, d->n_merge * sizeof (MERGE_TABLE)); d->mtbl[d->n_merge - 1].to_var = to_var; d->mtbl[d->n_merge - 1].col_this_X = col_this_X; d->mtbl[d->n_merge - 1].col_other_X = col_other_X; return 0; } DATA_GRIDMAP *gsetup_gridmap(double x_ul, double y_ul, double cellsizex, double cellsizey, unsigned int rows, unsigned int cols) { DATA_GRIDMAP *t; int i, j; t = (DATA_GRIDMAP *) emalloc(sizeof(DATA_GRIDMAP)); t->x_ul = x_ul; t->y_ul = y_ul; t->cellsizex = cellsizex; t->cellsizey = cellsizey; t->rows = rows; t->cols = cols; t->dpt = (DPOINT ***) emalloc(t->rows * sizeof(DPOINT **)); t->grid_base = (DPOINT **) emalloc(t->rows * t->cols * sizeof(DPOINT *)); for (i = 0; i < t->rows; i++) t->dpt[i] = &(t->grid_base[i * t->cols]); for (i = 0; i < t->rows; i++) for (j = 0; j < t->cols; j++) t->dpt[i][j] = NULL; return t; } void free_data_gridmap(DATA_GRIDMAP *t) { efree(t->grid_base); efree(t->dpt); efree(t); } static void grid_push_point(DATA *d, DPOINT *p, int adjust_to_gridcentres) { int row, col; if (d->grid) { row = floor((d->grid->y_ul - p->y)/d->grid->cellsizey); col = floor((p->x - d->grid->x_ul)/d->grid->cellsizex); row = MAX(0, row); row = MIN(row, d->grid->rows - 1); col = MAX(0, col); col = MIN(col, d->grid->cols - 1); d->grid->dpt[row][col] = p; if (adjust_to_gridcentres) { p->x = d->grid->x_ul + (col + 0.5) * d->grid->cellsizex; p->y = d->grid->y_ul - (row + 0.5) * d->grid->cellsizey; } } return; } void datagrid_rebuild(DATA *d, int adjust_to_gridcentres) { int i; if (d->grid) for (i = 0; i < d->n_list; i++) grid_push_point(d, d->list[i], adjust_to_gridcentres); return; } double data_block_diagonal(DATA *data) { DPOINT a, b; a.x = data->maxX; b.x = data->minX; if (data->mode & Y_BIT_SET) { a.y = data->maxY; b.y = data->minY; } else { a.y = 0.0; b.y = 0.0; } if (data->mode & Z_BIT_SET) { a.z = data->maxZ; b.z = data->minZ; } else { a.z = 0.0; b.z = 0.0; } return sqrt(data->pp_norm2(&a, &b)); } D_VECTOR *push_d_vector(double d, D_VECTOR *v) { if (v == NULL) { v = (D_VECTOR *) emalloc(sizeof(D_VECTOR)); v->size = v->max_size = 0; v->val = NULL; } v->size++; if (v->size > v->max_size) { /* (re)allocate v->val */ if (v->val == NULL) v->val = (double *) emalloc(v->size * sizeof(double)); else v->val = (double *) erealloc(v->val, v->size * sizeof(double)); v->max_size = v->size; } v->val[v->size - 1] = d; return v; } void free_d_vector(D_VECTOR *v) { if (v != NULL) { if (v->size > 0) efree(v->val); efree(v); } } int intercept_only(const DATA *d) { assert(d != NULL); return (d->n_X == 1 && d->colX[0] == 0); } double v_mu(double mu) { return mu; } double v_mu2(double mu) { return mu * mu; } double v_mu3(double mu) { return mu * mu * mu; } double v_bin(double mu) { return (mu * (1.0 - mu)); } double v_identity(double mu) { return 1.0; } gstat/src/mapio.h0000644000176200001440000001133113777370515013457 0ustar liggesusers#ifndef MAPIO_H /* avoid multiple inclusion */ #define MAPIO_H #ifdef HAVE_LIBGDAL # include "gdal.h" #endif /*! \file mapio.h \brief functions for reading and writing grid map in several formats */ /*! type of grid map format */ typedef enum { MT_UNKNOWN = 0, MT_CSF, /*!< PCRaster format (binary), API in csf directory */ MT_GDAL, /*!< GDAL format */ MT_ARCGRID, /*!< ArcInfo gridfile, gridascii (ascii) or gridfloat (binary) */ MT_IDRISI, /*!< Idrisi 32image file, ascii or binary */ MT_GNUPLOT, /*!< binary gnuplot 2d matrix format (cannot handle MV's) */ MT_T2, /*!< MIKE SHE ``T2'' 2d grid map format (www.dhi.dk) */ MT_ERMAPPER, /*!< ER-Mapper V5.0+ dataset with a single image channel */ MT_GRASS, /*!< Grass raster format, uses grass' gis library */ MT_GMT, /*!< GMT Grid format, uses NetCDF library */ MT_SURFER, /*!< Surfer DSAA (ascii grid) format */ MT_GSLIB /*!< GSLIB grid format (only a 2D subset) */ } MAPTYPE; /*! ER-Mapper celltypes used for read/write_binary */ typedef enum { CT_NONE = 0, CT_UNKNOWN = 1, CT_UINT8 = 2, CT_UINT16 = 3, CT_UINT32 = 4, CT_INT8 = 5, CT_INT16 = 6, CT_INT32 = 7, CT_IEEE4 = 8, CT_IEEE8 = 9 } CellType; #define UINT8 unsigned char #define UINT16 unsigned short int #define UINT32 unsigned long int #define INT8 char #define INT16 short int #define INT32 long int #define IEEE4 float #define IEEE8 double typedef enum { READ_ONLY = 0, WRITE_ONLY = 1 } MAP_READ_STATUS; /*! structure to hold grid map information */ typedef struct gridmap { MAPTYPE type; /*!< type of grid map */ MAP_READ_STATUS status; /*! READ_ONLY or WRITE_ONLY */ const char *filename; /*!< name (or base name) of grid map */ char *history, /*!< only used for CSF maps */ *description; /*!< only used for some maps */ unsigned int rows, /*!< number of rows in map */ cols, /*!< number of colums in map */ base_size, /*!< size of malloced area (cells), in case of blocked allocation */ current_row, /*!< current row, if reading/writing is row-wise */ *first_time_row; /*!< have we been at this row before? */ CellType celltype; /*!< cell type */ int is_binary, /*!< is this a binary map format */ swap_buf; /*!< swap contents of base buffer? */ double x_ul, /*!< x-coordinate upper left corner of map area */ y_ul, /*!< y-coordinate of upper left corner of map area */ cellsizex, /*!< size of grid cells in x-direction */ cellsizey; /*!< size of grid cells in y-direction */ float cellmin, /*!< minimum value of grid map */ cellmax, /*!< maximum value of grid map */ misval; /*!< missing value flag (if present) */ float **grid, /*!< 2d matrix holding the values (pointer array) */ *base; /*!< base pointer to malloc'ed or mmap'ed area */ void *CSF_MAP; /*!< cast to MAP * */ #ifdef HAVE_LIBGDAL GDALDatasetH hDataset; GDALDriverH hDriver; double *GeoTransform; #endif struct gridmap * (*write)(struct gridmap *m); /*!< write & close a map */ void (*read_row)(struct gridmap *m, float *buf, unsigned int row); void (*write_row)(struct gridmap *m, float *buf, unsigned int row); /* see mapio.c remark around #define CSF_ROWWISE for the last two */ } GRIDMAP; #define SQUARECELLSIZE(map) ((map->cellsizex != map->cellsizey ? \ ErrMsg(ER_IMPOSVAL, "cannot deal with non-square cells"), 0.0 : \ map->cellsizex)) GRIDMAP *map_read(GRIDMAP *m); int map_cell_is_mv(GRIDMAP *m, unsigned int row, unsigned int col); float map_get_cell(GRIDMAP *m, unsigned int row, unsigned int col); int map_put_cell(GRIDMAP *m, unsigned int row, unsigned int col, float value); int map_xy2rowcol(GRIDMAP *m, double x, double y, unsigned int *row, unsigned int *col); int map_rowcol2xy(GRIDMAP *m, unsigned int row, unsigned int col, double *x, double *y); GRIDMAP *map_dup(const char *fname, GRIDMAP *m); GRIDMAP *new_map(MAP_READ_STATUS status); void map_free(GRIDMAP *m); GRIDMAP *map_switch_type(GRIDMAP *in, MAPTYPE type); void map_name_nr(GRIDMAP *mask, const char *base, char *name, int nr, int max); int map_equal(GRIDMAP *a, GRIDMAP *b); #endif gstat/src/userio.c0000644000176200001440000000620514127262566013653 0ustar liggesusers/* * userio.c: i/o routines for error, warning, log and progress messages */ #include #include "R.h" #include "defs.h" #include "debug.h" #include "utils.h" #include "s.h" #include "userio.h" static const char *error_messages[MAX_ERRNO+1] = { /* 0 */ "%s", /* 1 */ "bug in function `%s'", /* 2 */ "variable not set: %s", /* 3 */ "variable outside valid range: %s", /* 4 */ "value not allowed for: %s", /* 5 */ "no filename set %s", /* 6 */ "write failed on file `%s'", /* 7 */ "read failed on file `%s'", /* 9 */ "cannot read real value from `%s'", /* 9 */ "cannot read integer from `%s'", /* 10 */ "syntax error: %s", /* 11 */ "illegal option or missing argument on `%s'", /* 12 */ "domain (math) error on `%s'", /* 13 */ "out of dynamic memory (try local kriging?)", /* 14 */ "i/o error: %s", /* 15 */ "no command file%s", /* 16 */ "%s user interface not compiled in this version", /* 17 */ "writing to pipe `%s' failed", /* 18 */ "reading from pipe `%s' failed", /* 19 */ "function call prevented by secure mode%s" }; /* * error handling function -- print message and error to string, and * call error message handler. */ void gstat_error(char *fname, int line, enum Gstat_errno err_nr, const char *msg) { assert(err_nr <= MAX_ERRNO); if (DEBUG_DUMP || err_nr == ER_NULL) /* print file&line */ Rprintf("(%s, line %d)", fname, line); if (err_nr == ER_NULL) error("NULL error: this indicates a bug, please consider reporting this\n"); if (msg == NULL) error(" message: indicating a software bug, please report\n"); else error(error_messages[err_nr], msg); return; } /* message() calls for messages preceding a call to ErrMsg() */ void message(char *fmt, ...) { va_list args; /* char *buf = NULL; */ char w[ERROR_BUFFER_SIZE]; w[0] = '\0'; va_start(args, fmt); vsnprintf(w, ERROR_BUFFER_SIZE, fmt, args); va_end(args); Rprintf("%s", w); } /* print a warning message to string, and call warning message handler */ void pr_warning(char *fmt, ...) { va_list args; char w[ERROR_BUFFER_SIZE]; if (DEBUG_SILENT) return; w[0] = '\0'; va_start(args, fmt); vsnprintf(w, ERROR_BUFFER_SIZE, fmt, args); va_end(args); warning("%s\n", w); } void printlog(const char *fmt, ...) { va_list args; char w[ERROR_BUFFER_SIZE]; if (DEBUG_SILENT) return; w[0] = '\0'; va_start(args, fmt); vsnprintf(w, ERROR_BUFFER_SIZE, fmt, args); va_end(args); Rprintf("%s", w); } void print_progress(unsigned int current, unsigned int total) { static int perc_last = -1, sec_last = -1; int perc, sec; static time_t start; R_CheckUserInterrupt(); /* allow for user interrupt */ if (total <= 0 || DEBUG_SILENT || ! do_print_progress) return; if (sec_last == -1) { start = time(NULL); sec_last = 0; } perc = floor(100.0 * current / total); if (perc != perc_last) { /* another percentage -> calculate time: */ if (current == total) { /* 100% done, reset: */ Rprintf("\r%3d%% done\n", 100); perc_last = sec_last = -1; } else { sec = difftime(time(NULL), start); if (sec != sec_last) { /* another second -- don't print too often */ Rprintf("\r%3d%% done", perc); perc_last = perc; sec_last = sec; } } } } gstat/src/getest.c0000644000176200001440000004127113777370515013646 0ustar liggesusers/* * getest.c: choose the predicion function at one prediction location */ #include #include #include #include #include #include "defs.h" #include "data.h" #include "utils.h" #include "mapio.h" #include "userio.h" #include "debug.h" #include "vario.h" #include "sem.h" #include "fit.h" #include "glvars.h" #include "mtrx.h" #include "lm.h" #include "gls.h" #include "sim.h" #include "msim.h" #include "block.h" #include "getest.h" static void est_quantile_div(DATA *data, double *est, int div); static void est_skew_kurt(DATA *data, double *est); static double inverse_dist(DATA *data, DPOINT *where, double idPow); static void save_variogram_parameters(VARIOGRAM *v); static void reset_variogram_parameters(VARIOGRAM *v); static double sample_mean(double *list, int n); static double sample_var(double *list, double mean, int n); static double sample_std(double *list, double mean, int n); static double est_quant(double *list, double p, int n); static int CDECL d_cmp(const double *a, const double *b); static double *vgm_pars = NULL; void get_est(DATA **data, METHOD method, DPOINT *where, double *est) { /* * given all data[i]->sel, get_est returns one or more values to *est, * according to the method of calculation set in *method * sel must be not NULL, where contains the location of the estimate * PRE: data, where, est; * USES: several estimation routines. */ DPOINT *block = NULL; VARIOGRAM *v; int i, j, n_vars, n_sel, *is_pt; double *X_ori = NULL, *local_sim; enum GLS_WHAT gls_mode = GLS_BLUP; const double *sim = NULL; /* return value of cond_sim() */ for (i = 0; i < get_n_outputs(); i++) set_mv_double(&est[i]); block = get_block_p(); if (get_mode() == MODE_NSP) ErrMsg(ER_IMPOSVAL, "Getest(): mode not specified"); if (block->x > 0.0 || block->y > 0.0 || block->z > 0.0 || get_data_area()) SET_BLOCK(where); else SET_POINT(where); n_vars = get_n_vars(); if (get_mode() == STRATIFY && (where->u.stratum < 0 || where->u.stratum >= n_vars)) return; local_sim = (double *) emalloc(n_vars * sizeof(double)); is_pt = (int *) emalloc(n_vars * sizeof(int)); for (i = 0; i < n_vars; i++) { set_mv_double(&(local_sim[i])); is_pt[i] = 0; } if (DEBUG_COV) { printlog("we're at location X: %g Y: %g Z: %g\n", where->x, where->y, where->z); if (IS_BLOCK(where)) { if (get_data_area()) printlog("block set in area()\n"); else printlog("block size: dx: %g dy: %g dz: %g\n", block->x, block->y, block->z); } else printlog("zero block size\n"); if (get_mode() == STRATIFY) printlog("stratum: %d\n", where->u.stratum); } switch (method) { case DIV: /* BREAKTHROUGH */ case MED: if (get_mode() == STRATIFY) est_quantile_div(data[where->u.stratum], est, method == DIV); else for (i = 0; i < n_vars; i++) est_quantile_div(data[i], &(est[2*i]), method == DIV); break; case SKEW: if (get_mode() == STRATIFY) est_skew_kurt(data[where->u.stratum], est); else for (i = 0; i < n_vars; i++) est_skew_kurt(data[i], &(est[2*i])); break; case IDW: if (gl_idp < 0.0) ErrMsg(ER_RANGE, "idp must be non-negative"); if (get_mode() == STRATIFY) { if (data[where->u.stratum]->n_sel > 0) est[0] = inverse_dist(data[where->u.stratum], where, gl_idp); } else { for (i = 0; i < n_vars; i++) if (data[i]->n_sel > 0) est[2 * i] = inverse_dist(data[i], where, gl_idp); } break; case LSLM: if (n_variograms_set()) { switch(get_mode()) { case SIMPLE: X_ori = where->X; /* remember... */ for (i = 0; i < n_vars; i++) { if (data[i]->n_sel > 0) gls(&data[i], 1, GLS_BLUE, where, &(est[2 * i])); where->X += data[i]->n_X; } where->X = X_ori; /* and put back */ break; case STRATIFY: X_ori = where->X; /* remember... */ for (i = 0; i < where->u.stratum; i++) where->X += data[i]->n_X; if (data[where->u.stratum]->n_sel > 0) { where->X += where->u.stratum; /* strictly unnecessary */ gls(&data[where->u.stratum], 1, GLS_BLUE, where, est); } where->X = X_ori; /* and put back */ break; case MULTIVARIABLE: gls(data, n_vars, GLS_BLUE, where, est); break; default: ErrMsg(ER_IMPOSVAL, "Getest(): wrong mode"); break; } } else { switch(get_mode()) { case STRATIFY: X_ori = where->X; /* remember... */ for (i = 0; i < where->u.stratum; i++) where->X += data[i]->n_X; if (data[where->u.stratum]->n_sel > 0) pred_lm(&data[where->u.stratum], 1, where, est); where->X = X_ori; /* and put back */ break; case MULTIVARIABLE: pred_lm(data, n_vars, where, est); break; case SIMPLE: X_ori = where->X; /* remember... */ for (i = 0; i < n_vars; i++) { if (data[i]->n_sel > 0) { pred_lm(&data[i], 1, where, &(est[2*i])); where->X += data[i]->n_X; } } where->X = X_ori; /* and put back */ break; default: ErrMsg(ER_IMPOSVAL, "Getest(): wrong mode"); break; } } /* else */ break; case SKR: /* BREAK THROUGH (SK handled in gls()) */ case OKR: /* BREAK THROUGH: (OK is special case of UK) */ case UKR: if (method == SKR) gls_mode = GLS_BLP; else gls_mode = GLS_BLUP; switch (get_mode()) { case SIMPLE: X_ori = where->X; /* remember... */ for (i = 0; i < n_vars; i++) { gls(&data[i], 1, gls_mode, where, &(est[2 * i])); where->X += data[i]->n_X; } where->X = X_ori; /* and put back */ break; case STRATIFY: X_ori = where->X; /* remember... */ for (i = 0; i < where->u.stratum; i++) where->X += data[i]->n_X; gls(&data[where->u.stratum], 1, gls_mode, where, est); where->X = X_ori; /* and put back */ break; case MULTIVARIABLE: gls(data, n_vars, gls_mode, where, est); break; default: ErrMsg(ER_IMPOSVAL, "Getest(): wrong mode"); break; } if (gl_order) /* order relation violations: */ correct_orv(est, n_vars, gl_order); break; case GSI: /* BREAK TRHOUGH: */ case ISI: switch (get_mode()) { case SIMPLE: /* estimates go to est[0+1],est[2+3],... */ X_ori = where->X; /* remember... */ for (i = 0; i < gl_nsim; i++) { restore_data_sel(data, i, n_vars); set_beta(data, i, n_vars, method); for (j = 0; j < n_vars; j++) { /* estimate or update: */ if (i == 0) /* estimate */ gls(&data[j], 1, data[j]->n_sel < gl_n_uk ? GLS_BLP : GLS_BLUP, where, &(est[2*j])); else /* update */ gls(&data[j], 1, UPDATE, where, &(est[2*j])); /* new simulation: */ if (gl_order <= 1) { sim = cond_sim(&(est[2*j]), 1, method, &(is_pt[j]), gl_order); /* put data from simulation i; */ local_sim[j] = sim[0]; } where->X += data[j]->n_X; } where->X = X_ori; /* reset */ if (gl_order > 1) { /* 2,3 if pdf, 4 if cdf: */ sim = cond_sim(est, n_vars, method, is_pt, gl_order); for (j = 0; j < n_vars; j++) local_sim[j] = sim[j]; } save_sim(data, where, i, n_vars, local_sim, is_pt); } X_ori = where->X; /* remember... */ for (i = 0; i < n_vars; i++) { if (! is_pt[i]) { where->attr = est[2 * i] = local_sim[i]; /* last simulation */ push_point(data[i], where); } else data[i]->nsim_at_data++; where->X += data[i]->n_X; } where->X = X_ori; /* reset */ break; case STRATIFY: /* estimate goes to est[0] and est[1] */ X_ori = where->X; /* remember... */ for (i = 0; i < where->u.stratum; i++) where->X += data[i]->n_X; for (i = 0; i < gl_nsim; i++) { /* load data from simulation i; */ restore_data_sel(&data[where->u.stratum], i, 0); set_beta(&data[where->u.stratum], i, 0, method); if (i == 0) /* estimate: */ gls(&data[where->u.stratum], 1, data[where->u.stratum]->n_sel < gl_n_uk ? GLS_BLP : GLS_BLUP, where, est); else /* update */ gls(&data[where->u.stratum], 1, UPDATE, where, est); sim = cond_sim(est, 1, method, is_pt, gl_order); /* save data from simulation i; */ save_sim_strat(data[where->u.stratum], where, i, sim[0], is_pt[0]); } /* store & push */ if (! is_pt[0]) { where->attr = est[0] = sim[0]; /* last simulation */ push_point(data[where->u.stratum], where); } else data[where->u.stratum]->nsim_at_data++; where->X = X_ori; /* and put back */ break; case MULTIVARIABLE: for (i = 0, n_sel = 0; i < n_vars; i++) n_sel += data[i]->n_sel; if (n_sel < gl_n_uk) gls_mode = GLS_BLP; else gls_mode = GLS_BLUP; for (i = 0; i < gl_nsim; i++) { /* load data from simulation i; */ restore_data_sel(data, i, n_vars); set_beta(data, i, n_vars, method); /* estimate or update: */ if (i == 0) gls(data, n_vars, gls_mode, where, est); else gls(data, n_vars, UPDATE, where, est); /* new simulation: */ sim = cond_sim(est, n_vars, method, is_pt, gl_order); /* put data from simulation i; */ save_sim(data, where, i, n_vars, sim, is_pt); } X_ori = where->X; /* remember... */ for (i = 0; i < n_vars; i++) { if (! is_pt[i]) { est[2 * i] = where->attr = sim[i]; /* last simulation */ push_point(data[i], where); } else data[i]->nsim_at_data++; where->X += data[i]->n_X; } where->X = X_ori; /* and put back */ break; default: ErrMsg(ER_IMPOSVAL, "Getest(): wrong mode"); break; } /* switch (get_mode()) */ for (i = 0; i < n_vars; i++) set_mv_double(&(est[2 * i + 1])); for (i = 2 * n_vars; i < get_n_outputs(); i++) set_mv_double(&(est[i])); /* print_sim(); */ break; case NRS: if (get_mode() != STRATIFY) { for (i = 0; i < n_vars; i++) { est[2 * i] = (double) data[i]->n_sel; est[2 * i + 1] = (double) data[i]->oct_filled; } } else { est[0] = (double) data[where->u.stratum]->n_sel; est[1] = (double) data[where->u.stratum]->oct_filled; } break; case SPREAD: if (get_mode() == STRATIFY) { if (data[where->u.stratum]->n_sel > 0) { if (data[where->u.stratum]->what_is_u != U_ISDIST) ErrMsg(ER_IMPOSVAL, "getest() needs distances"); n_sel = data[where->u.stratum]->n_sel; est[0] = sqrt(data[where->u.stratum]->sel[0]->u.dist2); est[1] = sqrt(data[where->u.stratum]->sel[n_sel - 1]->u.dist2); } } else { for (i = 0; i < n_vars; i++) { if (data[i]->n_sel > 0) { if (data[i]->what_is_u != U_ISDIST) ErrMsg(ER_IMPOSVAL, "getest() needs distances"); n_sel = data[i]->n_sel; est[2 * i] = sqrt(data[i]->sel[0]->u.dist2); est[2 * i + 1] = sqrt(data[i]->sel[n_sel - 1]->u.dist2); } } } break; case LSEM: v = get_vgm(LTI(0,0)); assert(v); v->id1 = v->id2 = v->id = 0; v->ev->evt = SEMIVARIOGRAM; if (data[0]->is_residual == 0) data[0]->is_residual = 1; /* !! */ v->ev->recalc = 1; calc_variogram(v, NULL); if (gl_fit) { v->ev->refit = 1; v->ev->fit = gl_fit; save_variogram_parameters(v); fit_variogram(v); /* write back locally fitted variogram model parameters: */ for (i = j = 0; i < MIN(get_n_vars(), v->n_models); i++) { est[2 * i + 0] = v->part[i].sill; est[2 * i + 1] = v->part[i].range[0]; j += 2; } if (j < get_n_vars()) est[j] = 1.0 * v->fit_is_singular; reset_variogram_parameters(v); update_variogram(v); /* not sure if this is needed */ } else { /* write back locally estimated sample variogram values: */ for (i = 0; i < MIN(get_n_vars(), v->ev->n_est); i++) { est[2 * i + 0] = v->ev->gamma[i]; est[2 * i + 1] = 1.0 * v->ev->nh[i]; } } break; case NSP: /* FALLTHROUGH: */ default: ErrMsg(ER_IMPOSVAL, "getest(): method not specified"); } /* switch */ efree(local_sim); efree(is_pt); return; } static void est_quantile_div(DATA *data, double *est, int div) { static double *list = NULL; static int i, size = 0; double mod = -9999.0; int n, run, longest_run = 0; if (data->n_sel > size) list = (double *) erealloc(list, (size = data->n_sel) * sizeof(double)); for (i = 0; i < data->n_sel; i++) list[i] = data->sel[i]->attr; qsort(list, (size_t) data->n_sel, sizeof(double), (int CDECL (*)(const void *, const void *)) d_cmp); if (div) { /* get diversity and modus in sel: */ n = data->n_sel; for (i = 0; i < data->n_sel - 2; i += run) { run = 1; while (i + run < data->n_sel && list[i] == list[i + run]) { run++; n--; } if (run > longest_run) { longest_run = run; mod = list[i]; } } est[0] = 1.0 * n; est[1] = mod; } else { if (data->n_sel < 2) return; if (gl_quantile == 0.5) est[0] = est[1] = est_quant(list, gl_quantile, data->n_sel); else { est[0] = est_quant(list, gl_quantile, data->n_sel); est[1] = est_quant(list, 1.0 - gl_quantile, data->n_sel); } } return; } static void est_skew_kurt(DATA *data, double *est) { static double *list = NULL; double mean, std, skewness = 0.0, kurtosis = 0.0, d; static int i, size = 0; if (data->n_sel <= 1) /* need at least 2 for variance */ return; if (data->n_sel > size) list = (double *) erealloc(list, (size = data->n_sel) * sizeof(double)); for (i = 0; i < data->n_sel; i++) list[i] = data->sel[i]->attr; mean = sample_mean(list, data->n_sel); std = sample_std(list, mean, data->n_sel); for (i = 0; i < data->n_sel; i++) { d = (data->sel[i]->attr - mean)/std; skewness += pow(d, 3.0); kurtosis += pow(d, 4.0); } est[0] = skewness/data->n_sel; est[1] = kurtosis/data->n_sel; } static double inverse_dist(DATA *data, DPOINT *where, double idPow) { int i, j; double sumweights, sumvals, value, weight, dist2; static DATA *blockd = NULL; if (data->n_sel <= 0) ErrMsg(ER_IMPOSVAL, "zero neighbourhood in inverse_dist()"); if (data->n_sel == 1) return data->sel[0]->attr; blockd = block_discr(blockd, get_block_p(), where); for (i = 0, value = 0.0; i < blockd->n_list; i++) { for (j = 0, sumweights = sumvals = 0.0; j < data->n_sel; j++) { dist2 = data->pp_norm2(data->sel[j], blockd->list[i]); if (dist2 == 0.0) { sumvals = data->sel[j]->attr; sumweights = 1.0; j = data->n_sel; /* break j loop */ } else { if (idPow == 2.0) weight = 1.0 / dist2; else weight = pow(dist2, -0.5 * idPow); sumweights += weight; sumvals += weight * data->sel[j]->attr; } } value += blockd->list[i]->u.weight * sumvals/sumweights; } return value; } void save_variogram_parameters(VARIOGRAM *v) { int i; if (vgm_pars == NULL) vgm_pars = (double *) emalloc(3 * v->n_models * sizeof(double)); for (i = 0; i < v->n_models; i++) { vgm_pars[3 * i + 0] = v->part[i].sill; vgm_pars[3 * i + 1] = v->part[i].range[0]; vgm_pars[3 * i + 2] = v->part[i].range[1]; } } void reset_variogram_parameters(VARIOGRAM *v) { int i; for (i = 0; i < v->n_models; i++) { v->part[i].sill = vgm_pars[3 * i + 0]; v->part[i].range[0] = vgm_pars[3 * i + 1]; v->part[i].range[1] = vgm_pars[3 * i + 2]; } v->fit_is_singular = 0; } static double sample_mean(double *list, int n) { int i; double mn = 0.0; if (list == NULL) ErrMsg(ER_NULL, "sample_mean()"); if (n == 0) ErrMsg(ER_RANGE, "sample_mean(): no values"); for (i = 0; i < n; i++) mn += list[i]; return mn/(1.0 * n); } static double sample_var(double *list, double mean, int n) { int i; double var = 0.0; if (list == NULL) ErrMsg(ER_NULL, "sample_var()"); if (n <= 1 || list == NULL) ErrMsg(ER_RANGE, "sample_var(): <= 1 values"); for (i = 0; i < n; i++) var += SQR(list[i] - mean); return (var / (n - 1.0)); } static double sample_std(double *list, double mean, int n) { return sqrt(sample_var(list, mean, n)); } static double est_quant(double *list, double p, int n) { /* * function returns the value of the p-th quantile * of the ordered list *list, row exists from list[0]..list[length-1], * p is in [0..1]; * a missing value is generated when the quantile lies not within * the valid data range, and is undetermined therefore */ double order, where; int below, above; if (n < 2) ErrMsg(ER_RANGE, "est_quant(): < 2 obs."); if (p < 0.0 || p > 1.0) ErrMsg(ER_RANGE, "can't calculate quantile outside [0,1]"); order = p * (n - 1); /* order = n * (p * n)/(n + 1); */ below = (int) floor(order); /* the index below order */ if (below < 0) return list[0]; above = below + 1; /* the index above order */ if (above >= n) return list[n - 1]; where = order - below; return (1 - where) * list[below] + where * list[above]; } int CDECL d_cmp(const double *a, const double *b) { if (*a < *b) return -1; if (*a > *b) return 1; return 0; } gstat/src/sim.c0000644000176200001440000001631014232776373013136 0ustar liggesusers/* * sim.c: functions, special to (un)conditional simulation */ #include #include #include "mtrx.h" #include "defs.h" #include "debug.h" #include "glvars.h" /* gl_nsim */ #include "userio.h" #include "data.h" #include "gls.h" #include "utils.h" #include "lm.h" #include "s.h" /* r_uniform(), r_normal() */ #include "sim.h" static void simulate_mvn(const double *est, VEC *result, const int *is_datum); static void simulate_uniform(double *est, VEC *result, int orc); static unsigned int n_orvc = 0, n_total = 0; const double *cond_sim(double *est, int dim, METHOD m, int *is_datum, int orc) { /* * distributions come as { est1, var1, est2, var2,..., cov1-1,.. } * and return as { sim-1, sim-2, sim-3, ..., sim-dim } */ int i; static VEC *result = VNULL; static double *sim = NULL; static int max_dim = -1; assert(dim > 0); assert(est != NULL); assert(dim >= 1); assert(is_simulation(m)); assert(est != NULL); assert(is_datum != NULL); if (dim > max_dim) { sim = (double *) erealloc(sim, dim * sizeof(double)); max_dim = dim; } result = v_resize(result, dim); for (i = 0; i < dim; i++) is_datum[i] = (fabs(est[2 * i + 1]) < gl_zero); /* `zero' variance */ if (m == GSI) /* generate zero mean correlated noise: */ simulate_mvn(est, result, is_datum); else { /* m == IS */ correct_orv(est, dim, orc); /* affects est */ simulate_uniform(est, result, orc); } for (i = 0; i < dim; i++) sim[i] = result->ve[i]; return sim; } static void simulate_mvn(const double *est, VEC *result, const int *is_datum) { static MAT *M = MNULL; static VEC *ind = VNULL, *sim = VNULL; static PERM *p = PNULL; int i, j, info; volatile int dim; p = px_resize(p, result->dim); for (i = dim = 0; i < result->dim; i++) { if (is_datum[i] == 0) /* non-``zero'' variance -- do simulate */ p->pe[dim++] = i; /* index of simulation point */ } p->size = dim; /* * now dim is the number of pos. variances, * p points their position */ if (dim > 0) { /* there is something to be simulated */ M = m_resize(M, dim, dim); for (i = 0; i < dim; i++) { ME(M, i, i) = est[2 * p->pe[i] + 1]; /* variances on diagonal */ for (j = 0; j < i; j++) /* off-diagonal: covariances */ ME(M, j, i) = ME(M, i, j) = est[2 * result->dim + LTI2(p->pe[j],p->pe[i])]; } if (DEBUG_COV) { printlog("# simulation covariance matrix:\n"); m_logoutput(M); } /* decompose M: */ M = CHfactor(M, PNULL, &info); /* LT is zero */ if (info != 0) pr_warning("singular simulation covariance matrix"); if (DEBUG_COV) { printlog("# decomposed error covariance matrix, with zero LT:\n"); m_logoutput(M); } /* make ind a iid N(0,1) vector */ ind = v_resize(ind, dim); for (i = 0; i < dim; i++) ind->ve[i] = r_normal(); /* generate N(0,1) independent samples */ /* make MVN */ sim = v_resize(sim, dim); sim = vm_mlt(M, ind, sim); /* create zero mean correlated noise */ if (DEBUG_COV) { printlog("# correlated noise vector:\n"); v_logoutput(sim); } } /* fill result vector: */ for (i = j = 0; i < result->dim; i++) { if (j < dim && i == p->pe[j]) { /* simulated */ result->ve[i] = est[2 * i] + sim->ve[j]; j++; } else result->ve[i] = est[2 * i]; } if (DEBUG_COV) { printlog("\n# simulated values:\n"); if (is_datum != NULL) { for (i = 0; i < result->dim; i++) { printlog("%g # (%s)\n", result->ve[i], is_datum[i] ? "datum point" : "simulated"); } } else { for (i = 0; i < result->dim; i++) printlog(" %g", result->ve[i]); printlog("\n"); } } } static void simulate_uniform(double *est, VEC *result, int orc) { /* * depending on gl_is_pdf, assume indicative (1) or cumulative (0) * densitiy function in est; * sum of all estimates should equal about 1, which is not * the case when cumulative, when last estimate should be * close to 1. */ int i, hit; double cdf, rn; static double *pdf = NULL; if (result->dim == 1) { result->ve[0] = 1.0 * (r_uniform() < est[0]); if (DEBUG_ORDER && (est[0] < 0.0 || est[0] > 1.0)) pr_warning("order relation violation: P %g not in [0,1]\n", est[0]); return; } if (pdf == NULL) pdf = (double *) emalloc(result->dim * sizeof(double)); for (i = 0; i < result->dim; i++) pdf[i] = est[2 * i]; /* local copy */ if (orc == 4) /* cumulative indicators: make raw pdf */ for (i = 1; i < result->dim; i++) pdf[i] -= pdf[i-1]; /* make pdf from cdf */ rn = r_uniform(); hit = 0; cdf = pdf[0]; while (rn > cdf) { hit++; if (hit < result->dim) cdf += pdf[hit]; else break; /* fix hit at this interval */ } /* hit now denotes the class in [ 0 ... dim ] in which rn falls */ for (i = 0; i < result->dim; i++) if (orc <= 3) result->ve[i] = (hit == i ? 1.0 : 0.0); else result->ve[i] = (hit <= i ? 1.0 : 0.0); } void correct_orv(double *est, int n_vars, int orc) { /* * does ``order relation violations corrections'' (acc. to GSLIB pages 77-81); * if IS_PDF: correct < 0, > 1, sum <= 1; * if not IS_PDF: average upward/downward correction as in GSLIB's ik3d. */ int i; static int violation = -1, size = -1; static double *down = NULL, *up = NULL, *ori = NULL; double sum = 0.0; if (down == NULL || size < n_vars) { down = (double *) erealloc(down, n_vars * sizeof(double)); up = (double *) erealloc(up, n_vars * sizeof(double)); ori = (double *) erealloc(ori, n_vars * sizeof(double)); size = n_vars; } /* save original */ for (i = 0; i < n_vars; i++) ori[i] = est[2 * i]; if (orc <= 3) { for (i = 0; i < n_vars; i++) { est[2 * i] = MAX(est[2 * i], 0.0); est[2 * i] = MIN(est[2 * i], 1.0); sum += est[2 * i]; } if (orc == 3 && sum != 1.0) { if (DEBUG_ORDER) printlog("sum!=1: "); for (i = 0; i < n_vars; i++) est[2 * i] /= sum; } else if (orc == 2 && sum > 1.0) { if (DEBUG_ORDER) printlog("sum>1: "); for (i = 0; i < n_vars; i++) est[2 * i] /= sum; } } else { /* orc == 4: cdf; do the GSLIB upward/downward averaging: */ /* upward correction: */ up[0] = MAX(0.0, MIN(1.0, est[0])); for (i = 1; i < n_vars; i++) /* don't go down && stay < 1 */ up[i] = MAX(up[i-1], MIN(1.0, est[2 * i])); /* downward correction: */ down[n_vars-1] = MAX(0.0, MIN(1.0, est[2 * (n_vars-1)])); for (i = n_vars - 2; i >= 0; i--) /* don't go up && stay > 0 */ down[i] = MIN(down[i+1], MAX(0.0, est[2 * i])); /* average upward/downward: */ for (i = 0; i < n_vars; i++) est[2 * i] = 0.5 * (down[i] + up[i]); } if (n_total == 0) { /* first time */ if (DEBUG_ORDER) printlog("order relation violation:\n(before correction) --> (after correction)\n"); } n_total++; for (i = violation = 0; !violation && i < n_vars; i++) if (ori[i] != est[2 * i]) violation = 1; n_orvc += violation; if (DEBUG_ORDER) { if (violation) { /* print the order correction */ for (i = 0; i < n_vars; i++) printlog("%g ", ori[i]); printlog("--> "); for (i = 0; i < n_vars; i++) printlog("%g ", est[2 * i]); printlog("\n"); } } } void print_orvc(void) { if (n_total > 0) { if (n_orvc > 0) printlog( "number of corrected order relation violations: %u of %u (%.1f%%)\n", n_orvc, n_total, (100.0 * n_orvc)/n_total); else printlog("no order relation violations\n"); n_orvc = 0; n_total = 0; } } gstat/src/block.c0000644000176200001440000001662013777370515013445 0ustar liggesusers/* * block.c: calculate block discretization at a prediction location */ #include "defs.h" #include "userio.h" #include "debug.h" #include "data.h" #include "utils.h" #include "glvars.h" #include "block.h" /* Gaussian quadrature adapted from Carr & Palmer, MG 25(5), p. 514: gauss[4]: -0.8611363116, -0.3399810436, 0.3399810436, 0.8611363116 gauss_w[4]: 0.3478548452, 0.6521451548, 0.6521451548, 0.3478548452 both divided by 2 */ static double gauss[4] = { -0.4305681558, -0.1699905218, 0.1699905218, 0.4305681558 }; double gauss_w[4] = { 0.1739274226, 0.3260725774, 0.3260725774, 0.1739274226 }; int reset_anyway = 0; void reset_block_discr(void) { reset_anyway = 1; } DATA *block_discr(DATA *d, const DPOINT *block, const DPOINT *where) { /* * Purpose : get locations that discretize the estimation area * Created by : Edzer J. Pebesma * Date : april 6th, 1992 * Modified : jan 13, 1993, june 3, 1993, june 23 1993 * Prerequisites : where; * the contents of block (if not NULL) may not change * during the run of the program: only once the full * discretisation is calculated. * Returns : DATA list with 1 point (x,y,z) or a list; * Side effects : dynamic memory (re)allocation for d; * uses IS_BLOCK(where) to determine whether point or block is needed; * discretisations is rectangular using dimensions of *block; * * only the x, y and z field are used for locations, * weights are put in the weight union. */ int i, k, l, m, ndim; int ndiscr = 0, restart = 0; /* * if restart != 0, block descretizations are re-calculated. */ /* * ndim: number of dimensions (x, y, z, ..?) in data * ndiscr: total number of points discretizing the block in this run * lastndiscr: number of discretizing points in last call * gl_nblockdiscr: number of points in each dimension in discretizing grid */ static double *dx = NULL, *dy = NULL, *dz = NULL; static double *weight = NULL; static int max = 0; DATA *area = NULL, **data; /* * d has the points of the discretization of the estimation area; * dx, dy, dz and weight are remembered in case blockdiscretization has not * changed */ if (IS_POINT(where) && d != NULL) { /* point shortcut */ d->list[0]->x = where->x; d->list[0]->y = where->y; d->list[0]->z = where->z; d->list[0]->u.weight = 1.0; /* weight */ d->n_list = 1; if (DEBUG_BLOCK) { printlog("block discretization (dist is weight):\n"); d->mode = X_BIT_SET | Y_BIT_SET | Z_BIT_SET; print_data_list(d); } return d; } /* * calculate the neccesary number of block discrimination points: */ ndim = 0; ndiscr = 1; if (IS_BLOCK(where)) { if ((area = get_data_area()) == NULL) { if (block->x > 0.0) ndim++; if (block->y > 0.0) ndim++; if (block->z > 0.0) ndim++; for (i = 0; i < ndim; i++) ndiscr *= gl_nblockdiscr; } else ndiscr = area->n_list; } if (area == NULL && ndiscr > max) { dx = (double *) erealloc(dx, ndiscr * sizeof(double)); dy = (double *) erealloc(dy, ndiscr * sizeof(double)); dz = (double *) erealloc(dz, ndiscr * sizeof(double)); weight = (double *) erealloc(weight, ndiscr * sizeof(double)); max = ndiscr; } /* * (re)allocate the memory neccesary: */ if (d == NULL) { /* allocate ndiscr: */ d = (DATA *) emalloc (sizeof(DATA)); init_one_data(d); assert(get_n_vars() > 0); data = get_gstat_data(); d->pp_norm2 = data[0]->pp_norm2; /* assign distance function */ d->what_is_u = U_ISWEIGHT; d->n_X = 0; d->colnx = d->colny = d->colnz = 1; d->list = (DPOINT **) emalloc(ndiscr * sizeof(DPOINT *)); for (i = 0; i < ndiscr; i++) d->list[i] = (DPOINT *) emalloc (sizeof(DPOINT)); d->n_max = d->n_list = ndiscr; restart = 1; } else if (ndiscr > d->n_max) { /* resize if n_max < ndiscr: */ d->list = (DPOINT **) erealloc(d->list, ndiscr * sizeof(DPOINT *)); for (i = d->n_max; i < ndiscr; i++) d->list[i] = (DPOINT *) emalloc (sizeof(DPOINT)); d->n_max = d->n_list = ndiscr; restart = 1; } else if (reset_anyway) { reset_anyway = 0; restart = 1; } if (restart && ndim > 0 && area == NULL) { /* set up block regular or Gaussian block discretisation */ i = 0; switch (ndim) { case 1: if (block->y > 0 || block->z > 0) ErrMsg(ER_IMPOSVAL, "block_discr(): block y and z dimensions must be 0"); if (gl_gauss) { for (k = 0; k < 4; k++) { dx[i] = block->x * gauss[k]; dy[i] = dz[i] = 0.0; weight[i] = gauss_w[k]; i++; } } else { for (k = 0; k < gl_nblockdiscr; k++) { dx[i] = block->x * (-0.5 + (1.0/gl_nblockdiscr) * (0.5 + k)); dy[i] = dz[i] = 0.0; weight[i] = 1.0 / (1.0 * ndiscr); i++; } } break; case 2: if (block->z > 0) ErrMsg(ER_IMPOSVAL, "block_discr(): 2D block->z must be zero"); if (gl_gauss) { for (k = 0; k < 4; k++) { for (l = 0; l < 4; l++) { dx[i] = block->x * gauss[k]; dy[i] = block->y * gauss[l]; weight[i] = gauss_w[k] * gauss_w[l]; dz[i] = 0.0; i++; } /* for l */ } /* for k */ } else { for (k = 0; k < gl_nblockdiscr; k++) { for (l = 0; l < gl_nblockdiscr; l++) { dx[i] = block->x * (-0.5 + (1.0/gl_nblockdiscr) * (0.5 + k)); dy[i] = block->y * (-0.5 + (1.0/gl_nblockdiscr) * (0.5 + l)); dz[i] = 0.0; weight[i] = 1.0 / (1.0 * ndiscr); i++; } /* for l */ } /* for k */ } break; case 3: if (gl_gauss) { for (k = 0; k < 4; k++) { for (l = 0; l < 4; l++) { for (m = 0; m < 4; m++) { dx[i] = block->x * gauss[k]; dy[i] = block->y * gauss[l]; dz[i] = block->z * gauss[m]; weight[i] = gauss_w[k] * gauss_w[l] * gauss_w[m]; i++; } /* for m */ } /* for l */ } /* for k */ } else { for (k = 0; k < gl_nblockdiscr; k++) { for (l = 0; l < gl_nblockdiscr; l++) { for (m = 0; m < gl_nblockdiscr; m++) { dx[i] = block->x * (-0.5+(1.0/gl_nblockdiscr) * (0.5 + k)); dy[i] = block->y * (-0.5+(1.0/gl_nblockdiscr) * (0.5 + l)); dz[i] = block->z * (-0.5+(1.0/gl_nblockdiscr) * (0.5 + m)); weight[i] = 1.0 / (1.0 * ndiscr); i++; } /* for m */ } /* for l */ } /* for k */ } break; default: ErrMsg(ER_IMPOSVAL, "block_discr()"); } /* switch */ if (i != ndiscr) /* silly check ! */ ErrMsg(ER_IMPOSVAL, "block_discr()"); } /* end if restart */ if (IS_BLOCK(where)) { if (area != NULL) { for (i = 0; i < ndiscr; i++) { d->list[i]->x = area->list[i]->x + where->x; d->list[i]->y = area->list[i]->y + where->y; d->list[i]->z = area->list[i]->z + where->z; if (area->colnvariance) d->list[i]->u.weight = area->list[i]->variance; else d->list[i]->u.weight = 1.0 / ndiscr; } } else { for (i = 0; i < ndiscr; i++) { d->list[i]->x = where->x - dx[i]; d->list[i]->y = where->y - dy[i]; d->list[i]->z = where->z - dz[i]; d->list[i]->u.weight = weight[i]; } } } else { /* where is point */ d->list[0]->x = where->x; d->list[0]->y = where->y; d->list[0]->z = where->z; d->list[0]->u.weight = 1.0; /* weight */ } d->n_list = ndiscr; if (DEBUG_BLOCK) { printlog("block discretization (dist is weight):\n"); d->mode = X_BIT_SET | Y_BIT_SET | Z_BIT_SET; print_data_list(d); } return d; } gstat/src/lm.h0000644000176200001440000000216613777370515012770 0ustar liggesusers#ifndef LM_H # define LM_H void pred_lm(DATA **data, int n_vars, DPOINT *where, double *est); void make_residuals_lm(DATA *d); double *make_ols(DATA *d); MAT *get_X(DATA **d, MAT *X, int nvars); MAT *get_X0(DATA **d, MAT *X0, DPOINT *where, int nvars); double calc_mu(const DATA *d, const DPOINT *pt); VEC *get_y(DATA **d, VEC *y, int nvars); int is_singular(MAT *X, double epsilon); typedef struct { VEC *beta, /* parameter vector */ *y, /* data vector */ *Xty, /* X'y */ *weights; /* weights in a WLS model: V-1, 1/sigma^2_i */ MAT *X, /* design matrix */ *Cov, /* covariance matrix of beta */ *Chol; /* Choleski decomposition of X'X or X'V-1X */ double MSErr, /* Mean Square Error */ MSReg, /* Mean Square due to regression */ SSErr, /* Sum of Squares error */ SSReg; /* Sum of Squares regression */ int dfE, /* degrees of freedom error */ dfReg, /* degrees of freedom regression */ is_singular, /* flag if X'X is singular */ has_intercept; /* model has intercept, J is part of X */ } LM ; LM *calc_lm(LM *lm); void logprint_lm(DATA *d, LM *lm); LM *init_lm(LM *lm); void free_lm(LM *lm); #endif /* LM_H */ gstat/src/fit.c0000644000176200001440000002125413777370515013134 0ustar liggesusers/* * fit.c: fit variogram model to experimental variograms; gnuplot fit driver */ #include #include /* getenv() */ #include /* strstr() */ #include /* fabs(), sqrt() */ #include /* Rprintf() */ #include "mtrx.h" #include "defs.h" #include "defaults.h" #include "userio.h" #include "data.h" #include "utils.h" #include "debug.h" #include "vario.h" #include "sem.h" #include "glvars.h" #include "reml.h" #include "lm.h" #include "fit.h" #define NEARLY_ZERO 1.0e-30 static void wls_fit(VARIOGRAM *vp); static double getSSErr(const VARIOGRAM *vp, PERM *p, LM *lm); static int fill_weights(const VARIOGRAM *vp, PERM *p, LM *lm); static int fit_GaussNewton(VARIOGRAM *vp, PERM *p, LM *lm, int iter, int *bounded); int fit_variogram(VARIOGRAM *v) { DATA **d = NULL; int i = 0; long n = 0; if (v->ev->refit == 0) return 0; if (v->ev->fit != NO_FIT && v->ev->fit != MIVQUE_FIT) { if (! v->ev->cloud) { while (n == 0 && i < v->ev->n_est) n += v->ev->nh[i++]; /* check if estimates exist */ if (n == 0) /* bad luck */ return 1; } else if (v->ev->n_est == 0) return 1; } if (v->ev->fit != NO_FIT) { if (v->ev->map) ErrMsg(ER_IMPOSVAL, "cannot fit model to variogram map"); for (i = 0; i < v->n_models; i++) if (v->part[i].sill == 0.0 && v->part[i].fit_sill != 0) v->part[i].sill = 1.0; /* avoid lot'o trouble */ } if (v->ev->fit == WLS_FIT_MOD && !is_variogram(v)) pr_warning("this fit method is not recommended for covariograms"); v->ev->direction.x = sin(gl_alpha * PI / 180.0) * cos(gl_beta * PI / 180.0); v->ev->direction.y = cos(gl_alpha * PI / 180.0) * cos(gl_beta * PI / 180.0); v->ev->direction.z = sin(gl_beta * PI / 180.0); switch (v->ev->fit) { case NO_FIT: break; case OLS_FIT: /* BREAKTHROUGH: */ case WLS_FIT: /* BREAKTHROUGH: */ case WLS_FIT_MOD: case WLS_NHH: wls_fit(v); break; case MIVQUE_FIT: if (v->id1 != v->id2) return 1; d = get_gstat_data(); reml_sills(d[v->id1], v); break; default: Rprintf("%d\n", v->ev->fit); ErrMsg(ER_IMPOSVAL, "fit_vgm(): value for fit not recognized or not implemented"); /* no default: force compile warning on missing option! */ } return 0; } static void wls_fit(VARIOGRAM *vp) { /* * non-linear iterative reweighted least squares fitting of variogram model to * sample variogram (..covariogram model to sample covariogram, cross, etc.) * all information necessary is contained in *vp. * * uses Marquardt-Levenberg algorithm; * the implementation follows gnuplot's fit.c */ static PERM *p = PNULL; int i, j, n_iter = 0, bounded = 0, timetostop; double SSErr, oldSSErr = DBL_MAX, step; LM *lm; p = px_resize(p, vp->ev->n_est); if (! vp->ev->cloud) { for (i = j = 0; i < (vp->ev->zero == ZERO_AVOID ? vp->ev->n_est-1 : vp->ev->n_est); i++) { if (vp->ev->nh[i] > 0) p->pe[j++] = i; } p->size = j; } lm = init_lm(NULL); /* oldSSErr = getSSErr(vp, p, lm); */ do { print_progress(n_iter, gl_iter); /* if (DEBUG_VGMFIT) printlog("%s: ", vp->descr); */ if ((vp->fit_is_singular = fit_GaussNewton(vp, p, lm, n_iter, &bounded))) { pr_warning("singular model in variogram fit"); print_progress(gl_iter, gl_iter); vp->SSErr = getSSErr(vp, p, lm); return; } update_variogram(vp); SSErr = getSSErr(vp, p, lm); /* we can't use lm->SSErr here since that's only in the X-filled-with-derivatives, not the true residuals */ step = oldSSErr - SSErr; if (SSErr > gl_zero) step /= SSErr; n_iter++; if (DEBUG_VGMFIT) printlog("after it. %d: SSErr %g->%g, step=%g (fit_limit %g%s)\n", n_iter, oldSSErr, SSErr, step, gl_fit_limit, bounded ? "; bounded" : ""); oldSSErr = SSErr; timetostop = (step < gl_fit_limit && step >= 0.0 && bounded == 0) || n_iter == gl_iter; } while (! timetostop); print_progress(gl_iter, gl_iter); if (n_iter == gl_iter) pr_warning("No convergence after %d iterations: try different initial values?", n_iter); if (DEBUG_VGMFIT) { printlog("# iterations: %d, SSErr %g, last step %g", n_iter, SSErr, step); if (step < 0.0) printlog(", last step was in the wrong direction.\n"); else printlog("\n"); } free_lm(lm); vp->SSErr = SSErr; return; } /* wls_fit */ static double getSSErr(const VARIOGRAM *vp, PERM *p, LM *lm) { int i; double x, y, z, dz, SSErr; /* if (fill_weights(vp, p, lm)) return 0.0; */ for (i = 0, SSErr = 0.0; i < p->size; i++) { x = vp->ev->direction.x * vp->ev->dist[p->pe[i]]; y = vp->ev->direction.y * vp->ev->dist[p->pe[i]]; z = vp->ev->direction.z * vp->ev->dist[p->pe[i]]; /* fill y with current residuals: */ dz = vp->ev->gamma[p->pe[i]] - (is_variogram(vp) ? get_semivariance(vp, x, y, z) : get_covariance(vp, x, y, z)); if (lm->weights != NULL) SSErr += dz * dz * lm->weights->ve[i]; else SSErr += dz * dz; } return SSErr; } static int fit_GaussNewton(VARIOGRAM *vp, PERM *p, LM *lm, int iter, int *bounded) { double s = 0.0, x, y, z; int i, j, n_fit, model, fit_ranges = 0; IVEC *fit = NULL; VEC *start = NULL; if (p->size == 0) return 1; fit = iv_resize(fit, 2 * vp->n_models); /* index fit parameters: parameter fit->ive[j] corresponds to model i */ for (i = n_fit = 0; i < vp->n_models; i++) { if (vp->part[i].fit_sill) fit->ive[n_fit++] = i; if (vp->part[i].fit_range) { fit->ive[n_fit++] = i + vp->n_models; /* large -->> ranges */ fit_ranges = 1; } } if (n_fit == 0) { iv_free(fit); return 0; } fit = iv_resize(fit, n_fit); /* shrink to fit */ lm->X = m_resize(lm->X, p->size, n_fit); lm->y = v_resize(lm->y, p->size); start = v_resize(start, n_fit); for (i = 0; i < n_fit; i++) { if (fit->ive[i] < vp->n_models) { model = fit->ive[i]; start->ve[i] = vp->part[model].sill; } else { model = fit->ive[i] - vp->n_models; start->ve[i] = vp->part[model].range[0]; } } for (i = 0; i < p->size; i++) { x = vp->ev->direction.x * vp->ev->dist[p->pe[i]]; y = vp->ev->direction.y * vp->ev->dist[p->pe[i]]; z = vp->ev->direction.z * vp->ev->dist[p->pe[i]]; /* fill y with current residuals: */ if (is_variogram(vp)) s = get_semivariance(vp, x, y, z); else s = get_covariance(vp, x, y, z); lm->y->ve[i] = vp->ev->gamma[p->pe[i]] - s; /* fill X: */ for (j = 0; j < n_fit; j++) { /* cols */ if (fit->ive[j] < vp->n_models) { model = fit->ive[j]; ME(lm->X, i, j) = (is_variogram(vp) ? UnitSemivariance(vp->part[model],x,y,z) : UnitCovariance(vp->part[model],x,y,z)); } else { model = fit->ive[j] - vp->n_models; ME(lm->X, i, j) = (is_variogram(vp) ? da_Semivariance(vp->part[model],x,y,z) : -da_Semivariance(vp->part[model],x,y,z)); } } } if (iter == 0 && fill_weights(vp, p, lm)) { iv_free(fit); v_free(start); return 1; } lm->has_intercept = 1; /* does not affect the fit */ lm = calc_lm(lm); /* solve WLS eqs. for beta */ if (DEBUG_FIT) { Rprintf("beta: "); v_logoutput(lm->beta); } if (lm->is_singular) { iv_free(fit); v_free(start); return 1; } if (fit_ranges) { s = v_norm2(lm->beta) / v_norm2(start); if (s > 0.2) { /* don't allow steps > 20% ---- */ sv_mlt(0.2 / s, lm->beta, lm->beta); *bounded = 1; } else *bounded = 0; /* a `free', voluntary step */ } else /* we're basically doing linear regression here: */ *bounded = 0; for (i = 0; i < n_fit; i++) { if (fit->ive[i] < vp->n_models) { model = fit->ive[i]; vp->part[model].sill = start->ve[i] + lm->beta->ve[i]; } else { model = fit->ive[i] - vp->n_models;; vp->part[model].range[0] = start->ve[i] + lm->beta->ve[i]; } } iv_free(fit); v_free(start); return 0; } static int fill_weights(const VARIOGRAM *vp, PERM *p, LM *lm) { double x, y, z, s; int i, retval = 0; if (vp->ev->fit == OLS_FIT || (vp->ev->cloud && vp->ev->fit == WLS_FIT)) { if (lm->weights != NULL) v_free(lm->weights); lm->weights = NULL; return 0; } lm->weights = v_resize(lm->weights, p->size); for (i = 0; i < p->size; i++) { if (vp->ev->fit == WLS_NHH) s = vp->ev->dist[p->pe[i]]; else { x = vp->ev->direction.x * vp->ev->dist[p->pe[i]]; y = vp->ev->direction.y * vp->ev->dist[p->pe[i]]; z = vp->ev->direction.z * vp->ev->dist[p->pe[i]]; s = get_semivariance(vp, x, y, z); } if (vp->ev->cloud) { lm->weights->ve[i] = 1.0; if (fabs(s) > NEARLY_ZERO) lm->weights->ve[i] /= s * s; else { pr_warning("infinite weight during fit"); retval = 1; break; } } else { /* no cloud: */ lm->weights->ve[i] = vp->ev->nh[p->pe[i]]; if (vp->ev->fit != WLS_FIT) { if (fabs(s) > NEARLY_ZERO) lm->weights->ve[i] /= (s * s); else { pr_warning("infinite weight during fit"); retval = 1; break; } } } /* else cloud */ } /* for i */ return retval; } gstat/src/direct.h0000644000176200001440000000022313777370515013622 0ustar liggesusersdouble valid_direction(DPOINT *a, DPOINT *b, int symmetric, const DATA *d); void set_direction_values(double a, double b, double t_h, double t_v); gstat/src/sim.h0000644000176200001440000000023213777370515013140 0ustar liggesusersconst double *cond_sim(double *est, int n_sim, METHOD m, int *is_pt, int orc); void correct_orv(double *est, int n_vars, int orc); void print_orvc(void); gstat/src/pqueue.c0000644000176200001440000001110513777370515013650 0ustar liggesusers/* * priority queue, Jan-Apr 1998 * * I did a net search one day, and found so many implementations of * priority queues that I decided to write my own. For the fun of it. * * This one has no limits and needs a generic (qsort-like) comparison * function for element comparison at initialisation. To enqueue an * unordered array of elements, elements are sorted with qsort(), before * they are merged into the ordered queue. Only pointers to the next * element are stored (so it's basically an ordered single linked list). */ #include #include #include #include "defs.h" #include "userio.h" #include "data.h" #include "utils.h" #include "nsearch.h" #include "pqueue.h" static void enlarge_queue(QUEUE *q); static void enlarge_queue(QUEUE *q) { /* * don't use realloc() on `empty': all pointers to the * first element would have to be moved along with itself. */ int i; Q_ELEMENT *block; block = (Q_ELEMENT *) emalloc(Q_BUFFER_SIZE * sizeof(Q_ELEMENT)); for (i = 0; i < Q_BUFFER_SIZE - 1; i++) block[i].next = &(block[i+1]); block[Q_BUFFER_SIZE - 1].next = NULL; if (q->empty == NULL) q->empty = block; else q->empty->next = block; q->max_length += Q_BUFFER_SIZE; /* register block to free later on... */ q->blocks += 1; q->block = (Q_ELEMENT **) erealloc(q->block, q->blocks * sizeof(Q_ELEMENT *)); q->block[q->blocks - 1] = block; } QUEUE *init_queue(QUEUE *q, int (CDECL *cmp)(const QUEUE_NODE *a, const QUEUE_NODE *b)) { int i, j; if (q == NULL) { q = (QUEUE *) emalloc(sizeof(QUEUE)); q->max_length = q->blocks = 0; q->empty = NULL; q->block = NULL; q->cmp = cmp; enlarge_queue(q); } else { q->empty = q->block[0]; for (i = 0; i < q->blocks; i++) { for (j = 0; j < Q_BUFFER_SIZE - 1; j++) /* connect elements: */ q->block[i][j].next = &(q->block[i][j+1]); if (i < q->blocks - 1) /* connect elements between blocks: */ q->block[i][Q_BUFFER_SIZE - 1].next = &(q->block[i+1][0]); } q->block[q->blocks - 1][Q_BUFFER_SIZE - 1].next = NULL; } q->length = 0; q->head = NULL; return q; } void free_queue(QUEUE *q) { int i; if (q != NULL) { for (i = 0; i < q->blocks; i++) efree(q->block[i]); /* queue buffers */ if (q->block != NULL) efree(q->block); efree(q); } } static Q_ELEMENT *get_free(QUEUE *q) { Q_ELEMENT *e; if (q->empty->next == NULL) enlarge_queue(q); e = q->empty; q->empty = q->empty->next; return e; } void enqueue(QUEUE *q, QUEUE_NODE *el, int n) { /* * insert n elements in array el into the priority queue q */ Q_ELEMENT *e, *where, *next; int i = 0, p; if (q == NULL || el == NULL || n <= 0) ErrMsg(ER_NULL, "enqueue"); /* * first sort array el */ qsort(el, (size_t) n, sizeof(QUEUE_NODE), (int CDECL (*)(const void *,const void *)) q->cmp); /* * and then merge them with the priority queue q */ /* * find p, the number of elements in el[] that are smaller than * the first element in the queue, if any. * (Yes, we expect at least some of them to be closer than q->head) */ for (p = n; q->head != NULL && p > 0; p--) if (q->cmp(&(el[p-1]), &(q->head->el)) <= 0) break; /* out of this for loop */ /* * put these p elements in order at the queue head: */ for (i = p; i > 0; i--) { e = get_free(q); e->el = el[i-1]; e->next = q->head; q->head = e; } q->length += p; n -= p; /* * We might be done by now (n zero). * Process the remaining elements: */ where = q->head; /* starting point for insertion: */ next = where->next; /* the next element */ el += p; /* start of the remaining elements */ for (i = 0; i < n; i++) { e = get_free(q); /* get a free queue element */ e->el = el[i]; /* copy contents: */ /* * unless where is the last element, shift a position in the queue * when the element is larger than the insertion element e: */ while (next != NULL && q->cmp(&(e->el), &(next->el)) > 0) { where = next; next = where->next; } /* * now next points either to NULL or to the first element smaller * than or equal to e. So, insert e after where and before next: */ e->next = next; where->next = e; /* * the next element in el[] will should follow after e, * so shift where one position to start looking after e: */ where = e; } q->length += n; return; } QUEUE_NODE dequeue(QUEUE *q) { Q_ELEMENT *e; if (q->length == 0) ErrMsg(ER_NULL, "cannot dequeue empty queue"); e = q->head; /* get first queue element */ q->head = q->head->next; /* reset first to next */ e->next = q->empty; /* put the dequeued element in the empty queue */ q->empty = e; q->length--; return e->el; } gstat/src/gcdist.c0000644000176200001440000000256613777370515013634 0ustar liggesusers#include /* sin() etc */ #include #include #include #define POWDI(x,i) R_pow_di(x,i) #include "gcdist.h" double gstat_gcdist(double lon1, double lon2, double lat1, double lat2) { /* http://home.att.net/~srschmitt/script_greatcircle.html */ /* taken from R package sp source; Copyright by Roger Bivand (C) 2005 */ double F, G, L, sinG2, cosG2, sinF2, cosF2, sinL2, cosL2, S, C; double w, R, a, f, D, H1, H2; double lat1R, lat2R, lon1R, lon2R, DE2RA; if (lon1 == lon2 && lat1 == lat2) return 0.0; DE2RA = M_PI/180; a = 6378.137; /* WGS-84 equatorial radius in km */ f = 1.0/298.257223563; /* WGS-84 ellipsoid flattening factor */ lat1R = lat1 * DE2RA; lat2R = lat2 * DE2RA; lon1R = lon1 * DE2RA; lon2R = lon2 * DE2RA; F = (lat1R + lat2R) / 2.0; G = (lat1R - lat2R) / 2.0; L = (lon1R - lon2R) / 2.0; sinG2 = POWDI(sin(G), 2); cosG2 = POWDI(cos(G), 2); sinF2 = POWDI(sin(F), 2); cosF2 = POWDI(cos(F), 2); sinL2 = POWDI(sin(L), 2); cosL2 = POWDI(cos(L), 2); S = sinG2 * cosL2 + cosF2 * sinL2; C = cosG2 * cosL2 + sinF2 * sinL2; w = atan(sqrt(S / C)); R = sqrt(S * C) / w; D = 2 * w * a; H1 = (3 * R - 1)/(2 * C); H2 = (3 * R + 1)/(2 * S); return D * (1 + f * H1 * sinF2 * cosG2 - f * H2 * cosF2 * sinG2); } gstat/src/reml.c0000644000176200001440000002604413777370515013313 0ustar liggesusers/* * iterated mivque (reml) estimate of covariance components, following * Christensen's 1994 derivations Math.Geol. 25 (5), 541-558, and * Kitanidis' 1985 derivation (for estimate covariances) Math.Geol. 17 (2). * * Pre: data pointer (later: extend to 2 or more, crossvariograms?) * initial variogram for *data * Post: returns pointer to the updated variogram * if output != NULL, all iteration steps are printed to log device, * with final variogram model parameter covariances * Aug 1994; * Mod. (I-Aw) Nov 1998 */ #include #include /* fabs() */ #include "mtrx.h" #include "defs.h" #include "userio.h" #include "debug.h" #include "data.h" #include "utils.h" #include "vario.h" #include "glvars.h" #include "select.h" #include "mtrx.h" #include "lm.h" /* get_X, get_y */ #include "reml.h" static int reml(VEC *Y, MAT *X, MAT **Vk, int n_k, int max_iter, double fit_limit, VEC *teta); static double trace_matrix(MAT *m); static MAT *calc_VinvIminAw(MAT *Vw, MAT *X, MAT *VinvIminAw, int calc_Aw); static void calc_rhs_Tr_m(int n_models, MAT **Vk,MAT *VinvIminAw, VEC *Y, VEC *rhs, MAT *Tr_m); static double calc_ll(MAT *Vw, MAT *X, VEC *y, int n); static MAT *XVXt_mlt(MAT *X, MAT *V, MAT *out); static MAT *IminAw = MNULL; VARIOGRAM *reml_sills(DATA *data, VARIOGRAM *vp) { int i, j, k; MAT **Vk = NULL, *X = MNULL; VEC *Y = VNULL, *init = VNULL; DPOINT *dpa, *dpb; double dx, dy = 0.0, dz = 0.0, dzero2; if (data == NULL || vp == NULL) ErrMsg(ER_NULL, "reml()"); select_at(data, (DPOINT *) NULL); if (vp->n_models <= 0) ErrMsg(ER_VARNOTSET, "reml: please define initial variogram model"); /* * create Y, X, Vk's only once: */ Y = get_y(&data, Y, 1); X = get_X(&data, X, 1); Vk = (MAT **) emalloc(vp->n_models * sizeof(MAT *)); init = v_resize(init, vp->n_models); for (i = 0; i < vp->n_models; i++) { init->ve[i] = vp->part[i].sill; /* remember init. values for updating */ vp->part[i].sill = 1; Vk[i] = m_resize(MNULL, X->m, X->m); } dzero2 = gl_zero * gl_zero; for (i = 0; i < data->n_list; i++) { for (j = 0; j < vp->n_models; j++) /* fill diagonals */ ME(Vk[j], i, i) = Covariance(vp->part[j], 0.0, 0.0, 0.0); for (j = 0; j < i; j++) { /* off-diagonal elements: */ dpa = data->list[i]; dpb = data->list[j]; /* * if different points coincide on a locations, shift them, * or the covariance matrix will become singular */ dx = dpa->x - dpb->x; dy = dpa->y - dpb->y; dz = dpa->z - dpb->z; if (data->pp_norm2(dpa, dpb) < dzero2) { if (data->mode & X_BIT_SET) dx = (dx >= 0 ? gl_zero : -gl_zero); if (data->mode & Y_BIT_SET) dy = (dy >= 0 ? gl_zero : -gl_zero); if (data->mode & Z_BIT_SET) dz = (dz >= 0 ? gl_zero : -gl_zero); } for (k = 0; k < vp->n_models; k++) ME(Vk[k], i, j) = ME(Vk[k], j, i) = Covariance(vp->part[k], dx, dy, dz); } } if (reml(Y, X, Vk, vp->n_models, gl_iter, gl_fit_limit, init)) vp->ev->refit = 0; else /* on convergence */ pr_warning("no convergence while fitting variogram"); for (i = 0; i < vp->n_models; i++) vp->part[i].sill = init->ve[i]; update_variogram(vp); if (DEBUG_VGMFIT) logprint_variogram(vp, 1); for (i = 0; i < vp->n_models; i++) m_free(Vk[i]); efree(Vk); m_free(X); v_free(Y); v_free(init); return vp; } static int reml(VEC *Y, MAT *X, MAT **Vk, int n_k, int max_iter, double fit_limit, VEC *teta) { volatile int n_iter = 0; int i, info; volatile double rel_step = DBL_MAX; VEC *rhs = VNULL; VEC *dteta = VNULL; MAT *Vw = MNULL, *Tr_m = MNULL, *VinvIminAw = MNULL; Vw = m_resize(Vw, X->m, X->m); VinvIminAw = m_resize(VinvIminAw, X->m, X->m); rhs = v_resize(rhs, n_k); Tr_m = m_resize(Tr_m, n_k, n_k); dteta = v_resize(dteta, n_k); while (n_iter < max_iter && rel_step > fit_limit) { print_progress(n_iter, max_iter); n_iter++; dteta = v_copy(teta, dteta); /* fill Vw, calc VinvIminAw, rhs; */ for (i = 0, m_zero(Vw); i < n_k; i++) ms_mltadd(Vw, Vk[i], teta->ve[i], Vw); /* Vw = Sum_i teta[i]*V[i] */ VinvIminAw = calc_VinvIminAw(Vw, X, VinvIminAw, n_iter == 1); calc_rhs_Tr_m(n_k, Vk, VinvIminAw, Y, rhs, Tr_m); /* Tr_m * teta = Rhs; symmetric, solve for teta: */ CHfactor(Tr_m, PNULL, &info); if (info != 0) { pr_warning("singular matrix in reml"); return(0); } CHsolve1(Tr_m, rhs, teta, PNULL); if (DEBUG_VGMFIT) { printlog("teta_%d [", n_iter); for (i = 0; i < teta->dim; i++) printlog(" %g", teta->ve[i]); printlog("] -(log.likelyhood): %g\n", calc_ll(Vw, X, Y, n_k)); } v_sub(teta, dteta, dteta); /* dteta = teta_prev - teta_curr */ if (v_norm2(teta) == 0.0) rel_step = 0.0; else rel_step = v_norm2(dteta) / v_norm2(teta); } /* while (n_iter < gl_iter && rel_step > fit_limit) */ print_progress(max_iter, max_iter); if (n_iter == gl_iter) pr_warning("No convergence after %d iterations", n_iter); if (DEBUG_VGMFIT) { /* calculate and report covariance matrix */ /* first, update to current est */ for (i = 0, m_zero(Vw); i < n_k; i++) ms_mltadd(Vw, Vk[i], teta->ve[i], Vw); /* Vw = Sum_i teta[i]*V[i] */ VinvIminAw = calc_VinvIminAw(Vw, X, VinvIminAw, 0); calc_rhs_Tr_m(n_k, Vk, VinvIminAw, Y, rhs, Tr_m); m_inverse(Tr_m, &info); sm_mlt(2.0, Tr_m, Tr_m); /* Var(YAY)=2tr(AVAV) */ printlog("Lower bound of parameter covariance matrix:\n"); m_logoutput(Tr_m); printlog("# Negative log-likelyhood: %g\n", calc_ll(Vw, X, Y, n_k)); } m_free(Vw); m_free(VinvIminAw); m_free(Tr_m); v_free(rhs); v_free(dteta); return (n_iter < max_iter && rel_step < fit_limit); /* converged? */ } static MAT *calc_VinvIminAw(MAT *Vw, MAT *X, MAT *VinvIminAw, int calc_Aw) { /* * calculate V_w^-1(I-A_w) (==VinvIminAw), * A = X(X'X)^-1 X' (AY = XBeta; Beta = (X'X)^-1 X'Y) * * on second thought (Nov 1998 -- more than 4 years later :-)) * calc (I-Aw) only once and keep this constant during iteration. */ MAT *tmp = MNULL, *V = MNULL; /* VEC *b = VNULL, *rhs = VNULL; */ int i, j, info; if (X->m != Vw->n || VinvIminAw->m != X->m) ErrMsg(ER_IMPOSVAL, "calc_VinvIminAw: sizes don't match"); if (calc_Aw) { IminAw = m_resize(IminAw, X->m, X->m); tmp = m_resize(tmp, X->n, X->n); tmp = mtrm_mlt(X, X, tmp); /* X'X */ m_inverse(tmp, &info); /* (X'X)-1 */ if (info != 0) pr_warning("singular matrix in calc_VinvIminAw"); /* X(X'X)-1 -> X(X'X)-1 X') */ IminAw = XVXt_mlt(X, tmp, IminAw); for (i = 0; i < IminAw->m; i++) /* I - Aw */ for (j = 0; j <= i; j++) if (i == j) ME(IminAw, i, j) = 1.0 - ME(IminAw, i, j); else ME(IminAw, i, j) = ME(IminAw, j, i) = -(ME(IminAw, i, j)); } V = m_copy(Vw, V); CHfactor(V, PNULL, &info); if (info != 0) pr_warning("singular V matrix in calc_VinvIminAw"); CHsolve(V, IminAw, VinvIminAw, PNULL); m_free(V); if (tmp) m_free(tmp); return VinvIminAw; } static void calc_rhs_Tr_m(int n_models, MAT **Vk,MAT *VinvIminAw, VEC *y, VEC *rhs, MAT *Tr_m) { int j, k; MAT **Pr = NULL, *Tmp = MNULL; VEC *v_tmp = VNULL, *v_tmp2; Pr = (MAT **) emalloc(n_models * sizeof(MAT *)); v_tmp2 = vm_mlt(VinvIminAw, y, VNULL); /* Vw-(I-Aw)Y == Y'(I-Aw)'Vw- */ for (j = 0; j < n_models; j++) { Pr[j] = m_mlt(Vk[j], VinvIminAw, MNULL); Tmp = m_mlt(Pr[j], Pr[j], Tmp); ME(Tr_m, j, j) = trace_matrix(Tmp); /* diagonal */ /* using Tr(A B) == Tr(B A) */ for (k = 0; k < j; k++) { /* we did Pr[k] and Pr[j], so */ Tmp = m_mlt(Pr[j], Pr[k], Tmp); /* off-diagonal */ ME(Tr_m, j, k) = ME(Tr_m, k, j) = trace_matrix(Tmp); } v_tmp = vm_mlt(Vk[j], v_tmp2, v_tmp); /* Vw-1(I-Aw)Y */ rhs->ve[j] = in_prod(v_tmp2, v_tmp); } for (j = 0; j < n_models; j++) m_free(Pr[j]); efree(Pr); m_free(Tmp); v_free(v_tmp); v_free(v_tmp2); return; } static double calc_ll(MAT *Vw, MAT *X, VEC *y, int n) { /* * calculate negative log-likelyhood */ static MAT *M1 = MNULL; static VEC *res = VNULL, *tmp = VNULL; double zQz; volatile double ldet; int i, info; IminAw->m -= n; /* |B'(I-A)Vw(I-A)'B|, pretty inefficiently, can 4 x as fast: */ /* M1 = m_mlt(IminAw, Vw, M1); M2 = mmtr_mlt(M1, IminAw, M2); */ M1 = XVXt_mlt(IminAw, Vw, M1); CHfactor(M1, PNULL, &info); for (i = 0, ldet = 0.0; i < M1->m; i++) { assert(ME(M1, i, i) > 0.0); ldet += log(ME(M1, i, i)); } /* y'B'A'(B'A'Vw A B)-1 A B y */ res = mv_mlt(IminAw, y, res); /* the m-n residuals B(I-A)'Y */ tmp = CHsolve1(M1, res, tmp, PNULL); /* M1 tmp = res -> tmp = M1-1 res */ zQz = in_prod(res, tmp); /* res' M1inv res */ IminAw->m += n; return 0.5 * ((Vw->m - n)*log(2*PI) + ldet + zQz); } static double trace_matrix(MAT *m) { /* returns trace of a square matrix */ int i; double trace; if (m == NULL) ErrMsg(ER_NULL, "trace_matrix: NULL argument"); if (m->m != m->n) ErrMsg(ER_IMPOSVAL, "trace_matrix: non-square matrix"); for (i = 0, trace = 0.0; i < m->m; i++) trace += ME(m, i, i); return trace; } MAT *XtVX_mlt(MAT *X, MAT *V, MAT *out) { /* for a symmetric matrix V, return X' V X */ static MAT *VX = MNULL; int i, j, k; if (X==(MAT *)NULL || V==(MAT *)NULL ) ErrMsg(ER_IMPOSVAL, "XtVX_mlt"); if (X->m != V->m) ErrMsg(ER_IMPOSVAL, "XtVX_mlt"); if (V->m != V->n) ErrMsg(ER_IMPOSVAL, "XtVX_mlt"); out = m_resize(out, X->n, X->n); VX = m_resize(VX, V->m, X->n); m_zero(out); VX = m_mlt(V, X, VX); for (i = 0; i < X->n; i++) { for (j = i; j < X->n; j++) for (k = 0; k < X->m; k++) ME(out, i, j) += ME(X, k, i) * ME(VX, k, j); for (j = 0; j <= i; j++) /* symmetry */ ME(out, i, j) = ME(out, j, i); } return out; } static MAT *XVXt_mlt(MAT *X, MAT *V, MAT *out) { /* for a symmetric matrix V, return X V X' */ static MAT *VXt = MNULL; int i, j, k; if (X==(MAT *)NULL || V==(MAT *)NULL ) ErrMsg(ER_IMPOSVAL, "XtVX_mlt"); if (X->n != V->m) ErrMsg(ER_IMPOSVAL, "XtVX_mlt"); if (V->m != V->n) ErrMsg(ER_IMPOSVAL, "XtVX_mlt"); out = m_resize(out, X->m, X->m); VXt = m_resize(VXt, V->m, X->n); m_zero(out); VXt = mmtr_mlt(V, X, VXt); for (i = 0; i < X->m; i++) { for (j = i; j < X->m; j++) for (k = 0; k < X->n; k++) ME(out, i, j) += ME(X, i, k) * ME(VXt, k, j); for (j = 0; j <= i; j++) /* symmetry */ ME(out, i, j) = ME(out, j, i); } return out; } MAT *XdXt_mlt(MAT *X, VEC *d, MAT *out) { /* for a diagonal matrix in d, return X d X' */ int i, j, k; if (X==(MAT *)NULL || d==(VEC *)NULL ) ErrMsg(ER_IMPOSVAL, "XVXt_mlt"); if (X->n != d->dim) ErrMsg(ER_IMPOSVAL, "XVXt_mlt"); out = m_resize(out, X->n, X->n); m_zero(out); for (i = 0; i < X->m; i++) { for (j = i; j < X->m; j++) for (k = 0; k < X->n; k++) ME(out, i, j) += ME(X, i, k) * ME(X, j, k) * d->ve[k]; for (j = 0; j <= i; j++) /* symmetry */ ME(out, i, j) = ME(out, j, i); } return out; } MAT *XtdX_mlt(MAT *X, VEC *d, MAT *out) { /* for a diagonal matrix in d, return X' d X */ int i, j, k; if (X==(MAT *)NULL || d==(VEC *)NULL ) ErrMsg(ER_IMPOSVAL, "XtVX_mlt"); if (X->m != d->dim) ErrMsg(ER_IMPOSVAL, "XtVX_mlt"); out = m_resize(out, X->n, X->n); m_zero(out); for (i = 0; i < X->n; i++) { for (j = i; j < X->n; j++) for (k = 0; k < X->m; k++) ME(out, i, j) += ME(X, k, i) * ME(X, k, j) * d->ve[k]; for (j = 0; j <= i; j++) /* symmetry */ ME(out, i, j) = ME(out, j, i); } return out; } gstat/src/init.c0000644000176200001440000000435013777370515013313 0ustar liggesusers#include #include #include // for NULL #include extern SEXP gstat_init(SEXP s_debug_level); extern SEXP gstat_load_ev(SEXP np, SEXP dist, SEXP gamma); extern SEXP gstat_fit_variogram(SEXP fit, SEXP fit_sill, SEXP fit_range); extern SEXP gstat_exit(SEXP x); extern SEXP gstat_new_data(SEXP sy, SEXP slocs, SEXP sX, SEXP has_intercept, SEXP beta, SEXP nmax, SEXP nmin, SEXP maxdist, SEXP force, SEXP vfn, SEXP sw, SEXP grid, SEXP degree, SEXP is_projected, SEXP vdist, SEXP lambda, SEXP omax); extern SEXP gstat_new_dummy_data(SEXP loc_dim, SEXP has_intercept, SEXP beta, SEXP nmax, SEXP nmin, SEXP maxdist, SEXP vfn, SEXP is_projected, SEXP vdist); extern SEXP gstat_debug_level(SEXP level); extern SEXP gstat_load_variogram(SEXP s_ids, SEXP s_model, SEXP s_sills, SEXP s_ranges, SEXP s_kappas, SEXP s_anis_all, SEXP s_table, SEXP s_max_val); extern SEXP gstat_predict(SEXP sn, SEXP slocs, SEXP sX, SEXP block_cols, SEXP block, SEXP weights, SEXP nsim, SEXP blue); extern SEXP gstat_set_method(SEXP to); extern SEXP gstat_set_set(SEXP arg, SEXP val); extern SEXP gstat_set_merge(SEXP a, SEXP b, SEXP c, SEXP d); extern SEXP gstat_variogram(SEXP s_ids, SEXP cutoff, SEXP width, SEXP direction, SEXP cressie, SEXP dX, SEXP boundaries, SEXP grid, SEXP cov, SEXP pseudo); extern SEXP gstat_variogram_values(SEXP ids, SEXP pars, SEXP covariance, SEXP dist_values); extern SEXP gstat_get_variogram_models(SEXP dolong); #define CALLDEF(name, n) {#name, (DL_FUNC) &name, n} const static R_CallMethodDef R_CallDef[] = { CALLDEF(gstat_init, 1), CALLDEF(gstat_load_ev, 3), CALLDEF(gstat_fit_variogram, 3), CALLDEF(gstat_exit, 1), CALLDEF(gstat_new_data, 17), CALLDEF(gstat_new_dummy_data, 9), CALLDEF(gstat_debug_level, 1), CALLDEF(gstat_load_variogram, 8), CALLDEF(gstat_predict, 8), CALLDEF(gstat_set_method, 1), CALLDEF(gstat_set_set, 2), CALLDEF(gstat_set_merge, 4), CALLDEF(gstat_variogram, 10), CALLDEF(gstat_variogram_values, 4), CALLDEF(gstat_get_variogram_models, 1), {NULL, NULL, 0} }; void // attribute_visible // optional R_init_gstat(DllInfo *dll) { R_registerRoutines(dll, NULL, R_CallDef, NULL, NULL); R_useDynamicSymbols(dll, FALSE); R_forceSymbols(dll, TRUE); } gstat/src/pqueue.h0000644000176200001440000000166313777370515013665 0ustar liggesusers#define Q_BUFFER_SIZE 100 /* something more practical */ typedef struct { union { QTREE_NODE *n; DPOINT *p; } u; int is_node; /* is u the QTREE_NODE (1) or rather the DPOINT (0) ? */ double dist2; /* squared distance to target location */ } QUEUE_NODE; typedef struct q_element { struct q_element *next; QUEUE_NODE el; } Q_ELEMENT; typedef struct { int length, max_length; Q_ELEMENT *head, /* pointer to first element in queue, NULL if empty */ *empty; /* pointer to empty elements (a stack), NULL if none left */ int blocks; /* size of memory block */ Q_ELEMENT **block; /* pointers to malloc'ed memory blocks */ int (CDECL *cmp)(const QUEUE_NODE *a, const QUEUE_NODE *b); /* qsort-able element comparison function */ } QUEUE; QUEUE *init_queue(QUEUE *q, int (CDECL *cmp)(const QUEUE_NODE *a, const QUEUE_NODE *b)); QUEUE_NODE dequeue(QUEUE *q); void enqueue(QUEUE *q, QUEUE_NODE *qpt, int n); void free_queue(QUEUE *q); gstat/src/glvars.c0000644000176200001440000006025714314525262013643 0ustar liggesusers/* * glvars.c: has global variables, choose defaults, check setting integrity */ #include #include #include #include #include "defs.h" #include "userio.h" #include "debug.h" #include "data.h" #include "utils.h" #include "vario.h" #include "defaults.h" /* default values for gl_* variables */ #include "glvars.h" #include "gls.h" #include "block.h" /* * this module contains all global variables, along with some * routines for initialisation (of structures), resizing during runtime, * checks after reading command file and before starting real calculations, * obtaining some "local" global structures, printing all that's held, * and so on. get_n_vars() etc. are for clarity that these variables are not * changed outside the area where they're set. */ static void init_gstat_data(int n); static void clean_up(void); /* * global variables (glvars.h, defautls.h): */ int debug_level; /* debug level */ int gl_blas; int gl_choleski; /* do choleski instead of LDL? */ int gl_coincide; /* do the variable locations coincide? */ int gl_cressie; /* use cressie's estimator ? */ int gl_fit; /* do not fit a variogram */ int gl_gauss; /* gaussian quadr. block covariances ? */ int gl_iter; /* max. n. iter for mivque estimates */ int gl_jgraph; /* do jgraph plot in batch mode ? */ int gl_lhs; /* apply Latin hypercube sampling to Gaussian simulations */ int gl_longlat; /* indicates whether coordinates are longitude/latitude, or Euclidian */ int gl_nblockdiscr; /* block discrimination in each dimension */ int gl_n_intervals; /* n variogram intervals */ int gl_n_marginals; /* the n marginal distributions */ int gl_nsim; /* number of simultanious simulations */ int gl_n_uk; /* min. # of cs points to use ok */ int gl_numbers; /* plot numbers on variogram plot? */ int gl_nocheck; /* do not check LMC/IC ? */ int gl_order; /* do order relation correction */ int gl_plotweights; /* plot kriging weights? */ int gl_register_pairs; /* register sample variogram pairs? */ int gl_rowwise; /* deal with raster maps row-wise, or as complete blocks? */ int gl_rp; /* follow random path for gs/is? */ int gl_seed; /* seed is set? */ int gl_sim_beta; /* simulation mode for beta: 0 multiv GLS, 1 univ GLS, 2 OLS */ int gl_spiral; /* do spiral search if possible? */ int gl_split; /* see nsearch.c: was Q_SPLIT_AT */ int gl_sym_ev; /* default symmetric ps.cr.v./cr.cv. ? */ int gl_gls_residuals; /* calc. gls residuals? */ int gl_sparse; /* use sparse covariance matrices? */ int gl_xvalid; /* do cross validation on first variable */ int gl_zero_est; /* est. variogram at h 0 seperately? */ double *gl_bounds; /* boundaries semivariogram intervals */ double gl_cutoff; /* variogram cutoff */ double gl_fit_limit; /* convergence criterion on fit */ double gl_fraction; /* fraction of max dist for cutoff */ double gl_idp; /* default inverse distance power */ double gl_iwidth; /* variogram class width */ double gl_quantile; /* sample quantile */ double gl_zmap; /* height of the map */ double gl_alpha; /* alpha, beta, tol_[hor|ver]: anisotropy parameters */ double gl_beta; double gl_tol_hor; double gl_tol_ver; double gl_zero; /* zero tolerance; 2-squared */ const METHODS methods[] = { /* methods and codes */ { NSP, 0, "nsp" }, /* do nothing */ { UIF, 0, "ui" }, /* variogram modelling user interface */ { OKR, 0, "ok" }, /* ordinary kriging */ { UKR, 0, "uk" }, /* universal kriging */ { SKR, 0, "sk" }, /* simple kriging */ { IDW, 0, "id" }, /* inverse distance interpolation */ { MED, 0, "med" }, /* (local) sample median or quantiles */ { NRS, 0, "n$r" }, /* neighbourhood size */ { LSLM, 0, "tr$end" }, /* uncorrelated (or weighted) linear model */ { GSI, 1, "gs" }, /* gaussian (conditional) simulation */ { ISI, 1, "is" }, /* indicator (conditional) simulation */ { SEM, 0, "se$mivariogram" }, /* sample (cross) semivariance */ { COV, 0, "co$variogram" }, /* sample (cross) covariance */ { SPREAD, 0, "di$stance" }, /* distance to nearest sample */ { DIV, 0, "div" }, /* diversity and modus */ { SKEW, 0, "skew" }, /* skewness and kurtosis */ { LSEM, 0, "lsem" }, /* locally estimated/fitted variogram parameters */ { TEST, 0, "test" }, /* do-nothing? */ { NSP, 0, NULL } /* terminating field */ }; /* * "local" database, accesible through get_* functions */ static VARIOGRAM **vgm = NULL; static DATA **data = NULL; static char **outfile_names = NULL, **ids = NULL; static DATA *valdata = NULL; static DATA *data_area = NULL; /* area that discretises block */ static DPOINT block; static METHOD method = NSP; static int n_vars = 0; static int n_last = 0, n_v_last = 0, n_o_last = 0; static MODE mode = MODE_NSP; /* MODE_NSP, SIMPLE, STRATIFY or MULTIVARIABLE */ int init_global_variables(void) { /* * global variables init. (glvars.h; defautls.h): */ method = NSP; mode = MODE_NSP; debug_level = DB_NORMAL; gl_blas = DEF_blas; gl_choleski = DEF_choleski; gl_coincide = DEF_coincide; gl_cressie = DEF_cressie; gl_fit = DEF_fit; gl_gauss = DEF_gauss; gl_iter = DEF_iter; gl_jgraph = DEF_jgraph; gl_lhs = DEF_lhs; gl_longlat = DEF_longlat; gl_nblockdiscr = DEF_nblockdiscr; gl_n_intervals = DEF_intervals; gl_n_marginals = DEF_n_marginals; gl_nsim = DEF_nsim; gl_n_uk = DEF_n_uk; gl_numbers = DEF_numbers; gl_nocheck = DEF_nocheck; gl_order = DEF_order; gl_register_pairs = DEF_pairs; gl_rowwise = DEF_rowwise; gl_rp = DEF_rp; gl_seed = DEF_seed; gl_sim_beta = DEF_sim_beta; gl_spiral = DEF_spiral; gl_split = DEF_split; gl_sym_ev = DEF_sym_ev; gl_gls_residuals = DEF_gls_residuals; gl_sparse = DEF_sparse; gl_xvalid = DEF_xvalid; gl_zero_est = DEF_zero_est; gl_bounds = DEF_bounds; gl_cutoff = DEF_cutoff; gl_fit_limit = DEF_fit_limit; gl_fraction = DEF_fraction; gl_idp = DEF_idp; gl_iwidth = DEF_iwidth; gl_quantile = DEF_quantile; gl_zmap = DEF_zmap; gl_alpha = DEF_alpha; gl_beta = DEF_beta; gl_tol_hor = DEF_tol_hor; gl_tol_ver = DEF_tol_ver; gl_zero = DEF_zero; init_gstat_data(0); /* EJPXX * if (valdata == NULL) * */ valdata = init_one_data(valdata); block.x = block.y = block.z = 0.0; set_mv_double(&gl_zmap); get_covariance(NULL, 0, 0, 0); return 0; } void push_bound(double value) { static int n_bound; if (gl_bounds == NULL) { n_bound = 0; gl_bounds = (double *) emalloc((n_bound+2) * sizeof(double)); } else gl_bounds = (double *) erealloc(gl_bounds,(n_bound+2) * sizeof(double)); gl_bounds[n_bound] = value; gl_bounds[n_bound + 1] = -1.0; if (n_bound > 0 && gl_bounds[n_bound] <= gl_bounds[n_bound-1]) ErrMsg(ER_IMPOSVAL, "bounds must be strictly increasing"); n_bound++; } int n_variograms_set(void) { int i, n; for (i = 0, n = 0; i < get_n_vgms(); i++) if (vgm[i] != NULL && vgm[i]->id >= 0) n++; return n; } static void init_gstat_data(int n) { int i, n_vgms, n_outfl; n_vgms = (n * (n + 1))/2; n_outfl = n + n_vgms; if (n <= n_last) return; data = (DATA **) erealloc(data, n * sizeof(DATA *)); for (i = n_last; i < n; i++) data[i] = init_one_data(NULL); vgm = (VARIOGRAM **) erealloc(vgm, n_vgms * sizeof(VARIOGRAM *)); for (i = n_v_last; i < n_vgms; i++) vgm[i] = NULL; outfile_names = (char **) erealloc (outfile_names, n_outfl * sizeof(char *)); for (i = n_o_last; i < n_outfl; i++) outfile_names[i] = NULL; n_last = n; n_o_last = n_outfl; n_v_last = n_vgms; n_vars = n; return; } int which_identifier(const char *id) { assert(id); for (int i = 0; i < n_vars; i++) { if (ids[i] == NULL) ErrMsg(ER_IMPOSVAL, "which_identifier(): ids[i] == NULL"); if (strcmp(ids[i], id) == 0) return i; } /* else: extend data space */ n_vars++; ids = (char **) erealloc(ids, n_vars * sizeof(char *)); int Length = strlen(id) + 1; ids[n_vars - 1] = (char *) emalloc(Length * sizeof(char)); snprintf(ids[n_vars - 1], Length, "%s", id); init_gstat_data(n_vars); return n_vars - 1; } const char *name_identifier(int i) { static const char *cp_val = "data()", *cp_area = "area"; switch (i) { case ID_OF_VALDATA: return cp_val; case ID_OF_AREA: return cp_area; default: if (i >= get_n_vars() || i < 0) { pr_warning("i = %d", i); ErrMsg(ER_RANGE, "name_identifier(i): i outside range"); } return ids[i]; } } const char *method_string(METHOD i) { #define MSTR_SIZE 100 static char mstr[MSTR_SIZE]; char *str, *co, *un, *gsum = ""; if ((i == ISI || i == GSI) && gl_n_uk == DEF_n_uk && get_n_beta_set() != get_n_vars()) gsum = " with unknown means"; str = (get_mode() == STRATIFY ? "stratified " : ""); un = (get_n_vars() > 0 && data[0]->dummy ? "un" : ""); co = (get_mode() == MULTIVARIABLE ? "co" : ""); switch (i) { case NSP: snprintf(mstr, MSTR_SIZE, "exit"); break; case TEST: snprintf(mstr, MSTR_SIZE, "Test Option"); break; case UIF: snprintf(mstr, MSTR_SIZE, "starting interactive mode"); break; case SEM: snprintf(mstr, MSTR_SIZE, "calculating sample variogram"); break; case COV: snprintf(mstr, MSTR_SIZE, "calculating sample covariogram"); break; case SPREAD: snprintf(mstr, MSTR_SIZE, "spread value (distance to nearest observation) on output"); break; case IDW: snprintf(mstr, MSTR_SIZE, "%sinverse distance weighted interpolation", str); break; case MED: if (gl_quantile == 0.5) snprintf(mstr, MSTR_SIZE, "%smedian estimation", str); else snprintf(mstr, MSTR_SIZE, "%s%g-quantile estimation", str, gl_quantile); break; case NRS: snprintf(mstr, MSTR_SIZE, "(%s:) neighbourhood size on first output variable", str); break; case LSLM: if (n_variograms_set()) snprintf(mstr, MSTR_SIZE, "%sgeneralized least squares trend estimation", str); else snprintf(mstr, MSTR_SIZE, "%sordinary or weighted least squares prediction", str); break; case OKR: snprintf(mstr, MSTR_SIZE, "using %sordinary %skriging", str, co); break; case SKR: snprintf(mstr, MSTR_SIZE, "using %ssimple %skriging", str, co); break; case UKR: snprintf(mstr, MSTR_SIZE, "using %suniversal %skriging", str, co); break; case GSI: snprintf(mstr, MSTR_SIZE, "using %s%sconditional Gaussian %ssimulation%s", str, un, co, gsum); break; case ISI: snprintf(mstr, MSTR_SIZE, "using %s%sconditional indicator %ssimulation", str, un, co); break; case DIV: snprintf(mstr, MSTR_SIZE, "within-neighbourhood diversity and modus"); break; case SKEW: snprintf(mstr, MSTR_SIZE, "skewness and kurtosis"); break; case LSEM: snprintf(mstr, MSTR_SIZE, "local semivariance or locally fitted semivariogram parameters"); break; } return mstr; } int get_n_vars(void) { return n_vars; } int get_n_beta_set(void) { int i, nbeta; for (i = nbeta = 0; i < get_n_vars(); i++) if (data[i]->beta != NULL) nbeta++; return nbeta; } MODE get_mode(void) { return mode; } int get_n_vgms(void) { int n; n = get_n_vars(); return (n * (n + 1))/2; } int get_n_outputs(void) { return get_n_vars() + get_n_vgms(); } const char **get_outfile_name(void) { return (const char **) outfile_names; } VARIOGRAM *get_vgm(int i) { assert(i < get_n_vgms()); assert(i >= 0); if (vgm[i] == NULL) vgm[i] = init_variogram(NULL); return vgm[i]; } DATA **get_gstat_data(void) { return data; } DATA *get_dataval(void) { return valdata; } DATA *get_data_area(void) { return data_area; } DATA *create_data_area(void) { data_area = init_one_data(NULL); return data_area; } DPOINT *get_block_p(void) { return █ } METHOD get_method(void) { return method; } void set_method(METHOD m) { method = m; return; } int is_simulation(METHOD m) { assert(methods[m].m == m); return methods[m].is_simulation; } double max_block_dimension(int reset) { static double dim = -1.0; if (reset) dim = -1.0; if (dim < 0.0) { if (data_area != NULL) dim = data_block_diagonal(data_area); else dim = sqrt(SQR(block.x)+SQR(block.y)+SQR(block.z)); } return dim; } void setup_valdata_X(DATA *d) { /* * fills '0'-X columns (intercept) at the right place * e.g. data(a): .. X=1&2;data(b): .. X=3&4; data(): .. X=1&2&3&4; * this leads to "0 1 2 3 4" for colX, but should be "0 1 2 0 3 4"; */ int i = 0, j = 0, n_d, n_all; /* * # positive X's in all variables should equal # positive X's in this */ for (i = 0, n_all = 0; i < get_n_vars(); i++) for (j = 0; j < data[i]->n_X; j++) if (data[i]->colX[j] > 0) n_all++; for (i = 0, n_d = 0; i < d->n_X; i++) if (d->colX[i] > 0) n_d++; if (n_all != n_d) { pr_warning( "nr of X's in data: (%d) should match X's in other data(...) (%d)", n_d, n_all); ErrMsg(ER_IMPOSVAL, "X column definition mismatch"); } /* * now correct for 0's */ for (i = 0, n_all = 0; i < get_n_vars(); i++) n_all += data[i]->n_X; if (n_all == d->n_X) return; /* we're done */ n_d = d->n_X; d->n_X = n_all; d->colX = (int *) realloc(d->colX, d->n_X * sizeof(int)); /* fill backwards */ for (i = get_n_vars() - 1; i >= 0; i--) { for (j = data[i]->n_X - 1; j >= 0; j--) { n_all--; /* position of current X in d */ if (data[i]->colX[j] <= 0) /* intercept, x, xy, x2, etc. */ d->colX[n_all] = data[i]->colX[j]; else { n_d--; if (n_d < 0) ErrMsg(ER_IMPOSVAL, "setup_X(): n_d < 0"); if (d->colX[n_d] == 0) ErrMsg(ER_IMPOSVAL, "setup_X(): zero error"); d->colX[n_all] = d->colX[n_d]; } if (n_all < 0) ErrMsg(ER_IMPOSVAL, "setup_X(): n_all < 0"); } } return; } METHOD get_default_method(void) { int i, Xset, Vgm_set; /* * no no prediction locations or no data: */ if (get_n_vars() == 0) return NSP; if (valdata->id < 0 && gl_xvalid == 0 && data_area == NULL) { return UIF; } /* * check on X variables */ for (i = Xset = 0; i < get_n_vars(); i++) if (!(data[i]->n_X == 1 && data[i]->colX[0] == 0)) Xset++; /* * check on variograms */ for (i = 0, Vgm_set = 0; i < get_n_vars(); i++) if (vgm[LTI(i,i)] != NULL && (vgm[LTI(i,i)]->n_models > 0 || vgm[LTI(i,i)]->table != NULL)) /* was: ->id >= 0*/ Vgm_set++; if (!(Vgm_set == 0 || Vgm_set == get_n_vars())) ErrMsg(ER_SYNTAX, "set either all or no variograms"); if (Vgm_set > 0) { if (get_n_beta_set() > 0) return SKR; else return (Xset > 0 ? UKR : OKR); } else return (Xset > 0 ? LSLM : IDW); } void set_mode(void) { int i, j, check_failed = 0; if (method == NSP) return; /* * simple, univariate: */ if (get_n_vars() <= 1) { mode = SIMPLE; return; } /* * (get_n_vars() > 1): * multivariable prediction if all cross variograms set parameters merge */ for (i = check_failed = 0; i < get_n_vars(); i++) for (j = 0; j < i; j++) if (vgm[LTI(i,j)] == NULL || vgm[LTI(i,j)]->id < 0) check_failed = 1; if (check_failed == 0) { mode = MULTIVARIABLE; return; } if (n_variograms_set() == 0) { for (i = 0; i < get_n_vars(); i++) if (data[i]->n_merge > 0) { mode = MULTIVARIABLE; return; } } /* * stratify? ONLY if: * 0. get_n_vars() > 1; no cross variograms set ==>> has been checked. * 1. no pred(): or var(): except for first variable; * 2. No masks and valdata->what_is_u == U_ISSTRATUM * 3. mask is a valid strata map, n categories > 1 */ mode = (valdata->what_is_u == U_ISSTRATUM) ? STRATIFY : SIMPLE; return; } int decide_on_coincide(void) { int i, j; if (get_n_vars() <= 1) return 0; if (get_mode() == STRATIFY) return 0; /* data may coincide, but prediction locations won't */ for (i = 1; i < get_n_vars(); i++) { if (data[i]->n_list != data[0]->n_list || data[i]->colnx != data[0]->colnx || data[i]->colny != data[0]->colny || data[i]->colnz != data[0]->colnz || data[i]->sel_min != data[0]->sel_min || data[i]->sel_max != data[0]->sel_max || data[i]->force != data[0]->force || data[i]->sel_rad != data[0]->sel_rad) return 0; /* don't check filename: 'file.dat' and './file.dat' */ /* * Consider the data file * 1 2 NA 3 * 2 3 4 NA * with x=1, y=2, v=3 (for var 1), v=4 (for var 2). * This is only distinguishable by doing it the ``hard way'': */ for (j = 0; j < data[0]->n_list; j++) { if (data[0]->list[j]->x != data[i]->list[j]->x || data[0]->list[j]->y != data[i]->list[j]->y || data[0]->list[j]->z != data[i]->list[j]->z) return 0; } } if (DEBUG_DUMP) printlog("(identical search conditions found for all variables)\n"); return 1; } void check_global_variables(void) { /* * Purpose : check internal variable consistency, add some parameters * Created by : Edzer J. Pebesma * Date : april 13, 1992 * Prerequisites : none * Returns : - * Side effects : none * also check Cauchy-Schwartz unequality on cross/variograms. */ int i, j, n_merge = 0; METHOD m; VARIOGRAM *v_tmp; /* UK: check if n_masks equals total nr of unbiasedness cond. */ if (gl_nblockdiscr < 2) ErrMsg(ER_RANGE, "nblockdiscr must be >= 2"); if (method == SPREAD) { for (i = 0; i < get_n_vars(); i++) if (data[i]->sel_rad == DBL_MAX) data[i]->sel_rad *= 0.99; /* force distance calculation */ } if (get_n_beta_set() != 0 && get_n_beta_set() != get_n_vars()) ErrMsg(ER_SYNTAX, "set sk_mean or beta either for all or for no variables"); if (!(method == ISI || method == GSI)) { if (gl_nsim > 1) ErrMsg(ER_IMPOSVAL, "nsim only allowed for simulation"); } if (method == ISI && max_block_dimension(0) > 0.0) ErrMsg(ER_IMPOSVAL, "indicator simulation only for points"); /* * check if both block and area are set */ if (data_area != NULL && (block.x > 0.0 || block.y > 0.0 || block.z > 0.0)) ErrMsg(ER_IMPOSVAL, "both block and area set: choose one"); /* * check for equality of coordinate dimensions: */ for (i = 1; i < get_n_vars(); i++) { if ((data[i]->mode & V_BIT_SET) != (data[0]->mode & V_BIT_SET)) { message("data(%s) and data(%s):\n", name_identifier(0), name_identifier(i)); ErrMsg(ER_IMPOSVAL, "data have different coordinate dimensions"); } } if (valdata->id > 0 && data[0]->dummy == 0 && ((data[0]->mode | (V_BIT_SET | S_BIT_SET)) != (valdata->mode | (V_BIT_SET | S_BIT_SET)))) { message("data() and data(%s):\n", name_identifier(0)); ErrMsg(ER_IMPOSVAL, "data have different coordinate dimensions"); for (i = 0; i < get_n_vars(); i++) { if (data[i]->dummy) { data[i]->mode = (valdata->mode | V_BIT_SET); data[i]->minX = valdata->minX; data[i]->minY = valdata->minY; data[i]->minZ = valdata->minZ; data[i]->maxX = valdata->maxX; data[i]->maxY = valdata->maxY; data[i]->maxZ = valdata->maxZ; set_norm_fns(data[i]); } } } for (i = 0; i < get_n_vars(); i++) { if (data[i]->fname == NULL && !data[i]->dummy) { message("file name for data(%s) not set\n", name_identifier(i)); ErrMsg(ER_NULL, " "); } if (data[i]->id < 0) { message("data(%s) not set\n", name_identifier(i)); ErrMsg(ER_NULL, " "); } if (data[i]->beta && data[i]->beta->size != data[i]->n_X) { pr_warning("beta dimension (%d) should equal n_X (%d)", data[i]->beta->size, data[i]->n_X); ErrMsg(ER_IMPOSVAL, "sizes of beta and X don't match"); } if (data[i]->sel_rad == DBL_MAX && data[i]->oct_max > 0) ErrMsg(ER_IMPOSVAL, "define maximum search radius (rad) for octant search"); if (data[i]->vdist && data[i]->sel_rad == DBL_MAX) ErrMsg(ER_IMPOSVAL, "when using vdist, radius should be set"); if (! data[i]->dummy && ! (data[i]->mode & V_BIT_SET)) { message("no v attribute set for data(%s)\n", name_identifier(data[i]->id)); ErrMsg(ER_NULL, " "); } if (method != SEM && method != COV) { /* check neighbourhood settings */ if (data[i]->sel_rad < 0.0 || data[i]->sel_min < 0 || data[i]->sel_max < 0 || (data[i]->sel_min > data[i]->sel_max)) { message( "invalid neighbourhood selection: radius %g max %d min %d\n", data[i]->sel_rad, data[i]->sel_max, data[i]->sel_min); ErrMsg(ER_IMPOSVAL, " "); } } if (data[i]->id > -1 && (method == OKR || method == SKR || is_simulation(method) || method == UKR)) { if (vgm[LTI(i,i)] == NULL || vgm[LTI(i,i)]->id < 0) { message("variogram(%s) not set\n", name_identifier(i)); ErrMsg(ER_VARNOTSET, "variogram()"); } } n_merge += data[i]->n_merge; } if (n_merge && get_mode() != MULTIVARIABLE) ErrMsg(ER_IMPOSVAL, "merge only works in multivariable mode"); if (mode == SIMPLE && get_method() != UIF) { /* check if it's clean: */ for (i = 0; i < get_n_vars(); i++) for (j = 0; j < i; j++) if (vgm[LTI(i,j)] != NULL && vgm[LTI(i,j)]->id > 0) { message("variogram(%s, %s) %s\n", name_identifier(i), name_identifier(j), "can only be set for ck, cs, uk, sk, ok, sem or cov"); ErrMsg(ER_IMPOSVAL, "variogram()"); } } if ((m = get_default_method()) != get_method()) { if (m == UKR && (get_method() == OKR || get_method() == SKR)) ErrMsg(ER_IMPOSVAL, "\nremove X=... settings for ordinary or simple kriging"); if (m == OKR && get_method() == SKR) ErrMsg(ER_IMPOSVAL, "method: something's terribly wrong!"); if (m == OKR && get_method() == UKR) { message("I would recommend:\n"); message("Do not specify uk if ok is all you'll get\n"); } } if (mode == MULTIVARIABLE && get_method() != UIF && get_method() != SEM && get_method() != COV && n_variograms_set() > 0) check_variography((const VARIOGRAM **) vgm, get_n_vars()); v_tmp = init_variogram(NULL); free_variogram(v_tmp); } void remove_all(void) { while (n_vars) remove_id(0); /* hard way */ /* for (i = n_vars-1; i >= 0; i--) remove_id(i); */ /* remove_id(n_vars - 1); */ /* the hard way; remove_id(n_vars-1) would be the ``easy'' alternative */ gls(NULL, 0, GLS_INIT, NULL, NULL); /* cleans up static arrays */ reset_block_discr(); /* resets block settings */ max_block_dimension(1); /* reset */ if (gl_bounds != NULL) { efree(gl_bounds); gl_bounds = NULL; } if (valdata != NULL) free_data(valdata); valdata = NULL; } int remove_id(const int id) { /* * remove id id, and reset data, vgm, ids, outfile_names */ int i, j, id_new, id_old; VARIOGRAM *vp; assert(id >= 0 && id < n_vars); /* reset data */ free_data(data[id]); data[id] = NULL; for (i = id; i < n_vars - 1; i++) { data[i] = data[i+1]; data[i]->id = i; } for (i = 0; i < n_vars; i++) { j = LTI(i,id); if (vgm[j]) { free_variogram(vgm[j]); vgm[j] = NULL; } } /* copy variograms: */ for (i = id; i < n_vars - 1; i++) { for (j = id; j <= i; j++) { id_new = LTI(i,j); id_old = LTI(i+1,j+1); vp = vgm[id_new] = vgm[id_old]; if ((vp != NULL) && (vp->id1 >= 0 || vp->id2 >= 0)) { vp->id1 = i; vp->id2 = j; vp->id = id_new; } } } /* reset identifiers: */ efree(ids[id]); for (i = id; i < n_vars - 1; i++) ids[i] = ids[i+1]; /* free outfilenames */ if (outfile_names[2 * id]) { efree(outfile_names[2 * id]); outfile_names[2 * id] = NULL; } if (outfile_names[2 * id + 1]) { efree(outfile_names[2 * id + 1]); outfile_names[2 * id + 1] = NULL; } /* shift pred(xx)/variances(xx) names: */ for (i = id; i < n_vars - 1; i++) { outfile_names[2 * i] = outfile_names[2 * (i + 1)]; outfile_names[2 * i + 1] = outfile_names[2 * (i + 1) + 1]; } /* shift covariances(xx): */ for (i = id; i < n_vars - 1; i++) { id_old = 2 * n_vars + LTI2(i,id); if (outfile_names[id_old]) { efree(outfile_names[id_old]); outfile_names[id_old] = NULL; } for (j = id; j < i; j++) { id_new = 2 * (n_vars - 1) + LTI2(i,j); id_old = 2 * n_vars + LTI2(i+1,j+1); outfile_names[id_new] = outfile_names[id_old]; } } n_vars -= 1; if (n_vars == 0) clean_up(); init_gstat_data(n_vars); /* reset sizes */ return n_vars; } static void clean_up(void) { /* free variograms */ if (vgm) { efree(vgm); vgm = NULL; } /* free data */ if (data) { efree(data); data = NULL; } /* free valdata */ if (valdata) { free_data(valdata); valdata = NULL; } /* free data_area */ if (data_area) { free_data(data_area); data_area = NULL; } /* free outfile names */ if (outfile_names) { efree(outfile_names); outfile_names = NULL; } /* free identifiers */ if (ids) { efree(ids); ids = NULL; } n_vars = 0; n_last = 0; n_v_last = 0; n_o_last = 0; mode = MODE_NSP; } gstat/src/nsearch.c0000644000176200001440000005246414314525262013771 0ustar liggesusers/* This software module is copyright 1997 (c): Steve Joyce mailto:steve.joyce@resgeom.slu.se Remote Sensing Laboratory http://www-umea.slu.se/~fjasj/ Dept. of Forest Resource Mgmt. & Geomatics Tel: +46 90 16 69 57 Swedish University of Agricultural Sciences Fax: +46 90 14 19 15 S-901 83 Umea, Sweden Distributed freely under the terms of the GNU General Public License as a component of: Gstat, a program for geostatistical modelling, prediction and simulation Copyright 1992-2009 (C) Edzer J. Pebesma Edzer J. Pebesma (E.Pebesma@geo.uu.nl) Landscape and environmental research group Faculty of geographical sciences University of Amsterdam Nieuwe Prinsengracht 130 1018 VZ Amsterdam -- The Netherlands */ /* * qtree.c: quick neighbourhood selection routines for gstat */ /* * Edzer's CHANGE LOG from Steve's original contribution: * converted most float to double; * bbox size initialization -1.0 * added some ErrMsg() error message checks * changed qtree_quick_select() call (DPOINTX disappeared) * made is_leaf(node) a macro; removed max_ppnode -> Q_SPLIT_AT * added flexible 1/2/3d tree support: detect from data->mode; * added bbox.mode field; * modified routines like in_bbox, sub_bbox to detect tree dimension * qtree_free(): node->n_node should be N_NODES(node) * init_qtree is now called from qtree_quick_select() * added bbox_from_* routines * added get_index macro: searching is not required * added qtree_print() functions * might have missed some. * (after 2.0:) * Q_SPLIT_AT -> gl_split * implemented the priority queue mechanism, see PR bucket quad trees * demonstrated at http://www.cs.umd.edu/~brabec/quadtree/index.html. * (this enables efficient search when only max is defined, i.e. without * a radius -- especially in case of simulation this seems really * efficient) * removed min_bbox -->> this became obsolete with the priority queue * * I guess many of my modifications assume you have sufficient memory, * and that you want to use it to speed things up. */ #include #include /* qsort() */ #include /* sqrt() */ #include /* DBL_MAX */ #include /* INT_MAX */ #include "defs.h" #include "userio.h" #include "debug.h" #include "data.h" #include "utils.h" #include "glvars.h" /* get_method(), name_identifier() */ #include "mapio.h" #include "nsearch.h" #include "pqueue.h" /* include _after_ search.h! */ #define N_NODES(x) (x==NULL?0:(-((x)->n_node))) /* a negative n_node means it's not a leaf */ /* * this is a 'tuning' parameter defining the number of points in * a quad before it is split into 4 * #define Q_SPLIT_AT 4 */ /* * another tuning parameter defining the minimum quad size allowed. * (multiplied by d->sel_rad) #define Q_STOP_AT 0.5 (now obsolete) */ #define is_leaf(node) (((node) == NULL) || (((node)->n_node) >= 0)) #define is_qtree_search(d) (d->qtree_root != NULL) #define get_index(pt, bb) \ ((pt->x >= bb.x + 0.5 * bb.size) | \ (((bb.mode & Y_BIT_SET) && (pt->y >= bb.y + 0.5 * bb.size)) << 1) | \ (((bb.mode & Z_BIT_SET) && (pt->z >= bb.z + 0.5 * bb.size)) << 2)) static void init_qtree(DATA *d); static void init_qnode(QTREE_NODE **p_node, int is_leaf, BBOX bb); static void qtree_push(DPOINT *p, QTREE_NODE **p_node, int recursion_depth); static BBOX sub_bbox(const BBOX bb, int i); static int in_bbox(const DPOINT *p, BBOX bb); static void qtree_split_node(QTREE_NODE *node, BBOX bb, int rec_level); static QTREE_NODE *qtree_expand(const DPOINT *p, QTREE_NODE *root); static QTREE_NODE **qtree_find_node(const DPOINT *p, QTREE_NODE **p_node, BBOX *bbox); void qtree_print(DATA *d); static void logprint_qtree(QTREE_NODE *node, int depth); static BBOX bbox_from_grid(const GRIDMAP *gt, const DATA_GRIDMAP *dg); static BBOX bbox_from_data(DATA *d); static void qtree_zero_all_leaves(QTREE_NODE *node); static int CDECL node_cmp(const QUEUE_NODE *a, const QUEUE_NODE *b); void logprint_queue(QUEUE *queue); static void init_qtree(DATA *d) { /* * Initialize the root of the search tree: * Since this is called from qtree_quick_select(), we know allready * quite a lot. This helps choosing sensible values for the * top level bbox origin and size. */ const GRIDMAP *gt = NULL; DATA *simlocs = NULL; int i, mode; BBOX bbox; if (is_simulation(get_method())) { /* * sequential simulation: the simulation path (through DATA or GRIDMAP) * will make up for (most of) the search locations: */ gt = (const GRIDMAP *) NULL; simlocs = get_dataval(); /* in case of simulation one of them will be non-NULL */ } /* get initial estimate for top level bbox: */ if (gt != NULL) bbox = bbox_from_grid(gt, NULL); else if (simlocs != NULL) { bbox = bbox_from_data(simlocs); if (bbox.size <= 0.0) bbox = bbox_from_data(d); } else bbox = bbox_from_data(d); if (bbox.size <= 0.0) bbox = bbox_from_data(get_dataval()); if (bbox.size <= 0.0) ErrMsg(ER_IMPOSVAL, "bbox with zero size: remove neighbourhood settings?"); init_qnode(&(d->qtree_root), d->n_list < gl_split, bbox); /* ML1 */ mode = bbox.mode; for (i = 0; i < d->n_list; i++) qtree_push_point(d, d->list[i]); /* now they won't be rejected */ /* ML2 */ if (DEBUG_DUMP) { printlog("top level search tree statistics for data(%s):\n", name_identifier(d->id)); printlog("bounding box origin ["); if (mode & X_BIT_SET) printlog("%g", d->qtree_root->bb.x); if (mode & Y_BIT_SET) printlog(",%g", d->qtree_root->bb.y); if (mode & Z_BIT_SET) printlog(",%g", d->qtree_root->bb.z); printlog("]; dimension %g\n", d->qtree_root->bb.size); } /* qtree_print(d); */ return; } static void init_qnode(QTREE_NODE **p_node, int isleaf, BBOX bb) { /* * initialize a node in the search tree. * bb.mode tells the dimension of the tree (1D/2D/3D) */ int i; if (*p_node == NULL) { *p_node = (QTREE_NODE *) emalloc(sizeof(QTREE_NODE)); /* ML1 */ (*p_node)->bb = bb; } if (isleaf) (*p_node)->n_node = 0; else { if (bb.mode & Z_BIT_SET) /* 3D: oct-tree */ (*p_node)->n_node = -8; else if (bb.mode & Y_BIT_SET) /* 2D: quad-tree */ (*p_node)->n_node = -4; else if (bb.mode & X_BIT_SET) /* 1D: binary tree */ (*p_node)->n_node = -2; else /* no x/y/z bit set...??? */ ErrMsg(ER_IMPOSVAL, "init_qnode: invalid mode"); (*p_node)->u.node = (QTREE_NODE **) emalloc(N_NODES(*p_node) * sizeof(QTREE_NODE *)); for (i = 0; i < N_NODES(*p_node); i++) (*p_node)->u.node[i] = NULL; } return; } void qtree_push_point(DATA *d, DPOINT *where) { /* add a single point to the search tree structure in d->qtree_root */ /* * do not do this while reading the data: suppose we'll never need * a neighbourhood selection after all! */ if (! is_qtree_search(d)) return; /* min_bbox = d->sel_rad * Q_STOP_AT; */ /* * if this point is outside the current search tree, * we need to add another level to the top and try again: */ while (! in_bbox(where, d->qtree_root->bb)) d->qtree_root = qtree_expand(where, d->qtree_root); /* * finally push the point onto the tree: */ qtree_push(where, &(d->qtree_root), 0); return; } static void qtree_push(DPOINT *where, QTREE_NODE **p_node, int recursion_depth) { /* add a data point to the quad tree starting at the node specified. */ QTREE_NODE **p_leaf, *node; BBOX bb; bb = (*p_node)->bb; recursion_depth += 1; /* printf("recursion_depth: %d, max %d\n", recursion_depth, MAX_RECURSION_DEPTH); */ /* find the leaf node where this point belongs */ p_leaf = qtree_find_node(where, p_node, &bb); if (*p_leaf == NULL) init_qnode(p_leaf, 1, bb); /* leaf == 1: sets ->n_node to 0 */ node = *p_leaf; /* If it is already full, split it into another level and try again: */ if (node->n_node == gl_split && recursion_depth < MAX_RECURSION_DEPTH) { qtree_split_node(node, (*p_node)->bb, recursion_depth); qtree_push(where, &node, recursion_depth); return; } /* XXX */ if (node->n_node == 0) node->u.list = (DPOINT **) emalloc(sizeof(DPOINT *)); else node->u.list = (DPOINT **) erealloc(node->u.list, (node->n_node + 1) * sizeof(DPOINT *)); /* ML2 */ node->u.list[node->n_node] = where; node->n_node++; return; } void qtree_pop_point(DPOINT *where, DATA *d) { int i; QTREE_NODE *node, **p_node; /* delete a point from the search tree */ if (! is_qtree_search(d)) /* don't bother */ return; p_node = qtree_find_node(where, &(d->qtree_root), NULL); if (*p_node == NULL) ErrMsg(ER_IMPOSVAL, "qtree_pop_point(): could not find node"); node = *p_node; for (i = 0; i < node->n_node; i++) { if (where == node->u.list[i]) { /* don't preserve order: copy last to this one: */ node->u.list[i] = node->u.list[node->n_node - 1]; break; /* from for loop */ } } node->n_node--; /* free memory if empty list: */ if (node->n_node == 0) { efree(node->u.list); efree(node); *p_node = NULL; } return; } void qtree_free(QTREE_NODE *node) { /* * If a push or search fails, you might want to consider getting rid of * whole tree and default to exhaustive search. (SJ) * [If you ever get so far, exhaustive search will take * a nearly infinite amount of time. Instead, tweek gl_split. --EJP] */ int i; if (node == NULL) return; if (!is_leaf(node)) { for (i = 0; i < N_NODES(node); i++) qtree_free(node->u.node[i]); efree(node->u.node); } else efree(node->u.list); efree(node); return; } static void qtree_split_node(QTREE_NODE *node, BBOX bbox, int rec_level) { /* * split the quadtree at 'node' and redistribute its points */ DPOINT **list; int i, n; /* first copy the points to a temporary location and free the pointers */ n = node->n_node; list = node->u.list; /* save temporary copy */ /* make a node from this leaf, overwrite u: */ init_qnode(&node, 0, bbox); /* redistribute the points into the child nodes where they belong */ for (i = 0; i < n; i++) qtree_push(list[i], &node, rec_level); efree(list); return; } static QTREE_NODE *qtree_expand(const DPOINT *where, QTREE_NODE *root) { /* * expand the top level of the search tree */ QTREE_NODE *new_top = NULL; DPOINT old_centre; BBOX old_bb, new_bb; int i; old_bb = root->bb; old_centre.x = old_centre.y = old_centre.z = 0.0; if (old_bb.mode & X_BIT_SET) old_centre.x = old_bb.x + old_bb.size / 2.0; if (old_bb.mode & Y_BIT_SET) old_centre.y = old_bb.y + old_bb.size / 2.0; if (old_bb.mode & Z_BIT_SET) old_centre.z = old_bb.z + old_bb.size / 2.0; new_bb = old_bb; /* * set the new bounding box: Steve, could you check this? * (I didn't grasp your original bbox setting here:) * * set the root bbox to the new_top bbox: */ if ((old_bb.mode & X_BIT_SET) && (where->x < old_bb.x)) new_bb.x -= old_bb.size; if ((old_bb.mode & Y_BIT_SET) && (where->y < old_bb.y)) new_bb.y -= old_bb.size; if ((old_bb.mode & Z_BIT_SET) && (where->z < old_bb.z)) new_bb.z -= old_bb.size; new_bb.size *= 2.0; /* link the old root node to the proper spot in new_top: */ init_qnode(&new_top, 0, old_bb); i = get_index((&old_centre), new_bb); new_top->u.node[i] = root; new_top->bb = new_bb; /* make this one the new root */ return new_top; } static QTREE_NODE **qtree_find_node(const DPOINT *where, QTREE_NODE **p_node, BBOX *bb) { /* * find the deepest leaf (end node) in the tree that bounds this point's * coordinates. * It's bounding box is saved in the location pointed to by p_bbox */ int i; if (is_leaf(*p_node)) return p_node; /* find in which node we are: */ i = get_index(where, (*p_node)->bb); if (bb != NULL) *bb = sub_bbox(*bb, i); /* recurse into this node: */ return qtree_find_node(where, &((*p_node)->u.node[i]), bb); } static BBOX sub_bbox(const BBOX bbox, int index) { /* * return the bounding box of a quad-tree child node based on the index * layout of octree index: * * | dz <= 0 dz > 0 * --------|-------------------- * dy > 0 | 2 3 6 7 * dy <= 0 | 0 1 4 5 * | * dx ? 0 | <= > <= > */ double size; BBOX b; b = bbox; b.size = size = bbox.size / 2.0; if (index & X_BIT_SET) /* 1, 3, 5, 7 */ b.x += size; if (index & Y_BIT_SET) /* 2, 3, 6, 7 */ b.y += size; if (index & Z_BIT_SET) /* 4, 5, 6, 7 */ b.z += size; return b; } static int in_bbox(const DPOINT *where, BBOX bbox) { /* * check if where is inside the bounding box: * _on_ the left/lower/downside boundary or is inside the box */ if ((bbox.mode & X_BIT_SET) && ((where->x < bbox.x) || (where->x >= bbox.x + bbox.size))) return 0; if ((bbox.mode & Y_BIT_SET) && ((where->y < bbox.y) || (where->y >= bbox.y + bbox.size))) return 0; if ((bbox.mode & Z_BIT_SET) && ((where->z < bbox.z) || (where->z >= bbox.z + bbox.size))) return 0; /* so, where apparently in ... */ return 1; } /* * pb_norm2_?D() functions: * calculate shortest (squared) euclidian distance from a point to a BBOX, * for ? being 1, 2 or 3 dimensions */ double pb_norm_1D(const DPOINT *where, BBOX bbox) { double x, dx; x = where->x; if (x < bbox.x) { dx = bbox.x - x; return dx * dx; } bbox.x += bbox.size; if (x > bbox.x) { dx = x - bbox.x; return dx * dx; } return 0.0; /* inside box */ } double pb_norm_2D(const DPOINT *where, BBOX bbox) { double x, y, dx = 0.0, dy = 0.0; x = where->x; y = where->y; if (x < bbox.x) dx = bbox.x - x; else { bbox.x += bbox.size; if (x > bbox.x) dx = x - bbox.x; } if (y < bbox.y) dy = bbox.y - y; else { bbox.y += bbox.size; if (y > bbox.y) dy = y - bbox.y; } return dx * dx + dy * dy; } double pb_norm_3D(const DPOINT *where, BBOX bbox) { double x, y, z, dx = 0.0, dy = 0.0, dz = 0; x = where->x; y = where->y; z = where->z; if (x < bbox.x) dx = bbox.x - x; else { bbox.x += bbox.size; if (x > bbox.x) dx = x - bbox.x; } if (y < bbox.y) dy = bbox.y - y; else { bbox.y += bbox.size; if (y > bbox.y) dy = y - bbox.y; } if (z < bbox.z) dz = bbox.z - z; else { bbox.z += bbox.size; if (z > bbox.z) dz = z - bbox.z; } return dx * dx + dy * dy + dz * dz; } void qtree_print(DATA *d) { /* * plot the full tree (2D), in a format that can be read by jgraph, found * at netlib or at http://kenner.cs.utk.edu/~plank/plank/jgraph/jgraph.html */ printlog("newgraph\nxaxis size 3\nyaxis size 3\n"); printlog("title : %s [n = %d]\n", name_identifier(d->id), d->n_list); logprint_qtree(d->qtree_root, 0); return; } static void logprint_qtree(QTREE_NODE *node, int depth) { BBOX b; int i; if (node == NULL) return; b = node->bb; if (!is_leaf(node)) { printlog("newline linethickness 0.3 pts %g %g %g %g %g %g %g %g %g %g\n", b.x, b.y, b.x+b.size, b.y, b.x+b.size, b.y+b.size, b.x, b.y+b.size, b.x, b.y); for (i = 0; i < N_NODES(node); i++) logprint_qtree(node->u.node[i], depth+1); } else { printlog("newline pts %g %g %g %g %g %g %g %g %g %g\n", b.x, b.y, b.x+b.size, b.y, b.x+b.size, b.y+b.size, b.x, b.y+b.size, b.x, b.y); /* if (node == NULL) printlog("newcurve marktype circle fill 1 pts %g %g\n", b.x+0.5*b.size, b.y+0.5*b.size); */ if (node->n_node > 0) { printlog("newcurve marktype cross pts"); for (i = 0; i < node->n_node; i++) printlog(" %g %g", node->u.list[i]->x, node->u.list[i]->y); printlog("\n"); } } } static BBOX bbox_from_grid(const GRIDMAP *gt, const DATA_GRIDMAP *dg) { /* derive a sensible top level bounding box from grid map topology */ double sizex, sizey; BBOX bbox; if (gt) { sizex = gt->cols * gt->cellsizex; sizey = gt->rows * gt->cellsizey; bbox.x = gt->x_ul; bbox.y = gt->y_ul - sizey; /* * bbox.size should be set to such a value that the smallest * leaf fits exactly over 4 grid map cells */ bbox.size = MIN(gt->cellsizex, gt->cellsizey); } else { sizex = dg->cols * dg->cellsizex; sizey = dg->rows * dg->cellsizey; bbox.x = dg->x_ul; bbox.y = dg->y_ul - sizey; bbox.size = MIN(dg->cellsizex, dg->cellsizey); } bbox.z = DBL_MAX; while (bbox.size < MAX(sizex, sizey)) bbox.size *= 2; bbox.mode = (X_BIT_SET | Y_BIT_SET); /* i.e. 3 */ return bbox; } static BBOX bbox_from_data(DATA *d) { /* derive a sensible top level bounding box from a data var */ double maxspan, dy, dz; BBOX bbox; if (d->grid) return bbox_from_grid(NULL, d->grid); bbox.x = d->minX; bbox.y = d->minY; bbox.z = d->minZ; bbox.mode = d->mode; /* ??? */ /* bbox.mode = d->mode & (X_BIT_SET|Y_BIT_SET|Z_BIT_SET); maxspan = MAX((d->maxX-d->minX), MAX((d->maxY-d->minY),(d->maxZ-d->minZ))); */ maxspan = fabs(d->maxX - d->minX); dy = fabs(d->maxY - d->minY); if (dy > maxspan) maxspan = dy; dz = fabs(d->maxZ - d->minZ); if (dz > maxspan) maxspan = dz; /* with d->grid_size entered by user: if (d->grid_size > 0.0) { bbox.x -= 0.5 * d->grid_size; bbox.y -= 0.5 * d->grid_size; bbox.z -= 0.5 * d->grid_size; bbox.size = d->grid_size; do { bbox.size *= 2; } while (bbox.size < (maxspan + d->grid_size)); } */ bbox.size = maxspan * 1.01; return bbox; } static void qtree_zero_all_leaves(QTREE_NODE *node) { int i; if (!is_leaf(node)) { for (i = 0; i < N_NODES(node); i++) qtree_zero_all_leaves(node->u.node[i]); } else if (node != NULL) node->n_node = 0; return; } void qtree_rebuild(DATA *d) { /* rebuild tree */ int i; QTREE_NODE **p_leaf, *leaf; if (d->n_list <= 0 || d->qtree_root == NULL) return; qtree_zero_all_leaves(d->qtree_root); for (i = 0; i < d->n_list; i++) { p_leaf = qtree_find_node(d->list[i], &(d->qtree_root), NULL); leaf = *p_leaf; leaf->u.list[leaf->n_node] = d->list[i]; leaf->n_node++; } return; } static DPOINT *get_nearest_point(QUEUE *q, DPOINT *where, DATA *d) { /* * returns the first (closest) DPOINT in the priority queue q, after all * unwinding necessary (which is effectively recursion into the tree). * * this and the following functions: Copyright (GPL) 1998 Edzer J. Pebesma */ QUEUE_NODE head, *el = NULL /* temporary storage */ ; QTREE_NODE *node; int i, n; while (q->length > 0) { /* try: */ /* logprint_queue(q); */ head = dequeue(q); if (! head.is_node) { /* nearest element is a point: */ if (el != NULL) efree(el); return head.u.p; } node = head.u.n; if (is_leaf(node)) { /* ah, the node dequeued is a leaf: */ /* printf("node->n_node: %d\n", node->n_node); */ if (node->n_node > 0) el = (QUEUE_NODE *) erealloc(el, node->n_node * sizeof(QUEUE_NODE)); for (i = 0; i < node->n_node; i++) { /* enqueue it's DPOINT's: */ el[i].is_node = 0; el[i].u.p = node->u.list[i]; el[i].dist2 = node->u.list[i]->u.dist2 = d->pp_norm2(where, node->u.list[i]); } n = node->n_node; } else { /* nope, but enqueue its sub-nodes: */ if (N_NODES(node) > 0) el = (QUEUE_NODE *) erealloc(el, N_NODES(node) * sizeof(QUEUE_NODE)); for (i = n = 0; i < N_NODES(node); i++) { if (node->u.node[i] != NULL) { el[n].is_node = 1; el[n].u.n = node->u.node[i]; el[n].dist2 = d->pb_norm2(where, node->u.node[i]->bb); n++; } } } if (n > 0) enqueue(q, el, n); } /* the while-loop terminates when the queue is empty */ if (el != NULL) efree(el); return NULL; } void logprint_queue(QUEUE *queue) { Q_ELEMENT *q; QUEUE_NODE *e; printlog("current priority queue size: %d\n", queue->length); for (q = queue->head; q != NULL; q = q->next) { e = &(q->el); printlog("%s %12.6g", e->is_node ? "Node at " : "Point at", sqrt(e->dist2)); if (e->is_node) printlog(" [xll=%g,yll=%g,size=%g] (with %d %s)\n", e->u.n->bb.x, e->u.n->bb.y, e->u.n->bb.size, ABS(e->u.n->n_node), e->u.n->n_node < 0 ? "nodes" : "points"); else printlog(" [index %d, value %g]\n", GET_INDEX(e->u.p), e->u.p->attr); } } static int CDECL node_cmp(const QUEUE_NODE *a, const QUEUE_NODE *b) { /* ANSI qsort() conformant comparison function */ if (a->dist2 < b->dist2) return -1; if (a->dist2 > b->dist2) return 1; /* equal distances: prefer DPOINT over a node to speed up things */ if (a->is_node != b->is_node) return (a->is_node ? 1 : -1); return 0; } int qtree_select(DPOINT *where, DATA *d) { DPOINT *p = NULL; static QUEUE *q = NULL; static QUEUE_NODE root; int sel_max; double rad2; /* if this is the first time calling with this d: */ if (d->qtree_root == NULL) init_qtree(d); root.is_node = 1; root.u.n = d->qtree_root; root.dist2 = 0.0; q = init_queue(q, node_cmp); enqueue(q, &root, 1); if (d->sel_rad >= DBL_MAX) { /* * simply get the d->sel_max nearest: */ for (d->n_sel = 0; d->n_sel < d->sel_max; d->n_sel++) d->sel[d->n_sel] = get_nearest_point(q, where, d); } else { /* * also consider a maximum distance to where */ if (d->vdist) /* select everything within sel_rad; cut later on */ sel_max = INT_MAX; else sel_max = d->sel_max; rad2 = d->sel_rad * d->sel_rad; d->n_sel = 0; while (d->n_sel < sel_max) { p = get_nearest_point(q, where, d); if (p != NULL && p->u.dist2 <= rad2) { /* accept this point */ d->sel[d->n_sel] = p; d->n_sel++; } else break; /* reject, and break while loop */ } if (d->n_sel < d->sel_min) { /* * d->sel_min was set: consider points beyond radius */ if (d->force) /* proceed beyond d->sel_rad */ while (d->n_sel < d->sel_min) { if (p != NULL) { d->sel[d->n_sel] = p; p = get_nearest_point(q, where, d); d->n_sel++; } else { /* a zero d->n_sel will result in a missing value */ d->n_sel = 0; break; } } else /* stop: a zero d->n_sel will result in a missing value */ d->n_sel = 0; } } return d->n_sel; } gstat/src/mtrx.c0000644000176200001440000003016014314525262013325 0ustar liggesusers/* interface roughly follows meschach; implementation rewritten from scratch */ #include /* memcpy, memset */ #include /* fabs */ #define USE_FC_LEN_T #include #ifndef FCONE # define FCONE #endif #include #include "defs.h" /* CDECL */ #include "utils.h" /* efree, emalloc */ #include "userio.h" /* ErrMsg */ #include "glvars.h" /* gl_blas */ #include "debug.h" #include "mtrx.h" /* get rid of -0.000000 output: */ #define _zero_(x) (fabs(x) < 1.e-7 ? 0.0 : x) /* 0. book keeping: initialisation, memory allocation, zero, copy, print */ void m_free(MAT *m) { efree(m->v); efree(m); } void v_free(VEC *v) { efree(v->ve); efree(v); } void iv_free(IVEC *iv) { efree(iv->ive); efree(iv); } void px_free(PERM *p) { efree(p->pe); efree(p); } MAT *m_init(void) { MAT *mat = emalloc(sizeof(MAT)); mat->n = mat->m = mat->max = 0; mat->v = (double *) NULL; return(mat); } MAT *m_resize(MAT *mat, size_t m, size_t n) { if (mat == MNULL) mat = m_init(); if (m * n > mat->max) { mat->max = m * n; mat->v = (double *) erealloc(mat->v, mat->max * sizeof(double)); /* takes care of NULL m */ } mat->m = m; mat->n = n; return(mat); } VEC *v_init(void) { VEC *v = emalloc(sizeof(VEC)); v->dim = v->max = 0; v->ve = NULL; return(v); } VEC *v_resize(VEC *v, size_t n) { if (v == NULL) v = v_init(); if (n > v->max) { v->ve = erealloc(v->ve, n * sizeof(double)); v->max = n; } v->dim = n; return(v); } PERM *p_init(void) { PERM *p = emalloc(sizeof(PERM)); p->size = p->max = 0; p->pe = (int *) NULL; return(p); } PERM *px_resize(PERM *p, size_t n) { if (p == PNULL) p = p_init(); if (n > p->max) { p->pe = erealloc(p->pe, n * sizeof(size_t)); p->max = n; } p->size = n; return(p); } IVEC *iv_init(void) { IVEC *iv = emalloc(sizeof(IVEC)); iv->size = iv->max = 0; iv->ive = (int *) NULL; return(iv); } IVEC *iv_resize(IVEC *iv, size_t n) { if (iv == IVNULL) iv = iv_init(); if (n > iv->max) { iv->ive = erealloc(iv->ive, n * sizeof(int)); iv->max = n; } iv->size = n; return(iv); } MAT *m_zero(MAT *m) { if (m != MNULL) memset(m->v, 0x00, m->m * m->n * sizeof(double)); return(m); } VEC *v_zero(VEC *v) { if (v != VNULL) memset(v->ve, 0x00, v->dim * sizeof(double)); return(v); } MAT *m_copy(MAT *in, MAT *out) { if (in == out) return(out); out = m_resize(out, in->m, in->n); memcpy(out->v, in->v, in->m * in->n * sizeof(double)); return(out); } VEC *v_copy(VEC *in, VEC *out) { if (in == out) return(out); out = v_resize(out, in->dim); memcpy(out->ve, in->ve, in->dim * sizeof(double)); return(out); } void m_logoutput(MAT * a) { unsigned int i, j, tmp; if (a == (MAT *) NULL) { printlog("#Matrix: NULL\n"); return; } printlog("#Matrix: %d by %d\n", a->m, a->n); if (a->v == NULL) { printlog("NULL\n"); return; } printlog("rbind(\n"); for (i = 0; i < a->m; i++) { /* for each row... */ printlog("c("); for (j = 0, tmp = 2; j < a->n; j++, tmp++) { /* for each col in row: */ printlog("%9f", _zero_(ME(a, i, j))); if (j + 1 < a->n) printlog(", "); else printlog(")"); } if (i + 1 < a->m) printlog(", "); else printlog(" "); printlog("# row %u\n", i + 1); } printlog(")\n"); } void v_logoutput(VEC * x) { unsigned int i, tmp; if (x == (VEC *) NULL) { printlog("#Vector: NULL\n"); return; } printlog("#Vector: dim: %d\n", x->dim); if (x->ve == NULL) { printlog("NULL\n"); return; } printlog("c("); for (i = 0, tmp = 0; i < x->dim; i++, tmp++) { printlog("%9f", _zero_(x->ve[i])); if (i + 1 < x->dim) printlog(", "); } printlog(")"); } /* 1: vector-scalar, vector-vector (BLAS-1) */ VEC *sv_mlt(double s, VEC *v, VEC *out) { /* out <- s * v */ out = v_resize(out, v->dim); for (int i = 0; i < v->dim; i++) out->ve[i] = s * v->ve[i]; return(out); } double v_norm2(VEC *v) { /* 2-norm */ return(in_prod(v, v)); } VEC *v_add(VEC *v1, VEC *v2, VEC *out) { /* out = v1 + v2 */ if (v1->dim != v2->dim) ErrMsg(ER_IMPOSVAL, "v_sub size mismatch"); out = v_resize(out, v1->dim); for (int i = 0; i < out->dim; i++) out->ve[i] = v1->ve[i] + v2->ve[i]; return(out); } VEC *v_sub(VEC *v1, VEC *v2, VEC *out) { /* out = v1 - v2 = -1 * v2 + v1 */ if (v1->dim != v2->dim) ErrMsg(ER_IMPOSVAL, "v_sub size mismatch"); out = v_resize(out, v1->dim); for (int i = 0; i < out->dim; i++) out->ve[i] = v1->ve[i] - v2->ve[i]; return(out); } double in_prod(VEC *a, VEC *b) { /* a'b */ if (a->dim != b->dim) ErrMsg(ER_IMPOSVAL, "in_prod: dimensions don't match"); if (! gl_blas) { double d = 0.0; for (int i = 0; i < a->dim; i++) d += a->ve[i] * b->ve[i]; return(d); } else { int one = 1; return(F77_CALL(ddot)((int *) &(a->dim), a->ve, &one, b->ve, &one)); } } /* 2: vector-matrix (BLAS-2) */ VEC *vm_mlt(MAT *m, VEC *v, VEC *out) { /* out <- v m */ if (m->m != v->dim) ErrMsg(ER_IMPOSVAL, "vm_mlt: dimensions"); out = v_zero(v_resize(out, m->n)); if (! gl_blas) { for (size_t i = 0; i < m->n; i++) for (size_t j = 0; j < v->dim; j++) out->ve[i] += v->ve[j] * ME(m, j, i); } else { double alpha = 1.0, beta = 0.0; int one = 1; F77_CALL(dgemv)("T", (int *) &(m->m), (int *) &(m->n), &alpha, m->v, (int *) &(m->m), v->ve, &one, &beta, out->ve, &one FCONE); } return(out); } VEC *mv_mlt(MAT *m, VEC *v, VEC *out) { /* out <- m v */ if (v == out) ErrMsg(ER_IMPOSVAL, "mv_mlt in situ"); if (m->n != v->dim) ErrMsg(ER_IMPOSVAL, "mv_mlt non-matching sizes"); out = v_zero(v_resize(out, m->m)); if (! gl_blas) { for (int j = 0; j < m->m; j++) for (int i = 0; i < m->n; i++) out->ve[j] += ME(m, j, i) * v->ve[i]; } else { double alpha = 1.0, beta = 0.0; int one = 1; F77_CALL(dgemv)("N", (int *) &(m->m), (int *) &(m->n), &alpha, m->v, (int *) &(m->m), v->ve, &one, &beta, out->ve, &one FCONE); } return(out); } /* 3: matrix-matrix (BLAS-3) */ MAT *m_mlt(MAT *m1, MAT *m2, MAT *out) { /* out <- m1 %*% m2 */ if (m1->n != m2->m) ErrMsg(ER_IMPOSVAL, "mv_mlt non-matching sizes"); if (! gl_blas) { out = m_zero(m_resize(out, m1->m, m2->n)); for (int i = 0; i < m1->m; i++) for (int j = 0; j < m2->n; j++) for (int k = 0; k < m1->n; k++) ME(out, i, j) += ME(m1, i, k) * ME(m2, k, j); } else { double alpha = 1.0, beta = 0.0; out = m_resize(out, m1->m, m2->n); F77_CALL(dgemm)("N", "N", (int *) &(m1->m), (int *) &(m2->n), (int *) &(m1->n), &alpha, m1->v, (int *)&(m1->m), m2->v, (int *)&(m2->m), &beta, out->v, (int *) &(m1->m) FCONE FCONE); } return(out); } MAT *mtrm_mlt(MAT *m1, MAT *m2, MAT *out) { /* out <- t(m1) %*% m2 */ if (m1->m != m2->m) ErrMsg(ER_IMPOSVAL, "mtrm_mlt non-matching m arrays"); out = m_zero(m_resize(out, m1->n, m2->n)); if (! gl_blas) { for (int i = 0; i < m1->n; i++) for (int j = 0; j < m2->n; j++) for (int k = 0; k < m1->m; k++) ME(out, i, j) += ME(m1, k, i) * ME(m2, k, j); } else { double alpha = 1.0, beta = 0.0; F77_CALL(dgemm)("T", "N", (int *) &(m1->n), (int *) &(m2->n), (int *) &(m1->m), &alpha, m1->v, (int *)&(m1->m), m2->v, (int *)&(m2->m), &beta, out->v, (int *) &(m1->n) FCONE FCONE); } return(out); } MAT *mmtr_mlt(MAT *m1, MAT *m2, MAT *out) { /* out <- m1 m2' */ if (m1->n != m2->n) ErrMsg(ER_IMPOSVAL, "mmtr_mlt non-matching m arrays"); out = m_zero(m_resize(out, m1->m, m2->m)); if (! gl_blas) { for (int i = 0; i < m1->m; i++) for (int j = 0; j < m2->m; j++) for (int k = 0; k < m1->n; k++) ME(out, i, j) += ME(m1, i, k) * ME(m2, j, k); } else { double alpha = 1.0, beta = 0.0; F77_CALL(dgemm)("N", "T", (int *) &(m1->m), (int *) &(m2->m), (int *) &(m1->n), &alpha, m1->v, (int *)&(m1->m), m2->v, (int *)&(m2->m), &beta, out->v, (int *) &(m1->m) FCONE FCONE); } return(out); } MAT *ms_mltadd(MAT *m1, MAT *m2, double s, MAT *out) { /* out <- m1 + s * m2 */ /* return m1 + s * m2 */ if (m1->m != m2->m || m1->n != m2->n) ErrMsg(ER_IMPOSVAL, "ms_mltadd: dimension mismatch"); out = m_resize(out, m1->m, m1->n); for (int j = 0; j < m1->n; j++) for (int i = 0; i < m1->m; i++) ME(out, i, j) = ME(m1, i, j) + s * ME(m2, i, j); return(out); } MAT *sm_mlt(double s, MAT *m1, MAT *out) { /* out <- s * m1 */ out = m_resize(out, m1->m, m1->n); for (int j = 0; j < m1->n; j++) for (int i = 0; i < m1->m; i++) ME(out, i, j) = s * ME(m1, i, j); return(out); } MAT *m_add(MAT *m1, MAT *m2, MAT *out) { /* out <- m1 + m2 */ if (m1->m != m2->m || m1->n != m2->n) ErrMsg(ER_IMPOSVAL, "m_add size mismatch"); out = m_resize(out, m1->m, m1->n); for (int j = 0; j < m1->n; j++) for (int i = 0; i < m1->m; i++) ME(out, i, j) = ME(m1, i, j) + ME(m2, i, j); return(out); } MAT *m_sub(MAT *m1, MAT *m2, MAT *out) { /* out <- m1 - m2 */ if (m1->m != m2->m || m1->n != m2->n) ErrMsg(ER_IMPOSVAL, "m_sub size mismatch"); out = m_resize(out, m1->m, m1->n); for (int j = 0; j < m1->n; j++) for (int i = 0; i < m1->m; i++) ME(out, i, j) = ME(m1, i, j) - ME(m2, i, j); return(out); } /* 4: matrix factorisation, solving systems of equations */ MAT *CHfactor(MAT *m, PERM *piv, int *info) { if (m->m != m->n) error("CHfactor: 'm' must be a square matrix"); for (int i = 1; i < m->m; i++) for (int j = 0; j < i; j++) ME(m, i, j) = 0.0; /* zero lower triangle of Fortran order */ if (piv == PNULL) { /* Choleski: */ F77_CALL(dpotrf)("Upper", (int *)&(m->n), m->v, (int *)&(m->n), info, (FC_LEN_T) 5); if (*info != 0) { if (*info > 0 && DEBUG_COV) warning("the leading minor of order %d is not positive definite", *info); if (*info < 0) error("argument %d of Lapack routine %s had invalid value", -(*info), "dpotrf"); } } else { /* LDL': */ if (piv->size != m->n) error("CHfactor: 'piv' must have dimension equal to m->n"); double w, *work; /* first query for size of work, then allocate work, then factorize m: */ int lwork = -1; F77_CALL(dsytrf)("Upper", (int *)&(m->n), m->v, (int *)&(m->n), (int *) piv->pe, &w, &lwork, info, (FC_LEN_T) 5); lwork = (int) w; work = emalloc(lwork * sizeof(double)); F77_CALL(dsytrf)("Upper", (int *)&(m->n), m->v, (int *)&(m->n), (int *) piv->pe, work, &lwork, info, (FC_LEN_T) 5); efree(work); if (*info != 0) { if (*info > 0 && DEBUG_COV) warning("D[%d,%d] is exactly zero, meaning that D is singular", *info, *info); if (*info < 0) error("argument %d of Lapack routine %s had invalid value", -(*info), "dsytrf"); } } return(m); } MAT *CHsolve(MAT *m, MAT *b, MAT *out, PERM *piv) { /* solve A X = B after factorizing A */ int info; if (m->m != m->n) error("CHsolve: 'm' must be a square matrix"); if (m->m != b->m) error("CHsolve: b does not match m"); out = m_copy(b, out); /* column-major */ if (piv == PNULL) /* Choleski */ F77_CALL(dpotrs)("Upper", (int *) &(m->m), (int *) &(b->n), m->v, (int *) &(m->m), out->v, (int *) &(m->m), &info, (FC_LEN_T) 5); else /* LDL' */ F77_CALL(dsytrs)("Upper", (int *) &(m->m), (int *) &(b->n), m->v, (int *) &(m->m), piv->pe, out->v, (int *) &(m->m), &info, (FC_LEN_T) 5); if (info < 0) error("CHsolve: argument %d of Lapack routine %s had invalid value", -info, piv == NULL ? "dpotrs" : "dsytrs"); return(out); } VEC *CHsolve1(MAT *m, VEC *b, VEC *out, PERM *piv) { /* solve A x = b after factorizing A */ int one = 1, info; if (m->m != m->n) error("CHsolve1: 'm' must be a square matrix"); if (m->m != b->dim) error("CHsolve1: vector b does not match m"); out = v_copy(b, out); if (piv == PNULL) F77_CALL(dpotrs)("U", (int *) &(m->m), (int *) &one, m->v, (int *) &(m->m), out->ve, (int *) &(m->m), &info FCONE); else F77_CALL(dsytrs)("L", (int *) &(m->m), (int *) &one, m->v, (int *) &(m->m), piv->pe, out->ve, (int *) &(m->m), &info FCONE); if (info < 0) error("CHsolve1: argument %d of Lapack routine %s had invalid value", -info, piv == NULL ? "dpotrs" : "dsytrs"); return(out); } MAT *m_inverse(MAT *in, int *info) { /* out <- in^{-1} */ PERM *piv = px_resize(PNULL, in->m); in = CHfactor(in, piv, info); if (*info != 0) { /* singular */ px_free(piv); return(in); } MAT *rhs = m_zero(m_resize(MNULL, in->m, in->m)); for (int i = 0; i < rhs->m; i++) ME(rhs, i, i) = 1.0; rhs = CHsolve(in, rhs, rhs, piv); in = m_copy(rhs, in); m_free(rhs); px_free(piv); return(in); } gstat/src/data.h0000644000176200001440000002677113777370515013301 0ustar liggesusers#ifndef DATA_H # define DATA_H /* avoid multiple inclusion */ #include /* INT_MAX */ #include /* FLT_MAX */ #define ID_OF_VALDATA INT_MAX #define ID_OF_AREA (INT_MAX-1) #define IS_GLOBAL(d) (d->sel_rad >= DBL_MAX && d->sel_max >= INT_MAX) #define DELIMITERS " \t,\n\r" #define N_POLY 18 #define POLY_MIN (-19) /* lowest index */ #define POLY_X (-19) #define POLY_Y (-18) #define POLY_Z (-17) #define POLY_X2 (-16) #define POLY_Y2 (-15) #define POLY_Z2 (-14) #define POLY_XY (-13) #define POLY_XZ (-12) #define POLY_YZ (-11) #define POLY_X3 (-10) #define POLY_Y3 (-9) #define POLY_Z3 (-8) #define POLY_X2Y (-7) #define POLY_XY2 (-6) #define POLY_X2Z (-5) #define POLY_XZ2 (-4) #define POLY_Y2Z (-3) #define POLY_YZ2 (-2) /* -1 is reserved for "no intercept" */ typedef struct { int poly_nr; char *name; int degree, mode; } POLY_NM; typedef struct { /* structure to hold one point value: */ double x, y, z, /* x, y and z coordinate */ variance, /* the attribute's variance */ attr; /* attribut value (data value) */ union { float dist2; /* squared distance to estimate point */ float weight; /* weight in block discretization */ int stratum; /* stratum of current point in data() list */ } u; double *X; /* row entry in X matrix for this DPOINT */ unsigned int bitfield; /* most right bit: IS_POINT (0) or IS_BLOCK (1), remaining left bits: index of this point in d->list */ } DPOINT; /* qtree_search structs (nsearch.c): */ typedef struct { /* defining a rectangular bounding box */ double x, y, z, size; int mode; } BBOX; typedef struct qnode { /* the struct used to define nodes in the search tree */ int n_node; /* >= 0: number of data points in this node */ /* negative (-1) if u is a node list */ union { struct qnode **node;/* pointers to 4 or 8 other nodes */ DPOINT **list; /* or pointers to data points within this leaf */ } u; BBOX bb; } QTREE_NODE; typedef struct { double x_ul, y_ul, cellsizex, cellsizey; unsigned int rows, cols; DPOINT ***dpt, /* 2d array to (DPOINT *) entries in list */ **grid_base; /* base of blocked memory allocation */ } DATA_GRIDMAP; /* the management summary */ /* polygon structs: */ typedef struct { double x, y; } PLOT_POINT; typedef struct { PLOT_POINT min, max; } MBR; typedef struct polygon { MBR mbr; int lines; PLOT_POINT *p; int close; /* 1 - is closed polygon */ } POLYGON; typedef enum { DATA_UNKNOWN = 0, DATA_ASCII_TABLE, /* ascii table */ DATA_EAS, /* simplified GeoEAS format */ DATA_IDRISI_VEC, /* idrisi .vec */ DATA_IDRISI32_VEC, /* idrisi .vct */ DATA_IDRISI_BIN, /* Idrisi .img binary */ DATA_IDRISI_ASCII, /* Idrisi .img ascii */ DATA_IDRISI32_BIN, /* Idrisi32 .rst binary */ DATA_IDRISI32_ASCII,/* Idrisi32 .rst ascii */ DATA_GRIDASCII, /* ArcInfo */ DATA_GRIDFLOAT, /* ArcInfo */ DATA_CSF, /* PCRaster */ DATA_T2, /* Mike-SHE grid format */ DATA_ERMAPPER, /* ER-Mapper raster dataset */ DATA_GNUPLOT, /* gnuplot binary grid */ DATA_GMT, /* GMT netCDF format */ DATA_SURFER_DSAA, /* Surfer DSAA ascii grid */ DATA_GSLIB, /* GSLIB ascii grid */ DATA_GRASS, /* GRASS site list */ DATA_GRASS_GRID, /* GRASS raster */ DATA_GDAL, /* GDAL raster */ DATA_EXT_DBASE /* CW external database */ } DATA_TYPE_; typedef struct { DATA_TYPE_ type; const char *name; } DATA_TYPE; extern const DATA_TYPE data_types[]; typedef struct { int to_var, /* merge from current data to this variable */ col_this_X, /* merge this column number */ col_other_X; /* to this column number in the other variable */ } MERGE_TABLE; typedef struct { int size, max_size; double *val; } D_VECTOR; D_VECTOR *push_d_vector(double d, D_VECTOR *v); void free_d_vector(D_VECTOR *v); /* CW added, FTTB copies of DATA members * SEARCH_CRITERIA should become part of DATA * Dit zijn degene die ik begrijp */ typedef struct { /* DATA::prob sample later */ int force, /* force neighbourhood selection */ sel_min, sel_max, /* min and max number for neighbourhood selection */ oct_max, /* max # pts for each octant; 0: use no octant search */ oct_filled, /* RETURN VALUE? number of non-empty octants in selection */ square; /* use square search neighbourhood, default circular */ double sel_rad; /* radius for neighbourhhood selection */ }SEARCH_CRITERIA; typedef struct { /* structure that holds data info and lists */ char *variable, /* attr name, log(..) */ *x_coord, /* name of x coordinate */ *y_coord, /* name of y coordinate */ *z_coord, /* name of z coordinate */ *s_coord, /* name of stratum variable */ *V_coord, /* name of variance */ *Category, /* category value, for indicator transform */ *id_name, /* name of ID column*/ *fname, /* file name */ **point_ids, /* IDs of points */ *var_fn_str, /* VarFunction string */ *nscore_table; /* normal score table output file name */ DATA_TYPE type; /* what is this file? */ int id, /* id of data, number in command file */ n_list, /* # points in list */ n_original, /* # real data (read from file, not simulated) */ n_sel, /* # of points in selection: sel */ n_max, /* maximum # in list */ nsim_at_data, /* nr. of pts at simulation locations */ init_max, /* user-specified maximum n (to save memory) */ n_sel_max, /* maximum number in sel */ n_X, *colX, /* number and columns in X matrix */ log, /* is attr.value log-transformed ? */ force, /* force neighbourhood selection */ vdist, /* use variogram value as distance crit. */ n_averaged, /* number of averaged data so far */ colnx, colny, colnz, /* column-numbers */ colnvariance, /* column that holds variance */ colnvalue, /* column that holds attribute values */ colns, /* column that holds u (if strata) */ coln_id, /* column with ID */ sel_min, sel_max, /* min and max number for neighbourhood selection */ oct_max, /* max # pts for each octant; 0: use no octant search */ oct_filled, /* number of non-empty octants in selection */ mode, /* mode: 1(x),2(y),3(xy),4(z),5(xz).. */ dummy, /* is this variable a dummy variable? */ standard, /* if standard: data are standardized by dividing all values by data->std */ calc_residuals, /* 1: do calculate OLS residuals for vgm est */ is_residual, /* attr values are residuals lm X */ polynomial_degree, /* degree of coordinate polynomial */ togrid, /* shift data values to grid centres */ square, /* use square search neighbourhood */ centre, /* centre area + points() at area centre? */ region, /* select data in region? */ average, /* average measurements at identical location? */ every, /* sample only every x-th observation */ offset, skip, /* starting at offset */ datatype, /*KS added what idrisi data type 0=integer,1=real 1/18/99*/ filetype; /*KS added what idrisi file type 0=ascii,1=binary 1/18/99*/ enum { U_UNKNOWN, U_ISDIST, U_ISWEIGHT, U_ISSTRATUM } what_is_u; double sel_rad, /* radius for neighbourhhood selection */ Icutoff, /* cutoff value for indicator variable: */ /* colnvalue = ("real value" <= Icutoff) */ minX, maxX, minY, maxY, minZ, maxZ, /* min/max of coordinates */ minvariance, maxvariance, /* min/max variance */ mv, /* missing value */ dX, /* max. vector norm X-space distance */ prob, /* inclusion probability (to sample data file) */ lambda; /* lambda value for box-cox transform */ int minstratum, maxstratum; /* min/max stratum */ double mean, std; /* sample mean and st.dev. of attribute */ /* CW members to hold data in this struct (DATA_TYPE!= DATA_EXT_DBASE) */ DPOINT **list; /* list of data points, of length n_list */ DPOINT *P_base; /* base for pointer array, if allocated blockwise */ DPOINT **sel; /* list of selection indices, of length n_sel */ double (*point_norm)(const DPOINT *); /* eucl. vector length */ double (*pp_norm2)(const DPOINT *, const DPOINT *); /* point-point squared distance */ double (*pb_norm2)(const DPOINT *, BBOX); /* point-BBOX distance: nsearch.c */ double (*variance_fn)(double mu); /* variance function */ double *X_base; /* base pointer for X arrays, when allocated blockwise */ void *lm, /* cast to LM *, see lm.h */ *glm; /* remember: several matrices/vecs needed in gls.c */ /* next 2 entries are for merging regressors across variables */ /* to avoid double references, each entry var should be less than ->id */ int n_merge; /* merge_table size */ MERGE_TABLE *mtbl; /* entries in merge table */ QTREE_NODE *qtree_root; /* a tree-based structure with pointers to list[] for fast neighbourhood search */ /* POLYGON *poly; */ /* where the polygons go */ #ifdef WITH_SPIRAL SPIRAL *spiral; /* spiral search index structure */ #endif DATA_GRIDMAP *grid; /* grid map topology if data was read from a map */ D_VECTOR *beta; } DATA; #define X_BIT_SET 1 /* also used in nsearch.c */ #define Y_BIT_SET 2 #define Z_BIT_SET 4 #define V_BIT_SET 8 #define S_BIT_SET 16 #define D_HAS_WEIGHT(d) (d->what_is_u == U_ISWEIGHT) #define D_HAS_DIST(d) (d->what_is_u == U_ISDIST) #define D_HAS_STRATA(d) (d->colnu && d->what_is_u == U_ISSTRATA) /* following routines do not depend on sizeof(int) (K&R II, p. 48, 49) */ #define left_bits(x) ((x) >> 1) /* shift one, zero most left bit */ /* #define right_bit(x) ((x) & ~(~0 << 1)) */ /* zero all except right bit */ #define right_bit(x) ((x) & ~((unsigned long)~0 << 1)) #define set_right_bit_on(x) (x = (x) | 1) #define set_right_bit_off(x) (x = (x) & ((unsigned long)~0 << 1)) #define set_left_bits(x,val) (x = ((unsigned long)val << 1) | right_bit(x)) #define GET_INDEX(p) (left_bits((p)->bitfield)) #define SET_INDEX(p,val) (set_left_bits((p)->bitfield,val)) #define IS_BLOCK(p) (right_bit((p)->bitfield)) #define IS_POINT(p) (!right_bit((p)->bitfield)) #define SET_BLOCK(p) (set_right_bit_on((p)->bitfield)) #define SET_POINT(p) (set_right_bit_off((p)->bitfield)) #if defined(__cplusplus) extern "C" { #endif DATA *read_gstat_data(DATA *d); DATA *get_area_centre(DATA *area, DATA *valdata); void centre_area(DATA *area); void push_point(DATA *d, const DPOINT *p); void pop_point(DATA *d, int list_nr); void free_data(DATA *tmp); #define print_data_list(d) print_data(d, 1) #define print_data_selection(d) print_data(d, 0) void print_data(const DATA *d, int list); void logprint_point(const DPOINT *p, const DATA *d); DATA *init_one_data(DATA *data); int coordinates_are_equal(const DATA *a, const DATA *b); void init_data_minmax(void); void setup_data_minmax(DATA *d); void calc_polynomials(DATA *d); double calc_polynomial(DPOINT *p, int colX); char *print_data_line(const DATA *d, char **to); extern const POLY_NM polynomial[N_POLY]; #define POLY_NAME(i) polynomial[i - POLY_MIN].name #define POLY_DEGREE(i) polynomial[i - POLY_MIN].degree void data_add_X(DATA *d, int i); int push_to_merge_table(DATA *d, int to_var, int col_this_X, int col_other_X); DATA_GRIDMAP *gsetup_gridmap(double x_ul, double y_ul, double cellsizex, double cellsizey, unsigned int rows, unsigned int cols); void datagrid_rebuild(DATA *d, int adjust_to_gridcentres); void set_norm_fns(DATA *d); double data_block_diagonal(DATA *data); int intercept_only(const DATA *d); double v_mu(double mu); double v_mu2(double mu); double v_mu3(double mu); double v_bin(double mu); double v_identity(double mu); void setup_polynomial_X(DATA *d); void calc_polynomial_point(DATA *d, DPOINT *pt); double pp_norm_gc(const DPOINT *a, const DPOINT *b); void free_data_gridmap(DATA_GRIDMAP *t); #if defined(__cplusplus) } #endif #endif /* DATA_H */ gstat/src/select.h0000644000176200001440000000004713777370515013633 0ustar liggesusersint select_at(DATA *d, DPOINT *where); gstat/src/utils.c0000644000176200001440000000472113777370515013512 0ustar liggesusers/* * utils.c: error checking functions for file, memory and string handling */ #include /* free(), malloc() etc */ #include /* tolower(), isspace() */ #include /* strlen(), memcmp() */ #include "defs.h" #include "userio.h" #include "utils.h" #include "glvars.h" #include "debug.h" void efree(void *p) { if (p == NULL) pr_warning("efree(): NULL pointer as argument"); else /* there's little point in calling free(NULL) */ free(p); } void *emalloc(size_t size) { void *p = NULL; if (size == 0) { pr_warning("emalloc(): size 0 requested"); return NULL; } p = (void *) malloc(size); if (p == NULL) { if (DEBUG_DUMP) message("malloc(%u) returned NULL", size); ErrMsg(ER_MEMORY, ""); } return p; } void *ecalloc(size_t nobj, size_t size) { void *p = NULL; if (size == 0) { pr_warning("ecalloc(): size 0 requested"); return NULL; } p = (void *) calloc(nobj, size); if (p == NULL) { if (DEBUG_DUMP) message("calloc(%u,%u) returned NULL", nobj, size); ErrMsg(ER_MEMORY, ""); } return p; } void *erealloc(void *p, size_t size) { if (size == 0) { pr_warning("erealloc(): size 0 requested"); return NULL; } if (p == NULL) p = (void *) malloc(size); else p = (void *) realloc(p, size); if (p == NULL) { if (DEBUG_DUMP) message("realloc(%u) returned NULL\n", size); ErrMsg(ER_MEMORY, ""); } return p; } void set_mv_float(float *f) { memset(f, 0xFF, sizeof(float)); } void set_mv_double(double *d) { memset(d, 0xFF, sizeof(double)); } int is_mv_float(const float *f) { const unsigned char u[sizeof(float)] = { 0xFF, 0xFF, 0xFF, 0xFF }; /* will choke if sizeof(float) != 4 */ return (memcmp(f, u, sizeof(float)) == 0); } int is_mv_double(const double *d) { const unsigned char u[sizeof(double)] = { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF }; /* will choke if sizeof(double) != 8 */ return (memcmp(d, &u, sizeof(double)) == 0); } /* * almost_equals() compares string value of token tok with str[], and * returns TRUE if they are identical up to the first $ in str[]. */ int almost_equals(const char *tok, const char *str) { int i, after = 0, start = 0, len; if (tok == NULL) return 0; /* must be a value--can't be equal */ len = strlen(tok); for (i = 0; i < len + after; i++) { if (str[i] != tok[start + i]) { if (str[i] != '$') return 0; else { after = 1; start--; } } } /* i now beyond end of token string */ return(after || str[i] == '$' || str[i] == '\0'); } gstat/src/vario_fn.c0000644000176200001440000001300613777370515014151 0ustar liggesusers/* * vario_fn.c: contains elementary variogram model functions */ #include /* req'd by userio.h */ #include #include #include "defs.h" /* #define MATHLIB_STANDALONE */ #include #include "userio.h" #include "utils.h" #include "vario_fn.h" /* * Copyright (C) 1994, Edzer J. Pebesma * * basic variogram functions */ #define MIN_BESS 1.0e-3 #ifndef PI # define PI 3.14159265359 #endif double fn_nugget(double h, double *r) { return (h == 0.0 ? 0.0 : 1.0); } double fn_linear(double h, double *r) { if (h == 0) return 0.0; if (*r == 0) return h; /* 1lin() or 1 lin(0): slope 1 (and no range) */ return (h >= *r ? 1.0 : h/(*r)); } double da_fn_linear(double h, double *r) { if (*r == 0) return 0.0; /* 1lin() or 1 lin(0): slope 1 (and no range) */ if (h > *r) return 0.0; return -h/((*r) * (*r)); } double fn_circular(double h, double *r) { double hr; if (h == 0.0) return 0.0; if (h >= *r) return 1.0; hr = h/(*r); /* * return 1.0 + (2.0/PI) * (hr * sqrt(1.0 - hr * hr) - acos(hr)); * probably equivalent to: */ return (2.0/PI) * (hr * sqrt(1.0 - hr * hr) + asin(hr)); } double fn_spherical(double h, double *r) { double hr; if (h == 0) return 0.0; if (h >= *r) return 1.0; hr = h/(*r); return hr * (1.5 - 0.5 * hr * hr); } double da_fn_spherical(double h, double *r) { double hr2; if (h > *r) return 0.0; hr2 = h / ((*r) * (*r)); return 1.5 * hr2 * (-1.0 + h * hr2); } double fn_bessel(double h, double *r) { double hr; hr = h/(*r); if (hr < MIN_BESS) return 0.0; /* return 1.0 - hr * bessk1(hr); */ return 1.0 - hr * bessel_k(hr, 1.0, 1.0); } double fn_gaussian(double h, double *r) { double hr; if (h == 0.0) return 0.0; hr = h/(*r); return 1.0 - exp(-(hr*hr)); } double da_fn_gaussian(double h, double *r) { double hr; hr = h / (*r); return (-hr /(*r)) * exp(-(hr * hr)); } double fn_exponential(double h, double *r) { if (h == 0.0) return 0.0; return 1.0 - exp(-h/(*r)); } double fn_exclass(double h, double *r) { if (h == 0.0) return 0.0; return 1.0 - exp(-pow(h/r[0],r[1])); } double da_fn_exponential(double h, double *r) { double hr; hr = -h/(*r); return (hr / (*r)) * exp(hr); } double fn_pentaspherical(double h, double *r) { double hr, h2r2; if (h == 0.0) return 0.0; if (h >= *r) return 1.0; hr = h/(*r); h2r2 = hr * hr; return hr * ((15.0/8.0) + h2r2 * ((-5.0/4.0) + h2r2 * (3.0/8.0))); } double da_fn_pentaspherical(double h, double *r) { double hr2; if (h >= *r) return 0.0; hr2 = h / ((*r) * (*r)); return hr2*((-15.0/8.0) + hr2*((15.0/4.0)*h - (15.0/8.0)*h*h*hr2)); } double fn_periodic(double h, double *r) { if (h == 0.0) return 0.0; return 1.0 - cos(2.0 * PI * h/(*r)); } double da_fn_periodic(double h, double *r) { return (2.0 * PI * h/((*r) * (*r))) * sin(2.0 * PI * h/(*r)); } double fn_wave(double h, double *r) { if (h == 0.0) return 0.0; return 1.0 - (*r) * sin(PI * h/(*r)) / (PI * h); } double da_fn_wave(double h, double *r) { return cos(PI * h / (*r)) / (*r) - sin(PI * h / (*r)) / PI * h; } double fn_hole(double h, double *r) { if (h == 0.0) return 0.0; return 1.0 - sin(h/(*r))/(h/(*r)); } double da_fn_hole(double h, double *r) { double hr, hr2; hr = h/(*r); hr2 = h/((*r)*(*r)); return hr2 * sin(hr) + hr * hr2 * cos(hr); } double fn_logarithmic(double h, double *r) { if (h == 0.0) return 0.0; return log(h + *r); } double da_fn_logarithmic(double h, double *r) { return 1/(*r); } double fn_power(double h, double *r) { if (h == 0.0) return 0.0; return pow(h, *r); } double da_fn_power(double h, double *r) { return log(h) * pow(h, *r); } double fn_spline(double h, double *r) { if (h == 0.0) return 0.0; return h * h * log(h); } double fn_legendre(double h, double *r) { /* *r is range; h is angular lag */ double r2, ang; if (h == 0.0) return 0.0; r2 = r[0] * r[0]; ang = h / (PI * 6378.137); /* printf("dist: %g, ang: %g\n", h, ang); */ return 2.0 - (1.0 - r2)/(1 - 2.0 * r[0] * cos(ang) + r2); } double fn_intercept(double h, double *r) { return 1.0; } double da_is_zero(double h, double *r) { return 0.0; } double fn_matern(double h, double *p) { double hr, ans, phi, kappa; phi = p[0]; kappa = p[1]; if (h == 0.0) return(0.0); if (h > 600 * phi) return(1.0); hr = h/phi; ans = (pow(2.0, -(kappa - 1.0))/gammafn(kappa)) * pow(hr, kappa) * bessel_k(hr, kappa, 1.0); /* ans was for correlation; */ return 1.0 - ans; } /* * Ste: M. Stein's representation of the Matern model * * According to Hannes Kazianka, in R this would be h=distance matrix delta=c(RANGE,KAPPA) maternmodel<-function(h,delta){ matern<-besselK(2*delta[2]^(1/2)*h/delta[1],delta[2]) ifelse(matern==0,0,ifelse(!is.finite(matern),1, 1/(2^(delta[2] - 1)*gamma(delta[2]))*(2*delta[2]^(1/2)*h/delta[1])^delta[2]*matern)) } delta<-c(RANGE,KAPPA) h=Distance Matrix maternmodel<-function(h,delta){ matern<-besselK(2*delta[2]^(1/2)*h/delta[1],delta[2]) multipl<-1/(2^(delta[2] - 1)*gamma(delta[2]))*(2*delta[2]^(1/2)*h/delta[1])^delta[2] ifelse(matern==0 | !is.finite(multipl),0,ifelse(!is.finite(matern),1, multipl*matern)) } Now 0*Inf is impossible. Hannes */ double fn_matern2(double h, double *p) { double *delta, bes, mult; if (h == 0.0) return 0.0; delta = p; h = h / delta[0]; bes = bessel_k(2.0 * sqrt(delta[1]) * h, delta[1], 1.0); if (!isfinite(bes)) return 0.0; if (bes == 0.0) return 1.0; mult = pow(2.0, 1.0 - delta[1]) / gammafn(delta[1]) * pow((2.0 * sqrt(delta[1]) * h), delta[1]); if (!isfinite(mult)) return 1.0; return 1.0 - bes * mult; } gstat/src/vario.c0000644000176200001440000005617113777370515013500 0ustar liggesusers/* * vario.c: basic variogram model functions (init, print, update, etc.) */ #include #include /* getenv() */ #include /* toupper() */ #include /* DBL_MIN */ #include #include #include "R.h" /* Rprintf() */ #include "defs.h" #include "mtrx.h" #include "userio.h" #include "data.h" #include "utils.h" #include "debug.h" #include "vario.h" #include "vario_fn.h" #include "glvars.h" #include "lm.h" static int is_valid_cs(const VARIOGRAM *aa, const VARIOGRAM *bb, const VARIOGRAM *ab); static int is_posdef(MAT *m); static ANIS_TM *get_tm(double anis[5]); static void init_variogram_part(VGM_MODEL *v); const V_MODEL v_models[] = { /* the variogram model catalogue: */ /* first one needs to be NOT_SP: */ { NOT_SP, "Nsp", "Nsp (not specified)", NULL, NULL }, { NUGGET, "Nug", "Nug (nugget)", fn_nugget, da_is_zero }, { EXPONENTIAL, "Exp", "Exp (exponential)", fn_exponential, da_fn_exponential }, { SPHERICAL, "Sph", "Sph (spherical)", fn_spherical, da_fn_spherical }, { GAUSSIAN, "Gau", "Gau (gaussian)", fn_gaussian, da_fn_gaussian }, { EXCLASS, "Exc", "Exclass (Exponential class/stable)", fn_exclass, NULL }, { MATERN, "Mat", "Mat (Matern)", fn_matern, NULL }, { STEIN, "Ste", "Mat (Matern, M. Stein's parameterization)", fn_matern2, NULL }, { CIRCULAR, "Cir", "Cir (circular)", fn_circular, NULL }, { LINEAR, "Lin", "Lin (linear)", fn_linear, da_fn_linear }, /* one-parameter (a = 0), or two-parameter with sill */ { BESSEL, "Bes", "Bes (bessel)", fn_bessel, NULL }, { PENTASPHERICAL, "Pen", "Pen (pentaspherical)", fn_pentaspherical, da_fn_pentaspherical }, { PERIODIC, "Per", "Per (periodic)", fn_periodic, da_fn_periodic }, { WAVE, "Wav", "Wav (wave)", fn_wave, da_fn_wave }, { HOLE, "Hol", "Hol (hole)", fn_hole, da_fn_hole }, { LOGARITHMIC, "Log", "Log (logarithmic)", fn_logarithmic, da_fn_logarithmic }, { POWER, "Pow", "Pow (power)", fn_power, da_fn_power }, /* Wackernagel 2nd ed., p. 225 -- not working yet */ { SPLINE, "Spl", "Spl (spline)", fn_spline, NULL }, { LEGENDRE, "Leg", "Leg (Legendre)", fn_legendre, NULL }, { MERROR, "Err", "Err (Measurement error)", fn_nugget, da_is_zero }, /* the folowing two should always be the last ``valid'' one: */ { INTERCEPT, "Int", "Int (Intercept)", fn_intercept, da_is_zero }, { NOT_SP, NULL, NULL, NULL, NULL } /* THIS SHOULD BE LAST */ }; const char *vgm_type_str[] = { "not specified", "semivariogram", "cross variogram", "covariogram", "cross covariogram" }; VARIOGRAM *init_variogram(VARIOGRAM *v) { /* * initializes one variogram structure * if v is NULL, memory is allocated for the structure */ int i; if (v == NULL) v = (VARIOGRAM *) emalloc(sizeof(VARIOGRAM)); v->id = v->id1 = v->id2 = -1; v->n_models = 0; v->is_valid_covariance = 1; v->isotropic = 1; v->n_fit = 0; v->fit_is_singular = 0; v->max_range = (double) DBL_MIN; v->sum_sills = 0.0; v->measurement_error = 0.0; v->max_val = 0.0; v->min_val = 0.0; vgm_init_block_values(v); v->part = (VGM_MODEL *) emalloc(INIT_N_VGMM * sizeof(VGM_MODEL)); v->table = NULL; for (i = 0; i < INIT_N_VGMM; i++) init_variogram_part(&(v->part[i])); v->max_n_models = INIT_N_VGMM; v->SSErr = 0.0; v->ev = init_ev(); return v; } void vgm_init_block_values(VARIOGRAM *v) { v->block_semivariance_set = 0; v->block_covariance_set = 0; v->block_covariance = -999999.0; v->block_semivariance = -999999.0; } static void init_variogram_part(VGM_MODEL *p) { int i; p->sill = 0.0; for (i = 0; i < NRANGEPARS; i++) { p->range[i] = 0.0; /* quiets valgrind? */ set_mv_double(&(p->range[i])); /* trigger errors if misused */ } p->model = NOT_SP; p->fit_sill = p->fit_range = 1; p->fnct = p->da_fnct = NULL; p->tm_range = NULL; p->id = -1; } SAMPLE_VGM *init_ev(void) { SAMPLE_VGM *ev = NULL; ev = (SAMPLE_VGM *) emalloc(sizeof(SAMPLE_VGM)); set_mv_double(&(ev->cutoff)); set_mv_double(&(ev->iwidth)); ev->gamma = NULL; ev->dist = NULL; ev->nh = NULL; ev->pairs = NULL; ev->n_max = 0; ev->n_est = 0; ev->zero = ZERO_DEFAULT; ev->plot_numbers = 1; ev->is_directional = 0; ev->evt = NOTSPECIFIED; ev->fit = NO_FIT; ev->recalc = 1; ev->refit = 1; ev->pseudo = 0; ev->is_asym = -1; ev->map = NULL; ev->S_grid = NULL; ev->direction.x = 1.0; ev->direction.y = ev->direction.z = 0.0; return ev; } void free_variogram(VARIOGRAM *v) { int i; assert(v != NULL); if (v->ev) { if (v->ev->n_max > 0) { efree(v->ev->gamma); efree(v->ev->dist); efree(v->ev->nh); if (v->ev->pairs) efree(v->ev->pairs); } if (v->ev->map) efree(v->ev->map); efree(v->ev); } for (i = 0; i < v->max_n_models; i++) if (v->part[i].tm_range != NULL) efree(v->part[i].tm_range); efree(v->part); if (v->table) { efree(v->table->values); efree(v->table); } efree(v); } void logprint_variogram(const VARIOGRAM *v, int verbose) { /* prints contents of VARIOGRAM v to R console */ if (v->id1 < 0 && v->id2 < 0) return; /* never set */ if (v->id1 == v->id2) Rprintf("variogram(%s):\n", name_identifier(v->id1)); else Rprintf("variogram(%s,%s):\n", name_identifier(v->id1), name_identifier(v->id2)); for (int i = 0; i < v->n_models; i++) { Rprintf("# model: %d type: %s sill: %g range: %g\n", i, v_models[v->part[i].model].name_long, v->part[i].sill, v->part[i].range[0]); if (v->part[i].tm_range != NULL) { Rprintf("# range anisotropy, rotation matrix:\n"); for (int j = 0; j < 3; j++) { for (int k = 0; k < 3; k++) Rprintf("%s%8.4f", k == 0 ? "# " : " ", v->part[i].tm_range->tm[j][k]); Rprintf("\n"); } } } Rprintf( "# sum sills %g, max %g, min %g, flat at distance %g\n", v->sum_sills, v->max_val, v->min_val, v->max_range); return; } void update_variogram(VARIOGRAM *vp) { /* * update min/max, n_fit, descr * assumes that models are not changed: they can only be changed through * read_variogram(); */ VGM_MODEL *p; vp->sum_sills = vp->min_val = vp->max_val = 0.0; vp->measurement_error = 0.0; vp->n_fit = 0; vp->max_range = DBL_MIN; for (int i = 0; i < vp->n_models; i++) { p = &(vp->part[i]); vp->sum_sills += p->sill; if (p->sill < 0.0) vp->min_val += p->sill; /* else */ /* up to gstat_1.1-1 else was there; see https://stat.ethz.ch/pipermail/r-sig-geo/2015-December/023814.html */ vp->max_val += p->sill; vp->max_range = MAX(p->range[0], vp->max_range); if (p->model == BESSEL || p->model == GAUSSIAN || p->model == EXPONENTIAL || p->model == LOGARITHMIC || p->model == POWER || p->model == PERIODIC || p->model == EXCLASS || p->model == LEGENDRE || p->model == HOLE || p->model == WAVE || /* more??? */ p->model == MATERN || p->model == STEIN || (p->model == LINEAR && p->range[0] == 0)) /* sill is reached asymptotically or oscillates */ vp->max_range = DBL_MAX; else /* transitive model: */ vp->max_range = MAX(p->range[0], vp->max_range); if ((p->model == LINEAR && p->range[0] == 0.0) || p->model == NUGGET || p->model == INTERCEPT) p->fit_range = 0; /* 1 would lead to singularity */ if (p->model == LOGARITHMIC || p->model == POWER || p->model == INTERCEPT || (p->model == LINEAR && p->range[0] == 0)) vp->is_valid_covariance = 0; if (p->fit_sill) vp->n_fit++; if (p->fit_range) vp->n_fit++; if (p->model == MERROR) vp->measurement_error += p->sill; } if (vp->table != NULL) { vp->sum_sills = vp->table->values[0]; vp->max_val = vp->table->values[0]; vp->min_val = vp->table->values[0]; for (int i = 1; i < vp->table->n; i++) { vp->max_val = MAX(vp->max_val, vp->table->values[i]); vp->min_val = MIN(vp->min_val, vp->table->values[i]); } } return; } /* double get_max_sill(int n) { int i, j; VARIOGRAM *vp; static double max_sill; vp = get_vgm(0); max_sill = vp->max_val; for (i = 0; i < n; i++) { for (j = 0; j <= i; j++) { vp = get_vgm(LTI(i,j)); max_sill = MAX(max_sill, vp->max_val); } } return max_sill; } */ double get_semivariance(const VARIOGRAM *vp, double dx, double dy, double dz) { /* returns gamma(dx,dy,dz) for variogram v: gamma(h) = cov(0) - cov(h) */ int i; double sv = 0.0, dist = 0.0; if (vp->table != NULL) return(SEM_TABLE_VALUE(vp->table, transform_norm(vp->table->tm_range, dx, dy, dz))); if (! vp->isotropic) { for (i = 0; i < vp->n_models; i++) sv += vp->part[i].sill * vp->part[i].fnct( transform_norm(vp->part[i].tm_range, dx, dy, dz), vp->part[i].range); } else { dist = transform_norm(NULL, dx, dy, dz); if (dist > vp->max_range) return vp->sum_sills; for (i = 0; i < vp->n_models; i++) sv += vp->part[i].sill * vp->part[i].fnct(dist, vp->part[i].range); } return sv; } double get_covariance(const VARIOGRAM *vp, double dx, double dy, double dz) { /* returns cov(dx,dy,dz) for variogram v */ int i; static int warning = 0; double ctmp = 0.0, dist; if (vp == NULL) { warning = 0; return 0.0; } if (! vp->is_valid_covariance && !warning) { pr_warning("non-transitive variogram model not allowed as covariance function"); warning = 1; } if (!vp->is_valid_covariance && !DEBUG_FORCE) ErrMsg(ER_IMPOSVAL, "covariance from non-transitive variogram not allowed "); if (vp->table != NULL) return(COV_TABLE_VALUE(vp->table, transform_norm(vp->table->tm_range, dx, dy, dz))); if (! vp->isotropic) { for (i = 0; i < vp->n_models; i++) ctmp += vp->part[i].sill * (1.0 - vp->part[i].fnct( transform_norm(vp->part[i].tm_range, dx, dy, dz), vp->part[i].range)); } else { dist = transform_norm(NULL, dx, dy, dz); for (i = 0; i < vp->n_models; i++) ctmp += vp->part[i].sill * (1.0 - vp->part[i].fnct(dist, vp->part[i].range)); } return ctmp; } static int is_valid_cs(const VARIOGRAM *aa, const VARIOGRAM *bb, const VARIOGRAM *ab) /* * Purpose : Check Cauchy-Schwartz inequality on cross/variograms * Created by : Edzer J. Pebesma * Date : may 6th 1992 * Prerequisites : * Returns : return nonzero if |g_ab(h)| > sqrt(g_aa(h)g_bb(h)) * Side effects : none */ { int i, check_failed = 0; double maxrange = 0, dist, dx, dy, dz; for (i = 0; i < aa->n_models; i++) if (aa->part[i].range[0] > maxrange) maxrange = aa->part[i].range[0]; for (i = 0; i < ab->n_models; i++) if (ab->part[i].range[0] > maxrange) maxrange = ab->part[i].range[0]; for (i = 0; i < bb->n_models; i++) if (bb->part[i].range[0] > maxrange) maxrange = bb->part[i].range[0]; for (i = 0; i < 101 && !check_failed; i++) { dist = (i * maxrange)/100; dx = dy = dz = 0.0; if (i % 3 == 0) dx = dist; if (i % 3 == 1) dy = dist; if (i % 3 == 2) dz = dist; if (fabs(get_semivariance(ab, dx, dy, dz)) > sqrt(get_semivariance(aa, dx, dy, dz) * get_semivariance(bb, dx, dy, dz))) { check_failed = 1; /* yes, the check failed */ pr_warning("%s %d %s %d %s %d\n%s %g %g %g\n", "Cauchy-Schwartz violation: variogram", aa->id,",",bb->id, "and cross variogram", ab->id, "first failure on dx, dy and dz:", dx, dy, dz); } } /* for */ if (check_failed) return 0; else return 1; } void check_variography(const VARIOGRAM **v, int n_vars) /* * check for intrinsic correlation, linear model of coregionalisation * or else (with warning) Cauchy Swartz */ { int i, j, k, ic = 0, lmc, posdef = 1; MAT **a = NULL; double b; char *reason = NULL; if (n_vars <= 1) return; /* * find out if lmc (linear model of coregionalization) hold: * all models must have equal base models (sequence and range) */ for (i = 1, lmc = 1; lmc && i < get_n_vgms(); i++) { if (v[0]->n_models != v[i]->n_models) { reason = "number of models differ"; lmc = 0; } for (k = 0; lmc && k < v[0]->n_models; k++) { if (v[0]->part[k].model != v[i]->part[k].model) { reason = "model types differ"; lmc = 0; } if (v[0]->part[k].range[0] != v[i]->part[k].range[0]) { reason = "ranges differ"; lmc = 0; } } for (k = 0; lmc && k < v[0]->n_models; k++) if (v[0]->part[k].tm_range != NULL) { if (v[i]->part[k].tm_range == NULL) { reason = "anisotropy for part of models"; lmc = 0; } else if ( v[0]->part[k].tm_range->ratio[0] != v[i]->part[k].tm_range->ratio[0] || v[0]->part[k].tm_range->ratio[1] != v[i]->part[k].tm_range->ratio[1] || v[0]->part[k].tm_range->angle[0] != v[i]->part[k].tm_range->angle[0] || v[0]->part[k].tm_range->angle[1] != v[i]->part[k].tm_range->angle[1] || v[0]->part[k].tm_range->angle[2] != v[i]->part[k].tm_range->angle[2] ) { reason = "anisotropy parameters are not equal"; lmc = 0; } } else if (v[i]->part[k].tm_range != NULL) { reason = "anisotropy for part of models"; lmc = 0; } } if (lmc) { /* * check for ic: */ a = (MAT **) emalloc(v[0]->n_models * sizeof(MAT *)); for (k = 0; k < v[0]->n_models; k++) a[k] = m_get(n_vars, n_vars); for (i = 0; i < n_vars; i++) { for (j = 0; j < n_vars; j++) { /* for all variogram triplets: */ for (k = 0; k < v[0]->n_models; k++) ME(a[k], i, j) = v[LTI(i,j)]->part[k].sill; } } /* for ic: a's must be scaled versions of each other: */ ic = 1; for (k = 1, ic = 1; ic && k < v[0]->n_models; k++) { b = ME(a[0], 0, 0)/ME(a[k], 0, 0); for (i = 0; ic && i < n_vars; i++) for (j = 0; ic && j < n_vars; j++) if (fabs(ME(a[0], i, j) / ME(a[k], i, j) - b) > EPSILON) ic = 0; } /* check posdef matrices */ for (i = 0, lmc = 1, posdef = 1; i < v[0]->n_models; i++) { posdef = is_posdef(a[i]); if (posdef == 0) { reason = "coefficient matrix not positive definite"; if (DEBUG_COV) { printlog("non-positive definite coefficient matrix %d:\n", i); m_logoutput(a[i]); } ic = lmc = 0; } if (! posdef) printlog( "non-positive definite coefficient matrix in structure %d", i+1); } for (k = 0; k < v[0]->n_models; k++) m_free(a[k]); efree(a); if (ic) { printlog("Intrinsic Correlation found. Good.\n"); return; } else if (lmc) { printlog("Linear Model of Coregionalization found. Good.\n"); return; } } /* * lmc does not hold: check on Cauchy Swartz */ pr_warning("No Intrinsic Correlation or Linear Model of Coregionalization found\nReason: %s", reason ? reason : "unknown"); if (gl_nocheck == 0) { pr_warning("[add `set = list(nocheck = 1)' to the gstat() or krige() to ignore the following error]\n"); ErrMsg(ER_IMPOSVAL, "variograms do not satisfy a legal model"); } printlog("Now checking for Cauchy-Schwartz inequalities:\n"); for (i = 0; i < n_vars; i++) for (j = 0; j < i; j++) if (is_valid_cs(v[LTI(i,i)], v[LTI(j,j)], v[LTI(i,j)])) { printlog("variogram(%s,%s) passed Cauchy-Schwartz\n", name_identifier(j), name_identifier(i)); } else pr_warning("Cauchy-Schwartz inequality found for variogram(%s,%s)", name_identifier(j), name_identifier(i) ); return; } static int is_posdef(MAT *A) { MAT *b = m_copy(A, MNULL); int info; CHfactor(b, PNULL, &info); m_free(b); return (info == 0); } double transform_norm(const ANIS_TM *tm, double dx, double dy, double dz) { /* returns variogram distance given dx, dy, dz and VARIOGRAM v */ double dist = 0.0, tmp; int i; if (dx == 0.0 && dy == 0.0 && dz == 0.0) return 0.0; if (tm != NULL) { for (i = 0, tmp = 0.0; i < 3; i++) { tmp = tm->tm[i][0] * dx + tm->tm[i][1] * dy + tm->tm[i][2] * dz; dist += tmp * tmp; } return sqrt(dist); } return sqrt((dx * dx) + (dy * dy) + (dz * dz)); } double da_general(VGM_MODEL *part, double h) { /* numerical approximation of derivative: */ int i; double low, high, range, r[NRANGEPARS]; for (i = 0; i < NRANGEPARS; i++) { if (is_mv_double(&(part->range[i]))) set_mv_double(&(r[i])); else r[i] = part->range[i]; } range = MAX(1e-20, part->range[0]); r[0] = range * (1.0 + DA_DELTA); low = part->fnct(h, r); r[0] = range * (1.0 - DA_DELTA); high = part->fnct(h, r); return part->sill * (low - high) / (2.0 * range * DA_DELTA); } int push_variogram_model(VARIOGRAM *v, VGM_MODEL part) { int i, max_id, where = -1; /* * add the part submodel to v (if part.id < 0) or else * modify the appropriate part of v, having the id of part.id. * do a lot of checks, and set .fn and .da_fn functions. */ if (v->n_models == v->max_n_models) { v->part = (VGM_MODEL *) erealloc(v->part, (v->max_n_models + INIT_N_VGMM) * sizeof(VGM_MODEL)); for (i = v->max_n_models; i < v->max_n_models + INIT_N_VGMM; i++) init_variogram_part(&(v->part[i])); v->max_n_models += INIT_N_VGMM; } /* * check some things: */ if (part.model == NOT_SP) ErrMsg(ER_IMPOSVAL, "model NSP not allowed in variogram structure"); if (part.range[0] < 0.0) ErrMsg(ER_RANGE, "variogram range cannot be negative"); if (part.model == LINEAR) { if (part.range[0] == 0.0) part.fit_range = 0; } else if (part.model == NUGGET || part.model == INTERCEPT || part.model == MERROR) { part.fit_range = 0; if (part.range[0] > 0.0) ErrMsg(ER_RANGE, "range must be zero"); } else if (part.range[0] == 0.0) ErrMsg(ER_RANGE, "range must be positive"); if (part.model == POWER && part.range[0] > 2.0) ErrMsg(ER_RANGE, "power model range (parameter) cannot exceed 2.0"); if (part.model == EXCLASS && part.range[1] > 2.0) ErrMsg(ER_RANGE, "exponentical class model shape parameter cannot exceed 2.0"); if (part.id < 0) { where = v->n_models; v->n_models++; for (i = max_id = 0; i < v->n_models; i++) max_id = MAX(v->part[i].id, max_id); part.id = max_id + 1; } else { /* search in list: */ for (i = 0; where < 0 && i < v->n_models; i++) if (v->part[i].id == part.id) where = i; assert(where >= 0); /* i.e., it should really be in the list */ } if (v->isotropic) v->isotropic = (part.tm_range == NULL); /* * check that the .fn and .da_fn functions in v_models * will indeed be the correct ones: */ assert(part.model == v_models[part.model].model); v->part[where] = part; v->part[where].fnct = v_models[part.model].fn; v->part[where].da_fnct = v_models[part.model].da_fn; return part.id; } VGM_MODEL_TYPE which_variogram_model(const char *m) { char s[4]; strncpy(s, m, 3); s[0] = toupper(s[0]); s[1] = tolower(s[1]); s[2] = tolower(s[2]); s[3] = '\0'; for (int i = 1; v_models[i].name != NULL; i++) if (strcmp(s, v_models[i].name) == 0) return v_models[i].model; return NOT_SP; } double relative_nugget(VARIOGRAM *v) { int i; double nug = 0.0, sill = 0.0; assert(v->n_models != 0); if (v->n_models == 1) return (v->part[0].model == NUGGET ? 1.0 : 0.0); for (i = 0; i < v->n_models; i++) { if (v->part[i].model == NUGGET) nug += v->part[i].sill; else sill += v->part[i].sill; } assert(nug + sill > 0.0); return (nug/(nug+sill)); } DO_AT_ZERO zero_int2enum(int zero) { switch(zero) { case 0: return ZERO_DEFAULT; case 1: return ZERO_INCLUDE; case 2: return ZERO_AVOID; case 3: return ZERO_SPECIAL; } ErrMsg(ER_IMPOSVAL, "invalid value for zero"); return ZERO_DEFAULT; /* never reached */ } void push_to_v(VARIOGRAM *v, const char *mod, double sill, double *range, int nrangepars, double *d, int fit_sill, int fit_range) { VGM_MODEL vm; int i; init_variogram_part(&vm); vm.model = which_variogram_model(mod); if (nrangepars > NRANGEPARS) ErrMsg(ER_IMPOSVAL, "too many range parameters"); for (i = 0; i < nrangepars; i++) vm.range[i] = range[i]; vm.sill = sill; vm.fit_sill = fit_sill; vm.fit_range = fit_range; if (d != NULL && d[0] != -9999.0) vm.tm_range = get_tm(d); if (vm.model == STEIN && range[1] > 100.0) { vm.model = GAUSSIAN; vm.range[1] = 0.0; pr_warning("kappa values over 100 overflow gammafn: taking Gaussian approximation"); } push_variogram_model(v, vm); } void push_to_v_table(VARIOGRAM *v, double maxdist, int length, double *values, double *anis) { int i; v->table = (COV_TABLE *) emalloc(sizeof(COV_TABLE)); v->table->n = length; v->table->maxdist = maxdist; v->table->values = (double *) emalloc(length * sizeof(double)); for (i = 0; i < length; i++) v->table->values[i] = values[i]; if (anis != NULL) v->table->tm_range = get_tm(anis); else v->table->tm_range = NULL; } static ANIS_TM *get_tm(double anis[5]) { /* Part of this routine was inspired by FORTRAN code in GSLIB, first edition: C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% C % C Copyright (C) 1992 Stanford Center for Reservoir Forecasting. All % C rights reserved. Distributed with: C.V. Deutsch and A.G. Journel. % C ``GSLIB: Geostatistical Software Library and User's Guide,'' Oxford % C University Press, New York, 1992. % C % C The programs in GSLIB are distributed in the hope that they will be % C useful, but WITHOUT ANY WARRANTY. No author or distributor accepts % C responsibility to anyone for the consequences of using them or for % C whether they serve any particular purpose or work at all, unless he % C says so in writing. Everyone is granted permission to copy, modify % C and redistribute the programs in GSLIB, but only under the condition % C that this notice and the above copyright notice remain intact. % C % C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ int i; double alpha, beta, theta, sina, sinb, sint, cosa, cosb, cost, afac1, afac2; ANIS_TM *t = NULL; /* About naming convention: gstat GSLIB =============== anis[0] ang1 (first anis. par. for 2D) anis[1] ang2 anis[2] ang3 anis[3] anis1 (second anis. par. for 2D) anis[4] anis2 */ #define ANIS_ERR(x) message("parsing anis. pars. %g,%g,%g,%g,%g -- error on %g\n", \ anis[0],anis[1],anis[2],anis[3],anis[4],x) #define DEG2RAD (PI/180.0) for (i = 0; i < 3; i++) { if (anis[i] < 0 || anis[i] >= 360) { ANIS_ERR(anis[i]); ErrMsg(ER_RANGE, "this value should be in [0..360>"); } } for (i = 3; i < 5; i++) { if (anis[i] <= 0.0 || anis[i] > 1.0) { ANIS_ERR(anis[i]); ErrMsg(ER_RANGE, "this value should be in <0..1]"); } } /* from GSLIB: */ if (anis[0] >= 0.0 && anis[0] < 270) alpha = (double) (90.0 - anis[0]) * DEG2RAD; else alpha = (double) (450.0 - anis[0]) * DEG2RAD; beta = -1.0 * (double) anis[1] * DEG2RAD; theta = (double) anis[2] * DEG2RAD; sina = sin(alpha); sinb = sin(beta); sint = sin(theta); cosa = cos(alpha); cosb = cos(beta); cost = cos(theta); afac1 = 1.0 / MAX((double) anis[3], (double) EPSILON); afac2 = 1.0 / MAX((double) anis[4], (double) EPSILON); t = emalloc(sizeof(ANIS_TM)); t->angle[0] = anis[0]; t->angle[1] = anis[1]; t->angle[2] = anis[2]; t->ratio[0] = anis[3]; t->ratio[1] = anis[4]; t->tm[0][0] = (cosb * cosa); t->tm[0][1] = (cosb * sina); t->tm[0][2] = (-sinb); t->tm[1][0] = afac1*(-cost*sina + sint*sinb*cosa); t->tm[1][1] = afac1*(cost*cosa + sint*sinb*sina); t->tm[1][2] = afac1*( sint * cosb); t->tm[2][0] = afac2*(sint*sina + cost*sinb*cosa); t->tm[2][1] = afac2*(-sint*cosa + cost*sinb*sina); t->tm[2][2] = afac2*(cost * cosb); return t; } gstat/src/msim.c0000644000176200001440000002321313777370515013314 0ustar liggesusers/* * msim.c: multiple simulation database + output * Written during my Post Doc at UvA, end of 1996. * Rewrite started on Sat Apr 10 20:54:05 WET DST 1999 */ #include #include /* qsort() */ #include /* memmove() */ #include /* sqrt(), ... */ #include "defs.h" #include #include "debug.h" #include "data.h" #include "utils.h" #include "vario.h" #include "glvars.h" /* gl_nsim, gl_format */ #include "userio.h" #include "mapio.h" #include "mtrx.h" #include "lm.h" #include "gls.h" #include "sim.h" #include "msim.h" static DPOINT *which_point(DATA *d, DPOINT *where); static unsigned int *get_n_sim_locs_table(unsigned int *size); /* global variables formerly in predict.c; set in s.c */ unsigned int n_pred_locs = 0; #ifdef SIM_DOUBLE typedef double Float; /* doubles the memory requirement -> may be pretty much */ #else typedef float Float; #endif static Float ***msim = NULL, /* * The msim table entry for variable i, for simulation node j, * replicate k is msim[i][j][k] */ **msim_base = NULL; /* base structure for blocked allocation */ static double ***beta = NULL; /* * the beta realisation for variable i, draw j is in * beta[i][j] -- and has dimension data[i]->beta->size */ static unsigned int *n_sim_locs = NULL, /* n simulation locations per data variable */ table_size = 0, /* offset strata table size */ **s2d = NULL, /* * s2d: -- find (POINT *) from msim: * msim[i][j][...] -->> data[i]->list[s2d[i][j]] */ **d2s = NULL; /* * d2s: find msim entry from (POINT *): * data[i]->list[j] -->> msim[i][d2s[i][j]][...] * ((the latter two are necessary because simple counting fails * when point simulation locations coincide with data locations. In * this case, a data DPOINT is not added to the data list, and so we * need to keep track _where_ simulated values were located in order * to write them back to output (file/maps) at the end)) */ void print_sim(void) { /* print complete contents of sim_values -- for debug purposes only */ int i, j, k; for (i = 0; i < get_n_vars(); i++) { printlog("variable %d:\n", i); for (j = 0; j < n_sim_locs[i]; j++) { for (k = 0; k < gl_nsim; k++) printlog(" %g", msim[i][j][k]); printlog("\n"); } } } void init_simulations(DATA **d) { int i, j, size; assert(n_pred_locs > 0); /* should be set by now... */ if (msim != NULL) free_simulations(); n_sim_locs = get_n_sim_locs_table(&table_size); if (DEBUG_DUMP) { printlog("n_sim_locs_table: "); for (i = 0; i < table_size; i++) printlog("[%d] ", n_sim_locs[i]); printlog("\n"); } msim = (Float ***) emalloc(get_n_vars() * sizeof(Float **)); msim_base = (Float **) emalloc(get_n_vars() * sizeof(Float *)); s2d = (unsigned int **) emalloc(get_n_vars() * sizeof(unsigned int *)); d2s = (unsigned int **) emalloc(get_n_vars() * sizeof(unsigned int *)); for (i = 0; i < get_n_vars(); i++) { /* msim stuff: */ size = n_sim_locs[i] * gl_nsim; msim_base[i] = (Float *) emalloc(size * sizeof(Float)); memset(msim_base[i], 0xFF, size * sizeof(Float)); msim[i] = (Float **) emalloc(n_sim_locs[i] * sizeof(Float *)); for (j = 0; j < n_sim_locs[i]; j++) msim[i][j] = &(msim_base[i][j * gl_nsim]); /* index stuff: */ s2d[i] = (unsigned int *) emalloc(n_sim_locs[i] * sizeof(unsigned int)); d2s[i] = (unsigned int *) emalloc(n_sim_locs[i] * sizeof(unsigned int)); /* now let's trigger some Seg Faults if on error: */ memset(s2d[i], 0xFF, n_sim_locs[i] * sizeof(unsigned int)); memset(d2s[i], 0xFF, n_sim_locs[i] * sizeof(unsigned int)); } } void save_sim(DATA **data, DPOINT *where, int sim, int n_vars, const double *value, int *is_pt) { /* * save the last simulated value(s) in msim; * data[0]->n_list and data[0]->n_original (mode != STRATIFY) or * else n_vars (..) denote where it should go. */ int i, row; DPOINT *which = NULL; if (gl_nsim <= 1) return; for (i = 0; i < n_vars; i++) { /* store current simulation */ row = data[i]->n_list - data[i]->n_original + data[i]->nsim_at_data; if (sim == 0) { /* fill d2s and s2d entries: */ assert(row >= 0 && row < n_sim_locs[i]); if (is_pt[i]) { which = which_point(data[i], where); s2d[i][row] = GET_INDEX(which); /* d2s remains MV */ } else { /* newly simulated */ s2d[i][row] = data[i]->n_list; d2s[i][data[i]->n_list - data[i]->n_original] = row; /* please go and check it -- this last line took me 4 hours to get right */ } } msim[i][row][sim] = value[i]; } } void save_sim_strat(DATA *d, DPOINT *where, int sim, double value, int is_pt) { /* the same, but for stratified mode */ int row; DPOINT *which = NULL; if (gl_nsim <= 1) return; row = d->n_list - d->n_original + d->nsim_at_data; if (sim == 0) { /* fill d2s and s2d entries: */ assert(row >= 0 && row < n_sim_locs[d->id]); if (is_pt) { which = which_point(d, where); s2d[d->id][row] = GET_INDEX(which); /* the entry for d2s does not exist */ } else { /* not an original point, but a simulated one: */ s2d[d->id][row] = d->n_list; /* newly simulated */ d2s[d->id][d->n_list - d->n_original] = row; } } msim[d->id][row][sim] = value; } static DPOINT *which_point(DATA *d, DPOINT *where) { int i; double dzero2; #define WPWARNING "if you are simulating with a Gaussian variogram model without nugget\n\ then try to add a small nugget variance to avoid the following error message" dzero2 = gl_zero * gl_zero; for (i = 0; i < d->n_sel; i++) if (fabs(d->pp_norm2(d->sel[i], where)) <= dzero2) return d->sel[i]; pr_warning(WPWARNING); ErrMsg(ER_NULL, "which_point(): point not found"); return where; /* never reached */ } void restore_data_sel(DATA **data, int sim, int n_vars) { unsigned int i, j; int id, idx; DATA *d0 = NULL; if (gl_nsim <= 1) return; if (n_vars == 0) { assert(get_mode() == STRATIFY); d0 = data[0]; for (j = 0; j < d0->n_sel; j++) { id = d0->id; idx = GET_INDEX(d0->sel[j]) - d0->n_original; /* current sim: */ if (idx >= 0 && d2s[id][idx] != 0xFFFFFFFF) d0->sel[j]->attr = msim[id][d2s[id][idx]][sim]; } } else { for (i = 0; i < n_vars; i++) { for (j = 0; j < data[i]->n_sel; j++) { idx = GET_INDEX(data[i]->sel[j]) - data[i]->n_original; /* idx < 0 -->> original data, don't restore */ if (idx >= 0 && d2s[i][idx] != 0xFFFFFFFF) data[i]->sel[j]->attr = msim[i][d2s[i][idx]][sim]; /* data[i]->list[j] -->> msim[i][d2s[i][j]][...] */ } } } } void free_simulations(void) { int i, j; if (msim != NULL) { for (i = 0; i < get_n_vars(); i++) { efree(msim[i]); efree(msim_base[i]); efree(s2d[i]); efree(d2s[i]); } efree(msim); msim = NULL; efree(msim_base); msim_base = NULL; } if (s2d != NULL) { efree(s2d); s2d = NULL; } if (d2s != NULL) { efree(d2s); d2s = NULL; } if (beta != NULL) { for (i = 0; i < get_n_vars(); i++) { for (j = 0; j < gl_nsim; j++) efree(beta[i][j]); efree(beta[i]); } efree(beta); beta = NULL; } if (n_sim_locs != NULL) free(n_sim_locs); n_sim_locs = NULL; } void setup_beta(DATA **d, int n_vars, int n_sim) { double *est; const double *sim = NULL; int i, j, k, sum_n_X = 0, offset, *is_pt = NULL; assert(beta == NULL); /* entered only once */ /* allocate beta */ beta = (double ***) emalloc(n_vars * sizeof(double **)); for (i = 0; i < n_vars; i++) { assert(d[i]->n_list > 0); beta[i] = (double **) emalloc(n_sim * sizeof(double *)); for (j = 0; j < n_sim; j++) beta[i][j] = (double *) emalloc(d[i]->n_X * sizeof(double)); } for (i = 0; i < n_vars; i++) { if (d[i]->beta == NULL) /* push bogus values */ for (j = 0; j < d[i]->n_X; j++) d[i]->beta = push_d_vector(-9999.9, d[i]->beta); sum_n_X += d[i]->n_X; } printlog("drawing %d %s%s realisation%s of beta...\n", n_sim, n_vars > 1 ? (gl_sim_beta == 0 ? "multivariate " : "univariate ") : "", gl_sim_beta == 2 ? "OLS" : "GLS", n_sim > 1 ? "s" : ""); is_pt = (int *) emalloc(sum_n_X * sizeof(int)); if (gl_sim_beta == 0) { est = make_gls_mv(d, n_vars); for (j = 0; j < n_sim; j++) { sim = cond_sim(est, sum_n_X, GSI, is_pt, 0); /* length sum_n_X */ for (i = offset = 0; i < n_vars; i++) { for (k = 0; k < d[i]->n_X; k++) beta[i][j][k] = sim[offset + k]; offset += d[i]->n_X; if (DEBUG_DUMP || DEBUG_COV) { printlog("var=%d, sim=%d, beta=[ ", i, j); for (k = 0; k < d[i]->n_X; k++) printlog("%g ", beta[i][j][k]); printlog("]\n"); } } } efree(est); } else { for (i = 0; i < n_vars; i++) { if (gl_sim_beta == 1) est = make_gls(d[i], 0); else /* gl_sim_beta == 2 */ est = make_ols(d[i]); for (j = 0; j < n_sim; j++) { sim = cond_sim(est, d[i]->n_X, GSI, is_pt, 0); for (k = 0; k < d[i]->n_X; k++) beta[i][j][k] = sim[k]; if (DEBUG_DUMP || DEBUG_COV) { printlog("var=%d, sim=%d, beta=[ ", i, j); for (k = 0; k < d[i]->n_X; k++) printlog("%g ", beta[i][j][k]); printlog("]\n"); } } efree(est); } } efree(is_pt); return; } void set_beta(DATA **d, int sim, int n_vars, METHOD method) { /* n_vars == 0 --> stratified mode, check d[0]->id to find out which * data we've got here */ int i; assert(d[0]->beta); if (beta == NULL) /* use the values entered by the user */ return; if (get_mode() != STRATIFY) { for (i = 0; i < n_vars; i++) d[i]->beta->val = beta[i][sim]; } else d[0]->beta->val = beta[d[0]->id][sim]; return; } float ***get_msim(void) { return msim; } static unsigned int *get_n_sim_locs_table(unsigned int *size) { unsigned int i, *table; *size = (int) get_n_vars(); table = (unsigned int *) emalloc(*size * sizeof(int)); for (i = 0; i < *size; i++) table[i] = n_pred_locs; return table; } gstat/src/utils.h0000644000176200001440000000272613777370515013522 0ustar liggesusers#ifndef UTILS_H #define UTILS_H # include /* size_t */ /* some famous beware-of-side-effects macro's ! */ #ifndef MAX # define MAX(a,b) (((a) > (b)) ? (a) : (b)) #endif #ifndef MIN # define MIN(a,b) (((a) < (b)) ? (a) : (b)) #endif #ifndef ABS #define ABS(a) (((a) >= 0) ? (a) : (-(a))) #endif #ifndef SQR # define SQR(a) ((a)*(a)) #endif #ifndef PI # define PI 3.14159265359 #endif #define NULS(a) (a==NULL ? "" : a) /* LTI: lower triangular matrix index, stored in an array: col | 0 1 2 3 ----+------- 0 | 0 r 1 | 1 2 o 2 | 3 4 5 w 3 | 6 7 8 9 row and col may be interchanged: LTI(a,b)==LTI(b,a) LTI2(a,b) is the index of an off-diagonal lower triangular matrix: col | 0 1 2 3 ----+------- 0 | x r 1 | 0 x o 2 | 1 2 x w 3 | 3 4 5 x */ #define LTI(r,c) ((r) >= (c) ? (((r)*(r+1))>>1)+(c) : (((c)*(c+1))>>1)+(r)) #define LTI2(r,c) ((r) >= (c) ? (((r)*(r-1))>>1)+(c) : (((c)*(c-1))>>1)+(r)) /* Note: `>>1' replaced `/2' to circumvent an hp 10.20 optimizer bug */ #if defined(__cplusplus) extern "C" { #endif typedef struct { char *str; unsigned int max_length; } STRING_BUFFER; void set_mv_float(float *f); void set_mv_double(double *d); int is_mv_float(const float *f); int is_mv_double(const double *d); int almost_equals(const char *tok, const char *str); void *emalloc(size_t size); void *ecalloc(size_t nobj, size_t size); void *erealloc(void *p, size_t size); void efree(void *p); #if defined(__cplusplus) } #endif #endif /* UTILS_H */ gstat/src/getest.h0000644000176200001440000000010613777370515013643 0ustar liggesusersvoid get_est(DATA **data, METHOD method, DPOINT *where, double *est); gstat/src/msim.h0000644000176200001440000000112513777370515013317 0ustar liggesusersvoid save_sim(DATA **data, DPOINT *where, int sim, int n_vars, const double *value, int *is_pt); void save_sim_strat(DATA *d, DPOINT *where, int sim, double value, int is_pt); void restore_data_sel(DATA **data, int sim, int n_vars); void save_simulations_to_ascii(const char *fname); void save_simulations_to_maps(GRIDMAP *mask); void lhs(DATA **d, int n_vars, int stratify); void init_simulations(DATA **d); void set_beta(DATA **d, int sim, int n_vars, METHOD method); void setup_beta(DATA **d, int n_vars, int n_sim); void print_sim(void); void free_simulations(void); float ***get_msim(void); gstat/src/vario.h0000644000176200001440000001470113777370515013476 0ustar liggesusers#ifndef VARIO_H # define VARIO_H /* avoid multiple inclusion */ typedef enum { NOTSPECIFIED = 0, SEMIVARIOGRAM, CROSSVARIOGRAM, COVARIOGRAM, CROSSCOVARIOGRAM, PRSEMIVARIOGRAM /* pairwise relative semivariogram */ } SAMPLE_VGM_TYPE; extern const char *vgm_type_str[]; #define LENGTH_OF_MODEL 100 /* max string length for one variogram model */ typedef enum { ZERO_DEFAULT = 0, ZERO_INCLUDE, ZERO_AVOID, ZERO_SPECIAL } DO_AT_ZERO; typedef struct { double tm[3][3]; /* 3D-transformation matrix */ double angle[3]; /* angle in , ccl from pos x; angle up; rot. angle */ double ratio[2]; /* ratio axis2:axis1, ratio axis axis3:axis1 */ } ANIS_TM; typedef enum { NO_FIT = 0, WLS_FIT = 1, WLS_FIT_MOD = 2, /* 3, 4: gnuplot fits not supported */ MIVQUE_FIT = 5, OLS_FIT = 6, WLS_NHH = 7 } FIT_TYPE; typedef struct { int n_est, n_max, cloud, plot_numbers, is_asym; int recalc, refit, pseudo, is_directional; double *gamma, *dist; unsigned long *nh; double cutoff, iwidth; SAMPLE_VGM_TYPE evt; FIT_TYPE fit; DO_AT_ZERO zero; void *map, /* variogram map structure, i/o using files */ *S_grid /* variogram map structure, passed from S interface*/ ; struct { double x, y, z; } direction; DPOINT ***pairs; /* optionally, the point pair list -- for j in [ 0, nh[i] > ((DPOINT ***)pairs)[i][j*2] and its successor are two pointers to a pair of data points that were used to calculate gamma[i]. The length of pairs is (at least) nh[i] * 2. See register_pairs() */ } SAMPLE_VGM; /* a sample variogram */ typedef enum { NOT_SP = 0, NUGGET, EXPONENTIAL, SPHERICAL, GAUSSIAN, EXCLASS, MATERN, STEIN, CIRCULAR, LINEAR, BESSEL, PENTASPHERICAL, PERIODIC, WAVE, HOLE, LOGARITHMIC, POWER, SPLINE, LEGENDRE, MERROR, INTERCEPT } VGM_MODEL_TYPE; typedef struct { VGM_MODEL_TYPE model; const char *name, *name_long; double (*fn)(double h, double *r), /* variogram value at h of basic model */ (*da_fn)(double h, double *r); /* it's derivative to the range parm. */ } V_MODEL; extern const V_MODEL v_models[]; #define NRANGEPARS 2 /* max number of range parameters in variogram models */ typedef struct { VGM_MODEL_TYPE model; int fit_sill, fit_range, id; double range[NRANGEPARS], sill, (*fnct)(double h, double *r), /* (partial) unit variogram function */ (*da_fnct)(double h, double *r); /* (partial) derivative to range of unit variogram */ ANIS_TM *tm_range; } VGM_MODEL; typedef struct { long n; /* length */ double maxdist, *values; ANIS_TM *tm_range; } COV_TABLE; #define COV_TABLE_VALUE(tablep, dist) \ (dist >= tablep->maxdist ? tablep->values[tablep->n - 1] : \ tablep->values[(int) (tablep->n * (dist / tablep->maxdist))]) #define SEM_TABLE_VALUE(tablep, dist) \ (tablep->values[0] - COV_TABLE_VALUE(tablep, dist)) typedef struct { int n_models, max_n_models, n_fit, id, id1, id2, block_semivariance_set, block_covariance_set, isotropic, is_valid_covariance, fit_is_singular; VGM_MODEL *part; /* the basic models */ COV_TABLE *table; /* covariance value table */ double block_semivariance, /* average within-block semivariance */ block_covariance, /* average within-block covariance */ max_range, /* maximum range: where sill is reached */ sum_sills, /* sum of partial sill's */ measurement_error, /* measurement error value--def. zero */ max_val, /* maximum value that is ever reached */ min_val, /* minimum value that is ever reached */ SSErr; /* fit result */ SAMPLE_VGM *ev; } VARIOGRAM; #define dist2(x,y,z) (x*x+y*y+z*z) #define TM_IS3D(tm) \ (tm->angle[1] != 0.0 || tm->angle[2] != 0.0 || tm->ratio[1] < 1.0) #define relative_norm(v,x,y,z) ((v == NULL || dist2(x,y,z) == 0.0) ? 1.0 : \ (transform_norm(NULL,x,y,z)/transform_norm(v,x,y,z))) #define UnitCovariance(part,x,y,z) \ (part.model == INTERCEPT ? (1.0) :\ (1.0 - part.fnct(transform_norm(part.tm_range,x,y,z), part.range))) #define UnitSemivariance(part,x,y,z) \ (part.fnct(transform_norm(part.tm_range,x,y,z), part.range)) #define Covariance(part,x,y,z) (part.sill * UnitCovariance(part,x,y,z)) #define Semivariance(part,x,y,z) (part.sill * UnitSemivariance(part,x,y,z)) #define DA_DELTA 0.001 #define da_Semivariance(part,x,y,z) \ (part.da_fnct != NULL ? \ (part.sill * part.da_fnct(transform_norm(part.tm_range,x,y,z), part.range)) : \ da_general(&(part), transform_norm(part.tm_range, x,y,z))) /* (part.sill * \ (part.fnct(transform_norm(part.tm_range,x,y,z), part.range * (1.0 + DA_DELTA)) - \ part.fnct(transform_norm(part.tm_range,x,y,z), part.range * (1.0 - DA_DELTA))) \ / (2 * part.range * DA_DELTA))) */ #define EPSILON 1.0e-30 /* for small, non-zero anisotropy ratios */ #define is_covariogram(v) \ ((v->ev->evt==COVARIOGRAM||v->ev->evt==CROSSCOVARIOGRAM)) #define is_variogram(v) \ ((v->ev->evt==SEMIVARIOGRAM||v->ev->evt==CROSSVARIOGRAM)) #define is_direct(v) \ ((v->ev->evt==COVARIOGRAM||v->ev->evt==SEMIVARIOGRAM)) #define is_cross(v) \ ((v->ev->evt==CROSSCOVARIOGRAM||v->ev->evt==CROSSVARIOGRAM)) #define MODELHASNORANGE(m) (m == NUGGET || m == INTERCEPT) #define PARTHASNORANGE(m) (m->model == NUGGET || m->model == INTERCEPT || \ (m->model == LINEAR && m->range == 0.0)) #if defined(__cplusplus) extern "C" { #endif extern const char *v_model_gnuplot[]; extern const char *v_model_names[]; extern const char *c_model_gnuplot[]; VARIOGRAM *init_variogram(VARIOGRAM *v); SAMPLE_VGM *init_ev(void); void vgm_init_block_values(VARIOGRAM *v); void free_variogram(VARIOGRAM *v); void logprint_variogram(const VARIOGRAM *v, int verbose); void fprint_variogram(FILE *f, const VARIOGRAM *v, int verbose); const char *sprint_variogram(const VARIOGRAM *v, int verbose); double get_semivariance(const VARIOGRAM *v, double dx, double dy, double dz); double get_covariance (const VARIOGRAM *v, double dx, double dy, double dz); double transform_norm(const ANIS_TM *tm, double dx, double dy, double dz); void check_variography(const VARIOGRAM **v, int n); void update_variogram(VARIOGRAM *vp); double get_max_sills(int n); double da_general(VGM_MODEL *p, double h); int push_variogram_model(VARIOGRAM *v, VGM_MODEL part); VGM_MODEL_TYPE which_variogram_model(const char *m); double relative_nugget(VARIOGRAM *v); int vario(int argc, char **argv); DO_AT_ZERO zero_int2enum(int zero); void push_to_v(VARIOGRAM *v, const char *mod, double sill, double *range, int nrangepars, double *d, int fit_sill, int fit_range); void push_to_v_table(VARIOGRAM *v, double maxdist, int length, double *values, double *anis); #if defined(__cplusplus) } #endif #endif /* VARIO_H */ gstat/src/nsearch.h0000644000176200001440000000137013777370515013777 0ustar liggesusers#ifndef SEARCH_H # define SEARCH_H /* avoid multiple inclusion */ void qtree_free(QTREE_NODE *node); void qtree_pop_point(DPOINT *p, DATA *d); void qtree_push_point(DATA *d, DPOINT *p); void qtree_rebuild(DATA *d); int qtree_select(DPOINT *where, DATA *d); /* 2-norm distances from point to block: */ double pb_norm_3D(const DPOINT *where, BBOX bbox); double pb_norm_2D(const DPOINT *where, BBOX bbox); double pb_norm_1D(const DPOINT *where, BBOX bbox); /* define the maximum depth of the quadtree; * Fri Jul 4 12:05:47 CEST 2003 * if this is not defined, more than gl_split points at * a single spatial location cause infinite recursion * 10 seems a reasonable value: 1/2048 of the bbox dim * */ #define MAX_RECURSION_DEPTH 11 #endif /* SEARCH_H */ gstat/src/block.h0000644000176200001440000000014413777370515013444 0ustar liggesusersDATA *block_discr(DATA *d, const DPOINT *block, const DPOINT *where); void reset_block_discr(void); gstat/src/reml.h0000644000176200001440000000035213777370515013312 0ustar liggesusersVARIOGRAM *reml_sills(DATA *d, VARIOGRAM *vp); #ifdef MATRIXH MAT *XVXt_mlt(MAT *X, MAT *V, MAT *out); MAT *XtVX_mlt(MAT *X, MAT *V, MAT *out); MAT *XdXt_mlt(MAT *X, VEC *d, MAT *out); MAT *XtdX_mlt(MAT *X, VEC *d, MAT *out); #endif gstat/src/s.h0000644000176200001440000000024613777370515012617 0ustar liggesusersvoid s_gstat_error(const char *mess, int level); void s_gstat_warning(const char *mess); double r_normal(void); double r_uniform(void); extern int do_print_progress; gstat/src/mapio.c0000644000176200001440000000622513777370515013460 0ustar liggesusers/* * former mapio io functions, now only skeleton things doing row/col <--> x/y */ #include /* floor() */ #include /* FLT_MAX */ #include "defs.h" #include "glvars.h" #include "utils.h" #include "debug.h" #include "userio.h" #include "mapio.h" static GRIDMAP *write_error(GRIDMAP * m); #define SWAP_N(a,n) swap_floats((unsigned char *)a,n) #define SWAP_M_N(a,m,n) swap_multiformat((unsigned char *)a,m,n) #define CHECK_ROWS 1 #define CHECK_COLS 2 #define CHECK_CELLSIZE 4 #define CHECK_X_UL 8 #define CHECK_Y_UL 16 #define CHECK_SUM 31 /* sum of all checks */ #define BINARY_NATIVE 1 #define BINARY_NON_NATIVE 2 #define DEFAULT_MISVAL -9999.0 #define SURFER_MISVAL 1.70141E+38 /* * create a new GRIDMAP structure * allocates memory and initializes all fields for a GRIDMAP structure * returns: pointer to GRIDMAP structure */ GRIDMAP *new_map(MAP_READ_STATUS status) { GRIDMAP *map; map = (GRIDMAP *) emalloc(sizeof(GRIDMAP)); map->status = status; map->type = MT_UNKNOWN; map->history = NULL; map->description = NULL; map->filename = NULL; map->rows = 0; map->cols = 0; map->base_size = 0; map->grid = NULL; map->base = NULL; map->first_time_row = NULL; map->is_binary = 0; map->celltype = CT_UNKNOWN; map->misval = DEFAULT_MISVAL; /* only for arcgrid */ map->cellmin = map->cellmax = FLT_MAX; map->CSF_MAP = NULL; map->write = write_error; map->read_row = map->write_row = NULL; map->current_row = 0; return map; } static GRIDMAP *write_error(GRIDMAP * m) { pr_warning("%s: writing this map format is not supported", m->filename); assert(0); return NULL; } /* * give x,y coordinate of cell center for cell [row, col] * libcsf has it's own function; other formats assume increasing x * for increasing cols and decreasing y for increasing rows * returns: non-zero if row or col are outside map limits */ int map_rowcol2xy(GRIDMAP * m, /* pointer to gridmap */ unsigned int row, /* current row number */ unsigned int col, /* current column number */ double *x, /* return value: pointer to x-coordinate */ double *y /* return value: pointer to y-coordinate */ ) { assert(m); assert(x); assert(y); if (row >= m->rows || col >= m->cols) return 1; *x = m->x_ul + (col + 0.5) * m->cellsizex; *y = m->y_ul - (row + 0.5) * m->cellsizey; return 0; } /* * converts x and y coordinate to (row,col) pair. * * see comment for map_rowcol2xy() * * returns: non-zero if x or y are outside map limits */ int map_xy2rowcol(GRIDMAP * m /* pointer to map */ , double x, /* x-coordinate */ double y, /* y-coordinate */ unsigned int *row, /* output value: pointer to row number */ unsigned int *col /* output value: pointer to column number */ ) { assert(m); assert(row); assert(col); if (x < m->x_ul || x > m->x_ul + m->cols * m->cellsizex || y > m->y_ul || y < m->y_ul - m->rows * m->cellsizey) return 1; *row = (unsigned int) floor((m->y_ul - y) / m->cellsizey); *col = (unsigned int) floor((x - m->x_ul) / m->cellsizex); if (*row == m->rows) /* on the bottom edge */ *row = *row - 1; if (*col == m->cols) /* on the right edge */ *col = *col - 1; return 0; } gstat/src/gls.h0000644000176200001440000000074213777370515013143 0ustar liggesusersenum GLS_WHAT { GLS_BLUE /* generalized least squares best linear unbiased estimate */, GLS_BLUP /* gls best linear unbiased predictor */, GLS_BLP /* gls best linear predictor */, UPDATE /* update estimate: use previously calculated weights */, GLS_INIT /* initial value */ }; void gls(DATA **d, int n_vars, enum GLS_WHAT pred, DPOINT *where, double *est); double *make_gls(DATA *d, int calc_residuals); double *make_gls_mv(DATA **d, int n_vars); void free_glm(void *v_glm); gstat/src/userio.h0000644000176200001440000000302413777370515013660 0ustar liggesusers#ifndef USERIO_H #define USERIO_H enum Gstat_errno { ER_NOERROR = 0 /* no error */, ER_NULL = 1 /* internal error: should not occur */, ER_VARNOTSET = 2 /* a required variable was not set by the user */, ER_RANGE = 3 /* range error (outside permitted values) */, ER_IMPOSVAL = 4 /* a variable was set to an illegal value */, ER_WRITE = 6 /* write error on file */, ER_READ = 7 /* read error on file */, ER_RDFLT = 8 /* error while converting a string to a float */, ER_RDINT = 9 /* error while converting a string to an int */, ER_SYNTAX = 10 /* syntax error */, ER_ARGOPT = 11 /* error in command line option arguments */, ER_DOMAIN = 12 /* math error */, ER_MEMORY = 13 /* memory exhausted */, ER_IO = 14 /* i/o conflict (e.g. redirection not permitted) */, ER_NOCMD = 15 /* no command file specified */, ER_NOCURSES = 16 /* no curses user interface compiled in */, ER_PWRITE = 17 /* error while writing to a pipe */, ER_PREAD = 18 /* error while reading from a pipe */, ER_SECURE = 19 /* secure mode: operation not allowed */ }; #define MAX_ERRNO 19 void message(char *fmt, ...); /* message() calls always preceed ErrMsg() */ #define ErrMsg(a,b) gstat_error(__FILE__,__LINE__,a,b) void gstat_error(char *fname, int line, enum Gstat_errno err_nr, const char *msg); void pr_warning(char *fmt, ...); void printlog(const char *fmt, ...); void print_progress(unsigned int current, unsigned int total); #endif /* USERIO_H */ gstat/src/Makevars0000644000176200001440000000006013777370515013672 0ustar liggesusersPKG_LIBS = $(LAPACK_LIBS) $(BLAS_LIBS) $(FLIBS) gstat/src/mtrx.h0000644000176200001440000000377013777370515013354 0ustar liggesusers#ifndef MTRXH # define MTRXH /* interface copied from meschach; implementation rewritten from scratch */ typedef struct { size_t m, n, /* #rows, #cols */ max; /* max size, memory allocated */ double *v; } MAT; /* dense matrix */ #define ME(X,i,j) X->v[j * X->m + i] /* row i, column j, column-major access */ typedef struct { size_t dim, max; double *ve; } VEC; /* vector: row or column, whatever matches */ typedef struct { size_t size, max; int *pe; } PERM; typedef struct { size_t size, max; int *ive; } IVEC; #define PNULL (PERM *) NULL #define MNULL (MAT *) NULL #define VNULL (VEC *) NULL #define IVNULL (IVEC *) NULL #define M_FREE(x) { if (x != NULL) m_free(x); x = MNULL; } #define V_FREE(x) { if (x != NULL) v_free(x); x = VNULL; } #define P_FREE(x) { if (x != NULL) px_free(x); x = PNULL; } void m_free(MAT *m); void v_free(VEC *v); void iv_free(IVEC *v); void px_free(PERM *p); #define m_get(i,j) m_resize(MNULL, i, j) #define v_get(i) v_resize(VNULL, i) MAT *m_resize(MAT *mat, size_t m, size_t n); VEC *v_resize(VEC *v, size_t n); PERM *px_resize(PERM *p, size_t n); IVEC *iv_resize(IVEC *v, size_t n); MAT *m_zero(MAT *m); VEC *v_zero(VEC *v); MAT *m_inverse(MAT *in, int *info); VEC *vm_mlt(MAT *m, VEC *v, VEC *out); VEC *mv_mlt(MAT *m, VEC *v, VEC *out); MAT *m_mlt(MAT *m1, MAT *m2, MAT *out); MAT *mtrm_mlt(MAT *m1, MAT *m2, MAT *out); VEC *v_sub(VEC *v1, VEC *v2, VEC *out); MAT *m_sub(MAT *m1, MAT *m2, MAT *out); VEC *v_add(VEC *v1, VEC *v2, VEC *out); VEC *sv_mlt(double s, VEC *v1, VEC *v2); MAT *m_add(MAT *m1, MAT *m2, MAT *out); MAT *m_copy(MAT *in, MAT *out); VEC *v_copy(VEC *in, VEC *out); double v_norm2(VEC *v); MAT *CHsolve(MAT *A, MAT *b, MAT *out, PERM *piv); VEC *CHsolve1(MAT *A, VEC *b, VEC *out, PERM *piv); MAT *CHfactor(MAT *A, PERM *piv, int *info); double in_prod(VEC *a, VEC *b); MAT *sm_mlt(double s, MAT *m1, MAT *out); MAT *ms_mltadd(MAT *m1, MAT *m2, double s, MAT *out); MAT *mmtr_mlt(MAT *m1, MAT *m2, MAT *out); void m_logoutput(MAT *a); void v_logoutput(VEC *x); #endif gstat/src/gcdist.h0000644000176200001440000000011113777370515013621 0ustar liggesusersdouble gstat_gcdist(double lon1, double lon2, double lat1, double lat2); gstat/src/vario_io.c0000644000176200001440000001011113777370515014147 0ustar liggesusers/* * vario_io.c: functions for point-point, point-block (co/semi)variances */ #include #include #include #include "userio.h" #include "debug.h" #include "data.h" #include "vario.h" #include "block.h" #include "glvars.h" /* get_block_p(), gl_zero, gl_longlat */ #include "vario_io.h" static double sem_cov_blocks(VARIOGRAM *v, DATA *a, DATA *b, int sem); double sem_cov_ab(VARIOGRAM *v, DPOINT *a, DPOINT *b, int sem) /* * return Cov(a,b) or Sem(a,b), * taking care of IS_BLOCK(a) and IS_BLOCK(b): */ { static DATA *Discr_a = NULL, *Discr_b = NULL; static DPOINT *block_p = NULL; DPOINT *tmp; if (block_p == NULL) block_p = get_block_p(); if (a == b) { if (IS_POINT(a)) return sem_cov_blocks(v, NULL, NULL, sem); Discr_a = block_discr(Discr_a, block_p, a); return sem_cov_blocks(v, Discr_a, Discr_a, sem); } /* * if one of them IS_BLOCK, make sure it's a: * (because block_discr() will otherwise store block * discretisations in both Discr_a and Discr_b) */ if (IS_POINT(a) && IS_BLOCK(b)) { tmp = a; a = b; b = tmp; /* swap a and b */ } Discr_a = block_discr(Discr_a, block_p, a); Discr_b = block_discr(Discr_b, block_p, b); return sem_cov_blocks(v, Discr_a, Discr_b, sem); } static double sem_cov_blocks(VARIOGRAM *v, DATA *a, DATA *b, int sem) { /* * Purpose : calculates (once) and returns Cov(a,b); * if a==b && a denotes a block discretisation, the value * is put in a->block_variance and a->block_xxx_set gets 1 * Created by : Edzer J. Pebesma * Date : 25 jan 1992, 3 june 1993 * Prerequisites : none * Returns : sem == 1 ? Sem(a,b) : Cov(a,b) * Side effects : none */ int i, j; double block_value, dx, dy = 0.0, dz = 0.0, dist, ret, weight, dzero2; DPOINT *dpa, *dpb; /* if (a->what_is_u != U_ISWEIGHT || b->what_is_u != U_ISWEIGHT) ErrMsg(ER_IMPOSVAL, "weights needed in SevCov_Blocks()"); */ if (a == NULL) return sem ? get_semivariance(v, 0.0, 0.0, 0.0) : get_covariance(v, 0.0, 0.0, 0.0); if (a->n_list == 1 && b->n_list == 1) { /* point--point */ if (gl_longlat) { if (! v->isotropic) ErrMsg(ER_IMPOSVAL, "for long/lat data, anisotropy cannot be defined"); dist = pp_norm_gc(a->list[0], b->list[0]); ret = sem ? get_semivariance(v, dist, 0.0, 0.0): get_covariance(v, dist, 0.0, 0.0); /* printf("ll dist: %g, ret.val %g\n", dist, ret); */ return ret; } else { return sem ? get_semivariance(v, a->list[0]->x - b->list[0]->x, a->list[0]->y - b->list[0]->y, a->list[0]->z - b->list[0]->z): get_covariance(v, a->list[0]->x - b->list[0]->x, a->list[0]->y - b->list[0]->y, a->list[0]->z - b->list[0]->z); } } /* now a->n_list > 1 or b->n_list > 1: block--block or point--block */ if (gl_longlat) ErrMsg(ER_IMPOSVAL, "block kriging for long-lat data undefined"); if (a == b) { /* block--block for a single block */ if (sem && v->block_semivariance_set) return v->block_semivariance; if (!sem && v->block_covariance_set) return v->block_covariance; } /* else: continue */ dzero2 = gl_zero * gl_zero; block_value = 0.0; for (i = 0; i < a->n_list; i++) { for (j = 0; j < b->n_list; j++) { /* compare all points with all p */ dpa = a->list[i]; dpb = b->list[j]; weight = dpa->u.weight * dpb->u.weight; /* avoid the "zero-effect" if a or b is block: */ dx = dpa->x - dpb->x; dy = dpa->y - dpb->y; dz = dpa->z - dpb->z; /* avoid ``zero-effect'': */ if (a->pp_norm2(dpa, dpb) < dzero2) { dx = (dx >= 0 ? gl_zero : -gl_zero); if (a->mode & Y_BIT_SET) dy = (dy >= 0 ? gl_zero : -gl_zero); if (a->mode & Z_BIT_SET) dz = (dz >= 0 ? gl_zero : -gl_zero); } if (sem) block_value += weight * get_semivariance(v, dx, dy, dz); else block_value += weight * get_covariance(v, dx, dy, dz); } /* for j */ } /* for i */ if (a == b) { /* remember within block cov./sem.: */ if (sem) { v->block_semivariance = block_value; v->block_semivariance_set = 1; } else { v->block_covariance = block_value; v->block_covariance_set = 1; } } return block_value; } gstat/src/defaults.h0000644000176200001440000000366013777370515014167 0ustar liggesusers#ifndef DEFAULTS_H #include /* INT_MAX */ #include /* DBL_EPSILON */ # define DEFAULTS_H /* avoid multiple inclusion */ #define DEF_alpha 0.0 #define DEF_beta 0.0 #define DEF_blas 1 #define DEF_bounds NULL #define DEF_coincide -1 #define DEF_choleski 1 #define DEF_cressie 0 #define DEF_cutoff -1.0 #define DEF_dots 500 #define DEF_fit 0 #define DEF_fit_limit 1.0E-5 #define DEF_fraction 0.33333 /* fraction of max_dist for def. cutoff */ #define DEF_gauss 1 #define DEF_gpterm NULL #define DEF_idp 2.0 #define DEF_intervals 15 /* default number of intervals */ #define DEF_is_pdf 0 /* default to cdf indicator simulation */ #define DEF_iter 200 #define DEF_iwidth -1.0 #define DEF_jgraph 0 #define DEF_lhs 0 #define DEF_longlat 0 #define DEF_n_marginals 0 #define DEF_nocheck 0 /* do check */ #define DEF_marginal_names NULL #define DEF_marginal_values NULL #define DEF_nblockdiscr 4 #define DEF_n_uk INT_MAX #define DEF_numbers 1 #define DEF_nsim 1 #define DEF_ofilename NULL #define DEF_order 0 #define DEF_plotweights 0 #define DEF_pairs 0 #define DEF_quantile 0.5 #define DEF_rowwise 1 #define DEF_rp 1 #define DEF_seed 0 #define DEF_sim_beta 0 #define DEF_sparse 0 #define DEF_spiral 0 #define DEF_split 4 #define DEF_sym_ev 0 #define DEF_table_size 0 #define DEF_tol_hor 180.0 #define DEF_tol_ver 180.0 #define DEF_gls_residuals 0 #define DEF_xvalid 0 #define DEF_zero (DBL_EPSILON * 10.0) #define DEF_zero_est 0 /* ZERO_DEFAULT */ #define DEF_zmap 0.0 #endif /* DEFAULTS_H */ gstat/src/debug.h0000644000176200001440000000412313777370515013441 0ustar liggesusers#ifndef DEBUG_H # define DEBUG_H /* avoid multiple inclusion */ extern int debug_level; /* * DEBUG macro's: */ #define DB_HELP (-1) /* print debug help */ #define DB_SILENT (0) #define DB_NORMAL (1UL << 0) #define DB_DUMP (1UL << 1) /* dump global variabels */ #define DB_FIT (1UL << 2) /* fit diagnostics */ #define DB_DATA (1UL << 3) /* drop data */ #define DB_SEL (1UL << 4) /* drop selection */ #define DB_COV (1UL << 5) /* drop covariances */ #define DB_ORDER (1UL << 6) /* order relation violation */ #define DB_FORCE (1UL << 7) /* print warning if neighbourhood selection */ #define DB_TRACE (1UL << 8) /* print numbers */ #define DB_BLOCK (1UL << 9) /* block discretization diagnostics (data) */ extern void printlog(const char *fmt, ...); #define DUMP(a); {if(debug_level & DB_DUMP) { printlog("%s", a); }} #define DEBUG_HELP (debug_level & DB_HELP) #define DEBUG_SILENT (debug_level == DB_SILENT) #define DEBUG_NORMAL (debug_level & DB_NORMAL) #define DEBUG_DUMP (debug_level & DB_DUMP) #define DEBUG_FIT (debug_level & DB_FIT) #define DEBUG_DATA (debug_level & DB_DATA) #define DEBUG_SEL (debug_level & DB_SEL) #define DEBUG_COV (debug_level & DB_COV) #define DEBUG_ORDER (debug_level & DB_ORDER) #define DEBUG_VGMFIT (debug_level & DB_ORDER) #define DEBUG_FORCE (debug_level & DB_FORCE) #define DEBUG_TRACE (debug_level & DB_TRACE) #define DEBUG_BLOCK (debug_level & DB_BLOCK) #define DEBUG_OPTIONS "\ # gstat debug option values:\n\ 0: no output, be silent (same as -s)\n\ 1: normal output (default value)\n\ 2: print all global variables and extended error messages\n\ 4: print OLS and WLS fit diagnostics\n\ 8: print all data\n\ 16: print every neighbourhood selection\n\ 32: print all covariance matrices, solutions, design matrices etc.\n\ 64: print variogram fit diagnostics and order relation violations\n\ 128: print warning on forced neighbourhoods\n\ 256: print current row,column or record number\n\ 512: print block discretization points (data)\n\ to combine options, sum their values -- 1023 invokes them all\n" #endif /* DEBUG_H */ gstat/src/vario_io.h0000644000176200001440000000156513777370515014171 0ustar liggesusersdouble sem_cov_ab(VARIOGRAM *v, DPOINT *a, DPOINT *b, int sem); /* covariance: */ #define COVARIANCE(v,a,b) ((IS_POINT(a) && IS_POINT(b) && !gl_longlat) ? \ (get_covariance(v,a->x - b->x,a->y - b->y, a->z - b->z)) : \ sem_cov_ab(v,a,b,0)) /* generalized covariance: */ #define GCV(v,a,b) ((IS_POINT(a) && IS_POINT(b) && !gl_longlat) ? \ (v->max_val - get_semivariance(v,a->x - b->x,a->y - b->y, a->z - b->z)) : \ (v->max_val - sem_cov_ab(v,a,b,1))) /* * CME is the measurement error-adjustment to GCV or COVARIANCE: * see Cressie, Statistics for Spatial Data, revised ed. 1993, * eq. 3.2.25-3.2.27, and page 379 */ #define CME(v,a,b,dist) ((IS_POINT(a) && IS_POINT(b) && \ (a == b || dist(a, b) == 0.0)) ? v->measurement_error : 0.0) #define GCV0(v,a,b,dist) (GCV(v,a,b) - CME(v,a,b,dist)) #define COVARIANCE0(v,a,b,dist) (COVARIANCE(v,a,b) - CME(v,a,b,dist)) gstat/src/s.c0000644000176200001440000007431714127264041012606 0ustar liggesusers/* * all functions exposed to R */ #include #include /* #include */ #include "defs.h" #include "data.h" #include "select.h" #include "utils.h" #include "userio.h" #include "vario.h" #include "fit.h" #include "sem.h" #include "glvars.h" #include "debug.h" #include "mapio.h" #include "msim.h" #include "getest.h" #include "s.h" static DATA_GRIDMAP *gstat_S_fillgrid(SEXP gridparams); static void gstat_set_block(long i, SEXP block, SEXP block_cols, DPOINT *current); int do_print_progress = 0; #define NAME_SIZE 20 /* buffer size for name */ extern unsigned int n_pred_locs; /* msim.c */ SEXP gstat_init(SEXP s_debug_level) { do_print_progress = 0; remove_all(); init_global_variables(); init_data_minmax(); GetRNGstate(); debug_level = INTEGER(s_debug_level)[0]; if (debug_level < 0) { debug_level = -debug_level; do_print_progress = 1; } return(s_debug_level); } SEXP gstat_exit(SEXP x) { PutRNGstate(); /* write seed back to R/S engine */ remove_all(); return(x); } SEXP gstat_new_data(SEXP sy, SEXP slocs, SEXP sX, SEXP has_intercept, SEXP beta, SEXP nmax, SEXP nmin, SEXP maxdist, SEXP force, SEXP vfn, SEXP sw, SEXP grid, SEXP degree, SEXP is_projected, SEXP vdist, SEXP lambda, SEXP omax) { double *y, *locs, *X, *w = NULL; long i, j, id, n, dim, n_X, has_int; DPOINT current; DATA **d; char name[NAME_SIZE]; PROTECT(sy = coerceVector(sy, REALSXP)); n = LENGTH(sy); y = REAL(sy); if (n == 0) ErrMsg(ER_IMPOSVAL, "no data read"); if (LENGTH(slocs) % n != 0) error("dimensions do not match: locations %d and data %ld", (int) LENGTH(slocs), n); dim = LENGTH(slocs) / n; if (dim <= 0) error("too few spatial dimensions: %ld", dim); if (dim > 3) error("too many spatial dimensions: %ld", dim); locs = REAL(slocs); if (LENGTH(sw) == n) w = REAL(sw); if (LENGTH(sX) % n != 0) error("dimensions do not match: X %d and data %ld: missing values in data?", (int) LENGTH(sX), n); n_X = LENGTH(sX) / n; X = REAL(sX); assert(n_X > 0); current.z = 0.0; current.bitfield = 0; id = get_n_vars(); snprintf(name, NAME_SIZE, "var%ld", id); which_identifier(name); d = get_gstat_data(); d[id]->id = id; d[id]->n_list = d[id]->n_max = 0; d[id]->colnx = d[id]->colny = d[id]->colnvalue = d[id]->colnz = 0; d[id]->x_coord = "x"; d[id]->y_coord = "y"; d[id]->z_coord = "z"; d[id]->variable = "R data"; d[id]->fname = "R data"; d[id]->lambda = REAL(lambda)[0]; has_int = INTEGER(has_intercept)[0]; /* increase d[id]->n_X and set d[id]->colX[i]: */ for (i = d[id]->n_X = 0; i < n_X; i++) data_add_X(d[id], i + (has_int ? 0 : 1)); assert(d[id]->n_X == n_X); for (i = 0; i < LENGTH(beta); i++) /* do nothing if beta is numeric(0) */ d[id]->beta = push_d_vector(REAL(beta)[i], d[id]->beta); if (INTEGER(nmax)[0] > 0) /* leave default (large) if < 0 */ d[id]->sel_max = INTEGER(nmax)[0]; if (INTEGER(omax)[0] > 0) /* leave default (0) if <= 0 */ d[id]->oct_max = INTEGER(omax)[0]; if (INTEGER(nmin)[0] > 0) /* leave default (0) if <= 0 */ d[id]->sel_min = INTEGER(nmin)[0]; if (REAL(maxdist)[0] > 0.0) d[id]->sel_rad = REAL(maxdist)[0]; if (INTEGER(force)[0] > 0) d[id]->force = INTEGER(force)[0]; switch(INTEGER(vfn)[0]) { case 1: /* d[id]->variance_fn = v_identity; == leave NULL */ break; case 2: d[id]->variance_fn = v_mu; break; case 3: d[id]->variance_fn = v_bin; break; case 4: d[id]->variance_fn = v_mu2; break; case 5: d[id]->variance_fn = v_mu3; break; default: error("unknown variance function %d", INTEGER(vfn)[0]); } gl_longlat = (INTEGER(is_projected)[0] == 0); d[id]->mode = X_BIT_SET | V_BIT_SET; if (dim > 1) d[id]->mode = d[id]->mode | Y_BIT_SET; if (dim > 2) d[id]->mode = d[id]->mode | Z_BIT_SET; set_norm_fns(d[id]); /* so gstat can calculate distances */ if (w != NULL) d[id]->colnvariance = 1; /* it is set */ switch(LENGTH(grid)) { case 0: case 1: break; /* empty, i.e., numeric(0) */ case 6: d[id]->grid = gstat_S_fillgrid(grid); break; default: error("length of grid topology %d unrecognized", (int) LENGTH(grid)); } d[id]->polynomial_degree = INTEGER(degree)[0]; if (d[id]->polynomial_degree < 0 || d[id]->polynomial_degree > 3) { error("polynomial degree should be 0, 1, 2 or 3"); } if (d[id]->polynomial_degree > 0) { /* we're doing polynomials through degree: */ if (id > 0) { error("polynomial degree will only work for a single variable"); } if (n_X > 1) { error("polynomial degree only works when no other predictors are given"); } setup_polynomial_X(d[id]); /* standardized coordinate polynomials */ } d[id]->vdist = INTEGER(vdist)[0]; assert(n_X <= d[id]->n_X); current.X = (double *) emalloc(d[id]->n_X * sizeof(double)); SET_POINT(¤t); current.u.stratum = 0; current.attr = current.x = current.y = current.z = 0.0; for (i = 0; i < n; i++) { /* loop over points */ current.attr = y[i]; current.x = locs[i]; if (dim >= 2) current.y = locs[n + i]; if (dim >= 3) current.z = locs[2 * n + i]; /* track min/max coordinates, also for z, for the qtree bbox */ if (i == 0) { d[id]->maxX = d[id]->minX = current.x; d[id]->maxY = d[id]->minY = current.y; d[id]->maxZ = d[id]->minZ = current.z; } else { d[id]->minX = MIN(d[id]->minX, current.x); d[id]->maxX = MAX(d[id]->maxX, current.x); d[id]->minY = MIN(d[id]->minY, current.y); d[id]->maxY = MAX(d[id]->maxY, current.y); d[id]->minZ = MIN(d[id]->minZ, current.z); d[id]->minZ = MIN(d[id]->minZ, current.z); } for (j = 0; j < n_X; j++) current.X[j] = X[j * n + i]; if (w != NULL) current.variance = 1.0/(w[i]); push_point(d[id], ¤t); } check_global_variables(); d[id]->n_original = d[id]->n_list; efree(current.X); UNPROTECT(1); /* sy */ return(sy); } SEXP gstat_new_dummy_data(SEXP loc_dim, SEXP has_intercept, SEXP beta, SEXP nmax, SEXP nmin, SEXP maxdist, SEXP vfn, SEXP is_projected, SEXP vdist) { int i, id, dim, has_int; char name[NAME_SIZE]; DATA **d = NULL; dim = INTEGER(loc_dim)[0]; if (dim <= 0) error("dimension value impossible: %d", dim); if (dim > 3) error("too many dimensions: %d", dim); assert(LENGTH(beta) > 0); id = get_n_vars(); snprintf(name, NAME_SIZE, "var%d", id); which_identifier(name); d = get_gstat_data(); d[id]->id = id; d[id]->n_list = d[id]->n_max = 0; d[id]->colnx = d[id]->colny = d[id]->colnvalue = d[id]->colnz = 0; d[id]->x_coord = "x"; d[id]->y_coord = "y"; d[id]->z_coord = "z"; d[id]->variable = "R data"; d[id]->fname = "R data"; has_int = INTEGER(has_intercept)[0]; for (i = d[id]->n_X = 0; i < LENGTH(beta); i++) data_add_X(d[id], i + (has_int ? 0 : 1)); assert(d[id]->n_X == LENGTH(beta)); d[id]->dummy = 1; for (i = 0; i < LENGTH(beta); i++) d[id]->beta = push_d_vector(REAL(beta)[i], d[id]->beta); if (INTEGER(nmax)[0] > 0) /* leave default (large) if < 0 */ d[id]->sel_max = INTEGER(nmax)[0]; /* I doubt whether using nmin for dummy data _ever_ can have a * meaning, but hey, let's add it anyway. */ if (INTEGER(nmin)[0] > 0) /* leave default (0) if <= 0 */ d[id]->sel_min = INTEGER(nmin)[0]; if (REAL(maxdist)[0] > 0.0) d[id]->sel_rad = REAL(maxdist)[0]; switch(INTEGER(vfn)[0]) { case 1: /* d[id]->variance_fn = v_identity; -> leave NULL */ break; case 2: d[id]->variance_fn = v_mu; break; case 3: d[id]->variance_fn = v_bin; break; case 4: d[id]->variance_fn = v_mu2; break; case 5: d[id]->variance_fn = v_mu3; break; default: error("unknown variance function %d", INTEGER(vfn)[0]); } gl_longlat = (INTEGER(is_projected)[0] == 0); d[id]->vdist = INTEGER(vdist)[0]; d[id]->mode = X_BIT_SET | V_BIT_SET; if (dim > 1) d[id]->mode = d[id]->mode | Y_BIT_SET; if (dim > 2) d[id]->mode = d[id]->mode | Z_BIT_SET; set_norm_fns(d[id]); /* so gstat can calculate distances */ check_global_variables(); d[id]->n_original = d[id]->n_list; return(loc_dim); } SEXP gstat_predict(SEXP sn, SEXP slocs, SEXP sX, SEXP block_cols, SEXP block, SEXP weights, SEXP nsim, SEXP blue) { double *locs, **est_all, *X; long i, j, k, n, nvars, nest, dim, n_X, ncols_block, nrows_block, pos; DPOINT current, *bp = NULL; DATA **d = NULL, *vd = NULL, *area = NULL; SEXP ret; SEXP retvector; SEXP retvector_dim; extern unsigned int n_pred_locs; /* predict.c, used in msim.c */ float ***msim = NULL; nvars = get_n_vars(); nest = nvars + (nvars * (nvars + 1))/2; n = INTEGER(sn)[0]; if (n <= 0 || LENGTH(slocs) == 0 || LENGTH(sX) == 0) ErrMsg(ER_IMPOSVAL, "newdata empty or only NA's"); if (LENGTH(slocs) % n != 0) error("dimensions do not match: locations %d, nrows in X %ld", (int) LENGTH(slocs), n); dim = LENGTH(slocs) / n; if (dim > 3) error("too many spatial dimensions: %ld", dim); if (dim <= 0) error("too few spatial dimensions: %ld", dim); locs = REAL(slocs); if (LENGTH(sX) % n != 0) error("dimensions do not match: X %d and data %ld", (int) LENGTH(sX), n); n_X = LENGTH(sX) / n; current.attr = current.x = current.y = current.z = 0.0; current.bitfield = 0; /* assuming points ... */ SET_POINT(¤t); /* and then do the block thing: */ if (LENGTH(block_cols) == 0) { bp = get_block_p(); bp->x = bp->y = bp->z = 0.0; /* obsolete, I'd guess */ if (LENGTH(block) >= 1) { bp->x = REAL(block)[0]; SET_BLOCK(¤t); } if (LENGTH(block) >= 2) bp->y = REAL(block)[1]; if (LENGTH(block) >= 3) bp->z = REAL(block)[2]; if (LENGTH(block) > 3) pr_warning("block dimension can only be 3; using the first 3"); } else if (LENGTH(block_cols) == 1) { /* if > 1, block contains multiple 2D blocks */ ncols_block = INTEGER(block_cols)[0]; if (ncols_block < 1 || ncols_block > 3) ErrMsg(ER_IMPOSVAL, "block dimensions should be in [1..3]"); nrows_block = LENGTH(block) / ncols_block; /* nr of rows */ if (nrows_block > 0) { area = create_data_area(); area->colnvariance = 0; area->n_list = area->n_max = 0; area->id = ID_OF_AREA; area->mode = X_BIT_SET; if (ncols_block > 1) area->mode = area->mode & Y_BIT_SET; if (ncols_block > 2) area->mode = area->mode & Z_BIT_SET; for (i = 0; i < nrows_block; i++) { current.x = REAL(block)[i]; if (ncols_block > 1) current.y = REAL(block)[nrows_block + i]; if (ncols_block > 2) current.z = REAL(block)[2 * nrows_block + i]; if (LENGTH(weights) > 0) { area->colnvariance = 1; current.variance = REAL(weights)[i]; } push_point(area, ¤t); } SET_BLOCK(¤t); } if (DEBUG_FORCE) print_data_list(area); } X = REAL(sX); assert(n_X > 0); current.X = (double *) emalloc(n_X * sizeof(double)); current.u.stratum = 0; d = get_gstat_data(); est_all = (double **) emalloc(n * sizeof(double *)); for (i = 0; i < n; i++) est_all[i] = (double *) emalloc(nest * sizeof(double)); /* * the following is to fake gstat's default method handling: * we got to suggest that we'll go through a list of prediction * locations, a la the gstat ``data(): ... ;'' command. */ vd = get_dataval(); vd->id = ID_OF_VALDATA; vd->mode = d[0]->mode; /* set min/max[XYZ] */ vd->minY = vd->maxY = vd->minZ = vd->maxZ = 0.0; vd->minX = vd->maxX = locs[0]; for (i = 1; i < n; i++) { vd->minX = MIN(vd->minX, locs[i]); vd->maxX = MAX(vd->maxX, locs[i]); } if (dim >= 2) { vd->minY = vd->maxY = locs[n]; for (i = 1; i < n; i++) { vd->minY = MIN(vd->minY, locs[n + i]); vd->maxY = MAX(vd->maxY, locs[n + i]); } } if (dim >= 3) { vd->minZ = vd->maxZ = locs[2 * n]; for (i = 1; i < n; i++) { vd->minZ = MIN(vd->minZ, locs[2 * n + i]); vd->maxZ = MAX(vd->maxZ, locs[2 * n + i]); } } /* fill, and standardize coordinate predictors from degree = x */ for (i = 0; i < nvars; i++) setup_data_minmax(d[i]); setup_data_minmax(vd); for (i = 0; i < nvars; i++) calc_polynomials(d[i]); /* calc_polynomials(vd); */ /* still no data in fake vd */ vd->polynomial_degree = d[0]->polynomial_degree; if (vd->polynomial_degree > 0) { setup_polynomial_X(vd); /* standardized coordinate polynomials */ current.X = (double *) erealloc(current.X, vd->n_X * sizeof(double)); } /* so far for the faking; now let's see what gstat makes out of this: */ if (INTEGER(nsim)[0] == 0) { if (INTEGER(blue)[0] == 0) { /* FALSE */ if (get_method() == NSP) /* choose default */ set_method(get_default_method()); } else set_method(LSLM); } else { if (INTEGER(nsim)[0] < 0) { gl_nsim = -(INTEGER(nsim)[0]); set_method(ISI); } else { gl_nsim = INTEGER(nsim)[0]; set_method(GSI); } n_pred_locs = n; if (gl_nsim > 1) init_simulations(d); if (get_n_beta_set() != get_n_vars()) setup_beta(d, get_n_vars(), gl_nsim); } set_mode(); /* simple, stratified, multivariable? */ check_global_variables(); /* it's there, better do it now */ if (debug_level) Rprintf("[%s]\n", method_string(get_method())); #ifdef WIN32 R_FlushConsole(); R_ProcessEvents(); #endif for (i = 0; i < n; i++) { print_progress(i, n); if (LENGTH(block_cols) > 1) gstat_set_block(i, block, block_cols, ¤t); current.x = locs[i]; if (dim >= 2) current.y = locs[n + i]; if (dim >= 3) current.z = locs[2 * n + i]; for (j = 0; j < n_X; j++) current.X[j] = X[j * n + i]; /* transform standardized coordinate polynomial here */ if (vd->polynomial_degree) calc_polynomial_point(vd, ¤t); for (j = 0; j < get_n_vars(); j++) select_at(d[j], ¤t); get_est(d, get_method(), ¤t, est_all[i]); #ifdef WIN32 R_ProcessEvents(); /* avoid terminal freeze in R/Win */ #endif R_CheckUserInterrupt(); } print_progress(100, 100); PROTECT(ret = allocVector(VECSXP, 1)); PROTECT(retvector_dim = allocVector(REALSXP, 2)); REAL(retvector_dim)[0] = n; /* nrows */ if (gl_nsim > 1) { PROTECT(retvector = allocVector(REALSXP, gl_nsim * nvars * n)); msim = get_msim(); for (i = pos = 0; i < nvars; i++) for (j = 0; j < gl_nsim; j++) for (k = 0; k < n; k++) { if (is_mv_float(&(msim[i][k][j]))) REAL(retvector)[pos++] = NA_REAL; else REAL(retvector)[pos++] = msim[i][k][j]; } REAL(retvector_dim)[1] = nvars * gl_nsim; /* ncols */ } else { PROTECT(retvector = allocVector(REALSXP, n * nest)); for (j = pos = 0; j < nest; j++) { for (i = 0; i < n; i++) { if (is_mv_double(&(est_all[i][j]))) REAL(retvector)[pos] = NA_REAL; else REAL(retvector)[pos] = est_all[i][j]; pos++; } } REAL(retvector_dim)[1] = nest; /* ncols */ } if (gl_nsim > 0) free_simulations(); /* SET_DIM(retvector, retvector_dim); */ setAttrib(retvector, R_DimSymbol, retvector_dim); SET_VECTOR_ELT(ret, 0, retvector); for (i = 0; i < n; i++) efree(est_all[i]); efree(est_all); efree(current.X); UNPROTECT(3); return(ret); } static void gstat_set_block(long i, SEXP block, SEXP block_cols, DPOINT *current) { DATA *area; VARIOGRAM *v; long nrows_block, start, end, j; if (i >= LENGTH(block_cols) || i < 0) ErrMsg(ER_IMPOSVAL, "block_cols length less than nr of prediction locations"); nrows_block = LENGTH(block) / 2; /* nr of rows */ start = INTEGER(block_cols)[i]; if (i == LENGTH(block_cols) - 1) end = nrows_block; else end = INTEGER(block_cols)[i+1] - 1; area = get_data_area(); if (area != NULL) free_data(area); area = create_data_area(); area->n_list = area->n_max = 0; area->id = ID_OF_AREA; area->mode = X_BIT_SET & Y_BIT_SET; for (j = start - 1; j < end; j++) { current->x = REAL(block)[j]; current->y = REAL(block)[nrows_block + j]; push_point(area, current); } SET_BLOCK(current); if (DEBUG_FORCE) print_data_list(area); for (j = 0; j < get_n_vgms(); j++) { v = get_vgm(j); if (v != NULL) v->block_semivariance_set = v->block_covariance_set = 0; /* don't store under these circumstances! */ } return; } SEXP gstat_variogram(SEXP s_ids, SEXP cutoff, SEXP width, SEXP direction, SEXP cressie, SEXP dX, SEXP boundaries, SEXP grid, SEXP cov, SEXP pseudo) { SEXP ret; SEXP np; SEXP dist; SEXP gamma; SEXP sx; SEXP sy; SEXP ev_parameters; /* SEXP y; */ long i, id1, id2, nest; VARIOGRAM *vgm; DATA **d; GRIDMAP *m; unsigned int row, col, n; id1 = INTEGER(s_ids)[0]; if (LENGTH(s_ids) > 1) id2 = INTEGER(s_ids)[1]; else id2 = id1; vgm = get_vgm(LTI(id1,id2)); vgm->id = LTI(id1,id2); vgm->id1 = id1; vgm->id2 = id2; if (INTEGER(cov)[0] == 0) vgm->ev->evt = (id1 == id2 ? SEMIVARIOGRAM : CROSSVARIOGRAM); else if (INTEGER(cov)[0] == 1) vgm->ev->evt = (id1 == id2 ? COVARIOGRAM : CROSSCOVARIOGRAM); else { if (id1 != id2) ErrMsg(ER_IMPOSVAL, "cannot compute pairwise relative cross semivariogram"); if (INTEGER(cov)[0] == 2) vgm->ev->evt = PRSEMIVARIOGRAM; } /* vgm->ev->is_asym = INTEGER(asym)[0]; */ vgm->ev->pseudo = INTEGER(pseudo)[0]; vgm->ev->recalc = 1; if (LENGTH(cutoff) > 0) gl_cutoff = REAL(cutoff)[0]; if (LENGTH(width) > 0) gl_iwidth = REAL(width)[0]; gl_alpha = REAL(direction)[0]; gl_beta = REAL(direction)[1]; gl_tol_hor = REAL(direction)[2]; gl_tol_ver = REAL(direction)[3]; gl_cressie = INTEGER(cressie)[0]; if (LENGTH(dX) > 0) { d = get_gstat_data(); d[id1]->dX = REAL(dX)[0]; d[id2]->dX = REAL(dX)[0]; } for (i = 0; i < LENGTH(boundaries); i++) /* does nothing if LENGTH is 0 */ push_bound(REAL(boundaries)[i]); switch (LENGTH(grid)) { case 0: case 1: break; case 6: vgm->ev->S_grid = gstat_S_fillgrid(grid); break; default: error("unrecognized grid length in gstat_variogram"); break; } calc_variogram(vgm, NULL); if (vgm->ev->S_grid != NULL) { PROTECT(ret = allocVector(VECSXP, 4)); m = vgm->ev->map; n = m->rows * m->cols; PROTECT(np = allocVector(REALSXP, n)); PROTECT(gamma = allocVector(REALSXP, n)); PROTECT(sx = allocVector(REALSXP, n)); PROTECT(sy = allocVector(REALSXP, n)); for (row = i = 0; row < m->rows; row++) { for (col = 0; col < m->cols; col++) { map_rowcol2xy(m, row, col, &(REAL(sx)[i]), &(REAL(sy)[i])); REAL(np)[i] = vgm->ev->nh[i]; if (vgm->ev->nh[i] > 0) REAL(gamma)[i] = vgm->ev->gamma[i]; else REAL(gamma)[i] = NA_REAL; i++; } } SET_VECTOR_ELT(ret, 0, sx); SET_VECTOR_ELT(ret, 1, sy); SET_VECTOR_ELT(ret, 2, np); SET_VECTOR_ELT(ret, 3, gamma); free_data_gridmap(vgm->ev->S_grid); UNPROTECT(5); } else { if (vgm->ev->cloud) nest = vgm->ev->n_est; else { if (vgm->ev->zero == ZERO_SPECIAL) nest = vgm->ev->n_est; else nest = vgm->ev->n_est - 1; } PROTECT(ret = allocVector(VECSXP, 4)); if (nest <= 0) { UNPROTECT(1); return(ret); } PROTECT(np = allocVector(REALSXP, nest)); PROTECT(dist = allocVector(REALSXP, nest)); PROTECT(gamma = allocVector(REALSXP, nest)); PROTECT(ev_parameters = allocVector(REALSXP, 4)); REAL(ev_parameters)[0] = vgm->ev->cutoff; REAL(ev_parameters)[1] = vgm->ev->iwidth; REAL(ev_parameters)[2] = vgm->ev->pseudo; REAL(ev_parameters)[3] = vgm->ev->is_asym; for (i = 0; i < nest; i++) { REAL(np)[i] = vgm->ev->nh[i]; REAL(dist)[i] = vgm->ev->dist[i]; REAL(gamma)[i] = vgm->ev->gamma[i]; } SET_VECTOR_ELT(ret, 0, np); SET_VECTOR_ELT(ret, 1, dist); SET_VECTOR_ELT(ret, 2, gamma); SET_VECTOR_ELT(ret, 3, ev_parameters); UNPROTECT(5); } return(ret); } SEXP gstat_load_variogram(SEXP s_ids, SEXP s_model, SEXP s_sills, SEXP s_ranges, SEXP s_kappas, SEXP s_anis_all, SEXP s_table, SEXP s_max_val) { VARIOGRAM *vgm; long i, n, id1, id2, max_id; double anis[5] = {0.0, 0.0, 0.0, 1.0, 1.0}, rpars[2], *sills, *ranges, *kappas, *anis_all; const char *model; sills = REAL(s_sills); ranges = REAL(s_ranges); kappas = REAL(s_kappas); anis_all = REAL(s_anis_all); id1 = INTEGER(s_ids)[0]; id2 = INTEGER(s_ids)[1]; max_id = MAX(id1, id2); if (get_n_vars() == 0) which_identifier("xx"); /* at least "load" one dummy var */ if (max_id >= get_n_vars()) ErrMsg(ER_IMPOSVAL, "gstat_load_variogram has been called with max_id >= n_vars"); vgm = get_vgm(LTI(id1,id2)); assert(vgm != NULL); vgm->id = LTI(id1,id2); vgm->id1 = id1; vgm->id2 = id2; vgm->n_models = vgm->n_fit = 0; n = LENGTH(s_sills); for (i = 0; i < n; i++) { /* loop over sub models */ model = CHAR(STRING_ELT(s_model, i)); anis[0] = anis_all[0 * n + i]; anis[1] = anis_all[1 * n + i]; anis[2] = anis_all[2 * n + i]; anis[3] = anis_all[3 * n + i]; anis[4] = anis_all[4 * n + i]; rpars[0] = ranges[i]; rpars[1] = kappas[i]; if (LENGTH(s_table) > 0) push_to_v_table(vgm, rpars[0], LENGTH(s_table), REAL(s_table), (anis[3] == 1.0 && anis[4] == 1.0) ? NULL : anis); else push_to_v(vgm, model, sills[i], rpars, 2, (anis[3] == 1.0 && anis[4] == 1.0) ? NULL : anis, 1, 1); } update_variogram(vgm); if (REAL(s_max_val)[0] > 0.0 || REAL(s_max_val)[1] > 0.0 || REAL(s_max_val)[2] > 0.0) vgm->max_val = get_semivariance(vgm, REAL(s_max_val)[0], REAL(s_max_val)[1], REAL(s_max_val)[2]); if (DEBUG_DUMP) logprint_variogram(vgm, 1); return(s_model); } SEXP gstat_variogram_values(SEXP ids, SEXP pars, SEXP covariance, SEXP dist_values) { double from, to, n, d, x = 1.0, y = 0.0, z = 0.0; int i, id1, id2, cov = 0, ndist = 0; VARIOGRAM *vgm; SEXP dist; SEXP gamma; SEXP ret; if (LENGTH(pars) != 3 && LENGTH(pars) != 6) error("supply three or six distance parameters"); from = REAL(pars)[0]; to = REAL(pars)[1]; n = REAL(pars)[2]; ndist = LENGTH(dist_values); cov = INTEGER(covariance)[0]; if (LENGTH(pars) == 6) { x = REAL(pars)[3]; y = REAL(pars)[4]; z = REAL(pars)[5]; } id1 = INTEGER(ids)[0]; id2 = INTEGER(ids)[1]; vgm = get_vgm(LTI(id1,id2)); if (ndist > 0) { PROTECT(dist = allocVector(REALSXP, ndist)); PROTECT(gamma = allocVector(REALSXP, ndist)); for (i = 0; i < ndist; i++) { d = REAL(dist_values)[i]; REAL(dist)[i] = d; REAL(gamma)[i] = (cov ? get_covariance(vgm, d * x, d * y, d * z) : get_semivariance(vgm, d * x, d * y, d * z)); } } else { PROTECT(dist = allocVector(REALSXP, n)); PROTECT(gamma = allocVector(REALSXP, n)); for (i = 0; i < n; i++) { d = from; if (i > 0) /* implies n > 1 */ d += (i/(n-1))*(to-from); REAL(dist)[i] = d; REAL(gamma)[i] = (cov ? get_covariance(vgm, d * x, d * y, d * z) : get_semivariance(vgm, d * x, d * y, d * z)); } } PROTECT(ret = allocVector(VECSXP, 2)); SET_VECTOR_ELT(ret, 0, dist); SET_VECTOR_ELT(ret, 1, gamma); UNPROTECT(3); return(ret); } // Added by Paul Hiemstra, 30-06-2008 SEXP get_covariance_list(SEXP ids, SEXP covariance, SEXP dist_list) { double d, x = 1.0, y = 0.0, z = 0.0; int i, id1, id2, cov = 0; VARIOGRAM *vgm; SEXP dist; SEXP gamma; SEXP ret; int length_list = LENGTH(dist_list); cov = INTEGER(covariance)[0]; id1 = INTEGER(ids)[0]; id2 = INTEGER(ids)[1]; vgm = get_vgm(LTI(id1,id2)); PROTECT(dist = allocVector(REALSXP, length_list)); PROTECT(gamma = allocVector(REALSXP, length_list)); for (i = 0; i < length_list; i++) { d = REAL(dist_list)[i]; REAL(dist)[i] = d; REAL(gamma)[i] = (cov ? get_covariance(vgm, d * x, d * y, d * z) : get_semivariance(vgm, d * x, d * y, d * z)); } PROTECT(ret = allocVector(VECSXP, 2)); SET_VECTOR_ELT(ret, 0, dist); SET_VECTOR_ELT(ret, 1, gamma); UNPROTECT(3); return(ret); } SEXP gstat_get_variogram_models(SEXP dolong) { SEXP ret; int i, n = 0, do_long; for (i = 1; v_models[i].model != NOT_SP; i++) n++; do_long = INTEGER(dolong)[0]; PROTECT(ret = allocVector(STRSXP, n)); for (i = 1; v_models[i].model != NOT_SP; i++) SET_STRING_ELT(ret, i-1, mkChar(do_long ? v_models[i].name_long : v_models[i].name)); UNPROTECT(1); return(ret); } SEXP gstat_load_ev(SEXP np, SEXP dist, SEXP gamma) { int i, cloud = 1; VARIOGRAM *vgm; which_identifier("xx"); /* * vgm = get_vgm(LTI(INTEGER(id)[0], INTEGER(id)[1])); * */ vgm = get_vgm(LTI(0, 0)); if (vgm->ev == NULL) vgm->ev = init_ev(); vgm->ev->evt = SEMIVARIOGRAM; vgm->ev->n_est = LENGTH(np); vgm->ev->n_max = LENGTH(np); vgm->ev->gamma = (double *) emalloc (sizeof(double) * vgm->ev->n_max); vgm->ev->dist = (double *) emalloc (sizeof(double) * vgm->ev->n_max); vgm->ev->nh = (unsigned long *) emalloc (sizeof(long) * vgm->ev->n_max); for (i = 0; i < vgm->ev->n_est; i++) { vgm->ev->nh[i] = REAL(np)[i]; vgm->ev->dist[i] = REAL(dist)[i]; vgm->ev->gamma[i] = REAL(gamma)[i]; if (cloud && vgm->ev->nh[i] > 1) cloud = 0; } vgm->ev->cloud = cloud; if (DEBUG_VGMFIT) fprint_sample_vgm(vgm->ev); return(np); } SEXP gstat_fit_variogram(SEXP fit, SEXP fit_sill, SEXP fit_range) { int i; VARIOGRAM *vgm; SEXP ret; SEXP sills; SEXP ranges; SEXP SSErr; SEXP fit_is_singular; vgm = get_vgm(LTI(0, 0)); vgm->ev->fit = INTEGER(fit)[0]; for (i = 0; i < vgm->n_models; i++) { vgm->part[i].fit_sill = INTEGER(fit_sill)[i]; vgm->part[i].fit_range = INTEGER(fit_range)[i]; } update_variogram(vgm); if (DEBUG_VGMFIT) logprint_variogram(vgm, 1); fit_variogram(vgm); if (DEBUG_VGMFIT) logprint_variogram(vgm, 1); PROTECT(sills = allocVector(REALSXP, vgm->n_models)); PROTECT(ranges = allocVector(REALSXP, vgm->n_models)); for (i = 0; i < vgm->n_models; i++) { REAL(sills)[i] = vgm->part[i].sill; REAL(ranges)[i] = vgm->part[i].range[0]; } PROTECT(ret = allocVector(VECSXP, 4)); SET_VECTOR_ELT(ret, 0, sills); SET_VECTOR_ELT(ret, 1, ranges); PROTECT(fit_is_singular = allocVector(REALSXP, 1)); REAL(fit_is_singular)[0] = vgm->fit_is_singular; SET_VECTOR_ELT(ret, 2, fit_is_singular); PROTECT(SSErr = allocVector(REALSXP, 1)); REAL(SSErr)[0] = vgm->SSErr; SET_VECTOR_ELT(ret, 3, SSErr); UNPROTECT(5); return(ret); } SEXP gstat_debug_level(SEXP level) { debug_level = INTEGER(level)[0]; return(level); } SEXP gstat_set_method(SEXP to) { const char *what; what = CHAR(STRING_ELT(to, 0)); for (int id = 1; methods[id].name != NULL; id++) { if (almost_equals(what, methods[id].name)) { set_method(methods[id].m); break; /* id-loop */ } } return(to); } SEXP gstat_set_set(SEXP arg, SEXP val) { const char *name; int i; typedef struct { const char *name; void *ptr; enum { UNKNOWN, IS_INT, IS_UINT, IS_REAL, IS_STRING, IS_D_VECTOR, NO_ARG } what; enum { NOLIMIT, GEZERO, GTZERO } limit; } GSTAT_EXPR; const GSTAT_EXPR set_options[] = { { "alpha", &gl_alpha, IS_REAL, GEZERO }, { "beta", &gl_beta, IS_REAL, GEZERO }, { "blas", &gl_blas, IS_INT, GEZERO }, { "choleski", &gl_choleski, IS_INT, GEZERO }, { "co$incide", &gl_coincide, IS_INT, GEZERO }, { "Cr$essie", &gl_cressie, IS_INT, GEZERO }, { "cutoff", &gl_cutoff, IS_REAL, GTZERO }, { "de$bug", &debug_level, IS_INT, GEZERO }, { "fit", &gl_fit, IS_INT, GEZERO }, { "fit_l$imit", &gl_fit_limit, IS_REAL, GTZERO }, { "fr$action", &gl_fraction, IS_REAL, GTZERO }, /* { "display", &gl_display, IS_STRING, NOLIMIT }, */ { "gls$_residuals", &gl_gls_residuals, IS_INT, GEZERO }, { "id$p", &gl_idp, IS_REAL, GEZERO }, { "in$tervals", &gl_n_intervals, IS_INT, GTZERO }, { "it$er", &gl_iter, IS_INT, GEZERO }, { "lhs", &gl_lhs, IS_INT, GEZERO }, { "longlat", &gl_longlat, IS_INT, GEZERO }, { "sim_beta", &gl_sim_beta, IS_INT, GEZERO }, { "n_uk", &gl_n_uk, IS_INT, GEZERO }, { "numbers", &gl_numbers, IS_INT, GEZERO }, { "nb$lockdiscr", &gl_nblockdiscr, IS_INT, GTZERO }, { "no$check", &gl_nocheck, IS_INT, GEZERO }, { "ns$im", &gl_nsim, IS_INT, GTZERO }, { "or$der", &gl_order, IS_INT, GEZERO }, { "q$uantile", &gl_quantile, IS_REAL, GEZERO }, { "rowwise", &gl_rowwise, IS_INT, GEZERO }, { "rp", &gl_rp, IS_INT, GEZERO }, { "see$d", &gl_seed, IS_INT, GTZERO }, { "useed", &gl_seed, IS_UINT, GEZERO }, { "spa$rse", &gl_sparse, IS_INT, GEZERO }, { "spi$ral", &gl_spiral, IS_INT, GEZERO }, { "spl$it", &gl_split, IS_INT, GTZERO }, { "sy$mmetric", &gl_sym_ev, IS_INT, GEZERO }, { "tol_h$or", &gl_tol_hor, IS_REAL, GEZERO }, { "tol_v$er", &gl_tol_ver, IS_REAL, GEZERO }, { "v$erbose", &debug_level, IS_INT, GEZERO }, { "w$idth", &gl_iwidth, IS_REAL, GEZERO }, { "x$valid", &gl_xvalid, IS_INT, GEZERO }, { "zero_di$st", &gl_zero_est, IS_INT, GEZERO }, { "zero", &gl_zero, IS_REAL, GEZERO }, { "zm$ap", &gl_zmap, IS_REAL, NOLIMIT }, { NULL, NULL, 0, 0 } }; name = CHAR(STRING_ELT(arg, 0)); for (i = 0; set_options[i].name; i++) if (almost_equals(name, set_options[i].name)) break; /* break out i-loop */ if (set_options[i].name == NULL) ErrMsg(ER_SYNTAX, name); if (almost_equals((const char *)name, "nb$lockdiscr")) gl_gauss = 0; /* side effect */ switch (set_options[i].what) { case IS_INT: *((int *) set_options[i].ptr) = asInteger(val); /* Rprintf("int arg: %s val %d\n", name, asInteger(val)); */ break; case IS_UINT: *((unsigned int *) set_options[i].ptr) = (unsigned int) asInteger(val); /* Rprintf("uint arg: %s val %d\n", name, asInteger(val)); */ break; case IS_REAL: *((double *) set_options[i].ptr) = asReal(val); /* Rprintf("real arg: %s val %d\n", name, asReal(val)); */ break; case IS_STRING: *((const char **) set_options[i].ptr) = CHAR(STRING_ELT(val, 0)); break; default: ErrMsg(ER_SYNTAX, name); break; } return val; } SEXP gstat_set_merge(SEXP a, SEXP b, SEXP c, SEXP d) { /* merge a(b) with c(d); */ DATA **dpp; int id, id1, id2, col1, col2; id1 = asInteger(a); id2 = asInteger(c); if (id1 >= get_n_vars() || id2 >= get_n_vars() || id1 < 0 || id2 < 0) ErrMsg(ER_IMPOSVAL, "id values out of range"); col1 = asInteger(b); col2 = asInteger(d); if (id1 < id2) { /* swap id and col */ id = id1; id1 = id2; id2 = id; id = col1; col1 = col2; col2 = id; } dpp = get_gstat_data(); if (push_to_merge_table(dpp[id1], id2, col1, col2)) ErrMsg(ER_IMPOSVAL, "attempt to merge failed"); return(a); } double r_uniform(void) { return(unif_rand()); } double r_normal(void) { return(norm_rand()); } static DATA_GRIDMAP *gstat_S_fillgrid(SEXP gridparams) { double x_ul, y_ul, cellsizex, cellsizey; unsigned int rows, cols; cellsizex = REAL(gridparams)[2]; cellsizey = REAL(gridparams)[3]; rows = (unsigned int) REAL(gridparams)[5]; cols = (unsigned int) REAL(gridparams)[4]; x_ul = REAL(gridparams)[0] - 0.5 * cellsizex; y_ul = REAL(gridparams)[1] + (rows - 0.5) * cellsizey; return gsetup_gridmap(x_ul, y_ul, cellsizex, cellsizey, rows, cols); } gstat/src/sem.c0000644000176200001440000005542413777370515013144 0ustar liggesusers/* * sem.c: calculate sample (cross, co-) variogram from data * K.M. refers to changes by Konstantin Malakhanov, see also mapio.c */ #include #include #include "defs.h" #include "mapio.h" #include "userio.h" #include "data.h" #include "utils.h" #include "debug.h" #include "vario.h" #include "glvars.h" #include "select.h" #include "gls.h" #include "mtrx.h" #include "lm.h" #include "defaults.h" #include "direct.h" #include "sem.h" #define SEM_INCREMENT 1000 static double valid_distance(DPOINT *a, DPOINT *b, double max, int symmetric, DATA *d1, DATA *d2, GRIDMAP *m); static void divide(SAMPLE_VGM *ev); static SAMPLE_VGM *alloc_exp_variogram(DATA *a, DATA *b, SAMPLE_VGM *ev); /* variograms: */ static SAMPLE_VGM *semivariogram(DATA *a, SAMPLE_VGM *ev); static SAMPLE_VGM *cross_variogram(DATA *a, DATA *b, SAMPLE_VGM *ev); /* covariograms: */ static SAMPLE_VGM *covariogram(DATA *a, SAMPLE_VGM *ev); static SAMPLE_VGM *cross_covariogram(DATA *a, DATA *b, SAMPLE_VGM *ev); static int get_index(double dist, SAMPLE_VGM *ev); static SAMPLE_VGM *semivariogram_list(DATA *d, SAMPLE_VGM *ev); static SAMPLE_VGM *semivariogram_grid(DATA *d, SAMPLE_VGM *ev); static void push_to_cloud(SAMPLE_VGM *ev, double gamma, double dist, unsigned long index); static void resize_ev(SAMPLE_VGM *ev, unsigned int size); static void *register_pairs(void *p, unsigned long nh, DPOINT *a, DPOINT *b); /* * gl_cressie: use Cressie's sqrt(absdiff) estimator; * ev->zero: * case ZERO_INCLUDE: use zero distances in first interval (omit); * case ZERO_AVOID: avoid zero distances; * case ZERO_SPECIAL: make special estimate for distance zero; */ /* * calculate sample variogram from data * calculates variogram, crossvariogram, covariogram or crosscovariogram * from sample data. Data are obtained from the central data base (glvars) * using get_gstat_data(), and the variogram requested is that of data id * v->id1 and v->id2 -- a direct (co) variogram when id1 == id2, a cross * (co) variogram when id1 != id2. * * if [[v->fname is set and]] (one of) id1 or id2 is a dummy data, the * actual sample variogram is not calculated but rather read from the * file v->fname. This is done to enable separate sample variogram * calculation (in batch or on a fast remote computer) and model fitting * (e.g. on the desk top). * * returns: non-zero if writing sample variogram to file failed. */ int calc_variogram(VARIOGRAM *v /* pointer to VARIOGRAM structure */, const char *fname /* pointer to output file name, or NULL if no output has to be written to file */ ) { DATA **d = NULL, *d1 = NULL, *d2 = NULL; assert(v); d = get_gstat_data(); d1 = d[v->id1]; d2 = d[v->id2]; if (d1->sel == NULL) select_at(d1, NULL); /* global selection (sel = list) */ if (d2->sel == NULL) select_at(d2, NULL); if (v->ev->evt == CROSSVARIOGRAM && (v->ev->pseudo == -1 || v->ev->is_asym == -1)) { if (v->ev->pseudo == -1) { /* v's first time, need to find out pseudo */ if (coordinates_are_equal(d[v->id1], d[v->id2])) v->ev->pseudo = 0; else v->ev->pseudo = 1; } if (gl_sym_ev == 0) v->ev->is_asym = v->ev->pseudo; /* pseudo: always, else: only if set */ else v->ev->is_asym = 0; } else v->ev->is_asym = v->ev->pseudo = 0; if (gl_zero_est == ZERO_DEFAULT) { /* choose a suitable default */ if (is_covariogram(v)) v->ev->zero = ZERO_SPECIAL; else { /* v is variogram */ if (v->ev->pseudo) v->ev->zero = ZERO_SPECIAL; else v->ev->zero = ZERO_INCLUDE; } } else v->ev->zero = zero_int2enum(gl_zero_est); assert(v->ev->zero != ZERO_DEFAULT); fill_cutoff_width(d1, v); if (v->ev->map && v->ev->S_grid == NULL) return -1; v->ev->cloud = (v->ev->iwidth <= 0.0); if (v->ev->cloud && (d[v->id1]->n_sel >= MAX_NH || d[v->id2]->n_sel >= MAX_NH)) pr_warning("observation numbers in cloud will be wrong"); set_direction_values(gl_alpha, gl_beta, gl_tol_hor, gl_tol_ver); v->ev->is_directional = is_directional(v); if (v->ev->recalc) { switch (v->ev->evt) { case PRSEMIVARIOGRAM: case SEMIVARIOGRAM: semivariogram(d[v->id1], v->ev); break; case CROSSVARIOGRAM: cross_variogram(d[v->id1], d[v->id2], v->ev); break; case COVARIOGRAM: v->ev->is_asym = gl_sym_ev; covariogram(d[v->id1], v->ev); break; case CROSSCOVARIOGRAM: cross_covariogram(d[v->id1], d[v->id2], v->ev); break; case NOTSPECIFIED: default: assert(0); /* aborts */ break; } } return 0; } static SAMPLE_VGM *semivariogram(DATA *d, SAMPLE_VGM *ev) { /* * calculate sample variogram of 0.5 E[(Z(x)-Z(x+h))2] */ if (ev->evt == PRSEMIVARIOGRAM) d->calc_residuals = 0; ev = alloc_exp_variogram(d, NULL, ev); if (d->grid != NULL && d->prob > 0.5 && d->every == 1) ev = semivariogram_grid(d, ev); else ev = semivariogram_list(d, ev); divide(ev); ev->recalc = 0; return ev; } /* semivariogram() */ static SAMPLE_VGM *semivariogram_list(DATA *d, SAMPLE_VGM *ev) { unsigned long uli, ulj; int i, j, index = 0, divide_by = 1; unsigned int total_steps; double gamma, ddist, head, tail, gam; while (d->n_sel / divide_by > 0.5 * sqrt(INT_MAX)) divide_by <<= 1; /* prevent overflow on calculating total_steps */ total_steps = (d->n_sel / divide_by) * (d->n_sel - 1) / 2; print_progress(0, total_steps); if (DEBUG_DUMP) printlog("Calculating semivariogram from %d points...\n", d->n_sel); for (i = 0; i < d->n_sel; i++) { print_progress((i / divide_by) * (i - 1) / 2, total_steps); R_CheckUserInterrupt(); /* printlog("step: %u of %u\n", (i /divide_by) * (i - 1) / 2, total_steps); */ for (j = 0; j < (ev->map != NULL ? d->n_sel : i); j++) { ddist = valid_distance(d->sel[i], d->sel[j], ev->cutoff, 1, d, d, (GRIDMAP *) ev->map); if (ddist >= 0.0 && i != j) { head = d->sel[i]->attr; tail = d->sel[j]->attr; if (! ev->cloud) { index = get_index(ddist, ev); if (gl_cressie) /* sqrt abs diff */ ev->gamma[index] += sqrt(fabs(head - tail)); else if (ev->evt == PRSEMIVARIOGRAM) { gam = 2.0 * (head - tail)/(head + tail); ev->gamma[index] += SQR(gam); } else { /* SEMIVARIOGRAM: */ ev->gamma[index] += SQR(head - tail); #ifdef ADJUST_VARIANCE if (d->colnvariance) ev->gamma[index] -= d->sel[i]->variance + d->sel[j]->variance; #endif } ev->dist[index] += ddist; ev->pairs[index] = register_pairs(ev->pairs[index], ev->nh[index], d->sel[i], d->sel[j]); ev->nh[index]++; } else { /* cloud: */ if (! (ev->zero == ZERO_AVOID && ddist == 0.0)) { if (gl_cressie) gamma = sqrt(fabs(head - tail)); else if (ev->evt == PRSEMIVARIOGRAM) { gam = 2.0 * (head - tail)/(head + tail); gamma = gam * gam; } else { gamma = SQR(head - tail); #ifdef ADJUST_VARIANCE if (d->colnvariance) gamma -= d->sel[i]->variance + d->sel[j]->variance; #endif } uli = i; ulj = j; push_to_cloud(ev, gamma / 2.0, ddist, TO_NH(uli,ulj)); } } }/* if ddist >= 0 */ } /* for j */ } /* for i */ print_progress(total_steps, total_steps); if (DEBUG_DUMP) printlog("ready\n"); return ev; } static SAMPLE_VGM *semivariogram_grid(DATA *d, SAMPLE_VGM *ev) { typedef struct { int row, col, ev_index; double dist; } grid_index; struct { int n; grid_index *gi; } grid_ev; int row, col, irow, icol, i, max_index, index; unsigned long ula, ulb; double gamma, ddist, head, tail, gam; DPOINT a, b, *dpa = NULL, *dpb = NULL; max_index = (int) floor(ev->cutoff / SQUARECELLSIZE(d->grid)); grid_ev.gi = (grid_index *) emalloc(2 * (max_index + 1) * (max_index + 1) * sizeof(grid_index)); grid_ev.n = 0; a.x = a.y = a.z = b.z = 0.0; /* setup the grid: */ for (row = 0; row <= max_index; row++) { for (col = (row == 0 ? 1 : -max_index); col <= max_index; col++) { b.x = col * SQUARECELLSIZE(d->grid); b.y = - row * SQUARECELLSIZE(d->grid); ddist = valid_distance(&a, &b, ev->cutoff, 1, d, d, (GRIDMAP *) ev->map); if (ddist > 0.0) { grid_ev.gi[grid_ev.n].row = row; grid_ev.gi[grid_ev.n].col = col; grid_ev.gi[grid_ev.n].dist = ddist; if (! ev->cloud) grid_ev.gi[grid_ev.n].ev_index = get_index(ddist, ev); if (DEBUG_DUMP) printlog("row %d col %d index %d\n", row, col, grid_ev.gi[grid_ev.n].ev_index); grid_ev.n++; } } } print_progress(0, d->grid->rows); for (row = 0; row < d->grid->rows; row++) { for (col = 0; col < d->grid->cols; col++) { if ((dpa = d->grid->dpt[row][col]) != NULL) { for (i = 0; i < grid_ev.n; i++) { irow = row + grid_ev.gi[i].row; icol = col + grid_ev.gi[i].col; if (irow >= 0 && icol >= 0 && irow < d->grid->rows && icol < d->grid->cols && ((dpb = d->grid->dpt[irow][icol]) != NULL)) { ddist = grid_ev.gi[i].dist; head = dpa->attr; tail = dpb->attr; if (! ev->cloud) { index = grid_ev.gi[i].ev_index; if (gl_cressie) /* sqrt abs diff */ ev->gamma[index] += sqrt(fabs(head - tail)); else { if (ev->evt == PRSEMIVARIOGRAM) { gam = 2.0 * (head - tail)/(head + tail); ev->gamma[index] += gam * gam; } else ev->gamma[index] += SQR(head - tail); #ifdef ADJUST_VARIANCE if (d->colnvariance) ev->gamma[index] -= dpa->variance + dpb->variance; #endif } ev->dist[index] += ddist; ev->pairs[index] = register_pairs(ev->pairs[index], ev->nh[index], dpa, dpb); ev->nh[index]++; } else { /* cloud: */ if (gl_cressie) gamma = sqrt(fabs(head - tail)); else if (ev->evt == PRSEMIVARIOGRAM) { gam = 2.0 * (head - tail)/(head + tail); gamma = gam * gam; } else { gamma = SQR(head - tail); #ifdef ADJUST_VARIANCE if (d->colnvariance) gamma -= dpa->variance + dpb->variance; #endif } ula = GET_INDEX(dpa); ulb = GET_INDEX(dpb); push_to_cloud(ev, gamma / 2.0, ddist, TO_NH(ula,ulb)); } /* else !cloud */ } /* if we have two non-NULL points */ } /* for all possibly relevant pairs */ } /* if this grid cell is non-NULL */ } /* for all cols */ print_progress(row + 1, d->grid->rows); R_CheckUserInterrupt(); } /* for all rows */ efree(grid_ev.gi); return ev; } /* covariograms: */ static SAMPLE_VGM *covariogram(DATA *d, SAMPLE_VGM *ev) { int i, j, index = 0; unsigned long uli, ulj; double gamma, ddist; ev->evt = COVARIOGRAM; ev = alloc_exp_variogram(d, NULL, ev); for (i = 0; i < d->n_sel; i++) { print_progress(i, d->n_sel); R_CheckUserInterrupt(); for (j = 0; j <= (ev->map != NULL ? d->n_sel-1 : i); j++) { ddist = valid_distance(d->sel[i], d->sel[j], ev->cutoff, 1, d, d, (GRIDMAP *) ev->map); if (ddist >= 0.0) { if (! ev->cloud) { index = get_index(ddist, ev); ev->gamma[index] += d->sel[i]->attr * d->sel[j]->attr; #ifdef ADJUST_VARIANCE if (d->colnvariance && i == j) ev->gamma[index] -= d->sel[i]->variance; #endif ev->dist[index] += ddist; ev->pairs[index] = register_pairs(ev->pairs[index], ev->nh[index], d->sel[i], d->sel[j]); ev->nh[index]++; } else { if (! (ev->zero == ZERO_AVOID && ddist == 0.0)) { gamma = d->sel[i]->attr * d->sel[j]->attr; #ifdef ADJUST_VARIANCE if (d->colnvariance && i == j) gamma -= d->sel[i]->variance; #endif uli = i; ulj = j; push_to_cloud(ev, gamma, ddist, TO_NH(uli,ulj)); } } }/* if ddist >= 0 */ } /* for j */ } /* for i */ print_progress(d->n_sel, d->n_sel); divide(ev); ev->recalc = 0; return ev; } /* covariogram() */ static SAMPLE_VGM *cross_variogram(DATA *a, DATA *b, SAMPLE_VGM *ev) { int i, j, index = 0; unsigned long uli, ulj; double gamma, ddist; ev->evt = CROSSVARIOGRAM; ev = alloc_exp_variogram(a, b, ev); for (i = 0; i < a->n_sel; i++) { print_progress(i, a->n_sel); R_CheckUserInterrupt(); for (j = 0; j < b->n_sel; j++) { ddist = valid_distance(a->sel[i], b->sel[j], ev->cutoff, gl_sym_ev || !ev->pseudo, a, b, (GRIDMAP *) ev->map); if (ddist >= 0.0) { if (!ev->pseudo && i != j) { if (! ev->cloud) { index = get_index(ddist, ev); ev->gamma[index] += (a->sel[i]->attr - a->sel[j]->attr) * (b->sel[i]->attr - b->sel[j]->attr); ev->dist[index] += ddist; ev->pairs[index] = register_pairs(ev->pairs[index], ev->nh[index], a->sel[i], a->sel[j]); ev->nh[index]++; } else if (!(ddist == 0.0 && ev->zero == ZERO_AVOID)) { gamma = (a->sel[i]->attr - a->sel[j]->attr) * (b->sel[i]->attr - b->sel[j]->attr); uli = i; ulj = j; push_to_cloud(ev, gamma / 2.0, ddist, TO_NH(uli,ulj)); } } else if (ev->pseudo) { if (! ev->cloud) { index = get_index(ddist, ev); ev->gamma[index] += SQR(a->sel[i]->attr - b->sel[j]->attr); #ifdef ADJUST_VARIANCE if (a->colnvariance || b->colnvariance) ev->gamma[index] -= a->sel[i]->variance + b->sel[j]->variance; #endif ev->dist[index] += ddist; ev->pairs[index] = register_pairs(ev->pairs[index], ev->nh[index], a->sel[i], b->sel[j]); ev->nh[index]++; } else if (! (ev->zero == ZERO_AVOID && ddist == 0.0)) { gamma = SQR(a->sel[i]->attr - b->sel[j]->attr); #ifdef ADJUST_VARIANCE if (a->colnvariance || b->colnvariance) gamma -= a->sel[i]->variance + b->sel[j]->variance; #endif uli = i; ulj = j; push_to_cloud(ev, gamma / 2.0, ddist, TO_NH(uli,ulj)); } } }/* if ddist >= 0 */ } /* for j */ } /* for i */ print_progress(a->n_sel, a->n_sel); divide(ev); ev->recalc = 0; return ev; } /* cross_variogram */ static SAMPLE_VGM *cross_covariogram(DATA *a, DATA *b, SAMPLE_VGM *ev) { int i, j, index = 0; unsigned long uli, ulj; double gamma, ddist; ev->evt = CROSSCOVARIOGRAM; ev = alloc_exp_variogram(a, b, ev); for (i = 0; i < a->n_sel; i++) { /* i -> a */ R_CheckUserInterrupt(); print_progress(i, a->n_sel); for (j = 0; j < b->n_sel; j++) { /* j -> b */ ddist = valid_distance(a->sel[i], b->sel[j], ev->cutoff, gl_sym_ev, a, b, (GRIDMAP *) ev->map); if (ddist >= 0.0) { if (! ev->cloud) { index = get_index(ddist, ev); ev->gamma[index] += a->sel[i]->attr * b->sel[j]->attr; ev->dist[index] += ddist; ev->pairs[index] = register_pairs(ev->pairs[index], ev->nh[index], a->sel[i], b->sel[j]); ev->nh[index]++; } else if (! (ev->zero == ZERO_AVOID && ddist == 0.0)) { gamma = a->sel[i]->attr * b->sel[j]->attr; uli = i; ulj = j; push_to_cloud(ev, gamma, ddist, TO_NH(uli,ulj)); } }/* if ddist >= 0 */ } /* for j */ } /* for i */ print_progress(a->n_sel, a->n_sel); divide(ev); ev->recalc = 0; return ev; } /* cross_covariogram() */ static double valid_distance(DPOINT *a, DPOINT *b, double max, int symmetric, DATA *d1, DATA *d2, GRIDMAP *map) { double ddist, dX, dX2, inprod; DPOINT p; int /* mode = 0, */ i; unsigned int row, col; assert(a != NULL); assert(b != NULL); assert(d1 != NULL); assert(d2 != NULL); /* mode = d1->mode & d2->mode; */ /* * even if modes don't correspond, valid_direction() will * calculate valid distances */ p.x = a->x - b->x; p.y = a->y - b->y; p.z = a->z - b->z; if (map && !gl_longlat) { /* transform here p to allow directional 2d cuts in a 3d world */ if (map_xy2rowcol(map, p.x, p.y, &row, &col)) return -1.0; else ddist = (1.0 * row) * map->cols + col + 0.5; } else { if (!gl_longlat && (p.x > max || p.y > max || p.z > max)) return -1.0; /* Changed K.M. Fri Feb 27 15:56:57 1998 */ /* if ddist < 0.0 then we don't need to check for dX! */ if ((ddist = valid_direction(a, b, symmetric, d1)) > max || ddist < 0.0) return -1.0; } dX = MIN(d1->dX, d2->dX); if (dX < DBL_MAX) { dX2 = dX * dX; /* allow only points for which 2-norm ||x_i-x_j|| < dX */ if (d1->n_X != d2->n_X) ErrMsg(ER_IMPOSVAL, "valid_distance(): d1->n_X != d2->n_X"); for (i = 0, inprod = 0.0; i < d1->n_X; i++) { inprod += SQR(a->X[i] - b->X[i]); /* printf("a->X[%d]: %g, b->X[%d]: %g", i, a->X[i], i, b->X[i]); */ } if (inprod > dX2) ddist = -1.0; /* printf("dX2: %g, inprod: %g ddist: %g\n", dX2, inprod, ddist); */ } return ddist; } int is_directional(VARIOGRAM *v) { switch(v->ev->evt) { case CROSSCOVARIOGRAM: if (gl_sym_ev == 0) /* asymmetric cross(co)variances: */ return (gl_tol_hor < 180.0 || gl_tol_ver < 180.0); else return (gl_tol_hor < 90.0 || gl_tol_ver < 90.0); case CROSSVARIOGRAM: if (v->ev->is_asym && gl_sym_ev == 0) /* asymm. cross(co)variances: */ return (gl_tol_hor < 180.0 || gl_tol_ver < 180.0); else return (gl_tol_hor < 90.0 || gl_tol_ver < 90.0); default: /* symmetric (co)variances */ return (gl_tol_hor < 90.0 || gl_tol_ver < 90.0); } } /* * this function should be changed--the mask map stack is misused as * to define the topology of variogram maps. * * use min/max coordinates for block diagonal as maximum cutoff * Returns: about 1/3 the max. dist between any two points in data. */ void fill_cutoff_width(DATA *data /* pointer to DATA structure to derive the values from */, VARIOGRAM *v /* pointer to VARIOGRAM structure */) { double d = 0.0; int i; GRIDMAP *m; DATA_GRIDMAP *dg; SAMPLE_VGM *ev; assert(data); assert(v); ev = v->ev; if (ev->S_grid != NULL) { m = new_map(READ_ONLY); /* process S_grid to m */ dg = (DATA_GRIDMAP *) ev->S_grid; m->x_ul = dg->x_ul; m->y_ul = dg->y_ul; m->cellsizex = dg->cellsizex; m->cellsizey = dg->cellsizey; m->rows = dg->rows; m->cols = dg->cols; ev->iwidth = 1.0; ev->cutoff = m->rows * m->cols; /* not a real cutoff, but rather the size of the container array */ ev->map = m; } else if (gl_bounds != NULL) { i = 0; while (gl_bounds[i] >= 0.0) /* count length */ i++; ev->cutoff = gl_bounds[i-1]; ev->iwidth = ev->cutoff / i; } else { if (is_mv_double(&(ev->cutoff))) { if (gl_cutoff < 0.0) { d = data_block_diagonal(data); if (d == 0.0) ev->cutoff = 1.0; /* ha ha ha */ else ev->cutoff = d * gl_fraction; } else ev->cutoff = gl_cutoff; } if (is_mv_double(&(ev->iwidth))) { if (gl_iwidth < 0.0) ev->iwidth = ev->cutoff / gl_n_intervals; else ev->iwidth = gl_iwidth; } } } static SAMPLE_VGM *alloc_exp_variogram(DATA *a, DATA *b, SAMPLE_VGM *ev) { int i; double nd; assert(a != NULL); assert(ev != NULL); if (gl_zero_est != ZERO_DEFAULT && ev->zero != gl_zero_est) ev->zero = zero_int2enum(gl_zero_est); if (gl_gls_residuals) { if (a->calc_residuals) make_gls(a, 1); if (b != NULL && b->calc_residuals) make_gls(b, 1); } else { if (a->calc_residuals) make_residuals_lm(a); if (b != NULL && b->calc_residuals) make_residuals_lm(b); } if (ev->cloud) { ev->n_est = 0; return ev; } if (gl_bounds != NULL) { for (i = ev->n_est = 0; gl_bounds[i] >= 0.0; i++) ev->n_est++; } else { /* check for overflow: */ nd = floor(ev->cutoff / ev->iwidth) + 1; if (nd > INT_MAX) { pr_warning("choose a larger width or a smaller cutoff value"); ErrMsg(ER_MEMORY, "(experimental variogram too large)"); } ev->n_est = (int) nd; } /* * zero est go to ev->gamma[ev->n_est - 1], ev->nh[ev->n_est - 1] */ if (ev->zero) ev->n_est++; resize_ev(ev, ev->n_est); /* initialize: */ for (i = 0; i < ev->n_est; i++) { ev->gamma[i] = 0.0; ev->dist[i] = 0.0; ev->nh[i] = 0; ev->pairs[i] = (DPOINT **) NULL; } return ev; } static void resize_ev(SAMPLE_VGM *ev, unsigned int size) { if (size > ev->n_max) { ev->n_max = size; ev->gamma = (double *) erealloc (ev->gamma, ev->n_max * sizeof(double)); ev->dist = (double *) erealloc (ev->dist, ev->n_max * sizeof(double)); ev->nh = (unsigned long *) erealloc (ev->nh, ev->n_max * sizeof(long)); ev->pairs = (DPOINT ***) erealloc(ev->pairs, ev->n_max * sizeof(DPOINT **)); } } static void *register_pairs(void *pairs, unsigned long nh, DPOINT *a, DPOINT *b) { /* * while I'm here -- there may be a problem when ->list != ->sel on * the DATA used, but I don't know why. Probably will never be used. */ /* resize pairs; add a and b to it */ if (gl_register_pairs == 0) return NULL; if (nh % SEM_INCREMENT == 0) pairs = erealloc(pairs, 2 * (nh + SEM_INCREMENT + 1) * sizeof(DPOINT **)); ((DPOINT **) pairs)[2 * nh] = a; ((DPOINT **) pairs)[2 * nh + 1] = b; return pairs; } static void push_to_cloud(SAMPLE_VGM *ev, double gamma, double dist, unsigned long index) { if (ev->n_est == ev->n_max) resize_ev(ev, ev->n_max + SEM_INCREMENT); ev->gamma[ev->n_est] = gamma; ev->dist[ev->n_est] = dist; ev->nh[ev->n_est] = index; ev->pairs[ev->n_est] = NULL; ev->n_est++; } static int get_index(double dist, SAMPLE_VGM *ev) { double frac; int i = 0; if (dist == 0.0 && ev->zero != ZERO_INCLUDE) return ev->n_est - 1; if (gl_bounds != DEF_bounds) { for (i = 0; gl_bounds[i] >= 0.0; i++) if (dist <= gl_bounds[i]) return i; assert(0); } if (ev->iwidth <= 0.0) { pr_warning("iwidth: %g", ev->iwidth); ErrMsg(ER_IMPOSVAL, "ev->iwidth <= 0.0"); } frac = dist / ev->iwidth; if (dist > 0.0 && frac == floor(frac)) return (int) (floor(frac)) - 1; else return (int) floor(frac); } static void divide(SAMPLE_VGM *ev) { int i; if (ev->cloud) return; /* has been done in the first round */ for (i = 0; i < ev->n_est; i++) { if (ev->nh[i]) { ev->dist[i] /= ev->nh[i]; switch (ev->evt) { case SEMIVARIOGRAM: if (gl_cressie) ev->gamma[i] = 0.5 * pow(ev->gamma[i]/ev->nh[i], 4.0) /(0.457 + 0.494 / ev->nh[i]); else ev->gamma[i] /= (2.0 * ev->nh[i]); break; case CROSSVARIOGRAM: ev->gamma[i] /= (2.0 * ev->nh[i]); break; case COVARIOGRAM: /* BREAKTHROUGH */ case CROSSCOVARIOGRAM: ev->gamma[i] /= (1.0 * ev->nh[i]); break; case PRSEMIVARIOGRAM: ev->gamma[i] /= (2.0 * ev->nh[i]); break; case NOTSPECIFIED: /* BREAKTHROUGH */ default: assert(0); break; } } } } void fprint_sample_vgm(const SAMPLE_VGM *ev) { #define EVFMT "%8g %8g %8lu %8g %8g\n" int i, n; double from, to; if (! ev->cloud) { /* start writing: distance 0 */ if (ev->zero == ZERO_SPECIAL && ev->nh[ev->n_est-1]) Rprintf(EVFMT, 0.0, 0.0, ev->nh[ev->n_est-1], ev->dist[ev->n_est-1], ev->gamma[ev->n_est-1]); /* continue writing: */ if (ev->zero == ZERO_SPECIAL || ev->zero == ZERO_AVOID) n = ev->n_est - 1; else n = ev->n_est; for (i = 0; i < n; i++) { if (ev->nh[i] > 0) { if (gl_bounds == NULL) { from = i*ev->iwidth; to = (i+1)*ev->iwidth; } else { if (i == 0) from = 0.0; else from = gl_bounds[i-1]; to = gl_bounds[i]; } to = MIN(ev->cutoff, to); Rprintf(EVFMT, from, to, ev->nh[i], ev->dist[i], ev->gamma[i]); } } } else { for (i = 0; i < ev->n_est; i++) Rprintf("%ld %ld %g %g\n", HIGH_NH(ev->nh[i]) + 1, LOW_NH(ev->nh[i]) + 1, ev->dist[i], ev->gamma[i]); } return; } /* fprint_sample_vgm */ gstat/src/gls.c0000644000176200001440000005136613777370515013146 0ustar liggesusers/* gls.c: module for multivariable generalized least squares prediction given a linear model Y = X Beta + e, gls() calculates from the selection d[0]->sel,...,d[n_vars-1]->sel, the multivariable BLUE estimation of x0 beta (and Cov(x0[i] Beta, x0[j] Beta)), or BLUP of Y(x0) (multivariable universal kriging) (and MSPE Y(x0)) BLP of Y(x0) (multivariable simple kriging) (and MSPE Y(x0)) (BLUE: Generalized Least Squares (GLS) best linear unbiased estimate; BLUP: GLS best linear unbiased prediction; BLP: GLS best linear prediction) UPDATE: only update y, beta (BLUP); References: a. Christensen, Ronald, 1991. Linear Models for Multivariate, Time Series, and Spatial Data. Springer Verlag, New York. (Ch. VI.2, VI.3) b. Ver Hoef, Jay M., Noel Cressie, 1993. Multivariable Spatial Prediction. Mathematical Geology, 25 (2), pp. 219--240. [[[Note: eq. (18) should have a `+' between SIGMA_0 and C'SIGMA-1 C ]]] Notation (variables and comment): v' the transpose of (matrix or vector) v C-1 the inverse of matrix v (`Cinv' in a variable name) n total number of observations in data selections (rows_C) m total number of variables [n_vars] p sum of number of X columns (for non-empty data selections) [cols of X] y data vector (y[0]',...,y[n_vars-1]')', y[i] is the i-th variable [n x 1] C (generalized) covariance matrix, C[i][j] = Cov(element(y,i),element(y,j)) (element(y,i) is the i-th element in y, not the i-th variable) [n x n] X design matrix [n x p]; beta parameter vector [p x 1]: E(y) = X beta C0 (generalized) covariance matrix with y(x0): C0[i][j] = Cov(element(y,i),y[j](x0)) [n x m] X0 the value that X would have at location "where" [p x m] (Note: Christensen's x0 is Ver Hoefs X0'; I use x0: e.g. x0'beta). */ #include /* size_t */ #include /* sqrt() */ #include "defs.h" #include "data.h" #include "utils.h" #include "select.h" #include "mtrx.h" #include "lm.h" #include "vario.h" #include "vario_io.h" #include "glvars.h" #include "userio.h" #include "debug.h" #include "gls.h" static void fill_est(DATA **d, VEC *blup, MAT *MSPE, int n_vars, double *est); static void debug_result(VEC *blup, MAT *MSPE, enum GLS_WHAT pred); static VEC *get_mu(VEC *mu, const VEC *y, DATA **d, int nvars); static MAT *get_corr_mat(MAT *C, MAT *R); #define M_DEBUG(a,b) { if (DEBUG_COV){printlog("\n# %s:\n", b); \ m_logoutput(a);}} #define V_DEBUG(a,b) {if (DEBUG_COV){printlog("\n# %s:\n", b); \ v_logoutput(a);}} #define UPDATE_BLP (pred == UPDATE && last_pred == GLS_BLP) #define UPDATE_BLUP (pred == UPDATE && last_pred == GLS_BLUP) /* static MAT *convert_vmuC(MAT *C, DATA *d); static MAT *convert_vmuC0(MAT *C0, DATA *d, double v); static MAT *convert_vmuC00(MAT *MSPE, double v); */ static void convert_C(MAT *C, VEC *mu, double (*fn)(double)); static void convert_C0(MAT *C0, VEC *mu, VEC *mu0, double (*fn)(double)); static void convert_MSPE(MAT *MSPE, VEC *mu0, double (*fn)(double)); typedef struct { MAT *C, /* (Generalized) Covariance matrix */ *X, /* design matrix, y = X beta + e */ *CinvX, /* C-1 X */ *XCinvX; /* X' C-1 X */ VEC *y, /* measurement vector */ *mu, /* mu vector, E(y) */ *mu0, /* mu at loc x0 */ *beta; /* parameter vector */ } GLM; /* structure is locally defined, will be held in void *glm in DATA */ static GLM *new_glm(void); /* * n_vars is the number of variables to be considered, * d is the data array of variables d[0],...,d[n_vars-1], * pred determines which estimate is required: BLUE, BLUP, or BLP */ void gls(DATA **d /* pointer to DATA array */, int n_vars, /* length of DATA array (to consider) */ enum GLS_WHAT pred, /* what type of prediction is requested */ DPOINT *where, /* prediction location */ double *est /* output: array that holds the predicted values and variances */) { GLM *glm = NULL; /* to be copied to/from d */ static MAT *X0 = MNULL, *C0 = MNULL, *MSPE = MNULL, *CinvC0 = MNULL, *Tmp1 = MNULL, *Tmp2 = MNULL, *Tmp3 = MNULL, *R = MNULL; static VEC *blup = VNULL, *tmpa = VNULL, *tmpb = VNULL; PERM *piv = PNULL; volatile unsigned int i, rows_C; unsigned int j, k, l = 0, row, col, start_i, start_j, start_X, global, one_nbh_empty; VARIOGRAM *v = NULL; static enum GLS_WHAT last_pred = GLS_INIT; /* the initial value */ double c_value, *X_ori; int info; if (d == NULL) { /* clean up */ if (X0 != MNULL) M_FREE(X0); if (C0 != MNULL) M_FREE(C0); if (MSPE != MNULL) M_FREE(MSPE); if (CinvC0 != MNULL) M_FREE(CinvC0); if (Tmp1 != MNULL) M_FREE(Tmp1); if (Tmp2 != MNULL) M_FREE(Tmp2); if (Tmp3 != MNULL) M_FREE(Tmp3); if (R != MNULL) M_FREE(R); if (blup != VNULL) V_FREE(blup); if (tmpa != VNULL) V_FREE(tmpa); if (tmpb != VNULL) V_FREE(tmpb); last_pred = GLS_INIT; return; } if (DEBUG_COV) { printlog("we're at %s X: %g Y: %g Z: %g\n", IS_BLOCK(where) ? "block" : "point", where->x, where->y, where->z); } if (pred != UPDATE) /* it right away: */ last_pred = pred; assert(last_pred != GLS_INIT); if (d[0]->glm == NULL) { /* allocate and initialize: */ glm = new_glm(); d[0]->glm = (void *) glm; } else glm = (GLM *) d[0]->glm; glm->mu0 = v_resize(glm->mu0, n_vars); MSPE = m_resize(MSPE, n_vars, n_vars); if (pred == GLS_BLP || UPDATE_BLP) { X_ori = where->X; for (i = 0; i < n_vars; i++) { /* mu(0) */ glm->mu0->ve[i] = calc_mu(d[i], where); blup = v_copy(glm->mu0, v_resize(blup, glm->mu0->dim)); where->X += d[i]->n_X; /* shift to next x0 entry */ } where->X = X_ori; /* ... and set back */ for (i = 0; i < n_vars; i++) { /* Cij(0,0): */ for (j = 0; j <= i; j++) { v = get_vgm(LTI(d[i]->id,d[j]->id)); ME(MSPE, i, j) = ME(MSPE, j, i) = COVARIANCE0(v, where, where, d[j]->pp_norm2); } } fill_est(NULL, blup, MSPE, n_vars, est); /* in case of empty neighbourhood */ } /* logprint_variogram(v, 1); */ /* * selection dependent problem dimensions: */ for (i = rows_C = 0, one_nbh_empty = 0; i < n_vars; i++) { rows_C += d[i]->n_sel; if (d[i]->n_sel == 0) one_nbh_empty = 1; } if (rows_C == 0 /* all selection lists empty */ || one_nbh_empty == 1) { /* one selection list empty */ if (pred == GLS_BLP || UPDATE_BLP) debug_result(blup, MSPE, pred); return; } for (i = 0, global = 1; i < n_vars && global; i++) global = (d[i]->sel == d[i]->list && d[i]->n_list == d[i]->n_original && d[i]->n_list == d[i]->n_sel); /* * global things: enter whenever (a) first time, (b) local selections or * (c) the size of the problem grew since the last call (e.g. simulation) */ if (glm->C == NULL || !global || rows_C > glm->C->m) { /* * fill y: */ glm->y = get_y(d, glm->y, n_vars); if (pred != UPDATE) { glm->C = m_resize(glm->C, rows_C, rows_C); if (gl_choleski == 0) /* use LDL' decomposition, allocate piv: */ piv = px_resize(piv, rows_C); m_zero(glm->C); glm->X = get_X(d, glm->X, n_vars); M_DEBUG(glm->X, "X"); glm->CinvX = m_resize(glm->CinvX, rows_C, glm->X->n); glm->XCinvX = m_resize(glm->XCinvX, glm->X->n, glm->X->n); glm->beta = v_resize(glm->beta, glm->X->n); for (i = start_X = start_i = 0; i < n_vars; i++) { /* row var */ /* fill C, mu: */ for (j = start_j = 0; j <= i; j++) { /* col var */ v = get_vgm(LTI(d[i]->id,d[j]->id)); for (k = 0; k < d[i]->n_sel; k++) { /* rows */ row = start_i + k; for (l = 0, col = start_j; col <= row && l < d[j]->n_sel; l++, col++) { if (pred == GLS_BLUP) c_value = GCV(v, d[i]->sel[k], d[j]->sel[l]); else c_value = COVARIANCE(v, d[i]->sel[k], d[j]->sel[l]); /* on the diagonal, if necessary, add measurement error variance */ if (d[i]->colnvariance && i == j && k == l) c_value += d[i]->sel[k]->variance; ME(glm->C, col, row) = c_value; /* fill upper */ if (col != row) ME(glm->C, row, col) = c_value; /* fill all */ } /* for l */ } /* for k */ start_j += d[j]->n_sel; } /* for j */ start_i += d[i]->n_sel; if (d[i]->n_sel > 0) start_X += d[i]->n_X - d[i]->n_merge; } /* for i */ /* if (d[0]->colnvmu) glm->C = convert_vmuC(glm->C, d[0]); */ if (d[0]->variance_fn) { glm->mu = get_mu(glm->mu, glm->y, d, n_vars); convert_C(glm->C, glm->mu, d[0]->variance_fn); } if (DEBUG_COV && pred == GLS_BLUP) printlog("[using generalized covariances: max_val - semivariance()]"); M_DEBUG(glm->C, "Covariances (x_i, x_j) matrix C (upper triangle)"); /* * factorize C: */ CHfactor(glm->C, piv, &info); if (info != 0) { /* singular: */ pr_warning("Covariance matrix singular at location [%g,%g,%g]: skipping...", where->x, where->y, where->z); m_free(glm->C); glm->C = MNULL; /* assure re-entrance if global */ P_FREE(piv); set_mv_double(&est[0]); return; } if (piv == NULL) M_DEBUG(glm->C, "glm->C, Choleski decomposed:") else M_DEBUG(glm->C, "glm->C, LDL' decomposed:") } /* if (pred != UPDATE) */ if (pred != GLS_BLP && !UPDATE_BLP) { /* C-1 X and X'C-1 X, beta */ /* * calculate CinvX: */ glm->CinvX = CHsolve(glm->C, glm->X, glm->CinvX, piv); /* M_DEBUG(glm->CinvX, "C-1 X"); */ /* * calculate X'C-1 X: */ glm->XCinvX = mtrm_mlt(glm->X, glm->CinvX, glm->XCinvX); /* X'C-1 X */ M_DEBUG(glm->XCinvX, "X'C-1 X"); m_inverse(glm->XCinvX, &info); if (info != 0) { /* singular: */ pr_warning("X'C-1 X matrix singular at location [%g,%g,%g]: skipping...", where->x, where->y, where->z); m_free(glm->C); glm->C = MNULL; /* assure re-entrance if global */ P_FREE(piv); set_mv_double(&est[0]); return; } /* * calculate beta: */ tmpa = v_resize(tmpa, rows_C); tmpa = vm_mlt(glm->CinvX, glm->y, tmpa); /* X'C-1 y */ glm->beta = vm_mlt(glm->XCinvX, tmpa, glm->beta); /* (X'C-1 X)-1 X'C-1 y */ V_DEBUG(glm->beta, "beta"); M_DEBUG(glm->XCinvX, "Cov(beta), (X'C-1 X)-1"); M_DEBUG(R = get_corr_mat(glm->XCinvX, R), "Corr(beta)"); } /* if pred != GLS_BLP */ } /* if redo the heavy part */ if (pred != GLS_BLP && !UPDATE_BLP) { /* but BLUE or BLUP */ X0 = get_X0(d, X0, where, n_vars); M_DEBUG(X0, "X0 (X values at prediction location x0)"); blup = vm_mlt(X0, glm->beta, blup); /* X0' beta = beta'X0 -> vm_ */ if (pred == GLS_BLUP) V_DEBUG(blup, "BLUE(mu), E(y(x0)) = X0'beta"); } if (pred == GLS_BLUE) { /* we did the blue, it's in blup */ /* * BLUE = X0 beta; Cov(X0 beta)= X0'(X'C-1X)-1 X0 */ Tmp1 = mtrm_mlt(X0, glm->XCinvX, Tmp1); m_mlt(Tmp1, X0, MSPE); /* X0'(X'C-1X)-1 X0 */ fill_est(d, blup, MSPE, n_vars, est); debug_result(blup, MSPE, pred); P_FREE(piv); return; /* Quit function */ } /* * now the part that's got to be done every time, for x0 and where change: * resize matrices (BLP, BLUP): */ C0 = m_resize(C0, rows_C, n_vars); CinvC0 = m_resize(CinvC0, rows_C, n_vars); /* * fill C0: */ for (i = 0; i < n_vars; i++) { /* cols */ for (j = 0, start_j = 0; j < n_vars; j++) { /* rows */ v = get_vgm(LTI(d[i]->id, d[j]->id)); for (k = 0; k < d[j]->n_sel; k++) { if (pred == GLS_BLUP) ME(C0, start_j+k, i) = GCV0(v, d[j]->sel[k], where, d[j]->pp_norm2); else ME(C0, start_j+k, i) = COVARIANCE0(v, d[j]->sel[k], where, d[j]->pp_norm2); } start_j += d[j]->n_sel; } } /* if (d[0]->colnvmu) { X0 = get_X0(d, X0, where, n_vars); C0 = convert_vmuC0(C0, d[0], X0->me[0][0]); } */ if (d[0]->variance_fn) convert_C0(C0, glm->mu, glm->mu0, d[0]->variance_fn); M_DEBUG(C0, "Covariances (x_i, x_0), C0"); /* https://github.com/r-spatial/gstat/issues/80 : */ if (glm->C == NULL) { /* ErrMsg(ER_IMPOSVAL, "covariance matrix NULL;\nsee: https://github.com/r-spatial/gstat/issues/80"); */ pr_warning("C or X'C-1 X matrix singular at location [%g,%g,%g]: skipping...", where->x, where->y, where->z); set_mv_double(&est[0]); return; /* xxx: return NA's? */ } /* * calculate CinvC0: */ CinvC0 = CHsolve(glm->C, C0, CinvC0, piv); M_DEBUG(CinvC0, "C-1 C0"); if (pred == GLS_BLP || UPDATE_BLP) { /* * BLP = mu_0 + C0'C-1 (y-mu_i) */ V_DEBUG(glm->y, "data values y"); if (DEBUG_COV) { printlog("beta is:\n"); for (i = 0; i < n_vars; i++) for (j = 0; j < d[i]->beta->size; j++) printlog("%g%s", d[i]->beta->val[j], j == d[i]->beta->size - 1 ? "\n" : " "); } glm->mu = get_mu(glm->mu, glm->y, d, n_vars); V_DEBUG(glm->mu, "mean values (mu_i)"); /* y - mu_i: */ tmpa = v_resize(tmpa, rows_C); v_sub(glm->y, glm->mu, tmpa); V_DEBUG(tmpa, "Residual vector (y - mu_i)"); tmpb = vm_mlt(CinvC0, tmpa, tmpb); /* C0'C-1 (y-mu_i) */ V_DEBUG(tmpb, "Weighted res. vector, C0'C-1 (y-mu_i)"); v_add(blup, tmpb, blup); /* mu_0 + C0'C-1 (y-mu_i) */ /* * MSPE = C(0,0) - C0'C-1 C0 */ Tmp2 = mtrm_mlt(CinvC0, C0, Tmp2); /* C0'C-1 C0 */ /* if (d[0]->colnvmu) MSPE = convert_vmuC00(MSPE, X0->me[0][0]); */ if (d[0]->variance_fn) convert_MSPE(MSPE, glm->mu0, d[0]->variance_fn); m_sub(MSPE, Tmp2, MSPE); /* C(0,0) - C0'C-1 C0 */ fill_est(d, blup, MSPE, n_vars, est); debug_result(blup, MSPE, pred); P_FREE(piv); return; /* Quit function */ } /* * GLS_BLUP, universal kriging estimate remains: */ tmpa = mv_mlt(glm->X, glm->beta, tmpa); /* X beta */ tmpb = v_sub(glm->y, tmpa, tmpb); /* y - X beta */ tmpa = vm_mlt(CinvC0, tmpb, tmpa); /* c0'C-1 (Y - X beta) */ blup = v_add(blup, tmpa, blup); /* x0 beta + c0'C-1 (Y - X beta) */ /* * universal kriging MSPE: * (a) Cov_ij(0,0): */ for (i = 0; i < n_vars; i++) { for (j = 0; j <= i; j++) { v = get_vgm(LTI(d[i]->id, d[j]->id)); ME(MSPE, i, j) = ME(MSPE, j, i) = GCV0(v, where, where, d[j]->pp_norm2); } } M_DEBUG(MSPE, "[a] Cov_ij(B,B) or Cov_ij(0,0)"); /* * (c) (x0-X'C-1 c0)'(X'C-1X)-1 (x0-X'C-1 c0): */ Tmp1 = mtrm_mlt(glm->CinvX, C0, Tmp1); /* X'C-1 c0 */ Tmp1 = m_sub(X0, Tmp1, Tmp1); /* (x0 - X'C-1 c0) */ Tmp2 = m_copy(Tmp1, m_resize(Tmp2, Tmp1->m, Tmp1->n)); Tmp3 = m_mlt(glm->XCinvX, Tmp1, Tmp3); /* (X'C-1 X)-1 (x0 - X'C-1 c0) */ Tmp1 = mtrm_mlt(Tmp2, Tmp3, Tmp1); M_DEBUG(Tmp1, "[c] (x0-X'C-1 c0)'(X'C-1 X)-1(x0-X'C-1 c0)"); /* * (b) c0'C-1 c0: */ Tmp2 = mtrm_mlt(C0, CinvC0, Tmp2); M_DEBUG(Tmp2, "[b] c0'C-1 c0"); /* * (a - b + c) = * Cov_ij(0,0) - c0'C-1 c0 + (x0-X'C-1 c0)'(X'C-1 X)-1 (x0-X'C-1 c0): */ m_sub(MSPE, Tmp2, MSPE); /* a-b */ m_add(MSPE, Tmp1, MSPE); /* +c */ /* * done: */ fill_est(d, blup, MSPE, n_vars, est); debug_result(blup, MSPE, pred); if (DEBUG_COV) { /* calculate kriging weights explicitly: */ /* Tmp3' * glm->CinvX' + CinvC0 */ Tmp1 = m_mlt(glm->CinvX, Tmp3, Tmp1); Tmp2 = m_add(Tmp1, CinvC0, Tmp2); M_DEBUG(Tmp2, "kriging weights"); if (DEBUG_COV) printlog("\n\n"); } P_FREE(piv); return; } static void fill_est(DATA **d, VEC *blup, MAT *MSPE, int n_vars, double *est) { int i, j, n_filled; static IVEC *v = IVNULL; if (n_vars == 1) { est[0] = blup->ve[0]; est[1] = ME(MSPE, 0, 0); return; } v = iv_resize(v, n_vars); if (d == NULL) { /* GLS_BLP, initializing */ for (i = 0; i < n_vars; i++) v->ive[i] = i; n_filled = n_vars; } else { /* n_vars > 1: avoid possibly empty variables -> NA */ for (i = j = 0; i < n_vars; i++) { if (d[i]->n_sel > 0) { v->ive[j] = i; j++; } } n_filled = j; } for (i = 0; i < n_filled; i++) { /* only adress non-empty variables */ est[2 * v->ive[i]] = blup->ve[v->ive[i]]; est[2 * v->ive[i] + 1] = ME(MSPE, v->ive[i], v->ive[i]); for (j = 0; j < i; j++) est[2 * n_vars + LTI2(v->ive[i], v->ive[j])] = ME(MSPE, v->ive[i], v->ive[j]); } return; } static void debug_result(VEC *blup, MAT *MSPE, enum GLS_WHAT pred) { if (! DEBUG_COV) return; switch (pred) { case GLS_BLP: V_DEBUG(blup, "Best Linear Predictor"); M_DEBUG(MSPE, "Prediction Covariances"); break; case GLS_BLUE: V_DEBUG(blup, "Best Linear Unbiased Estimate (X0'beta)"); M_DEBUG(MSPE, "Estimation Covariances, Cov(X0'beta)"); break; case GLS_BLUP: V_DEBUG(blup, "Best Linear Unbiased Predictor"); M_DEBUG(MSPE, "MSPE ([a]-[b]+[c])"); break; case UPDATE: V_DEBUG(blup, "Updated predictor"); M_DEBUG(MSPE, "MSPE (updated)"); break; case GLS_INIT: ErrMsg(ER_IMPOSVAL, "invalid value for pred"); break; } } double *make_gls(DATA *d, int calc_residuals) { /* * if calc_residuals == 0, return value is allocated, but not freed */ int i, j, size; double *est = NULL; DATA **data; GLM *glm; glm = (GLM *) d->glm; if (glm == NULL) { data = get_gstat_data(); glm = (GLM *) data[0]->glm; } if (glm && glm->C) { /* renew: variogram may have changed */ m_free((MAT *) glm->C); glm->C = MNULL; } select_at(d, NULL); /* where == NULL --> global selection */ if (calc_residuals) { est = (double *) emalloc(get_n_outputs() * sizeof(double)); for (i = 0; i < d->n_list; i++) { gls(&d, 1, GLS_BLUE, d->list[i], est); glm = (GLM *) d->glm; d->list[i]->attr = glm->y->ve[i] - est[0]; } efree(est); est = NULL; } else { /* no residuals -- return beta & Cov(beta) */ size = d->n_X * (1 + d->n_X); est = (double *) emalloc(size * sizeof(double)); /* fill the GLM stuff: */ gls(&d, 1, GLS_BLUE, d->list[0], est); glm = (GLM *) d->glm; for (i = 0; i < glm->beta->dim; i++) { est[2 * i] = glm->beta->ve[i]; est[2 * i + 1] = ME(glm->XCinvX, i, i); for (j = 0; j < i; j++) est[2 * glm->beta->dim + LTI2(i,j)] = ME(glm->XCinvX, i, j); } } gls(NULL, 0, GLS_INIT, NULL, NULL); return est; /* possibly NULL */ } double *make_gls_mv(DATA **d, int n_vars) { /* * allocates memory for est (return value) but does not free it */ int i, j, sum_X, index, size = 0; double *est = NULL; GLM *glm; DPOINT where; for (i = sum_X = 0; i < n_vars; i++) { select_at(d[i], NULL); /* where == NULL --> global selection */ sum_X += d[i]->n_X; } where = *d[0]->list[0]; where.X = (double *) emalloc(sum_X * sizeof(double)); /* replace */ for (i = 0; i < sum_X; i++) /* fill with nonsense values: */ where.X[i] = 0.0; size = sum_X + (sum_X * (sum_X + 1))/2; est = (double *) emalloc(size * sizeof(double)); /* fill the GLM stuff: */ gls(d, n_vars, GLS_BLUE, &where, est); glm = (GLM *) d[0]->glm; assert(glm != NULL); for (i = 0; i < glm->beta->dim; i++) { assert((2 * i + 1) < size); est[2 * i] = glm->beta->ve[i]; est[2 * i + 1] = ME(glm->XCinvX, i, i); for (j = 0; j < i; j++) { index = 2 * glm->beta->dim + LTI2(i,j); assert(index < size); est[index] = ME(glm->XCinvX, i, j); } } gls(NULL, 0, GLS_INIT, NULL, NULL); efree(where.X); return est; } static GLM *new_glm(void) { GLM *glm; glm = (GLM *) emalloc(sizeof(GLM)); glm->X = glm->C = glm->CinvX = glm->XCinvX = MNULL; glm->y = glm->mu = glm->mu0 = glm->beta = VNULL; return glm; } void free_glm(void *v_glm) { GLM *glm; if (v_glm == NULL) return; glm = (GLM *) v_glm; if (glm->X) m_free(glm->X); if (glm->C) m_free(glm->C); if (glm->CinvX) m_free(glm->CinvX); if (glm->XCinvX) m_free(glm->XCinvX); if (glm->y) v_free(glm->y); if (glm->beta) v_free(glm->beta); if (glm->mu0) v_free(glm->mu0); if (glm->mu) v_free(glm->mu); efree(glm); } static void convert_C(MAT *C, VEC *mu, double (*fn)(double)) { int i, j; double sqrtfni; assert(C && mu); assert(C->m == mu->dim); for (i = 0; i < mu->dim; i++) { /* assert(mu->ve[i] >= 0.0); */ /* be more friendly: */ if (mu->ve[i] < 0.0) ErrMsg(ER_IMPOSVAL, "can not take square root of negative mean values!"); ME(C, i, i) *= fn(mu->ve[i]); sqrtfni = sqrt(fn(mu->ve[i])); for (j = 0; j < i; j++) ME(C, i, j) *= sqrtfni * sqrt(fn(mu->ve[j])); } } static void convert_C0(MAT *C0, VEC *mu, VEC *mu0, double (*fn)(double)) { int i, j; double sqrtfni; assert(C0 && mu && mu0); assert(C0->m == mu->dim); assert(C0->n == mu0->dim); for (i = 0; i < mu->dim; i++) { assert(mu->ve[i] >= 0.0); sqrtfni = sqrt(fn(mu->ve[i])); for (j = 0; j < mu0->dim; j++) ME(C0, i, j) *= sqrtfni * sqrt(fn(mu0->ve[j])); } } static void convert_MSPE(MAT *MSPE, VEC *mu0, double (*fn)(double)) { int i, j; double sqrtfni; assert(MSPE && mu0); assert(MSPE->m == mu0->dim); for (i = 0; i < mu0->dim; i++) { assert(mu0->ve[i] >= 0.0); ME(MSPE, i, i) *= fn(mu0->ve[i]); sqrtfni = sqrt(fn(mu0->ve[i])); for (j = 0; j < i; j++) { ME(MSPE, i, j) *= sqrtfni * sqrt(fn(mu0->ve[j])); ME(MSPE, j, i) = ME(MSPE, i, j); } } } static VEC *get_mu(VEC *mu, const VEC *y, DATA **d, int n_vars) { int i, start_j, j; mu = v_resize(mu, y->dim); for (i = start_j = 0; i < n_vars; i++) { for (j = 0; j < d[i]->n_sel; j++) mu->ve[start_j + j] = calc_mu(d[i], d[i]->sel[j]); start_j += d[i]->n_sel; } return mu; } static MAT *get_corr_mat(MAT *C, MAT *R) { int i, j; assert(C); assert(C->m == C->n); R = m_copy(C, m_resize(R, C->m, C->n)); for (i = R->m - 1; i >= 0; i--) { assert(ME(R, i, i) > 0.0); for (j = 0; j < i; j++) ME(R, i, j) /= sqrt(ME(R, i, i) * ME(R, j, j)); for (j = i + 1; j < R->m; j++) ME(R, i, j) = ME(R, j, i); } for (i = 0; i < R->m; i++) ME(R, i, i) = 1.0; return(R); } gstat/src/fit.h0000644000176200001440000000023013777370515013130 0ustar liggesusers#ifndef FIT_H # define FIT_H #if defined(__cplusplus) extern "C" { #endif int fit_variogram(VARIOGRAM *v); #if defined(__cplusplus) } #endif #endif gstat/src/direct.c0000644000176200001440000000727013777370515013626 0ustar liggesusers/* * direction.c: evaluation of directions for variogram pair inclusion * Optimized by Konstantin Malakhanov (K.M.), march 1998 */ #include /* cos() */ #include "defs.h" #include "userio.h" #include "data.h" #include "utils.h" #include "debug.h" #include "defaults.h" #include "glvars.h" #include "direct.h" #define MAX_ANG (PI/2.0) /* * direct's little private data base: */ static double alpha = 0.0, beta = 0.0, tol_hor = PI, tol_ver = PI, cos_tol_hor = -1.0, cos_tol_ver = -1.0, /* Changed K.M. Fri Feb 27 11:13:47 1998 */ dir_v[2] = { 1.0, 0.0 } , dir_h[2] = { 0.0, 1.0 }; static int all_directions = -1; void set_direction_values(double a, double b, double t_h, double t_v) { /* do some checks: */ if (a < 0.0 || a > 360.0) pr_warning( "alpha must be in [0..360]"); if (b < 0.0 || b > 360.0) pr_warning( "beta must be in [0..360]"); if (t_h < 0.0 || t_h > DEF_tol_hor) pr_warning( "horizontal tolerance must be in <0..180>"); if (t_v < 0.0 || t_v > DEF_tol_ver) pr_warning( "vertical tolerance must be in <0..180>"); if (t_h == DEF_tol_hor && t_v == DEF_tol_ver) { all_directions = 1; return; } else all_directions = 0; alpha = a * PI / 180.0; beta = b * PI / 180.0; tol_hor = t_h * PI / 180.0; tol_ver = t_v * PI / 180.0; cos_tol_hor = cos(tol_hor); /* Changed K.M. Fri Feb 27 11:14:15 1998 */ cos_tol_ver = cos(tol_ver); /* Changed K.M. Fri Feb 27 11:14:15 1998 */ dir_h[0] = sin(alpha); /* */ dir_h[1] = cos(alpha); /* */ dir_v[0] = cos(beta); /* */ dir_v[1] = sin(beta); /* */ return; } double valid_direction(DPOINT *a, DPOINT *b, int symmetric, const DATA *d) { /* * return distance when vector is within the tolerance section; * return -1.0 when vector is outside tolerance section. */ double norm, inprod, dist, px, py, pz; /* Changed K.M. Fri Feb 27 11:06:07 1998 */ /* dist = d->point_norm(p); */ dist = sqrt(d->pp_norm2(a, b)); if (all_directions == 1) return dist; px = a->x - b->x; py = a->y - b->y; pz = a->z - b->z; if (tol_hor >= MAX_ANG && tol_ver >= MAX_ANG) return dist; if (tol_hor >= MAX_ANG && pz == 0.0) return dist; if (tol_ver >= MAX_ANG && px == 0.0 && py == 0.0) return dist; if (tol_hor < MAX_ANG && (px != 0.0 || py != 0.0)) { /* * check in plane: */ norm = sqrt(px * px + py * py); inprod = (px * dir_h[0] + py * dir_h[1])/norm; if (symmetric) { /* the most often case */ if ( fabs(inprod) < cos_tol_hor) /* if cos(alpha) < cos(tol) then alpha > tol! */ return -1.0; } else if (inprod < cos_tol_hor) return -1.0; /* Changed K.M. Fri Feb 27 11:18:24 1998: I have eliminated most of checks for the following reasons: if (because of numerical reasons) we get fabs(inprod)>1.0, then it really means that inprod is either +1.0 or -1.0, i.e. the angle between point vector and variogram direction is either 0 or pi. In case of SYMMETRIC it doesn't matter - fabs(inprod) is then bigger then cos_tol_hor, so we accept this point pair as it should be. In the case of not SYMMETRIC - if inprod>1 then inprod is bigger then cos_tol_hor and we accept this pair, if inprod < -1.0 then it is smaller then cos_tol_hor and we reject this pair. This way we also do not need to calculate acos and to check for domain errors afterwards. */ } if (tol_ver < MAX_ANG && (px != 0.0 || py != 0.0 || pz != 0.0)) { /* * inproduct in */ /* Changed K.M. Fri Feb 27 15:47:13 1998 */ inprod = (sqrt(px * px + py * py) * dir_v[0] + pz * dir_v[1])/dist; if (symmetric) { /* the most often case */ if ( fabs(inprod) < cos_tol_ver) /* if cos(alpha) < cos(tol) then alpha > tol! */ return -1.0; } else if (inprod < cos_tol_ver) return -1.0; } return dist; } gstat/src/lm.c0000644000176200001440000003175314115426745012761 0ustar liggesusers/* * lm.c: contains routines for linear model y=Xb+e, e independent. */ #include #include /* size_t for DJGPP */ #include /* DBL_MAX */ #include /* sqrt() */ #include "mtrx.h" #include "defs.h" #include "userio.h" #include "data.h" #include "utils.h" #include "debug.h" #include "select.h" #include "glvars.h" #include "lm.h" static void predict_lm(LM *lms, MAT *X0, double *est); static void create_lm(DATA **d, int nvars); static VEC *get_weights(DATA **d, VEC *weights, int nvars); static int get_colX_nr(DATA **d, int var, int x); static int zero_weights_count(LM *lm); void pred_lm(DATA **data, int n_vars, DPOINT *where, double *est) { int i = 0, global = 1; LM *lm; static MAT *X0 = MNULL; global = 1; while (global && i < n_vars) { if (data[i]->sel != data[i]->list) /* local selection */ global = 0; /* and jump out of this loop */ i++; } if (data[0]->lm == NULL || !global) { create_lm(data, n_vars); if (DEBUG_FIT) { printlog("at location [%g,%g,%g]:\n", where->x, where->y, where->z); logprint_lm(data[0], data[0]->lm); } } lm = (LM *) data[0]->lm; if (lm == NULL || lm->y->dim == 0 || lm->is_singular) { for (i = 0; i < n_vars; i++) { set_mv_double(&(est[2 * i])); set_mv_double(&(est[2 * i + 1])); } if (lm && lm->is_singular) pr_warning("singular X matrix at x[%g], y[%g], z[%g]:", where->x, where->y, where->z); } else { X0 = get_X0(data, X0, where, n_vars); if (DEBUG_COV) { printlog("#X0 is "); m_logoutput(X0); } predict_lm(lm, X0, est); } return; } double *make_ols(DATA *d) { /* return value is allocated, but not freed */ int i, j, size; double *est = NULL; DATA **data; LM *lm; lm = (LM *) d->lm; if (lm == NULL) { data = get_gstat_data(); lm = (LM *) data[0]->lm; } select_at(d, NULL); /* where == NULL --> global selection */ /* return beta & Cov(beta) */ size = d->n_X * (1 + d->n_X); est = (double *) emalloc(size * sizeof(double)); for (i = 0; i < size; i++) set_mv_double(&(est[i])); /* fill the LM stuff: */ create_lm(&d, 1); if (DEBUG_FIT) logprint_lm(d, d->lm); lm = (LM *) d->lm; if (lm->is_singular) return est; /* all NA's */ for (i = 0; i < lm->beta->dim; i++) { est[2 * i] = lm->beta->ve[i]; est[2 * i + 1] = ME(lm->Cov, i, i); for (j = 0; j < i; j++) est[2 * lm->beta->dim + LTI2(i,j)] = ME(lm->Cov, i, j); } free_lm(d->lm); d->lm = NULL; return est; } LM *init_lm(LM *lm) { if (lm == NULL) lm = (LM *) emalloc(sizeof(LM)); lm->y = VNULL; lm->weights = VNULL; lm->beta = VNULL; lm->Xty = VNULL; lm->X = MNULL; lm->Cov = MNULL; lm->Chol = MNULL; lm->SSReg = lm->MSReg = DBL_MAX; lm->SSErr = lm->MSErr = DBL_MAX; lm->is_singular = 0; return lm; } void free_lm(LM *lm) { if (lm->y) v_free(lm->y); if (lm->weights) v_free(lm->weights); if (lm->beta) v_free(lm->beta); if (lm->Xty) v_free(lm->Xty); if (lm->X) m_free(lm->X); if (lm->Chol) m_free(lm->Chol); if (lm->Cov) m_free(lm->Cov); efree(lm); } static void create_lm(DATA **data, int nvars) { /* * obtain base necessities (y, X, weights), and calculate the rest */ LM *lm; int i; lm = (LM *) data[0]->lm; if (lm == NULL) /* create */ data[0]->lm = lm = init_lm(NULL); lm->X = get_X(data, lm->X, nvars); lm->y = get_y(data, lm->y, nvars); lm->weights = get_weights(data, lm->weights, nvars); /* * check for intercept: */ if (nvars == 1) { lm->has_intercept = (data[0]->colX[0] == 0); for (i = 1; i < data[0]->n_X && ! lm->has_intercept; i++) lm->has_intercept = (data[0]->colX[i] == 0); } /* * calculate: */ data[0]->lm = (void *) calc_lm(lm); return; } void make_residuals_lm(DATA *d) { /* * make (local or global) residuals */ int i; double est[2]; static MAT *X0 = MNULL; if (d->is_residual) return; if (d->beta) { /* pr_warning("calculating residuals with respect to pre-defined mean"); */ for (i = 0; i < d->n_list; i++) d->list[i]->attr -= calc_mu(d, d->list[i]); } else { select_at(d, NULL); create_lm(&d, 1); if (DEBUG_FIT) logprint_lm(d, d->lm); for (i = 0; i < d->n_list; i++) { X0 = get_X0(&d, X0, d->list[i], 1); predict_lm((LM *) d->lm, X0, est); d->list[i]->attr -= est[0]; /* y = Xb + e, so e^ = y - Xb^ */ } } d->is_residual = 1; return; } static void predict_lm(LM *lm, MAT *X0, double *est) { /* * make a prediction for x0, store pred. and variance in est[0] and est[1] */ VEC *blup = VNULL; MAT *tmp = MNULL, *ans = MNULL; if (lm->beta == NULL) ErrMsg(ER_IMPOSVAL, "lm->beta NULL: sample too small?"); blup = vm_mlt(X0, lm->beta, blup); /* X0' beta = beta'X0 -> vm_ */ /* * Cov(y0^ - y0) = x0'X'X-1 x0 MSErr, or x0'(X'WX)-1 x0 MSErr * for this, solve X'X b = x0 for b, then b = X'X-1 x0; ans = x0'b * MSErr added when prediction is pointwise */ tmp = CHsolve(lm->Chol, X0, tmp, PNULL); ans = mtrm_mlt(X0, tmp, ans); ans = sm_mlt(lm->MSErr, ans, ans); for (int i = 0; i < ans->m; i++) { est[2 * i] = blup->ve[i]; est[2 * i + 1] = ME(ans, i, i); if (max_block_dimension(1) == 0.0) /* pointwise prediction */ est[2 * i + 1] += lm->MSErr; for (int j = 0; j < i; j++) est[2 * ans->m + LTI2(i,j)] = ME(ans, i, j); } v_free(blup); m_free(tmp); m_free(ans); return; } MAT *get_X(DATA **d, MAT *X, int nvars) { int i, j, k, rows, cols, colX; for (i = rows = cols = 0; i < nvars; i++) { rows += d[i]->n_sel; if (d[i]->n_sel > 0) cols += d[i]->n_X - d[i]->n_merge; } /* if (rows <= 0 || cols <= 0) ErrMsg(ER_IMPOSVAL, "get_X: size <= 0"); */ X = m_resize(X, rows, cols); m_zero(X); for (i = rows = 0; i < nvars; i++) { /* i: var block index */ for (j = 0; d[i]->n_sel && j < d[i]->n_X; j++) { /* j: column index */ colX = get_colX_nr(d, i, j); for (k = 0; k < d[i]->n_sel; k++) /* k: row index */ ME(X, rows + k, colX) = d[i]->sel[k]->X[j]; } rows += d[i]->n_sel; } return X; } MAT *get_X0(DATA **d, MAT *X0, DPOINT *where, int nvars) { int i, j, start_i, cols, colX; for (i = cols = 0; i < nvars; i++) { if (d[i]->n_sel > 0) cols += d[i]->n_X - d[i]->n_merge; } X0 = m_resize(X0, cols, nvars); m_zero(X0); /* initialize; now fill non-zero entries: */ for (i = start_i = 0; i < nvars; i++) { for (j = 0; d[i]->n_sel && j < d[i]->n_X; j++) { /* for X-column k+.. */ colX = get_colX_nr(d, i, j); ME(X0, colX, i) = where->X[start_i+j]; /* colX is row index: X0' */ } start_i += d[i]->n_X; } return X0; } VEC *get_y(DATA **d, VEC *y, int nvars) { int i, j, offset, size; for (i = size = 0; i < nvars; i++) size += d[i]->n_sel; /* if (size <= 0) ErrMsg(ER_IMPOSVAL, "get_X: size <= 0"); */ y = v_resize(y, size); for (j = offset = 0; j < nvars; j++) { for (i = 0; i < d[j]->n_sel; i++) y->ve[offset + i] = d[j]->sel[i]->attr; offset += d[j]->n_sel; } return y; } static int get_colX_nr(DATA **d, int var, int this_x) { int offset_x = 0, colX, i, j; for (i = 0; i < var; i++) if (d[i]->n_sel) offset_x += d[i]->n_X - d[i]->n_merge; if (d[var]->n_merge == 0) return offset_x + this_x; for (i = 0; i < d[var]->n_merge; i++) { if (d[var]->mtbl[i].col_this_X == this_x) { /* hit: merge this one! */ colX = d[var]->mtbl[i].col_other_X; if (d[var]->mtbl[i].to_var > 0) for (j = 0; j < d[var]->mtbl[i].to_var - 1; j++) colX += d[j]->n_X - d[j]->n_merge; return colX; } } /* so, we're at least at offset_x, but how much should we add? */ colX = offset_x + this_x; /* i.e. the maximum... */ for (i = 0; i < d[var]->n_merge; i++) for (j = 0; j < this_x; j++) if (d[var]->mtbl[i].col_this_X == j) colX--; /* ...minus all previously merged entries */ return colX; } static VEC *get_weights(DATA **d, VEC *weights, int nvars) { int i, j, size; for (i = size = 0; i < nvars; i++) { if (d[i]->colnvariance <= 0) /* no weights */ return VNULL; if (d[i]->n_sel > 0) size += d[i]->n_sel; } if (size <= 0) return VNULL; weights = v_resize(weights, size); for (i = size = 0; i < nvars; i++) { for (j = 0; j < d[i]->n_sel; j++) weights->ve[size + j] = 1.0 / d[i]->sel[j]->variance; /* ->variance > 0 is assured in data.c */ size += d[i]->n_sel; } return weights; } void logprint_lm(DATA *d, LM *lm) { double SSTot; char line[] = "-----------------------------------------------------------"; int i, coords = 0; if (lm->dfReg <= 0) return; SSTot = lm->SSReg + lm->SSErr; if (d != NULL) { printlog("\nmodel: %s = ", d->variable); for (i = 0; i < d->n_X; i++) { if (i > 0) { printlog(" + "); if ((i + 2) % 5 == 0) printlog("\n"); } printlog("%g", lm->beta->ve[i]); if (d->colX[i] > 0) printlog(" [col %d]", d->colX[i]); if (d->colX[i] < 0) { printlog(" %s", POLY_NAME(d->colX[i])); coords = 0; } } printlog(" + e\n"); if (coords) printlog( "(Note: coordinate coefficients apply to normalized coordinates)\n\n"); } printlog("Summary statistics (model %s intercept):\n", lm->has_intercept ? "with" : "without"); printlog("Source df SS MS F\n"); printlog("%s\n", line); printlog("Regression %3d %12.6g %12.6g", lm->dfReg, lm->SSReg, lm->MSReg); if (lm->MSErr <= 0.0) printlog(" Inf\n"); else printlog(" %12.6g\n", lm->MSReg/lm->MSErr); printlog("Error %3d %12.6g %12.6g\n", lm->dfE, lm->SSErr, lm->MSErr); printlog("%s\nTotal, %s %3d %12.6g\n%s\n\n", line, lm->has_intercept ? "corrected" : "uncorr. ", lm->dfReg + lm->dfE, SSTot, line); /* if (SSTot > 0.0) printlog("R2: %g\n", lm->SSReg / SSTot); */ return; } LM *calc_lm(LM *lm) { /* * calculate Chol,Xty,beta,SSErr,SSReg,MSErr^... * ASSUMES lm->X, lm->y and optionally lm->weights to be filled! */ double y_mean = 0, w; int i, j; /* static MAT *QR = MNULL; */ static VEC *tmp = VNULL; if (lm->X == MNULL || lm->y == VNULL) ErrMsg(ER_NULL, "calc_lm(): y or X"); if (lm->X->m != lm->y->dim) { message("size: %d %d %d\n", lm->X->m, lm->y->dim, lm->X->n); ErrMsg(ER_IMPOSVAL, "calc_lm: matrices wrong size"); } if (lm->X->m < lm->X->n) { lm->is_singular = 1; return lm; } /* * allocate structures: */ lm->is_singular = 0; lm->beta = v_resize(lm->beta, lm->X->n); lm->Xty = v_resize(lm->Xty, lm->X->n); tmp = v_resize(tmp, lm->X->n); if (lm->X->n == 0 || lm->y->dim == 0) return lm; if (DEBUG_COV) { printlog("#y is "); v_logoutput(lm->y); printlog("#X is "); m_logoutput(lm->X); if (lm->weights) { printlog("#w is "); v_logoutput(lm->weights); } } /* * create, in case of weights, V^{-1/2}X and V^{-1/2}y: */ if (lm->weights != VNULL) { for (i = 0; i < lm->X->m; i++) { /* rows */ w = sqrt(lm->weights->ve[i]); for (j = 0; j < lm->X->n; j++) /* cols */ ME(lm->X, i, j) *= w; lm->y->ve[i] *= w; } } /* * create Chol = X'X (or X'WX) and XtY = (y'X)' = X'y (X'Wy) */ lm->Xty = vm_mlt(lm->X, lm->y, lm->Xty); if (DEBUG_COV) { printlog("#X'y is "); v_logoutput(lm->Xty); } lm->Chol = mtrm_mlt(lm->X, lm->X, lm->Chol); if (DEBUG_COV) { printlog("#X'X is "); m_logoutput(lm->Chol); } lm->Cov = m_copy(lm->Chol, lm->Cov); /* save copy of X'X */ int info; lm->Chol = CHfactor(lm->Chol, PNULL, &info); if (info != 0) { lm->is_singular = 1; return lm; } lm->beta = CHsolve1(lm->Chol, lm->Xty, lm->beta, PNULL); if (DEBUG_COV) { printlog("#beta is "); v_logoutput(lm->beta); } /* * estimate error variance: */ tmp = mv_mlt(lm->X, lm->beta, tmp); /* X b */ tmp = v_sub(lm->y, tmp, tmp); /* e = y - X b */ if (lm->weights) { for (i = 0, lm->SSErr = 0.0; i < lm->X->m; i++) lm->SSErr += lm->weights->ve[i] * SQR(tmp->ve[i]); } else lm->SSErr = in_prod(tmp, tmp); /* e'e */ if (DEBUG_COV) printlog("#SSErr is %g\n", lm->SSErr); /* * estimate SSReg (Draper & Smith, p. 81, Section 2.2) * (unweighted, corrected): beta' X'X beta - n * y_mean^2 * (weighted, corrected): sum weight_i * (x_i beta - beta_0)^2 * (unweighted): beta' X'X beta * (weighted): see below */ tmp = v_resize(tmp, lm->X->n); tmp = vm_mlt(lm->Cov, lm->beta, tmp); lm->SSReg = in_prod(lm->beta, tmp); if (lm->has_intercept) { for (i = 0, y_mean = 0.0; i < lm->y->dim; i++) y_mean += lm->y->ve[i]; y_mean /= lm->y->dim; lm->SSReg -= SQR(y_mean) * lm->y->dim; } lm->dfReg = lm->X->n; if (lm->has_intercept) lm->dfReg -= 1; if (lm->dfReg > 0) lm->MSReg = lm->SSReg/lm->dfReg; else lm->MSReg = DBL_MAX; lm->dfE = lm->X->m - zero_weights_count(lm) - lm->X->n; if (lm->dfE == 0) lm->MSErr = DBL_MAX; else lm->MSErr = lm->SSErr/lm->dfE; lm->Cov = m_inverse(lm->Cov, &info); /* (X'X)-1 */ if (info != 0) pr_warning("linear model has singular covariance matrix"); /* next, multiply with sigma^2 */ sm_mlt(lm->MSErr, lm->Cov, lm->Cov); /* in situ mlt */ return lm; } static int zero_weights_count(LM *lm) { int i, n_zero = 0; if (lm->weights == VNULL) return 0; for (i = 0; i < lm->weights->dim; i++) if (lm->weights->ve[i] < gl_zero) n_zero++; return n_zero; } double calc_mu(const DATA *d, const DPOINT *where) { int i; double mu, *from; assert(d->beta); mu = 0.0; from = where->X; for (i = 0; i < d->beta->size; i++) mu += from[i] * d->beta->val[i]; return mu; } gstat/src/glvars.h0000644000176200001440000000516313777370515013656 0ustar liggesusers#ifndef GLVARS_H # define GLVARS_H /* avoid multiple inclusion */ typedef enum { NSP = 0, /* initial value */ UIF, /* variogram modelling user interface */ OKR, UKR, SKR, /* ordinary, universal or simple kriging */ IDW, /* inverse distance interpolation */ MED, /* (local) sample median or quantile */ NRS, /* neighbourhood size */ LSLM, /* uncorrelated (or weighted) linear model */ GSI, ISI, /* Gaussian/indicator (conditional) simulation */ SEM, COV, /* sample (cross) semivariance or covariance */ SPREAD, /* distance to nearest sample */ DIV, /* diversity, range */ SKEW, /* skewness, kurtosis */ LSEM, /* locally fitted semivariogram parameters */ TEST /* does nothing really */ } METHOD; typedef struct { METHOD m; int is_simulation; const char *name; } METHODS; extern const METHODS methods[]; typedef enum { MODE_NSP = 0, SIMPLE, STRATIFY, MULTIVARIABLE } MODE; #if defined(__cplusplus) extern "C" { #endif int init_global_variables(void); const char *get_outfile_namei(int i); const char **get_outfile_name(void); int dump_all(void); void check_global_variables(void); const char *method_string(METHOD i); int get_n_vars(void); int get_n_vgms(void); int get_n_outputs(void); int get_n_beta_set(void); int which_identifier(const char *id); const char *name_identifier(int i); void push_bound(double value); void set_method(METHOD); int is_simulation(METHOD m); METHOD get_default_method(void); METHOD get_method(void); void set_mode(void); MODE get_mode(void); double max_block_dimension(int reset); int n_variograms_set(void); int decide_on_coincide(void); int remove_id(const int id); void remove_all(void); #ifdef VARIO_H /* vario.h was included before this point: */ VARIOGRAM *get_vgm(int i); #endif #ifdef DATA_H /* data.h was included before this point: */ DATA **get_gstat_data(void); DATA *get_dataval(void); DATA *get_data_area(void); DATA *create_data_area(void); DPOINT *get_block_p(void); void setup_valdata_X(DATA *d); #endif #if defined(__cplusplus) } #endif extern int gl_nblockdiscr, gl_seed, gl_n_uk, gl_cressie, gl_zero_est, gl_fit, gl_iter, gl_xvalid, gl_gauss, gl_sym_ev, gl_jgraph, gl_blas, gl_order, gl_n_intervals, gl_gls_residuals, gl_asym_vgm, gl_numbers, gl_nsim, gl_lhs, gl_longlat, gl_n_marginals, gl_sparse, gl_rp, gl_coincide, gl_nocheck, gl_spiral, gl_secure, gl_split, gl_register_pairs, gl_sim_beta, gl_rowwise, gl_choleski; extern double gl_rho, gl_idp, gl_cutoff, gl_iwidth, gl_zmap, gl_quantile, gl_fit_limit, gl_fraction, gl_alpha, gl_beta, gl_tol_hor, gl_tol_ver, *gl_bounds, *gl_marginal_values, gl_zero, gl_zero2; extern const char *method_code[]; #endif /* GLVARS_H */ gstat/src/defs.h0000644000176200001440000000072313777370515013276 0ustar liggesusers/* * provides some definitions */ #ifndef DEFS_H #define DEFS_H /* avoid multiple inclusion */ #include /* but assertions are off, by default */ #define CDECL /* empty */ /* * several buffer sizes */ #define MAX_DATA 1250 /* not a maximum, but an increment step size */ #define INIT_N_VGMM 2 /* * (for glvars.c:) something, not bigger than 127 * because of user interface (crazy though) */ #define ERROR_BUFFER_SIZE 1280 #endif /* DEFS_H */ gstat/src/select.c0000644000176200001440000001636614127264064013630 0ustar liggesusers/* * select.c: neighborhood selection for local prediction */ #include #include /* qsort() */ #include /* memcpy() */ #include /* sqrt(), fabs() */ #include "defs.h" void Rprintf(const char *,...); #include "userio.h" #include "data.h" #include "utils.h" #include "debug.h" #include "vario.h" #include "defaults.h" #include "glvars.h" #include "nsearch.h" #include "select.h" static int octant_select(DATA *d, DPOINT *where); static int which_octant(DPOINT *where, DPOINT *p, int mode); int CDECL dist_cmp(const DPOINT **ap, const DPOINT **bp); static void print_selection(DATA *d, DPOINT *where); /* beware-of-side-effect macro: don't call with ++/--'s */ #define DPSWAP(a,b) { if (a != b) { tmp = a; a = b; b = tmp; }} static int select_qtree(DATA *d, DPOINT *where) { if (d->n_list <= 0 || d->id < 0 || d->sel_max == 0) return (d->n_sel = 0); /* * global neighbourhood? */ if (IS_GLOBAL(d) || where == NULL) { d->sel = d->list; d->n_sel = d->n_sel_max = d->n_list; if (DEBUG_SEL) { print_selection(d, where); } return d->n_sel; } /* set up or resize selection list, d->sel */ if (d->sel == NULL || d->sel == d->list) { /* first time or after forced global selection: */ d->sel = (DPOINT **) emalloc(d->n_list * sizeof(DPOINT *)); d->n_sel_max = d->n_list; } else if (d->n_list > d->n_sel_max) { /* no, something has changed... */ d->n_sel_max += MAX(MAX_DATA, d->n_list - d->n_sel_max); d->sel = (DPOINT **) erealloc(d->sel, d->n_sel_max * sizeof(DPOINT *)); } if (d->id > 0) { /* 2nd, 3d,..., n_vars-th variable */ if (gl_coincide == DEF_coincide) gl_coincide = decide_on_coincide(); /* establish first ... */ if (gl_coincide) { int i; DATA **data = get_gstat_data(); d->n_sel = data[0]->n_sel; for (i = 0; i < d->n_sel; i++) /* copy previous selection: */ d->sel[i] = d->list[GET_INDEX(data[0]->sel[i])]; if (DEBUG_SEL) print_selection(d, where); return d->n_sel; /* and we're done!! */ } } /* * So far, no selection has been done. * Let's see if today's job is easily done: */ memcpy(d->sel, d->list, d->n_list * sizeof(DPOINT *)); if (d->sel_rad >= DBL_MAX && d->sel_max >= d->n_list && d->oct_max == 0) { d->n_sel = d->n_list; if (DEBUG_SEL) print_selection(d, where); return d->n_sel; } /* * now we're sure that (a) sel_rad is set, or (b) sel_max < n_list, * or (c) oct_max is set, so let's do the smart thing: */ qtree_select(where, d); return -1; /* more work to do */ } int select_at(DATA *d, DPOINT *where) { /* * fill the array d->sel appropriatly given x,y,z,d->sel_min,d->sel_max * and d->sel_rad: possibly by corresponding semivariance value * first select all points within a distance d->sel_rad from where * then select at max the d->sel_max nearest and return no selection * if there are less then d->sel_min * if "FORCE", then select ALWAYS the d->sel_min nearest points. * * corrected variogram distance feb. 16th 1993 * changed search to normalizing to (0,0,0) first, aug 1993 */ if (d->what_is_u == U_UNKNOWN) d->what_is_u = U_ISDIST; /* we're going to fill this right now */ else if (d->what_is_u != U_ISDIST) ErrMsg(ER_IMPOSVAL, "select_at() needs distances"); if (select_qtree(d,where) != -1) return d->n_sel; /* * so, now we're at the stage where one of the following conditions holds: * (a) we selected all points within d->sel_rad * (b) we selected (at least) the nearest d->sel_max * (c) we selected (forced) at least d->sel_min, possibly beyond d->sel_rad * Now, should we select further, sorting on distance? * */ if (d->vdist) { /* use variogram distance as sort criterium */ int i; for (i = 0; i < d->n_sel; i++) d->sel[i]->u.dist2 = get_semivariance(get_vgm(LTI(d->id,d->id)), where->x - d->sel[i]->x, where->y - d->sel[i]->y, where->z - d->sel[i]->z); } if (d->oct_max) { /* do octant selection */ d->oct_filled = octant_select(d, where); /* sorts, adjusts n_sel and destroys distance order, so only */ if (get_method() == SPREAD) /* then we've got to re-order them */ qsort(d->sel, (size_t) d->n_sel, sizeof(DPOINT *), (int CDECL (*)(const void *,const void *)) dist_cmp); } if (d->vdist) { qsort(d->sel, (size_t) d->n_sel, sizeof(DPOINT *), (int CDECL (*)(const void *, const void *)) dist_cmp); /* pick d->sel_[max|min] nearest: */ if (d->sel_min && d->n_sel == d->sel_min && d->sel[d->n_sel]->u.dist2 > d->sel_rad) /* we forced: */ d->n_sel = d->sel_min; if (d->n_sel > d->sel_max) d->n_sel = d->sel_max; } if (DEBUG_SEL) print_selection(d, where); return d->n_sel; } static int octant_select(DATA *d, DPOINT *where) { /* * selects the d->oct_max nearest points per octant/quadrant/secant, * using euclidian or variogram distance */ int i, j, noct = 1, n, start = 0, end = 0, n_notempty = 0; DPOINT **sel, *tmp; if (d->mode & Z_BIT_SET) noct = 8; else if (d->mode & Y_BIT_SET) noct = 4; else noct = 2; sel = d->sel; for (i = 0; i < noct; i++) { /* for each octant: */ /* start == end: */ for (j = start; j < d->n_sel; j++) { /* for the remaining of sel: */ if (which_octant(where, sel[j], d->mode) == i) { DPSWAP(sel[end], sel[j]); end++; /* j >= end */ } } n = end - start; /* # of pts in octant i */ if (n > 0) n_notempty++; /* Yahoo, another non-empty octant! */ if (n > d->oct_max) { /* to get the closest n: sort sel from start to end: */ qsort(sel + start, (size_t) n, sizeof(DPOINT *), (int CDECL (*)(const void *, const void *)) dist_cmp); /* swap the remaining ones to the end of sel and forget about'm: */ for (j = start + d->oct_max; j < end; j++) { d->n_sel--; DPSWAP(sel[j], sel[d->n_sel]); } /* accept the first d->oct_max: */ start += d->oct_max; /* proceed with the next octant: */ end = start; } else /* accept all n: */ start = end; } if (end != d->n_sel) { Rprintf("end: %d, n_sel: %d\n", end, d->n_sel); ErrMsg(ER_IMPOSVAL, "octant_select(): remaining points"); } return n_notempty; /* # non-empty octants */ } static int which_octant(DPOINT *where, DPOINT *p, int mode) { /* * it's pretty hard to get this right for perfectly alligned 3D data: * in case of omax=1 and only one point at exactly equal distances * in each of the 6 directions, not all 6 are taken. * For 2D (omax=1, 4 points) this works, however. */ double dx, dy, dz; int x = 0, y = 0, z = 0; dx = p->x - where->x; /* < 0 : p in west half */ dy = p->y - where->y; /* < 0 : p in south half */ dz = p->z - where->z; /* < 0 : p in lower half */ if (mode & Z_BIT_SET) z = (dz < 0); if (mode & Y_BIT_SET) { x = (dy < 0 ? dx > 0 : dx >= 0); y = (dx < 0 ? dy >= 0 : dy > 0); } else x = (where->x < p->x); return (x | (y << 1) | (z << 2)); } int CDECL dist_cmp(const DPOINT **pa, const DPOINT **pb) { /* ANSI qsort() conformant dist_cmp */ if ( (*pa)->u.dist2 < (*pb)->u.dist2 ) return -1; if ( (*pa)->u.dist2 > (*pb)->u.dist2 ) return 1; return 0; } static void print_selection(DATA *d, DPOINT *where) { /* Add this statement to filter out * empty selections if (!d->n_sel) return; */ if (where) { printlog("selection at "); logprint_point(where, d); } else printlog("(NULL selection location)"); print_data_selection(d); } gstat/src/vario_fn.h0000644000176200001440000000305713777370515014163 0ustar liggesusers/* unit basic variogram models */ double fn_nugget(double h, double *r); double fn_linear(double h, double *r); double fn_circular(double h, double *r); double fn_spherical(double h, double *r); double fn_bessel(double h, double *r); double fn_gaussian(double h, double *r); double fn_exclass(double h, double *r); double fn_matern(double h, double *r); double fn_matern2(double h, double *r); double fn_exponential(double h, double *r); double fn_pentaspherical(double h, double *r); double fn_periodic(double h, double *r); double fn_wave(double h, double *r); double fn_hole(double h, double *r); double fn_logarithmic(double h, double *r); double fn_power(double h, double *r); double fn_spline(double h, double *r); double fn_legendre(double h, double *r); double fn_intercept(double h, double *r); /* the following functions are not all defined */ double da_is_zero(double h, double *r); /* NUG, INT */ double da_fn_linear(double h, double *r); double da_fn_circular(double h, double *r); double da_fn_spherical(double h, double *r); double da_fn_bessel(double h, double *r); double da_fn_gaussian(double h, double *r); double da_fn_exponential(double h, double *r); double da_fn_pentaspherical(double h, double *r); double da_fn_periodic(double h, double *r); double da_fn_wave(double h, double *r); double da_fn_hole(double h, double *r); double da_fn_logarithmic(double h, double *r); double da_fn_power(double h, double *r); /* unit derivative-to-range of basic variogram models */ double da_fn_exponential(double h, double *r); double da_fn_nugget(double h, double *r); gstat/vignettes/0000755000176200001440000000000014413507474013415 5ustar liggesusersgstat/vignettes/spatio-temporal-kriging.bib0000644000176200001440000003163513777370515020661 0ustar liggesusers% Encoding: windows-1252 @Article{bakar2015, author = {Bakar, Khandoker Shuvo and Sahu, Sujit K}, title = {{spTimer}: Spatio-Temporal Bayesian Modelling Using {R}}, journal = {Journal of Statistical Software}, year = {2015}, volume = {63}, number = {15}, pages = {1--32}, url = {http://dx.doi.org/10.18637/jss.v063.i15} } @Manual{Beygelzimer2013, Title = {{FNN}: Fast Nearest Neighbor Search Algorithms and Applications}, Author = {Alina Beygelzimer and Sham Kakadet and John Langford and Sunil Arya and David Mount and Shengqiao Li}, Note = {R package version 1.1}, Year = {2013}, Url = {https://CRAN.R-project.org/package=FNN} } @Article{Bilonick1988, Title = {Monthly hydrogen ion deposition maps for the northeastern {U.S.} from {J}uly 1982 to {S}eptember 1984}, Author = {Richard A. 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Various spatio-temporal covariance models have been implemented, such as the separable, product-sum, metric and sum-metric models. In a real-world application we compare spatio-temporal interpolations using these models with a purely spatial kriging approach. The target variable of the application is the daily mean $\rm{PM}_{10}$ concentration measured at rural air quality monitoring stations across Germany in 2005. R code for variogram fitting and interpolation is presented in this paper to illustrate the workflow of spatio-temporal interpolation using \pkg{gstat}. We conclude that the system works properly and that the extension of \pkg{gstat} facilitates and eases spatio-temporal geostatistical modelling and prediction for R users. } %% main text \section{Introduction}\label{sec:intro} The collection and processing of spatio-temporal data is rapidly increasing due to technological advances and the societal need for analysis of variables that vary in space and time, such as weather and air quality variables, and crop yields. Analysis of spatial and temporal correlations is useful in itself to get insight into the character and causes of variability, but they are also important to predict values at points from neighbouring observations. Spatio-temporal interpolation can potentially provide more accurate predictions than spatial interpolation because observations taken at other times can be included. In addition, spatio-temporal interpolation allows predictions to be made at single locations or entire fields in between and beyond observation times. However, adding the temporal domain implies that variability in space and time must be modelled, which is more complicated than modelling purely spatial or purely temporal variability. The spatial, temporal and spatio-temporal dependence structures, for instance represented as variograms, do not necessarily coincide with each other in terms of their parameters nor in terms of their family. In the simplest case, a spatio-temporal anisotropy parameter might be enough to deal with the different dependence structures, but this poses strong assumptions on the process. Interpolation of spatial random fields is a common task in geostatistics. Simple approaches like inverse distance weighted predictions or the well known kriging procedures have routinely been applied for many years. Nowadays, modern sensors allow to monitor different variables at an increasing temporal resolution producing rich spatio-temporal data sets. This calls as well for theory and methods to deal with these data sets to gain a better understanding of the observed spatio-temporal processes. While the theoretical aspects of spatio-temporal geostatistics show good progress \citep{Cressie2011}, implementations lack behind. This hinders a wide application of spatio-temporal modelling, as typically extensive scripting and thorough understanding is necessary to build spatio-temporal models. Handling of spatio-temporal data in R is provided by the \CRANpkg{spacetime} package \citep{Pebesma2012}. In this paper, we present an extension of the \CRANpkg{gstat} package \citep{Pebesma2004} (version 1.1-3) that reuses the \pkg{spacetime} classes for the estimation of spatio-temporal covariance/variogram models and to perform spatio-temporal interpolation. Our implementation handles various types of spatio-temporal covariance structures and facilitates spatio-temporal interpolation. The notation of functions in \pkg{gstat} are extended in a way closely following the purely spatial design. This allows a researcher acquainted with \pkg{gstat} to readily use spatio-temporal tools. The use of the newly implemented functions is presented and illustrated by mapping spatio-temporal air-quality data. Another package that offers extensive spatio-temporal geostatistical functionality is \CRANpkg{RandomFields} \citep{Schlather2014}; further packages are mentioned in the SpatioTemporal CRAN task view\footnote{\url{https://cran.r-project.org/web/views/SpatioTemporal.html}}. The paper is organised as follows. The next section introduces the general interpolation routine and describes the different spatio-temporal covariance models, followed by a section introducing the German rural background data set for 2005 and performing the parameter estimation (i.e.\ covariance model fitting). Cross-validation results are presented and discussed in the section thereafter. Conclusions are drawn in the closing section. R scripts reproducing this study are available from within the \pkg{gstat} package as demos. \code{stkrige} re-estimates the variogram models, \code{stkrige-prediction} re-executes the prediction for a time series and a couple of stations, and \code{stkrige-crossvalidation} re-runs the entire leave-one-out cross-validation (note that the latter takes a few hours). \section{Spatio-temporal dependence modelling and kriging}\label{sec:theory} In the following, we will assume a Gaussian spatio-temporal random field $Z$ defined over a spatial domain $\mathcal{S}$ and temporal domain $\mathcal{T}$. Typically, a sample $\mathbf{z} = \left(z(s_1,t_1),\dots,z(s_n,t_n)\right)$ has been observed at a set of distinct spatio-temporal locations $(s_1, t_1), \dots, (s_n,t_n) \in \mathcal{S}\times \mathcal{T} \subseteq \mathbb{R}^2 \times \mathbb{R}$ that may include repeated measurements at the same location or simultaneous measurements at multiple spatial locations. Often, one is interested in modelling $Z$ from the sample $\mathbf{z}$ in order to predict at unobserved locations in space and time or simulate from the conditional distribution. Across our domain of interest $\mathcal{S} \times \mathcal{T}$, we assume the random field $Z$ to be stationary and spatially isotropic. Hence, the field can be characterised through a mean $\mu$ and a covariance function $C_{\rm st}$ where the spatio-temporal covariance only depends on the separating distances across space $h \in \mathbb{R}_{\geq 0}$ and time $u \in \mathbb{R}_{\geq 0}$. Note that extensions beyond this set-up can easily be derived as has been done for the pure spatial case using for instance universal kriging to overcome the stationarity of the mean. The general spatio-temporal covariance function is given by $C_{\rm st}(h,u) = {\rm Cov}\left(Z(s,t), Z(\tilde{s},\tilde{t})\right)$ for a separating spatial distance $h$ and temporal distance $u$ and any pair of points $(s,t), (\tilde{s},\tilde{t}) \in \mathcal{S}\times\mathcal{T}$ with $||s-\tilde{s}||=h$ and $|t-\tilde{t}|=u$. In general, this covariance function is hard to estimate but a couple of models using simplifying assumptions will be presented in the following together with their spatio-temporal variograms $\gamma_{\rm st}(h,u) = C_{\rm st}(0,0)-C_{\rm st}(h,u)$ and encoding in \pkg{gstat}. Given a valid covariance function, the covariance matrices used in the linear predictor are easily obtained and the same algebraic operations as in the well known spatial case yield predictions of the desired random field \citep{Cressie2011}. A major difference is, however, the computational complexity of the matrix inversion. Typically, observations are made at a rather high temporal frequency leading to a number of spatio-temporal locations that is too large for global kriging. Hence, interpolation based on a selected neighbourhood of a subset of all data points becomes beneficial. Additionally, this relaxes the assumption of stationarity, as smooth variations in the mean value across the domain can be respected. The related class of dynamic models also addresses the computational complexity resulting in a temporal Markov structure. Implementations can be found in \CRANpkg{spTimer} by \citet{bakar2015}, \CRANpkg{spBayes} by \citet{finley2015}, \CRANpkg{spate} by \citet{sigrist2015} or \pkg{INLA} by \citet{lindgren2015}. \subsection{Covariance models} The covariance models implemented in \pkg{gstat} and presented in this paper are introduced in the following. Besides further extensions we focus on the basic classes of the \emph{separable}, \emph{product-sum}, \emph{metric} and \emph{sum-metric} spatio-temporal covariance functions. The building blocks (in the following denoted as \code{spatialVgm}, \code{temporalVgm} or \code{jointVgm}) of the spatio-temporal covariance functions are any of the purely spatial variogram models already available in \pkg{gstat}. Each one of the building blocks is created by a call of the function \code{gstat::vgm()}. Remaining arguments such as \code{sill} (the joint sill), \code{nug} (the joint nugget component) or \code{stAni} (the spatio-temporal anisotropy used in the \code{jointVgm}) are scalars and refer to parameters of the entire spatio-temporal covariance function: \begin{enumerate}[a)] \item The \dfn{separable covariance model} assumes that the spatio-temporal covariance function can be represented as the product of a spatial and temporal term: $$C_{\rm sep}(h,u)=C_{\rm s}(h)C_t(u)$$ Its variogram is given by (see Appendix for details): $$\gamma_{\rm sep}(h,u) = {\rm sill} \cdot \left( \bar{\gamma}_s(h)+\bar{\gamma}_t(u)-\bar{\gamma}_s(h)\bar{\gamma}_t(u) \right)$$ where $\bar{\gamma}_s$ and $\bar{\gamma}_t$ are standardised spatial and temporal variograms with separate nugget effects and (joint) sill of 1. The overall sill parameter is denoted by "sill". The R package \pkg{gstat} encodes this model as: \code{vgmST("separable", space = spatialVgm, time = temporalVgm, sill = sill)} The separable model has a strong computational advantage in the setting where each spatial location has an observation at each temporal instance (a \code{"STFDF"} without \samp{NA}s, \cite{Pebesma2012}). In these cases, the covariance matrix (and its inverse) can be composed using the Kronecker-product of the purely spatial and purely temporal covariance matrices (respectively their inverse). \item The above model extends to the \dfn{product-sum covariance model} that we give here in a slightly different notation as \citet{DeCesare2001} and \citet{DeIaco2001} by $$C_{\rm ps}(h,u)=k C_{\rm s}(h)C_{\rm t}(u) + C_{\rm s}(h) + C_{\rm t}(u)$$ with $k > 0$. The corresponding variogram can be written as $$\gamma_{\rm ps}(h,u) = \left(k \cdot {\rm sill}_{\rm t} + 1\right) \gamma_{\rm s}(h) + \left(k \cdot {\rm sill}_{\rm s} + 1\right) \gamma_{\rm t}(u) - k \gamma_{\rm s}(h) \gamma_{\rm t}(u)$$ where ${\gamma}_{\rm s}$ and $\gamma_{\rm t}$ are spatial and temporal variograms (see Appendix for details). The parameter $k$ needs to be positive and the following identity defines the overall sill (${\rm sill}_{\rm st}$) of the model in terms of the model's spatial and temporal sills: $${\rm sill}_{\rm st} = k \cdot {\rm sill}_{\rm s} \cdot {\rm sill}_{\rm t} + {\rm sill}_{\rm s} + {\rm sill}_{\rm t}$$ The above equation can also be used to estimate $k$ based on the three sill values. An alternative formulation of the product-sum variogram can be found in \citet{DeIaco2001}. The \pkg{gstat} definition of this model reads: \begin{example*} vgmST("productSum", space = spatialVgm, time = temporalVgm, k = k) \end{example*} \item Assuming identical spatial and temporal covariance functions except for spatio-temporal anisotropy, allows to use a spatio-temporal \dfn{metric covariance model} where, after matching space and time by an anisotropy correction $\kappa$ (\code{stAni}), the spatial, temporal and spatio-temporal distances are treated equally resulting in a single covariance model $C_{\rm joint}$: $$C_{\rm m}(h,u)=C_{\rm joint}\left(\sqrt{h^2+(\kappa\cdot u)^2}\right)$$ The variogram evaluates to $$ \gamma_{\rm m} (h,u) = \gamma_{\rm joint}\left(\sqrt{h^2+(\kappa\cdot u)^2}\right) $$ where $\gamma_{\rm joint}$ (\code{jointVgm}) is any known variogram that may include a nugget effect. The following line generates the model in \pkg{gstat}: \begin{example*} vgmST("metric", joint = jointVgm, stAni = stAni) \end{example*} The spatio-temporal anisotropy parameter $\kappa$ (\code{stAni}) is given as spatial unit per temporal unit. In many cases, this will be in m/second, as these are the base units in our implementation. All temporal distances are hence internally re-scaled to an equivalent spatial distance using \code{stAni} and treated as metric 3D-space. \item A combination of spatial, temporal and a metric model including an anisotropy parameter $\kappa$ is found in \citet{Bilonick1988} and revisited by \citet{Snepvangers2003} as the \dfn{sum-metric covariance model}: $$C_{\rm sm}(h,u)=C_{\rm s}(h)+C_{\rm t}(u)+C_{\rm joint}\left(\sqrt{h^2+(\kappa\cdot u)^2}\right)$$ This model allows for spatial, temporal and joint nugget effects. Thus, the variogram is given by $$ \gamma_{\rm sm}(h,u)= \gamma_{\rm s}(h) + \gamma_{\rm t}(u) + \gamma_{\rm joint}\left(\sqrt{h^2+(\kappa\cdot u)^2}\right)$$ where $\gamma_{\rm s}$, $\gamma_{\rm t}$ and $\gamma_{\rm joint}$ are spatial, temporal and joint variograms with separate nugget-effects. This model can be defined in \pkg{gstat} through: \begin{example*} vgmST("sumMetric", space = spatialVgm, time = temporalVgm, joint = jointVgm, stAni = stAni) \end{example*} \item A simplified version of the above model is to restrict the spatial, temporal and joint variograms to nugget free models. Additionally, a single spatio-temporal nugget is introduced and the variogram takes the representation: $$\gamma_{\rm ssm}(h,u) = {\rm nug}\cdot {\bf1}_{h>0 \vee u>0} + \gamma_{\rm s}(h) + \gamma_{\rm t}(u) + \gamma_{\rm joint}\left(\sqrt{h^2+(\kappa\cdot u)^2}\right)$$ The \dfn{simple sum-metric covariance model} can be obtained by: \begin{example*} vgmST("simpleSumMetric", space = spatialVgm, time = temporalVgm, joint = jointVgm, nugget = nug, stAni = stAni) \end{example*} \end{enumerate} \noindent Note that the above mentioned spatial, temporal and joint components of the spatio-temporal covariance and variogram models need not necessarily exhibit the same structure. Taking for instance the product-sum and sum-metric models that both contain single temporal and spatial variogram models: the best fits of the respective spatio-temporal models might suggest different variogram families and parameters for the pure spatial and temporal ones. This is due to the target of finding the best overall variogram surface resulting in (potentially) different marginal models. \subsection{Parameter estimation} Fitting routines for the above variogram models are implemented in \pkg{gstat} through the function \code{fit.StVariogram()}, which calls \code{optim()} from the R core package \pkg{stats}. Additional parameters to improve the numerical optimisation can be provided to \code{fit.StVariogram()} and will be passed on to \code{optim()} (using R's three-dots mechanism). As some of the parameters are limited to certain ranges (nuggets need to be non-negative, ranges must be positive), it is advised to use an optimisation routine that allows to impose limits on the search space (i.e.\ \code{L-BFGS-B}) and provide sensible limits via \code{lower} and \code{upper}. By default, the method \code{L-BFGS-B} is called and the smallest lower and largest upper bounds supported by the model are given. The estimation of the spatio-temporal variogram models relies on a sample variogram empirically derived from the data. In contrast to the spatial variogram line, the spatio-temporal variogram is represented by a surface for lag classes composed of a spatial and temporal separation distance. Different from the spatial case, a spatio-temporal sample variogram contains lag-classes of zero spatial separation describing pure temporal dependencies. Without duplicate observations, no estimates can be made for the lag-class with both zero spatial and zero temporal separation. The sample variogram is calculated through the function \code{variogram()} that dispatches the call for spatio-temporal data objects (of class \code{"STFDF"}, \code{"STSDF"}, or \code{"STIDF"}) from \pkg{spacetime}. For a visual judgement of the fit between sample and fitted variograms the \code{plot()} function can be called to show the variogram surfaces next to each other as coloured level plots. Alternatively, a wireframe plot is obtained by setting the parameter \code{wireframe = TRUE} (Figure~\ref{fig:allVgmsWireframe}). A further option is to plot the differences between the sample and model variogram surfaces by setting \code{diff = TRUE}, see Figure~\ref{fig:allVgmsDiffWireframe}. Additionally to visual comparison, \code{fit.StVariogram()} provides the output of \code{optim} as attribute \code{optim.out} of the returned S3-class \code{"StVariogram"}. This attribute includes valuable information to diagnose the success of the \code{optim} routine. It contains for instance the convergence code (\code{\$convergence}) or message (\code{\$message}) and the optimised value (\code{\$value}), which is the mean of the (weighted) squared deviations between sample and fitted variogram surface. Furthermore, it is advised to check the estimated parameters against the parameter boundaries and starting values. Additionally, starting values might also influence the success and result of the optimisation, as local optima may occur due to the interdependence of the parameters. Alternatively, the user might want to start a grid search in order to better asses the sensitivity of the estimates. The fitting approach is identical for all covariance models. However, with the flexibility of the model also the number of parameters increases, making a numerical estimation at times cumbersome. Starting values can in most cases be read from the sample variogram. Parameters of the spatial and temporal variograms can be assessed from the spatio-temporal surface fixing the counterpart at 0. The overall spatio-temporal sill including the nugget can be deducted from the plateau that a nicely behaving sample variogram reaches for 'large' spatial and temporal distances. An important issue is the potentially different orders of magnitude of the parameters. It is at times advisable to rescale spatial and temporal distances to ranges similar to the ones of sills and nuggets using the parameter \code{parscale}. \code{parscale} needs to be provided via \code{control = list(parscale=\dots)} and holds a vector of the same length as the number of parameters to be optimised (see the documentation of \code{optim} for further details). \begin{table} \center \caption{List of implemented weighting schemes for variogram optimisation. Methods 3, 4, and 5 are kept for compatibility reasons with the purely spatial \code{fit.variogram} function. The following notation is used: $N_j$ number of pairs, $h_j$ mean spatial distance and $u_j$ mean temporal distance for each bin $j$, $\gamma$ the actual proposed variogram model and \code{stAni} a spatio-temporal anisotropy scaling.}\label{tab:weighting} {\small \begin{tabular}{ll} \toprule \code{fit.method} & weights \\ \midrule 0 & no fitting\\ 1 and 3 & $N_j$ \\ 2 and 4 & $N_j/\gamma\left(h_j, u_j\right)^2$ \\ 5 & reserved for REML \\ 6 & 1, no weighting\\ 7 & $N_j/\left(h_j^2 + {\rm stAni}^2\cdot u_j^2\right)$ \\ 8 & $N_j/h_j^2$ \\ 9 & $N_j/u_j^2$ \\ 10 & $1/\gamma\left(h_j,u_j\right)^2$ \\ 11 & $1/\left(h_j^2 + {\rm stAni}^2\cdot u_j^2\right)$ \\ 12 & $1/h_j^2$ \\ 13 & $1/u_j^2$ \\ \bottomrule \end{tabular}} \end{table} Currently, the implemented fitting routines are based on the (weighted) mean squared difference between model and sample variogram surfaces. By default, all values are associated the same weight (\code{fit.method = 6}), but other options are available that allow for different weighting schemes based on the number of pairs, spatial, temporal and spatio-temporal distances or the variogram's value. Table~\ref{tab:weighting} lists all currently implemented options. Depending on the target neighbourhood size of the desired interpolation, it might be beneficial to narrow down the spatial and temporal distances and to introduce a cutoff. This ensures that the model is fitted to the differences over space and time actually used in the interpolation, and reduces the risk of overfitting the variogram model to large distances not used for prediction. Please note that methods 2 and 10 (Table~\ref{tab:weighting}) involve weights based on the fitted variogram that might lead to bad convergence properties of the parameter estimates. Furthermore, the scalar \code{stAni} in methods 7 and 11 will either be the actual fitted spatio-temporal anisotropy if it is included in the model or a fixed value that has to be passed as \code{stAni} by the user to \code{fit.StVariogram}. The latter is advised, as the former might lead to bad convergence properties as in the case of weights based on the fitted variogram mentioned above. As the estimation of an anisotropy scaling might be cumbersome on a visual basis, we provide the function \code{estiStAni} that provides estimates based on the empirical spatio-temporal variogram. Four heuristics are available based on (i) rescaling a linear model (\code{linear}), (ii) estimating equal ranges (\code{range}), (iii) rescaling a pure spatial variogram (\code{vgm}) or (iv) estimating a complete spatio-temporal metric variogram model and returning its spatio-temporal anisotropy parameter (\code{metric}). The choice of the weighting scheme will influence the selected model and different weightings might be further assessed in a cross-validation of the selected model. To increase numerical stability, it is advisable to use weights that do not change with the current model fit. \subsection{Kriging} Standard kriging (\code{krigeST}) and trans Gaussian kriging (\code{krigeSTTg}) have been implemented. As spatio-temporal kriging based on the complete data set might be too computationally expensive, local kriging is an attractive alternative. This poses the question of how to select the "nearest" neighbours from the spatio-temporal space $\mathcal{S}\times\mathcal{T}$. A natural choice would be to select the spatio-temporal locations exhibiting the strongest correlation to the unobserved location. Depending on the spatio-temporal covariance model, the relation between spatial and temporal distance in determining the strength of correlation will vary. As a proxy, we use a spatio-temporal anisotropy parameter that relates spatial and temporal distances in the same manner as in the metric covariance models. The k-nearest neighbours within this metric spatio-temporal space $\mathcal{S}\times\mathcal{T}$ are selected using the R package \CRANpkg{FNN} \citep{Beygelzimer2013}. The interpolation performs iteratively for each spatio-temporal prediction location with a local subset of the data set. Without neighbourhood selection, kriging uses all data. As the metric induced by the spatial and rescaled temporal distances are only proxies to the strength of correlation between locations (see Figure~\ref{fig:vgmVsDist}), we provide an option to search a larger metric neighbourhood. Within this larger neighbourhood, the covariance function is evaluated for all spatio-temporal locations and the neighbouring locations with the largest covariance values are then selected for prediction. However, this approach might still suffer from a clustering of locations and alternatives such as a staged search (find spatial neighbours first and select a set of temporal instances for each spatial neighbour) or an octant search (select neighbours per spatial quadrant from preceding and following time stamps separately) could be considered. However, these alternatives are not yet available in \pkg{gstat}. \begin{figure} \centering \includegraphics[width=0.9\textwidth]{vgmVsMetricDist.png} \caption{A contourplot showing how the spatio-temporal sum-metric variogram model (as estimated in the application below) and a metric distance relate to each other. Distances are rescaled by 1/5 for easy plotting.}\label{fig:vgmVsDist} \end{figure} \section{Application and illustration}\label{sec:data} The data set used is taken from AirBase\footnote{\href{http://www.eea.europa.eu/data-and-maps/data/airbase-the-european-air-quality-database-6}{AirBase - The European air quality database}}, the air quality data base for Europe provided by the European Environmental Agency (EEA). We focus on a single air quality indicator, particulate matter with a diameter less than 10~$\mu\rm m$, measured at rural background stations for 2005 (${\rm PM}_{10}$). The data base contains data for many years. Besides rural, also urban areas are monitored and not only at background locations (e.g.\ traffic stations). However, these processes are considered to be of a different nature and should be treated separately. As a use case, we therefore limit our data set to the rural background stations in Germany. Figure \ref{fig:dailyMeans} shows for 8 randomly chosen days daily mean values of ${\rm PM}_{10}$ concentrations for the entire monitoring network over Germany in 2005 with 69 rural background stations. \begin{figure} \centering \includegraphics[width=0.95\textwidth]{daily_means_PM10.png} \caption{Daily mean $\rm{PM}_{10}$ concentration $[\mu\rm{g/m}^3]$ at 8 randomly selected days in 2005.}\label{fig:dailyMeans} \end{figure} In order to fit a spatio-temporal model to the air quality data set, the empirical variogram surface is computed and used as input for the fitting routines of the different models. The empirical variogram is based on spatio-temporal bins that span regularly over space and time. Regular measurements over time (i.e.\ hourly, daily) motivate regular binning intervals of the same temporal resolution. Nevertheless, flexible binning boundaries can be passed for spatial and temporal dimensions. This allows for instance to use smaller bins at small distances and larger ones for large distances. Temporal boundaries, instead of lags, are required when the sampling of the data is non-regular. In cases where regular temporal observations can be assumed, this is utilised in the sample variogram calculations and any two temporal consecutive observations are assumed to have the same temporal distance. Figure~\ref{fig:allVgmsWireframe} shows the empirical variogram along with the proposed best fitting model of each spatio-temporal variogram family as perspective wireframe plots. In order to better identify structural shortcomings of the selected model, a difference plot (Figure~\ref{fig:allVgmsDiffWireframe}) is a helpful visual diagnostic plot. Beyond the selection of the spatio-temporal variogram family, each component of this model can be chosen from any implemented one-dimensional variogram. In Table~\ref{tab:vgmFits} a selection of fitted models in terms of their residuals compared to the sample variogram surface are shown. The best fitting spatio-temporal model of each family is given as: \begin{enumerate}[a)] \item separable model (weighted MSE: 6.82): \nopagebreak \begin{tabular}{l|rlrlrr} \toprule & partial sill & model & \multicolumn{2}{c}{range} & nugget & sp.-temp. sill \\ \midrule space & 0.86 & Exp & 558 & \hspace{-2\tabcolsep}~km & 0.14 & \multirow{2}{*}{124} \\ time & 1.00 & Sph & 5.6 & \hspace{-2\tabcolsep}~days & 0.00 & \\ \bottomrule \end{tabular} obtained via: \begin{example*} separableModel <- vgmST("separable", space = vgm(0.9, "Exp", 200, 0.1), time = vgm(0.9, "Sph", 3.5, 0.1), sill = 124) fit.StVariogram(empVgm, separableModel, fit.method = 7, stAni = 117.3, method = "L-BFGS-B", control = list(parscale = c(100, 1, 10, 1, 100)), lower = c(10, 0, 0.1, 0, 0.1), upper = c(2000, 1, 12, 1, 200)) \end{example*} \item product-sum model (weighted MSE: 6.91) \nopagebreak \begin{tabular}{l|rlrlrc} \toprule & partial sill & model & \multicolumn{2}{c}{range} & nugget & k\\ \midrule space & 6.8 & Exp & 542 & \hspace{-2\tabcolsep}~km & 1.2 & \multirow{2}{*}{1.61} \\ time & 8.7 & Sph & 5.5 & \hspace{-2\tabcolsep}~days & 0.0 & \\ \bottomrule \end{tabular} obtained via \begin{example*} prodSumModel <- vgmST("productSum", space = vgm(10, "Exp", 200, 1), time = vgm(10, "Sph", 2, 1), k=2) fit.StVariogram(empVgm, prodSumModel, fit.method = 7, stAni = 117.3, method = "L-BFGS-B", control = list(parscale = c(1, 10, 1, 1, 0.1, 1, 10)), lower = rep(0.0001, 7)) \end{example*} \item metric model (weighted MSE: 10.05) \nopagebreak \begin{tabular}{l|rlrlrrl} \toprule & partial sill & model & \multicolumn{2}{c}{range} & nugget & \multicolumn{2}{c}{anisotropy}\\ \midrule joint & 123.4 & ${\rm Mat}_{\kappa=0.6}$ & 453 & \hspace{-2\tabcolsep}~km & 17.4 & 189 & \hspace{-2\tabcolsep}~km/day \\ \bottomrule \end{tabular} obtained via \begin{example*} metricModel <- vgmST("metric", joint = vgm(60, "Mat", 150, 10, kappa = 0.6), stAni = 60) fit.StVariogram(empVgm, metricModel, fit.method = 7, stAni = 117.3, method = "L-BFGS-B", control = list(parscale = c(10, 20, 5, 10)), lower = c(80, 50, 5, 50), upper = c(200, 1500, 60, 300)) \end{example*} \item\label{bestfit} sum-metric model (weighted MSE: 3.31) \nopagebreak \begin{tabular}{l|rlrlrrl} \toprule & partial sill & model & \multicolumn{2}{c}{range} & nugget & \multicolumn{2}{c}{anisotropy}\\ \midrule space & 16.4 & Sph & 67 & \hspace{-2\tabcolsep}~km & 0 & & \\ time & 9.3 & Exp & 0.9 & \hspace{-2\tabcolsep}~days & 0 & & \\ joint & 91.5 & Sph & 999 & \hspace{-2\tabcolsep}~km & 7.3 & 185 & \hspace{-2\tabcolsep}~km/day \\ \bottomrule \end{tabular} obtained via \begin{example*} sumMetricModel <- vgmST("sumMetric", space = vgm(20, "Sph", 150, 1), time = vgm(10, "Exp", 2, 0.5), joint = vgm(80, "Sph", 1500, 2.5), stAni = 120) fit.StVariogram(empVgm, sumMetricModel, fit.method = 7, stAni = 117.3, method = "L-BFGS-B", control = list(parscale = c(1, 100, 1, 1, 0.5, 1, 1, 100, 1, 100), maxit=10000), lower = c(sill.s = 0, range.s = 10, nugget.s = 0, sill.t = 0, range.t = 0.1, nugget.t = 0, sill.st = 0, range.st = 10, nugget.st = 0, anis = 40), upper = c(sill.s = 200, range.s = 1000, nugget.s = 20, sill.t = 200, range.t = 75, nugget.t = 20, sill.st= 200, range.st = 5000, nugget.st = 20, anis = 500)) \end{example*} \item simple sum-metric model (weighted MSE: 3.31) \nopagebreak \begin{tabular}{l|rlrlrlc} \toprule & partial sill & model & \multicolumn{2}{c}{range} & \multicolumn{2}{c}{anisotropy} & sp.-temp. nugget \\ \midrule space & 16.4 & Sph & 67 & \hspace{-2\tabcolsep}~km & & & \multirow{3}{*}{$\Bigg\}$ 7.3} \\ time & 9.3 & Exp & 0.9 & \hspace{-2\tabcolsep}~days & & & \\ joint & 91.5 & Sph & 999 & \hspace{-2\tabcolsep}~km & 185 & \hspace{-2\tabcolsep}~km/day & \\ \bottomrule \end{tabular} obtained via \begin{example*} simpleSumMetricModel <- vgmST("simpleSumMetric", space=vgm(120, "Sph", 150), time =vgm(120, "Exp", 10), joint=vgm(120, "Sph", 150), nugget = 10, stAni = 150) fit.StVariogram(empVgm, simpleSumMetricModel, fit.method = 7, stAni = 117.3, method = "L-BFGS-B", control = list(parscale = c(1, 10, 1, 1, 1, 100, 1, 10)) lower = c(sill.s = 0, range.s = 10, sill.t = 0, range.t = 0.1, sill.st= 0, range.st= 10, nugget = 0, anis = 40), upper = c(sill.s = 200, range.s = 500, sill.t = 200, range.t = 20, sill.st= 200, range.st = 5000#, nugget = 100, anis = 1000)) \end{example*} \end{enumerate} The variogram parameters are numerically optimised using the function \code{fit.StVariogram} and the \code{L-BFGS-B} routine of \code{optim}. The parameter \code{fit.method} that controls the weighing of the residuals between empirical and model surface of \code{fit.StVariogram} is set to \code{7} (the spatio-temporal analog to the commonly used spatial weighting). A full list of all weighting schemes is presented in Table~\ref{tab:weighting}. In our application, the residuals are multiplied by the number of pairs in the corresponding spatio-temporal bin divided by the metric distance: $N_j/(h_j^2 + {\rm stAni}^2\cdot u_j^2)$. The spatio-temporal anisotropy is estimated beforehand and fixed at 118~km/day. This weighting scheme puts higher confidence in lags filled with many pairs of spatio-temporal locations, but respects to some degree the need of an accurate model for short distances, as these short distances are the main source of information in the prediction step. Note, that different weighting schemes will in general result in different model parameters generating different interpolation values. Our selection is based on the assumption that well filled bins provide more reliable empirical variogram estimates and the fact that short distances are the most important ones for a local interpolation. \begin{table}[t!] \centering \caption{Weighted MSE (\code{fit.method = 7, see Table~\ref{tab:weighting}}) for different spatio-temporal variogram families and different choices for the one-dimensional variogram components. Columns denote the spatial and temporal variogram choices. The metric model is only applicable if both domains use the same family.}\label{tab:vgmFits} \begin{tabular}{ll|rrrrr} \toprule model & joint & Exp+Exp & Exp+Sph & Sph+Exp & Sph+Sph & ${\rm Mat}_{\kappa=0.6}$ \\ \midrule {separable} & $~~\cdot$ & 9.87 & \bf{6.82} & 10.42 & 7.50 & $\cdot~~$ \\ {product-sum} & $~~\cdot$ & 10.09 & \bf{6.91} & 10.64 & 7.59 & $\cdot~~$ \\ {metric} & $~~\cdot$ & 10.25 & $\cdot~~$ & $\cdot~~$ & 10.59 & \bf{10.05} \\ \multirow{2}{*}{sum-metric} & Exp & 4.10 & 3.60 & 3.89 & 3.32 & $\cdot~~$ \\ & Sph & 3.74 & 3.73 & \bf{3.31} & 3.36 & $\cdot~~$ \\ \multirow{2}{*}{simple sum-metric}& Exp & 4.10 & 3.60 & 3.94 & 3.32 & $\cdot~~$ \\ & Sph & 3.74 & 3.98 & \bf{3.31} & 3.56 & $\cdot~~$ \\ \bottomrule \end{tabular} \end{table} \begin{figure} \centering \includegraphics[width=0.95\textwidth]{allVgmsWireframe.png} \caption{Sample and the best fitting spatio-temporal variogram of each family.}\label{fig:allVgmsWireframe} \end{figure} \begin{figure} \centering \includegraphics[width=0.95\textwidth]{allVgmsDiffWireframe.png} \caption{Differences between the sample and the best fitting spatio-temporal variogram of each family.}\label{fig:allVgmsDiffWireframe} \end{figure} \begin{figure}[b!] \centering \includegraphics[width=0.95\textwidth]{pred_daily_means_PM10.png} \caption{Spatio-temporal interpolation of daily mean $\rm{PM}_{10}$ concentrations using the sum-metric covariance model with the closest 50 neighbouring spatio-temporal locations. The crosses indicate sampling locations. The cell size of the grid in UTM projection is $10~\rm{km}\times10~\rm{km}$.}\label{fig:pred_daily} \end{figure} For comparison with classical approaches, we interpolate across Germany iteratively for each single day using all available data for variogram estimation. The purely spatial empirical variogram can directly be obtained from the empirical spatio-temporal variogram, by fixing the temporal lag at 0 separation. From the same set of variogram models as investigated for the spatio-temporal models, the exponential model (partial sill:~66.5, range:~224~km, nugget:~13.5) is the best suited based on the optimisation criterion. Alternatively, we could have fitted the spatial variogram for each day separately using observations from that day only. However, given the small number of observation stations, this produced unstable variograms for several days and we decided to use the single spatial variogram derived from all spatio-temporal locations treating time slices as uncorrelated copies of the spatial random field. Once the best fitting spatio-temporal variogram model is identified, the interpolation can be executed with the help of the function \code{krigeST}. We use the sum-metric model that obtained the smallest RMSE (compare Table~\ref{tab:vgmFits}) to produce a gridded prediction. The interpolation domain consists of daily values for a regular grid spanning over Germany in UTM projection. The cell size is $10~\rm{km}\times10~\rm{km}$. Figure~\ref{fig:pred_daily} shows the interpolated grid for the same days as Figure~\ref{fig:dailyMeans} alongside with all sampling locations. Additionally, maps depicting the differences from a leave-one-out cross-validation are presented in Figure~\ref{fig:diffs_daily}. A time series view is presented in Figure~\ref{fig:timeseries} showing the observed and predicted time series at a single location along with its 95~\% prediction intervals. An animation of the entire year of daily mean ${\rm PM}_{10}$ prediction maps can be viewed online.\footnote{\url{http://gstat.r-forge.r-project.org/STpred.html}}. The interpolated maps are generated for a set of time stamps \code{tIDs} and a grid over Germany \code{DE\_pred} by \begin{example*} krigeST(PM10~1, data = DE_RB_2005[ , tIDS], newdata = DE_pred, fitSumMetricModel, nmax = 50, stAni = fitMetricModel$stAni/24/3600) \end{example*} \begin{figure}[t!] \centering \includegraphics[width=0.95\textwidth]{diffs_daily_means_PM10.png} \caption{Differences of spatio-temporal predictions and observed daily mean $\rm{PM}_{10}$ concentrations using the sum-metric covariance model with the closest (approx. strongest correlated) 50 neighbouring spatio-temporal locations.}\label{fig:diffs_daily} \end{figure} \begin{figure}[h!] \centering \includegraphics[width=0.9\textwidth]{singleStationTimeSeries.png} \caption{Subset of the time series of observed and predicted ${\rm PM}_{10}$ at a single station in Lower Saxony along with its 95~\% prediction intervals.}\label{fig:timeseries} \end{figure} To further compare the different approaches, a leave-one-out cross-validation was carried out. The spatio-temporal interpolations are done for the closest 50 and 10 neighbours assessing the impact of the neighbourhood size. Inspection of the ranges of the variograms in the temporal domain, suggests that any station more than at most 6 days apart does not meaningfully contribute. Furthermore, the local estimation allows the spatio-temporal random field to have a varying mean value over space and time. The purely spatial interpolation can be considered as the extreme temporally local case, where only observations from the same time instance are considered. \begin{table} \caption{Leave-one-out cross-validation results. The column wMSE refers to the optimised value from the variogram estimation.}\label{tab:cv} \centering \begin{tabular}{lrr|rrrr} \toprule covariance model & wMSE & neigh. & RMSE & MAE & ME & COR \\ \midrule pure Spatial & & 10 & 6.15 & 4.09 & -0.01 & 0.84 \\ separable &\hspace{-\tabcolsep}[6.82]& 10 & 6.08 & 4.04 & -0.01 & 0.84 \\ product-sum &\hspace{-\tabcolsep}[6.91]& 10 & 6.08& 4.04& -0.01 & 0.84 \\ metric &\hspace{-\tabcolsep}[10.05]& 10 & 6.11 & 4.07 & 0.03 & 0.84 \\ sum-metric &\hspace{-\tabcolsep}[3.31]& 10 & 6.16 & 4.08 & -0.06 & 0.84 \\ simple sum-metric &\hspace{-\tabcolsep}[3.31]& 10 & 6.14 & 4.08 & -0.02 & 0.84 \\ \midrule pure Spatial & & 50 & 6.10 & 4.07 & 0.00 & 0.84 \\ separable &\hspace{-\tabcolsep}[6.82]& 50 & 6.05 & 4.04 & 0.01 & 0.84 \\ product-sum &\hspace{-\tabcolsep}[6.91]& 50 & 6.05 & 4.04 & 0.00 & 0.84 \\ metric &\hspace{-\tabcolsep}[10.05]& 50 & 6.07 & 4.08 & 0.03 & 0.84 \\ sum-metric &\hspace{-\tabcolsep}[3.31]& 50 & 6.14 & 4.09 & -0.01 & 0.84 \\ simple sum-metric &\hspace{-\tabcolsep}[3.31]& 50 & 6.14 & 4.08 & -0.02 & 0.84 \\ \bottomrule \end{tabular} \end{table} \section{Results and discussion}\label{sec:resultsDiscuss} In terms of added value of spatio-temporal kriging measured in cross-validation results, Table~\ref{tab:cv} shows hardly any benefit in the illustrative example. This effect can to a large degree already be explained from the spatio-temporal variograms: a temporal lag of one or a few days leads already to a large variability compared to spatial distances of few hundred kilometres, implying that the temporal correlation is too weak to considerably improve the overall prediction. Nevertheless, investigating a process with a higher temporal frequency will likely show a stronger correlation in the temporal domain. Looking into station-wise cross-validation statistics (not shown), the four stations with an RMSE of 10 and larger correspond to the locations with the largest annual mean concentrations ($>22~\mu{\rm g}/{\rm m}^3$). The added value of spatio-temporal kriging lies in the flexibility of the model. We are now in the position to not only interpolate at unobserved locations in space, but also at unobserved time instances. This makes spatio-temporal kriging a suitable tool to fill gaps in time series not only based on the time series solely, but also including some of its spatial neighbours. A very irregular sampled data set would as well largely benefit from a spatio-temporal approach, as spatially close but unobserved locations in one time slice are not of any help in a purely spatial approach, but the spatio-temporal model would benefit from the observed value nearby at another time instance. In a completely regular data set, the distance to a spatio-temporal neighbour is at least as large as the pure spatial distance and hence the correlation is weaker. Furthermore, being able to capture the covariance structure over space and time might foster a better understanding of the process under study. While we see spatio-temporal modelling being a powerful tool, the cross-validation results in Table~\ref{tab:cv} show that spatio-temporal kriging will not solve the problem of all poorly spatially captured phenomena. Further preprocessing steps might be necessary to improve the modelling of this $\rm{PM}_{10}$ data set such as for instance a temporal AR-model followed by spatio-temporal residual kriging or using further covariates in a preceding (linear) modelling step. Providing the best possible model of $\rm{PM}_{10}$ concentrations across Germany was beyond the scope of this paper. The selection of a spatio-temporal covariance model should not only be made based on the (weighted) mean squared difference between the empirical and model variogram surfaces (presented in Table~\ref{tab:vgmFits}), but also on conceptional choices and visual (Figure~\ref{fig:allVgmsWireframe}) judgement of the fits. Even though the function \code{fit.StVariogram} provides optimisation routines to fit different spatio-temporal variogram models, the numerical routines in the background may struggle to find the optimal parameters. Besides the lower and upper boundaries of the parameter space, the control parameter \code{parscale} of the \code{optim} function is a valuable option to improve the convergence of the optimisation. With passing \code{parscale} as entry of the list \code{control} a vector of scalars must be passed that controls the different levels of magnitude of the variogram parameters. In most applications, a change of 1 in the sills will have a stronger influence on the variogram surface than a change of 1 in the ranges. The problem becomes more difficult with an increasing number of parameters. In our application, using the simple sum-metric model as starting values for the full sum-metric model improved the convergence speed of the more complex model. In the presented application, the sum-metric models turns out to be the same as the simple sum-metric model. While this might at first sight be due to using the simpler model to generate starting values, different non simplified starting models converged to the same result. Generally, it is important to keep in mind the strong interaction of the model parameters. It is typically not easy to distinguish how much of the spatio-temporal nugget and sill is attributed to spatial, temporal or joint components. In this paper we considered a joint numerical approach, but step-wise approaches where the components are estimated separately could as well be considered. The interested reader is also referred to \cite{Nash2014}. However, all optimisation approaches follow the premise that the studied process can be approximated with the given model and available data. If this premise fails, no optimal model can be selected. An extension towards a restricted maximum likelihood method (REML) to fit the spatio-temporal variogram model would be desirable, as it overcomes some of the above mentioned drawbacks of the method of moments based approaches and would additionally provide standard errors for the parameter estimates. A REML approach would allow to take into account that sample variogram values are correlated. However, for large datasets (as in the spatio-temporal case), it is computationally more feasible to use a least squares fitting. To reduce the correlation of the variogram values, some randomisation could be implemented in large data sets, to calculate the sample variogram based on partially overlapping or even disjoint sets of observations. The selected anisotropy as proxy to the relation of spatial and temporal distance in determining the strongest correlated neighbours might show a distortion for some models when only few neighbours are used towards the true set of the most correlated locations. However, this effect vanishes as soon as the spatio-temporal range of the model is sufficiently represented through the set of nearest neighbours. As mentioned by \cite{kj99}, an alternative to space-time kriging might be co-kriging. However, this is only feasible if the number of time replicates is (very) small, as the number of cross variograms to be modelled equals the number of {\em pairs} of time replicates. Also, co-kriging can only interpolate for these time slices, and not inbetween or beyond them. It does however provide prediction error covariances, which can help assessing the significance of estimated {\em change} parameters \citep{pe1,pe2}. Several of the space-time variograms presented here may be approximated by sets of direct variograms and cross-variograms. Fitting variogram models to sample space-time variograms is in our implementation done by \code{stats::optim}. Our example script uses method \code{L-BFGS-B} and provides upper and lower parameter boundaries, e.g.\ to make sure sill parameters do not become negative. There has been a lot of research in optimization since the methods in \code{optim}, some of which has been reported in the special issue of the Journal of Statistical Software \citep{optim}, and we do see potential to improve the options in this respect. The approximate selection of the most correlated neighbours solves the lack of a natural notion of a joint distance across space and time. However, other sampling properties might introduce a bias in the prediction. The prediction at an unobserved location with a cluster of observations at one side will be biased towards this cluster and neglect the locations towards the other directions. Similar as the quadrant search in the pure spatial case an octant wise search strategy for the local neighbourhood would solve this limitation. A simpler stepwise approach to define an $n$-dimensional neighbourhood might already be sufficient in which at first $n_s$ spatial neighbours and then from each spatial neighbour $n_t$ time instances are selected, such that $n_s \cdot n_t \approx n$. The presented example considers stationary random fields that are isotropic in space. Further extensions towards more sophisticated variogram estimations allowing also for spatial geometric anisotropy are desirable. One could for instance plot variogram maps for spatial separation in North and South direction for each temporal lag. However, the current implementation does not allow to use the anisotropy parameter \code{anis} of the pure spatial variogram definition. Nevertheless, a preliminary rescaling of coordinates would be a possible workaround. This route has for instance been taken by \citet{Gasch2015} performing 3D+T kriging . The soil profiles in their study show a clear difference in horizontal and vertical variography. To correct for this, the depth dimension of the data has been rescaled to correspond with the dimensions of the horizontal distances before hand. In the subsequent study, these pseudo 3D coordinates have been used to fit the spatio-temporal variograms and perform kriging. The code in model definitions is meant to be kept both flexible and simple. This is based on i) re-producing the notion of the geostatistical models in the R code and in ii) reusing existing definitions and functions of the pure spatial cases that have been available for many years in \pkg{gstat}. The data handling benefits to a large degree from the implementations in the \pkg{spacetime} R package. \section{Conclusions}\label{sec:conclusions} The spatio-temporal extensions to \pkg{gstat} allow to model a set of spatio-temporal covariance functions. The implemented functionality eases estimation, visualisation and understanding of spatio-temporal covariance functions. The extension and reuse of already available function structures and nomenclature facilitates an easy translation of spatial workflows to handle spatio-temporal data. The numerical estimation of the variogram parameters might be tricky and needs a large degree of the users attention. It is advised to carefully check the outcome of the \code{optim} routine after optimisation. Spatio-temporal kriging predictions can be made in a global and a local neighbourhood set-up, while the latter will be the preferred solution for most spatio-temporal data sets and common computer hardware configurations. Spatio-temporal covariance structures carry valuable information, but a spatio-temporal model is not guaranteed to outperform pure spatial predictions. The benefit in terms of prediction quality of spatio-temporal kriging becomes only apparent if sufficiently strong correlated locations are added with the temporal dimension (i.e.\, if the model permits strong correlation across time). Nevertheless, the spatio-temporal covariance model might be of interest in itself. Besides some publications where the authors of this paper were involved in, such as \cite{Kilibarda2014}, the software presented here has proven useful in several independent publications, examples of which are \citep{marek, biondi, hu, yoon}. \section{Acknowledgements} This research has partly been funded by the German Research Foundation (DFG) under project number PE 1632/4-1. We thank two anonymous reviewers for their valuable comments. \bibliography{spatio-temporal-kriging} \pagebreak \address{Benedikt Gr{\"a}ler\\ Institute for Geoinformatics, University of M{\"u}nster\\ Heisenbergstr. 2, 48149, M{\"u}nster\\ Germany}\\ \email{ben.graeler@uni-muenster.de} \address{Edzer Pebesma\\ Institute for Geoinformatics, University of M{\"u}nster\\ Heisenbergstr. 2, 48149, M{\"u}nster\\ Germany}\\ \email{edzer.pebesma@uni-muenster.de} \address{Gerard Heuvelink\\ Department of Environmental Sciences, Wageningen University\\ PO Box 47, 6700AA, Wageningen\\ The Netherlands}\\ \email{gerard.heuvelink@wur.nl} \section{Appendix} \subsection{Derivation of the separable covariance and variogram identities}\label{sec:derivSep} The separable covariance and variogram identity is readily available through \begin{align*} C_{\rm sep}(h,u) &= C_{\rm s}(h)C_{\rm t}(u) = sill \cdot \bar{c}_s(h)\bar{c}_t(u) \\ \gamma_{\rm sep}(h,u) &= C_{\rm sep}(0,0) - C_{\rm sep}(h,u) \\ &= sill \left(1- \bar{c}_s(h) \cdot \bar{c}_t(u) \right) \\ &= sill \left(1- \left(1-\bar{\gamma}_s(h)\right)\left(1-\bar{\gamma}_t(u)\right) \right) \\ &= sill \left(1- \left(1-\bar{\gamma}_s(h) -\bar{\gamma}_t(u) + \bar{\gamma}_s(h)\bar{\gamma}_t(u)\right) \right) \\ &= sill \left(\bar{\gamma}_s(h) + \bar{\gamma}_t(u) - \bar{\gamma}_s(h)\bar{\gamma}_t(u)\right) \end{align*} where $\bar{c}$ and $\bar{\gamma}$ are normalised correlation and correlogram functions respectively. \subsection{Derivation of the product-sum covariance and variogram identities}\label{sec:derivPs} The product-sum covariance and variogram identity is readily available through: \begin{align*} C_{\rm ps}(h,u) = & \ k \cdot C_{\rm s}(h)C_{\rm t}(u) + C_{\rm s}(h) + C_{\rm t}(u) \\ \gamma_{\rm ps}(h,u) = & \ C_{\rm ps}(0,0) - C_{\rm ps}(h,u) \\ = & \ k \cdot C_{\rm s}(0)C_{\rm t}(0) + C_{\rm s}(0) + C_{\rm t}(0) \\ & - \left(k \cdot C_{\rm s}(h)C_{\rm t}(u) + C_{\rm s}(h) + C_{\rm t}(u)\right) \\ = & \ k \cdot {\rm sill}_{\rm s} \cdot {\rm sill}_{\rm t} + {\rm sill}_{\rm s} + {\rm sill}_{\rm t} \\ & - k \cdot \left[ \left({\rm sill}_{\rm s} - \gamma_{\rm s}(h)\right)\left({\rm sill}_{\rm t} - \gamma_{\rm t}(u)\right)\right] - \left({\rm sill}_{\rm s} - \gamma_{\rm s}(h)\right) - \left({\rm sill}_{\rm t} - \gamma_{\rm t}(u)\right) \\ = & \ k \cdot {\rm sill}_{\rm s} \cdot {\rm sill}_{\rm t} + {\rm sill}_{\rm s} + {\rm sill}_{\rm t} \\ & - k \cdot \left[ {\rm sill}_{\rm s} \cdot {\rm sill}_{\rm t} - {\rm sill}_{\rm s} \cdot \gamma_{\rm t}(u) - {\rm sill}_{\rm t} \cdot \gamma_{\rm s}(h) + \gamma_{\rm s}(h) \gamma_{\rm t}(u) \right] \\ & - {\rm sill}_{\rm s} + \gamma_{\rm s}(h) - {\rm sill}_{\rm t} + \gamma_{\rm t}(u) \\ = & \ k \cdot {\rm sill}_{\rm t} \gamma_{\rm s}(h) + k \cdot {\rm sill}_{\rm s} \gamma_{\rm t}(u) - k \gamma_{\rm s}(h) \gamma_{\rm t}(u) + \gamma_{\rm s}(h) + \gamma_{\rm t}(u) \\ = & \ (k \cdot {\rm sill}_{\rm t} + 1) \gamma_{\rm s}(h) + (k \cdot {\rm sill}_{\rm s} + 1) \gamma_{\rm t}(u) - k \gamma_{\rm s}(h) \gamma_{\rm t}(u) \end{align*} %%%%%%%%%% \end{document} gstat/vignettes/ifgi-logo_int.pdf0000644000176200001440000002421513777370515016650 0ustar liggesusers%PDF-1.4 % 4 0 obj << /Length 37 /Filter /FlateDecode >> stream x+2T0BC]C]\.}\C|@._I endstream endobj 3 0 obj << /Type /Page /Contents 4 0 R /Resources 2 0 R /MediaBox [0 0 240 86] /Parent 5 0 R >> endobj 1 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (./ifgi-logos-crop.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 6 0 R /BBox [0 0 254 182] /Resources << /XObject << /Im1 7 0 R >>/ProcSet [ /PDF ] >> /Length 38 /Filter /FlateDecode >> stream x+2T0BC]#K ajj˥km  endstream endobj 6 0 obj << /Producer (pdfTeX-1.40.3) /Creator (TeX) /CreationDate (D:20080508123050+02'00') /ModDate (D:20080508123050+02'00') /Trapped /False /PTEX.Fullbanner (This is pdfTeX using libpoppler, Version 3.141592-1.40.3-2.2 \(Web2C 7.5.6\) kpathsea version 3.5.6) >> endobj 7 0 obj << /Type /XObject /Subtype /Form 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Oh, shame. % \VignetteIndexEntry{ The pairwise relative semivariogram } \documentclass[a4paper]{article} \usepackage[colorlinks=true,urlcolor=blue]{hyperref} \usepackage{alltt} \newcommand{\code}[1]{{\tt #1}} \SweaveOpts{echo=TRUE} \title{The pairwise relative semivariogram} \author{ \includegraphics[width=.4\columnwidth]{ifgi-logo_int}\\ \href{mailto:edzer.pebesma@uni-muenster.de}{Edzer Pebesma} } \date{\small Aug 29, 2011 } \begin{document} \maketitle \section{Introduction} The general relative variogram (Deutsch and Journel, 1997) is defined as $$ \gamma(h) = \frac{1}{2N_h} \sum_{i=1}^{N_h} \left(\frac{2(Z(s_i)-Z(s_i+h))}{Z(s_i)+Z(s_i+h)}\right)^2. $$ It is claimed to reveal spatial structure (correlation) better when data are skewed and/or clustered. The \code{cluster.dat} data set used in this vignette, from the GSLIB distribution\footnote{F77 source code for Linux, downloaded Aug 28, 2011 from \code{http://www.gslib.com/}}, seems to confirm this. From version 1.02 on, R package \code{gstat} provides computation of the {\em pairwise relative semivariogram}. The following code provides an example and verification of the computation using direct R code and using the GSLIB program \code{gamv}. The following code imports the \code{cluster.dat} data from GSLIB, which has been converted to have a single-line header containing column names, packaged with the R gstat package, and converts it into a \code{SpatialPointsDataFrame} object: <<>>= library(gstat) cluster = read.table(system.file("external/cluster.txt", package="gstat"), header = TRUE) summary(cluster) library(sp) coordinates(cluster) = ~X+Y @ The following commands specify a sequence of lag boundaries that correspond to the GSLIB conventions, and compute a regular variogram using these boundaries: <<>>= bnd = c(0,2.5,7.5,12.5,17.5,22.5,27.5,32.5,37.5,42.5,47.5,52.5) variogram(Primary~1, cluster, boundaries = bnd) @ To compute the relative pairwise variogram, the logical argument \code{PR} ({\em pairwise relative}) needs to be set to \code{TRUE}: <<>>= variogram(Primary~1, cluster, boundaries=bnd, PR = TRUE) @ Figure \ref{fig:vgm} shows the two variograms, as plots, side by side \begin{figure} <>= pl1 = plot(variogram(Primary~1, cluster, boundaries=bnd, PR = FALSE)) pl2 = plot(variogram(Primary~1, cluster, boundaries=bnd, PR = TRUE)) print(pl1, split = c(1,1,2,1), more = TRUE) print(pl2, split = c(2,1,2,1), more = FALSE) @ \caption{Regular variogram (left) and pairwise relative variogram (right) for the GSLIB data set \code{cluster.dat}.} \label{fig:vgm} \end{figure} \section{Verification with plain R code} The following R code reproduces the relative pairwise semivariogram values for the first three lags, i.e. 0-2.5, 2.5-7.5 and 7.5-12.5. <<>>= z = cluster$Primary d = spDists(cluster) zd = outer(z, z, "-") zs = outer(z, z, "+") pr = (2 * zd / zs )^2 prv = as.vector(pr) dv = as.vector(d) mean(prv[dv > 0 & dv < 2.5])/2 mean(prv[dv > 2.5 & dv < 7.5])/2 mean(prv[dv > 7.5 & dv < 12.5])/2 @ \section{Verification with GSLIB} In a verification with the GSLIB (Deutsch and Journel, 1997) code of \code{gamv}, the following file was used: \begin{alltt} Parameters for GAMV ******************* START OF PARAMETERS: ../data/cluster.dat \\file with data 1 2 0 \\ columns for X, Y, Z coordinates 1 3 \\ number of varables,column numbers -1.0e21 1.0e21 \\ trimming limits gamv.out \\file for variogram output 10 \\number of lags 5.0 \\lag separation distance 2.5 \\lag tolerance 1 \\number of directions 0.0 90.0 50.0 0.0 90.0 50.0 \\azm,atol,bandh,dip,dtol,bandv 0 \\standardize sills? (0=no, 1=yes) 2 \\number of variograms 1 1 1 \\tail var., head var., variogram type 1 1 6 \\tail var., head var., variogram type \end{alltt} Running this program with these parameters gave the following output: \begin{alltt} Semivariogram tail:Primary head:Primary direction 1 1 .000 .00000 280 4.35043 4.35043 2 1.528 58.07709 298 8.62309 8.62309 3 5.473 54.09188 1248 5.41315 5.41315 4 10.151 48.85144 1978 4.42758 4.42758 5 15.112 40.08909 2498 4.25680 4.25680 6 20.033 42.45081 2296 3.74311 3.74311 7 25.020 48.60365 2734 4.09575 4.09575 8 29.996 46.88879 2622 4.15950 4.15950 9 34.907 44.36890 2170 3.77190 3.77190 10 39.876 47.34666 1808 4.54173 4.54173 11 44.717 38.72725 1222 5.15251 5.15251 12 49.387 30.67908 438 4.56539 4.56539 Pairwise Relative tail:Primary head:Primary direction 1 1 .000 .00000 280 4.35043 4.35043 2 1.528 .36084 298 8.62309 8.62309 3 5.473 .63071 1248 5.41315 5.41315 4 10.151 .83764 1978 4.42758 4.42758 5 15.112 .77691 2498 4.25680 4.25680 6 20.033 .87746 2296 3.74311 3.74311 7 25.020 .89610 2734 4.09575 4.09575 8 29.996 .90023 2622 4.15950 4.15950 9 34.907 .96043 2170 3.77190 3.77190 10 39.876 .90554 1808 4.54173 4.54173 11 44.717 .75545 1222 5.15251 5.15251 12 49.387 .82268 438 4.56539 4.56539 \end{alltt} As can be seen, the values in the third column (semivariogram for the first section, pairwise relative semivariogram for the second) correspond to the output generated by \code{variogram} of package \code{gstat}. Two differences with respect to the gstat output are: \begin{itemize} \item for the first lag with distance zero, GSLIB reports that the semivariance value is zero based on 280 point pairs; \item the number of point pairs in GSLIB is double the number reported by gstat. \end{itemize} The ground for these differences seems that the GSLIB \code{gamv} uses a single routine for computing variograms as well as cross variograms and cross covariances. For cross variograms or covariograms, considering two variables $Z_a$ and $Z_b$ each having $N$ observations, the $N^2$ point pairs $Z_a(s_i),Z_b(s_i+h)$ and $Z_a(s_i+h),Z_b(s_i)$ need to be evaluated, and all contribute information. For direct (non-cross) variograms or covariograms, $Z_a=Z_b$ and the $N^2$ pairs considered contain the $N$ trivial pairs $(Z(s_i)-Z(s_i))^2=0$, which contribute no information, as well as all duplicate pairs, i.e. in addition to $(Z(s_i)-Z(s_i+h))^2$, the identical pair $(Z(s_i+h)-Z(s_i))^2$ is also considered. This leads to correct variogram value estimates, but incorrect unique point pair numbers. (Data set \code{cluster} contains $N=140$ observations.) In contrast, \code{gstat} considers (and reports) only the number of unique pairs for each lag. \section*{References} \begin{itemize} \item Deutsch, C.V., A.G. Journel, 1997. GSLIB: Geostatistical Software Library and User's Guide, second edition. Oxford University Press. \end{itemize} \end{document} gstat/vignettes/gstat.Rnw0000644000176200001440000003154014207202535015221 0ustar liggesusers%% Document started, Sat Jul 3 19:30:52 CEST 2004, my 37th birthday, %% while being stuck for 24 hours at Philadelphia airport, on my way %% back from the joint TIES/Accuracy 2004 symposium in Portland, ME. %% Continued, Oct 28, during the Apmosphere mid-term review. Oh, shame. % \VignetteIndexEntry{ The meuse data set: a tutorial for the gstat R package } \documentclass[a4paper]{article} \usepackage{hyperref} \newcommand{\code}[1]{{\tt #1}} \SweaveOpts{echo=TRUE} \title{The meuse data set: a brief tutorial\\ for the {\tt gstat} R package } \author{\href{mailto:edzer.pebesma@uni-muenster.de}{Edzer Pebesma}} \date{\today} \begin{document} \maketitle \section{Introduction} The \code{meuse} data set provided by package \code{sp} is a data set comprising of four heavy metals measured in the top soil in a flood plain along the river Meuse, along with a handful of covariates. The process governing heavy metal distribution seems that polluted sediment is carried by the river, and mostly deposited close to the river bank, and areas with low elevation. This document shows a geostatistical analysis of this data set. The data set was introduced by Burrough and McDonnell, 1998. This tutorial introduced the functionality of the R package \code{gstat}, used in conjunction with package \code{sp}. Package \code{gstat} provides a wide range of univariable and multivariable geostatistical modelling, prediction and simulation functions, where package \code{sp} provides general purpose classes and methods for defining, importing/exporting and visualizing spatial data. \section{R geostatistics packages} Package \code{gstat} (Pebesma, 2004) is an R package that provides basic functionality for univariable and multivariable geostatistical analysis, including \begin{itemize} \item variogram modelling, residual variogram modelling, and cross variogram modelling using fitting of parametric models to sample variograms \item geometric anisotropy specfied for each partial variogram model \item restricted maximum likelihood fitting of partial sills \item variogram and cross variogram maps \item simple, ordinary, universal and external drift (co)kriging \item (sequential) Gaussian (co)simulation equivalents for each of the kriging varieties \item indicator (co)kriging and sequential indicator (co)simulation \item kriging in a local or global neighbourhood \item block (co)kriging or simulation for each of the varieties, for rectangular or irregular blocks \end{itemize} Other geostatistical packages for R usually lack part of these options (e.g. block kriging, local kriging, or cokriging) but provide others: e.g. package \code{geoR} and \code{geoRglm} (by Paulo Ribeiro and Ole Christensen) provide the model-based geostatistics framework described in Diggle et al. (1998), package \code{fields} (Doug Nychka and others) provides thin plate spline interpolation, covariance functions for spherical coordinates (unprojected data), and routines for spatial sampling design optimization. \section{Spatial data frames} As an example, we will look at the meuse data set, which is a regular data frame that comes with package \code{gstat} (remove the 88 from the colour strings to make a plot without alpha transparency on windows or X11): <>= library(sp) data(meuse) class(meuse) names(meuse) coordinates(meuse) = ~x+y class(meuse) summary(meuse) coordinates(meuse)[1:5,] bubble(meuse, "zinc", col=c("#00ff0088", "#00ff0088"), main = "zinc concentrations (ppm)") @ % the following is needed because lattice plots (bubble wraps xyplot) do not % show without an explicit print; in order not to confuse users, we hide this: <>= print(bubble(meuse, "zinc", col=c("#00ff0088", "#00ff0088"), main = "zinc concentrations (ppm)") ) @ and note the following: \begin{enumerate} \item the function \code{coordinates}, when assigned (i.e. on the left-hand side of an \verb|=| or \verb|<-| sign), promotes the \code{data.frame} meuse into a \code{SpatialPointsDataFrame}, which knows about its spatial coordinates; coordinates may be specified by a formula, a character vector, or a numeric matrix or data frame with the actual coordinates \item the function \code{coordinates}, when not assigned, {\em retrieves} the spatial coordinates from a \code{SpatialPointsDataFrame}. \item the two plotting functions used, \code{plot} and \code{bubble} assume that the $x$- and $y$-axis are the spatial coordinates. \end{enumerate} \section{Spatial data on a regular grid} <>= data(meuse.grid) summary(meuse.grid) class(meuse.grid) coordinates(meuse.grid) = ~x+y class(meuse.grid) gridded(meuse.grid) = TRUE class(meuse.grid) image(meuse.grid["dist"]) title("distance to river (red = 0)") library(gstat) zinc.idw = idw(zinc~1, meuse, meuse.grid) class(zinc.idw) spplot(zinc.idw["var1.pred"], main = "zinc inverse distance weighted interpolations") @ <>= print(spplot(zinc.idw["var1.pred"], main = "zinc inverse distance weighted interpolations")) @ If you compare the bubble plot of zinc measurements with the map with distances to the river, it becomes evident that the larger concentrations are measured at locations close to the river. This relationship can be linearized by log-transforming the zinc concentrations, and taking the square root of distance to the river: <>= plot(log(zinc)~sqrt(dist), meuse) abline(lm(log(zinc)~sqrt(dist), meuse)) @ \section{Variograms } Variograms are calculated using the function \code{variogram}, which takes a formula as its first argument: \verb|log(zinc)~1| means that we assume a constant trend for the variable log(zinc). <>= lzn.vgm = variogram(log(zinc)~1, meuse) lzn.vgm lzn.fit = fit.variogram(lzn.vgm, model = vgm(1, "Sph", 900, 1)) lzn.fit plot(lzn.vgm, lzn.fit) @ <>= print(plot(lzn.vgm, lzn.fit)) @ Instead of the constant mean, denoted by \verb|~1|, we can specify a mean function, e.g. using \verb|~sqrt(dist)| as a predictor variable: <>= lznr.vgm = variogram(log(zinc)~sqrt(dist), meuse) lznr.fit = fit.variogram(lznr.vgm, model = vgm(1, "Exp", 300, 1)) lznr.fit plot(lznr.vgm, lznr.fit) @ <>= print(plot(lznr.vgm, lznr.fit)) @ In this case, the variogram of residuals with respect to a fitted mean function are shown. Residuals were calculated using ordinary least squares. \section{Kriging} <>= lzn.kriged = krige(log(zinc)~1, meuse, meuse.grid, model = lzn.fit) spplot(lzn.kriged["var1.pred"]) @ <>= print(spplot(lzn.kriged["var1.pred"])) @ \section{Conditional simulation} <>= lzn.condsim = krige(log(zinc)~1, meuse, meuse.grid, model = lzn.fit, nmax = 30, nsim = 4) spplot(lzn.condsim, main = "four conditional simulations") @ <>= print(spplot(lzn.condsim, main = "four conditional simulations")) @ For UK/residuals: <>= lzn.condsim2 = krige(log(zinc)~sqrt(dist), meuse, meuse.grid, model = lznr.fit, nmax = 30, nsim = 4) spplot(lzn.condsim2, main = "four UK conditional simulations") @ <>= print(spplot(lzn.condsim2, main = "four UK conditional simulations")) @ \section{Directional variograms} The following command calculates a directional sample variogram, where directions are binned by direction angle alone. For two point pairs, $Z(s)$ and $Z(s+h)$, the separation vector is $h$, and it has a direction. Here, we will classify directions into four direction intervals: <>= lzn.dir = variogram(log(zinc)~1, meuse, alpha = c(0, 45, 90, 135)) lzndir.fit = vgm(.59, "Sph", 1200, .05, anis = c(45, .4)) plot(lzn.dir, lzndir.fit, as.table = TRUE) @ <>= print(plot(lzn.dir, lzndir.fit, as.table = TRUE)) @ Looking at directions between 180 and 360 degrees will repeat the image shown above, because the variogram is a symmetric measure: $(Z(s)-Z(s+h))^2=(Z(s+h)-Z(s))^2$. The first plot gives the variogram in the zero direction, which is North; 90 degrees is East. By default, point pairs are assigned to the directional variorgram panel with their nearest direction, so North contains everything between -22.5 and 22.5 degrees (North-West to North-East). After classifying by direction, point pairs are binned by separation distance class, as is done in the usual omnidirectional case. In the figure, the partial sill, nugget and model type of the model are equal to those of the omnidirectional model fitted above; the range is that in the direction with the largest range (45$^o$), and the anisotropy ratio, the range in the 135 direction and the range in the 45 direction, estimated ``by eye'' by comparing the 45 and 135 degrees sample variograms. Gstat does not fit anisotropy parameters automatically. We do not claim that the model fitted here is ``best'' in some way; in order to get to a better model we may want to look at more directions, other directions (e.g. try {\tt alpha = c(22, 67, 112, 157) }), and to variogram maps (see below). More elaborate approaches may use directions in three dimensions, and want to further control the direction tolerance (which may be set such that direction intervals overlap). For the residual variogram from the linear regression model using \code{sqrt(dist)} as covariate, the directional dependence is much less obvious; the fitted model here is the fitted isotropic model (equal in all directions). <>= lznr.dir = variogram(log(zinc)~sqrt(dist), meuse, alpha = c(0, 45, 90, 135)) plot(lznr.dir, lznr.fit, as.table = TRUE) @ <>= print(plot(lznr.dir, lznr.fit, as.table = TRUE)) @ \section{Variogram maps} Another means of looking at directional dependence in semivariograms is obtained by looking at variogram maps. Instead of classifying point pairs $Z(s)$ and $Z(s+h)$ by direction and distance class {\em separately}, we can classify them {\em jointly}. If $h=\{x,y\}$ be the two-dimentional coordinates of the separation vector, in the variogram map the semivariance contribution of each point pair $(Z(s)-Z(s+h))^2$ is attributed to the grid cell in which $h$ lies. The map is centered around $(0,0)$, as $h$ is geographical distance rather than geographical location. Cutoff and width correspond to some extent to map extent and cell size; the semivariance map is point symmetric around $(0,0)$, as $\gamma(h)=\gamma(-h)$. <>= vgm.map = variogram(log(zinc)~sqrt(dist), meuse, cutoff = 1500, width = 100, map = TRUE) plot(vgm.map, threshold = 5) @ <>= print(plot(vgm.map, threshold = 5)) @ The threshold assures that only semivariogram map values based on at least 5 point pairs are shown, removing too noisy estimation. % The plot is plagued by one or two extreme values, corresponding to cells % with very small number of point pairs, which should be removed. \section{Cross variography} Fitting a linear model of coregionalization. <>= g = gstat(NULL, "log(zn)", log(zinc)~sqrt(dist), meuse) g = gstat(g, "log(cd)", log(cadmium)~sqrt(dist), meuse) g = gstat(g, "log(pb)", log(lead)~sqrt(dist), meuse) g = gstat(g, "log(cu)", log(copper)~sqrt(dist), meuse) v = variogram(g) g = gstat(g, model = vgm(1, "Exp", 300, 1), fill.all = TRUE) g.fit = fit.lmc(v, g) g.fit plot(v, g.fit) vgm.map = variogram(g, cutoff = 1500, width = 100, map = TRUE) plot(vgm.map, threshold = 5, col.regions = bpy.colors(), xlab = "", ylab = "") @ <>= print(plot(v, g.fit)) @ <>= print(plot(vgm.map, threshold = 5, col.regions = bpy.colors(), ylab = "", xlab = "")) @ \section*{References} \begin{itemize} % \item Abrahamsen, P., F. Espen Benth, 2001. Kriging with inequality % constraints. Mathematical Geology 33 (6), 719--744. % \item Bivand, R.S., 2003. Approaches to classes for spatial data in R. % In: K.~Hornik \& F.~Leisch (Eds.), Proceedings of the 3rd International % Workshop on Distributed Statistical Computing (DSC 2003) March 20--22, % Vienna, Austria. ISSN 1609-395X; available from [1]. \item Burrough, P.A., R.A. McDonnell, 1998. Principles of Geographical Information Systems, 2nd Edition. Oxford University Press. \item Diggle, P.J., J.A. Tawn, R.A. Moyeed, 1998. Model-based geostatistics. Applied Statistics 47(3), pp 299-350. % \item Pebesma, E.J., Wesseling, C.G., 1998. Gstat, a program for % geostatistical modelling, prediction and simulation. Computers \& % Geosciences, 24 (1), pp. 17--31. \item Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers \& Geosciences \href{http://dx.doi.org/10.1016/j.cageo.2004.03.012}{30: 683-691}. % \item Ver Hoef, J.M., Cressie, N.A.C, 1993. Multivariable Spatial % Prediction. Mathematical Geology, 25 (2), pp. 219--240. \item Wackernagel, H., 1998. Multivariate Geostatistics; an introduction with applications, $2^{\mbox{nd}}$ edn., Springer, Berlin, 291 pp. \end{itemize} \end{document} # g = gstat(NULL, "log.zinc", log(zinc)~1, meuse) # g = gstat(g, "log.zinc.res", log(zinc)~sqrt(dist), meuse) # lplot(vgm.map[["map"]], c("log.zinc", "log.zinc.res")) % vim:syntax=tex gstat/vignettes/st.Rnw0000644000176200001440000003643513777370515014554 0ustar liggesusers%% Document started, Sat Jul 3 19:30:52 CEST 2004, my 37th birthday, %% while being stuck for 24 hours at Philadelphia airport, on my way %% back from the joint TIES/Accuracy 2004 symposium in Portland, ME. %% Continued, Oct 28, during the Apmosphere mid-term review. Oh, shame. \documentclass[a4paper]{article} \usepackage[colorlinks=true,urlcolor=blue]{hyperref} \newcommand{\code}[1]{{\tt #1}} \SweaveOpts{echo=TRUE} \title{Introduction to Spatio-Temporal Variography } % \VignetteIndexEntry{ Introduction to Spatio-Temporal Variography } \author{ \includegraphics[width=.4\columnwidth]{ifgi-logo_int}\\ \href{mailto:edzer.pebesma@uni-muenster.de}{Edzer Pebesma}, \href{mailto:ben.graeler@uni-muenster.de}{Benedikt Gr\"{a}ler} } \date{\small \today } \begin{document} \setkeys{Gin}{width=0.9\textwidth} \maketitle \section{Introduction} Since \code{gstat} package version 1.0-0, a dependency of gstat on the R package \code{spacetime} was introduced, allowing the code in \code{gstat} to exploit spatio-temporal data structures from that package. This vignette describes the possibilities and limitations of the package for spatio-temporal geostatistics. To understand some of the possibilities and limitations, some knowledge of the history of the software is needed. The original \code{gstat} software (Pebesma and Wesseling, 1998) was a standalone computer {\em program} written in around 25,000 lines of C code, and would do geostatistical modelling, prediction and simulation. The \code{gstat} R package (Pebesma, 2004) consisted mostly of an R interface to this C code, together with convenience functions to use R's modelling interface (formula's, see \code{?lm}) and graphic capabilities (trellis graphics in package \code{lattice} to show cross variogram as matrix plots; interaction with variogram clouds using base plots). Starting 2003, a group of programmers developed a set of classes and methods for dealing with spatial data in R (points, lines, polygons, grids), which was supported by the publications of the well-known ASDAR book (Bivand et al. 2008; see also \url{http://www.asdar-book.org/}) and helped convergence in the user community, with in 2011 over 2000 subscribers on the {\tt r-sig-geo} mailing list. Package \code{gstat} was one of the first packages that adopted and benefited from these classes. To realize a particular idea, writing code in C typically takes about 10-20 times as long as writing it in R. C code can be more efficient, gives more control over memory usage, but is also more error prone--mistakes in C code make an R session crash, something that is hard to do when writing R code. The original C code of \code{gstat} (Pebesma and Wesseling, 1998) provides all kriging varieties (universal, ordinary, simple; univariable, or multivariable as in cokriging) for two- or three-dimensional data. When the spatial domain is constrained to two dimensions (and this might cover over 99\% of the use cases!), the third dimension might be used to represent time. As such, the {\em metric} variogram model, which allows for geometric anisotropy definition in three dimensions, can be used for spatio-temporal kriging. When defining the three-dimensional variogram as the sum of 2 or more nested variogram (summed) models, one can choose anisotropy coefficients for a single model such that this model is {\em effectively} zero in some directions, e.g. in space {\em or} in time; this allows one to approximate the so-called space-time sum model. It should be noted that at the C code there is no knowledge whether a third dimension represents space, or time. As such, particular characteristics of time cannot be taken care of. Since the second half of 2010, the development of an R package \code{spacetime} started. It provides methods and classes for spatio-temporal data, and builds on the spatial data classes in \code{sp} and time series classes in \code{xts}. This document will explain how data in this form, and methods provided by this package, can be used for spatio-temporal geostatistics. We will work with a data set with air quality (PM10) measurements over germany, taken from rural background stations available in the data sets provided by the European Environmental Agency. <<>>= library(spacetime) rm(list = ls()) data(air) ls() @ \section{Variography} \subsection{Temporal autocorrelation and cross correlation} We will look into a subset of the data, ranging from 2005 to 2010, and remove stations that have only missing values in this period: <<>>= if (!exists("rural")) rural = STFDF(stations, dates, data.frame(PM10 = as.vector(air))) rr = rural[,"2005::2010"] unsel = which(apply(as(rr, "xts"), 2, function(x) all(is.na(x)))) r5to10 = rr[-unsel,] summary(r5to10) @ Next, we will (rather arbitrarily) select four stations, which have the following labels: <<>>= rn = row.names(r5to10@sp)[4:7] rn @ In the following, autocorrelation functions are computed and plotted. The resulting plot is shown in Figure~\ref{fig:acf}. <>= par(mfrow=c(2,2)) # select 4, 5, 6, 7 for(i in rn) acf(na.omit(r5to10[i,]), main = i) par(mfrow=c(1,1)) @ \begin{figure}[hbt] \begin{center} <>= par(mfrow=c(2,2)) # select 4, 5, 6, 7 rn = row.names(r5to10@sp)[4:7] for(i in rn) acf(na.omit(r5to10[i,]), main = i) @ \end{center} \caption{Autocorrelations for PM10; time lag unit in days.} \label{fig:acf} \end{figure} Auto- and cross correlations can be computed when a multivariate time series object is passed to {\tt acf}: <>= acf(na.omit(as(r5to10[rn,], "xts"))) @ The resulting plot is shown in Figure~\ref{fig:ccf}. \begin{figure}[hbt] \begin{center} <>= acf(na.omit(as(r5to10[rn,], "xts"))) @ \end{center} \caption{autocorrelations (diagonal) and cross correlations (off-diagonal) for the four stations selected; time lag unit in days. } \label{fig:ccf} \end{figure} From these graphs one should be able to observe the following \begin{itemize} \item autocorrelations for lag 0 are always 1 \item cross correlations for lag 0 are not always 1 \item cross correlations can be asymmetric, meaning that when $\rho_{AB}(h)$ is the correlation between $Z(s_A,t)$ and $Z(s_B,t+h)$, $$\rho_{AB}(h) = \rho_{BA}(-h) \ne \rho_{AB}(-h)$$ with $s_A$ and $s_B$ the two stations between which a cross correlation is computed, and $h$ the (directional!) lag between the series. \end{itemize} The plot further more shows that for these four stations the asymmetry is not very strong, but that cross correlations are fairly strong and of a similar form of autocorrelations. This kind of plot does not work very well in layouts of e.g. 10 x 10 sub-plots; {\tt acf} automatically chooses 4 x 4 as the maximum a single plot. To try this out, do a 7 x 7 plot <>= acf(na.omit(as(r5to10[4:10,], "xts"))) @ and note that here we see in the last figure (DESH \& DESN04) a pair of plots with nearly no cross correlation. This might have to do with the spatial distance between these two stations: <<>>= library(sp) print(spDists(r5to10[4:10,]@sp), digits=3) @ (What is the spatial distance between stations DESH and DESN04?) \subsection{Spatial correlation, variograms} In the next steps, we will sample 100 time instances randomly, <<>>= rs = sample(dim(r5to10)[2], 100) @ we select these instances as a {\tt SpatialPointsDataFrame} and add a time index to them. After this we bind them together in a single {\tt SpatialPointsDataFrame} which has a time index {\tt ti}: <<>>= lst = lapply(rs, function(i) { x = r5to10[,i]; x$ti = i; rownames(x@coords) = NULL; x} ) pts = do.call(rbind, lst) @ Then, we can compute the pooled variogram <<>>= library(gstat) v = variogram(PM10~ti, pts[!is.na(pts$PM10),], dX=0) @ and plot it (Figure~\ref{fig:vgm}): <>= # plot(v, fit.variogram(v, vgm(1, "Exp", 200, 1))) vmod = fit.variogram(v, vgm(100, "Exp", 200)) plot(v, vmod) @ \begin{figure}[hbt] \begin{center} <>= # plot(v, fit.variogram(v, vgm(1, "Exp", 200, 1))) vmod = fit.variogram(v, vgm(100, "Exp", 200)) print(plot(v, vmod)) @ \end{center} \caption{sample spatial variogram, averaged over 100 randomly chosen time steps} \label{fig:vgm} \end{figure} The fitted model is this: <<>>= vmod @ One should note that the fit is rather poor, and not forget that we only have 53 stations selected. The time resolution is rich (1862 days) but the number of stations is small: <<>>= dim(r5to10) @ We can fit a spatio-temporal variogram the usual way, by passing an object of class {\tt STFDF} (Pebesma, 2012): <>= vv = variogram(PM10~1, r5to10, width=20, cutoff = 200, tlags=0:5) @ Alternatively, if this takes too long, a temporal subset can be taken, e.g. using the first 200 days: <>= vv = variogram(PM10~1, r5to10, width=20, cutoff = 200, tlags=0:5) @ taking random days from the full period will lead to the a wrong assumption that every time index increment reflect a constant lag increase. As an alternative, we will here load the precomputed S/T variogram: <<>>= data(vv) @ % remove the model column to keep text and figures in line. <>= vv <- vv[c("np", "dist", "gamma", "id", "timelag", "spacelag")] @ Plotting this object can be done in several ways, two 2D-plots are shown in Figure~\ref{fig:map} and a 3D wireplot is shown in Figure~\ref{fig:wire}: <>= plot(vv) plot(vv, map = FALSE) @ \begin{figure}[hbt] \begin{center} <>= print(plot(vv), split = c(1,1,1,2), more = TRUE) print(plot(vv, map = FALSE), split = c(1,2,1,2)) @ \end{center} \caption{Spatio-temporal sample variogram map (top) and sample variograms for each time lag (bottom); both figures depict the information of object {\tt vv}.} \label{fig:map} \end{figure} \subsection{Fitting a spatio-temporal variogram model} At first, we try to fit a metric model with spatio-temporal anisotropy: <<>>== metricVgm <- vgmST("metric", joint=vgm(50,"Exp",100,0), stAni=50) metricVgm <- fit.StVariogram(vv, metricVgm) @ As numerical criterion to judge the goodness of fit of model and sample variogram, the root-mean-squared-difference between the surfaces can be obtained by: <<>>= attr(metricVgm, "optim")$value @ The final model can be plotted with the sample variogram (Figure~\ref{fig:mm}): <>= plot(vv, metricVgm) @ \begin{figure}[hbt] \begin{center} <>= print(plot(vv, metricVgm)) @ \end{center} \caption{Sample variogram map (left) and fitted metric model (right).} \label{fig:mm} \end{figure} \pagebreak Now, let us try to fit and plot a separable model (Figure~\ref{fig:sm}): <<>>== sepVgm <- vgmST("separable", space=vgm(0.9,"Exp", 123, 0.1), time =vgm(0.9,"Exp", 2.9, 0.1), sill=100) sepVgm <- fit.StVariogram(vv, sepVgm, method = "L-BFGS-B", lower = c(10,0,0.01,0,1), upper = c(500,1,20,1,200)) @ To compare this model with the previous one, we look at the optimized root-mean-squared-differences between the two surfaces and plot sample and both models: <<>>= attr(sepVgm, "optim")$value plot(vv, list(sepVgm, metricVgm)) @ \begin{figure}[hbt] \begin{center} <>= print(plot(vv, list(sepVgm, metricVgm))) @ \end{center} \caption{Sample variogram map (left), fitted separable model (middle) and fittted metric model (right).} \label{fig:sm} \end{figure} A wireframe (3D) plot of sample variogram and fitted variogram models can be obtained e.g. by <>= library(lattice) plot(vv, list(sepVgm, metricVgm), all=T, wireframe=T, zlim=c(0,120), zlab=NULL, xlab=list("distance (km)", rot=30), ylab=list("time lag (days)", rot=-35), scales=list(arrows=F, z = list(distance = 5))) @ which is shown in Figure~\ref{fig:wire}. Further spatio-temporal model definitions can be found in the help pages of {\tt fit.StVariogram} and {\tt variogramSurface}. The demo {\tt stkrige} presents further examples and illustrates an interactive 3D-plot of sample variogram and the fitted variogram model. An interactive variogram exploration web-tool is avaialble at \url{http://giv-graeler.uni-muenster.de:3838/spacetime/}. \begin{figure}[hbt] \begin{center} <>= library(lattice) print(plot(vv, list(sepVgm, metricVgm), all=T, wireframe=T, zlim=c(0,120), zlab=NULL, xlab=list("distance (km)", rot=30), ylab=list("time lag (days)", rot=-35), scales=list(arrows=F, z = list(distance = 5)))) @ \end{center} \caption{Wireframe plots of sample and fitted space-time variograms.} \label{fig:wire} \end{figure} \clearpage \section{Spatio-temporal prediction} The vignette in package \code{spacetime} gives an example of using the gstat function \code{krigeST} for spatio-temporal kriging of the Irish wind data. The \code{krigeST} function uses global kriging, but only needs to invert the purely spatial and purely time covariance matrices in the separable case. For more generic spatio-temporal kriging where space is two-dimensional, one could use \code{krige}, defining the observations and prediction locations as three-dimensional data sets, see for an example <>= demo(gstat3D) @ It needs to be pointed out that in that case, the time (typically the third dimension) needs to be numeric, and three-dimensional anisotropy needs to be defined properly (see \code{?vgm}). In case the data set is too large for global kriging, one could try to use local kriging, and select data within some distance, or by specifying \code{nmax} (the nearest $n$ observations). In both cases, it is advisable to transform time such that one can use an {\em isotropic} variogram model in the three dimensions, as only in that case the nearest $n$ observations correspond to the $n$ most correlated observations. \code{krigeST} provides a solution where a \code{bufferNmax}-times larger neighbourhood is evaluated within the covariance model and the strongest correlated \code{nmax} neighbours are selected. An additional consideration is that in space-time, observations may not be regularly spaced. In some cases, the nearest $n$ observations may come from a single measurement location, which may lead to sharp jumps/boundaries in the interpolated values. This might be solved by using larger neighbourhoods, or by setting the \code{omax} in \code{krige} or \code{gstat} calls to the neighbourhood size to select {\em per octant} (this should be combined with specifying \code{maxdist}). %\section{Spatio-temporal simulation} \section*{References} \begin{itemize} \item Bivand, R., E. Pebesma and V. Gomez-Rubio, 2008. Applied Spatial Data Analysis with R. Springer. \item Cressie, N.A.C., 1993. Statistics for Spatial Data. Wiley. \item Cressie, N. and C. Wikle, 2011. Statistics for Spatio-temporal Data. Wiley. \item Pebesma, E., 2012. spacetime: Spatio-Temporal Data in R. Journal of Statistical Software, volume 51, issue 7; \href{http://www.jstatsoft.org/v51/i07/}{1-30}. \item Pebesma, E.J., Wesseling, C.G., 1998. Gstat, a program for geostatistical modelling, prediction and simulation. Computers \& Geosciences, 24 (1), pp. 17--31. \item Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers \& Geosciences \href{http://www.sciencedirect.com/science/journal/00983004}{30: 683-691} \item Ver Hoef, J.M., Cressie, N.A.C, 1993. Multivariable Spatial Prediction. Mathematical Geology, 25 (2), pp. 219--240. \end{itemize} \end{document} gstat/R/0000755000176200001440000000000014413347046011603 5ustar liggesusersgstat/R/set.R0000644000176200001440000000304313777370515012532 0ustar liggesusers# $Id: set.q,v 1.7 2008-12-16 14:59:22 edzer Exp $ gstat.set <- function(set) { if(!is.list(set)) stop("set should be a list") if (length(set) == 0) return(NULL) ret = NULL n = names(set) for (i in (1:length(set))) { val = set[[i]] if (n[i] == "method") str = paste("method: ", val, ";", sep="") else { if (is.character(val)) val = paste("'", val, "'", sep = "") str = paste("set ", n[i], " = ", val, ";", sep="") } ret = c(ret, str) } ret } gstat.load.set <- function(set) { if(!is.list(set)) stop("set should be a list") if (length(set) == 0) return(NULL) n = names(set) for (i in (1:length(set))) { if (n[i] == "method") ret = .Call(gstat_set_method, set[[i]]) else ret = .Call(gstat_set_set, n[i], set[[i]]) } invisible(ret) } gstat.load.merge <- function(obj) { if (is.character(obj$merge) && length(obj$merge) == 2) obj$merge = list(c(obj$merge[1], 1, obj$merge[2], 1)) if (!is.list(obj$merge)) stop("merge argument should be list or character vector of lenght 2") ret = NULL for (i in 1:length(obj$merge)) { m = obj$merge[[i]] if (is.character(m) && length(m) == 4) { id = match(m[c(1,3)], names(obj$data)) - 1 # name ->> id if (any(is.na(id))) stop(paste("could not match all ids:", m[c(1,3)])) col = as.integer(m[c(2,4)]) - 1 if (any(is.na(col)) || any(col < 0)) stop("merge: parameters should be positive integers") ret = .Call(gstat_set_merge, id[1], col[1], id[2], col[2]) } else stop( "list elements of merge should be lenght 4 character vectors") } ret } gstat/R/fit.variogram.R0000644000176200001440000000766614406630061014507 0ustar liggesusers# $Id: fit.variogram.q,v 1.10 2008-12-15 14:27:29 edzer Exp $ "fit.variogram" <- function (object, model, fit.sills = TRUE, fit.ranges = TRUE, fit.method = 7, debug.level = 1, warn.if.neg = FALSE, fit.kappa = FALSE) { cl = match.call() if (missing(object)) stop("nothing to fit to") if (!inherits(object, "gstatVariogram") && !inherits(object, "variogramCloud")) stop("object should be of class gstatVariogram or variogramCloud") if (inherits(object, "variogramCloud")) object$np = rep(1, nrow(object)) if (length(unique(object$id)) > 1) stop("to use fit.variogram, variogram object should be univariable") if (missing(model)) stop("no model to fit") if (is(model, "variogramModelList")) { ret = lapply(model, function(x) fit.variogram(object, x, fit.sills = fit.sills, fit.ranges = fit.ranges, fit.method = fit.method, debug.level = debug.level, warn.if.neg = warn.if.neg, fit.kappa = fit.kappa)) sse = sapply(ret, function(x) attr(x, "SSErr")) return(ret[[which.min(sse)]]) } if (!inherits(model, "variogramModel")) stop("model should be of class variogramModel (use vgm)") if (fit.method == 5) stop("use function fit.variogram.reml() to use REML") if (length(fit.sills) < length(model$model)) fit.sills = rep(fit.sills, length(model$model)) if (length(fit.ranges) < length(model$model)) fit.ranges = rep(fit.ranges, length(model$model)) if (fit.method == 7 && any(object$dist == 0)) stop("fit.method 7 will not work with zero distance semivariances; use another fit.method value") if (any(is.na(model$psill)) || any(is.na(model$range))) model = vgm_fill_na(model, object) fit.ranges = fit.ranges & !(model$model %in% c("Nug", "Err")) # no ranges to fit for Nug/Err if (isTRUE(fit.kappa)) fit.kappa = seq(0.3, 5, 0.1) if (any(model$model %in% c("Mat", "Ste")) && length(fit.kappa) > 1) { f = function(x, o, m) { m[m$model %in% c("Mat", "Ste"), "kappa"] = x fit.variogram(o, m, fit.kappa = FALSE, fit.method = fit.method, debug.level = debug.level) # fits range } ret = lapply(fit.kappa, f, object, model) return(ret[[ which.min(sapply(ret, function(x) attr(x, "SSErr"))) ]]) } initialRange = model$range .Call(gstat_init, as.integer(debug.level)) .Call(gstat_load_ev, object$np, object$dist, object$gamma) load.variogram.model(model) ret = .Call(gstat_fit_variogram, as.integer(fit.method), as.integer(fit.sills), as.integer(fit.ranges)) .Call(gstat_exit, 0) model$psill = ret[[1]] model$range = ret[[2]] attr(model, "singular") = as.logical(ret[[3]]); attr(model, "SSErr") = ret[[4]] direct = attr(object, "direct") if (!is.null(direct)) { id = unique(object$id) if (any(direct[direct$id == id, "is.direct"]) && any(model$psill < 0)) { if (warn.if.neg) warning("partial sill or nugget fixed at zero value") fit.sills = model$psill > 0 model$psill[model$psill < 0] = 0.0 model$range = initialRange return(fit.variogram(object, model, fit.sills = fit.sills, fit.ranges = fit.ranges, fit.method = fit.method, debug.level = debug.level, warn.if.neg = warn.if.neg, fit.kappa = fit.kappa)) } } if (attr(model, "singular") && debug.level) { rat = mean(object$gamma) / mean(object$dist) if (rat > 1e6 || rat < 1e-6) print("a possible solution MIGHT be to scale semivariances and/or distances") } attr(model, "call") = cl model } vgm_fill_na = function(model, obj) { if (any(is.na(model$range))) { model[model$model %in% c("Nug", "Err"), "range"] = 0 model[!model$model %in% c("Nug", "Err"), "range"] = max(obj$dist) / 3 } if (any(model$model %in% "Nug") && is.na(model[model$model == "Nug","psill"])) model[model$model == "Nug", "psill"] = mean(head(obj$gamma, 3)) na_sills = is.na(model[model$model != "Nug", "psill"]) if (any(na_sills)) { n = length(model[model$model != "Nug",]$psill) model[model$model != "Nug", "psill"] = mean(tail(obj$gamma, 5)) / n } model } gstat/R/krigeTg.R0000644000176200001440000000437313777370515013342 0ustar liggesusers# $Id: krigeTg.q,v 1.4 2009-07-07 15:42:39 edzer Exp $ phiInv <- function (x, lambda) if (lambda==0) log(x) else (x^lambda-1)/lambda phi <- function(x, lambda) if (lambda==0) exp(x) else (x*lambda+1)^(1/lambda) phiPrime <- function (x, lambda) if (lambda==0) exp(x) else (x*lambda+1)^(1/lambda-1) phiDouble <- function (x, lambda) if (lambda==0) exp(x) else lambda * (1/lambda - 1) * (lambda * x + 1)^(1/lambda-2) krigeTg <- function(formula, locations, newdata, model = NULL, ..., nmax = Inf, nmin = 0, maxdist = Inf, block = numeric(0), nsim = 0, na.action = na.pass, debug.level = 1, lambda = 1.0) { m = model.frame(terms(formula), as.data.frame(locations)) Y = model.extract(m, "response") if (length(Y) == 0) stop("no response variable present in formula") Terms = attr(m, "terms") X = model.matrix(Terms, m) has.intercept = attr(Terms, "intercept") if (ncol(X) > 1) stop("only formula with intercept allowed, e.g. y ~ 1") locations$value = phiInv(Y, lambda) locations$value1 = rep(1, length(locations$value)) OK = krige(value ~ 1, locations, newdata, model, nmax = nmax, nmin = nmin, maxdist = maxdist, block = block, nsim = nsim, na.action = na.action, debug.level = debug.level, ...) if (nsim > 0) { OK@data = as.data.frame(phi(OK@data,lambda)) return(OK) } # else: # estimate mu: g = gstat(formula = value ~ 1, # locations = locations, data = locations, model = model, nmax = nmax, nmin = nmin, maxdist = maxdist, ...) mu = predict(g, newdata = newdata, block = block, nsim = nsim, na.action = na.action, debug.level = debug.level, BLUE = TRUE) OK$muhat = mu$var1.pred SK = krige(value1 ~ 1, locations, newdata, model = model, beta = 0.0, nmax = nmax, nmin = nmin, maxdist = maxdist, block = block, nsim = nsim, na.action = na.action, debug.level = debug.level, ...) # find m: OK$m = (OK$var1.var - SK$var1.var)/(1 - SK$var1.pred) # copy SK output: OK$var1SK.pred = SK$var1.pred OK$var1SK.var = SK$var1.var # compute transGaussian kriging estimate & variance: OK$var1TG.pred = phi(OK$var1.pred, lambda) + phiDouble(mu$var1.pred, lambda) * (OK$var1.var/2 - OK$m) OK$var1TG.var = phiPrime(mu$var1.pred, lambda)^2 * OK$var1.var OK } gstat/R/fit.variogram.gls.R0000644000176200001440000001152413777370515015276 0ustar liggesusersfit.variogram.gls <- function(formula, data, model, maxiter = 30, eps = .01, trace = TRUE, ignoreInitial = TRUE, cutoff = Inf, plot = FALSE) { v = as.data.frame(variogram(formula, data, cloud = TRUE, cutoff = cutoff)) i = v$left j = v$right y = v$gamma h0 = v$dist dists = spDists(data) n = length(i) iter = 0 converged = FALSE if (model$model[1] == 'Nug') { if (ignoreInitial) init = c(mean(y)/2, mean(y)/2, median(h0)/4) else init = c(model$psill, model$range[2]) gamfn0 = function(h, th, m = as.character(model$model[2])) variogramLine(vgm(th[2], m, th[3], th[1]), dist_vector=h)$gamma minfuncols0 = function(theta=rbind(1,1,1)) { res = y-gamfn0(h0,theta) sum(res^2) } # If variogram is Power model, maximum range should be 2. # Also if ignoreInitial change initial value of range to 1 if (any(model$model == 'Pow')) { upperOptim <- c(max(y), max(y), 2) if (ignoreInitial) init[3] <- 1 } else upperOptim = c(max(y), max(y), max(h0)) th = th0 = th.ols = optim(init, minfuncols0, gr=NULL, method="L-BFGS-B", lower=c(0,1e-9,1e-9), upper=upperOptim)$par if (trace) print(th) while (!converged && iter < maxiter) { comb = function(i,j) cbind(rep(i,length(j)), rep(j,each=length(i))) cov = matrix( variogramLine(model, dist_vector = dists[comb(i,i)])$gamma + variogramLine(model, dist_vector = dists[comb(j,j)])$gamma - variogramLine(model, dist_vector = dists[comb(i,j)])$gamma - variogramLine(model, dist_vector = dists[comb(j,i)])$gamma, length(j), length(j)) cov = 0.5 * cov ^ 2 #cov = solve(cov) cov = qr(cov) minfuncrange = function(range) { res = y-gamfn0(h0,c(th[1],th[2],range)) t(res) %*% solve(cov, res) } minfuncsill = function(sill) { res = y-gamfn0(h0, c(th[1],sill,th[3])) t(res) %*% solve(cov, res) } minfuncnugget = function(nugget) { res = y - gamfn0(h0, c(nugget, th[2], th[3])) t(res) %*% solve(cov, res) } th0 = th # Avoid calculating max every time th[1] = optimize(minfuncnugget,lower=0,upper=upperOptim[1])$minimum th[2] = optimize(minfuncsill,lower=1e-9,upper=upperOptim[2])$minimum th[3] = optimize(minfuncrange,lower=1e-9,upper=upperOptim[3])$minimum converged = sum(abs((th - th0)/th0)) < eps iter = iter + 1 if (trace) print(th) model$psill = c(th[1], th[2]) model$range[2] = th[3] } if (th[3] / max(h0) > .99) warning("range parameter at search space boundary") if (!converged) { warning("no convergence, returning OLS solution") th = th.ols model$psill = c(th[1], th[2]) model$range[2] = th[3] } } else { # No Nugget component. Use only psill = th[1] and range = th[2] parameters if (ignoreInitial) init = c(mean(y)/2, median(h0)/4) else init = c(model$psill, model$range) gamfn = function(h, th, m = as.character(model$model)) variogramLine(vgm(psill = th[1], model = m, range = th[2]), dist_vector=h)$gamma minfuncols = function(theta=rbind(1,1)) { res = y-gamfn(h0,theta) sum(res^2) } # If variogram is Power model, maximum range should be 2. # Also if ignoreInitial change initial value of range to 1 if (any(model$model == 'Pow')) { upperOptim <- c(max(y), 2) if (ignoreInitial) init[2] <- 1 } else { upperOptim = c(max(y), max(h0)) } th = th0 = th.ols = optim(init, minfuncols,gr=NULL, method="L-BFGS-B", lower=c(1e-9,1e-9), upper=upperOptim)$par if (trace) print(th) while (!converged && iter < maxiter) { comb = function(i,j) cbind(rep(i,length(j)), rep(j,each=length(i))) cov = matrix( variogramLine(model, dist_vector = dists[comb(i,i)])$gamma + variogramLine(model, dist_vector = dists[comb(j,j)])$gamma - variogramLine(model, dist_vector = dists[comb(i,j)])$gamma - variogramLine(model, dist_vector = dists[comb(j,i)])$gamma, length(j), length(j)) cov = 0.5 * cov ^ 2 #cov = solve(cov) cov = qr(cov) minfuncrange = function(range) { res = y-gamfn(h0,c(th[1],range)) t(res) %*% solve(cov, res) } minfuncsill = function(sill) { res = y-gamfn(h0, c(sill,th[2])) t(res) %*% solve(cov, res) } th0 = th th[1] = optimize(minfuncsill,lower=1e-9,upper=upperOptim[1])$minimum th[2] = optimize(minfuncrange,lower=1e-9,upper=upperOptim[2])$minimum converged = sum(abs((th - th0)/th0)) < eps iter = iter + 1 if (trace) print(th) model$psill = th[1] model$range = th[2] } if (th[2] / max(h0) > .99) warning("range parameter at search space boundary") if (!converged) { warning("no convergence, returning OLS solution") th = th.ols model$psill = th[1] model$range = th[2] } } if (plot) plot(variogram(formula, data, cloud = TRUE, cutoff = cutoff), model = model) else model } gstat/R/gstat.formula.R0000644000176200001440000000152513777370515014530 0ustar liggesusers# $Id: gstat.formula.q,v 1.8 2007-06-08 06:45:52 edzer Exp $ "gstat.formula" <- function (formula, data) { # check for duplicated pixels; if yes coerce to SpatialPointsDataFrame: if (is(data, "SpatialPixels") && anyDuplicated(data@grid.index) != 0) gridded(data) = FALSE m = model.frame(terms(formula), as(data, "data.frame"), na.action = na.fail) Y = model.extract(m, "response") if (length(Y) == 0) stop("no response variable present in formula") Terms = attr(m, "terms") X = model.matrix(Terms, m) has.intercept = attr(Terms, "intercept") if (gridded(data)) grid = gridparameters(data) else grid = numeric(0) xlevels = .getXlevels(Terms, m) list(y = Y, locations = coordinates(data), X = X, call = call, has.intercept = has.intercept, grid = as.double(unlist(grid)), xlevels = xlevels) } gstat/R/krigeST.R0000644000176200001440000004452414314525261013304 0ustar liggesusers############################# ## spatio-temporal kriging ## ############################# debug_time_unit = function(tUnit) { # message("Using the following time unit: ", tUnit) } STsolve = function(A, b, X) { # V = A$T %x% A$S -- a separable covariance; solve A x = b for x # kronecker: T %x% S vec(L) = vec(c0) <--> S L T = c0 # solve for L: use Y = L T # S Y = c0 -> Y = solve(S, c0) # L T = Y -> Tt Lt = Yt -> Lt = solve(Tt, Yt) #Tm = chol(A$Tm, LINPACK=TRUE) Tm = chol(A$Tm) #Sm = chol(A$Sm, LINPACK=TRUE) Sm = chol(A$Sm) STbacksolve = function(Tm, Cm, Sm) { MyChSolve = function(A, b) backsolve(A, forwardsolve(A, b, upper.tri = TRUE, transpose = TRUE)) # Y = MyChSolve(Sm, Cm) # L = MyChSolve(Tm, t(Y)) # as.vector(t(L)) as.vector(t(MyChSolve(Tm, t(MyChSolve(Sm, Cm))))) } # b comes separated: ret1 = apply(b$T, 2, function(x1) apply(b$S, 2, function(x2) STbacksolve(Tm, matrix(x1 %x% x2, nrow(Sm), nrow(Tm)), Sm))) d = dim(ret1) dim(ret1) = c(d[1] / ncol(b$S), d[2] * ncol(b$S)) # X comes full: ret2 = apply(X, 2, function(x) STbacksolve(Tm, matrix(x, nrow(Sm), nrow(Tm)), Sm)) cbind(ret1, ret2) } covfn.ST = function(x, y = x, model, ...) { switch(strsplit(model$stModel, "_")[[1]][1], separable=covSeparable(x, y, model, ...), productSumOld=covProdSumOld(x, y, model), productSum=covProdSum(x, y, model), sumMetric=covSumMetric(x, y, model), simpleSumMetric=covSimpleSumMetric(x, y, model), metric=covMetric(x, y, model), stop(paste("Provided spatio-temporal model (",model$stModel,") is not supported.",sep=""))) } ## krigeST krigeST <- function(formula, data, newdata, modelList, beta, y, ..., nmax=Inf, stAni=NULL, computeVar = FALSE, fullCovariance = FALSE, bufferNmax=2, progress=TRUE) { stopifnot(inherits(modelList, "StVariogramModel") || is.function(modelList)) to_sftime = FALSE return_stars = if (inherits(data, c("stars"))) { if (!requireNamespace("sf", quietly = TRUE)) stop("sf required: install that first") # nocov if (!requireNamespace("stars", quietly = TRUE)) stop("stars required: install that first") # nocov if (sf::st_crs(data) != sf::st_crs(newdata)) warning("CRS for data and newdata are not identical; assign CRS or use st_transform to correct") data = as(data, "STFDF") newdata = as(newdata, "STFDF") TRUE } else if (inherits(data, "sftime")) { if (sf::st_crs(data) != sf::st_crs(newdata)) warning("CRS for data and newdata are not identical; assign CRS or use st_transform to correct") data = as(data, "STIDF") if (inherits(newdata, "stars")) { if (length(newdata) == 0) newdata$._dummy = 0. newdata = as(newdata, "STFDF") } if (inherits(newdata, "sftime")) { to_sftime = TRUE newdata = as(newdata, "STIDF") } TRUE } else { if (!identical(data@sp@proj4string@projargs, newdata@sp@proj4string@projargs)) message("please verify that the CRSs of data and newdata are identical, or transform them first to make them identical") FALSE } stopifnot(inherits(data, c("STF", "STS", "STI", "sftime")) && inherits(newdata, c("STF", "STS", "STI", "sftime"))) if (inherits(data, "sftime")) data = as(data, "STIDF") if (inherits(newdata, "sftime")) data = as(data, "STI") stopifnot(class(data@time) == class(newdata@time)) stopifnot(nmax > 0) tUnitModel <- attr(modelList, "temporal unit") tUnitData <- units(abs(outer(index(data@time[1]), index(newdata@time[1]), "-"))) if (is.null(tUnitModel)) { warning("The spatio-temporal variogram model does not carry the strongly recommended attribute 'temporal unit'.\n The unit '", tUnitData, "' has been assumed. krigeST could not check whether the temporal distances between locations and in the variogram coincide.") tUnit <- tUnitData attr(modelList, "temporal unit") <- tUnit } else { tUnit <- tUnitModel debug_time_unit(tUnit) } if(nmax < Inf) { # local neighbourhood ST kriging: ret = krigeST.local( formula = formula, data = data, newdata = newdata, modelList = modelList, beta=beta, # y=y, # for later use nmax = nmax, stAni = stAni, computeVar = computeVar, fullCovariance = fullCovariance, bufferNmax = bufferNmax, progress = progress) if (return_stars) { ret$._dummy = NULL if (to_sftime) sftime::st_as_sftime(ret) else stars::st_as_stars(as(ret, "STFDF")) } else ret } else { df <- krigeST.df(formula = formula, data = data, newdata = newdata, modelList = modelList, beta = beta, y = y, ..., nmax=nmax, stAni=stAni, computeVar = computeVar, fullCovariance = fullCovariance, bufferNmax = bufferNmax, progress = progress) # wrapping the predictions in ST*DF again if (!fullCovariance) { ret = addAttrToGeom(geometry(newdata), df) if (return_stars) { ret$._dummy = NULL if (to_sftime) ret = sftime::st_as_sftime(ret) else ret = stars::st_as_stars(as(ret, "STFDF")) } ret } else df } } krigeST.df <- function(formula, data, newdata, modelList, beta, y, ..., nmax = Inf, stAni = NULL, computeVar = FALSE, fullCovariance = FALSE, bufferNmax = 2, progress = TRUE) { separate <- length(data) > 1 && length(newdata) > 1 && inherits(data, "STF") && inherits(newdata, "STF") lst = extractFormula(formula, data, newdata) X = lst$X x0 = lst$x0 if (missing(y)) y = lst$y if (inherits(modelList, "StVariogramModel")) { V = covfn.ST(data, model = modelList, separate=separate) v0 = covfn.ST(data, newdata, modelList) if (is(data,"STSDF")) d0 <- data[data@index[1,1], data@index[1,2], drop = FALSE] else d0 = data[1, 1, drop=FALSE] c0 = as.numeric(covfn.ST(d0, d0, modelList, separate = FALSE)) } else { V = modelList(data, data, ...) v0 = modelList(data, newdata, ...) if (computeVar) { if (is(newdata@sp, "SpatialLines") || is(newdata@sp, "SpatialPolygons")) stop("Varying target support (SpatialLines, SpatialPolygons) for kriging variance is not implemented.") c0 = as.numeric(modelList(newdata[1, drop=FALSE], newdata[1, drop=FALSE])) } } if (!missing(beta)) { # sk: skwts = CHsolve(V, v0) npts = length(newdata) ViX = skwts[,-(1:npts)] skwts = skwts[,1:npts] if (computeVar) var <- c0 - apply(v0*skwts, 2, sum) } else { if (!is.function(modelList) && (modelList$stModel == "separable" & separate)) skwts <- STsolve(V, v0, X) # use Kronecker trick else skwts <- CHsolve(V, cbind(v0, X)) npts = length(newdata) ViX = skwts[,-(1:npts)] skwts = skwts[,1:npts] beta = solve(t(X) %*% ViX, t(ViX) %*% y) if (computeVar) { # get (x0-X'C-1 c0)'(X'C-1X)-1 (x0-X'C-1 c0) -- precompute term 1+3: if(is.list(v0)) # in the separable case v0 = v0$Tm %x% v0$Sm Q = t(x0) - t(ViX) %*% v0 # suggested by Marius Appel var = c0 - apply(v0 * skwts, 2, sum) + apply(Q * CHsolve(t(X) %*% ViX, Q), 2, sum) if (fullCovariance) { corMat <- cov2cor(covfn.ST(newdata, newdata, modelList)) var <- corMat*matrix(sqrt(var) %x% sqrt(var), nrow(corMat), ncol(corMat)) # var = c0 - t(v0) %*% skwts + t(Q) %*% CHsolve(t(X) %*% ViX, Q) # return(list(pred=pred, var=var)) } } } pred = x0 %*% beta + t(skwts) %*% (y - X %*% beta) if(computeVar) { if (fullCovariance) list(pred=pred, var=var) else data.frame(var1.pred = pred, var1.var = var) } else data.frame(var1.pred = pred) } # local spatio-temporal kriging krigeST.local <- function(formula, data, newdata, modelList, beta, nmax, stAni=NULL, computeVar=FALSE, fullCovariance=FALSE, bufferNmax=2, progress=TRUE) { dimGeom <- ncol(coordinates(data)) if (fullCovariance) stop("fullCovariance cannot be returned for local ST kriging") if(is.null(stAni) & !is.null(modelList$stAni)) { stAni <- modelList$stAni # scale stAni [spatial/temporal] to seconds if(!is.null(attr(modelList,"temporal unit"))) stAni <- stAni/switch(attr(modelList, "temporal unit"), secs=1, mins=60, hours=3600, days=86400, stop("Temporal unit",attr(modelList, "temporal unit"),"not implemented.")) } if(is.null(stAni)) stop("The spatio-temporal model does not provide a spatio-temporal anisotropy scaling nor is the parameter stAni provided. One of these is necessary for local spatio-temporal kriging.") # check whether the model meets the coordinates' unit if(!is.null(attr(modelList, "spatial unit"))) stopifnot((is.projected(data) & (attr(modelList, "spatial unit") %in% c("km","m"))) | (!is.projected(data) & !(attr(modelList, "spatial unit") %in% c("km","m")))) if (inherits(data, c("STFDF", "STSDF", "sftime"))) data <- as(data, "STIDF") clnd <- class(newdata) if(inherits(newdata, c("STFDF", "STSDF", "sftime"))) newdata <- as(newdata, "STIDF") if(inherits(newdata, c("STF", "STS"))) newdata <- as(newdata, "STI") # from here on every data set is assumed to be STI* if(dimGeom == 2) { df = as(data, "data.frame")[,c(1,2,4)] df$time = as.numeric(df$time)*stAni query = as(newdata, "data.frame")[,c(1,2,4)] query$time = as.numeric(query$time)*stAni } else { df = as(data, "data.frame")[,c(1,2,3,5)] df$time = as.numeric(df$time)*stAni query = as(newdata, "data.frame")[,c(1,2,3,5)] query$time = as.numeric(query$time)*stAni } df <- as.matrix(df) query <- as.matrix(query) if (computeVar) { res <- data.frame(var1.pred = rep(NA, nrow(query)), var1.var = rep(NA, nrow(query))) } else { res <- data.frame(var1.pred = rep(NA, nrow(query))) } if(progress) pb = txtProgressBar(style = 3, max = nrow(query)) nb <- t(apply(get.knnx(df, query, ceiling(bufferNmax*nmax))[[1]],1,sort)) for (i in 1:nrow(query)) { nghbrData <- data[nb[i, ], , drop = FALSE] if(bufferNmax > 1) { nghbrCov <- covfn.ST(nghbrData, newdata[i, , drop = FALSE], modelList) nghbrData <- nghbrData[sort(order(nghbrCov, decreasing=T)[1:nmax]), , drop = FALSE] } res[i,] <- krigeST.df(formula, nghbrData, newdata[i, , drop = FALSE], modelList, computeVar=computeVar, beta = beta, fullCovariance=fullCovariance) if(progress) setTxtProgressBar(pb, i) } if(progress) close(pb) if (clnd %in% c("STI", "STS", "STF")) { newdata <- addAttrToGeom(newdata, as.data.frame(res)) newdata <- switch(clnd, STI = as(newdata, "STIDF"), STS = as(newdata, "STSDF"), STF = as(newdata, "STFDF")) } else { newdata@data <- cbind(newdata@data, res) newdata <- as(newdata, clnd) } newdata } ## Area to point kriging # define a spatio-temporal variogram model FUNCTION that can deal with x and y # being of ST* with @sp of class SpatialPolygons OR SpatialPoints; # SpatialGrid/Pixels are coerced to SpatialPolygons -- as in the so case, see # krige0.R # sts <- STS(meuse.grid, stf@time, cbind(sort(sample(length(meuse.grid), 500, replace = T)), # sample(21,500, replace=TRUE))) # # x <- sts # y <- stf # model <- separableModel vgmAreaST = function(x, y = x, model, ndiscrSpace = 16, verbose = FALSE, covariance = TRUE) { if (gridded(x@sp)) x@sp = as(x@sp, "SpatialPolygons") if (gridded(y@sp)) y@sp = as(y@sp, "SpatialPolygons") stopifnot(is(x@sp, "SpatialPolygons") || is(x@sp, "SpatialPoints")) stopifnot(is(y@sp, "SpatialPolygons") || is(y@sp, "SpatialPoints")) stopifnot(is(model, "StVariogramModel")) # make x and y both of type STS/STSDF if ("data" %in% slotNames(x)) { x <- as(x, "STSDF") } else { x <- as(x, "STS") } if ("data" %in% slotNames(y)) { y <- as(y, "STSDF") } else { y <- as(y, "STS") } nx = length(x) ny = length(y) V <- matrix(NA, nx, ny) # switch cases for polygons in x and y if (is(x@sp, "SpatialPolygons")) { # x contains polygons -> loop and sample indexX <- x@index if (verbose) pb <- txtProgressBar(style = 3, max = nx) for (ix in 1:nx) { # ix <- 1 px <- x[indexX[ix,,drop=F],drop=F] ptsx = STF(spsample(px@sp, ndiscrSpace, "regular", offset = c(.5,.5)), px@time, px@endTime) # does y also contain polygons? if (is(y@sp, "SpatialPolygons")) { # yes, also y contains polygons -> loop and sample indexY <- y@index for (iy in 1:ny) { # iy <- 1 py <- y[indexY[iy,,drop=F],drop=F] ptsy = STF(spsample(py@sp, ndiscrSpace, "regular", offset = c(.5,.5)), py@time, py@endTime) suppressMessages(subV <- covfn.ST(ptsx, ptsy, model, separate=FALSE)) V[ix, iy] <- mean(subV) } } else { # no, y contains points -> no second loop, calc covariance suppressMessages(subV <- covfn.ST(ptsx, y, model, separate=FALSE)) V[ix, ] <- apply(subV, 2, mean) } if (verbose) setTxtProgressBar(pb, ix) } if (verbose) close(pb) } else { # none of x and y contain polygons -> no loops, calc covariance suppressMessages(V <- covfn.ST(x, y, model)) } V } #################### ## trans Gaussian ## #################### krigeSTTg <- function(formula, data, newdata, modelList, y, nmax=Inf, stAni=NULL, bufferNmax=2, progress=TRUE, lambda = 0) { if(!is.infinite(nmax)) return(krigeSTTg.local(formula, data, newdata, modelList, y, nmax, stAni, bufferNmax, progress, lambda)) lst <- extractFormula(formula, data, newdata) Y <- lst$y X <- lst$X if (ncol(X) > 1) stop("only formula with intercept allowed, e.g. y ~ 1") data$value = phiInv(Y, lambda) data$value1 = rep(1, length(data$value)) OK = krigeST(value ~ 1, data, newdata, modelList, nmax = nmax, stAni = stAni, computeVar=TRUE, bufferNmax = bufferNmax, progress = progress) separate <- length(data) > 1 && length(newdata) > 1 && inherits(data, "STF") && inherits(newdata, "STF") V <- covfn.ST(data, model = modelList, separate=separate) Vi <- solve(V) muhat <- sum(Vi %*% data$value)/sum(Vi) # find m: v0 <- covfn.ST(data, newdata, model = modelList, separate=separate) m <- (1 - apply(Vi %*% v0,2,sum))/sum(Vi) # compute transGaussian kriging estimate & variance: OK$var1TG.pred = phi(OK$var1.pred, lambda) + phiDouble(muhat, lambda) * (OK$var1.var/2 - m) OK$var1TG.var = phiPrime(muhat, lambda)^2 * OK$var1.var OK } krigeSTTg.local <- function(formula, data, newdata, modelList, y, nmax=Inf, stAni=NULL, bufferNmax=2, progress=TRUE, lambda = 0) { stopifnot(!is.infinite(nmax)) dimGeom <- ncol(coordinates(data)) if(is.null(stAni) & !is.null(modelList$stAni)) { stAni <- modelList$stAni # scale stAni [spatial/temporal] to seconds if(!is.null(attr(modelList,"temporal unit"))) stAni <- stAni/switch(attr(modelList, "temporal unit"), secs=1, mins=60, hours=3600, days=86400, stop("Temporal unit",attr(modelList, "temporal unit"),"not implemented.")) } if(is.null(stAni)) stop("The spatio-temporal model does not provide a spatio-temporal anisotropy scaling nor is the parameter stAni provided. One of these is necessary for local spatio-temporal kriging.") # check whether the model meets the coordinates' unit if(!is.null(attr(modelList, "spatial unit"))) stopifnot((is.projected(data) & (attr(modelList, "spatial unit") %in% c("km","m"))) | (!is.projected(data) & !(attr(modelList, "spatial unit") %in% c("km","m")))) if(is(data, "STFDF") || is(data, "STSDF")) data <- as(data, "STIDF") clnd <- class(newdata) if(is(newdata, "STFDF") || is(newdata, "STSDF")) newdata <- as(newdata, "STIDF") if(is(newdata, "STF") || is(newdata, "STS")) newdata <- as(newdata, "STI") # from here on every data set is assumed to be STI* if(dimGeom == 2) { df = as(data, "data.frame")[,c(1,2,4)] df$time = as.numeric(df$time)*stAni query = as(newdata, "data.frame")[,c(1,2,4)] query$time = as.numeric(query$time)*stAni } else { df = as(data, "data.frame")[,c(1,2,3,5)] df$time = as.numeric(df$time)*stAni query = as(newdata, "data.frame")[,c(1,2,3,5)] query$time = as.numeric(query$time)*stAni } df <- as.matrix(df) query <- as.matrix(query) res <- data.frame(var1.pred = rep(NA, nrow(query)), var1.var = rep(NA, nrow(query)), var1TG.pred = rep(NA, nrow(query)), var1TG.var = rep(NA, nrow(query))) if(progress) pb = txtProgressBar(style = 3, max = nrow(query)) nb <- t(apply(get.knnx(df, query, ceiling(bufferNmax*nmax))[[1]],1,sort)) for (i in 1:nrow(query)) { nghbrData <- data[nb[i, ], , drop = FALSE] if(bufferNmax > 1) { nghbrCov <- covfn.ST(nghbrData, newdata[i, , drop = FALSE], modelList) nghbrData <- nghbrData[sort(order(nghbrCov, decreasing=T)[1:nmax]), , drop = FALSE] } res[i,] <- krigeSTTg(formula, nghbrData, newdata[i, , drop = FALSE], modelList, lambda)@data if(progress) setTxtProgressBar(pb, i) } if(progress) close(pb) if (clnd %in% c("STI", "STS", "STF")) { newdata <- addAttrToGeom(newdata, as.data.frame(res)) newdata <- switch(clnd, STI = as(newdata, "STIDF"), STS = as(newdata, "STSDF"), STF = as(newdata, "STFDF")) } else { newdata@data <- cbind(newdata@data, res) newdata <- as(newdata, clnd) } newdata } gstat/R/panel.pointPairs.R0000644000176200001440000000206113777370515015164 0ustar liggesusers# $Id: panel.pointPairs.q,v 1.3 2008-03-10 10:00:10 edzer Exp $ "panel.pointPairs" <- function (x, y, type = "p", pch = plot.symbol$pch, col, col.line = plot.line$col, col.symbol = plot.symbol$col, lty = plot.line$lty, cex = plot.symbol$cex, lwd = plot.line$lwd, pairs = pairs, line.pch = line.pch, ...) { x = as.numeric(x) y = as.numeric(y) if (length(x) > 0) { if (!missing(col)) { if (missing(col.line)) col.line = col if (missing(col.symbol)) col.symbol = col } plot.symbol = trellis.par.get("plot.symbol") plot.line = trellis.par.get("plot.line") lpoints(x = x, y = y, cex = cex, col = col.symbol, pch = pch, ...) if (!missing(pairs)) { for (i in seq(along = pairs[,1])) { xx = c(x[pairs[i,1]], x[pairs[i,2]]) yy = c(y[pairs[i,1]], y[pairs[i,2]]) llines(x = xx, y = yy, lty = lty, col = col.line, lwd = lwd) if (line.pch > 0) lpoints(mean(xx), mean(yy), pch = line.pch, col = col.line) } } } } gstat/R/zzz.R0000644000176200001440000000066613777370515012604 0ustar liggesusers# $Id: zzz.q,v 1.10 2006-02-10 19:01:07 edzer Exp $ ### NAMESPACE VERSION: .onLoad <- function(lib, pkg) { # remove the require() call for 2.0.0: # require(lattice) # .Call(gstat_init, as.integer(1)) } ### pre-NAMESPACE VERSION: ## ".First.lib" <- ## function(lib, pkg) { ## require(lattice) ## library.dynam("gstat", pkg, lib) ## .Call(gstat_init, as.integer(1)) ## } variogram <- function(object, ...) UseMethod("variogram") gstat/R/gstat.formula.predict.R0000644000176200001440000000427114002373634016145 0ustar liggesusers# $Id: gstat.formula.predict.q,v 1.14 2008-02-19 10:01:22 edzer Exp $ "gstat.formula.predict" <- function (formula, newdata, na.action, BLUE.estimates = FALSE, xlev = NULL) { if (is(newdata, "SpatialPolygons")) { # locs = coordinates(getSpatialPolygonsLabelPoints(newdata)) -- deprecated, now use: locs = t(sapply(slot(newdata, "polygons"), function(x) slot(x, "labpt"))) SpatialPoints(locs, slot(newdata, "proj4string")) locs = coordinates(locs) colnames(locs) = c("x", "y") if (is(newdata, "SpatialPolygonsDataFrame")) newdata = as.data.frame(newdata) else newdata = data.frame(a = rep(1, nrow(locs))) } else if (is(newdata, "SpatialLines")) { # locs = coordinates(getSpatialLinesMidPoints(newdata)) -- deprecated, now use: ret = lapply(newdata@lines, function(x) sapply(x@Lines, function(X) apply(X@coords, 2, mean) ) ) ret = t(sapply(ret, function(x) apply(x, 1, mean))) locs = coordinates(SpatialPoints(ret, slot(newdata, "proj4string"))) colnames(locs) = c("x", "y") if (is(newdata, "SpatialLinesDataFrame")) newdata = as.data.frame(newdata) else newdata = data.frame(a = rep(1, nrow(locs))) } else { if (gridded(newdata)) fullgrid(newdata) = FALSE locs = coordinates(newdata) newdata = as.data.frame(newdata) } # resolve formula: terms.f = delete.response(terms(formula)) mf.f = model.frame(terms.f, newdata, na.action = na.action, xlev = xlev) X = model.matrix(terms.f, mf.f) if (BLUE.estimates) { # fake the whole thing to get a matrix with BLUE parameter estimates: cnames = colnames(X) X = matrix(0, ncol(X), ncol(X)) diag(X) = 1 locs = locs[1,,drop=FALSE] if (ncol(X) > 1) { for (i in 2:ncol(X)) locs = rbind(locs, locs[1,]) } rownames(locs) = cnames } if (NROW(locs) != NROW(X)) { # NA's were filtered in X, but not in coords: mf.f = model.frame(terms.f, newdata, na.action = na.pass) valid.pattern = !(apply(mf.f, 1, function(x) any(is.na(x)))) X = model.matrix(terms.f, mf.f[valid.pattern, , drop = FALSE]) locs = locs[valid.pattern, ] if (NROW(locs) != NROW(X)) stop("NROW(locs) != NROW(X): this should not occur") } list(locations = as.matrix(locs), X = as.matrix(X)) } gstat/R/print.variogram.R0000644000176200001440000000021213777370515015054 0ustar liggesusers# $Id: print.variogram.q,v 1.3 2006-02-10 19:01:07 edzer Exp $ "print.gstatVariogram" <- function(x, ...) { print(data.frame(x), ...) } gstat/R/krige0.R0000644000176200001440000001064414147167560013121 0ustar liggesusersextractFormula = function(formula, data, newdata) { # extract y and X from data: m = model.frame(terms(formula), as(data, "data.frame"), na.action = na.fail) y = model.extract(m, "response") if (length(y) == 0) stop("no response variable present in formula") Terms = attr(m, "terms") X = model.matrix(Terms, m) # extract x0 from newdata: terms.f = delete.response(terms(formula)) mf.f = model.frame(terms.f, newdata) #, na.action = na.action) x0 = model.matrix(terms.f, mf.f) list(y = y, X = X, x0 = x0) } idw0 = function(formula, data, newdata, y, idp = 2.0) { s = coordinates(data) s0 = coordinates(newdata) if (missing(y)) y = extractFormula(formula, data, newdata)$y D = 1.0 / (spDists(s0, s) ^ idp) sumD = apply(D, 1, sum) D %*% y / sumD } CHsolve = function(A, b) { # solves A x = b for x if A is PD symmetric #A = chol(A, LINPACK=TRUE) -> deprecated A = chol(A) # but use pivot=TRUE? backsolve(A, forwardsolve(A, b, upper.tri = TRUE, transpose = TRUE)) } krige0 <- function(formula, data, newdata, model, beta, y, ..., computeVar = FALSE, fullCovariance = FALSE) { if (inherits(data, "ST")) stopifnot(identical(data@sp@proj4string@projargs, newdata@sp@proj4string@projargs)) else stopifnot(identical(data@proj4string@projargs, newdata@proj4string@projargs)) lst = extractFormula(formula, data, newdata) X = lst$X x0 = lst$x0 if (missing(y)) y = lst$y ll = (!is.na(is.projected(data)) && !is.projected(data)) s = coordinates(data) s0 = coordinates(newdata) if (is(model, "variogramModel")) { require(gstat) V = variogramLine(model, dist_vector = spDists(s, s, ll), covariance = TRUE) v0 = variogramLine(model, dist_vector = spDists(s, s0, ll), covariance = TRUE) c0 = variogramLine(model, dist_vector = c(0), covariance = TRUE)$gamma } else { V = model(data, data, ...) v0 = model(data, newdata, ...) if (computeVar) { if (is(newdata, "SpatialLines") || is(newdata, "SpatialPolygons")) stop("varying target support (SpatialLines, SpatialPolygons) is not implemented") c0 = as.numeric(model(newdata[1, drop=FALSE], newdata[1, drop=FALSE])) # ?check this: provide TWO arguments, so model(x,y) can target # eventually Y, instead of measurements Z=Y+e # with e measurement error term e } } if (!missing(beta)) { # sk: skwts = CHsolve(V, v0) if (computeVar) var <- c0 - apply(v0*skwts, 2, sum) } else { # ok/uk -- need to estimate beta: skwts = CHsolve(V, cbind(v0, X)) ViX = skwts[,-(1:nrow(s0))] skwts = skwts[,1:nrow(s0)] beta = solve(t(X) %*% ViX, t(ViX) %*% y) if (computeVar) { Q = t(x0) - t(ViX) %*% v0 var <- c0 - apply(v0*skwts, 2, sum) + apply(Q * CHsolve(t(X) %*% ViX, Q), 2, sum) } } pred = x0 %*% beta + t(skwts) %*% (y - X %*% beta) if (computeVar) { if (fullCovariance) { corMat <- cov2cor(variogramLine(model, dist_vector = spDists(s0, s0), covariance = TRUE)) var <- corMat*matrix(sqrt(var) %x% sqrt(var), nrow(corMat), ncol(corMat)) } list(pred = pred, var = var) } else pred } # define variogram model FUNCTION that can deal with x and y # being of class SpatialPolygons OR SpatialPoints; SpatialGrid/Pixels are coerced to SpatialPolygons vgmArea = function(x, y = x, vgm, ndiscr = 16, verbose = FALSE, covariance = TRUE) { if (gridded(x)) x = as(x, "SpatialPolygons") if (gridded(y)) y = as(y, "SpatialPolygons") stopifnot(is(x, "SpatialPolygons") || is(x, "SpatialPoints")) stopifnot(is(y, "SpatialPolygons") || is(y, "SpatialPoints")) stopifnot(is(vgm, "variogramModel")) nx = length(x) ny = length(y) V = matrix(NA, nx, ny) if (verbose) pb = txtProgressBar(style = 3, max = nx) for (i in 1:nx) { if (is(x, "SpatialPolygons")) px = spsample(x[i,], ndiscr, "regular", offset = c(.5,.5)) else px = x[i,] for (j in 1:ny) { if (is(y, "SpatialPolygons")) py = spsample(y[j,], ndiscr, "regular", offset = c(.5,.5)) else py = y[j,] D = spDists(px, py) D[D == 0] = 1e-10 V[i,j] = mean(variogramLine(vgm, dist_vector = D, covariance = covariance)) } if (verbose) setTxtProgressBar(pb, i) } if (verbose) close(pb) V } gstat/R/print.variogramModel.R0000644000176200001440000000130013777370515016034 0ustar liggesusers# $Id: print.variogramModel.q,v 1.5 2009-02-20 13:53:38 edzer Exp $ "print.variogramModel" = function (x, ...) { df = data.frame(x) shape.models = c("Mat", "Exc", "Cau", "Ste") if (!any(match(df[, "model"], shape.models, nomatch=0))) df$kappa = NULL if (!any(df[, "anis2"] != 1)) { df$anis2 = NULL df$ang2 = NULL df$ang3 = NULL if (!any(df[, "anis1"] != 1)) { df$anis1 = NULL df$ang1 = NULL } } if (any(match(df[, "model"], "Tab", nomatch=0))) { df$maxdist = df$range df$range = NULL print(df, ...) cat("covariance table:\n") tab = attr(x, "table") idx = round(seq(1, length(tab), length=6)) print(tab[idx]) } else print(df, ...) invisible(x) } gstat/R/plot.gstatVariogram.R0000644000176200001440000001130613777370515015707 0ustar liggesusers# $Id: plot.gstatVariogram.q,v 1.15 2007-06-08 18:03:25 edzer Exp $ "plot.gstatVariogram" <- function (x, model = NULL, ylim, xlim, xlab = "distance", ylab = attr(x, "what"), panel = vgm.panel.xyplot, multipanel = TRUE, plot.numbers = FALSE, scales = list(), ids = x$id, group.id = TRUE, skip, layout, ...) { if (missing(ylim)) { ylim = c(min(0, 1.04 * min(x$gamma)), 1.04 * max(x$gamma)) ylim.set = FALSE } else ylim.set = TRUE if (missing(xlim)) xlim = c(0, 1.04 * max(x$dist)) labels = NULL shift = 0.03 if (is.numeric(plot.numbers)) { shift = plot.numbers plot.numbers = TRUE } if (plot.numbers == TRUE) labels = as.character(x$np) if (length(unique(x$dir.ver)) > 1 || any(x$dir.ver != 0)) warning("vertical directions are not dealt with -- yet!") if (length(unique(x$dir.hor)) > 1 && group.id == TRUE) { # directional, grouped: if (multipanel) { if (length(levels(ids)) > 1) { # multivariate directional: xyplot(gamma ~ dist | as.factor(dir.hor), data = x, type = c("p", "l"), xlim = xlim, ylim = ylim, xlab = xlab, ylab = ylab, groups = ids, scales = scales, ...) } else # univariate directional, multipanel: xyplot(gamma ~ dist | as.factor(dir.hor), subscripts = TRUE, panel = panel, data = x, xlim = xlim, ylim = ylim, xlab = xlab, ylab = ylab, direction = x$dir.hor, labels = labels, model = model, shift = shift, mode = "directional", scales = scales, ...) } else { # univariate directional, using symbol/color to distinguish pch = as.integer(as.factor(x$dir.hor)) xyplot(gamma ~ dist, data = x, type = c("p", "l"), groups = pch, xlim = xlim, ylim = ylim, xlab = xlab, ylab = ylab, pch = pch, scales = scales, ...) } } else if (length(unique(ids)) > 1) { # multivariable: n = floor(sqrt(2 * length(unique(ids)))) if (missing(skip)) { skip = NULL for (row in n:1) for (col in 1:n) skip = c(skip, row < col) } if (missing(layout)) layout = c(n,n) if (missing(scales)) scales = list(y = list(relation = "free")) else if (!is.null(scales$relation) && scales$relation == "same") ylim.set = TRUE if (length(unique(x$dir.hor)) > 1) { # multiv.; directional groups if (ylim.set) { xyplot(gamma ~ dist | id, data = x, type = c("p", "l"), xlim = xlim, ylim = ylim, xlab = xlab, ylab = ylab, groups = as.factor(x$dir.hor), layout = layout, skip = skip, scales = scales, ...) } else { xyplot(gamma ~ dist | id, data = x, type = c("p", "l"), xlim = xlim, xlab = xlab, ylab = ylab, groups = as.factor(x$dir.hor), layout = layout, skip = skip, scales = scales, ...) } } else { # non-multi-directional, multivariable if (ylim.set) { xyplot(gamma ~ dist | id, data = x, xlim = xlim, ylim = ylim, xlab = xlab, ylab = ylab, ids = ids, panel= panel, labels = labels, scales = scales, layout = layout, skip = skip, prepanel = function(x, y) list(ylim = c(min(0, y), max(0, y))), model = model, direction = c(x$dir.hor[1], x$dir.ver[1]), shift = shift, mode = "cross", ...) } else { xyplot(gamma ~ dist | id, data = x, xlim = xlim, xlab = xlab, ylab = ylab, ids = ids, panel = panel, labels = labels, scales = scales, layout = layout, skip = skip, prepanel = function(x, y) list(ylim = c(min(0, y), max(0, y))), model = model, direction = c(x$dir.hor[1], x$dir.ver[1]), shift = shift, mode = "cross", ...) } } } else # non multi-directional, univariable -- mostly used of all: xyplot(gamma ~ dist, data = x, panel = panel, xlim = xlim, ylim = ylim, xlab = xlab, ylab = ylab, labels = labels, model = model, direction = c(x$dir.hor[1], x$dir.ver[1]), shift = shift, mode = "direct", scales = scales, ...) } "plot.variogramMap" <- function(x, np = FALSE, skip, threshold, ...) { x = x$map if (!is(x, "SpatialPixelsDataFrame")) stop("x should be of class, or extend, SpatialPixelsDataFrame") if (np) start = 2 else start = 1 idx = seq(start, ncol(x@data), by=2) n = floor(sqrt(length(idx) * 2)) if (missing(skip)) { skip = NULL for (row in n:1) for (col in 1:n) skip = c(skip, row < col) } if (!(missing(threshold))) x = x[x[[2]] >= threshold, ] levelplot(values ~ dx + dy | ind, as.data.frame(stack(x, select = idx)), asp = mapasp(x), layout = c(n, n), skip = skip, ...) } gstat/R/show.vgms.R0000644000176200001440000000535313777370515013700 0ustar liggesusers# $Id: show.vgms.q,v 1.6 2008-12-15 14:27:29 edzer Exp $ "show.vgms" <- function(min = 1e-12 * max, max = 3, n = 50, sill = 1, range = 1, models = as.character(vgm()$short[c(1:17)]), nugget = 0, kappa.range = 0.5, plot = TRUE, ..., as.groups = FALSE) { zero.range.models = c("Nug", "Int", "Lin", "Err") # print(models) L = max(length(sill), length(range), length(nugget), length(models), length(kappa.range)) sill = rep(sill, length.out = L) range = rep(range, length.out = L) nugget = rep(nugget, length.out = L) i = 0 if (length(kappa.range) > 1) { # loop over kappa values for Matern model: if (missing(models)) models = "Mat" stopifnot(models == "Mat" || models == "Ste" || models == "Exc") data = matrix(NA, n * length(kappa.range), 2) v.level = rep("", n * length(kappa.range)) for (kappa in kappa.range) { v = vgm(sill[i+1], models, range[i+1], nugget = nugget[i+1], kappa = kappa) x = variogramLine(v, 0, 1, 0) data[(i*n+1), ] = as.matrix(x) x = variogramLine(v, max, n - 1, min) data[(i*n+2):((i+1)*n), ] = as.matrix(x) m.name = paste("vgm(", sill[i+1], ",\"", models, "\",", range, sep = "") if (nugget[i+1] > 0) m.name = paste(m.name, ",nugget=", nugget[i+1], sep = "") m.name = paste(m.name, ",kappa=", kappa, ")", sep = "") v.level[(i*n+1):((i+1)*n)] = rep(m.name, n) i = i + 1 } } else { models = rep(models, length.out = L) data = matrix(NA, n * length(models), 2) v.level = rep("", n * length(models)) for (m in models) { this.range = ifelse(!is.na(pmatch(m, zero.range.models)), 0, range[i+1]) v = vgm(sill[i+1], m, this.range, nugget = nugget[i+1], kappa = kappa.range) x = variogramLine(v, 0, 1, 0) data[(i*n+1), ] = as.matrix(x) x = variogramLine(v, max, n - 1, min) data[(i*n+2):((i+1)*n), ] = as.matrix(x) m.name = paste("vgm(", sill[i+1], ",\"", m, "\",", this.range, sep = "") if (nugget[i+1] > 0) m.name = paste(m.name, ",nugget=", nugget[i+1], sep = "") m.name = paste(m.name, ")", sep = "") v.level[(i*n+1):((i+1)*n)] = rep(m.name, n) i = i + 1 } } dframe = data.frame(semivariance = data[,2], distance = data[,1], model = factor(v.level, levels = unique(v.level))) vgm.panel = function(x,y, ...) { n = length(x) lpoints(x[1],y[1]) llines(x[2:n],y[2:n]) } vgm.panel2 = function(x, y, subscripts, groups, ...) { lpoints(0, 0, col = 1) panel.superpose(x, y, subscripts, groups, ...) } if (!plot) dframe else { if (as.groups) { model = 0 # avoid NOTE on cran check xyplot(semivariance ~ distance, groups = model, dframe[dframe$distance > 0,], panel = vgm.panel2, as.table = TRUE, auto.key = TRUE, type = 'l', ...) } else xyplot(semivariance ~ distance | model, dframe, panel = vgm.panel, as.table = TRUE, ...) } } gstat/R/get.contr.R0000644000176200001440000000411013777370515013636 0ustar liggesusers# $Id: get.contr.q,v 1.8 2006-03-20 15:18:14 edzer Exp $ "get.contr" <- function (data, gstat.object, X, ids = names(gstat.object$data)) { contr.fun <- function(x, n, pr.idx, cov.idx, contr) { y = matrix(x[pr.idx], n, 1) V = matrix(x[cov.idx], n, n) beta = t(contr) %*% y Vbeta = t(contr) %*% V %*% contr ret = c(beta, diag(Vbeta)) for (j in 1:nrow(Vbeta)) { if (j > 1) for (k in 1:(j - 1)) ret = c(ret, Vbeta[j, k]) } ret } lti <- function(i, j) { # lower triangular matrix index, when repr as array mx = max(i, j) - 1 mn = min(i, j) - 1 ((mx) * (mx - 1))/2 + mn + 1 } n = length(ids) if (!is.matrix(X)) X = as.matrix(X) if (n != nrow(X)) stop("length(ids) should equal nrow(X) or length(X)") gstat.names = create.gstat.names(ids) names.pr = gstat.names[seq(1, 2 * n, 2)] names.cov = matrix("", n, n) for (i in 1:n) for (j in 1:n) names.cov[i, j] = ifelse(i == j, gstat.names[2 * i], gstat.names[2 * n + lti(i, j)]) pr.idx = match(names.pr, names(data)) cov.idx = match(names.cov, names(data)) if (any(is.na(pr.idx)) || any(is.na(cov.idx))) stop("colunn names in data not matched") res = data.frame(t(apply(as.data.frame(data)[names(data)], 1, contr.fun, n = n, pr.idx = pr.idx, cov.idx = cov.idx, contr = X))) col.names = NULL for (j in 1:NCOL(X)) col.names = c(col.names, paste("beta", j, sep = ".")) for (j in 1:NCOL(X)) col.names = c(col.names, paste("var.beta", j, sep = ".")) for (j in 1:NCOL(X)) { if (j > 1) { for (k in 1:(j - 1)) { col.names = c(col.names, paste("cov.beta", k, j, sep = ".")) } } } names(res) = col.names if (is(data, "data.frame")) row.names(res) = row.names(data) else if (is(data, "SpatialPolygonsDataFrame")) { rownames(res) = sapply(data@polygons, function(x) slot(x, "ID")) res = SpatialPolygonsDataFrame(as(data, "SpatialPolygons"), res, match.ID = TRUE) } else if (is(data, "Spatial")) { coordinates(res) = coordinates(data) gridded(res) = gridded(data) } res } gstat/R/stVariogramModels.R0000644000176200001440000010457714315124326015401 0ustar liggesusers# constructiong spatio-temporal variogram models vgmST <- function(stModel, ..., space, time, joint, sill, k, nugget, stAni, temporalUnit) { stopifnot(is.character(stModel) && length(stModel)==1) old.stModel <- stModel stModel <- strsplit(stModel, "_")[[1]][1] if (stModel == "productSum" && !missing(sill)) stop("The sill argument for the product-sum model has been removed due a change in notation of the spatio-temporal models. This affects as well how the spatial and temporal variograms are parameterised. Re-fit your model or use \"productSumOld\" instead.") if(!missing(sill)) if(sill <= 0) stop("\"sill\" must be positive.") if(!missing(k)) if(k <= 0) stop("\"k\" must be positive.") if(!missing(nugget)) if(nugget < 0) stop("\"nugget\" must be non-negative.") if(!missing(stAni)) if(stAni <= 0) stop("\"stAni\" must be positive.") vgmModel <- switch(stModel, separable = list(space = space, time = time, sill = sill), productSum = list(space = space, time = time, k = k), productSumOld = list(space = space, time = time, sill = sill, nugget = nugget), sumMetric = list(space = space, time = time, joint = joint, stAni = stAni), simpleSumMetric = list(space = space, time = time, joint = joint, nugget = nugget, stAni = stAni), metric = list(joint = joint, stAni = stAni), stop(paste("model", stModel, "unknown"))) vgmModel$stModel <- old.stModel if (!missing(temporalUnit)) attr(vgmModel, "temporal unit") = temporalUnit class(vgmModel) <- c("StVariogramModel", "list") vgmModel } # calculating spatio-temporal variogram surfaces variogramSurface <- function(model, dist_grid, covariance=FALSE) { stopifnot(inherits(model, "StVariogramModel")) stopifnot(all(c("spacelag", "timelag") %in% colnames(dist_grid))) if (covariance) { switch(strsplit(model$stModel, "_")[[1]][1], separable=covSurfSeparable(model, dist_grid), productSum=covSurfProdSum(model, dist_grid), productSumOld=covSurfProdSumOld(model, dist_grid), sumMetric=covSurfSumMetric(model, dist_grid), simpleSumMetric=covSurfSimpleSumMetric(model, dist_grid), metric=covSurfMetric(model, dist_grid), stop("Only \"separable\", \"productSum\", \"sumMetric\", \"simpleSumMetric\" and \"metric\" are implemented.")) } else { switch(strsplit(model$stModel, "_")[[1]][1], separable=vgmSeparable(model, dist_grid), productSum=vgmProdSum(model, dist_grid), productSumOld=vgmProdSumOld(model, dist_grid), sumMetric=vgmSumMetric(model, dist_grid), simpleSumMetric=vgmSimpleSumMetric(model, dist_grid), metric=vgmMetric(model, dist_grid), stop("Only \"separable\", \"productSum\", \"sumMetric\", \"simpleSumMetric\" and \"metric\" are implemented.")) } } ################################ ## separable model: C_s * C_t ## ################################ vgmSeparable <- function(model, dist_grid) { vs = variogramLine(model$space, dist_vector=dist_grid$spacelag)$gamma vt = variogramLine(model$time, dist_vector=dist_grid$timelag)$gamma cbind(dist_grid, "gamma" = model$sill*(vs+vt-vs*vt)) } covSeparable <- function(x, y, model, separate) { if(missing(separate)) separate <- inherits(x, "STF") && inherits(y, "STF") && length(x) > 1 && length(y) > 1 # the STF case if (inherits(x, "STF") && inherits(y, "STF")) { # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # compose the cov-matrix Sm = variogramLine(model$space, covariance = TRUE, dist_vector = ds)*model$sill Tm = variogramLine(model$time, covariance = TRUE, dist_vector = dt) if (separate) return(list(Sm = Sm, Tm = Tm)) else return(Tm %x% Sm) # kronecker product } # separate makes only sense if both of x and y inherit STF if (separate) stop("An efficient inversion by separating the covarinace model is only possible if both of \"x\" and \"y\" inherit \"STF\"") # the STI case if (inherits(x, c("STI", "sftime")) || inherits(y, c("STI", "sftime"))) { # make sure that now both are of type STI x <- as(x, "STI") y <- as(y, "STI") # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # compose the cov-matrix Sm = variogramLine(model$space, covariance = TRUE, dist_vector = ds)*model$sill Tm = variogramLine(model$time, covariance = TRUE, dist_vector = dt) return(Sm * Tm) } # the remaining cases, none of x and y is STI nor are both STF # make sure both are of type STS x <- as(x, "STS") y <- as(y, "STS") # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # re-arrange the spatial and temporal distances sMat <- matrix(NA, nrow(x@index), nrow(y@index)) tMat <- matrix(NA, nrow(x@index), nrow(y@index)) for(r in 1:nrow(x@index)) { sMat[r,] <- ds[x@index[r,1], y@index[,1]] tMat[r,] <- dt[x@index[r,2], y@index[,2]] } # compose the cov-matrix Sm = variogramLine(model$space, covariance = TRUE, dist_vector = sMat)*model$sill Tm = variogramLine(model$time, covariance = TRUE, dist_vector = tMat) return(Sm * Tm) } # covariance for the circulant embedding in ST covSurfSeparable <- function(model, dist_grid) { Sm = variogramLine(model$space, covariance = TRUE, dist_vector = dist_grid$spacelag)$gamma*model$sill Tm = variogramLine(model$time, covariance = TRUE, dist_vector = dist_grid$timelag)$gamma cbind(dist_grid, "gamma" = Tm * Sm) } ########################################### ## productSum model: C_s*C_t + C_s + C_t ## ########################################### vgmProdSumOld <- function(model, dist_grid) { .Deprecated("vgmProdSum", package = "gstat", msg="The former product-sum model is dprecited, consider to refit the new model specification", old = "vgmProdSumOld") vs = variogramLine(model$space, dist_vector=dist_grid$spacelag)$gamma vt = variogramLine(model$time, dist_vector=dist_grid$timelag)$gamma vn <- rep(model$nugget, length(vs)) vn[vs == 0 & vt == 0] <- 0 k <- (sum(model$space$psill)+sum(model$time$psill)-(model$sill+model$nugget))/(sum(model$space$psill)*sum(model$time$psill)) if (k <= 0 || k > 1/max(rev(model$space$psill)[1], rev(model$time$psill)[1])) k <- 10^6*abs(k) # distorting the model to let optim "hopefully" find suitable parameters cbind(dist_grid, "gamma" = as.vector(vs+vt-k*vs*vt+vn)) } covProdSumOld <- function(x, y, model) { .Deprecated("covProdSum", package = "gstat", msg="The former product-sum model is dprecited, consider to refit the new model specification", old = "covProdSumOld") stopifnot(inherits(x, c("STF", "STS", "STI", "sftime")) && inherits(y, c("STF", "STS", "STI", "sftime"))) # double check model for validity, i.e. k: k <- (sum(model$space$psill)+sum(model$time$psill)-model$sill)/(sum(model$space$psill)*sum(model$time$psill)) if (k <= 0 || k > 1/max(model$space$psill[model$space$model!="Nug"], model$time$psill[model$time$model!="Nug"])) stop(paste("k (",k,") is non-positive or too large: no valid model!",sep="")) # the STF case if (inherits(x, "STF") && inherits(y, "STF")) { # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # compose the cov-matrix vs = variogramLine(model$space, dist_vector = ds, covariance = TRUE) vt = variogramLine(model$time, dist_vector = dt, covariance = TRUE) return(model$sill-(vt %x% matrix(1,nrow(vs),ncol(vs)) + matrix(1,nrow(vt),ncol(vt)) %x% vs - k * vt %x% vs)) } # the STI case if(inherits(x, c("STI", "sftime")) || inherits(y, c("STI", "sftime"))) { # make sure that now both are of type STI x <- as(x, "STI") y <- as(y, "STI") # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # compose the cov-matrix vs = variogramLine(model$space, dist_vector = ds, covariance = TRUE) vt = variogramLine(model$time, dist_vector = dt, covariance = TRUE) return(model$sill-(vt + vs - k * vt * vs)) } # the remaining cases, none of x and y is STI nor are both STF # make sure both are of type STS x <- as(x, "STS") y <- as(y, "STS") # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # re-arrange the spatial and temporal distances sMat <- matrix(NA, nrow(x@index), nrow(y@index)) tMat <- matrix(NA, nrow(x@index), nrow(y@index)) for(r in 1:nrow(x@index)) { sMat[r,] <- ds[x@index[r,1], y@index[,1]] tMat[r,] <- dt[x@index[r,2], y@index[,2]] } # compose the cov-matrix vs = variogramLine(model$space, dist_vector = sMat, covariance = TRUE) vt = variogramLine(model$time, dist_vector = tMat, covariance = TRUE) return(model$sill-(vt + vs - k * vt * vs)) } # covariance for the circulant embedding in ST covSurfProdSumOld <- function(model, dist_grid) { .Deprecated("covSurfProdSum", package = "gstat", msg="The former product-sum model is dprecited, consider to refit the new model specification", old = "covSurfProdSumOld") vs = variogramLine(model$space, dist_vector = dist_grid$spacelag, covariance = TRUE)$gamma vt = variogramLine(model$time, dist_vector = dist_grid$timelag, covariance = TRUE)$gamma k <- (sum(model$space$psill)+sum(model$time$psill)-(model$sill+model$nugget))/(sum(model$space$psill)*sum(model$time$psill)) cbind(dist_grid, "gamma" = model$sill-(vt + vs - k * vt * vs)) } vgmProdSum <- function(model, dist_grid) { if(!is.null(model$sill)) # backwards compatibility vgmProdSumOld(model, dist_grid) vs = variogramLine(model$space, dist_vector=dist_grid$spacelag)$gamma vt = variogramLine(model$time, dist_vector=dist_grid$timelag)$gamma sill_s <- sum(model$space$psill) sill_t <- sum(model$time$psill) k <- model$k cbind(dist_grid, "gamma" = as.vector((k*sill_t+1)*vs + (k*sill_s+1)*vt-k*vs*vt)) } covProdSum <- function(x, y, model) { stopifnot(inherits(x, c("STF", "STS", "STI", "sftime")) && inherits(y, c("STF", "STS", "STI", "sftime"))) if(!is.null(model$sill)) # backwards compatibility covProdSumOld(x, y, model) # the STF case if (inherits(x, "STF") && inherits(y, "STF")) { # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # compose the cov-matrix vs = variogramLine(model$space, dist_vector = ds, covariance =TRUE) vt = variogramLine(model$time, dist_vector = dt, covariance =TRUE) return(vt %x% matrix(1,nrow(vs),ncol(vs)) + matrix(1,nrow(vt),ncol(vt)) %x% vs + model$k * vt %x% vs) } # the STI case if(inherits(x, c("STI", "sftime")) || inherits(y, c("STI", "sftime"))) { # make sure that now both are of type STI x <- as(x, "STI") y <- as(y, "STI") # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # compose the cov-matrix vs = variogramLine(model$space, dist_vector = ds, covariance=TRUE) vt = variogramLine(model$time, dist_vector = dt, covariance=TRUE) return(vt + vs + model$k * vt * vs) } # the remaining cases, none of x and y is STI nor are both STF # make sure both are of type STS x <- as(x, "STS") y <- as(y, "STS") # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # re-arrange the spatial and temporal distances sMat <- matrix(NA, nrow(x@index), nrow(y@index)) tMat <- matrix(NA, nrow(x@index), nrow(y@index)) for(r in 1:nrow(x@index)) { sMat[r,] <- ds[x@index[r,1], y@index[,1]] tMat[r,] <- dt[x@index[r,2], y@index[,2]] } # compose the cov-matrix vs = variogramLine(model$space, dist_vector = sMat, covariance = TRUE) vt = variogramLine(model$time, dist_vector = tMat, covariance = TRUE) return(vt + vs + model$k * vt * vs) } # covariance for the circulant embedding in ST covSurfProdSum <- function(model, dist_grid) { vs = variogramLine(model$space, dist_vector = dist_grid$spacelag, covariance = TRUE)$gamma vt = variogramLine(model$time, dist_vector = dist_grid$timelag, covariance = TRUE)$gamma cbind(dist_grid, "gamma" = vt + vs + model$k * vt * vs) } ######################################################### # sumMetric model: C_s + C_t + C_st (Gerard Heuvelink) ## ######################################################### vgmSumMetric <- function(model, dist_grid) { vs = variogramLine(model$space, dist_vector=dist_grid$spacelag)$gamma vt = variogramLine(model$time, dist_vector=dist_grid$timelag)$gamma h = sqrt(dist_grid$spacelag^2 + (model$stAni * as.numeric(dist_grid$timelag))^2) vst = variogramLine(model$joint, dist_vector=h)$gamma cbind(dist_grid, "gamma" = vs + vt + vst) } covSumMetric <- function(x, y, model) { stopifnot(inherits(x, c("STF", "STS", "STI", "sftime")) && inherits(y, c("STF", "STS", "STI", "sftime"))) # the STF case if (inherits(x, "STF") && inherits(y, "STF")) { # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # compose the cov-matrix Sm = variogramLine(model$space, covariance = TRUE, dist_vector = ds) Tm = variogramLine(model$time, covariance = TRUE, dist_vector = dt) h = sqrt((matrix(1,nrow(dt),ncol(dt)) %x% ds)^2 + (model$stAni * dt %x% matrix(1,nrow(ds),ncol(ds)))^2) Mm = variogramLine(model$joint, covariance = TRUE, dist_vector = h) return(matrix(1,nrow(Tm),ncol(Tm)) %x% Sm + Tm %x% matrix(1,nrow(Sm),ncol(Sm)) + Mm) } # the STI case if(inherits(x, c("STI", "sftime")) || inherits(y, c("STI", "sftime"))) { # make sure that now both are of type STI x <- as(x, "STI") y <- as(y, "STI") # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # compose the cov-matrix Sm = variogramLine(model$space, covariance = TRUE, dist_vector = ds) Tm = variogramLine(model$time, covariance = TRUE, dist_vector = dt) h = sqrt(ds^2 + (model$stAni * dt)^2) Mm = variogramLine(model$joint, covariance = TRUE, dist_vector = h) return(Sm + Tm + Mm) } # the remaining cases, none of x and y is STI nor are both STF # make sure both are of type STS x <- as(x, "STS") y <- as(y, "STS") # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # re-arrange the spatial and temporal distances sMat <- matrix(NA, nrow(x@index), nrow(y@index)) tMat <- matrix(NA, nrow(x@index), nrow(y@index)) for(r in 1:nrow(x@index)) { sMat[r,] <- ds[x@index[r,1], y@index[,1]] tMat[r,] <- dt[x@index[r,2], y@index[,2]] } # compose the cov-matrix Sm = variogramLine(model$space, covariance = TRUE, dist_vector = sMat) Tm = variogramLine(model$time, covariance = TRUE, dist_vector = tMat) h = sqrt(sMat^2 + (model$stAni * tMat)^2) Mm = variogramLine(model$joint, covariance = TRUE, dist_vector = h) return(Sm + Tm + Mm) } # covariance for the circulant embedding in ST covSurfSumMetric <- function(model, dist_grid) { Sm = variogramLine(model$space, covariance = TRUE, dist_vector = dist_grid$spacelag)$gamma Tm = variogramLine(model$time, covariance = TRUE, dist_vector = dist_grid$timelag)$gamma h = sqrt(dist_grid$spacelag^2 + (model$stAni * dist_grid$timelag)^2) Mm = variogramLine(model$joint, covariance = TRUE, dist_vector = h)$gamma cbind(dist_grid, "gamma" = Sm + Tm + Mm) } ################################ ## simplified sumMetric model ## ################################ vgmSimpleSumMetric <- function(model, dist_grid) { vs = variogramLine(model$space, dist_vector=dist_grid$spacelag)$gamma vt = variogramLine(model$time, dist_vector=dist_grid$timelag)$gamma h = sqrt(dist_grid$spacelag^2 + (model$stAni * as.numeric(dist_grid$timelag))^2) vm = variogramLine(model$joint, dist_vector=h)$gamma vn <- variogramLine(vgm(model$nugget, "Nug", 0), dist_vector=h)$gamma cbind(dist_grid, "gamma" = vs + vt + vm + vn) } covSimpleSumMetric <- function(x, y, model) { modelNew <- vgmST("sumMetric", space=model$space, time=model$time, joint=vgm(model$joint$psill[model$joint$model != "Nug"], model$joint$model[model$joint$model != "Nug"], model$joint$range[model$joint$model != "Nug"], model$nugget), stAni=model$stAni) if (!is.null(attr(model,"temporal unit"))) attr(modelNew,"temporal unit") <- attr(model,"temporal unit") covSumMetric(x, y, modelNew) } # covariance for the circulant embedding in ST covSurfSimpleSumMetric <- function(model, dist_grid) { modelNew <- vgmST("sumMetric", space=model$space, time=model$time, joint=vgm(model$joint$psill[model$joint$model != "Nug"], model$joint$model[model$joint$model != "Nug"], model$joint$range[model$joint$model != "Nug"], model$nugget), stAni=model$stAni) if (!is.null(attr(model,"temporal unit"))) attr(modelNew,"temporal unit") <- attr(model,"temporal unit") covSurfSumMetric(modelNew, dist_grid) } ################## ## metric model ## ################## vgmMetric <- function(model, dist_grid) { h = sqrt(dist_grid$spacelag^2 + (model$stAni * as.numeric(dist_grid$timelag))^2) cbind(dist_grid, "gamma" = variogramLine(model$joint, dist_vector=h)$gamma) } covMetric <- function(x, y, model) { stopifnot(inherits(x, c("STF", "STS", "STI", "sftime")) && inherits(y, c("STF", "STS", "STI", "sftime"))) # the STF case if (inherits(x, "STF") && inherits(y, "STF")) { # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # compose the cov-matrix h = sqrt((matrix(1,nrow(dt),ncol(dt)) %x% ds)^2 + (model$stAni * dt %x% matrix(1,nrow(ds),ncol(ds)))^2) Mm = variogramLine(model$joint, covariance = TRUE, dist_vector = h) return(Mm) } # the STI case if (inherits(x, c("STI", "sftime")) || inherits(y, c("STI", "sftime"))) { # make sure that now both are of type STI x <- as(x, "STI") y <- as(y, "STI") # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # compose the cov-matrix h = sqrt(ds^2 + (model$stAni * dt)^2) Mm = variogramLine(model$joint, covariance = TRUE, dist_vector = h) return(Mm) } # the remaining cases, none of x and y is STI nor are both STF # make sure both are of type STS x <- as(x, "STS") y <- as(y, "STS") # calculate all spatial and temporal distances ds = spDists(x@sp, y@sp) dt = abs(outer(index(x@time), index(y@time), "-")) if(!is.null(attr(model,"temporal unit"))) units(dt) <- attr(model, "temporal unit") # ensure the same temporal metric as in the variogram definition debug_time_unit(units(dt)) dt <- as(dt, "matrix") # re-arrange the spatial and temporal distances sMat <- matrix(NA, nrow(x@index), nrow(y@index)) tMat <- matrix(NA, nrow(x@index), nrow(y@index)) for(r in 1:nrow(x@index)) { sMat[r,] <- ds[x@index[r,1], y@index[,1]] tMat[r,] <- dt[x@index[r,2], y@index[,2]] } # compose the cov-matrix h = sqrt(sMat^2 + (model$stAni * tMat)^2) Mm = variogramLine(model$joint, covariance = TRUE, dist_vector = h) return(Mm) } # covariance for the circulant embedding in ST covSurfMetric <- function(model, dist_grid) { h = sqrt(dist_grid$spacelag^2 + (model$stAni * dist_grid$timelag)^2) cbind(dist_grid, "gamma" = variogramLine(model$joint, covariance = TRUE, dist_vector = h)$gamma) } ########################### ## fitting ST variograms ## ########################### fit.StVariogram <- function(object, model, ..., method = "L-BFGS-B", lower, upper, fit.method = 6, stAni=NA, wles) { stopifnot(inherits(object, "StVariogram"), inherits(model, "StVariogramModel")) sunit <- attr(object$spacelag, "units") tunit <- attr(object$timelag, "units") tu.obj = attr(model, "temporal unit") if (!is.null(tu.obj)) stopifnot(identical(tunit, tu.obj)) object$timelag = as.numeric(object$timelag) # needed for R 4.1 object <- na.omit(object) ret <- model if(!missing(wles)) { if (wles) fit.method = 1 else fit.method = 6 } if (fit.method == 0) { attr(ret,"optim.output") <- "no fit" attr(ret, "MSE") <- mean((object$gamma - variogramSurface(model, data.frame(spacelag=object$dist, timelag=object$timelag))$gamma)^2) attr(ret, "spatial unit") <- sunit attr(ret, "temporal unit") <- tunit return(ret) } if ((fit.method == 7 || fit.method == 11) && is.null(model$stAni) && is.na(stAni)) { message("[An uninformed spatio-temporal anisotropy value of '1 (spatial unit)/(temporal unit)' is automatically selected. Consider providing a sensible estimate for stAni or using a different fit.method.]") stAni <- 1 } weightingFun <- switch(fit.method, function(obj, ...) obj$np, # 1 function(obj, gamma, ...) obj$np/gamma^2, # 2 function(obj, ...) obj$np, # 3 function(obj, gamma, ...) obj$np/gamma^2, # 4 function(obj, ...) stop("fit.method = 5 (REML), is not yet implemented"), # 5 function(obj, ...) 1, # 6 function(obj, curStAni, ...) if(is.na(stAni)) obj$np/(obj$dist^2+(curStAni*obj$timelag)^2) else obj$np/(obj$dist^2+(stAni*obj$timelag)^2), # 7 function(obj, ...) { dist <- obj$dist dist[dist == 0] <- min(dist[dist != 0], na.rm = TRUE) obj$np/dist^2 # 8, pure space, 0 dist = min (dist > 0) }, function(obj, ...) { dist <- obj$timelag dist[dist == 0] <- min(dist[dist != 0], na.rm = TRUE) obj$np/dist^2 }, # 9, pure time function(obj, gamma, ...) 1/gamma^2, # 10 function(obj, curStAni, ...) { if(is.na(stAni)) 1/(obj$dist^2+(curStAni*obj$timelag)^2) else 1/(obj$dist^2+(stAni*obj$timelag)^2) }, # 11 function(obj, ...) { dist <- obj$dist dist[dist == 0] <- min(dist[dist != 0], na.rm = TRUE) 1/(obj$dist^2) # 12, pure space }, function(obj, ...) { dist <- obj$timelag dist[dist == 0] <- min(dist[dist != 0], na.rm = TRUE) 1/(obj$timelag^2) }) # 13, pure time if(is.null(weightingFun)) stop(paste("fit.method =", fit.method, "is not implementend")) fitFun = function(par, trace = FALSE, ...) { curModel <- insertPar(par, model) gammaMod <- variogramSurface(curModel, data.frame(spacelag=object$dist, timelag=object$timelag))$gamma resSq <- (object$gamma - gammaMod)^2 resSq <- resSq * weightingFun(object, gamma=gammaMod, curStAni=curModel$stAni) if (trace) print(c(par, MSE = mean(resSq))) mean(resSq) # seems numerically more well behaved } if(missing(lower)) { min.s <- min(object$dist[object$dist>0])*0.05 # 5 % of the minimum distance larger 0 min.t <- min(object$dist[object$timelag>0])*0.05 # 5 % of the minimum time lag 0), pos <- sqrt(.Machine$double.eps) # at least positive lower <- switch(strsplit(model$stModel, "_")[[1]][1], separable=c(min.s, 0, min.t, 0, 0), productSum=c(0, min.s, 0, 0, min.t, 0, pos), productSumOld=c(0, min.s, 0, 0, min.t, 0, 0), sumMetric=c(0, min.s, 0, 0, min.t, 0, 0, pos, 0, pos), simpleSumMetric=c(0, min.s, 0, min.t, 0, pos, 0, 0, pos), metric=c(0, pos, 0, pos), stop("Only \"separable\", \"productSum\", \"sumMetric\", \"simpleSumMetric\" and \"metric\" are implemented.")) } if(missing(upper)) upper <- switch(strsplit(model$stModel, "_")[[1]][1], separable=c(Inf, 1, Inf, 1, Inf), productSum=Inf, productSumOld=Inf, sumMetric=Inf, simpleSumMetric=Inf, metric=Inf, stop("Only \"separable\", \"productSum\", \"sumMetric\", \"simpleSumMetric\" and \"metric\" are implemented.")) pars.fit <- optim(extractPar(model), fitFun, ..., method = method, lower = lower, upper = upper) ret <- insertPar(pars.fit$par, model) attr(ret,"optim.output") <- pars.fit attr(ret, "MSE") <- mean((object$gamma - variogramSurface(insertPar(pars.fit$par, model), data.frame(spacelag=object$dist, timelag=object$timelag))$gamma)^2) attr(ret, "spatial unit") <- sunit attr(ret, "temporal unit") <- tunit return(ret) } ########### ## tools ## ########### # insert parameters into models insertPar <- function(par, model) { switch(strsplit(model$stModel, "_")[[1]][1], separable=insertParSeparable(par, model), productSum=insertParProdSum(par, model), productSumOld=insertParProdSumOld(par, model), sumMetric=insertParSumMetric(par, model), simpleSumMetric=insertParSimpleSumMetric(par,model), metric=insertParMetric(par,model), stop("Only \"separable\", \"productSum\", \"sumMetric\", \"simpleSumMetric\" and \"metric\" are implemented.")) } # extract parameters from models extractPar <- function(model) { switch(strsplit(model$stModel, "_")[[1]][1], separable=c(range.s=model$space$range[2], nugget.s=model$space$psill[1], range.t=model$time$range[2], nugget.t=model$time$psill[1], sill= model$sill[[1]]), productSumOld=c(sill.s = rev(model$space$psill)[1], range.s = rev(model$space$range)[1], sill.t = rev(model$time$psill)[1], range.t = rev(model$time$range)[1], sill=model$sill[[1]], nugget=model$nugget[[1]]), productSum=c(sill.s = model$space$psill[2], range.s = model$space$range[2], nugget.s = model$space$psill[1], sill.t = model$time$psill[2], range.t = model$time$range[2], nugget.t = model$time$psill[1], k=model$k), sumMetric=c(sill.s = model$space$psill[2], range.s = model$space$range[2], nugget.s = model$space$psill[1], sill.t = model$time$psill[2], range.t = model$time$range[2], nugget.t = model$time$psill[1], sill.st = model$joint$psill[2], range.st = model$joint$range[2], nugget.st = model$joint$psill[1], anis = model$stAni[[1]]), # simplified sumMetric model simpleSumMetric=c(sill.s = rev(model$space$psill)[1], range.s = rev(model$space$range)[1], sill.t = rev(model$time$psill)[1], range.t = rev(model$time$range)[1], sill.st = rev(model$joint$psill)[1], range.st = rev(model$joint$range)[1], nugget = model$nugget[[1]], anis = model$stAni[[1]]), metric=c(sill = model$joint$psill[2], range = model$joint$range[2], nugget = model$joint$psill[1], anis = model$stAni[[1]]), stop("Only \"separable\", \"productSum\", \"sumMetric\", \"simpleSumMetric\" and \"metric\" are implemented.")) } # extract names extractParNames <- function(model) { names(extractPar(model)) } ## dedicated insertion functions ################################ # separable model insertParSeparable <- function(par, model) { vgmST("separable", space=vgm(1-par[2],as.character(model$space$model[2]),par[1],par[2], kappa=model$space$kappa[2]), time= vgm(1-par[4],as.character(model$time$model[2]),par[3],par[4], kappa=model$time$kappa[2]), sill=par[5]) } # product sum model insertParProdSumOld <- function(par, model) { vgmST("productSumOld", space=vgm(par[1],as.character(rev(model$space$model)[1]),par[2], kappa=rev(model$space$kappa)[1]), time= vgm(par[3],as.character(rev(model$time$model)[1]),par[4], kappa=rev(model$time$kappa)[1]), sill=par[5], nugget=par[6]) } insertParProdSum <- function(par, model) { vgmST("productSum", space=vgm(par[1],as.character(model$space$model[2]),par[2],par[3], kappa=model$space$kappa[2]), time= vgm(par[4],as.character(model$time$model[2]),par[5], par[6], kappa=model$time$kappa[2]), k=par[7]) } # sum metric model insertParSumMetric <- function(par, model) { vgmST("sumMetric", space=vgm(par[1],as.character(model$space$model[2]),par[2],par[3], kappa=model$space$kappa[2]), time= vgm(par[4],as.character(model$time$model[2]),par[5],par[6], kappa=model$time$kappa[2]), joint=vgm(par[7],as.character(model$joint$model[2]),par[8],par[9], kappa=model$joint$kappa[2]), stAni=par[10]) } # simplified sum metric model insertParSimpleSumMetric <- function(par, model) { vgmST("simpleSumMetric", space=vgm(par[1],as.character(rev(model$space$model)[1]),par[2], kappa=rev(model$space$kappa)[1]), time= vgm(par[3],as.character(rev(model$time$model)[1]),par[4], kappa=rev(model$time$kappa)[1]), joint=vgm(par[5],as.character(rev(model$joint$model)[1]),par[6], kappa=rev(model$joint$kappa)[1]), nugget=par[7], stAni=par[8]) } # metric model insertParMetric <- function(par, model) { vgmST("metric", joint=vgm(par[1], as.character(model$joint$model[2]), par[2], par[3], kappa=model$joint$kappa[2]), stAni=par[4]) } gstat/R/fit.lmc.R0000644000176200001440000000354413777370515013301 0ustar liggesusers# $Id: fit.lmc.q,v 1.8 2009-10-06 07:52:00 edzer Exp $ "fit.lmc" <- function (v, g, model, fit.ranges = FALSE, fit.lmc = !fit.ranges, correct.diagonal = 1.0, ...) { posdef = function(X) { q = eigen(X) d = q$values d[d < 0] = 0 q$vectors %*% diag(d, nrow = length(d)) %*% t(q$vectors) } if (!inherits(v, "gstatVariogram")) stop("v should be of class gstatVariogram") if (!inherits(g, "gstat")) stop("g should be of class gstat") if (!missing(model)) { if (!inherits(model, "variogramModel")) stop("model should be of class variogramModel") } n = names(g$data) for (i in 1:length(n)) { for (j in i:length(n)) { name = ifelse(i == j, n[i], cross.name(n[i], n[j])) x = v[v$id == name, ] if (nrow(x) == 0) stop(paste("gstatVariogram", name, "not present")) m = g$model[[name]] if (!missing(model)) m = model g$model[[name]] = fit.variogram(x, m, fit.ranges = fit.ranges, ...) } } if (fit.lmc) { m = g$model[[n[1]]] for (k in 1:nrow(m)) { psill = matrix(NA, nrow = length(n), ncol = length(n)) for (i in 1:length(n)) { for (j in i:length(n)) { name = ifelse(i == j, n[i], cross.name(n[i], n[j])) psill[i, j] = psill[j, i] = g$model[[name]][k, "psill"] } } psill = posdef(psill) diag(psill) = diag(psill) * correct.diagonal for (i in 1:length(n)) { for (j in i:length(n)) { name = ifelse(i == j, n[i], cross.name(n[i], n[j])) g$model[[name]][k, "psill"] = psill[i, j] } } } } g } gstat/R/plot.variogramCloud.R0000644000176200001440000000437513777370515015703 0ustar liggesusers# $Id: plot.variogramCloud.q,v 1.7 2007-10-18 10:13:13 edzer Exp $ "plot.variogramCloud" <- function (x, identify = FALSE, digitize = FALSE, xlim = c(0, max(x$dist)), ylim, # = c(0, max(x$gamma)), xlab = "distance", ylab = "semivariance", keep = FALSE, ...) { if (identify || digitize) { if (missing(ylim)) ylim = c(0, max(x$gamma)) dots = list(...) if ("log" %in% names(dots)) { log = dots$log if (grep("x", log) & xlim[1] == 0) xlim[1] = min(x$dist)/2 if (grep("y", log) & ylim[1] == 0) ylim[1] = min(x$gamma)/2 } plot(x$dist, x$gamma, xlim = xlim, ylim = ylim, xlab = xlab, ylab = ylab, ...) .BigInt = attr(x, ".BigInt") head = floor(x$np %/% .BigInt) + 1 tail = floor(x$np %% .BigInt) + 1 if (identify) { print("mouse-left identifies, mouse-right or Esc stops") labs = paste(head, tail, sep = ",") sel = identify(x$dist, x$gamma, labs, pos = keep) ret = data.frame(cbind(head, tail)[sel,, drop = FALSE]) } else { print("mouse-left digitizes, mouse-right closes polygon") poly = locator(n = 512, type = "l") if (!is.null(poly)) sel = point.in.polygon(x$dist, x$gamma, poly$x, poly$y) else stop("digitized selection is empty") ret = data.frame(cbind(head, tail)[sel == 1,,drop = FALSE]) } class(ret) = c("pointPairs", "data.frame") if (keep) { if (identify) { attr(x, "sel") = sel attr(x, "text") = labs[sel$ind] } else # digitize attr(x, "poly") = poly attr(x, "ppairs") = ret return(x) } else return(ret) } else { sel = attr(x, "sel") lab = attr(x, "text") poly = attr(x, "poly") if (!is.null(sel) && !is.null(lab)) { if (missing(ylim)) ylim = c(0, max(x$gamma)) plot(x$dist, x$gamma, xlim = xlim, ylim = ylim, xlab = xlab, ylab = ylab, ...) text(x$dist[sel$ind], x$gamma[sel$ind], labels=lab, pos= sel$pos) } else if (!is.null(poly)) { if (missing(ylim)) ylim = c(0, max(x$gamma)) plot(x$dist, x$gamma, xlim = xlim, ylim = ylim, xlab = xlab, ylab = ylab, ...) lines(poly$x, poly$y) } else { x$np = rep(1, length(x$gamma)) plot.gstatVariogram(x, xlim = xlim, ylim = ylim, xlab = xlab, ylab = ylab, ...) } } } gstat/R/fit.variogram.reml.R0000644000176200001440000000312613777370515015447 0ustar liggesusers# $Id: fit.variogram.reml.q,v 1.14 2009-11-02 21:33:17 edzer Exp $ "fit.variogram.reml" <- function (formula, locations, data, model, debug.level = 1, set, degree = 0) { if (missing(formula)) stop("nothing to fit to") if (!inherits(formula, "formula")) stop("first argument should be of class formula") if (!missing(locations)) { if (inherits(locations, "formula")) coordinates(data) = locations else if (is(locations, "Spatial")) data = as(locations, "SpatialPointsDataFrame") } if (!is(data, "SpatialPointsDataFrame")) stop("data should (now) be of class SpatialPointsDataFrame") if (missing(model)) stop("no model to fit") if (!inherits(model, "variogramModel")) stop("model should be of class variogramModel (use vgm)") fit.sills = rep(TRUE, length(model$model)) fit.ranges = rep(FALSE, length(model$model)) .Call(gstat_init, as.integer(debug.level)) ret = gstat.formula(formula, data) ret$y <- residuals(lm(formula, data)) .Call(gstat_new_data, as.double(ret$y), as.double(ret$locations), as.double(ret$X), as.integer(1), double(0), as.integer(-1), as.integer(0), as.double(-1), as.integer(0), as.integer(1), double(0), double(0), as.integer(degree), as.integer(is.projected(data)), as.integer(0), as.double(1.0), as.integer(0)) load.variogram.model(model) if (!missing(set)) gstat.load.set(set) ret = .Call(gstat_fit_variogram, as.integer(5), as.integer(fit.sills), as.integer(fit.ranges)) .Call(gstat_exit, 0) model$psill = ret[[1]] model$range = ret[[2]] model } gstat/R/turningLayers.R0000644000176200001440000003052513777370515014612 0ustar liggesusers# # library(gstat) # # separable model: spatial and temporal sill will be ignored # # and kept constant at 1-nugget respectively. A joint sill is used. # separableModel <- vgmST("separable", # space=vgm(0.9,"Exp", 147, 0.1), # time =vgm(0.9,"Exp", 3.5, 0.1), # sill=40) # # covSTMat <- ceWrapSpaceTimeOnTorusCalcCovRow1(c(250,20), c(1,16), separableModel) # dim(covSTMat) # # image(matrix(ceSim(covSTMat, 1, c(20, 16)), # nrow=20, ncol=16), asp=1, ylab="time", xlab="space") # # # product sum model: spatial and temporal nugget will be ignored and kept # # constant at 0. Only a joint nugget is used. # prodSumModel <- vgmST("productSum", # space=vgm(39, "Sph", 343, 0), # time= vgm(36, "Exp", 3, 0), # k=15) # # covSTMat <- ceWrapSpaceTimeOnTorusCalcCovRow1(c(250,20), c(1,16), prodSumModel) # dim(covSTMat) # # image(matrix(ceSim(covSTMat, 1, c(20, 16)), # nrow=20, ncol=16), asp=1, ylab="time", xlab="space") # # # sum metric model: spatial, temporal and joint nugget will be estimated # sumMetricModel <- vgmST("sumMetric", # space=vgm( 6.9, "Lin", 200, 3.0), # time =vgm(10.3, "Lin", 15, 3.6), # joint=vgm(37.2, "Exp", 84,11.7), # stAni=77.7) # # covSTMat <- ceWrapSpaceTimeOnTorusCalcCovRow1(c(250,20), c(1,16), sumMetricModel) # dim(covSTMat) # # image(matrix(ceSim(covSTMat, 1, c(20, 16)), # nrow=20, ncol=16), asp=1, ylab="time", xlab="space") # # # simplified sumMetric model, only a overall nugget is fitted. The spatial, # # temporal and jont nuggets are set to 0. # simpleSumMetricModel <- vgmST("simpleSumMetric", # space=vgm(20,"Lin", 150, 0), # time =vgm(20,"Lin", 10, 0), # joint=vgm(20,"Exp", 150, 0), # nugget=1, stAni=15) # # covSTMat <- ceWrapSpaceTimeOnTorusCalcCovRow1(c(250,20), c(1,16), simpleSumMetricModel) # dim(covSTMat) # # image(matrix(ceSim(covSTMat, 1, c(20, 16)), # nrow=20, ncol=16), asp=1, ylab="time", xlab="space") # # # metric model # metricModel <- vgmST("metric", # joint=vgm(60, "Exp", 150, 10), # stAni=60) # # covSTMat <- ceWrapSpaceTimeOnTorusCalcCovRow1(c(250,20), c(1,16), metricModel, turningLayers = FALSE) # dim(covSTMat) # # image(matrix(ceSim(covSTMat, 1, c(20, 16)), # nrow=20, ncol=16), asp=1, ylab="time", xlab="space") ## turning bands: # for cov-functions valid in 3-dim # adjust the covariance matrix (Schlahter, Chap. 2, eq 2.25) # simulate several layers (up-right hyper-planes in the 3D+T-cube) with random directions on a unit hemi-sphere # orthogonally project target points onto rndm lyrs and average the values for all rndm lyrs # -> one simulation of a 3d+T Gaussian random field, for 2D use a hyperplane in 3D # the tunring bands operator (numerical, 3-dimensional case) # @input: # model target covariance function # dist_grid: data.frame wtih columns spacelag and timelag for which the covariances are calculated # # @value: data.frame with columns spacelag, timelag and gamma where the latter contains the covariances for the 1-dim spatial and temporal layers # model <- separableModel # dist_grid <- as.data.frame(cbind("spacelag" = rep(1:150*1., each=4), # "timelag" = rep(1:4, 150))) # CAVE: distgrid must ahve the correct spatial and temporal metrics tbOperator <- function(model, dist_grid) { r <- dist_grid$spacelag derFun <- function(r) r * variogramSurface(model, dist_grid = data.frame(spacelag=r, timelag=dist_grid$timelag), covariance = TRUE)$gamma cbind(dist_grid, "gamma" = diag(attr(numericDeriv(quote(derFun(r)), "r"), "gradient"))) } randomDirections <- function(n) { u <- runif(n, 0, 2*pi) v <- runif(n, 0, 1) s <- sqrt(1-v^2) cbind(s*cos(u), s*sin(u), v) } # library(rgl) # plot3d(randomDirections(100), aspect = c(1,1,0.5)) # nLyrs <- 500 # coordMat <- matrix(c(1,5,5, # 1,7,7, # 1,5,7, # 1,7,5), byrow=T, ncol=3) # # coordMat <- matrix(runif(3*1001,1,5), byrow=T, ncol=3) # # # random directions in 3D # rndDir <- randomDirections(nLyrs) # # # how much does each direction contribute to the point # cntrbtn <- rndDir %*% t(coordMat) # # -> each column corresponds to one location, each row i to the "contribution" of the i-th rndDir # # cl_cntrbtn <- ceiling(cntrbtn)+10 # centre for grid; mind spatial index # fl_cntrbtn <- floor(cntrbtn) +10 # # covRow1 <- ceWrapSpaceTimeOnTorusCalcCovRow1(c(250,20), c(1,16), metricModel, turningLayers = TRUE) # # sTime <- Sys.time() # simLyrs <- ceSim(covRow1, nLyrs, c(20,16)) # simLyrs <- lapply(1:nLyrs, function(col) matrix(simLyrs[,col], nrow=20, ncol=16)) # # lambda <- cl_cntrbtn - cntrbtn -10 # # cntrbSngSimLyr <- function(lyrId) { # simLyrs[[lyrId]][cl_cntrbtn[lyrId,],] * (1-lambda)[lyrId,] + simLyrs[[lyrId]][fl_cntrbtn[lyrId,],] * lambda[lyrId,] # } # # # reduce to the one realisation based on the combination of nLyrs turning bands # simTs <- Reduce('+', lapply(1:nLyrs, cntrbSngSimLyr))/sqrt(nLyrs) # eTime <- Sys.time() # # eTime - sTime # 0.7 secs/simulation of 100 random points # # image(simTs) # # dim(simTs) # # 1001 locations at 16 time stamps # # plot(simTs[500,]) # computes the covariance matrixes and weights once, applied to series of # variables/simulations where each variable/simulation is stored in one column of # the multiVarMatrix copied from krigeST to avoid repeted calls to krige with # multiple, identical inversions of the weights matrix # TODO: add functionality for temporal sandwich-wise processing: i.e. use the # +/- nmaxTime time slices to predict one time slice krigeSTMultiple <- function(formula, from, to, modelList, multiVarMatrix, nmaxTime=Inf) { lst = extractFormula(formula, from, to) separate <- length(from) > 1 && length(to) > 1 && inherits(from, "STF") && inherits(to, "STF") X = lst$X x0 = lst$x0 V = covfn.ST(from, model = modelList, separate=separate) v0 = covfn.ST(from, to, modelList) if (modelList$stModel == "separable" & separate) skwts <- STsolve(V, v0, X) # use Kronecker trick else skwts <- CHsolve(V, cbind(v0, X)) npts = length(to) ViX = skwts[,-(1:npts)] skwts = skwts[,1:npts] idPredFun <- function(sim) { sim <- matrix(sim, ncol = 1) beta = solve(t(X) %*% ViX, t(ViX) %*% sim) x0 %*% beta + t(skwts) %*% (sim - X %*% beta) } apply(multiVarMatrix, 2, idPredFun) } # unconcitional ## STFDF # library(sp) # library(spacetime) # library(zoo) # library(xts) # data(meuse, package = "sp") # coordinates(meuse) <- ~x+y # proj4string(meuse) <- CRS("+init=epsg:28992") # krigeST <- function(formula, data, newdata, modelList, y, beta, nmax=Inf, stAni=NULL, # computeVar = FALSE, fullCovariance = FALSE, # bufferNmax=2, progress=TRUE) ## krigeSTSimTB <- function(formula, data, newdata, modelList, nsim, progress=TRUE, nLyrs=500, tGrid=NULL, sGrid=NULL, ceExt=2, nmax=Inf) { stopifnot(zoo::is.regular(newdata@time)) condSim <- TRUE if (missing(data)) { condSim <- FALSE message("[No data provided: performing unconditional simulation.]") } else { message("[Performing conditional simulation.]") } pb <- txtProgressBar(0,nsim,style=3) # ST-simulation grid if (is.null(tGrid)) { tDis <- diff(c(index(newdata@time[1]), newdata@endTime[1])) if (!is.null(attr(modelList, "temporal unit"))) { units(tDis) <- attr(modelList, "temporal unit") } else { message("[The spatio-temporal variogram model does not carry a time unit attribute: krigeST cannot check whether the temporal distance metrics coincide.]") } tGrid <- c(as.numeric(tDis), length(newdata@time)) attr(tGrid, "units") <- c("", units(tDis)) debug_time_unit(units(tDis)) } if (is.null(sGrid)) { if (gridded(newdata@sp)) { # SpatialPixels/SpatialGrid: # based on GridTopology: use minimal cellsize of both directions; take enough to cover the diagonal sDis <- min(newdata@sp@grid@cellsize) sDim <- ceiling(sqrt(sum((newdata@sp@grid@cellsize * newdata@sp@grid@cells.dim)^2))/sDis) sGrid <- c(sDis, sDim) } else { # treat (as) SpatialPoints: # Average area per location --assuming-a-regular-squared-outline-taking-the-sqrt--> length/location --take-later-twice-as-many--> bboxExt <- apply(newdata@sp@bbox, 1, diff) sDis <- sqrt(prod(bboxExt)/length(newdata@sp)) sDim <- ceiling(sqrt(sum((bboxExt/sDis)^2))) sGrid <- c(sDis, sDim) } } # random directions in 3D rndDir <- randomDirections(nLyrs) # coordinates coordMat <- coordinates(newdata@sp) # coordinates (embedded in 3D) shifted + scaled to the grid index of the spatial gridding sGrid coordMat[,1] <- (coordMat[,1] - newdata@sp@bbox[1,1])/sGrid[1] coordMat[,2] <- (coordMat[,2] - newdata@sp@bbox[2,1])/sGrid[1] if (ncol(coordMat) == 2) { coordMat <- cbind(coordMat,1) } else { coordMat[,3] <- (coordMat[,3] - newdata@sp@bbox[3,1])/sGrid[1] } # how much does each direction contribute to the point cntrbtn <- rndDir %*% t(coordMat) # -> each column corresponds to one location, each row i to the "contribution" of the i-th rndDir # ceiling and floor + shifted to avoid negative indices cl_cntrbtn <- ceiling(cntrbtn) + sGrid[2] fl_cntrbtn <- floor(cntrbtn) + sGrid[2] covRow1 <- ceWrapSpaceTimeOnTorusCalcCovRow1(c(sGrid[1], 2*sGrid[2]), tGrid, modelList, turningLayers = TRUE, ext=ceExt) origDim <- c(2*sGrid[2], tGrid[2]) sims <- list() ## for (i in 1:nsim) { setTxtProgressBar(pb, i) simLyrs <- ceSim(covRow1, nLyrs, origDim) simLyrs <- lapply(1:nLyrs, function(col) matrix(simLyrs[,col], nrow=origDim[1], ncol=origDim[2])) lambda <- cl_cntrbtn - cntrbtn - sGrid[2] cntrbSngSimLyr <- function(lyrId) { simLyrs[[lyrId]][cl_cntrbtn[lyrId,],] * (1-lambda)[lyrId,] + simLyrs[[lyrId]][fl_cntrbtn[lyrId,],] * lambda[lyrId,] } # reduce to the one realisation based on the combination of nLyrs turning bands sims[[paste0("sim",i)]] <- Reduce('+', lapply(1:nLyrs, cntrbSngSimLyr))/sqrt(nLyrs) } close(pb) sims <- do.call(cbind, lapply(sims, as.numeric)) # bind simulations to newdata geometry if (!condSim) { if ("data" %in% slotNames(newdata)) newdata@data <- cbind(newdata@data, sims) else newdata <- addAttrToGeom(newdata, as.data.frame(sims)) return(newdata) } # function call ends here if no data has been provided -> unconditional case varName <- all.vars(formula[[2]]) ## conditioning # interpolate the observations to the simulation grid obsMeanField <- krigeST(formula=formula, data=data, newdata=newdata, modelList=modelList) # interpolate to observation locations from the simulated grids for each simulation simMeanObsLoc <- krigeSTMultiple(as.formula(paste0("var1.pred ~", formula[[3]])), obsMeanField, data, modelList, sims) # interpolate from kriged mean sim at observed locations back to the grid for mean surface of the simulations simMeanFields <- krigeSTMultiple(as.formula(paste0(varName, "~", formula[[3]])), data, newdata, modelList, simMeanObsLoc) # add up the mean field and the corrected data sims <- obsMeanField@data$var1.pred + sims - simMeanFields # bind simulations to newdata geometry if ("data" %in% slotNames(newdata)) { newdata@data <- cbind(newdata@data, sims) return(newdata) } addAttrToGeom(newdata, as.data.frame(sims)) } # # sTime <- Sys.time() # krigedSim <- krigeSTUncSimTB(stf, metricModel, 100) # Sys.time() - sTime # # # 27 secs for 100 simulated ST fields of 155 locations and 21 time steps: 325500 values # # # plot one simulation along time # stplot(krigedSim[,1:12]) # # # plot one simulation along time # stplot(krigedSim[1:12,,"sim1"], mode="ts") # # # plot the ten simulations of the first day # spplot(krigedSim[,1], paste0("sim",1:10), as.table=TRUE) gstat/R/circEmbed.R0000644000176200001440000002131514314525261013602 0ustar liggesusers## Benedikt Gräler (52North), 2018-05-25: ## circulant embedding following: Davies, Tilman M., and David Bryant. "On ## circulant embedding for Gaussian random fields in R." Journal of Statistical ## Software 55.9 (2013): 1-21. ## See i.e. the suplementary files at (retreived 2018-05-25): ## https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v055i09/v55i09.R # extend the grid # input: SpatialGrid/SpatialPixels/GridTopology # output: extended grid of class GridTopology ceExtGrid <- function(grid, ext=2) { if (!inherits(grid, "GridTopology")) { stopifnot(gridded(grid)) grid <- grid@grid } GridTopology(grid@cellcentre.offset, grid@cellsize, grid@cells.dim*ext) } # only for comaprission following the above paper # expand and wrap a grid on a torus + calc distances # input: SpatialGrid # output: distance matrix ceWrapOnTorusCalcDist <- function(grid, ext=2) { grid <- ceExtGrid(grid, ext) rangeXY <- grid@cellsize * grid@cells.dim MN.ext <- prod(grid@cells.dim) gridCoords <- coordinates(grid) mmat.ext <- matrix(rep(gridCoords[, 1], MN.ext), MN.ext, MN.ext) nmat.ext <- matrix(rep(gridCoords[, 2], MN.ext), MN.ext, MN.ext) mmat.diff <- mmat.ext - t(mmat.ext) nmat.diff <- nmat.ext - t(nmat.ext) mmat.torus <- pmin(abs(mmat.diff), rangeXY[1] - abs(mmat.diff)) nmat.torus <- pmin(abs(nmat.diff), rangeXY[2] - abs(nmat.diff)) sqrt(mmat.torus^2 + nmat.torus^2) } ## FFT preparation with only first row of cov-matrix ceWrapOnTorusCalcCovRow1 <- function(grid, vgmModel, ext=2) { grid <- ceExtGrid(grid, ext) stopifnot("variogramModel" %in% class(vgmModel)) rangeXY <- grid@cellsize * grid@cells.dim cenX <- seq(from = grid@cellcentre.offset[1], by = grid@cellsize[1], length.out = grid@cells.dim[1]) cenY <- seq(from = grid@cellcentre.offset[2], by = grid@cellsize[2], length.out = grid@cells.dim[2]) m.diff.row1 <- abs(cenX[1] - cenX) m.diff.row1 <- pmin(m.diff.row1, rangeXY[1] - m.diff.row1) n.diff.row1 <- abs(cenY[1] - cenY) n.diff.row1 <- pmin(n.diff.row1, rangeXY[2] - n.diff.row1) cent.ext.row1 <- expand.grid(m.diff.row1, n.diff.row1) D.ext.row1 <- matrix(sqrt(cent.ext.row1[, 1]^2 + cent.ext.row1[, 2]^2), grid@cells.dim[1], grid@cells.dim[2]) variogramLine(vgmModel, dist_vector = D.ext.row1, covariance = T) } # simulate GRF with given covariance structure using fft # @input # covMatRow1: the first row of the covariance matrix for the fft # n: number of simulations # cells.dim: the original dimrensions of the grid to clip from the larger embedded simulation # grid.index: grid.index of a SpatialPixels object to select the right pixels from the larger square-grid # @output # matrix where each column holds one simulated GRF corresponding to cells.dim (and grid.index if appropriate) ceSim <- function(covMatRow1, n=1, cells.dim, grid.index) { d <- dim(covMatRow1) dp <- prod(d) sdp <- sqrt(dp) prefix <- sqrt(Re(fft(covMatRow1, TRUE))) simFun <- function(x) { std <- rnorm(dp) realz <- prefix * (fft(matrix(std, d[1], d[2]))/sdp) as.numeric(Re(fft(realz, TRUE)/sdp)[1:cells.dim[1], 1:cells.dim[2]]) } simFunGridIndex <- function(x) { std <- rnorm(dp) realz <- prefix * (fft(matrix(std, d[1], d[2]))/sdp) as.numeric(Re(fft(realz, TRUE)/sdp)[1:cells.dim[1], 1:cells.dim[2]])[grid.index] } if (missing(grid.index)) do.call(cbind, lapply(1:n, simFun)) else do.call(cbind, lapply(1:n, simFunGridIndex)) } # computes the covariance matrixes and weights once, applied to series of # variables/simulations where each variable/simulation is stored in one column of # the multiVarMatrix copied from krige0 to avoid repeted calls to krige with # multiple, identical inversions of the weights matrix krigeMultiple <- function(formula, from, to, model, multiVarMatrix) { lst = extractFormula(formula, from, to) X = lst$X x0 = lst$x0 ll = (!is.na(is.projected(from)) && !is.projected(from)) s = coordinates(from) s0 = coordinates(to) V = variogramLine(model, dist_vector = spDists(s, s, ll), covariance = TRUE) v0 = variogramLine(model, dist_vector = spDists(s, s0, ll), covariance = TRUE) skwts = CHsolve(V, cbind(v0, X)) ViX = skwts[, -(1:nrow(s0))] skwts = skwts[, 1:nrow(s0)] idPredFun <- function(sim) { sim <- matrix(sim, ncol = 1) beta = solve(t(X) %*% ViX, t(ViX) %*% sim) x0 %*% beta + t(skwts) %*% (sim - X %*% beta) } apply(multiVarMatrix, 2, idPredFun) } ### pubic function ### # @input: # formula: definition of the dependent variable # data: optional Spatial*DataFrame for conditional simulation # newdata: SpatialGrid or SpatialPixels # model: variogram model of the GRF # n: number of desired simulations # ext: extension degree of the circulant embedding, default to 2 # @output # SpatialPixels or SpatailGridDataFrame with (additional) n columns holding one (un)conditional simulation each krigeSimCE <- function(formula, data, newdata, model, n = 1, ext = 2) { stopifnot(is(model, "variogramModel")) stopifnot(gridded(newdata)) if (!missing(data)) stopifnot(identical(data@proj4string@projargs, newdata@proj4string@projargs)) varName <- all.vars(formula[[2]]) condSim <- TRUE if (missing(data)) { condSim <- FALSE message("[No data provided: performing unconditional simulation.]") } else { message("[Performing conditional simulation.]") } # prepare covariance matrix covMat <- ceWrapOnTorusCalcCovRow1(newdata, model, ext = ext) # simulate sims <- ceSim(covMat, n, newdata@grid@cells.dim, newdata@grid.index) colnames(sims) <- paste0(varName, ".sim", 1:n) # bind simulations to newdata geometry if (!condSim) { if ("data" %in% slotNames(newdata)) newdata@data <- cbind(newdata@data, sims) else addAttrToGeom(newdata, as.data.frame(sims)) return(newdata) } # function call ends here if no data has been provided -> unconditional case ## conditioning # interpolate the observations to the simulation grid obsMeanField <- krige(formula, data, newdata, model) # interpolate to observation locations from the simulated grids for each simulation simMeanObsLoc <- krigeMultiple(as.formula(paste0("var1.pred ~", formula[[3]])), obsMeanField, data, model, sims) # interpolate from kriged mean sim at observed locations back to the grid for mean surface of the simulations simMeanFields <- krigeMultiple(as.formula(paste0(varName, "~", formula[[3]])), data, newdata, model, simMeanObsLoc) # add up the mean field and the corrected data sims <- obsMeanField@data$var1.pred + sims - simMeanFields # bind simulations to newdata geometry if ("data" %in% slotNames(newdata)) { newdata@data <- cbind(newdata@data, sims) return(newdata) } addAttrToGeom(newdata, as.data.frame(sims)) } ### # Note: to avoid the smoothing effect, the irregular observation locations could also be independently simulated by e.g. their surrounding grid values ### ## circulant embedding for ST-ocvariance functions with grids along one spatial and one temporal axis # inputs: # hDiscrete = c(hStep, hn): spatial step width and number of steps # tDiscrete = c(tStep, tn): temporal step length and number of steps # CAVE: hDiscrete and tDiscrete must have the correct spatial and temporal metrics ceWrapSpaceTimeOnTorusCalcCovRow1 <- function(hDiscrete, tDiscrete, vgmStModel, ext=2, turningLayers=TRUE) { stopifnot(is(vgmStModel) == "StVariogramModel") hDiscrete[2] <- hDiscrete[2]*ext tDiscrete[2] <- tDiscrete[2]*ext rangeST <- c(prod(hDiscrete), prod(tDiscrete)) cenX <- seq(from = 0, by = hDiscrete[1], length.out = hDiscrete[2]) cenY <- seq(from = 0, by = tDiscrete[1], length.out = tDiscrete[2]) m.diff.row1 <- abs(cenX[1] - cenX) m.diff.row1 <- pmin(m.diff.row1, rangeST[1] - m.diff.row1) n.diff.row1 <- abs(cenY[1] - cenY) n.diff.row1 <- pmin(n.diff.row1, rangeST[2] - n.diff.row1) cent.ext.row1 <- expand.grid(m.diff.row1, n.diff.row1) D.ext.row1 <- matrix(sqrt(cent.ext.row1[, 1]^2 + cent.ext.row1[, 2]^2), hDiscrete[2], tDiscrete[2]) colnames(cent.ext.row1) <- c("spacelag", "timelag") if (turningLayers) { return(matrix(tbOperator(vgmStModel, dist_grid = cent.ext.row1)$gamma, hDiscrete[2], tDiscrete[2])) } matrix(variogramSurface(vgmStModel, dist_grid = cent.ext.row1, covariance = TRUE)$gamma, hDiscrete[2], tDiscrete[2]) } gstat/R/hscat.R0000644000176200001440000000151313777370515013041 0ustar liggesusershscat = function(formula, data, breaks, pch = 3, cex = .6, mirror = FALSE, variogram.alpha = 0, as.table = TRUE, ...) { stopifnot(!missing(breaks)) x = variogram(formula, data, cloud = TRUE, cutoff = max(breaks), alpha = variogram.alpha, ...) x = as.data.frame(x) x$class = cut(x$dist, breaks = breaks) y = model.frame(formula, data)[[1]] x$xx = y[x$left] x$yy = y[x$right] if (mirror) x = data.frame( xx = c(x$yy, y[x$left]), yy = c(x$xx, y[x$right]), class = c(x$class, x$class)) lab = as.character(formula)[2] panel = function(x,y,subscripts, ...) { xr = c(min(x),max(x)) llines(xr, xr) lpoints(x,y,...) ltext(min(x), max(y), paste("r =", signif(cor(x,y),3)), adj=c(0,0.5)) } xyplot(xx~yy|class, x, panel = panel, main = "lagged scatterplots", xlab = lab, ylab = lab, as.table = as.table, ...) } gstat/R/plot.pointPairs.R0000644000176200001440000000121713777370515015045 0ustar liggesusers# $Id: plot.pointPairs.q,v 1.4 2006-02-10 19:01:07 edzer Exp $ "plot.pointPairs" <- function(x, data, xcol = data$x, ycol = data$y, xlab = "x coordinate", ylab = "y coordinate", col.line = 2, line.pch = 0, main = "selected point pairs", ...) { if (inherits(data, "sf")) data = as(data, "Spatial") if (is(data, "SpatialPoints")) { cc = coordinates(data) xcol = cc[,1] ycol = cc[,2] xlab = colnames(cc)[1] ylab = colnames(cc)[2] asp = mapasp(data) } else asp = "iso" xyplot(ycol ~ xcol, aspect = asp, panel = panel.pointPairs, xlab = xlab, ylab = ylab, pairs = x, col.line = col.line, line.pch = line.pch, main = main, ...) } gstat/R/print.gstat.R0000644000176200001440000000451713777370515014223 0ustar liggesusers# $Id: print.gstat.q,v 1.7 2006-02-10 19:01:07 edzer Exp $ "print.gstat" <- function (x, ...) { if (missing(x) || !inherits(x, "gstat")) stop("wrong call") data.names <- names(x$data) if (length(data.names)) cat("data:\n") for (n in data.names) { fstr = paste(x$data[[n]]$formula[c(2, 1, 3)], collapse = "") #lstr = paste(x$data[[n]]$locations[c(1, 2)], collapse = "") cat(n, ": formula =", fstr, ";") if (!is.null(x$data[[n]]$data)) { data.dim = dim(x$data[[n]]$data) cat(" data dim =", data.dim[1], "x", data.dim[2]) } else { if (x$data[[n]]$dummy) cat(" dummy data") else cat(" NULL data") } if (x$data[[n]]$nmax != Inf) cat(" nmax =", x$data[[n]]$nmax) if (x$data[[n]]$nmin > 0) cat(" nmin =", x$data[[n]]$nmin) if (x$data[[n]]$maxdist < Inf) cat(" radius =", x$data[[n]]$maxdist) if (x$data[[n]]$vfn > 1) cat(" variance function =", c("identity", "mu", "mu(1-mu)", "mu^2", "mu^3")[x$data[[n]]$vfn]) if (length(x$data[[n]]$beta) > 0) cat(" beta =", x$data[[n]]$beta) if (x$data[[n]]$degree > 0) cat(" degree =", x$data[[n]]$degree) cat("\n") } xx.names = xx = NULL for (n in data.names) { m = x$model[[n]] if (!is.null(m)) { xx = rbind(xx, m) if (nrow(m) == 1) xx.names = c(xx.names, n) else xx.names = c(xx.names, paste(n, "[", 1:nrow(m), "]", sep = "")) } } if (length(data.names) > 1) { for (j in 2:length(data.names)) { for (i in 1:(j - 1)) { n = cross.name(data.names[i], data.names[j]) m = x$model[[n]] if (!is.null(m)) { xx = rbind(xx, m) if (nrow(m) == 1) xx.names = c(xx.names, n) else xx.names = c(xx.names, paste(n, "[", 1:nrow(m), "]", sep = "")) } } } } if (!is.null(xx)) { cat("variograms:\n") row.names(xx) = xx.names print(xx, ...) } if (!is.null(x$set)) { s = gstat.set(x$set) for (i in 1:length(s)) cat(s[i], "\n") } if (!is.null(x$locations)) print(x$locations) invisible(x) } gstat/R/krige.cv.R0000644000176200001440000000345113777370515013452 0ustar liggesusers# $Id: krige.cv.q,v 1.18 2009-10-30 16:11:21 edzer Exp $ if (!isGeneric("krige.cv")) setGeneric("krige.cv", function(formula, locations, ...) standardGeneric("krige.cv")) krige.cv.locations = function (formula, locations, data = sys.frame(sys.frame(sys.parent())), model = NULL, ..., beta = NULL, nmax = Inf, nmin = 0, maxdist = Inf, nfold = nrow(data), verbose = interactive(), debug.level = 0) { gstat.cv(gstat(g = NULL, id = "var1", formula = formula, locations = locations, data = data, model = model, beta = beta, nmax = nmax, nmin = nmin, maxdist = maxdist, ...), nfold = nfold, verbose = verbose, debug.level = debug.level) } setMethod("krige.cv", c("formula", "formula"), krige.cv.locations) krige.cv.spatial = function (formula, locations, model = NULL, ..., beta = NULL, nmax = Inf, nmin = 0, maxdist = Inf, nfold = nrow(locations), verbose = interactive(), debug.level = 0) { # data = locations gstat.cv(gstat(g = NULL, id = "var1", formula = formula, data = locations, model = model, beta = beta, nmax = nmax, nmin = nmin, maxdist = maxdist, ...), nfold = nfold, verbose = verbose, debug.level = debug.level) } setMethod("krige.cv", c("formula", "Spatial"), krige.cv.spatial) krige.cv.sf = function (formula, locations, model = NULL, ..., beta = NULL, nmax = Inf, nmin = 0, maxdist = Inf, nfold = nrow(locations), verbose = interactive(), debug.level = 0) { # data = locations if (!requireNamespace("sf", quietly = TRUE)) stop("sf required: install that first") # nocov sf::st_as_sf(gstat.cv(gstat(g = NULL, id = "var1", formula = formula, data = as(locations, "Spatial"), model = model, beta = beta, nmax = nmax, nmin = nmin, maxdist = maxdist, ...), nfold = nfold, verbose = verbose, debug.level = debug.level)) } setMethod("krige.cv", c("formula", "sf"), krige.cv.sf) gstat/R/predict.gstat.R0000644000176200001440000002317414147167202014506 0ustar liggesusers# $Id: predict.gstat.q,v 1.35 2009-11-02 21:33:17 edzer Exp $ predict.gstat <- function (object, newdata, block = numeric(0), nsim = 0, indicators = FALSE, BLUE = FALSE, debug.level = 1, mask, na.action = na.pass, sps.args = list(n = 500, type = "regular", offset = c(.5, .5)), ...) { if (missing(object) || length(object$data) < 1) stop("no data available") if (!inherits(object, "gstat")) stop("first argument should be of class gstat") to_stars = FALSE to_sf = if (inherits(newdata, c("sf", "sfc", "stars"))) { to_stars = inherits(newdata, "stars") newdata = as(newdata, "Spatial") TRUE } else FALSE if (!is.null(object$locations) && inherits(object$locations, "formula") && !(is(newdata, "Spatial"))) { coordinates(newdata) = object$locations return.sp = FALSE } else return.sp = TRUE max_dist = getMaxDist(object$data, newdata) .Call(gstat_init, as.integer(debug.level)) bl_weights = numeric(0) if (!missing(mask)) { cat("argument mask is deprecated:") stop("use a missing value pattern in newdata instead") } nvars = length(object$data) new.X = NULL for (i in 1:length(object$data)) { name = names(object$data)[i] d = object$data[[i]] if (!is.null(d$data)) { if (!identical(d$data@proj4string@projargs, newdata@proj4string@projargs)) { print(proj4string(d$data)) print(proj4string(newdata)) stop(paste(name, ": data item in gstat object and newdata have different coordinate reference systems")) } } if (d$nmax == Inf) nmax = as.integer(-1) else nmax = as.integer(d$nmax) nmin = as.integer(max(0, d$nmin)) if (d$maxdist == Inf) maxdist = as.numeric(-1) else maxdist = d$maxdist if (d$dummy) { # tr = terms(d$locations) if (is.null(d$beta) || length(d$beta) == 0) stop("dummy data should have beta defined") if (d$degree != 0) stop("dummy data cannot have non-zero degree arg; use formula") # loc.dim = length(attr(tr, "term.labels")) loc.dim = dim(coordinates(newdata))[[2]] .Call(gstat_new_dummy_data, as.integer(loc.dim), as.integer(d$has.intercept), as.double(d$beta), nmax, nmin, maxdist, as.integer(d$vfn), as.integer(is.projected(newdata)), as.integer(d$vdist)) raw = list(xlevels = NULL) } else { if (is.null(d$weights)) w = numeric(0) else w = d$weights raw = gstat.formula(d$formula, d$data) .Call(gstat_new_data, as.double(raw$y), as.double(raw$locations), as.double(raw$X), as.integer(raw$has.intercept), as.double(d$beta), nmax, nmin, maxdist, as.integer(d$force), as.integer(d$vfn), as.numeric(w), double(0.0), as.integer(d$degree), as.integer(is.projected(d$data)), as.integer(d$vdist), as.double(d$lambda), as.integer(d$omax)) } if (!is.null(object$model[[name]])) load.variogram.model(object$model[[name]], c(i - 1, i - 1), max_dist = max_dist) raw = gstat.formula.predict(d$formula, newdata, na.action = na.action, (length(BLUE) == 2 && BLUE[2]), xlev = raw$xlevels) if (is.null(new.X)) new.X = raw$X else new.X = cbind(new.X, raw$X) if (i > 1) { for (j in 1:(i - 1)) { cross = cross.name(names(object$data)[j], name) if (!is.null(object$model[[cross]])) load.variogram.model(object$model[[cross]], c(i - 1, j - 1), max_dist = max_dist) } } } if (!is.null(object$set)) gstat.load.set(object$set) if (!is.null(object$merge)) gstat.load.merge(object) if (is(newdata, "SpatialPolygons")) { pol = newdata@polygons if (length(pol) != nrow(raw$locations)) stop("polygons and center points length mismatch") block = matrix(NA, 0, 2) nd = as(newdata, "SpatialPolygons") block.cols = rep(as.numeric(NA), length(pol)) for (i in seq(along = pol)) { sps.args$x = nd[i] cc = coordinates(do.call("spsample", sps.args)) cc[,1] = cc[,1] - raw$locations[i,1] cc[,2] = cc[,2] - raw$locations[i,2] block.cols[i] = nrow(block) + 1 block = rbind(block, cc) } if (length(pol) == 1) block.cols = 2 } else if (is(newdata, "SpatialLines")) { lin = newdata@lines if (length(lin) != nrow(raw$locations)) stop("lines and line midpoints length mismatch") block = matrix(NA, 0, 2) nd = as(newdata, "SpatialLines") block.cols = rep(as.numeric(NA), length(lin)) for (i in seq(along = lin)) { sps.args$x = nd[i] cc = coordinates(do.call("spsample", sps.args)) cc[,1] = cc[,1] - raw$locations[i,1] cc[,2] = cc[,2] - raw$locations[i,2] block.cols[i] = nrow(block) + 1 block = rbind(block, cc) } if (length(lin) == 1) block.cols = 2 } else if (!is.null(dim(block))) { # i.e., block is data.frame or matrix if (is.data.frame(block) && !is.null(block$weights)) { bl_weights = block$weights block$weights = NULL } block = data.matrix(block) # converts to numeric block.cols = ncol(block) } else { block = as.numeric(block) # make sure it's not integer block.cols = numeric(0) } # handle NA's in the parts of newdata used: valid.pattern = NULL if (any(is.na(raw$locations)) || any(is.na(new.X))) { valid.pattern = !(apply(cbind(raw$locations, new.X), 1, function(x) any(is.na(x)))) raw$locations.all = raw$locations raw$locations = as.matrix(raw$locations[valid.pattern, ]) new.X = as.matrix(new.X[valid.pattern, ]) } if (nsim) { if (indicators == TRUE) nsim = -abs(nsim) # random path: randomly permute row indices perm = sample(seq(along = new.X[, 1])) ret = .Call(gstat_predict, as.integer(nrow(as.matrix(new.X))), as.double(as.vector(raw$locations[perm, ])), as.double(as.vector(new.X[perm,])), as.integer(block.cols), as.vector(block), as.vector(bl_weights), as.integer(nsim), as.integer(BLUE))[[1]] if (nsim == 1) colsel = seq(1, by=2, length.out=nvars) # pred1 var1 pred2 var2 ... else colsel = TRUE ret = data.frame(cbind(raw$locations, matrix(ret[order(perm), colsel], nrow(as.matrix(new.X)), abs(nsim) * nvars))) } else { ret = .Call(gstat_predict, as.integer(nrow(as.matrix(new.X))), as.double(as.vector(raw$locations)), as.vector(new.X), as.integer(block.cols), as.vector(block), as.vector(bl_weights), as.integer(nsim), as.integer(BLUE))[[1]] ret = data.frame(cbind(raw$locations, ret)) } .Call(gstat_exit, NULL) if (!is.null(valid.pattern) && any(valid.pattern)) { ret.all = data.frame(matrix(NA, length(valid.pattern), ncol(ret))) ret.all[, 1:ncol(raw$locations.all)] = raw$locations.all ret.all[valid.pattern, ] = ret ret = ret.all } if (abs(nsim) > 0) { names.vars = names(object$data) if (length(names.vars) > 1) names.vars = paste(rep(names.vars, each = abs(nsim)), paste("sim", 1:abs(nsim), sep = ""), sep = ".") else names.vars = paste("sim", 1:abs(nsim), sep = "") } else names.vars = create.gstat.names(names(object$data)) names(ret) = c(dimnames(raw$locations)[[2]], names.vars) if (return.sp) { if (is(newdata, "SpatialPolygons")) { row.names(ret) = sapply(newdata@polygons, function(x) slot(x, "ID")) ret = SpatialPolygonsDataFrame(as(newdata, "SpatialPolygons"), ret, match.ID = TRUE) } else if (is(newdata, "SpatialLines")) { row.names(ret) = sapply(newdata@lines, function(x) slot(x, "ID")) ret = SpatialLinesDataFrame(as(newdata, "SpatialLines"), ret, match.ID = TRUE) } else { coordinates(ret) = dimnames(raw$locations)[[2]] if (gridded(newdata)) { returnFullGrid = fullgrid(newdata) fullgrid(newdata) = FALSE ret = new("SpatialPixelsDataFrame", new("SpatialPixels", as(ret, "SpatialPoints"), grid = newdata@grid, grid.index = newdata@grid.index, bbox = newdata@bbox), data = ret@data, coords.nrs = ret@coords.nrs) fullgrid(ret) = returnFullGrid } } slot(ret, "proj4string") = slot(newdata, "proj4string") if (to_sf) { ret = if (to_stars) { if (!requireNamespace("stars", quietly = TRUE)) stop("stars required: install that first") # nocov if (nsim) sim_to_dimension(stars::st_as_stars(ret), nsim) else stars::st_as_stars(ret) } else { if (gridded(ret) && fullgrid(ret)) fullgrid(ret) = FALSE if (!requireNamespace("sf", quietly = TRUE)) stop("sf required: install that first") # nocov sf::st_as_sf(ret) } } } return(ret) } # call with: create.gstat.names(names(object$data)) # creates the names of the output columns in case of (multivariable) prediction create.gstat.names <- function(ids, names.sep = ".") { nvars = length(ids) names.vars = character(nvars * 2 + nvars * (nvars - 1)/2) pos = 1 for (i in 1:length(ids)) { name = ids[i] names.vars[1 + (i - 1) * 2] = paste(name, "pred", sep = names.sep) names.vars[2 + (i - 1) * 2] = paste(name, "var", sep = names.sep) if (i > 1) { for (j in 1:(i - 1)) { cross = paste(ids[j], name, sep = names.sep) names.vars[nvars * 2 + pos] = paste("cov", cross, sep = names.sep) pos = pos + 1 } } } return(names.vars) } getMaxDist = function(dataLst, newdata) { spBbox <- SpatialPoints(cbind(newdata@bbox[cbind(c(1,1,1,1), c(1,2,1,1))], newdata@bbox[cbind(c(2,2,2,2), c(1,1,1,2))]), proj4string = newdata@proj4string) d <- c(spDists(spBbox)[cbind(c(1,3),c(2,4))]) # d = apply(bbox(newdata), 1, diff) if (!is.null(dataLst[[1]]$data)) { spBbox2 <- SpatialPoints(cbind(dataLst[[1]]$data@bbox[cbind(c(1,1,1,1), c(1,2,1,1))], dataLst[[1]]$data@bbox[cbind(c(2,2,2,2), c(1,1,1,2))]), proj4string = dataLst[[1]]$data@proj4string) d2 <- c(spDists(spBbox2)[cbind(c(1,3),c(2,4))]) # d2 = apply(bbox(dataLst[[1]]$data), 1, diff) d = apply(rbind(d,d2), 2, max) # there are pathetic cases where this would not be sufficient } if (length(d) == 2) d = c(d, 0) stopifnot(length(d) == 3) d } gstat/R/load.variogram.model.R0000644000176200001440000000244313777370515015746 0ustar liggesusers# $Id: load.variogram.model.q,v 1.7 2008-11-12 10:04:22 edzer Exp $ "load.variogram.model" <- function(model, ids = c(0, 0), max_dist = rep(-1.0, 3)) { if (missing(model)) stop("model is missing"); if (!inherits(model, "variogramModel")) stop("model should be of mode variogramModel (use function vgm)") if (any(model$range < 0.0)) { print(model) stop("variogram range can never be negative") } stopifnot(length(max_dist) == 3) anis = c(model$ang1, model$ang2, model$ang3, model$anis1, model$anis2) if (is.null(attr(model, "table"))) covtable = numeric(0) else { covtable = attr(model, "table") if (dim(model)[1] > 1 || model$model != "Tab") stop("table can only have one single model") } # max_dist hack here for Lin(0) models: # if (max_dist > 0) { # w = which(model$model %in% c("Lin") & model$range == 0) # if (length(w) > 0) { # model[w,"psill"] = max_dist * model[w,"psill"] # model[w,"range"] = max_dist # cat("Conversion into equivalent model:\n") # print(model) # } # } if (!any(model$model %in% c("Lin", "Pow"))) max_dist = rep(-1.0, 3) # ignore .Call(gstat_load_variogram, as.integer(ids), as.character(model$model), as.numeric(model$psill), as.numeric(model$range), as.numeric(model$kappa), as.numeric(anis), covtable, as.numeric(max_dist)) } gstat/R/gstat.cv.R0000644000176200001440000000525314013273067013461 0ustar liggesusers# $Id: gstat.cv.q,v 1.9 2009-10-30 16:11:21 edzer Exp $ "gstat.cv" <- function (object, nfold = nrow(object$data[[1]]$data), remove.all = FALSE, verbose = interactive(), all.residuals = FALSE, ...) { if (!inherits(object, "gstat")) stop("first argument should be of class gstat") var1 = object$data[[1]] data = var1$data formula = var1$formula if (all.residuals) { nc = length(object$data) ret = data.frame(matrix(NA, nrow(data), nc)) } else { cc = coordinates(data) rownames(cc) = NULL df = data.frame(matrix(as.numeric(NA), nrow(data), 2)) ret = SpatialPointsDataFrame(cc, df, proj4string = data@proj4string) } if (missing(nfold)) nfold = 1:nrow(data) if (length(nfold) == nrow(data)) fold = nfold else if (nfold < nrow(data)) fold = sample(nfold, nrow(data), replace = TRUE) else fold = 1:nrow(data) if (all.residuals || (remove.all && length(object$data) > 1)) { all.data = list() for (v in 1:length(object$data)) all.data[[v]] = object$data[[v]]$data } if (verbose) pb <- txtProgressBar(1,length(unique(fold)),style=3) for (i in sort(unique(fold))) { if (verbose) setTxtProgressBar(pb, i) sel = which(fold == i) object$data[[1]]$data = data[-sel, ] if (remove.all && length(object$data) > 1) { for (v in 2:length(object$data)) { varv = object$data[[v]] varv$data = all.data[[v]] #atv = gstat.formula(varv$formula, varv$data)$locations #at1 = gstat.formula(formula, data[sel, ])$locations atv = coordinates(varv$data) at1 = coordinates(data[sel,]) cc = rbind(atv, at1) rownames(cc) = NULL # as there will be duplicates all = SpatialPoints(cc, proj4string = data@proj4string) zd = zerodist(all) skip = zd[, 1] object$data[[v]]$data = varv$data[-skip, ] } } x = predict(object, newdata = data[sel, ], ...) if (all.residuals) { for (i in 1:length(object$data)) { var.i = object$data[[i]] data.i = all.data[[i]] formula.i = var.i$formula observed = gstat.formula(formula.i, data.i)$y[sel] pred.name = paste(names(object$data)[i], "pred", sep = ".") residual = as.numeric(observed - x[[pred.name]]) ret[sel, i] = residual } } else { ret[[1]][sel] = x[[1]] ret[[2]][sel] = x[[2]] } } if (verbose) cat("\n") if (! all.residuals) { names(ret) = names(x)[1:2] ret$observed = gstat.formula(formula, data)$y pred.name = paste(names(object$data)[1], "pred", sep = ".") ret$residual = ret$observed - ret[[pred.name]] var.name = paste(names(object$data)[1], "var", sep = ".") ret$zscore = ret$residual/sqrt(ret[[var.name]]) ret$fold = fold } else names(ret) = names(object$data) if (!is.null(object$locations)) ret = as.data.frame(ret) ret } gstat/R/vgm.panel.R0000644000176200001440000000472513777370515013636 0ustar liggesusers# $Id: vgm.panel.q,v 1.7 2007-06-08 06:45:52 edzer Exp $ "get.direction.unitv" <- function(alpha, beta) { cb = cos(beta) c(cb * sin(alpha), cb * cos(alpha), sin(beta)) } "vgm.panel.xyplot" <- function (x, y, subscripts, type = "p", pch = plot.symbol$pch, col, col.line = plot.line$col, col.symbol = plot.symbol$col, lty = plot.line$lty, cex = plot.symbol$cex, ids, lwd = plot.line$lwd, model = model, direction = direction, labels, shift = shift, mode = mode, ...) { x <- as.numeric(x) y <- as.numeric(y) if (length(x) > 0) { if (!missing(col)) { if (missing(col.line)) col.line <- col if (missing(col.symbol)) col.symbol <- col } plot.symbol <- trellis.par.get("plot.symbol") plot.line <- trellis.par.get("plot.line") lpoints(x = x, y = y, cex = cex, col = col.symbol, pch = pch, type = type, ...) if (!is.null(labels)) ltext(x = x + shift * max(x), y = y, labels = labels[subscripts]) if (mode == "direct") { if (!missing(model) && !is.null(model)) { ang.hor <- pi * (direction[1]/180) ang.ver <- pi * (direction[2]/180) dir <- get.direction.unitv(ang.hor, ang.ver) ret <- variogramLine(model, max(x), dir = dir) llines(x = ret$dist, y = ret$gamma, lty = lty, col = col.line, lwd = lwd) } } else if (mode == "cross") { id <- as.character(ids[subscripts][1]) if (!missing(model) && !is.null(model)) { if (inherits(model, "gstat")) m = model$model else m = model if (!is.list(m)) stop("model argument not of class gstat or list") if (is.list(m) && !is.null(m[[id]])) { ang.hor <- pi * (direction[1]/180) ang.ver <- pi * (direction[2]/180) dir <- get.direction.unitv(ang.hor, ang.ver) ret <- variogramLine(m[[id]], max(x), dir = dir) llines(x = ret$dist, y = ret$gamma, lty = lty, col = col.line, lwd = lwd) } } } else if (mode == "directional") { if (!missing(model) && !is.null(model)) { dir <- c(1, 0, 0) if (!missing(direction)) { ang.hor <- pi * (direction[subscripts][1]/180.0) dir <- get.direction.unitv(ang.hor, 0) } ret <- variogramLine(model, max(x), dir = dir) llines(x = ret$dist, y = ret$gamma, lty = lty, col = col.line, lwd = lwd) } } } } gstat/R/gstatOptions.R0000644000176200001440000000061513777370515014437 0ustar liggesusers.gstatOptions <- new.env(FALSE, globalenv()) assign("gstat_progress", TRUE, envir = .gstatOptions) get_gstat_progress <- function() { get("gstat_progress", envir = .gstatOptions) } set_gstat_progress <- function(value) { stopifnot(is.logical(value)) stopifnot(length(value) == 1) assign("gstat_progress", value, envir = .gstatOptions) get_gstat_progress() } gstat/R/map.to.lev.R0000644000176200001440000000146013777370515013723 0ustar liggesusers# $Id: map.to.lev.q,v 1.2 2006-02-10 19:01:07 edzer Exp $ "map.to.lev" <- function (data, xcol = 1, ycol = 2, zcol = c(3, 4), ns = names(data)[zcol]) { len = nrow(data) d = matrix(nrow = len * length(zcol), ncol = 3) xnames = NULL if (length(ns) > 1 && length(ns) != length(zcol)) stop("names should have length 1 or equal to length of zcol") nr = 1 for (i in zcol) { if (length(ns) == 1) nm = rep(paste(ns, nr), len) else nm = rep(ns[nr], len) range = (1 + (nr - 1) * len):(nr * len) d[range, ] = cbind(data[, xcol], data[, ycol], data[, i]) xnames = c(xnames, nm) nr = nr + 1 } nms <- factor(xnames, levels = unique(xnames)) d = data.frame(d, nms) names(d) = c("x", "y", "z", "name") d } gstat/R/variogram.gstat.R0000644000176200001440000000203714147167622015044 0ustar liggesusers# $Id: variogram.gstat.q,v 1.9 2007-04-06 11:29:58 edzer Exp $ "variogram.gstat" = function (object, ...) { if (!inherits(object, "gstat")) stop("first argument should be of class gstat") y = list() locations = list() X = list() beta = list() grid = list() projected = TRUE for (i in seq(along = object$data)) { d = object$data[[i]] beta[[i]] = d$beta if (i > 1 && !identical(object$data[[1]]$data@proj4string@projargs, d$data@proj4string@projargs)) stop("data items in gstat object have different coordinate reference systems") raw = gstat.formula(d$formula, d$data) y[[i]] = raw$y locations[[i]] = raw$locations X[[i]] = raw$X grid[[i]] = raw$grid if (is(d$data, "Spatial")) projected = is.projected(d$data) if (d$degree != 0) stop("degree != 0: residual variograms wrt coord trend using degree not supported") } names(y) = names(locations) = names(X) = names(object$data) # call variogram.default() next: variogram(y, locations, X, trend.beta = beta, grid = grid, g = object, ..., projected = projected) } gstat/R/gstat.debug.R0000644000176200001440000000023513777370515014146 0ustar liggesusers# $Id: gstat.debug.q,v 1.3 2006-02-10 19:01:07 edzer Exp $ "gstat.debug" <- function(level = 0) { invisible(.Call(gstat_debug_level, as.integer(level))) } gstat/R/variogramLine.R0000644000176200001440000000232013777370515014533 0ustar liggesusers# $Id: variogramLine.q,v 1.4 2008-08-18 16:32:42 edzer Exp $ "variogramLine" <- function(object, maxdist, n = 200, min=1.0e-6 * maxdist, dir = c(1,0,0), covariance = FALSE, ..., dist_vector = numeric(0), debug.level = 0) { if (missing(object)) stop("model is missing"); if (!inherits(object, "variogramModel")) stop("model should be of mode variogramModel (use function vgm)") if (length(dist_vector) > 0) maxdist = 0.0 else if (missing(maxdist)) stop("maxdist or dist_vector needs to be set"); if (length(dir) != 3) stop("dir should be numeric vector of length 3") .Call(gstat_init, as.integer(debug.level)) pars = c(min,maxdist,n,dir) load.variogram.model(object, c(0,0)) # loads object into gstat ret = .Call(gstat_variogram_values, as.integer(c(0,0)), as.numeric(pars), as.integer(covariance), as.numeric(dist_vector)) .Call(gstat_exit, 0); if (is.matrix(dist_vector)) matrix(ret[[2]], nrow(dist_vector), ncol(dist_vector)) else data.frame(dist=ret[[1]], gamma=ret[[2]]) } # Sat Mar 14 15:11:55 CET 2015: removed this: # "variogram.line" <- function(..., deprecate = TRUE) { # if (deprecate) # cat("variogram.line is DEPRECATED, please use variogramLine instead\n") # variogramLine(...) # } gstat/R/krige.R0000644000176200001440000001445014013273775013036 0ustar liggesusers# $Id: krige.q,v 1.15 2009-02-20 13:53:38 edzer Exp $ if (!isGeneric("krige")) setGeneric("krige", function(formula, locations, ...) standardGeneric("krige")) "krige.locations" <- function (formula, locations, data = sys.frame(sys.parent()), newdata, model = NULL, ..., beta = NULL, nmax = Inf, nmin = 0, omax = 0, maxdist = Inf, block = numeric(0), nsim = 0, indicators = FALSE, na.action = na.pass, debug.level = 1) { g = gstat(formula = formula, locations = locations, data = data, model = model, beta = beta, nmax = nmax, nmin = nmin, omax = omax, maxdist = maxdist, ...) predict(g, newdata = newdata, block = block, nsim = nsim, indicators = indicators, na.action = na.action, debug.level = debug.level) } setMethod("krige", c("formula", "formula"), krige.locations) krige.spatial <- function(formula, locations, newdata, model = NULL, ..., beta = NULL, nmax = Inf, nmin = 0, omax = 0, maxdist = Inf, block = numeric(0), nsim = 0, indicators = FALSE, na.action = na.pass, debug.level = 1) { # locations = coordinates(arg2) g = gstat(formula = formula, # locations = locations, data = locations, model = model, beta = beta, nmax = nmax, nmin = nmin, omax = omax, maxdist = maxdist, ...) predict(g, newdata = newdata, block = block, nsim = nsim, indicators = indicators, na.action = na.action, debug.level = debug.level) } setMethod("krige", c("formula", "Spatial"), krige.spatial) setMethod("krige", c("formula", "NULL"), function(formula, locations, newdata, ...) { # manual dispatch based on newdata: if (inherits(newdata, c("sf", "sfc", "stars"))) krige.sf(formula, locations, newdata = newdata, ...) else krige.spatial(formula, locations, newdata = newdata, ...) } ) krige.sf <- function(formula, locations, newdata, ..., nsim = 0) { if (!requireNamespace("sf", quietly = TRUE)) stop("sf required: install that first") # nocov if (!requireNamespace("stars", quietly = TRUE)) stop("stars required: install that first") # nocov crs = sf::st_crs(newdata) if (!is.null(locations)) { stopifnot(sf::st_crs(locations) == sf::st_crs(newdata)) crs = sf::st_crs(locations) if (!isTRUE(sf::st_is_longlat(locations))) { sf::st_crs(locations) = sf::NA_crs_ sf::st_crs(newdata) = sf::NA_crs_# to avoid problems not handled by sp... } locations = as(locations, "Spatial") } ret = krige(formula, locations, as(newdata, "Spatial"), ..., nsim = nsim) if (gridded(ret)) { st = stars::st_as_stars(ret) if (nsim > 0) st = sim_to_dimension(st, nsim) sf::st_set_crs(st, crs) } else sf::st_set_crs(sf::st_as_sf(ret), crs) } setMethod("krige", c("formula", "sf"), krige.sf) sim_to_dimension = function(st, nsim) { nms = names(stars::st_dimensions(st)) if (length(st) > nsim) { nvars = length(st) / nsim l = vector("list", nvars) vars = unique(sub("([^.]+)\\.[[:alnum:]]+$", "\\1", names(st))) for (i in 1:nvars) { range = seq((i-1) * nsim + 1, length.out = nsim) m = setNames(st[range], paste0("sim", 1:nsim)) l[[i]] = setNames(stars::st_set_dimensions(merge(m), names = c(nms, "sample")), vars[i]) } do.call(c, l) } else { if (nsim > 1) setNames(stars::st_set_dimensions(merge(st), names = c(nms, "sample")), "var1") else st } } setMethod(krige, signature("formula", "ST"), function(formula, locations, newdata, model, ...) { krigeST(formula, locations, newdata, model,...) } ) if (!isGeneric("idw")) setGeneric("idw", function(formula, locations, ...) standardGeneric("idw")) idw.locations <- function (formula, locations, data = sys.frame(sys.parent()), newdata, nmax = Inf, nmin = 0, omax = 0, maxdist = Inf, block = numeric(0), na.action = na.pass, idp = 2.0, debug.level = 1) { krige(formula, locations, data, newdata, nmax = nmax, nmin = nmin, omax = omax, maxdist = maxdist, block = block, na.action = na.action, set = list(idp = idp), debug.level = debug.level) } setMethod("idw", c("formula", "formula"), idw.locations) idw.spatial <- function (formula, locations, newdata, nmax = Inf, nmin = 0, omax = 0, maxdist = Inf, block = numeric(0), na.action = na.pass, idp = 2.0, debug.level = 1) { krige(formula, locations, newdata, nmax = nmax, nmin = nmin, omax = omax, maxdist = maxdist, block = block, na.action = na.action, set = list(idp = idp), debug.level = debug.level, model = NULL) } setMethod("idw", c("formula", "Spatial"), idw.spatial) idw.sf <- function (formula, locations, newdata, ..., idp = 2.0) { if (!requireNamespace("sf", quietly = TRUE)) stop("sf required: install that first") # nocov if (!requireNamespace("stars", quietly = TRUE)) stop("stars required: install that first") # nocov ret = krige(formula, locations, newdata, ..., set = list(idp = idp), model = NULL) if (inherits(newdata, c("sf", "sfc"))) sf::st_as_sf(ret) else if (inherits(newdata, "stars")) stars::st_as_stars(ret) else stop("newdata should be of class sf or stars") } setMethod("idw", c("formula", "sf"), idw.sf) STx2SpatialPoints = function(x, multiplyTimeWith = 1.0) { x = as(geometry(x), "STI") t1 = as.numeric(as.POSIXct(index(x@time))) t2 = as.numeric(x@endTime) time = multiplyTimeWith * (t1 + t2) / 2 cc = cbind(coordinates(x), time) SpatialPoints(cc, proj4string = x@sp@proj4string) } STxDF2SpatialPointsDataFrame = function(x, multiplyTimeWith = 1.0) { pts = STx2SpatialPoints(geometry(x), multiplyTimeWith) SpatialPointsDataFrame(pts, x@data) } SpatialPointsDataFrame2STxDF = function(x, class, tz = "", origin = as.POSIXct("1970-01-01",tz=tz)) { cc = coordinates(x) time = as.POSIXct(cc[,ncol(cc)], tz=tz, origin = origin) sp = SpatialPoints(cc[,-ncol(cc)], proj4string = x@sp@proj4string) st = as(STI(sp, time), class) addAttrToGeom(STI(sp, time), x@data) } idw.ST <- function (formula, locations, newdata, nmax = Inf, nmin = 0, omax = 0, maxdist = Inf, block = numeric(0), na.action = na.pass, idp = 2.0, debug.level = 1, multiplyTimeWith = 1.0) { stopifnot(ncol(coordinates(locations@sp)) == 2) ret = krige(formula, STxDF2SpatialPointsDataFrame(locations, multiplyTimeWith), STx2SpatialPoints(newdata, multiplyTimeWith), nmax = nmax, nmin = nmin, omax = omax, maxdist = maxdist, block = block, na.action = na.action, set = list(idp = idp), debug.level = debug.level, model = NULL) SpatialPointsDataFrame2STxDF(ret, class(geometry(newdata))) } setMethod("idw", c("formula", "ST"), idw.ST) gstat/R/vgm.R0000644000176200001440000001110013777370515012521 0ustar liggesusers# $Id: vgm.q,v 1.12 2007-02-27 22:09:32 edzer Exp $ warn.angle3 = TRUE "vgm" <- function(psill = NA, model, range = NA, nugget, add.to, anis, kappa = 0.5, ..., covtable, Err = 0) { add.to.df = function(x, y) { x = rbind(x, y) row.names(x) = 1:nrow(x) return(x) } if (is.character(psill)) { # as of ``vgm("Sph")'' if (length(psill) > 1) { ret = lapply(psill, function(x) vgm(x)) class(ret) = c("variogramModelList", "list") return(ret) } # else: if (psill == "Nug") return(vgm(NA, "Nug", NA)) else return(vgm(NA, psill, NA, NA)) } stopifnot(length(psill) == 1) stopifnot(length(range) == 1) stopifnot(missing(nugget) || length(nugget) == 1) stopifnot(length(kappa) == 1) m = .Call(gstat_get_variogram_models, as.integer(0)) n = length(m) mf = factor(m, levels = m) if (missing(model)) { ml = .Call(gstat_get_variogram_models, as.integer(1)) mlf = factor(ml, levels = ml) return(data.frame(short = mf, long = mlf)) } if (length(model) > 1) { ret = lapply(model, function(x) vgm(,x)) class(ret) = c("variogramModelList", "list") return(ret) } table = NULL if (model == "Tab" && !missing(covtable)) { table = as.matrix(covtable) if (NCOL(table) != 2) stop("covtable should be a 2-column matrix with distance and cov.") range = max(table[,1]) if (min(table[,1]) != 0.0) stop("the first covariance value should be at distance 0.0") table = table[,2] mf = factor(c(m, "Tab"), levels = c(m, "Tab")) if (!missing(add.to) || !missing(nugget) || Err > 0) stop("cannot add submodels or nugget to covariance Table model") } else if (!any(m == model)) stop(paste("variogram model", model, "unknown\n")) if (missing(anis)) anis = c(0,0,0,1,1) if (length(anis) == 2) anis = c(anis[1], 0, 0, anis[2], 1) else if (length(anis) != 5) stop("anis vector should have length 2 (2D) or 5 (3D)") if (warn.angle3 && anis[3] != 0.0) { warn.angle3 = FALSE warning("you are using the third rotation angle; this code is based on the GSLIB2 code\nand must contain the bug described at the end of http://pangea.stanford.edu/ERE/research/scrf/software/gslib/bug/") } if (!is.na(range)) { if (model != "Nug") { if (model != "Lin" && model != "Err" && model != "Int") if (range <= 0.0) stop("range should be positive") else if(range < 0.0) stop("range should be non-negative") } else { if (range != 0.0) stop("Nugget should have zero range") if (anis[4] != 1.0 || anis[5] != 1.0) stop("Nugget anisotropy is not meaningful") } } if (!missing(nugget)) { ret = data.frame(model=mf[mf==model], psill=psill, range=range, kappa = kappa, ang1=anis[1], ang2=anis[2], ang3=anis[3], anis1=anis[4], anis2=anis[5]) n.vgm = data.frame(model=mf[mf=="Nug"], psill=nugget, range=0, kappa = 0.0, ang1=0.0, ang2=0.0, ang3=0.0, anis1=1.0, anis2=1.0) ret = add.to.df(n.vgm, ret) } else ret = data.frame(model=mf[mf==model], psill=psill, range=range, kappa = kappa, ang1=anis[1], ang2=anis[2], ang3=anis[3], anis1=anis[4], anis2=anis[5]) if (!missing(add.to)) ret = add.to.df(data.frame(add.to), ret) if (Err > 0) ret = add.to.df(data.frame(model=mf[mf=="Err"], psill=Err, range=0.0, kappa = kappa, ang1=anis[1], ang2=anis[2], ang3=anis[3], anis1=anis[4], anis2=anis[5]), ret) if (!is.null(table)) attr(ret, "table") = table class(ret) = c("variogramModel", "data.frame") ret } as.vgm.variomodel = function(m) { model = NULL if (m$cov.model == "exponential") model = "Exp" else if (m$cov.model == "circular") model = "Cir" else if (m$cov.model == "gaussian") model = "Gau" else if (m$cov.model == "linear") # model = "Lin" stop("no correct conversion available; use power model with power 1?") else if (m$cov.model == "matern") model = "Mat" else if (m$cov.model == "wave") model = "Wav" else if (m$cov.model == "power") model = "Pow" else if (m$cov.model == "spherical") model = "Sph" else if (m$cov.model == "pure.nugget") return(vgm(m$nugget + m$cov.pars[1], "Nug", 0)) else stop("variogram model not supported") # "cauchy", #,"cubic", # "gneiting", # "gneiting.matern", # "powered.exponential", # "wave") ) { vgm(m$cov.pars[1], model, m$cov.pars[2], m$nugget, kappa = m$kappa) } #$lambda #[1] 1 #$trend #[1] "cte" #$max.dist #[1] 1441.83 #attr(,"class") #[1] "variomodel" plot.variogramModel = function(x, cutoff, ..., type = 'l') { if (missing(cutoff)) stop("parameter cutoff needs to be specified") l = variogramLine(x, cutoff, ...) xyplot(gamma ~ dist, l, ylim = c(0, 1.04 * max(l$gamma)), xlim = c(0, max(l$dist)), type = type, xlab = "distance", ylab = "semivariance") } gstat/R/variogram.formula.R0000644000176200001440000000163013777370515015372 0ustar liggesusers# $Id: variogram.formula.q,v 1.8 2006-02-10 19:01:07 edzer Exp $ "variogram.formula" <- function (object, locations = coordinates(data), data, ...) { if ((missing(locations) && inherits(data, "sf")) || (inherits(locations, "sf"))) { if (!requireNamespace("sf", quietly = TRUE)) stop("sf required: install that first") # nocov if (missing(locations)) data = as(data, "Spatial") else locations = as(locations, "Spatial") } # gstat.formula takes care of the case where locations contains # both data and coordinates --- see there. ## ret = gstat.formula(object, locations, data) ## variogram(object = ret$y, locations = ret$locations, X = ret$X, ...) if ((missing(locations) && is(data, "ST")) || (is(locations, "ST"))) variogramST(formula = object, locations = locations, data = data, ...) else { g = gstat(formula = object, locations = locations, data = data) variogram(g, ...) } } gstat/R/spplot.R0000644000176200001440000000121013777370515013252 0ustar liggesusersspplot.vcov = function(x, ...) { basenames = sub(".pred", "", names(x)[grep(".pred",names(x))]) n = length(basenames) names = NULL skip = NULL for (i in 1:n) { skp = rep(TRUE, n) pos = 1 if (i > 1) { for (j in 1:(i-1)) { names = c(names, paste("cov", basenames[j], basenames[i], sep = ".")) skp[pos] = FALSE pos = pos + 1 } } names = c(names, paste(basenames[i], ".var", sep = "")) skp[pos] = FALSE skip = c(skip, skp) } spplot(x, names, skip = skip, layout = c(n,n), as.table = TRUE, ...) } gstat/R/variogram.default.R0000644000176200001440000001477213777370515015364 0ustar liggesusers# $Id: variogram.default.q,v 1.29 2009-11-02 21:33:17 edzer Exp $ "variogram.default" <- function(object, locations, X, cutoff, width = cutoff/15.0, alpha = 0, beta = 0, tol.hor = 90/length(alpha), tol.ver = 90/length(beta), cressie = FALSE, dX = numeric(0), boundaries = numeric(0), cloud = FALSE, trend.beta = NULL, debug.level = 1, cross = TRUE, grid, map = FALSE, g = NULL, ..., projected = TRUE, lambda = 1.0, verbose = FALSE, covariogram = FALSE, PR = FALSE, pseudo = -1) { dots = list(...) if (length(dots) > 0) { warning(paste("the following arguments are ignored:", paste(dots, collapse = ", "))) } id1 = id2 = 0 ret = NULL if (missing(cutoff)) { if (is.logical(map) && map == TRUE) stop("for variogram maps, supply at least a cutoff") cutoff = numeric(0) } else if (width <= 0) stop("argument width should be positive") if (missing(width)) width = numeric(0) if (cloud == TRUE) width = 0 if (is.logical(map) && map == TRUE) { cells.dim = length(seq(-cutoff, cutoff, by = width)) grid.topology = GridTopology(rep(-cutoff, 2), rep(width, 2), rep(cells.dim, 2)) map = SpatialGrid(grid = grid.topology) } if (any(is.na(boundaries))) stop("no NA values allowed in boundaries") .Call(gstat_init, as.integer(debug.level)) if (!is.null(g) && !is.null(g$set)) gstat.load.set(g$set) id.names = NULL if (is.list(object) && is.list(locations)) { nvars = length(object) if (!is.null(names(object))) id.names = names(object) for (i in 1:nvars) { if (missing(X)) Xloc = rep(1, length(object[[i]])) else Xloc = X[[i]] t.beta = numeric(0) if (!is.null(trend.beta) && length(trend.beta) > 0) t.beta = trend.beta[[i]] else t.beta = numeric(0) if (missing(grid) || !is.list(grid)) { if (!is.null(g) && gridded(g$data[i]$data)) grd = unlist(gridparameters(g$data[i]$data)) else grd = numeric(0) } else grd = grid[[i]] .Call(gstat_new_data, as.double(object[[i]]), as.double(locations[[i]]), as.double(Xloc), as.integer(1), as.double(t.beta), as.integer(-1), as.integer(0), as.double(-1), as.integer(0), as.integer(1), double(0), grd, as.integer(0), as.integer(projected), as.integer(0), as.double(lambda), as.integer(0)) if (!is.null(g) && !is.null(g$model[[id.names[i]]])) load.variogram.model(g$model[[id.names[i]]], c(i - 1, i - 1)) } } else stop("argument object and locations should be lists") if (inherits(map, "SpatialGrid")) map = as.double(unlist(gridparameters(as(map, "SpatialGrid")))) pos = 0 ids = NULL bnd = NULL is.direct = NULL if (PR) { if (any(object[[1]] <= 0)) warning("pairwise relative variogram assumes non-negative data") covariogram = 2 } if (cross == "ONLY") { stopifnot(nvars >= 2) id.range = 2:nvars } else if (cross == TRUE) id.range = nvars:1 else id.range = 1:nvars for (id1 in id.range) { if (cross == "ST") id2range = 1 else if (cross == "ONLY") id2range = 1:(id1-1) else id2range = ifelse(cross, 1, id1):id1 for (id2 in id2range) { if (verbose) cat(".") if (is.null(id.names)) id = ifelse(id1 == id2, paste(id1), cross.name(id2, id1)) else id = ifelse(id1 == id2, paste(id.names[id1]), cross.name(id.names[id2], id.names[id1])) for (a in alpha) { for (b in beta) { direction = as.numeric(c(a, b, tol.hor, tol.ver)) # boundaries nees to be passed into the c code only ONCE: if (is.null(bnd)) bnd = boundaries else # NOT the first time we're here, so... bnd = numeric(0) ret.call = .Call(gstat_variogram, as.integer(c(id1 - 1, id2 - 1)), as.numeric(cutoff), as.numeric(width), as.numeric(direction), as.integer(cressie), as.numeric(dX), as.numeric(bnd), map, as.integer(covariogram), as.integer(pseudo)) if (is.logical(map) && map == FALSE) { np = ret.call[[1]] sel = np > 0 n.dir = length(sel[sel]) if (n.dir > 0) { dist = ret.call[[2]] gamma = ret.call[[3]] ret_cw = ret.call[[4]] # Sat Jul 16 16:19:59 CEST 2011 dir.a = rep(a, n.dir) dir.b = rep(b, n.dir) ids = c(ids, rep(id, n.dir)) is.direct = c(is.direct, id1 == id2) df = data.frame(np = np[sel], dist = dist[sel], gamma = gamma[sel], dir.hor = dir.a, dir.ver = dir.b) if (pos > 0) ret[(pos + 1):(pos + n.dir), ] = df else ret = df pos = pos + n.dir } } else { if (is.null(ret)) { ret = data.frame(ret.call[[1]], ret.call[[2]], ret.call[[4]], ret.call[[3]]) names = c("dx", "dy", id, paste("np", id, sep=".")) } else { ret = data.frame(ret, ret.call[[4]], ret.call[[3]]) names = c(names, id, paste("np", id, sep=".")) } names(ret) = names } } } } } if (verbose) cat("\n") .Call(gstat_exit, NULL) if (is.logical(map) && map == FALSE) { if (!is.null(ids)) { ret$id = factor(ids, levels = unique(ids)) attr(ret, "direct") = data.frame(id = unique(ids), is.direct = is.direct) if (cloud) { class(ret) = c("variogramCloud", "data.frame") attr(ret, ".BigInt") = 2^(4 * .Machine$sizeof.long) } else { class(ret) = c("gstatVariogram", "data.frame") if (length(boundaries) == 0) { cutoff = ret_cw[1] width = ret_cw[2] boundaries = seq(0, cutoff, width) if (!identical(max(boundaries), cutoff)) boundaries = c(boundaries, cutoff) } attr(ret, "boundaries") = boundaries attr(ret, "pseudo") = ret_cw[3] row.names(ret) = NULL } } } else { coordinates(ret) = c("dx", "dy") gridded(ret) = TRUE ret = list(map = ret) class(ret) = c("variogramMap", "list") } if (!is.null(ret)) { if (PR) attr(ret, "what") = "pairwise relative semivariance" else if (covariogram) attr(ret, "what") = "covariance" else if (cressie) attr(ret, "what") = "Cressie's semivariance" else attr(ret, "what") = "semivariance" } ret } gstat/R/ossfim.R0000644000176200001440000000143513777370515013242 0ustar liggesusers# $Id: ossfim.q,v 1.3 2006-02-10 19:01:07 edzer Exp $ "ossfim" <- function(spacings = 1:5, block.sizes = 1:5, model, nmax = 25, debug = 0) { n = floor(sqrt(nmax)) + 1 x = 0:(n-1) + .5 x = sort(c(-x, x)) ret = matrix(NA, length(spacings) * length(block.sizes), 3) r = 1 for (sp in spacings) { for (bl in block.sizes) { data.grid = data.frame(expand.grid(x * sp, x * sp), z = rep(1, length(x)^2)) names(data.grid) = c("x", "y", "z") gridded(data.grid) = c("x", "y") x0 = SpatialPoints(matrix(0, 1, 2)) kr = krige(z~1, data.grid, x0, block = c(bl, bl), model = model, nmax = nmax, set = list(debug = debug)) ret[r, ] = c(sp, bl, sqrt(kr[["var1.var"]][1])) r = r + 1 } } ret = data.frame(ret) names(ret) = c("spacing", "block.size", "kriging.se") ret } gstat/R/image.data.frame.R0000644000176200001440000000036313777370515015024 0ustar liggesusers# $Id: image.data.frame.q,v 1.4 2006-02-10 19:01:07 edzer Exp $ "image.data.frame" <- function (x, zcol = 3, xcol = 1, ycol = 2, asp = 1, ...) { image.default(xyz2img(xyz = x, zcol = zcol, xcol = xcol, ycol = ycol), asp = asp, ...) } gstat/R/xyz2img.R0000644000176200001440000000203113777370515013344 0ustar liggesusers# $Id: xyz2img.q,v 1.4 2006-02-10 19:01:07 edzer Exp $ "xyz2img" <- function (xyz, zcol = 3, xcol = 1, ycol = 2, tolerance = 10 * .Machine$double.eps) { if (ncol(xyz) < 3) stop("xyz object should have at least three columns") z = xyz[, zcol] x = xyz[, xcol] y = xyz[, ycol] xx = sort(unique(x)) yy = sort(unique(y)) nx = length(xx) ny = length(yy) nmax = max(nx, ny) difx = diff(xx) if (diff(range(unique(difx))) > tolerance) stop("x intervals are not constant") dify = diff(yy) if (diff(range(unique(dify))) > tolerance) stop("y intervals are not constant") dx = mean(difx) dy = mean(dify) xmin = min(xx) xmax = max(xx) xrange = xmax - xmin ymin = min(yy) ymax = max(yy) yrange = ymax - ymin row = round((x - xmin)/dx) + 1 col = round((y - ymin)/dy) + 1 zz = rep(as.numeric(NA), nx * ny) zz[row + nx * (col - 1)] = z zz = matrix(zz, nrow = nx, ncol = ny) list(x = seq(xmin, xmax, dx), y = seq(ymin, ymax, dy), z = zz) } gstat/R/print.variogramCloud.R0000644000176200001440000000054313777370515016052 0ustar liggesusers# $Id: print.variogramCloud.q,v 1.4 2007-10-18 10:13:13 edzer Exp $ as.data.frame.variogramCloud = function(x, row.names, optional, ...) { .BigInt = attr(x, ".BigInt") x$left = x$np %% .BigInt + 1 x$right = x$np %/% .BigInt + 1 x$np = NULL class(x) = "data.frame" x } print.variogramCloud <- function (x, ...) { print(as.data.frame(x), ...) } gstat/R/gstat.R0000644000176200001440000001033314147167535013057 0ustar liggesusers# $Id: gstat.q,v 1.28 2009-11-02 21:33:17 edzer Exp $ "cross.name" <- function(id1, id2) { paste(id1, id2, sep = ".") } "gstat" <- function (g, id, formula, locations, data = NULL, model = NULL, beta, nmax = Inf, nmin = 0, omax = 0, maxdist = Inf, force = FALSE, dummy = FALSE, set, fill.all = FALSE, fill.cross = TRUE, variance = "identity", weights = NULL, merge, degree = 0, vdist = FALSE, lambda = 1.0) { call = match.call() if (!missing(locations) && inherits(locations, "formula")) { if (!is.null(data)) coordinates(data) = locations # locations = NULL } else if (missing(data) && !missing(locations) && (is(locations, "Spatial") || inherits(locations, "sf"))) { data = locations locations = NULL } if (fill.all) { # fill all variogram models if (missing(g) || is.null(model)) stop("fill.all assumes object g and model are supplied") g.names = names(g$data) for (i in 1:length(g.names)) { g$model[[paste(g.names[i])]] = model if (fill.cross) { for (j in (i+1):length(g.names)) g$model[[cross.name(g.names[i], g.names[j])]] = model } } return(g) } if (!missing(g) && inherits(g, "gstat") && !missing(id) && !missing(model) && missing(formula) && missing(locations)) { # here, only direct or cross variogram model is defined g.names = names(g$data) if (length(id) == 2) { m1 = match(id[1], g.names) m2 = match(id[2], g.names) if (is.na(m1)) stop("first id does not match available data") if (is.na(m1)) stop("second id does not match available data") nm = cross.name(g.names[min(m1, m2)], g.names[max(m1, m2)]) } else if (length(id) == 1) { m1 = match(id, g.names) if (is.na(m1)) stop("id does not match available data") nm = g.names[m1] } else stop("id should have length 1 or 2") g$model[[nm]] = model return(g) } if (!inherits(formula, "formula")) stop("argument formula should be of class formula") #if (!inherits(locations, "formula") && !has.coordinates(data)) # stop("argument locations should be of class formula or matrix") if (inherits(data, "sf")) data = as(data, "Spatial") if (missing(beta) || is.null(beta)) beta = numeric(0) vfn = pmatch(variance, c("identity", "mu", "mu(1-mu)", "mu^2", "mu^3")) if (is.na(vfn)) stop("unknown value for variance function") if (vfn > 1 && length(beta) == 0) stop("non-identity variance function only allowed if beta is supplied") if (missing(g) || is.null(g)) { g = list() g[["data"]] = list() g[["model"]] = list() } else if (!dummy && inherits(g$data[[1]], "Spatial") && !identical(g$data[[1]]$data@proj4string@projargs, data@proj4string@projargs)) stop("data items in gstat object have different coordinate reference systems") if (missing(id)) id = paste("var", length(g$data) + 1, sep = "") g$data[[id]] = list(formula = formula, # locations = locations, data = data, has.intercept = attr(terms(formula), "intercept"), beta = beta, nmax = nmax, nmin = nmin, omax = omax, maxdist = maxdist, force = force, dummy = dummy, vfn = vfn, weights = weights, degree = degree, vdist = vdist, lambda = lambda) g$model[[id]] = model if (!missing(locations)) g$locations = locations if (!missing(set)) { if (!is.list(set)) stop("argument set should be a list") g$set = set } if (!missing(merge)) g$merge = merge g$call = call class(g) = c("gstat", "list") g } "[.gstat" <- function(x, ids) { if (is.numeric(ids)) { if (min(ids) < 1 || max(ids) > length(names(x$data))) stop("selection index(es) out of bound") ids = names(x$data)[ids] } else if (any(is.na(match(ids, names(x$data))))) stop("selected ids do not match those of gstat object") g = list() g$data = x$data[ids] if (length(ids) > 1) { ids.cross = NULL for (i in 2:length(ids)) for (j in 1:(i-1)) ids.cross = c(ids.cross, cross.name(ids[j], ids[i])) g$model = x$model[c(ids, ids.cross)] } else g$model = x$model[ids] if (!is.null(x$set)) g$set = x$set if (!is.null(g$merge)) g$merge = x$merge class(g) = c("gstat", "list") g } gstat/R/variogramST.R0000644000176200001440000003777614314525261014205 0ustar liggesusersVgmFillNA <- function(x, boundaries) { # pads the sample variogram with NA rows where no data are available. n = length(boundaries) - 1 ix = rep(NA, n) #ix[which(1:n %in% findInterval(x$dist, boundaries))] = 1:nrow(x) ix[ findInterval(x$dist, boundaries, rightmost.closed = TRUE) ] = 1:nrow(x) # x$b = boundaries[-1] x[ix,] } VgmAverage = function(ret, boundaries) { # take out NULL variograms: ret = ret[!sapply(ret, is.null)] # take care of missing rows... ret = lapply(ret, VgmFillNA, boundaries = c(0, 1e-6 * boundaries[2], boundaries[-1])) # weighted average: # sum np, weighted sum of gamma and dist devided by summed np np = apply(do.call(cbind, lapply(ret, function(x) x$np)), 1, sum, na.rm = TRUE) gamma = apply(do.call(cbind, lapply(ret, function(x) x$gamma*x$np)), 1, sum, na.rm = TRUE)/np dist = apply(do.call(cbind, lapply(ret, function(x) x$dist*x$np)), 1, sum, na.rm = TRUE)/np v = data.frame(np = np, dist = dist, gamma = gamma) class(v) = class(ret[[1]]) attr(v, "boundaries") = attr(ret[[1]], "boundaries") v[is.na(v)] = NA v } StVgmLag = function(formula, data, dt, pseudo, ...) { dotLst <- list(...) .ValidObs = function(formula, data) !is.na(data[[as.character(as.list(formula)[[2]])]]) d = dim(data) ret = vector("list", d[2] - dt) if (dt == 0) { for (i in 1:d[2]) { d0 = data[,i] valid = .ValidObs(formula, d0) if(sum(valid) <= 1) ret[[i]] <- NULL else { d0 = d0[valid,] ret[[i]] = variogram(formula, d0, ...) } } } else { for (i in 1:(d[2] - dt)) { d1 = data[, i] valid1 = .ValidObs(formula, d1) d2 = data[, i + dt] valid2 = .ValidObs(formula, d2) if(sum(valid1)==0 || sum(valid2)==0) ret[[i]] <- NULL else { d1 = d1[valid1,] d2 = d2[valid2,] obj = gstat(NULL, paste("D", i, sep=""), formula, d1, set = list(zero_dist = 3), beta = 0) obj = gstat(obj, paste("D", i+dt, sep=""), formula, d2, beta = 0) ret[[i]] = variogram(obj, cross = "ONLY", pseudo = pseudo, ...) } } } if(!is.null(dotLst$cloud)) { if(dotLst$cloud) ret <- do.call("rbind", ret) ret$id <- "var1" return(ret) } else { return(VgmAverage(ret, dotLst$boundaries)) } } variogramST = function(formula, locations, data, ..., tlags = 0:15, cutoff, width = cutoff/15, boundaries=seq(0,cutoff,width), progress = interactive(), pseudo = TRUE, assumeRegular=FALSE, na.omit=FALSE, cores = 1) { if (missing(data)) data = locations if (inherits(data, "stars")) { if (!requireNamespace("stars", quietly = TRUE)) stop("stars required: install that first") # nocov data = as(data, "STFDF") } if(missing(cutoff)) { ll = !is.na(is.projected(data@sp)) && !is.projected(data@sp) cutoff <- spDists(t(data@sp@bbox), longlat = ll)[1,2]/3 } if (formula[[3]] != 1) { # there is a regression model: data$resid = residuals(lm(formula, data, na.action = na.exclude)) formula = resid ~ 1 } if(inherits(data, c("STIDF", "sftime"))) return(variogramST.STIDF(formula, as(data, "STIDF"), tlags, cutoff, width, boundaries, progress, cores = cores, ...)) stopifnot(is(data, "STFDF") || is(data, "STSDF")) it = index(data@time) if (assumeRegular || is.regular(zoo(matrix(1:length(it)), order.by = it), strict = TRUE)) { twidth = diff(it)[1] tlags = tlags[tlags <= min(max(tlags), length(unique(it)) - 1)] } else { warning("strictly irregular time steps were assumed to be regular") twidth = mean(diff(it)) } obj = NULL t = twidth * tlags if (progress) pb = txtProgressBar(style = 3, max = length(tlags)) if (cores == 1) { ret = vector("list", length(tlags)) for (dt in seq(along = tlags)) { ret[[dt]] = StVgmLag(formula, data, tlags[dt], pseudo = pseudo, boundaries = boundaries, ...) ret[[dt]]$id = paste("lag", dt - 1, sep="") if (progress) setTxtProgressBar(pb, dt) } } else { if (!requireNamespace("future", quietly = TRUE) || !requireNamespace("future.apply", quietly = TRUE)) stop("For parallelization, future and future.apply packages are required") future::plan('multicore', workers = cores) ret <- split(seq(along=tlags), seq(along=tlags)) ret <- future.apply::future_lapply(X = ret, FUN = function(x){ xx <- StVgmLag(formula, data, tlags[x], pseudo = pseudo, boundaries = boundaries, ...) xx$id <- paste("lag", x - 1, sep="") if (progress) setTxtProgressBar(pb, x) return(xx) }, future.seed = NULL # silence warning ) } if (progress) close(pb) # add time lag: v = do.call(rbind, ret) v$timelag = rep(t, sapply(ret, nrow)) if (is(t, "yearmon")) class(v$timelag) = "yearmon" b = attr(ret[[min(length(tlags),2)]], "boundaries") b = c(0, b[2]/1e6, b[-1]) # ix = findInterval(v$dist, b) will use all spacelags b = b[-2] # spacelags = c(0, b[-length(b)] + diff(b)/2) will use all spacelags v$spacelag = c(0, b[-length(b)] + diff(b)/2) # spacelags[ix] will use all spacelags v$avgDist <- v$dist * v$np for (lagId in unique(v$spacelag)) { bool <- v$spacelag == lagId v$avgDist[bool] <- sum(v$avgDist[bool], na.rm = TRUE) / sum(v$np[bool], na.rm = TRUE) } class(v) = c("StVariogram", "data.frame") if(na.omit) v <- na.omit(v) # setting attributes to allow krigeST to check units attr(v$timelag, "units") <- attr(twidth,"units") if (isTRUE(!is.projected(data))) attr(v$spacelag, "units") = "km" return(v) } ## very irregular data variogramST.STIDF <- function (formula, data, tlags, cutoff, width, boundaries, progress, twindow, tunit, cores = 1) { ll = !is.na(is.projected(data@sp)) && !is.projected(data@sp) if (missing(cutoff)) cutoff <- spDists(t(data@sp@bbox), longlat = ll)[1, 2]/3 m = model.frame(terms(formula), as(data, "data.frame")) diffTime <- diff(index(data)) timeScale <- units(diffTime) if(missing(tunit)) warning(paste("The argument 'tunit' is missing: tlags are assumed to be given in ", timeScale, ".",sep="")) else { stopifnot(tunit %in% c("secs", "mins", "hours", "days", "weeks")) units(diffTime) <- tunit timeScale <- tunit } diffTime <- as.numeric(diffTime) if (missing(twindow)) { twindow <- round(2 * max(tlags, na.rm=TRUE)/mean(diffTime,na.rm=TRUE),0) } nData <- nrow(data) # re-using the order propertie of the time slot to only store the next "twindow" distances numTime <- as.numeric(index(data)) diffTimeMat <- matrix(NA, nData, twindow) for (i in 1:nData) { # i <- 1 diffTimeMat[i,1:min(nData,twindow)] <- cumsum(diffTime[i+0:(min(nData,twindow)-1)]) } nSp <- length(boundaries) nTp <- length(tlags) distTp <- matrix(NA, nSp-1, nTp-1) distSp <- matrix(NA, nSp-1, nTp-1) gamma <- matrix(NA, nSp-1, nTp-1) np <- matrix(NA, nSp-1 ,nTp-1) # temporal selection if(progress) pb <- txtProgressBar(0, nTp-1, 0, style=3) for (i in 1:(nTp-1)) { # i <- 1 ind <- which(diffTimeMat >= tlags[i] & diffTimeMat < tlags[i+1]) if (length(ind) < 1) next tmpInd <- matrix(NA,nrow=length(ind),4) tmpInd[,1] <- ind %% nData # row number tmpInd[,2] <- (ind %/% nData)+1 # col number if (cores == 1){ tmpInd[,3] <- apply(tmpInd[,1:2,drop=FALSE], 1, function(x) spDists(data@sp[x[1]], data@sp[x[2]+x[1],])) } else { if(!requireNamespace("future", quietly = TRUE) || !requireNamespace("future.apply", quietly = TRUE)) stop("For parallelization, future and future.apply packages are required") future::plan("multicore", workers = cores) tmpInd[,3] <- future.apply::future_apply(X = tmpInd[,1:2,drop=FALSE], MARGIN = 1, FUN = function(x) spDists(data@sp[x[1]], data@sp[x[2]+x[1],]), future.seed = NULL) } tmpInd[,4] <- diffTimeMat[tmpInd[,1:2, drop=FALSE]] # spatial selection for (j in 1:(nSp-1)) { # j <- 3 indSp <- which(tmpInd[,3] >= boundaries[j] & tmpInd[,3] < boundaries[j+1]) if (length(indSp) < 1) next distSp[j,i] <- mean(tmpInd[indSp,3]) distTp[j,i] <- mean(tmpInd[indSp,4]) indSp <- cbind(ind[indSp] %% nData, (ind[indSp] %/% nData)+1) np[j,i] <- nrow(indSp) # Issue #7, Thanks to Roelof. gamma[j,i] <- 0.5*mean((data[,,colnames(m)[1]]@data[indSp[,1],1] - data[,,colnames(m)[1]]@data[indSp[,1]+indSp[,2],1])^2, na.rm=TRUE) } if(progress) setTxtProgressBar(pb, value=i) } if(progress) close(pb) res <- data.frame(np=as.vector(np), dist=as.vector(distSp), gamma=as.vector(gamma), id=paste("lag",rep(1:(nTp-1),each=nSp-1), sep=""), timelag=rep(tlags[-nTp]+diff(tlags)/2,each=nSp-1), spacelag=rep(boundaries[-nSp]+diff(boundaries)/2, nTp-1)) res$avgDist <- res$dist * res$np for (lagId in unique(res$spacelag)) { bool <- res$spacelag == lagId res$avgDist[bool] <- sum(res$avgDist[bool], na.rm = TRUE) / sum(res$np[bool], na.rm = TRUE) } attr(res$timelag, "units") <- timeScale attr(res$spacelag, "units") <- ifelse(ll, "km", "m") class(res) <- c("StVariogram", "data.frame") return(res) } ## plotting plot.StVariogram = function(x, model=NULL, ..., col = bpy.colors(), xlab, ylab, map = TRUE, convertMonths = FALSE, as.table = TRUE, wireframe = FALSE, diff = FALSE, all=FALSE) { lst = list(...) if (!is.null(lst$col.regions)) col = lst$col.regions if (is(x$timelag, "yearmon")) { if (convertMonths) { x$timelag = as.numeric(x$timelag) * 12 attr(x$timelag, "units") = "months" } else attr(x$timelag, "units") = "years" } if (missing(xlab)) { xlab = "distance" u = attr(x$spacelag, "units") if (!is.null(u)) xlab = paste(xlab, " (", u, ")", sep="") } if (missing(ylab)) { ylab = "time lag" u = attr(x$timelag, "units") if (!is.null(u)) ylab = paste(ylab, " (", u, ")", sep="") } x$timelag = as.numeric(x$timelag) # check for older spatio-temporal variograms and compute avgDist on demand if(is.null(x$avgDist)) { x$avgDist <- x$dist * x$np for (lagId in unique(x$spacelag)) { bool <- x$spacelag == lagId x$avgDist[bool] <- sum(x$avgDist[bool] / sum(x$np[bool], na.rm = TRUE), na.rm = TRUE) } } if(!is.null(model)) { if (is(model,"StVariogramModel")) model <- list(model) for (mod in model) { slag <- x$avgDist slag[slag == 0 & x$timelag == 0] <- sqrt(.Machine$double.eps) x[[mod$stModel]] <- variogramSurface(mod, data.frame(spacelag = slag, timelag = x$timelag))$gamma if (diff) x[[mod$stModel]] <- x[[mod$stModel]] - x$gamma } } x0 = x # needed by wireframe() if (!is.null(model)) { modelNames <- sapply(model, function(x) x$stModel) if (all && !diff) v0 <- x[,c("dist", "id", "avgDist", "timelag")] else v0 <- NULL for (i in modelNames) v0 <- rbind(v0, x[,c("dist", "id", "avgDist", "timelag")]) if(all & !diff) {# we also need the sample v0$what = factor(c(rep("sample", nrow(x)), rep(modelNames, each=nrow(x))), levels=c("sample", modelNames), ordered = TRUE) v0$gamma = c(x$gamma, unlist(x[,modelNames])) } else { v0$what = factor(rep(modelNames, each=nrow(x)), levels=modelNames, ordered=TRUE) v0$gamma = c(unlist(x[,modelNames])) } x = v0 } if (wireframe) { if (!is.null(model)) { if (length(model) > 1 || all) wireframe(gamma ~ avgDist*timelag | what, x, drape = TRUE, col.regions = col, xlab = xlab, ylab = ylab, as.table=as.table, ...) else wireframe(as.formula(paste(model[[1]]$stModel,"~ avgDist*timelag")), x0, drape = TRUE, col.regions = col, xlab = xlab, ylab = ylab, as.table=as.table, ...) } else # without a model, plot only the sample variogram as a wireframe wireframe(gamma ~ avgDist * timelag, x0, drape = TRUE, col.regions = col, xlab = xlab, ylab = ylab, ...) } else if (map) { if (!is.null(model)) f = gamma ~ avgDist + timelag | what else f = gamma ~ avgDist + timelag levelplot(f, x, xlab = xlab, ylab = ylab, col.regions = col, as.table=as.table, ...) } else { # not map, not wireplot if (!is.null(model)) f = gamma ~ dist | what else f = gamma ~ dist x$id = factor(x$id, levels=unique(x$id)) bp = bpy.colors(length(levels(x$id))) ps = list(superpose.line=list(col=bp), superpose.symbol=list(col=bp)) xlim = c(0, max(x$dist) * 1.04) if (diff) { xyplot(f, x, groups = x$id, type='b', xlim = xlim, auto.key = list(space = "right"), xlab = xlab, par.settings = ps, as.table=as.table, ...) } else { ylim = c(0, max(x$gamma) * 1.04) xyplot(f, x, groups = x$id, type='b', ylim = ylim, xlim = xlim, auto.key = list(space = "right"), xlab = xlab, par.settings = ps, as.table=as.table, ...) } } } print.StVariogramModel <- function(x, ...) { possComp <- c("space", "time", "joint") for(comp in possComp[possComp %in% names(x)]) { rownames(x[[comp]]) <- 1:nrow(x[[comp]]) cat(paste(comp,"component: \n")) print(x[[comp]], ...) } possAddPar <- c("sill", "nugget", "stAni", "k") for(addPar in possAddPar[possAddPar %in% names(x)]) { cat(paste(addPar, ": ",x[[addPar]],"\n", sep="")) } } ## guess the spatio-temporal anisotropy without spatio-temporal models ###################################################################### estiStAni <- function(empVgm, interval, method="linear", spatialVgm, temporalVgm, s.range=NA, t.range=NA) { if (!is.na(s.range)) empVgm <- empVgm[empVgm$dist <= s.range,] if (!is.na(t.range)) empVgm <- empVgm[empVgm$timelag <= t.range,] empVgm$timelag = as.numeric(empVgm$timelag) # in case it is of class difftime, messes up on R 4.1 switch(method, linear = estiStAni.lin(empVgm, interval), range = estiAni.range(empVgm, spatialVgm, temporalVgm), vgm = estiAni.vgm(empVgm, spatialVgm, interval), metric = estiAni.metric(empVgm, spatialVgm, interval), stop(paste("Method", method,"is not implemented."))) } # linear estiStAni.lin <- function(empVgm, interval) { lmSp <- lm(gamma~dist, empVgm[empVgm$timelag == 0,]) optFun <- function(stAni, empVgm) { sqrt(mean((predict(lmSp, newdata = data.frame(dist=empVgm[empVgm$spacelag == 0,]$timelag*stAni)) - empVgm[empVgm$spacelag == 0,]$gamma)^2, na.rm=TRUE)) } optimise(optFun, interval, empVgm = empVgm)$minimum } # range estiAni.range <- function(empVgm, spatialVgm, temporalVgm) { spEmpVgm <- empVgm[empVgm$timelag == 0,] class(spEmpVgm) <- c("gstatVariogram","data.frame") spEmpVgm <- spEmpVgm[-1,1:3] spEmpVgm$dir.hor <- 0 spEmpVgm$dir.ver <- 0 spatialVgm <- fit.variogram(spEmpVgm, spatialVgm) tmpEmpVgm <- empVgm[empVgm$spacelag == 0,] class(tmpEmpVgm) <- c("gstatVariogram","data.frame") tmpEmpVgm <- tmpEmpVgm[-1,c("np","timelag","gamma")] colnames(tmpEmpVgm) <- c("np", "dist", "gamma") tmpEmpVgm$dir.hor <- 0 tmpEmpVgm$dir.ver <- 0 temporalVgm <- fit.variogram(tmpEmpVgm, temporalVgm) spatialVgm$range[2]/temporalVgm$range[2] } # variograms estiAni.vgm <- function(empVgm, spatialVgm, interval) { spEmpVgm <- empVgm[empVgm$timelag == 0,] class(spEmpVgm) <- c("gstatVariogram","data.frame") spEmpVgm <- spEmpVgm[-1,1:3] spEmpVgm$dir.hor <- 0 spEmpVgm$dir.ver <- 0 spatialVgm <- fit.variogram(spEmpVgm, spatialVgm) optFun <- function(stAni) { sqrt(mean((variogramLine(spatialVgm, dist_vector = empVgm[empVgm$spacelag == 0,]$timelag*stAni)$gamma - empVgm[empVgm$spacelag == 0,]$gamma)^2, na.rm=TRUE)) } optimise(optFun, interval)$minimum } # metric variogram estiAni.metric <- function(empVgm, spatialVgm, interval) { fit.StVariogram(empVgm, vgmST("metric", joint=spatialVgm, stAni=mean(interval)))$stAni[[1]] } gstat/NEWS.md0000644000176200001440000000666714314525261012514 0ustar liggesusers# version 2.1-0 * import `sftime`; modify `krigeST()` variogram functions to accept `sftime` objects for `data` (as alternative to `STI` or `STIDF`), and `stars` or `sftime` objects for `newdata`; #108 with great help from @henningte * fix Gaussian cosimulation, probably introduced in 2016, #106 # version 2.0-7 * return `NA` as estimate when prediction/simulation fails; #80 # version 2.0-6 * fixes `object 'ret' not found` bug introduced by #63; #65 #66 #70 # version 2.0-5 * use multiple cores in `variogramST`, using pkg future; #63 by @sigmafelix * fix bug with conditional simulation using `stars` target grid and nsim=1, #58 # version 2.0-4 * fix CRAN warning issue # version 2.0-3 * fix bug in support for `sf` objects; #46 * fix `krigeTg` for the case when data or newdata are of class `sf` or `sfc`; #51 # version 2.0-1 * try to fix CRS issue found on OSX * check for temporal unit in krigeST opposed to covariance function and assign the temporal unit found in krigeST to the spatio-temporal variogram for consistency in case none has been provided by the model; add warning when ST variogram doesn't have a `temporal unit` attribute; #42 # version 2.0-0 * add plot.variogramModel; #40 * support `sf` and `stars` objects, for vector and raster data, respectively; #39 # version 1.1-6 * address warnings from Tomas Kalibera's static code checking # version 1.1-5 * fix auto-choosing of variogram parameters if only variogram model type is given, https://github.com/edzer/gstat/issues/17 # version 1.1-4 * Fix #17 * Fix #14 * Fix #12 * Fix great circle distance bug; see https://stat.ethz.ch/pipermail/r-sig-geo/2016-December/025251.html # version 1.1-3 * Merge pull request #4 from BenGraeler/master r-journal ms merge updates vignette "spatio-temporal-kriging" to revised paper * Merge pull request #3 from BenGraeler/master update st paper demos * demo/stkrige.R: - remove empty station * demo/00Index, demo/stkrige-crossvalidation.R, demo/stkrige-prediction.R, demo/stkrige.R, man/krigeST.Rd: - adds R scripts from vignette spatio-temporal kriging as demos * Merge pull request #2 from BenGraeler/master additions for space-time paper * NAMESPACE, R/krige0.R, man/krigeST.Rd: - adds trans Gaussian kriging for space and time # version 1.1-2 * fixed `memcpy` for overlapping regions error, found in valgrind checks by Brian Ripley * fixed a few more (small) memory leaks # version 1.1-1 * Further cleaned up C source code, got rid of lex and yacc files * Improve `fit.variogram` to choose initial values for range, sill and nugget before fitting, and fit over a range of model types * allow `NA` values in `vgm` * Fixed #1 # version 1.1-0 * remove meschach matrix library, rewrote interface, link to R's lapack * improve notification in case of singular matrices * remove all C code that was not used by R package gstat * add `Makevars`, remove `configure` * remove links to `ai-geostats.org` * wrap `fit.StVariogram` example in `dontrun` # version 1.0-26 * use ordered spatial index when selecting nearest strongest correlated neighbours in local kriging to avoid warning of spacetime * update spatio-temporal geostatitics vignettes; add R Journal draft as vignette (Spatio-Temporal Geostatistics using gstat) * add spatio-temporal PM10 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zm'4r2\1V9D|v؞/ٞujC#s pN,7ۀtxm8byG@:{ ̴@l38b1m%ecv1}\5nEnp riv +J{/WyVߖJðVz#=2#֛Lɨ-Zg+0ěf78kNKg5}nxgMO2 L~WxUw GJddCIK6 X=lM7͔Ҁ ow.nq){-+>@\o=sVv&L)Gd( XN=/\bt 6q['g2i1>i\ G|!`@SGOzKW`p-^)hKhF}ܽ9j`.Û?ٜסOo?1u` kuX^C?a?'ip: .>sq+}\N-_q_/???ePtn̷oC_??~˿ K[q[_9]~k_ުmUo^Rú߾U~TPFo@e"j/|iN",@Uvrcq?W&>gU합q2Qݮ_DuvVWa1mg>m8w3|mDv"mBj$Xy ,; 7 |?\Ҧ |z<4p:#AzOyxsůWL/e wnp_lm e>oO9]-EobA8|_9:'*1L#k:]hr40n@xJv_'뼆#T;M#8^﯐?m򞛶Dд(Rt3`Դnsu0.u0;}s;u6۴mwcxsTDs|=΋/=%UwG@X>z[4t qQk4MO >@K2 8ȗ$7 Tiux qO~8XЈ&,~#O=5n (2ݹO=y'񃕋j"!"!C5x (J]6%T)Ѭov߇*\hdոꏘsaFtYhQU,^!۱dl*XOF,'#0뛃cGX/VƇyzW!C$??._zz<XUÈEDE8#3(u 9X80Ǵ8.PSE;q^0TFD{#w.EO F,F,> ȫsU9#Z6!OI(Ze0PHy d#(j]q ڲ6"9mErX"Eiߕs >stG,>Gw43Gs2 =,HwF?@!(?$K P$@\j tw H.@"O0Uuw*/ o?| vM5y 4i1Ѹm՚u΢byrC.r|;,m_6N?("^ś$Atw#B.DLu(8EEQ#J 7";|1M[kQ$Ӿ+{ߥt%00bFT+n %|# p؄D[hǹE;D;]RNŚiLw|q'Ӗ60/l=*@43FotG,|#&Bt/kv(yrQ&"e" e"(o.e"(j&#]&"FlH\;b(XL$onkҁv ; tG@#Am'xY9d(i;eӀe2tsApnd(jѭoatUF  >U]<1F^*ro\_xZۆ5 e! ٮbyʶeFVjà/H#xSGb[S^ⲊpW)hbE2)l 2YFO&" 2f/i 7F^gX`b{|Ȇ=-`n0`w$>NЬD=$^s*P$@G"Ç"F5xXF,C*؄ hST;RTȘa)1R/``D1|=&^%t^ܠpno7AJ#Om^_!%yн恥  ,P,] xrBB|D#>U&Twwj =b㝧;Ft|:k.:F: Tgȝ"53+QO-U˂ZWgs [kZHy#akP[{xxg>nq5xh4Zi'x>;XLOFsG%>3GfF\VFlTSY]=oM@|9j%>#6ؿ+Qg|xI$G 6sW\b#ٚތt3A0foύvvn6sK% &M.H6EMŢN7d?\|/M#)'-C5_~MGfa# dxVmmaF+hVGtpIK:\dA]b?؅}j5Wd `<t0ڝ!g)ml^,om;@frr̸麺3qNg ^:$u/8t*ҘP%"{^;|.U<% ^I$'H_AE_Wev 2o/8{7l%o]Q4Bbkm{F쒫y]b!݆MiW>a4WaN^ &+\e."0=>6\(DU0p^*]few8EJwJ<9Aƞ5mvTX/Awx0JÿTpμ/_NP9cIq8f HQ5dէ f:ӭgDuլX˦<~#ŵlbpendstream endobj 136 0 obj << /Type /XRef /Length 169 /Filter /FlateDecode /DecodeParms << /Columns 5 /Predictor 12 >> /W [ 1 3 1 ] /Info 3 0 R /Root 2 0 R /Size 137 /ID [<99224ba5d6eab833e1c7e633748cc0a6>] >> stream xcb&F~0 $8J$6/R3B R/V-@ym"EA$*00rT뒓Lr R';"6H`6%lZ`ٙ` ,R"-7H>W>̍ QXe+<&W^Y_Xr endstream endobj startxref 325730 %%EOF gstat/inst/doc/spatio-temporal-kriging.bib0000644000176200001440000003163513777370515020373 0ustar liggesusers% Encoding: windows-1252 @Article{bakar2015, author = {Bakar, Khandoker Shuvo and Sahu, Sujit K}, title = {{spTimer}: Spatio-Temporal Bayesian Modelling Using {R}}, journal = {Journal of Statistical Software}, year = {2015}, volume = {63}, number = {15}, pages = {1--32}, url = {http://dx.doi.org/10.18637/jss.v063.i15} } @Manual{Beygelzimer2013, Title = {{FNN}: Fast Nearest Neighbor Search Algorithms and Applications}, Author = {Alina Beygelzimer and Sham Kakadet and John Langford and Sunil Arya and David Mount and Shengqiao Li}, Note = {R package version 1.1}, Year = {2013}, Url = {https://CRAN.R-project.org/package=FNN} } @Article{Bilonick1988, Title = {Monthly hydrogen ion deposition maps for the northeastern {U.S.} from {J}uly 1982 to {S}eptember 1984}, Author = {Richard A. 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Goulias}, title = {Dynamic diurnal social taxonomy of urban environments using data from a geocoded time use activity-travel diary and point-based business establishment inventory }, journal = {Transportation Research Part A: Policy and Practice }, year = {2014}, volume = {68}, number = {0}, pages = {3 - 17}, url = {http://dx.doi.org/10.1016/j.tra.2014.01.004}, issn = {0965-8564} } gstat/inst/doc/spatio-temporal-kriging.Rnw0000644000176200001440000015665013777370515020412 0ustar liggesusers\documentclass[a4paper]{article} \usepackage[colorlinks=true,urlcolor=blue,citecolor=blue]{hyperref} \usepackage{alltt} \usepackage{amsfonts} \usepackage{enumerate} \usepackage{graphicx} \usepackage{multirow} \usepackage{natbib} %% following the RJournal.sty \usepackage{geometry} \usepackage{booktabs} \usepackage{amsmath} \RequirePackage{fancyvrb} \RequirePackage{alltt} \DefineVerbatimEnvironment{example}{Verbatim}{} \renewenvironment{example*}{\begin{alltt}}{\end{alltt}} \RequirePackage[font=small,labelfont=bf]{caption} \geometry{a4paper, textwidth=14cm, top=1cm, bottom=1cm, includehead,includefoot,centering, footskip=1.5cm} \raggedbottom \RequirePackage{setspace} \renewcommand{\abstract}[1]{% \setstretch{1}% \noindent% \small% \textbf{Abstract} #1 } \newcommand{\address}[1]{\addvspace{\baselineskip}\noindent\emph{#1}} \date{\footnotesize Mar 25, 2016} \newcommand{\code}[1]{{\footnotesize\tt #1}} \newcommand{\samp}[1]{{\tt #1}} \newcommand{\pkg}[1]{{\bf #1}} \newcommand{\CRANpkg}[1]{{\href{https://cran.r-project.org/package=#1}{\bf #1}}} \newcommand{\email}[1]{{\href{mailto:#1}{#1}}} \newcommand{\dfn}[1]{{\normalfont\textsl{#1}}} \bibliographystyle{plainnat} % \VignetteIndexEntry{Spatio-Temporal Geostatistics using gstat} \title{Spatio-Temporal Interpolation using \pkg{gstat}} % \VignetteIndexEntry{Spatio-Temporal Geostatistics using gstat} \author{by Benedikt Gr{\"a}ler, Edzer Pebesma and Gerard Heuvelink} \graphicspath{{figures/}} \begin{document} \SweaveOpts{concordance=TRUE} \maketitle \abstract{ We present new spatio-temporal geostatistical modelling and interpolation capabilities of the R package \pkg{gstat}. Various spatio-temporal covariance models have been implemented, such as the separable, product-sum, metric and sum-metric models. In a real-world application we compare spatio-temporal interpolations using these models with a purely spatial kriging approach. The target variable of the application is the daily mean $\rm{PM}_{10}$ concentration measured at rural air quality monitoring stations across Germany in 2005. R code for variogram fitting and interpolation is presented in this paper to illustrate the workflow of spatio-temporal interpolation using \pkg{gstat}. We conclude that the system works properly and that the extension of \pkg{gstat} facilitates and eases spatio-temporal geostatistical modelling and prediction for R users. } %% main text \section{Introduction}\label{sec:intro} The collection and processing of spatio-temporal data is rapidly increasing due to technological advances and the societal need for analysis of variables that vary in space and time, such as weather and air quality variables, and crop yields. Analysis of spatial and temporal correlations is useful in itself to get insight into the character and causes of variability, but they are also important to predict values at points from neighbouring observations. Spatio-temporal interpolation can potentially provide more accurate predictions than spatial interpolation because observations taken at other times can be included. In addition, spatio-temporal interpolation allows predictions to be made at single locations or entire fields in between and beyond observation times. However, adding the temporal domain implies that variability in space and time must be modelled, which is more complicated than modelling purely spatial or purely temporal variability. The spatial, temporal and spatio-temporal dependence structures, for instance represented as variograms, do not necessarily coincide with each other in terms of their parameters nor in terms of their family. In the simplest case, a spatio-temporal anisotropy parameter might be enough to deal with the different dependence structures, but this poses strong assumptions on the process. Interpolation of spatial random fields is a common task in geostatistics. Simple approaches like inverse distance weighted predictions or the well known kriging procedures have routinely been applied for many years. Nowadays, modern sensors allow to monitor different variables at an increasing temporal resolution producing rich spatio-temporal data sets. This calls as well for theory and methods to deal with these data sets to gain a better understanding of the observed spatio-temporal processes. While the theoretical aspects of spatio-temporal geostatistics show good progress \citep{Cressie2011}, implementations lack behind. This hinders a wide application of spatio-temporal modelling, as typically extensive scripting and thorough understanding is necessary to build spatio-temporal models. Handling of spatio-temporal data in R is provided by the \CRANpkg{spacetime} package \citep{Pebesma2012}. In this paper, we present an extension of the \CRANpkg{gstat} package \citep{Pebesma2004} (version 1.1-3) that reuses the \pkg{spacetime} classes for the estimation of spatio-temporal covariance/variogram models and to perform spatio-temporal interpolation. Our implementation handles various types of spatio-temporal covariance structures and facilitates spatio-temporal interpolation. The notation of functions in \pkg{gstat} are extended in a way closely following the purely spatial design. This allows a researcher acquainted with \pkg{gstat} to readily use spatio-temporal tools. The use of the newly implemented functions is presented and illustrated by mapping spatio-temporal air-quality data. Another package that offers extensive spatio-temporal geostatistical functionality is \CRANpkg{RandomFields} \citep{Schlather2014}; further packages are mentioned in the SpatioTemporal CRAN task view\footnote{\url{https://cran.r-project.org/web/views/SpatioTemporal.html}}. The paper is organised as follows. The next section introduces the general interpolation routine and describes the different spatio-temporal covariance models, followed by a section introducing the German rural background data set for 2005 and performing the parameter estimation (i.e.\ covariance model fitting). Cross-validation results are presented and discussed in the section thereafter. Conclusions are drawn in the closing section. R scripts reproducing this study are available from within the \pkg{gstat} package as demos. \code{stkrige} re-estimates the variogram models, \code{stkrige-prediction} re-executes the prediction for a time series and a couple of stations, and \code{stkrige-crossvalidation} re-runs the entire leave-one-out cross-validation (note that the latter takes a few hours). \section{Spatio-temporal dependence modelling and kriging}\label{sec:theory} In the following, we will assume a Gaussian spatio-temporal random field $Z$ defined over a spatial domain $\mathcal{S}$ and temporal domain $\mathcal{T}$. Typically, a sample $\mathbf{z} = \left(z(s_1,t_1),\dots,z(s_n,t_n)\right)$ has been observed at a set of distinct spatio-temporal locations $(s_1, t_1), \dots, (s_n,t_n) \in \mathcal{S}\times \mathcal{T} \subseteq \mathbb{R}^2 \times \mathbb{R}$ that may include repeated measurements at the same location or simultaneous measurements at multiple spatial locations. Often, one is interested in modelling $Z$ from the sample $\mathbf{z}$ in order to predict at unobserved locations in space and time or simulate from the conditional distribution. Across our domain of interest $\mathcal{S} \times \mathcal{T}$, we assume the random field $Z$ to be stationary and spatially isotropic. Hence, the field can be characterised through a mean $\mu$ and a covariance function $C_{\rm st}$ where the spatio-temporal covariance only depends on the separating distances across space $h \in \mathbb{R}_{\geq 0}$ and time $u \in \mathbb{R}_{\geq 0}$. Note that extensions beyond this set-up can easily be derived as has been done for the pure spatial case using for instance universal kriging to overcome the stationarity of the mean. The general spatio-temporal covariance function is given by $C_{\rm st}(h,u) = {\rm Cov}\left(Z(s,t), Z(\tilde{s},\tilde{t})\right)$ for a separating spatial distance $h$ and temporal distance $u$ and any pair of points $(s,t), (\tilde{s},\tilde{t}) \in \mathcal{S}\times\mathcal{T}$ with $||s-\tilde{s}||=h$ and $|t-\tilde{t}|=u$. In general, this covariance function is hard to estimate but a couple of models using simplifying assumptions will be presented in the following together with their spatio-temporal variograms $\gamma_{\rm st}(h,u) = C_{\rm st}(0,0)-C_{\rm st}(h,u)$ and encoding in \pkg{gstat}. Given a valid covariance function, the covariance matrices used in the linear predictor are easily obtained and the same algebraic operations as in the well known spatial case yield predictions of the desired random field \citep{Cressie2011}. A major difference is, however, the computational complexity of the matrix inversion. Typically, observations are made at a rather high temporal frequency leading to a number of spatio-temporal locations that is too large for global kriging. Hence, interpolation based on a selected neighbourhood of a subset of all data points becomes beneficial. Additionally, this relaxes the assumption of stationarity, as smooth variations in the mean value across the domain can be respected. The related class of dynamic models also addresses the computational complexity resulting in a temporal Markov structure. Implementations can be found in \CRANpkg{spTimer} by \citet{bakar2015}, \CRANpkg{spBayes} by \citet{finley2015}, \CRANpkg{spate} by \citet{sigrist2015} or \pkg{INLA} by \citet{lindgren2015}. \subsection{Covariance models} The covariance models implemented in \pkg{gstat} and presented in this paper are introduced in the following. Besides further extensions we focus on the basic classes of the \emph{separable}, \emph{product-sum}, \emph{metric} and \emph{sum-metric} spatio-temporal covariance functions. The building blocks (in the following denoted as \code{spatialVgm}, \code{temporalVgm} or \code{jointVgm}) of the spatio-temporal covariance functions are any of the purely spatial variogram models already available in \pkg{gstat}. Each one of the building blocks is created by a call of the function \code{gstat::vgm()}. Remaining arguments such as \code{sill} (the joint sill), \code{nug} (the joint nugget component) or \code{stAni} (the spatio-temporal anisotropy used in the \code{jointVgm}) are scalars and refer to parameters of the entire spatio-temporal covariance function: \begin{enumerate}[a)] \item The \dfn{separable covariance model} assumes that the spatio-temporal covariance function can be represented as the product of a spatial and temporal term: $$C_{\rm sep}(h,u)=C_{\rm s}(h)C_t(u)$$ Its variogram is given by (see Appendix for details): $$\gamma_{\rm sep}(h,u) = {\rm sill} \cdot \left( \bar{\gamma}_s(h)+\bar{\gamma}_t(u)-\bar{\gamma}_s(h)\bar{\gamma}_t(u) \right)$$ where $\bar{\gamma}_s$ and $\bar{\gamma}_t$ are standardised spatial and temporal variograms with separate nugget effects and (joint) sill of 1. The overall sill parameter is denoted by "sill". The R package \pkg{gstat} encodes this model as: \code{vgmST("separable", space = spatialVgm, time = temporalVgm, sill = sill)} The separable model has a strong computational advantage in the setting where each spatial location has an observation at each temporal instance (a \code{"STFDF"} without \samp{NA}s, \cite{Pebesma2012}). In these cases, the covariance matrix (and its inverse) can be composed using the Kronecker-product of the purely spatial and purely temporal covariance matrices (respectively their inverse). \item The above model extends to the \dfn{product-sum covariance model} that we give here in a slightly different notation as \citet{DeCesare2001} and \citet{DeIaco2001} by $$C_{\rm ps}(h,u)=k C_{\rm s}(h)C_{\rm t}(u) + C_{\rm s}(h) + C_{\rm t}(u)$$ with $k > 0$. The corresponding variogram can be written as $$\gamma_{\rm ps}(h,u) = \left(k \cdot {\rm sill}_{\rm t} + 1\right) \gamma_{\rm s}(h) + \left(k \cdot {\rm sill}_{\rm s} + 1\right) \gamma_{\rm t}(u) - k \gamma_{\rm s}(h) \gamma_{\rm t}(u)$$ where ${\gamma}_{\rm s}$ and $\gamma_{\rm t}$ are spatial and temporal variograms (see Appendix for details). The parameter $k$ needs to be positive and the following identity defines the overall sill (${\rm sill}_{\rm st}$) of the model in terms of the model's spatial and temporal sills: $${\rm sill}_{\rm st} = k \cdot {\rm sill}_{\rm s} \cdot {\rm sill}_{\rm t} + {\rm sill}_{\rm s} + {\rm sill}_{\rm t}$$ The above equation can also be used to estimate $k$ based on the three sill values. An alternative formulation of the product-sum variogram can be found in \citet{DeIaco2001}. The \pkg{gstat} definition of this model reads: \begin{example*} vgmST("productSum", space = spatialVgm, time = temporalVgm, k = k) \end{example*} \item Assuming identical spatial and temporal covariance functions except for spatio-temporal anisotropy, allows to use a spatio-temporal \dfn{metric covariance model} where, after matching space and time by an anisotropy correction $\kappa$ (\code{stAni}), the spatial, temporal and spatio-temporal distances are treated equally resulting in a single covariance model $C_{\rm joint}$: $$C_{\rm m}(h,u)=C_{\rm joint}\left(\sqrt{h^2+(\kappa\cdot u)^2}\right)$$ The variogram evaluates to $$ \gamma_{\rm m} (h,u) = \gamma_{\rm joint}\left(\sqrt{h^2+(\kappa\cdot u)^2}\right) $$ where $\gamma_{\rm joint}$ (\code{jointVgm}) is any known variogram that may include a nugget effect. The following line generates the model in \pkg{gstat}: \begin{example*} vgmST("metric", joint = jointVgm, stAni = stAni) \end{example*} The spatio-temporal anisotropy parameter $\kappa$ (\code{stAni}) is given as spatial unit per temporal unit. In many cases, this will be in m/second, as these are the base units in our implementation. All temporal distances are hence internally re-scaled to an equivalent spatial distance using \code{stAni} and treated as metric 3D-space. \item A combination of spatial, temporal and a metric model including an anisotropy parameter $\kappa$ is found in \citet{Bilonick1988} and revisited by \citet{Snepvangers2003} as the \dfn{sum-metric covariance model}: $$C_{\rm sm}(h,u)=C_{\rm s}(h)+C_{\rm t}(u)+C_{\rm joint}\left(\sqrt{h^2+(\kappa\cdot u)^2}\right)$$ This model allows for spatial, temporal and joint nugget effects. Thus, the variogram is given by $$ \gamma_{\rm sm}(h,u)= \gamma_{\rm s}(h) + \gamma_{\rm t}(u) + \gamma_{\rm joint}\left(\sqrt{h^2+(\kappa\cdot u)^2}\right)$$ where $\gamma_{\rm s}$, $\gamma_{\rm t}$ and $\gamma_{\rm joint}$ are spatial, temporal and joint variograms with separate nugget-effects. This model can be defined in \pkg{gstat} through: \begin{example*} vgmST("sumMetric", space = spatialVgm, time = temporalVgm, joint = jointVgm, stAni = stAni) \end{example*} \item A simplified version of the above model is to restrict the spatial, temporal and joint variograms to nugget free models. Additionally, a single spatio-temporal nugget is introduced and the variogram takes the representation: $$\gamma_{\rm ssm}(h,u) = {\rm nug}\cdot {\bf1}_{h>0 \vee u>0} + \gamma_{\rm s}(h) + \gamma_{\rm t}(u) + \gamma_{\rm joint}\left(\sqrt{h^2+(\kappa\cdot u)^2}\right)$$ The \dfn{simple sum-metric covariance model} can be obtained by: \begin{example*} vgmST("simpleSumMetric", space = spatialVgm, time = temporalVgm, joint = jointVgm, nugget = nug, stAni = stAni) \end{example*} \end{enumerate} \noindent Note that the above mentioned spatial, temporal and joint components of the spatio-temporal covariance and variogram models need not necessarily exhibit the same structure. Taking for instance the product-sum and sum-metric models that both contain single temporal and spatial variogram models: the best fits of the respective spatio-temporal models might suggest different variogram families and parameters for the pure spatial and temporal ones. This is due to the target of finding the best overall variogram surface resulting in (potentially) different marginal models. \subsection{Parameter estimation} Fitting routines for the above variogram models are implemented in \pkg{gstat} through the function \code{fit.StVariogram()}, which calls \code{optim()} from the R core package \pkg{stats}. Additional parameters to improve the numerical optimisation can be provided to \code{fit.StVariogram()} and will be passed on to \code{optim()} (using R's three-dots mechanism). As some of the parameters are limited to certain ranges (nuggets need to be non-negative, ranges must be positive), it is advised to use an optimisation routine that allows to impose limits on the search space (i.e.\ \code{L-BFGS-B}) and provide sensible limits via \code{lower} and \code{upper}. By default, the method \code{L-BFGS-B} is called and the smallest lower and largest upper bounds supported by the model are given. The estimation of the spatio-temporal variogram models relies on a sample variogram empirically derived from the data. In contrast to the spatial variogram line, the spatio-temporal variogram is represented by a surface for lag classes composed of a spatial and temporal separation distance. Different from the spatial case, a spatio-temporal sample variogram contains lag-classes of zero spatial separation describing pure temporal dependencies. Without duplicate observations, no estimates can be made for the lag-class with both zero spatial and zero temporal separation. The sample variogram is calculated through the function \code{variogram()} that dispatches the call for spatio-temporal data objects (of class \code{"STFDF"}, \code{"STSDF"}, or \code{"STIDF"}) from \pkg{spacetime}. For a visual judgement of the fit between sample and fitted variograms the \code{plot()} function can be called to show the variogram surfaces next to each other as coloured level plots. Alternatively, a wireframe plot is obtained by setting the parameter \code{wireframe = TRUE} (Figure~\ref{fig:allVgmsWireframe}). A further option is to plot the differences between the sample and model variogram surfaces by setting \code{diff = TRUE}, see Figure~\ref{fig:allVgmsDiffWireframe}. Additionally to visual comparison, \code{fit.StVariogram()} provides the output of \code{optim} as attribute \code{optim.out} of the returned S3-class \code{"StVariogram"}. This attribute includes valuable information to diagnose the success of the \code{optim} routine. It contains for instance the convergence code (\code{\$convergence}) or message (\code{\$message}) and the optimised value (\code{\$value}), which is the mean of the (weighted) squared deviations between sample and fitted variogram surface. Furthermore, it is advised to check the estimated parameters against the parameter boundaries and starting values. Additionally, starting values might also influence the success and result of the optimisation, as local optima may occur due to the interdependence of the parameters. Alternatively, the user might want to start a grid search in order to better asses the sensitivity of the estimates. The fitting approach is identical for all covariance models. However, with the flexibility of the model also the number of parameters increases, making a numerical estimation at times cumbersome. Starting values can in most cases be read from the sample variogram. Parameters of the spatial and temporal variograms can be assessed from the spatio-temporal surface fixing the counterpart at 0. The overall spatio-temporal sill including the nugget can be deducted from the plateau that a nicely behaving sample variogram reaches for 'large' spatial and temporal distances. An important issue is the potentially different orders of magnitude of the parameters. It is at times advisable to rescale spatial and temporal distances to ranges similar to the ones of sills and nuggets using the parameter \code{parscale}. \code{parscale} needs to be provided via \code{control = list(parscale=\dots)} and holds a vector of the same length as the number of parameters to be optimised (see the documentation of \code{optim} for further details). \begin{table} \center \caption{List of implemented weighting schemes for variogram optimisation. Methods 3, 4, and 5 are kept for compatibility reasons with the purely spatial \code{fit.variogram} function. The following notation is used: $N_j$ number of pairs, $h_j$ mean spatial distance and $u_j$ mean temporal distance for each bin $j$, $\gamma$ the actual proposed variogram model and \code{stAni} a spatio-temporal anisotropy scaling.}\label{tab:weighting} {\small \begin{tabular}{ll} \toprule \code{fit.method} & weights \\ \midrule 0 & no fitting\\ 1 and 3 & $N_j$ \\ 2 and 4 & $N_j/\gamma\left(h_j, u_j\right)^2$ \\ 5 & reserved for REML \\ 6 & 1, no weighting\\ 7 & $N_j/\left(h_j^2 + {\rm stAni}^2\cdot u_j^2\right)$ \\ 8 & $N_j/h_j^2$ \\ 9 & $N_j/u_j^2$ \\ 10 & $1/\gamma\left(h_j,u_j\right)^2$ \\ 11 & $1/\left(h_j^2 + {\rm stAni}^2\cdot u_j^2\right)$ \\ 12 & $1/h_j^2$ \\ 13 & $1/u_j^2$ \\ \bottomrule \end{tabular}} \end{table} Currently, the implemented fitting routines are based on the (weighted) mean squared difference between model and sample variogram surfaces. By default, all values are associated the same weight (\code{fit.method = 6}), but other options are available that allow for different weighting schemes based on the number of pairs, spatial, temporal and spatio-temporal distances or the variogram's value. Table~\ref{tab:weighting} lists all currently implemented options. Depending on the target neighbourhood size of the desired interpolation, it might be beneficial to narrow down the spatial and temporal distances and to introduce a cutoff. This ensures that the model is fitted to the differences over space and time actually used in the interpolation, and reduces the risk of overfitting the variogram model to large distances not used for prediction. Please note that methods 2 and 10 (Table~\ref{tab:weighting}) involve weights based on the fitted variogram that might lead to bad convergence properties of the parameter estimates. Furthermore, the scalar \code{stAni} in methods 7 and 11 will either be the actual fitted spatio-temporal anisotropy if it is included in the model or a fixed value that has to be passed as \code{stAni} by the user to \code{fit.StVariogram}. The latter is advised, as the former might lead to bad convergence properties as in the case of weights based on the fitted variogram mentioned above. As the estimation of an anisotropy scaling might be cumbersome on a visual basis, we provide the function \code{estiStAni} that provides estimates based on the empirical spatio-temporal variogram. Four heuristics are available based on (i) rescaling a linear model (\code{linear}), (ii) estimating equal ranges (\code{range}), (iii) rescaling a pure spatial variogram (\code{vgm}) or (iv) estimating a complete spatio-temporal metric variogram model and returning its spatio-temporal anisotropy parameter (\code{metric}). The choice of the weighting scheme will influence the selected model and different weightings might be further assessed in a cross-validation of the selected model. To increase numerical stability, it is advisable to use weights that do not change with the current model fit. \subsection{Kriging} Standard kriging (\code{krigeST}) and trans Gaussian kriging (\code{krigeSTTg}) have been implemented. As spatio-temporal kriging based on the complete data set might be too computationally expensive, local kriging is an attractive alternative. This poses the question of how to select the "nearest" neighbours from the spatio-temporal space $\mathcal{S}\times\mathcal{T}$. A natural choice would be to select the spatio-temporal locations exhibiting the strongest correlation to the unobserved location. Depending on the spatio-temporal covariance model, the relation between spatial and temporal distance in determining the strength of correlation will vary. As a proxy, we use a spatio-temporal anisotropy parameter that relates spatial and temporal distances in the same manner as in the metric covariance models. The k-nearest neighbours within this metric spatio-temporal space $\mathcal{S}\times\mathcal{T}$ are selected using the R package \CRANpkg{FNN} \citep{Beygelzimer2013}. The interpolation performs iteratively for each spatio-temporal prediction location with a local subset of the data set. Without neighbourhood selection, kriging uses all data. As the metric induced by the spatial and rescaled temporal distances are only proxies to the strength of correlation between locations (see Figure~\ref{fig:vgmVsDist}), we provide an option to search a larger metric neighbourhood. Within this larger neighbourhood, the covariance function is evaluated for all spatio-temporal locations and the neighbouring locations with the largest covariance values are then selected for prediction. However, this approach might still suffer from a clustering of locations and alternatives such as a staged search (find spatial neighbours first and select a set of temporal instances for each spatial neighbour) or an octant search (select neighbours per spatial quadrant from preceding and following time stamps separately) could be considered. However, these alternatives are not yet available in \pkg{gstat}. \begin{figure} \centering \includegraphics[width=0.9\textwidth]{vgmVsMetricDist.png} \caption{A contourplot showing how the spatio-temporal sum-metric variogram model (as estimated in the application below) and a metric distance relate to each other. Distances are rescaled by 1/5 for easy plotting.}\label{fig:vgmVsDist} \end{figure} \section{Application and illustration}\label{sec:data} The data set used is taken from AirBase\footnote{\href{http://www.eea.europa.eu/data-and-maps/data/airbase-the-european-air-quality-database-6}{AirBase - The European air quality database}}, the air quality data base for Europe provided by the European Environmental Agency (EEA). We focus on a single air quality indicator, particulate matter with a diameter less than 10~$\mu\rm m$, measured at rural background stations for 2005 (${\rm PM}_{10}$). The data base contains data for many years. Besides rural, also urban areas are monitored and not only at background locations (e.g.\ traffic stations). However, these processes are considered to be of a different nature and should be treated separately. As a use case, we therefore limit our data set to the rural background stations in Germany. Figure \ref{fig:dailyMeans} shows for 8 randomly chosen days daily mean values of ${\rm PM}_{10}$ concentrations for the entire monitoring network over Germany in 2005 with 69 rural background stations. \begin{figure} \centering \includegraphics[width=0.95\textwidth]{daily_means_PM10.png} \caption{Daily mean $\rm{PM}_{10}$ concentration $[\mu\rm{g/m}^3]$ at 8 randomly selected days in 2005.}\label{fig:dailyMeans} \end{figure} In order to fit a spatio-temporal model to the air quality data set, the empirical variogram surface is computed and used as input for the fitting routines of the different models. The empirical variogram is based on spatio-temporal bins that span regularly over space and time. Regular measurements over time (i.e.\ hourly, daily) motivate regular binning intervals of the same temporal resolution. Nevertheless, flexible binning boundaries can be passed for spatial and temporal dimensions. This allows for instance to use smaller bins at small distances and larger ones for large distances. Temporal boundaries, instead of lags, are required when the sampling of the data is non-regular. In cases where regular temporal observations can be assumed, this is utilised in the sample variogram calculations and any two temporal consecutive observations are assumed to have the same temporal distance. Figure~\ref{fig:allVgmsWireframe} shows the empirical variogram along with the proposed best fitting model of each spatio-temporal variogram family as perspective wireframe plots. In order to better identify structural shortcomings of the selected model, a difference plot (Figure~\ref{fig:allVgmsDiffWireframe}) is a helpful visual diagnostic plot. Beyond the selection of the spatio-temporal variogram family, each component of this model can be chosen from any implemented one-dimensional variogram. In Table~\ref{tab:vgmFits} a selection of fitted models in terms of their residuals compared to the sample variogram surface are shown. The best fitting spatio-temporal model of each family is given as: \begin{enumerate}[a)] \item separable model (weighted MSE: 6.82): \nopagebreak \begin{tabular}{l|rlrlrr} \toprule & partial sill & model & \multicolumn{2}{c}{range} & nugget & sp.-temp. sill \\ \midrule space & 0.86 & Exp & 558 & \hspace{-2\tabcolsep}~km & 0.14 & \multirow{2}{*}{124} \\ time & 1.00 & Sph & 5.6 & \hspace{-2\tabcolsep}~days & 0.00 & \\ \bottomrule \end{tabular} obtained via: \begin{example*} separableModel <- vgmST("separable", space = vgm(0.9, "Exp", 200, 0.1), time = vgm(0.9, "Sph", 3.5, 0.1), sill = 124) fit.StVariogram(empVgm, separableModel, fit.method = 7, stAni = 117.3, method = "L-BFGS-B", control = list(parscale = c(100, 1, 10, 1, 100)), lower = c(10, 0, 0.1, 0, 0.1), upper = c(2000, 1, 12, 1, 200)) \end{example*} \item product-sum model (weighted MSE: 6.91) \nopagebreak \begin{tabular}{l|rlrlrc} \toprule & partial sill & model & \multicolumn{2}{c}{range} & nugget & k\\ \midrule space & 6.8 & Exp & 542 & \hspace{-2\tabcolsep}~km & 1.2 & \multirow{2}{*}{1.61} \\ time & 8.7 & Sph & 5.5 & \hspace{-2\tabcolsep}~days & 0.0 & \\ \bottomrule \end{tabular} obtained via \begin{example*} prodSumModel <- vgmST("productSum", space = vgm(10, "Exp", 200, 1), time = vgm(10, "Sph", 2, 1), k=2) fit.StVariogram(empVgm, prodSumModel, fit.method = 7, stAni = 117.3, method = "L-BFGS-B", control = list(parscale = c(1, 10, 1, 1, 0.1, 1, 10)), lower = rep(0.0001, 7)) \end{example*} \item metric model (weighted MSE: 10.05) \nopagebreak \begin{tabular}{l|rlrlrrl} \toprule & partial sill & model & \multicolumn{2}{c}{range} & nugget & \multicolumn{2}{c}{anisotropy}\\ \midrule joint & 123.4 & ${\rm Mat}_{\kappa=0.6}$ & 453 & \hspace{-2\tabcolsep}~km & 17.4 & 189 & \hspace{-2\tabcolsep}~km/day \\ \bottomrule \end{tabular} obtained via \begin{example*} metricModel <- vgmST("metric", joint = vgm(60, "Mat", 150, 10, kappa = 0.6), stAni = 60) fit.StVariogram(empVgm, metricModel, fit.method = 7, stAni = 117.3, method = "L-BFGS-B", control = list(parscale = c(10, 20, 5, 10)), lower = c(80, 50, 5, 50), upper = c(200, 1500, 60, 300)) \end{example*} \item\label{bestfit} sum-metric model (weighted MSE: 3.31) \nopagebreak \begin{tabular}{l|rlrlrrl} \toprule & partial sill & model & \multicolumn{2}{c}{range} & nugget & \multicolumn{2}{c}{anisotropy}\\ \midrule space & 16.4 & Sph & 67 & \hspace{-2\tabcolsep}~km & 0 & & \\ time & 9.3 & Exp & 0.9 & \hspace{-2\tabcolsep}~days & 0 & & \\ joint & 91.5 & Sph & 999 & \hspace{-2\tabcolsep}~km & 7.3 & 185 & \hspace{-2\tabcolsep}~km/day \\ \bottomrule \end{tabular} obtained via \begin{example*} sumMetricModel <- vgmST("sumMetric", space = vgm(20, "Sph", 150, 1), time = vgm(10, "Exp", 2, 0.5), joint = vgm(80, "Sph", 1500, 2.5), stAni = 120) fit.StVariogram(empVgm, sumMetricModel, fit.method = 7, stAni = 117.3, method = "L-BFGS-B", control = list(parscale = c(1, 100, 1, 1, 0.5, 1, 1, 100, 1, 100), maxit=10000), lower = c(sill.s = 0, range.s = 10, nugget.s = 0, sill.t = 0, range.t = 0.1, nugget.t = 0, sill.st = 0, range.st = 10, nugget.st = 0, anis = 40), upper = c(sill.s = 200, range.s = 1000, nugget.s = 20, sill.t = 200, range.t = 75, nugget.t = 20, sill.st= 200, range.st = 5000, nugget.st = 20, anis = 500)) \end{example*} \item simple sum-metric model (weighted MSE: 3.31) \nopagebreak \begin{tabular}{l|rlrlrlc} \toprule & partial sill & model & \multicolumn{2}{c}{range} & \multicolumn{2}{c}{anisotropy} & sp.-temp. nugget \\ \midrule space & 16.4 & Sph & 67 & \hspace{-2\tabcolsep}~km & & & \multirow{3}{*}{$\Bigg\}$ 7.3} \\ time & 9.3 & Exp & 0.9 & \hspace{-2\tabcolsep}~days & & & \\ joint & 91.5 & Sph & 999 & \hspace{-2\tabcolsep}~km & 185 & \hspace{-2\tabcolsep}~km/day & \\ \bottomrule \end{tabular} obtained via \begin{example*} simpleSumMetricModel <- vgmST("simpleSumMetric", space=vgm(120, "Sph", 150), time =vgm(120, "Exp", 10), joint=vgm(120, "Sph", 150), nugget = 10, stAni = 150) fit.StVariogram(empVgm, simpleSumMetricModel, fit.method = 7, stAni = 117.3, method = "L-BFGS-B", control = list(parscale = c(1, 10, 1, 1, 1, 100, 1, 10)) lower = c(sill.s = 0, range.s = 10, sill.t = 0, range.t = 0.1, sill.st= 0, range.st= 10, nugget = 0, anis = 40), upper = c(sill.s = 200, range.s = 500, sill.t = 200, range.t = 20, sill.st= 200, range.st = 5000#, nugget = 100, anis = 1000)) \end{example*} \end{enumerate} The variogram parameters are numerically optimised using the function \code{fit.StVariogram} and the \code{L-BFGS-B} routine of \code{optim}. The parameter \code{fit.method} that controls the weighing of the residuals between empirical and model surface of \code{fit.StVariogram} is set to \code{7} (the spatio-temporal analog to the commonly used spatial weighting). A full list of all weighting schemes is presented in Table~\ref{tab:weighting}. In our application, the residuals are multiplied by the number of pairs in the corresponding spatio-temporal bin divided by the metric distance: $N_j/(h_j^2 + {\rm stAni}^2\cdot u_j^2)$. The spatio-temporal anisotropy is estimated beforehand and fixed at 118~km/day. This weighting scheme puts higher confidence in lags filled with many pairs of spatio-temporal locations, but respects to some degree the need of an accurate model for short distances, as these short distances are the main source of information in the prediction step. Note, that different weighting schemes will in general result in different model parameters generating different interpolation values. Our selection is based on the assumption that well filled bins provide more reliable empirical variogram estimates and the fact that short distances are the most important ones for a local interpolation. \begin{table}[t!] \centering \caption{Weighted MSE (\code{fit.method = 7, see Table~\ref{tab:weighting}}) for different spatio-temporal variogram families and different choices for the one-dimensional variogram components. Columns denote the spatial and temporal variogram choices. The metric model is only applicable if both domains use the same family.}\label{tab:vgmFits} \begin{tabular}{ll|rrrrr} \toprule model & joint & Exp+Exp & Exp+Sph & Sph+Exp & Sph+Sph & ${\rm Mat}_{\kappa=0.6}$ \\ \midrule {separable} & $~~\cdot$ & 9.87 & \bf{6.82} & 10.42 & 7.50 & $\cdot~~$ \\ {product-sum} & $~~\cdot$ & 10.09 & \bf{6.91} & 10.64 & 7.59 & $\cdot~~$ \\ {metric} & $~~\cdot$ & 10.25 & $\cdot~~$ & $\cdot~~$ & 10.59 & \bf{10.05} \\ \multirow{2}{*}{sum-metric} & Exp & 4.10 & 3.60 & 3.89 & 3.32 & $\cdot~~$ \\ & Sph & 3.74 & 3.73 & \bf{3.31} & 3.36 & $\cdot~~$ \\ \multirow{2}{*}{simple sum-metric}& Exp & 4.10 & 3.60 & 3.94 & 3.32 & $\cdot~~$ \\ & Sph & 3.74 & 3.98 & \bf{3.31} & 3.56 & $\cdot~~$ \\ \bottomrule \end{tabular} \end{table} \begin{figure} \centering \includegraphics[width=0.95\textwidth]{allVgmsWireframe.png} \caption{Sample and the best fitting spatio-temporal variogram of each family.}\label{fig:allVgmsWireframe} \end{figure} \begin{figure} \centering \includegraphics[width=0.95\textwidth]{allVgmsDiffWireframe.png} \caption{Differences between the sample and the best fitting spatio-temporal variogram of each family.}\label{fig:allVgmsDiffWireframe} \end{figure} \begin{figure}[b!] \centering \includegraphics[width=0.95\textwidth]{pred_daily_means_PM10.png} \caption{Spatio-temporal interpolation of daily mean $\rm{PM}_{10}$ concentrations using the sum-metric covariance model with the closest 50 neighbouring spatio-temporal locations. The crosses indicate sampling locations. The cell size of the grid in UTM projection is $10~\rm{km}\times10~\rm{km}$.}\label{fig:pred_daily} \end{figure} For comparison with classical approaches, we interpolate across Germany iteratively for each single day using all available data for variogram estimation. The purely spatial empirical variogram can directly be obtained from the empirical spatio-temporal variogram, by fixing the temporal lag at 0 separation. From the same set of variogram models as investigated for the spatio-temporal models, the exponential model (partial sill:~66.5, range:~224~km, nugget:~13.5) is the best suited based on the optimisation criterion. Alternatively, we could have fitted the spatial variogram for each day separately using observations from that day only. However, given the small number of observation stations, this produced unstable variograms for several days and we decided to use the single spatial variogram derived from all spatio-temporal locations treating time slices as uncorrelated copies of the spatial random field. Once the best fitting spatio-temporal variogram model is identified, the interpolation can be executed with the help of the function \code{krigeST}. We use the sum-metric model that obtained the smallest RMSE (compare Table~\ref{tab:vgmFits}) to produce a gridded prediction. The interpolation domain consists of daily values for a regular grid spanning over Germany in UTM projection. The cell size is $10~\rm{km}\times10~\rm{km}$. Figure~\ref{fig:pred_daily} shows the interpolated grid for the same days as Figure~\ref{fig:dailyMeans} alongside with all sampling locations. Additionally, maps depicting the differences from a leave-one-out cross-validation are presented in Figure~\ref{fig:diffs_daily}. A time series view is presented in Figure~\ref{fig:timeseries} showing the observed and predicted time series at a single location along with its 95~\% prediction intervals. An animation of the entire year of daily mean ${\rm PM}_{10}$ prediction maps can be viewed online.\footnote{\url{http://gstat.r-forge.r-project.org/STpred.html}}. The interpolated maps are generated for a set of time stamps \code{tIDs} and a grid over Germany \code{DE\_pred} by \begin{example*} krigeST(PM10~1, data = DE_RB_2005[ , tIDS], newdata = DE_pred, fitSumMetricModel, nmax = 50, stAni = fitMetricModel$stAni/24/3600) \end{example*} \begin{figure}[t!] \centering \includegraphics[width=0.95\textwidth]{diffs_daily_means_PM10.png} \caption{Differences of spatio-temporal predictions and observed daily mean $\rm{PM}_{10}$ concentrations using the sum-metric covariance model with the closest (approx. strongest correlated) 50 neighbouring spatio-temporal locations.}\label{fig:diffs_daily} \end{figure} \begin{figure}[h!] \centering \includegraphics[width=0.9\textwidth]{singleStationTimeSeries.png} \caption{Subset of the time series of observed and predicted ${\rm PM}_{10}$ at a single station in Lower Saxony along with its 95~\% prediction intervals.}\label{fig:timeseries} \end{figure} To further compare the different approaches, a leave-one-out cross-validation was carried out. The spatio-temporal interpolations are done for the closest 50 and 10 neighbours assessing the impact of the neighbourhood size. Inspection of the ranges of the variograms in the temporal domain, suggests that any station more than at most 6 days apart does not meaningfully contribute. Furthermore, the local estimation allows the spatio-temporal random field to have a varying mean value over space and time. The purely spatial interpolation can be considered as the extreme temporally local case, where only observations from the same time instance are considered. \begin{table} \caption{Leave-one-out cross-validation results. The column wMSE refers to the optimised value from the variogram estimation.}\label{tab:cv} \centering \begin{tabular}{lrr|rrrr} \toprule covariance model & wMSE & neigh. & RMSE & MAE & ME & COR \\ \midrule pure Spatial & & 10 & 6.15 & 4.09 & -0.01 & 0.84 \\ separable &\hspace{-\tabcolsep}[6.82]& 10 & 6.08 & 4.04 & -0.01 & 0.84 \\ product-sum &\hspace{-\tabcolsep}[6.91]& 10 & 6.08& 4.04& -0.01 & 0.84 \\ metric &\hspace{-\tabcolsep}[10.05]& 10 & 6.11 & 4.07 & 0.03 & 0.84 \\ sum-metric &\hspace{-\tabcolsep}[3.31]& 10 & 6.16 & 4.08 & -0.06 & 0.84 \\ simple sum-metric &\hspace{-\tabcolsep}[3.31]& 10 & 6.14 & 4.08 & -0.02 & 0.84 \\ \midrule pure Spatial & & 50 & 6.10 & 4.07 & 0.00 & 0.84 \\ separable &\hspace{-\tabcolsep}[6.82]& 50 & 6.05 & 4.04 & 0.01 & 0.84 \\ product-sum &\hspace{-\tabcolsep}[6.91]& 50 & 6.05 & 4.04 & 0.00 & 0.84 \\ metric &\hspace{-\tabcolsep}[10.05]& 50 & 6.07 & 4.08 & 0.03 & 0.84 \\ sum-metric &\hspace{-\tabcolsep}[3.31]& 50 & 6.14 & 4.09 & -0.01 & 0.84 \\ simple sum-metric &\hspace{-\tabcolsep}[3.31]& 50 & 6.14 & 4.08 & -0.02 & 0.84 \\ \bottomrule \end{tabular} \end{table} \section{Results and discussion}\label{sec:resultsDiscuss} In terms of added value of spatio-temporal kriging measured in cross-validation results, Table~\ref{tab:cv} shows hardly any benefit in the illustrative example. This effect can to a large degree already be explained from the spatio-temporal variograms: a temporal lag of one or a few days leads already to a large variability compared to spatial distances of few hundred kilometres, implying that the temporal correlation is too weak to considerably improve the overall prediction. Nevertheless, investigating a process with a higher temporal frequency will likely show a stronger correlation in the temporal domain. Looking into station-wise cross-validation statistics (not shown), the four stations with an RMSE of 10 and larger correspond to the locations with the largest annual mean concentrations ($>22~\mu{\rm g}/{\rm m}^3$). The added value of spatio-temporal kriging lies in the flexibility of the model. We are now in the position to not only interpolate at unobserved locations in space, but also at unobserved time instances. This makes spatio-temporal kriging a suitable tool to fill gaps in time series not only based on the time series solely, but also including some of its spatial neighbours. A very irregular sampled data set would as well largely benefit from a spatio-temporal approach, as spatially close but unobserved locations in one time slice are not of any help in a purely spatial approach, but the spatio-temporal model would benefit from the observed value nearby at another time instance. In a completely regular data set, the distance to a spatio-temporal neighbour is at least as large as the pure spatial distance and hence the correlation is weaker. Furthermore, being able to capture the covariance structure over space and time might foster a better understanding of the process under study. While we see spatio-temporal modelling being a powerful tool, the cross-validation results in Table~\ref{tab:cv} show that spatio-temporal kriging will not solve the problem of all poorly spatially captured phenomena. Further preprocessing steps might be necessary to improve the modelling of this $\rm{PM}_{10}$ data set such as for instance a temporal AR-model followed by spatio-temporal residual kriging or using further covariates in a preceding (linear) modelling step. Providing the best possible model of $\rm{PM}_{10}$ concentrations across Germany was beyond the scope of this paper. The selection of a spatio-temporal covariance model should not only be made based on the (weighted) mean squared difference between the empirical and model variogram surfaces (presented in Table~\ref{tab:vgmFits}), but also on conceptional choices and visual (Figure~\ref{fig:allVgmsWireframe}) judgement of the fits. Even though the function \code{fit.StVariogram} provides optimisation routines to fit different spatio-temporal variogram models, the numerical routines in the background may struggle to find the optimal parameters. Besides the lower and upper boundaries of the parameter space, the control parameter \code{parscale} of the \code{optim} function is a valuable option to improve the convergence of the optimisation. With passing \code{parscale} as entry of the list \code{control} a vector of scalars must be passed that controls the different levels of magnitude of the variogram parameters. In most applications, a change of 1 in the sills will have a stronger influence on the variogram surface than a change of 1 in the ranges. The problem becomes more difficult with an increasing number of parameters. In our application, using the simple sum-metric model as starting values for the full sum-metric model improved the convergence speed of the more complex model. In the presented application, the sum-metric models turns out to be the same as the simple sum-metric model. While this might at first sight be due to using the simpler model to generate starting values, different non simplified starting models converged to the same result. Generally, it is important to keep in mind the strong interaction of the model parameters. It is typically not easy to distinguish how much of the spatio-temporal nugget and sill is attributed to spatial, temporal or joint components. In this paper we considered a joint numerical approach, but step-wise approaches where the components are estimated separately could as well be considered. The interested reader is also referred to \cite{Nash2014}. However, all optimisation approaches follow the premise that the studied process can be approximated with the given model and available data. If this premise fails, no optimal model can be selected. An extension towards a restricted maximum likelihood method (REML) to fit the spatio-temporal variogram model would be desirable, as it overcomes some of the above mentioned drawbacks of the method of moments based approaches and would additionally provide standard errors for the parameter estimates. A REML approach would allow to take into account that sample variogram values are correlated. However, for large datasets (as in the spatio-temporal case), it is computationally more feasible to use a least squares fitting. To reduce the correlation of the variogram values, some randomisation could be implemented in large data sets, to calculate the sample variogram based on partially overlapping or even disjoint sets of observations. The selected anisotropy as proxy to the relation of spatial and temporal distance in determining the strongest correlated neighbours might show a distortion for some models when only few neighbours are used towards the true set of the most correlated locations. However, this effect vanishes as soon as the spatio-temporal range of the model is sufficiently represented through the set of nearest neighbours. As mentioned by \cite{kj99}, an alternative to space-time kriging might be co-kriging. However, this is only feasible if the number of time replicates is (very) small, as the number of cross variograms to be modelled equals the number of {\em pairs} of time replicates. Also, co-kriging can only interpolate for these time slices, and not inbetween or beyond them. It does however provide prediction error covariances, which can help assessing the significance of estimated {\em change} parameters \citep{pe1,pe2}. Several of the space-time variograms presented here may be approximated by sets of direct variograms and cross-variograms. Fitting variogram models to sample space-time variograms is in our implementation done by \code{stats::optim}. Our example script uses method \code{L-BFGS-B} and provides upper and lower parameter boundaries, e.g.\ to make sure sill parameters do not become negative. There has been a lot of research in optimization since the methods in \code{optim}, some of which has been reported in the special issue of the Journal of Statistical Software \citep{optim}, and we do see potential to improve the options in this respect. The approximate selection of the most correlated neighbours solves the lack of a natural notion of a joint distance across space and time. However, other sampling properties might introduce a bias in the prediction. The prediction at an unobserved location with a cluster of observations at one side will be biased towards this cluster and neglect the locations towards the other directions. Similar as the quadrant search in the pure spatial case an octant wise search strategy for the local neighbourhood would solve this limitation. A simpler stepwise approach to define an $n$-dimensional neighbourhood might already be sufficient in which at first $n_s$ spatial neighbours and then from each spatial neighbour $n_t$ time instances are selected, such that $n_s \cdot n_t \approx n$. The presented example considers stationary random fields that are isotropic in space. Further extensions towards more sophisticated variogram estimations allowing also for spatial geometric anisotropy are desirable. One could for instance plot variogram maps for spatial separation in North and South direction for each temporal lag. However, the current implementation does not allow to use the anisotropy parameter \code{anis} of the pure spatial variogram definition. Nevertheless, a preliminary rescaling of coordinates would be a possible workaround. This route has for instance been taken by \citet{Gasch2015} performing 3D+T kriging . The soil profiles in their study show a clear difference in horizontal and vertical variography. To correct for this, the depth dimension of the data has been rescaled to correspond with the dimensions of the horizontal distances before hand. In the subsequent study, these pseudo 3D coordinates have been used to fit the spatio-temporal variograms and perform kriging. The code in model definitions is meant to be kept both flexible and simple. This is based on i) re-producing the notion of the geostatistical models in the R code and in ii) reusing existing definitions and functions of the pure spatial cases that have been available for many years in \pkg{gstat}. The data handling benefits to a large degree from the implementations in the \pkg{spacetime} R package. \section{Conclusions}\label{sec:conclusions} The spatio-temporal extensions to \pkg{gstat} allow to model a set of spatio-temporal covariance functions. The implemented functionality eases estimation, visualisation and understanding of spatio-temporal covariance functions. The extension and reuse of already available function structures and nomenclature facilitates an easy translation of spatial workflows to handle spatio-temporal data. The numerical estimation of the variogram parameters might be tricky and needs a large degree of the users attention. It is advised to carefully check the outcome of the \code{optim} routine after optimisation. Spatio-temporal kriging predictions can be made in a global and a local neighbourhood set-up, while the latter will be the preferred solution for most spatio-temporal data sets and common computer hardware configurations. Spatio-temporal covariance structures carry valuable information, but a spatio-temporal model is not guaranteed to outperform pure spatial predictions. The benefit in terms of prediction quality of spatio-temporal kriging becomes only apparent if sufficiently strong correlated locations are added with the temporal dimension (i.e.\, if the model permits strong correlation across time). Nevertheless, the spatio-temporal covariance model might be of interest in itself. Besides some publications where the authors of this paper were involved in, such as \cite{Kilibarda2014}, the software presented here has proven useful in several independent publications, examples of which are \citep{marek, biondi, hu, yoon}. \section{Acknowledgements} This research has partly been funded by the German Research Foundation (DFG) under project number PE 1632/4-1. We thank two anonymous reviewers for their valuable comments. \bibliography{spatio-temporal-kriging} \pagebreak \address{Benedikt Gr{\"a}ler\\ Institute for Geoinformatics, University of M{\"u}nster\\ Heisenbergstr. 2, 48149, M{\"u}nster\\ Germany}\\ \email{ben.graeler@uni-muenster.de} \address{Edzer Pebesma\\ Institute for Geoinformatics, University of M{\"u}nster\\ Heisenbergstr. 2, 48149, M{\"u}nster\\ Germany}\\ \email{edzer.pebesma@uni-muenster.de} \address{Gerard Heuvelink\\ Department of Environmental Sciences, Wageningen University\\ PO Box 47, 6700AA, Wageningen\\ The Netherlands}\\ \email{gerard.heuvelink@wur.nl} \section{Appendix} \subsection{Derivation of the separable covariance and variogram identities}\label{sec:derivSep} The separable covariance and variogram identity is readily available through \begin{align*} C_{\rm sep}(h,u) &= C_{\rm s}(h)C_{\rm t}(u) = sill \cdot \bar{c}_s(h)\bar{c}_t(u) \\ \gamma_{\rm sep}(h,u) &= C_{\rm sep}(0,0) - C_{\rm sep}(h,u) \\ &= sill \left(1- \bar{c}_s(h) \cdot \bar{c}_t(u) \right) \\ &= sill \left(1- \left(1-\bar{\gamma}_s(h)\right)\left(1-\bar{\gamma}_t(u)\right) \right) \\ &= sill \left(1- \left(1-\bar{\gamma}_s(h) -\bar{\gamma}_t(u) + \bar{\gamma}_s(h)\bar{\gamma}_t(u)\right) \right) \\ &= sill \left(\bar{\gamma}_s(h) + \bar{\gamma}_t(u) - \bar{\gamma}_s(h)\bar{\gamma}_t(u)\right) \end{align*} where $\bar{c}$ and $\bar{\gamma}$ are normalised correlation and correlogram functions respectively. \subsection{Derivation of the product-sum covariance and variogram identities}\label{sec:derivPs} The product-sum covariance and variogram identity is readily available through: \begin{align*} C_{\rm ps}(h,u) = & \ k \cdot C_{\rm s}(h)C_{\rm t}(u) + C_{\rm s}(h) + C_{\rm t}(u) \\ \gamma_{\rm ps}(h,u) = & \ C_{\rm ps}(0,0) - C_{\rm ps}(h,u) \\ = & \ k \cdot C_{\rm s}(0)C_{\rm t}(0) + C_{\rm s}(0) + C_{\rm t}(0) \\ & - \left(k \cdot C_{\rm s}(h)C_{\rm t}(u) + C_{\rm s}(h) + C_{\rm t}(u)\right) \\ = & \ k \cdot {\rm sill}_{\rm s} \cdot {\rm sill}_{\rm t} + {\rm sill}_{\rm s} + {\rm sill}_{\rm t} \\ & - k \cdot \left[ \left({\rm sill}_{\rm s} - \gamma_{\rm s}(h)\right)\left({\rm sill}_{\rm t} - \gamma_{\rm t}(u)\right)\right] - \left({\rm sill}_{\rm s} - \gamma_{\rm s}(h)\right) - \left({\rm sill}_{\rm t} - \gamma_{\rm t}(u)\right) \\ = & \ k \cdot {\rm sill}_{\rm s} \cdot {\rm sill}_{\rm t} + {\rm sill}_{\rm s} + {\rm sill}_{\rm t} \\ & - k \cdot \left[ {\rm sill}_{\rm s} \cdot {\rm sill}_{\rm t} - {\rm sill}_{\rm s} \cdot \gamma_{\rm t}(u) - {\rm sill}_{\rm t} \cdot \gamma_{\rm s}(h) + \gamma_{\rm s}(h) \gamma_{\rm t}(u) \right] \\ & - {\rm sill}_{\rm s} + \gamma_{\rm s}(h) - {\rm sill}_{\rm t} + \gamma_{\rm t}(u) \\ = & \ k \cdot {\rm sill}_{\rm t} \gamma_{\rm s}(h) + k \cdot {\rm sill}_{\rm s} \gamma_{\rm t}(u) - k \gamma_{\rm s}(h) \gamma_{\rm t}(u) + \gamma_{\rm s}(h) + \gamma_{\rm t}(u) \\ = & \ (k \cdot {\rm sill}_{\rm t} + 1) \gamma_{\rm s}(h) + (k \cdot {\rm sill}_{\rm s} + 1) \gamma_{\rm t}(u) - k \gamma_{\rm s}(h) \gamma_{\rm t}(u) \end{align*} %%%%%%%%%% \end{document} gstat/inst/doc/prs.pdf0000644000176200001440000021201414413507475014427 0ustar liggesusers%PDF-1.5 % 1 0 obj << /Type /ObjStm /Length 4260 /Filter /FlateDecode /N 77 /First 632 >> stream x[Ys8~_TD R#رc;yP$֎,et__Hhǻ% M@2i&-g)3ˌp14%, xlLHɄxPLXz%2&AeRJ3' *.aThĔITI1-`R3a%x313EYE9` +xq 5sZ4 \ʱX`Xzl:6,&8Z8d b &X0: bTaA:F!!cb'H9ISH 42% (Bc@V:!`=*&\$T{#Ң@"K(`DFcF` #  Px@>0Jo٢ [ :@VhN΢t}8;gr1M9?o񠳇_Rxz^ v+jfi1NRqͭ V5ϸ',Qezžwgoߦ<;MA xΎ٫|1F_,hrt/GqJ|{dFoF@Zlt;'o.{G G:&ƒ0h\xo:Y4 8N11遪=pwt9`$ū!d30#l:H`@xQs Fe( Q|yt(]}^L2#r}Q 9~8js !=: tQt6KTX"TA5Ej\;\vɪIa͋8Ocx2ZC2u$Hnk?ī;>z%v/9:tzxp@Wr2G[}Mv&н HP{Um \F[xDl菣ˍW?,(86F.Vl { 4 `X/Ո&N%QFw(G4͢yF~dP,`A휼 ݂ }Ӊ돬`4NJmߧ-8 v& 砂GˋEzhUV(]KӰONC 1G{&;{}qlxXe|zߟq2ddn: I39!-Ur:pKѫ(:D!rN@ (;h:_4ZVI,t$MSNb$qM$`-46҅tz͇~v9;NP.nRtp ?*[\WmW O *feBIRqcqQY/#fOn!PZߡE!re% z9-P99H 5$N?PIn5R4JCRh2,{}|tGs4thef7NHm: ?ГHBHGsQ[DhY6v~DGiM% "Hu.~u4MlR(IaE+Ã݃LKF`֜MtֽYhxWFsL@)YaRT%$wM]SjZlmrK@68xM!+ҏǓάCgLΘ몫む4^~tOt=/_cj;Wv2uM>zU6 t "88a:&:ZXoeXu>8|wv(SaW!%Ðwd0Lg]5kŲ,SZglim]rX"-E-W,ӓʡfw_ox$T+rO ٘ifhws{KuP<()kg1MSQ.ȝ^xwrr$jWبU|BK;5s}Yu ]F3y WNU|}j $M z` EP6UgWzQض-F- wwϳLG╋R/pQ')ĻCFk{2+X%ݿ:~u/ꖴpWn  :=6PRq~V/a3p42PeY< nj ޠ\G֐UǤjP&TlMFY[OCE*hѲRAʵB*; 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C5R>RO8cf!$Z`l:ckHs[mC@W7qrH8ΞeWN}oHӃ>^ƋՄFgfee6^QKNHZӭkBUwY97k݃gOiV2C/^$ J۱>Uyses{Cim$ /K|cWd8u-x6 Q.-$e"kc6ջTU7y#+S2&]"#A;#}w#<E$V‹U( ʙ| 9z9/{ endstream endobj 85 0 obj << /Filter /FlateDecode /Subtype /Type1C /Length 2929 >> stream xV{PT?˲k[IƠAWQ 򆀼 FJhAC 7 uYdՄ(16NY4mfڙvܻ߹~;YZ Dbzl|VrdKd13U?)`wVKc%=dsVvg,s9b-S$] v$ְ v$DԦ~zgH/ b4ґ;_ψS-4p0 *B% dHq5.!,q/`n_]RzbGtDJࠀ|M<=oڬDMOK<{BN&vf]—p瑓'{zK>crLO 8,&˸]nni,kMx~Mfso}q\Aΐ,^7EThp ,DT;|kH{~muu==%wMтEvv;'?xE DȨA|5&%7E ,3x߁Y; bQX]bCuN,?ar)94, tT+r MZ3Ң&ot TMd/x]gZ|F8۾;IhPڻ:-՝}on[m7iRV}x:F z3l R80 9 ehyPF&;kqxe1]uw4o>Q>eìEx5ސ`| ӧ_ţxhO_[gE?+W8Wb-*8}=,TӅ>:ϯ:h.d%)Pu vO j:crmSböP7x4%faҨux3>LH9&}dnx dzNaL0ndJQ=ʦa%A0f RC|p=@m\4bwxJKbf瘲Z n.kmkyXeJݙ-@$% 47\WC/Q`䄴*DFhz?xyA3u);aAnx^foޯ=TVZYRJ;θ<- U2m:{xݩ֪.܉:aҿr-3˨+u} 1e8wHԸŬOM4XcPl`!30XO^B((GTv~>iBÛY cR>7@;5=Jdy.mge~AF ~ ŗ'Qdz>|^V.Kq7P~Cļ:Oe\akayi}U{۱snK /M++fFf)o?sˢVn4yOּQk^r`uC"dAl@.\TcRZ~6ehW3*Nj-紧߼0*5T I2-2QAՒ#㉝O ]wJoFŋP?ٟnv2uD8tٶx`w-RMMpg ~wEr2 DcNl{W6qqM翺љ&vwoYm\':ÿ29I՘֖sag6ު_fGi>tK@E?18xjv7ac yF0BS1 KTZ3j)J~2Gfe$m=,`1}O07%_`@MI/| ؋ :J.~ԥ"7Ԧ[oIpvGɨ\8c>dTA>&tijj1O "*'H tt- B1At@AXR/2r- 0΃ղ[TJܨHyjHA-E[&W׈OnpmXUSlYR^[&{jOL RtdLr4FPBe+9Zbjy)*2}zn%`/K2qK=ɠo9rȆ.=5CgaN!ũv'q\kr5WR՘ԘܳCqG|8}Z%C#Pv LԌdFeUӿlۘCl̛a{3DI:p~mޮLB GR>ᑃNYo ^e@Wyj4<%<BM+y auu5-_S\:m %JM6qX 7'۸Z\Ю+uq`yOׁJkkkv@Ip'LWPA_8 {KaKh`% K[(i$Iybxżj`hzzz'endstream endobj 86 0 obj << /Filter /FlateDecode /Subtype /Type1C /Length 1402 >> stream xmLSWo[X *]vdS͉bԸ7D͂ "h@+C޶ BG[RޔWS/[C_F4~Mq3䒸v%9Oy>lߔj%G jo&) PX{x̟7=x l*+,NJKdE{eo=!XػH4 ۉt"@"68"P@'8`W׼M[!ab{y8j r f>˺A_euI U(C!K9ݟEn7L^s6)RVj[ gg~u㖚2?~n罇U>+ƗsB.l5`UA3yu1MZQݡj**@RRtJ5hlOL?| z#pdpr/gXm %!8fŤa6pG)2j9T;F gW a>LNަفnWr01%#   x;"o))jHONOМJqGA:wbf+;K(mVl,\O~Q4edx˟Њee \x~.%>Cʿendstream endobj 87 0 obj << /Filter /FlateDecode /Subtype /Type1C /Length 1271 >> stream x]RkLg}['"hsyP&ŒLUDJJK> DJ ^g! ^fDfg,okƺy9P.p8sғR63, pCgT30a|_9QG\gr0W$U-IKŲ-B'Eqkm\Rm4 # soqOs!CWg99=l~دJ0Ǔ}:벻썢+t¡h--#~9URbjJ{c"u@ ʤE6" $E5AiN"gLC{т@P:WDUz(=MS N(|Y70 ý-C 01%V/҇ $nc}iGx8NPe xǨ6gq'Nr_5?g F? r(pu~%L:U}~#X&wzhWTL />+ o٨N90LOMmfw(cIXIRmf3V^(Zu:fGqy E?KXG u]q6X ~fg"]A'ULv6P߹n Cc `e-n% SO{'kZ0/I #7B^%փa&j9=y>!nKeA@A/YJ ߗ0^7_ט?`T`Oq~}έLgKc?tVЙҚ~Q&֖ʊ eL,Ð Q= 9p¦듗͢e;w$e|sn5A)(N *Ķ&F<X_zgт<<)`%vWJqDg|שZ!thrH}ƫqT '˾ej-ЄZY@?E`#/zFJ-`9IkXd ܬ=~NT{~!tjV9yG5ʎh#Y۵)YY,[a]Qg7:x/`T>T#SJU݌V td`l./EչLxH@\endstream endobj 88 0 obj << /Filter /FlateDecode /Subtype /Type1C /Length 3144 >> stream xmV{Xwi%@Qg8`=֪n϶V*+ "%@"KDȍ""8 R-ֶc۳,_x~캿^$'33oQH$ZǶJp^'"F.ݫUArXPS"1 hf^nRWHFbRvFZW<7)=1)nR2?#3;g{n΂ݲĤ#R>*CP^* Q~j=ES@* S;W)?*zr$ (O1ThH q(o:>xS?h_o,̦/Y$qK.=t9e(L>tHJ' K_?1{ö=RY+#Y;^ Zr5b;}?Sj fbP :TJiqbx 9`۰)K9om#n.fXs}'}_<ѵCS{,Q(B)iaPOe{L)H&!? w`IUT!UⲎ% b O~NU ^hV f[{Dkǥ#(f ]*I~5nN1hRwpGG}&U aPtվI9G( %6ZѨ,!:m[xC-0>; ]T~z0](nOi.4-O㦰cs:: Ţ"_TወءFZ5P4e iV t>%}?_0K'r^ gXU׺{ۻ{.FZbC")㴰SNwnCWpUwɷsҾs9=ٚUQ;~S& 9#ݠ7Ay1keNJ+FšB]!bK'EQ1Nu8 e/*T ]T@lYMy]Cc &HER 6wAtrw:5{:&C--?.O?rXM&[Ɉ<:ޯ<_FC l.:~ MЃ,o>x_^nX::r$ubMܻII-#u'|u ZhuHɶ#%&P{_B]^+Dgm/Q*P>њ=BW{QPrd\v܃Ͱ׬\PLYU]ΕrVyI9pD.Er* DCĚ.nE1I}1'?_"#q MggTH%':|HW.f3RzZMmNrB1Rkԙ (ſ]6CfmDY`[T@Ѝ Eq|x|f0 f;VNW[]jYsT^PqY QyQ$̞k(kqDc ˙6~ObP%3&2\"zٍEG7Q(`K?LZ+,);N(}+7a99?Sl@P&k!n`>E⧻ %?`fЙkhv!ZNIZXA Iax]R F@|p=y>\oL[>4rz\Z/ ~L[3ql,\h.i7V7zF7æv[vZ?FiͬNBXU\|,'=E/Kմ#~G7~ [b FN_C&ZƘLeYHiiUMi:> k^7S74-׊Ɠ ;2&8:X<9\eB*L+~ûmň"ƌ:3zǩt~CAC%/x?xՐF?fN]SwЗʚkO" d_cEi螷PZU)[Ʃ*o~PE>@$+P;.ƫe^ijuF4U|."{:%ON6$.rW107$^ʗ0ꍯ+|ް=*UU*em3&۝1A?T8[7.^4ς^3L\:d )n>#🶏==Mc$*n ThQ6fKA[hP:YӪc=zK4cj;P_~kzVE'd'cG: Ps>SK^3߰ߋX3g,9ݩ/@ @}>y@ '@я] 9GW|6Fr s1sYnZ۔\R^PZk^opkO P34ҋRq6%O} endstream endobj 89 0 obj << /Filter /FlateDecode /Subtype /Type1C /Length 7291 >> stream xy TS$8[\s :VTyT $ad"Ƅ)X:Ŋzk[;h'o~v}+,~y "AAAW/XtlDD!A!(C z^ݪ '}ڏ yIXI1"UI;%A&K"Z&^$Y,ݙkIFtfL+]:~MZĈOSN{{A#G3 ˉ7ěJb(XMM!ku;zbKl$M|b3 "Bb1XLL ]b)1XFB\UG'Db1DPDwH&}~A=ٸBI j [p7c'RXW{)7E#ȞM:{Zow}kǼ2_ئCܽ{+:o|j[  x|вAx%vM1o1Sx`?&#MҠz dUl †g9"`RXT%X t*5(FkBNH͓)t p:86̮y~8aSJ7<7I ?s4u H'pTfxM\^'bw=w? 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.vҮŠkjk#_)(О3 ">rm䄥I}tlXK:#Y?d; Tg>mfHu08Q[e&php_ i0C L3Y⟣:"ԇb؀ݶ?%o}fܖ'9bjhsvþ>gƒ ͔ -%Ƴ D &vNa(Ĉ߱8vmPX K`rMRoshu!L6Me:Z:(aIq֯ngnQ5__!%"rqa:qi:vu^Y%gY\D7Iؽ$ d&vɢ=Q1)I<0-&b׸"&WbuzZӦku wFjOmiƦ$hTvk7L3%s@%L?-ՐQF)▟S=Zg'F)Mμe[AJc !x;D% TtQZ9Ϛ'JLdAʂbxѾ~8UWJWG0BD.քQ1sx1k20 2gVK j:I:ΎΡPh[ffgQω@hm8®5-fW%' fK?A.Ito] endstream endobj 104 0 obj << /Filter /FlateDecode /Length 2624 >> stream xYˎ\WeOїo2Kda{1h r<ٿs,wȑFO="*m7v_\O ns5'rۻӾ!Xķsn_ޞxʖM%鶛-D6WcnOw.7:`볩.oV\!ï7.o^`j ?~}S09=n::X iq p<,黓i7>YPLK1.YP.:,RƂ 6W,^xغ*6ߕs@%:gEa+J9TK9TYQds@R;:Odd2>aׄ K2G +{B^ǶG9;dD[ !e29 i9 _ bp?Ps*f,3pr&.0ʥ55s1!wC!n5}dWLvE>P#jI>PK+j&d$܉gU5šjMZ?Vwv{dۙQוS 6&Dg&gY@U)L\Y4 ZlPB9N4X/9<qIy貜)dJK9W7Ѧ4`Ȼ5O n6 18ڦS6MI C.1 ,ܣȄ~Q) p+}{0GK4ָ 2ʄ_4(lr,yҴiJt/b5 rȅehQzV .9UB`V( ,XMpSb@6Q{PhE"~^hv".7\[m2!gQ/q+"abʉVvh@<.6M Bj8bx ى\WN5;VV$$&n8*yF8CM|*8$^勅F30uqM .r[a^Q,=+k525MOQ8.LJ6 .`#i4.(b85l 6T&e`M5=L{; R,P@9p_.WU>0hJ1|E!ytB|Zrɑ8#ןRO8iũ =fSä$5[5Űh4mP/U1-`ЏSNqӷ-zTT}'c. % EP馚 8aӔb5ݗG.!=v)AWyϘ>,5=c ȩ 3 EK8]Xc˺t]9|(@b-)YFԁ` whؠDٓ_5ٳiӔ^ Drh8b31ׅSQ/hT( )??q(OA7+eQQçF3*ÿ.,*2ZJR/m(42}s4DBAfM5 &ܴhJP/U1T-X\oL|ΤS؇Sk _qlz""(/|x)οzrn}ݕ|DL?޿~s=߽{D)1'>b9LJ7?P 6~5Fl7ۿ|~Q0v_}?$D^=ݑlD/_֮#w.o?4lYϜk_w#/,ȇ61}{/fendstream endobj 105 0 obj << /Filter /FlateDecode /Subtype /Type1C /Length 1923 >> stream xU{Tg!d2k%Q̤`](*BW[PyqX "TG?ʨvl9W*#\0l켜*ÿ r)uQ8m?=$uzM/߲492p6kSTclS~yHE`9Q0_xQLۗa^2łhLIw 8{mS)} 8wd>I6dT(J:sz,JJW}>ޣfbْ7oDDcnK/d-).SdՑRĮ(!j|$'QSӕ]/dǔNw"o\g(nS;~Q+|oGI;9Vcّ0*\ ϶b9+!R%0ߜT\-3yo-rI=Y<ֆ<}e{Dgvw%/70)]-ݩݿ6RpF.q$%b!bH|kUGI4Xy+v.W[[/52k s ׭S}=C)SFQ*T; *kLʼnƿnA=7ӸP5g/D /p5N9<0n&{)bbnMvsˆGe>|!<ex:v'43D{- yhgqyplX`҃}zƱje1uZ-0wċtETyNobj ho ~qi۵\-ċxS B_A|- uc@UJHr;"l{a L`Ƶ*([AЕiaOO["- {~$мn<(K!f(^0?w`{\@]4P^X.⠚GI2ͲԴHix갧V0Րֶ4c{'T']W{9 c;XflcYԡּe]]R(DWd}E==}@Dxendstream endobj 106 0 obj << /Filter /FlateDecode /Length 2439 >> stream xYK _H~ا*IJ9kjH☢vdS<V+w{O7js[V VM!VBsrVBpz!`[mv<~}k8w{׺ ÅJv}}8|MV }_|I '^Ⱦz PwƳϫ|ۨ=PlMYʎ&Mt'Rlw[mО]=IR c;<ŠvxhN jثc kOyez-ܵt` ,.ǝYePu<|N2)<(59x#_|۷ @Y<.}7ۡ nxSYPe; SB^:dIVBL:OB3,W:9x0Δ2@0 ޻ +(X`fYpCN / 'T| =@҇i w\'-,⃱$ v8N2Gd ̀KEBxB|W45V֨0B?xyзulacm?TAt @tkX üeOzB YP(* z-]0+guw8kY wNZ{&>F OdIJ O\a1e| M2MܯEb')_imgAqElDm}L7Y u𔝚&6P%IN&hY?7Y&ܶǼw@O|a@tQV,įjvА ޯUZ,mFtOh RbǑ%F9_ec`1|렁B.iT߭x5]z0!RK=cCR4ݑ@x V.t&L E^pW@ )ܮItS욥yJġL+ kKZ\Q$Wht \cxli|oҶ ;lU)c00@D6h|sZ.Aüm(x#F1>kcBߗC:D>c@䀥e3H1\ .Ç%ނF S3*լNNqO#5'#(Jd:Hl#ߥBt뉑uA~ʼnES+/6nM.iK53.Vrj|Dg=wgf1iũu d'…MWx̓[PMO688JsPwMYZ p3zn45Sۻ0N[ *nj9~u(U<}hc󏛛߿_kendstream endobj 107 0 obj << /Filter /FlateDecode /Subtype /Type1C /Length 196 >> stream xcd`ab`dd v 5400q~H3a#ewo_ 0012:)槤)& 2000v00t;gu`Í ʅ|(YQϡ;çg /xk76i?~뙱wh7{r\-< Fendstream endobj 108 0 obj << /Filter /FlateDecode /Length 1593 >> stream xXKFٿB7Fa=#U9lAQy!lZ[Vʖ@!tHZ+ T[$^,]Y6jsaO&Y,O*Xf(>YO1'HUK@)|³qrEʪ\iR| oSWܑ.:7bYWpSFH\= wT Xm?%1飬J:ƹMʋe}K"4V.x眙q39#fݑGר"g^uwf@1=(+71i\ޯqs̏yD"ZȨ" HΊIW-Rr굲*b9@YQ⊆q`ScɃM+{.ޢ<\Al` &A T\1N?߰EcDN` >`aˠSx3H*> 'I\(q,A qQ|R|d{ife!:iQK3f=ګHAZK砮1Sqifa[<9q}h*"|Ga}U{XXsd!#ɻTX(֑|z>Hxasx+Y@;*9MP0@["zMo]Űu5]%B KqM .0ok#yiοJ%OJ:і~5'A +6uBKLF :Eӑjek*|kWXd QdgA_`Kޒ5 3J9&+I To5[pWu0iYTl?;IǽBM[@Qαj/*z庪x3jSXw1xRL$b趵ja~:q u3hCgmvS]> /W [ 1 3 1 ] /Info 3 0 R /Root 2 0 R /Size 110 /ID [<1e273cd15fb6e74c0d02115752871a83>] >> stream xcb&F~0 $8Jy? u/(NyHv!ɺDr<@$iv,VD^,XD2{ 9D2H`*2`?6DrwIFv \j {pb endstream endobj startxref 70257 %%EOF gstat/inst/doc/st.R0000644000176200001440000001667314413507474013715 0ustar liggesusers### R code from vignette source 'st.Rnw' ################################################### ### code chunk number 1: st.Rnw:89-93 ################################################### library(spacetime) rm(list = ls()) data(air) ls() ################################################### ### code chunk number 2: st.Rnw:102-108 ################################################### if (!exists("rural")) rural = STFDF(stations, dates, data.frame(PM10 = as.vector(air))) rr = rural[,"2005::2010"] unsel = which(apply(as(rr, "xts"), 2, function(x) all(is.na(x)))) r5to10 = rr[-unsel,] summary(r5to10) ################################################### ### code chunk number 3: st.Rnw:112-114 ################################################### rn = row.names(r5to10@sp)[4:7] rn ################################################### ### code chunk number 4: st.Rnw:119-124 (eval = FALSE) ################################################### ## par(mfrow=c(2,2)) ## # select 4, 5, 6, 7 ## for(i in rn) ## acf(na.omit(r5to10[i,]), main = i) ## par(mfrow=c(1,1)) ################################################### ### code chunk number 5: st.Rnw:129-134 ################################################### par(mfrow=c(2,2)) # select 4, 5, 6, 7 rn = row.names(r5to10@sp)[4:7] for(i in rn) acf(na.omit(r5to10[i,]), main = i) ################################################### ### code chunk number 6: st.Rnw:143-144 (eval = FALSE) ################################################### ## acf(na.omit(as(r5to10[rn,], "xts"))) ################################################### ### code chunk number 7: st.Rnw:149-150 ################################################### acf(na.omit(as(r5to10[rn,], "xts"))) ################################################### ### code chunk number 8: st.Rnw:174-175 (eval = FALSE) ################################################### ## acf(na.omit(as(r5to10[4:10,], "xts"))) ################################################### ### code chunk number 9: st.Rnw:180-182 ################################################### library(sp) print(spDists(r5to10[4:10,]@sp), digits=3) ################################################### ### code chunk number 10: st.Rnw:189-190 ################################################### rs = sample(dim(r5to10)[2], 100) ################################################### ### code chunk number 11: st.Rnw:195-197 ################################################### lst = lapply(rs, function(i) { x = r5to10[,i]; x$ti = i; rownames(x@coords) = NULL; x} ) pts = do.call(rbind, lst) ################################################### ### code chunk number 12: st.Rnw:200-202 ################################################### library(gstat) v = variogram(PM10~ti, pts[!is.na(pts$PM10),], dX=0) ################################################### ### code chunk number 13: st.Rnw:205-208 (eval = FALSE) ################################################### ## # plot(v, fit.variogram(v, vgm(1, "Exp", 200, 1))) ## vmod = fit.variogram(v, vgm(100, "Exp", 200)) ## plot(v, vmod) ################################################### ### code chunk number 14: st.Rnw:212-215 ################################################### # plot(v, fit.variogram(v, vgm(1, "Exp", 200, 1))) vmod = fit.variogram(v, vgm(100, "Exp", 200)) print(plot(v, vmod)) ################################################### ### code chunk number 15: st.Rnw:223-224 ################################################### vmod ################################################### ### code chunk number 16: st.Rnw:229-230 ################################################### dim(r5to10) ################################################### ### code chunk number 17: st.Rnw:235-236 (eval = FALSE) ################################################### ## vv = variogram(PM10~1, r5to10, width=20, cutoff = 200, tlags=0:5) ################################################### ### code chunk number 18: st.Rnw:241-242 (eval = FALSE) ################################################### ## vv = variogram(PM10~1, r5to10, width=20, cutoff = 200, tlags=0:5) ################################################### ### code chunk number 19: st.Rnw:248-249 ################################################### data(vv) ################################################### ### code chunk number 20: st.Rnw:252-253 ################################################### vv <- vv[c("np", "dist", "gamma", "id", "timelag", "spacelag")] ################################################### ### code chunk number 21: st.Rnw:258-260 (eval = FALSE) ################################################### ## plot(vv) ## plot(vv, map = FALSE) ################################################### ### code chunk number 22: st.Rnw:264-266 ################################################### print(plot(vv), split = c(1,1,1,2), more = TRUE) print(plot(vv, map = FALSE), split = c(1,2,1,2)) ################################################### ### code chunk number 23: st.Rnw:278-283 ################################################### metricVgm <- vgmST("metric", joint=vgm(50,"Exp",100,0), stAni=50) metricVgm <- fit.StVariogram(vv, metricVgm) ################################################### ### code chunk number 24: st.Rnw:288-289 ################################################### attr(metricVgm, "optim")$value ################################################### ### code chunk number 25: st.Rnw:294-295 (eval = FALSE) ################################################### ## plot(vv, metricVgm) ################################################### ### code chunk number 26: st.Rnw:300-301 ################################################### print(plot(vv, metricVgm)) ################################################### ### code chunk number 27: st.Rnw:311-319 ################################################### sepVgm <- vgmST("separable", space=vgm(0.9,"Exp", 123, 0.1), time =vgm(0.9,"Exp", 2.9, 0.1), sill=100) sepVgm <- fit.StVariogram(vv, sepVgm, method = "L-BFGS-B", lower = c(10,0,0.01,0,1), upper = c(500,1,20,1,200)) ################################################### ### code chunk number 28: st.Rnw:325-327 ################################################### attr(sepVgm, "optim")$value plot(vv, list(sepVgm, metricVgm)) ################################################### ### code chunk number 29: st.Rnw:332-333 ################################################### print(plot(vv, list(sepVgm, metricVgm))) ################################################### ### code chunk number 30: st.Rnw:341-347 (eval = FALSE) ################################################### ## library(lattice) ## plot(vv, list(sepVgm, metricVgm), all=T, wireframe=T, zlim=c(0,120), ## zlab=NULL, ## xlab=list("distance (km)", rot=30), ## ylab=list("time lag (days)", rot=-35), ## scales=list(arrows=F, z = list(distance = 5))) ################################################### ### code chunk number 31: st.Rnw:358-364 ################################################### library(lattice) print(plot(vv, list(sepVgm, metricVgm), all=T, wireframe=T, zlim=c(0,120), zlab=NULL, xlab=list("distance (km)", rot=30), ylab=list("time lag (days)", rot=-35), scales=list(arrows=F, z = list(distance = 5)))) ################################################### ### code chunk number 32: st.Rnw:385-386 (eval = FALSE) ################################################### ## demo(gstat3D) gstat/inst/doc/prs.R0000644000176200001440000000304314413507461014052 0ustar liggesusers### R code from vignette source 'prs.Rnw' ################################################### ### code chunk number 1: prs.Rnw:48-54 ################################################### library(gstat) cluster = read.table(system.file("external/cluster.txt", package="gstat"), header = TRUE) summary(cluster) library(sp) coordinates(cluster) = ~X+Y ################################################### ### code chunk number 2: prs.Rnw:59-61 ################################################### bnd = c(0,2.5,7.5,12.5,17.5,22.5,27.5,32.5,37.5,42.5,47.5,52.5) variogram(Primary~1, cluster, boundaries = bnd) ################################################### ### code chunk number 3: prs.Rnw:66-67 ################################################### variogram(Primary~1, cluster, boundaries=bnd, PR = TRUE) ################################################### ### code chunk number 4: prs.Rnw:71-75 ################################################### pl1 = plot(variogram(Primary~1, cluster, boundaries=bnd, PR = FALSE)) pl2 = plot(variogram(Primary~1, cluster, boundaries=bnd, PR = TRUE)) print(pl1, split = c(1,1,2,1), more = TRUE) print(pl2, split = c(2,1,2,1), more = FALSE) ################################################### ### code chunk number 5: prs.Rnw:86-96 ################################################### z = cluster$Primary d = spDists(cluster) zd = outer(z, z, "-") zs = outer(z, z, "+") pr = (2 * zd / zs )^2 prv = as.vector(pr) dv = as.vector(d) mean(prv[dv > 0 & dv < 2.5])/2 mean(prv[dv > 2.5 & dv < 7.5])/2 mean(prv[dv > 7.5 & dv < 12.5])/2 gstat/inst/doc/prs.Rnw0000644000176200001440000002004513777370515014432 0ustar liggesusers%% Document started, Sat Jul 3 19:30:52 CEST 2004, my 37th birthday, %% while being stuck for 24 hours at Philadelphia airport, on my way %% back from the joint TIES/Accuracy 2004 symposium in Portland, ME. %% Continued, Oct 28, during the Apmosphere mid-term review. Oh, shame. % \VignetteIndexEntry{ The pairwise relative semivariogram } \documentclass[a4paper]{article} \usepackage[colorlinks=true,urlcolor=blue]{hyperref} \usepackage{alltt} \newcommand{\code}[1]{{\tt #1}} \SweaveOpts{echo=TRUE} \title{The pairwise relative semivariogram} \author{ \includegraphics[width=.4\columnwidth]{ifgi-logo_int}\\ \href{mailto:edzer.pebesma@uni-muenster.de}{Edzer Pebesma} } \date{\small Aug 29, 2011 } \begin{document} \maketitle \section{Introduction} The general relative variogram (Deutsch and Journel, 1997) is defined as $$ \gamma(h) = \frac{1}{2N_h} \sum_{i=1}^{N_h} \left(\frac{2(Z(s_i)-Z(s_i+h))}{Z(s_i)+Z(s_i+h)}\right)^2. $$ It is claimed to reveal spatial structure (correlation) better when data are skewed and/or clustered. The \code{cluster.dat} data set used in this vignette, from the GSLIB distribution\footnote{F77 source code for Linux, downloaded Aug 28, 2011 from \code{http://www.gslib.com/}}, seems to confirm this. From version 1.02 on, R package \code{gstat} provides computation of the {\em pairwise relative semivariogram}. The following code provides an example and verification of the computation using direct R code and using the GSLIB program \code{gamv}. The following code imports the \code{cluster.dat} data from GSLIB, which has been converted to have a single-line header containing column names, packaged with the R gstat package, and converts it into a \code{SpatialPointsDataFrame} object: <<>>= library(gstat) cluster = read.table(system.file("external/cluster.txt", package="gstat"), header = TRUE) summary(cluster) library(sp) coordinates(cluster) = ~X+Y @ The following commands specify a sequence of lag boundaries that correspond to the GSLIB conventions, and compute a regular variogram using these boundaries: <<>>= bnd = c(0,2.5,7.5,12.5,17.5,22.5,27.5,32.5,37.5,42.5,47.5,52.5) variogram(Primary~1, cluster, boundaries = bnd) @ To compute the relative pairwise variogram, the logical argument \code{PR} ({\em pairwise relative}) needs to be set to \code{TRUE}: <<>>= variogram(Primary~1, cluster, boundaries=bnd, PR = TRUE) @ Figure \ref{fig:vgm} shows the two variograms, as plots, side by side \begin{figure} <>= pl1 = plot(variogram(Primary~1, cluster, boundaries=bnd, PR = FALSE)) pl2 = plot(variogram(Primary~1, cluster, boundaries=bnd, PR = TRUE)) print(pl1, split = c(1,1,2,1), more = TRUE) print(pl2, split = c(2,1,2,1), more = FALSE) @ \caption{Regular variogram (left) and pairwise relative variogram (right) for the GSLIB data set \code{cluster.dat}.} \label{fig:vgm} \end{figure} \section{Verification with plain R code} The following R code reproduces the relative pairwise semivariogram values for the first three lags, i.e. 0-2.5, 2.5-7.5 and 7.5-12.5. <<>>= z = cluster$Primary d = spDists(cluster) zd = outer(z, z, "-") zs = outer(z, z, "+") pr = (2 * zd / zs )^2 prv = as.vector(pr) dv = as.vector(d) mean(prv[dv > 0 & dv < 2.5])/2 mean(prv[dv > 2.5 & dv < 7.5])/2 mean(prv[dv > 7.5 & dv < 12.5])/2 @ \section{Verification with GSLIB} In a verification with the GSLIB (Deutsch and Journel, 1997) code of \code{gamv}, the following file was used: \begin{alltt} Parameters for GAMV ******************* START OF PARAMETERS: ../data/cluster.dat \\file with data 1 2 0 \\ columns for X, Y, Z coordinates 1 3 \\ number of varables,column numbers -1.0e21 1.0e21 \\ trimming limits gamv.out \\file for variogram output 10 \\number of lags 5.0 \\lag separation distance 2.5 \\lag tolerance 1 \\number of directions 0.0 90.0 50.0 0.0 90.0 50.0 \\azm,atol,bandh,dip,dtol,bandv 0 \\standardize sills? (0=no, 1=yes) 2 \\number of variograms 1 1 1 \\tail var., head var., variogram type 1 1 6 \\tail var., head var., variogram type \end{alltt} Running this program with these parameters gave the following output: \begin{alltt} Semivariogram tail:Primary head:Primary direction 1 1 .000 .00000 280 4.35043 4.35043 2 1.528 58.07709 298 8.62309 8.62309 3 5.473 54.09188 1248 5.41315 5.41315 4 10.151 48.85144 1978 4.42758 4.42758 5 15.112 40.08909 2498 4.25680 4.25680 6 20.033 42.45081 2296 3.74311 3.74311 7 25.020 48.60365 2734 4.09575 4.09575 8 29.996 46.88879 2622 4.15950 4.15950 9 34.907 44.36890 2170 3.77190 3.77190 10 39.876 47.34666 1808 4.54173 4.54173 11 44.717 38.72725 1222 5.15251 5.15251 12 49.387 30.67908 438 4.56539 4.56539 Pairwise Relative tail:Primary head:Primary direction 1 1 .000 .00000 280 4.35043 4.35043 2 1.528 .36084 298 8.62309 8.62309 3 5.473 .63071 1248 5.41315 5.41315 4 10.151 .83764 1978 4.42758 4.42758 5 15.112 .77691 2498 4.25680 4.25680 6 20.033 .87746 2296 3.74311 3.74311 7 25.020 .89610 2734 4.09575 4.09575 8 29.996 .90023 2622 4.15950 4.15950 9 34.907 .96043 2170 3.77190 3.77190 10 39.876 .90554 1808 4.54173 4.54173 11 44.717 .75545 1222 5.15251 5.15251 12 49.387 .82268 438 4.56539 4.56539 \end{alltt} As can be seen, the values in the third column (semivariogram for the first section, pairwise relative semivariogram for the second) correspond to the output generated by \code{variogram} of package \code{gstat}. Two differences with respect to the gstat output are: \begin{itemize} \item for the first lag with distance zero, GSLIB reports that the semivariance value is zero based on 280 point pairs; \item the number of point pairs in GSLIB is double the number reported by gstat. \end{itemize} The ground for these differences seems that the GSLIB \code{gamv} uses a single routine for computing variograms as well as cross variograms and cross covariances. For cross variograms or covariograms, considering two variables $Z_a$ and $Z_b$ each having $N$ observations, the $N^2$ point pairs $Z_a(s_i),Z_b(s_i+h)$ and $Z_a(s_i+h),Z_b(s_i)$ need to be evaluated, and all contribute information. For direct (non-cross) variograms or covariograms, $Z_a=Z_b$ and the $N^2$ pairs considered contain the $N$ trivial pairs $(Z(s_i)-Z(s_i))^2=0$, which contribute no information, as well as all duplicate pairs, i.e. in addition to $(Z(s_i)-Z(s_i+h))^2$, the identical pair $(Z(s_i+h)-Z(s_i))^2$ is also considered. This leads to correct variogram value estimates, but incorrect unique point pair numbers. (Data set \code{cluster} contains $N=140$ observations.) In contrast, \code{gstat} considers (and reports) only the number of unique pairs for each lag. \section*{References} \begin{itemize} \item Deutsch, C.V., A.G. Journel, 1997. GSLIB: Geostatistical Software Library and User's Guide, second edition. 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Oh, shame. % \VignetteIndexEntry{ The meuse data set: a tutorial for the gstat R package } \documentclass[a4paper]{article} \usepackage{hyperref} \newcommand{\code}[1]{{\tt #1}} \SweaveOpts{echo=TRUE} \title{The meuse data set: a brief tutorial\\ for the {\tt gstat} R package } \author{\href{mailto:edzer.pebesma@uni-muenster.de}{Edzer Pebesma}} \date{\today} \begin{document} \maketitle \section{Introduction} The \code{meuse} data set provided by package \code{sp} is a data set comprising of four heavy metals measured in the top soil in a flood plain along the river Meuse, along with a handful of covariates. The process governing heavy metal distribution seems that polluted sediment is carried by the river, and mostly deposited close to the river bank, and areas with low elevation. This document shows a geostatistical analysis of this data set. The data set was introduced by Burrough and McDonnell, 1998. This tutorial introduced the functionality of the R package \code{gstat}, used in conjunction with package \code{sp}. Package \code{gstat} provides a wide range of univariable and multivariable geostatistical modelling, prediction and simulation functions, where package \code{sp} provides general purpose classes and methods for defining, importing/exporting and visualizing spatial data. \section{R geostatistics packages} Package \code{gstat} (Pebesma, 2004) is an R package that provides basic functionality for univariable and multivariable geostatistical analysis, including \begin{itemize} \item variogram modelling, residual variogram modelling, and cross variogram modelling using fitting of parametric models to sample variograms \item geometric anisotropy specfied for each partial variogram model \item restricted maximum likelihood fitting of partial sills \item variogram and cross variogram maps \item simple, ordinary, universal and external drift (co)kriging \item (sequential) Gaussian (co)simulation equivalents for each of the kriging varieties \item indicator (co)kriging and sequential indicator (co)simulation \item kriging in a local or global neighbourhood \item block (co)kriging or simulation for each of the varieties, for rectangular or irregular blocks \end{itemize} Other geostatistical packages for R usually lack part of these options (e.g. block kriging, local kriging, or cokriging) but provide others: e.g. package \code{geoR} and \code{geoRglm} (by Paulo Ribeiro and Ole Christensen) provide the model-based geostatistics framework described in Diggle et al. (1998), package \code{fields} (Doug Nychka and others) provides thin plate spline interpolation, covariance functions for spherical coordinates (unprojected data), and routines for spatial sampling design optimization. \section{Spatial data frames} As an example, we will look at the meuse data set, which is a regular data frame that comes with package \code{gstat} (remove the 88 from the colour strings to make a plot without alpha transparency on windows or X11): <>= library(sp) data(meuse) class(meuse) names(meuse) coordinates(meuse) = ~x+y class(meuse) summary(meuse) coordinates(meuse)[1:5,] bubble(meuse, "zinc", col=c("#00ff0088", "#00ff0088"), main = "zinc concentrations (ppm)") @ % the following is needed because lattice plots (bubble wraps xyplot) do not % show without an explicit print; in order not to confuse users, we hide this: <>= print(bubble(meuse, "zinc", col=c("#00ff0088", "#00ff0088"), main = "zinc concentrations (ppm)") ) @ and note the following: \begin{enumerate} \item the function \code{coordinates}, when assigned (i.e. on the left-hand side of an \verb|=| or \verb|<-| sign), promotes the \code{data.frame} meuse into a \code{SpatialPointsDataFrame}, which knows about its spatial coordinates; coordinates may be specified by a formula, a character vector, or a numeric matrix or data frame with the actual coordinates \item the function \code{coordinates}, when not assigned, {\em retrieves} the spatial coordinates from a \code{SpatialPointsDataFrame}. \item the two plotting functions used, \code{plot} and \code{bubble} assume that the $x$- and $y$-axis are the spatial coordinates. \end{enumerate} \section{Spatial data on a regular grid} <>= data(meuse.grid) summary(meuse.grid) class(meuse.grid) coordinates(meuse.grid) = ~x+y class(meuse.grid) gridded(meuse.grid) = TRUE class(meuse.grid) image(meuse.grid["dist"]) title("distance to river (red = 0)") library(gstat) zinc.idw = idw(zinc~1, meuse, meuse.grid) class(zinc.idw) spplot(zinc.idw["var1.pred"], main = "zinc inverse distance weighted interpolations") @ <>= print(spplot(zinc.idw["var1.pred"], main = "zinc inverse distance weighted interpolations")) @ If you compare the bubble plot of zinc measurements with the map with distances to the river, it becomes evident that the larger concentrations are measured at locations close to the river. This relationship can be linearized by log-transforming the zinc concentrations, and taking the square root of distance to the river: <>= plot(log(zinc)~sqrt(dist), meuse) abline(lm(log(zinc)~sqrt(dist), meuse)) @ \section{Variograms } Variograms are calculated using the function \code{variogram}, which takes a formula as its first argument: \verb|log(zinc)~1| means that we assume a constant trend for the variable log(zinc). <>= lzn.vgm = variogram(log(zinc)~1, meuse) lzn.vgm lzn.fit = fit.variogram(lzn.vgm, model = vgm(1, "Sph", 900, 1)) lzn.fit plot(lzn.vgm, lzn.fit) @ <>= print(plot(lzn.vgm, lzn.fit)) @ Instead of the constant mean, denoted by \verb|~1|, we can specify a mean function, e.g. using \verb|~sqrt(dist)| as a predictor variable: <>= lznr.vgm = variogram(log(zinc)~sqrt(dist), meuse) lznr.fit = fit.variogram(lznr.vgm, model = vgm(1, "Exp", 300, 1)) lznr.fit plot(lznr.vgm, lznr.fit) @ <>= print(plot(lznr.vgm, lznr.fit)) @ In this case, the variogram of residuals with respect to a fitted mean function are shown. Residuals were calculated using ordinary least squares. \section{Kriging} <>= lzn.kriged = krige(log(zinc)~1, meuse, meuse.grid, model = lzn.fit) spplot(lzn.kriged["var1.pred"]) @ <>= print(spplot(lzn.kriged["var1.pred"])) @ \section{Conditional simulation} <>= lzn.condsim = krige(log(zinc)~1, meuse, meuse.grid, model = lzn.fit, nmax = 30, nsim = 4) spplot(lzn.condsim, main = "four conditional simulations") @ <>= print(spplot(lzn.condsim, main = "four conditional simulations")) @ For UK/residuals: <>= lzn.condsim2 = krige(log(zinc)~sqrt(dist), meuse, meuse.grid, model = lznr.fit, nmax = 30, nsim = 4) spplot(lzn.condsim2, main = "four UK conditional simulations") @ <>= print(spplot(lzn.condsim2, main = "four UK conditional simulations")) @ \section{Directional variograms} The following command calculates a directional sample variogram, where directions are binned by direction angle alone. For two point pairs, $Z(s)$ and $Z(s+h)$, the separation vector is $h$, and it has a direction. Here, we will classify directions into four direction intervals: <>= lzn.dir = variogram(log(zinc)~1, meuse, alpha = c(0, 45, 90, 135)) lzndir.fit = vgm(.59, "Sph", 1200, .05, anis = c(45, .4)) plot(lzn.dir, lzndir.fit, as.table = TRUE) @ <>= print(plot(lzn.dir, lzndir.fit, as.table = TRUE)) @ Looking at directions between 180 and 360 degrees will repeat the image shown above, because the variogram is a symmetric measure: $(Z(s)-Z(s+h))^2=(Z(s+h)-Z(s))^2$. The first plot gives the variogram in the zero direction, which is North; 90 degrees is East. By default, point pairs are assigned to the directional variorgram panel with their nearest direction, so North contains everything between -22.5 and 22.5 degrees (North-West to North-East). After classifying by direction, point pairs are binned by separation distance class, as is done in the usual omnidirectional case. In the figure, the partial sill, nugget and model type of the model are equal to those of the omnidirectional model fitted above; the range is that in the direction with the largest range (45$^o$), and the anisotropy ratio, the range in the 135 direction and the range in the 45 direction, estimated ``by eye'' by comparing the 45 and 135 degrees sample variograms. Gstat does not fit anisotropy parameters automatically. We do not claim that the model fitted here is ``best'' in some way; in order to get to a better model we may want to look at more directions, other directions (e.g. try {\tt alpha = c(22, 67, 112, 157) }), and to variogram maps (see below). More elaborate approaches may use directions in three dimensions, and want to further control the direction tolerance (which may be set such that direction intervals overlap). For the residual variogram from the linear regression model using \code{sqrt(dist)} as covariate, the directional dependence is much less obvious; the fitted model here is the fitted isotropic model (equal in all directions). <>= lznr.dir = variogram(log(zinc)~sqrt(dist), meuse, alpha = c(0, 45, 90, 135)) plot(lznr.dir, lznr.fit, as.table = TRUE) @ <>= print(plot(lznr.dir, lznr.fit, as.table = TRUE)) @ \section{Variogram maps} Another means of looking at directional dependence in semivariograms is obtained by looking at variogram maps. Instead of classifying point pairs $Z(s)$ and $Z(s+h)$ by direction and distance class {\em separately}, we can classify them {\em jointly}. If $h=\{x,y\}$ be the two-dimentional coordinates of the separation vector, in the variogram map the semivariance contribution of each point pair $(Z(s)-Z(s+h))^2$ is attributed to the grid cell in which $h$ lies. The map is centered around $(0,0)$, as $h$ is geographical distance rather than geographical location. Cutoff and width correspond to some extent to map extent and cell size; the semivariance map is point symmetric around $(0,0)$, as $\gamma(h)=\gamma(-h)$. <>= vgm.map = variogram(log(zinc)~sqrt(dist), meuse, cutoff = 1500, width = 100, map = TRUE) plot(vgm.map, threshold = 5) @ <>= print(plot(vgm.map, threshold = 5)) @ The threshold assures that only semivariogram map values based on at least 5 point pairs are shown, removing too noisy estimation. % The plot is plagued by one or two extreme values, corresponding to cells % with very small number of point pairs, which should be removed. \section{Cross variography} Fitting a linear model of coregionalization. <>= g = gstat(NULL, "log(zn)", log(zinc)~sqrt(dist), meuse) g = gstat(g, "log(cd)", log(cadmium)~sqrt(dist), meuse) g = gstat(g, "log(pb)", log(lead)~sqrt(dist), meuse) g = gstat(g, "log(cu)", log(copper)~sqrt(dist), meuse) v = variogram(g) g = gstat(g, model = vgm(1, "Exp", 300, 1), fill.all = TRUE) g.fit = fit.lmc(v, g) g.fit plot(v, g.fit) vgm.map = variogram(g, cutoff = 1500, width = 100, map = TRUE) plot(vgm.map, threshold = 5, col.regions = bpy.colors(), xlab = "", ylab = "") @ <>= print(plot(v, g.fit)) @ <>= print(plot(vgm.map, threshold = 5, col.regions = bpy.colors(), ylab = "", xlab = "")) @ \section*{References} \begin{itemize} % \item Abrahamsen, P., F. Espen Benth, 2001. Kriging with inequality % constraints. Mathematical Geology 33 (6), 719--744. % \item Bivand, R.S., 2003. Approaches to classes for spatial data in R. % In: K.~Hornik \& F.~Leisch (Eds.), Proceedings of the 3rd International % Workshop on Distributed Statistical Computing (DSC 2003) March 20--22, % Vienna, Austria. ISSN 1609-395X; available from [1]. \item Burrough, P.A., R.A. McDonnell, 1998. Principles of Geographical Information Systems, 2nd Edition. Oxford University Press. \item Diggle, P.J., J.A. Tawn, R.A. Moyeed, 1998. Model-based geostatistics. Applied Statistics 47(3), pp 299-350. % \item Pebesma, E.J., Wesseling, C.G., 1998. Gstat, a program for % geostatistical modelling, prediction and simulation. Computers \& % Geosciences, 24 (1), pp. 17--31. \item Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers \& Geosciences \href{http://dx.doi.org/10.1016/j.cageo.2004.03.012}{30: 683-691}. % \item Ver Hoef, J.M., Cressie, N.A.C, 1993. Multivariable Spatial % Prediction. Mathematical Geology, 25 (2), pp. 219--240. \item Wackernagel, H., 1998. Multivariate Geostatistics; an introduction with applications, $2^{\mbox{nd}}$ edn., Springer, Berlin, 291 pp. \end{itemize} \end{document} # g = gstat(NULL, "log.zinc", log(zinc)~1, meuse) # g = gstat(g, "log.zinc.res", log(zinc)~sqrt(dist), meuse) # lplot(vgm.map[["map"]], c("log.zinc", "log.zinc.res")) % vim:syntax=tex gstat/inst/doc/st.Rnw0000644000176200001440000003643513777370515014266 0ustar liggesusers%% Document started, Sat Jul 3 19:30:52 CEST 2004, my 37th birthday, %% while being stuck for 24 hours at Philadelphia airport, on my way %% back from the joint TIES/Accuracy 2004 symposium in Portland, ME. %% Continued, Oct 28, during the Apmosphere mid-term review. Oh, shame. \documentclass[a4paper]{article} \usepackage[colorlinks=true,urlcolor=blue]{hyperref} \newcommand{\code}[1]{{\tt #1}} \SweaveOpts{echo=TRUE} \title{Introduction to Spatio-Temporal Variography } % \VignetteIndexEntry{ Introduction to Spatio-Temporal Variography } \author{ \includegraphics[width=.4\columnwidth]{ifgi-logo_int}\\ \href{mailto:edzer.pebesma@uni-muenster.de}{Edzer Pebesma}, \href{mailto:ben.graeler@uni-muenster.de}{Benedikt Gr\"{a}ler} } \date{\small \today } \begin{document} \setkeys{Gin}{width=0.9\textwidth} \maketitle \section{Introduction} Since \code{gstat} package version 1.0-0, a dependency of gstat on the R package \code{spacetime} was introduced, allowing the code in \code{gstat} to exploit spatio-temporal data structures from that package. This vignette describes the possibilities and limitations of the package for spatio-temporal geostatistics. To understand some of the possibilities and limitations, some knowledge of the history of the software is needed. The original \code{gstat} software (Pebesma and Wesseling, 1998) was a standalone computer {\em program} written in around 25,000 lines of C code, and would do geostatistical modelling, prediction and simulation. The \code{gstat} R package (Pebesma, 2004) consisted mostly of an R interface to this C code, together with convenience functions to use R's modelling interface (formula's, see \code{?lm}) and graphic capabilities (trellis graphics in package \code{lattice} to show cross variogram as matrix plots; interaction with variogram clouds using base plots). Starting 2003, a group of programmers developed a set of classes and methods for dealing with spatial data in R (points, lines, polygons, grids), which was supported by the publications of the well-known ASDAR book (Bivand et al. 2008; see also \url{http://www.asdar-book.org/}) and helped convergence in the user community, with in 2011 over 2000 subscribers on the {\tt r-sig-geo} mailing list. Package \code{gstat} was one of the first packages that adopted and benefited from these classes. To realize a particular idea, writing code in C typically takes about 10-20 times as long as writing it in R. C code can be more efficient, gives more control over memory usage, but is also more error prone--mistakes in C code make an R session crash, something that is hard to do when writing R code. The original C code of \code{gstat} (Pebesma and Wesseling, 1998) provides all kriging varieties (universal, ordinary, simple; univariable, or multivariable as in cokriging) for two- or three-dimensional data. When the spatial domain is constrained to two dimensions (and this might cover over 99\% of the use cases!), the third dimension might be used to represent time. As such, the {\em metric} variogram model, which allows for geometric anisotropy definition in three dimensions, can be used for spatio-temporal kriging. When defining the three-dimensional variogram as the sum of 2 or more nested variogram (summed) models, one can choose anisotropy coefficients for a single model such that this model is {\em effectively} zero in some directions, e.g. in space {\em or} in time; this allows one to approximate the so-called space-time sum model. It should be noted that at the C code there is no knowledge whether a third dimension represents space, or time. As such, particular characteristics of time cannot be taken care of. Since the second half of 2010, the development of an R package \code{spacetime} started. It provides methods and classes for spatio-temporal data, and builds on the spatial data classes in \code{sp} and time series classes in \code{xts}. This document will explain how data in this form, and methods provided by this package, can be used for spatio-temporal geostatistics. We will work with a data set with air quality (PM10) measurements over germany, taken from rural background stations available in the data sets provided by the European Environmental Agency. <<>>= library(spacetime) rm(list = ls()) data(air) ls() @ \section{Variography} \subsection{Temporal autocorrelation and cross correlation} We will look into a subset of the data, ranging from 2005 to 2010, and remove stations that have only missing values in this period: <<>>= if (!exists("rural")) rural = STFDF(stations, dates, data.frame(PM10 = as.vector(air))) rr = rural[,"2005::2010"] unsel = which(apply(as(rr, "xts"), 2, function(x) all(is.na(x)))) r5to10 = rr[-unsel,] summary(r5to10) @ Next, we will (rather arbitrarily) select four stations, which have the following labels: <<>>= rn = row.names(r5to10@sp)[4:7] rn @ In the following, autocorrelation functions are computed and plotted. The resulting plot is shown in Figure~\ref{fig:acf}. <>= par(mfrow=c(2,2)) # select 4, 5, 6, 7 for(i in rn) acf(na.omit(r5to10[i,]), main = i) par(mfrow=c(1,1)) @ \begin{figure}[hbt] \begin{center} <>= par(mfrow=c(2,2)) # select 4, 5, 6, 7 rn = row.names(r5to10@sp)[4:7] for(i in rn) acf(na.omit(r5to10[i,]), main = i) @ \end{center} \caption{Autocorrelations for PM10; time lag unit in days.} \label{fig:acf} \end{figure} Auto- and cross correlations can be computed when a multivariate time series object is passed to {\tt acf}: <>= acf(na.omit(as(r5to10[rn,], "xts"))) @ The resulting plot is shown in Figure~\ref{fig:ccf}. \begin{figure}[hbt] \begin{center} <>= acf(na.omit(as(r5to10[rn,], "xts"))) @ \end{center} \caption{autocorrelations (diagonal) and cross correlations (off-diagonal) for the four stations selected; time lag unit in days. } \label{fig:ccf} \end{figure} From these graphs one should be able to observe the following \begin{itemize} \item autocorrelations for lag 0 are always 1 \item cross correlations for lag 0 are not always 1 \item cross correlations can be asymmetric, meaning that when $\rho_{AB}(h)$ is the correlation between $Z(s_A,t)$ and $Z(s_B,t+h)$, $$\rho_{AB}(h) = \rho_{BA}(-h) \ne \rho_{AB}(-h)$$ with $s_A$ and $s_B$ the two stations between which a cross correlation is computed, and $h$ the (directional!) lag between the series. \end{itemize} The plot further more shows that for these four stations the asymmetry is not very strong, but that cross correlations are fairly strong and of a similar form of autocorrelations. This kind of plot does not work very well in layouts of e.g. 10 x 10 sub-plots; {\tt acf} automatically chooses 4 x 4 as the maximum a single plot. To try this out, do a 7 x 7 plot <>= acf(na.omit(as(r5to10[4:10,], "xts"))) @ and note that here we see in the last figure (DESH \& DESN04) a pair of plots with nearly no cross correlation. This might have to do with the spatial distance between these two stations: <<>>= library(sp) print(spDists(r5to10[4:10,]@sp), digits=3) @ (What is the spatial distance between stations DESH and DESN04?) \subsection{Spatial correlation, variograms} In the next steps, we will sample 100 time instances randomly, <<>>= rs = sample(dim(r5to10)[2], 100) @ we select these instances as a {\tt SpatialPointsDataFrame} and add a time index to them. After this we bind them together in a single {\tt SpatialPointsDataFrame} which has a time index {\tt ti}: <<>>= lst = lapply(rs, function(i) { x = r5to10[,i]; x$ti = i; rownames(x@coords) = NULL; x} ) pts = do.call(rbind, lst) @ Then, we can compute the pooled variogram <<>>= library(gstat) v = variogram(PM10~ti, pts[!is.na(pts$PM10),], dX=0) @ and plot it (Figure~\ref{fig:vgm}): <>= # plot(v, fit.variogram(v, vgm(1, "Exp", 200, 1))) vmod = fit.variogram(v, vgm(100, "Exp", 200)) plot(v, vmod) @ \begin{figure}[hbt] \begin{center} <>= # plot(v, fit.variogram(v, vgm(1, "Exp", 200, 1))) vmod = fit.variogram(v, vgm(100, "Exp", 200)) print(plot(v, vmod)) @ \end{center} \caption{sample spatial variogram, averaged over 100 randomly chosen time steps} \label{fig:vgm} \end{figure} The fitted model is this: <<>>= vmod @ One should note that the fit is rather poor, and not forget that we only have 53 stations selected. The time resolution is rich (1862 days) but the number of stations is small: <<>>= dim(r5to10) @ We can fit a spatio-temporal variogram the usual way, by passing an object of class {\tt STFDF} (Pebesma, 2012): <>= vv = variogram(PM10~1, r5to10, width=20, cutoff = 200, tlags=0:5) @ Alternatively, if this takes too long, a temporal subset can be taken, e.g. using the first 200 days: <>= vv = variogram(PM10~1, r5to10, width=20, cutoff = 200, tlags=0:5) @ taking random days from the full period will lead to the a wrong assumption that every time index increment reflect a constant lag increase. As an alternative, we will here load the precomputed S/T variogram: <<>>= data(vv) @ % remove the model column to keep text and figures in line. <>= vv <- vv[c("np", "dist", "gamma", "id", "timelag", "spacelag")] @ Plotting this object can be done in several ways, two 2D-plots are shown in Figure~\ref{fig:map} and a 3D wireplot is shown in Figure~\ref{fig:wire}: <>= plot(vv) plot(vv, map = FALSE) @ \begin{figure}[hbt] \begin{center} <>= print(plot(vv), split = c(1,1,1,2), more = TRUE) print(plot(vv, map = FALSE), split = c(1,2,1,2)) @ \end{center} \caption{Spatio-temporal sample variogram map (top) and sample variograms for each time lag (bottom); both figures depict the information of object {\tt vv}.} \label{fig:map} \end{figure} \subsection{Fitting a spatio-temporal variogram model} At first, we try to fit a metric model with spatio-temporal anisotropy: <<>>== metricVgm <- vgmST("metric", joint=vgm(50,"Exp",100,0), stAni=50) metricVgm <- fit.StVariogram(vv, metricVgm) @ As numerical criterion to judge the goodness of fit of model and sample variogram, the root-mean-squared-difference between the surfaces can be obtained by: <<>>= attr(metricVgm, "optim")$value @ The final model can be plotted with the sample variogram (Figure~\ref{fig:mm}): <>= plot(vv, metricVgm) @ \begin{figure}[hbt] \begin{center} <>= print(plot(vv, metricVgm)) @ \end{center} \caption{Sample variogram map (left) and fitted metric model (right).} \label{fig:mm} \end{figure} \pagebreak Now, let us try to fit and plot a separable model (Figure~\ref{fig:sm}): <<>>== sepVgm <- vgmST("separable", space=vgm(0.9,"Exp", 123, 0.1), time =vgm(0.9,"Exp", 2.9, 0.1), sill=100) sepVgm <- fit.StVariogram(vv, sepVgm, method = "L-BFGS-B", lower = c(10,0,0.01,0,1), upper = c(500,1,20,1,200)) @ To compare this model with the previous one, we look at the optimized root-mean-squared-differences between the two surfaces and plot sample and both models: <<>>= attr(sepVgm, "optim")$value plot(vv, list(sepVgm, metricVgm)) @ \begin{figure}[hbt] \begin{center} <>= print(plot(vv, list(sepVgm, metricVgm))) @ \end{center} \caption{Sample variogram map (left), fitted separable model (middle) and fittted metric model (right).} \label{fig:sm} \end{figure} A wireframe (3D) plot of sample variogram and fitted variogram models can be obtained e.g. by <>= library(lattice) plot(vv, list(sepVgm, metricVgm), all=T, wireframe=T, zlim=c(0,120), zlab=NULL, xlab=list("distance (km)", rot=30), ylab=list("time lag (days)", rot=-35), scales=list(arrows=F, z = list(distance = 5))) @ which is shown in Figure~\ref{fig:wire}. Further spatio-temporal model definitions can be found in the help pages of {\tt fit.StVariogram} and {\tt variogramSurface}. The demo {\tt stkrige} presents further examples and illustrates an interactive 3D-plot of sample variogram and the fitted variogram model. An interactive variogram exploration web-tool is avaialble at \url{http://giv-graeler.uni-muenster.de:3838/spacetime/}. \begin{figure}[hbt] \begin{center} <>= library(lattice) print(plot(vv, list(sepVgm, metricVgm), all=T, wireframe=T, zlim=c(0,120), zlab=NULL, xlab=list("distance (km)", rot=30), ylab=list("time lag (days)", rot=-35), scales=list(arrows=F, z = list(distance = 5)))) @ \end{center} \caption{Wireframe plots of sample and fitted space-time variograms.} \label{fig:wire} \end{figure} \clearpage \section{Spatio-temporal prediction} The vignette in package \code{spacetime} gives an example of using the gstat function \code{krigeST} for spatio-temporal kriging of the Irish wind data. The \code{krigeST} function uses global kriging, but only needs to invert the purely spatial and purely time covariance matrices in the separable case. For more generic spatio-temporal kriging where space is two-dimensional, one could use \code{krige}, defining the observations and prediction locations as three-dimensional data sets, see for an example <>= demo(gstat3D) @ It needs to be pointed out that in that case, the time (typically the third dimension) needs to be numeric, and three-dimensional anisotropy needs to be defined properly (see \code{?vgm}). In case the data set is too large for global kriging, one could try to use local kriging, and select data within some distance, or by specifying \code{nmax} (the nearest $n$ observations). In both cases, it is advisable to transform time such that one can use an {\em isotropic} variogram model in the three dimensions, as only in that case the nearest $n$ observations correspond to the $n$ most correlated observations. \code{krigeST} provides a solution where a \code{bufferNmax}-times larger neighbourhood is evaluated within the covariance model and the strongest correlated \code{nmax} neighbours are selected. An additional consideration is that in space-time, observations may not be regularly spaced. In some cases, the nearest $n$ observations may come from a single measurement location, which may lead to sharp jumps/boundaries in the interpolated values. This might be solved by using larger neighbourhoods, or by setting the \code{omax} in \code{krige} or \code{gstat} calls to the neighbourhood size to select {\em per octant} (this should be combined with specifying \code{maxdist}). %\section{Spatio-temporal simulation} \section*{References} \begin{itemize} \item Bivand, R., E. Pebesma and V. Gomez-Rubio, 2008. Applied Spatial Data Analysis with R. Springer. \item Cressie, N.A.C., 1993. Statistics for Spatial Data. Wiley. \item Cressie, N. and C. Wikle, 2011. Statistics for Spatio-temporal Data. Wiley. \item Pebesma, E., 2012. spacetime: Spatio-Temporal Data in R. Journal of Statistical Software, volume 51, issue 7; \href{http://www.jstatsoft.org/v51/i07/}{1-30}. \item Pebesma, E.J., Wesseling, C.G., 1998. Gstat, a program for geostatistical modelling, prediction and simulation. Computers \& Geosciences, 24 (1), pp. 17--31. \item Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers \& Geosciences \href{http://www.sciencedirect.com/science/journal/00983004}{30: 683-691} \item Ver Hoef, J.M., Cressie, N.A.C, 1993. Multivariable Spatial Prediction. 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Qm@SQސ叐:ñŻ4;yM 5E j? )?-0;qA45!=|ӈN]X^ + |]!j/9?5\Q[GW*3n\h3 VV!JrDZЎc5)DˈoԾh:(cѳ38?צ|&${~D C!|{{er.1ET! + FQ^DaV SW-ה^"ھa:Y RV1H;5蝰/˺WXjD˧нѡ{N I8tcCX6wN0=>PPzEV1F"m$Y4 :QĈ:ok1ڲ De2˖,OZ~_Έe={Yf٘{-,2,2,2,2,2,2,2,2,2,2!vendstream endobj 308 0 obj << /Type /XRef /Length 246 /Filter /FlateDecode /DecodeParms << /Columns 5 /Predictor 12 >> /W [ 1 3 1 ] /Info 3 0 R /Root 2 0 R /Size 309 /ID [] >> stream xcb&F~0 $8J ?@6^Px8FA;c-0Ggؗ]"VH6" A$X|X,dbl< >P)" @G9s@$S;"~H ؄ w?|"E3H {Al i7 lX؝SA$c| ;Fp:<e2{7`[`i , 2abe.U endstream endobj startxref 287618 %%EOF gstat/inst/doc/gstat.R0000644000176200001440000001466314413507461014402 0ustar liggesusers### R code from vignette source 'gstat.Rnw' ################################################### ### code chunk number 1: gstat.Rnw:73-83 ################################################### library(sp) data(meuse) class(meuse) names(meuse) coordinates(meuse) = ~x+y class(meuse) summary(meuse) coordinates(meuse)[1:5,] bubble(meuse, "zinc", col=c("#00ff0088", "#00ff0088"), main = "zinc concentrations (ppm)") ################################################### ### code chunk number 2: gstat.Rnw:88-91 ################################################### print(bubble(meuse, "zinc", col=c("#00ff0088", "#00ff0088"), main = "zinc concentrations (ppm)") ) ################################################### ### code chunk number 3: gstat.Rnw:110-123 ################################################### data(meuse.grid) summary(meuse.grid) class(meuse.grid) coordinates(meuse.grid) = ~x+y class(meuse.grid) gridded(meuse.grid) = TRUE class(meuse.grid) image(meuse.grid["dist"]) title("distance to river (red = 0)") library(gstat) zinc.idw = idw(zinc~1, meuse, meuse.grid) class(zinc.idw) spplot(zinc.idw["var1.pred"], main = "zinc inverse distance weighted interpolations") ################################################### ### code chunk number 4: gstat.Rnw:126-127 ################################################### print(spplot(zinc.idw["var1.pred"], main = "zinc inverse distance weighted interpolations")) ################################################### ### code chunk number 5: gstat.Rnw:136-138 ################################################### plot(log(zinc)~sqrt(dist), meuse) abline(lm(log(zinc)~sqrt(dist), meuse)) ################################################### ### code chunk number 6: gstat.Rnw:147-152 ################################################### lzn.vgm = variogram(log(zinc)~1, meuse) lzn.vgm lzn.fit = fit.variogram(lzn.vgm, model = vgm(1, "Sph", 900, 1)) lzn.fit plot(lzn.vgm, lzn.fit) ################################################### ### code chunk number 7: gstat.Rnw:155-156 ################################################### print(plot(lzn.vgm, lzn.fit)) ################################################### ### code chunk number 8: gstat.Rnw:162-166 ################################################### lznr.vgm = variogram(log(zinc)~sqrt(dist), meuse) lznr.fit = fit.variogram(lznr.vgm, model = vgm(1, "Exp", 300, 1)) lznr.fit plot(lznr.vgm, lznr.fit) ################################################### ### code chunk number 9: gstat.Rnw:169-170 ################################################### print(plot(lznr.vgm, lznr.fit)) ################################################### ### code chunk number 10: gstat.Rnw:179-181 ################################################### lzn.kriged = krige(log(zinc)~1, meuse, meuse.grid, model = lzn.fit) spplot(lzn.kriged["var1.pred"]) ################################################### ### code chunk number 11: gstat.Rnw:184-185 ################################################### print(spplot(lzn.kriged["var1.pred"])) ################################################### ### code chunk number 12: gstat.Rnw:189-192 ################################################### lzn.condsim = krige(log(zinc)~1, meuse, meuse.grid, model = lzn.fit, nmax = 30, nsim = 4) spplot(lzn.condsim, main = "four conditional simulations") ################################################### ### code chunk number 13: gstat.Rnw:195-196 ################################################### print(spplot(lzn.condsim, main = "four conditional simulations")) ################################################### ### code chunk number 14: gstat.Rnw:201-204 ################################################### lzn.condsim2 = krige(log(zinc)~sqrt(dist), meuse, meuse.grid, model = lznr.fit, nmax = 30, nsim = 4) spplot(lzn.condsim2, main = "four UK conditional simulations") ################################################### ### code chunk number 15: gstat.Rnw:207-208 ################################################### print(spplot(lzn.condsim2, main = "four UK conditional simulations")) ################################################### ### code chunk number 16: gstat.Rnw:217-220 ################################################### lzn.dir = variogram(log(zinc)~1, meuse, alpha = c(0, 45, 90, 135)) lzndir.fit = vgm(.59, "Sph", 1200, .05, anis = c(45, .4)) plot(lzn.dir, lzndir.fit, as.table = TRUE) ################################################### ### code chunk number 17: gstat.Rnw:223-224 ################################################### print(plot(lzn.dir, lzndir.fit, as.table = TRUE)) ################################################### ### code chunk number 18: gstat.Rnw:257-259 ################################################### lznr.dir = variogram(log(zinc)~sqrt(dist), meuse, alpha = c(0, 45, 90, 135)) plot(lznr.dir, lznr.fit, as.table = TRUE) ################################################### ### code chunk number 19: gstat.Rnw:262-263 ################################################### print(plot(lznr.dir, lznr.fit, as.table = TRUE)) ################################################### ### code chunk number 20: gstat.Rnw:280-283 ################################################### vgm.map = variogram(log(zinc)~sqrt(dist), meuse, cutoff = 1500, width = 100, map = TRUE) plot(vgm.map, threshold = 5) ################################################### ### code chunk number 21: gstat.Rnw:286-287 ################################################### print(plot(vgm.map, threshold = 5)) ################################################### ### code chunk number 22: gstat.Rnw:300-311 ################################################### g = gstat(NULL, "log(zn)", log(zinc)~sqrt(dist), meuse) g = gstat(g, "log(cd)", log(cadmium)~sqrt(dist), meuse) g = gstat(g, "log(pb)", log(lead)~sqrt(dist), meuse) g = gstat(g, "log(cu)", log(copper)~sqrt(dist), meuse) v = variogram(g) g = gstat(g, model = vgm(1, "Exp", 300, 1), fill.all = TRUE) g.fit = fit.lmc(v, g) g.fit plot(v, g.fit) vgm.map = variogram(g, cutoff = 1500, width = 100, map = TRUE) plot(vgm.map, threshold = 5, col.regions = bpy.colors(), xlab = "", ylab = "") ################################################### ### code chunk number 23: gstat.Rnw:314-315 ################################################### print(plot(v, g.fit)) ################################################### ### code chunk number 24: gstat.Rnw:318-319 ################################################### print(plot(vgm.map, threshold = 5, col.regions = bpy.colors(), ylab = "", xlab = "")) gstat/inst/CITATION0000644000176200001440000000157314413506220013511 0ustar liggesuserscitHeader("To cite package gstat in publications use:") bibentry(bibtype="Article", title = "Multivariable geostatistics in {S}: the gstat package", author = "Edzer J. Pebesma", journal = "Computers & Geosciences", year = 2004, volume = 30, pages = "683-691", textVersion = paste("Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package.", "Computers & Geosciences, 30: 683-691.") ) bibentry(bibtype="Article", title = "Spatio-Temporal Interpolation using gstat", author = "Benedikt Gräler and Edzer Pebesma and Gerard Heuvelink", year = 2016, journal = "The R Journal", volume = 8, issue = 1, pages = "204-218", url = "https://journal.r-project.org/archive/2016/RJ-2016-014/index.html", textVersion = paste("Benedikt Gräler, Edzer Pebesma and Gerard Heuvelink, 2016.", "Spatio-Temporal Interpolation using gstat. The R Journal 8(1), 204-218") ) gstat/inst/external/0000755000176200001440000000000014053224431014171 5ustar liggesusersgstat/inst/external/ncp.dbf0000644000176200001440000000457013777370515015455 0ustar liggesusersdrWAREAN PERIMETERN WSVGEB_N WSVGEB_IDN WSVGEBIEDC(WSVNUMNWSV_ENGELSC 31647227904 805264.750 2 1Centrale Noordzee 60Central North Sea 23836518400 991292.438 3 2Zuidelijke Noordzee 59Southern Bight 2996116992 608006.813 4 3Kustzone 58Coastal Zone 21310684.000 25581.318 5 4 0 529338496 176858.797 6 5Eems-Dollard 39 809406144 237455.656 7 6Waddenzee oost 63 2482308.000 8782.396 8 7 0 8828493.000 12204.778 9 8 0 37539448.000 36667.668 10 9 0 58258608.000 52365.965 11 10 0 92012928.000 71875.711 12 11 0 1566943488 222147.938 13 12Waddenzee West 62Wadden Sea 37442780.000 43513.047 14 14 0 160017344 60477.840 15 15 0 890277632 192198.391 16 16Voordelta 57Delta 116148648 69161.266 17 17Grevelingenmeer 56 371725664 182730.094 18 18Oosterschelde 55 455953504 212864.031 19 19Westerschelde 47 25196141.700 47435.919 0 0 0 gstat/inst/external/no2.csv0000644000176200001440000003022514053224431015406 0ustar liggesusersstation_european_code,station_local_code,country_iso_code,country_name,station_name,station_start_date,station_end_date,type_of_station,station_ozone_classification,station_type_of_area,station_subcat_rural_back,street_type,station_longitude_deg,station_latitude_deg,station_altitude,station_city,lau_level1_code,lau_level2_code,lau_level2_name,EMEP_station,NO2 DENI063,DENI063,DE,Germany,Altes Land,1999-02-11,,Background,rural,rural,unknown,,9.685031,53.524181,3,,,3359028,Jork,no,13.10280590444669 DEBY109,DEBY109,DE,Germany,Andechs/Rothenfeld,2003-04-17,,Background,rural,rural,regional,,11.220172,47.968754,700,,,9188117,Andechs,no,7.135128196791652 DEBE056,DEBE056,DE,Germany,B Friedrichshagen,1994-02-01,,Background,rural,rural,near city,,13.64705,52.447697,35,,,11000000,"Berlin, Stadt",no,12.7990107440876 DEBE062,DEBE062,DE,Germany,"B Frohnau, Funkturm (3.5 m)",1996-02-01,,Background,rural,rural,near city,,13.296081,52.653269,50,BERLIN,,11000000,"Berlin, Stadt",no,11.830893889864175 DEBE032,DEBE032,DE,Germany,B Grunewald (3.5 m),1986-10-01,,Background,rural,rural,near city,,13.225144,52.473192,50,BERLIN,,11000000,"Berlin, Stadt",no,11.980110277555427 DEHE046,DEHE046,DE,Germany,Bad Arolsen,1999-05-11,,Background,rural,rural,unknown,,8.928172,51.430901,343,BAD AROLSEN/KOHLGRUND,,6635002,"Bad Arolsen, Stadt",no,8.935610662702798 DEBY122,DEBY122,DE,Germany,Bad Hindelang/Oberjoch,2010-06-21,,Background,rural,rural,regional,,10.404233,47.518013,1169,,,9780123,"Bad Hindelang, M",no,7.020689619637259 DESL019,DESL019,DE,Germany,Biringen,2003-02-01,,Background,rural,rural,regional,,6.552036,49.416885,339,,,10044114,Rehlingen-Siersburg,no,9.226796157053245 DENW081,DENW081,DE,Germany,Borken-Gemen,1998-09-11,,Background,rural,rural,near city,,6.874553,51.862,45,BORKEN,,5554012,"Borken, Stadt",no,18.70002344794623 DESH008,DESH008,DE,Germany,Bornhöved,1988-11-08,,Background,rural,rural,regional,,10.240596,54.09323,45,,10575785,,Ruhwinkel,no,9.159836327480242 DESN093,DESN093,DE,Germany,Brockau,2011-01-01,,Background,rural,rural,regional,,12.211111,50.608135,430,,145235120,,"Netzschkau, Stadt",no,8.54799427254379 DEST039,DEST039,DE,Germany,Brocken,1993-01-28,,Background,rural background,rural,remote,,10.618275,51.798626,1142,SCHIERKE,,,,no,3.5893264081276546 DEHE039,DEHE039,DE,Germany,Burg Herzberg (Grebenau),1983-05-01,,Background,rural,rural,unknown,,9.459403,50.770382,491,HERZBERG,,6632004,Breitenbach a. Herzberg,no,8.400254268233276 DEBY124,DEBY124,DE,Germany,Burgbernheim/Am Hessinggraben,2012-01-01,,Background,rural,rural,regional,,10.316582,49.444516,384,,,,,no,12.012725102002506 DESN076,DESN076,DE,Germany,Collmberg,1998-10-01,,Background,rural background,rural,remote,,13.009405,51.303772,313,COLLM,,14730330,Wermsdorf,no,8.636825016306878 DEST104,DEST104,DE,Germany,Domäne Bobbe,2009-12-17,,Background,rural,rural,unknown,,11.891525,51.83728,71,,,15082256,Osternienburger Land,no,9.354437456798943 DETH026,DETH026,DE,Germany,Dreißigacker,1991-07-01,,Background,rural,rural,regional,,10.3753,50.561752,450,DREIßIGACKER,160665050,,"Meiningen, Stadt",no,8.995248039863394 DEBW004,DEBW004,DE,Germany,Eggenstein,1976-09-01,,Background,rural,rural,near city,Unknown,8.40666,49.07655,109,,,8215102,Eggenstein-Leopoldshafen,no,20.493843279960355 DENI059,DENI059,DE,Germany,Elbmündung,1998-03-20,,Background,rural,rural,unknown,,8.80122,53.83017,3,,,3352011,"Cuxhaven, Stadt",no,11.104789649054135 DEUB046,DEUB046,DE,Germany,Forellenbach,2000-01-01,,Background,rural background,rural,remote,,13.420573,48.947611,858,,92729444,,Gdefr. Geb. (Lkr Freyung-Grafenau),no,4.333945989382777 DEHE028,DEHE028,DE,Germany,Fürth/Odenwald,1986-10-01,,Background,rural,rural,unknown,,8.81725,49.653465,484,FÜRTH/ODENWALD,,6431007,Fürth,no,8.120225166556141 DEMV026,DEMV026,DE,Germany,Garz,2013-01-01,,Background,rural,rural,unknown,,13.342138,54.323514,17,,,,,no,4.383776623560161 DETH040,DETH040,DE,Germany,Großer Eisenberg,1994-12-04,,Background,rural background,rural,remote,Wide street: L/H > 1.5,10.787137,50.619179,907,EISENACH,160705008,,Schmiedefeld am Rennsteig,no,4.390458645846876 DEMV017,DEMV017,DE,Germany,Göhlen,1998-02-01,,Background,rural,rural,unknown,,11.362965,53.302353,25,GÖHLEN,130545416,,Göhlen,no,6.004551736946301 DEMV004,DEMV004,DE,Germany,Gülzow,1992-01-01,,Background,rural,rural,unknown,,12.064709,53.817772,17,,130535313,,Gülzow-Prüzen,no,6.843800975142158 DEBB053,DEBB053,DE,Germany,Hasenholz,2000-11-21,,Background,rural,rural,regional,,14.015253,52.563835,88,BUCKOW,120645408,,"Buckow (Märkische Schweiz), Stadt",no,9.110279139763184 DETH061,DETH061,DE,Germany,Hummelshain,1999-10-07,,Background,rural background,rural,remote,,11.661233,50.791618,357,,160745007,,Trockenborn-Wolfersdorf,no,5.704372785485123 DERP014,DERP014,DE,Germany,Hunsrück-Leisel,1984-01-01,,Background,rural,rural,unknown,,7.193486,49.741035,650,LEISEL,71345002,,Siesbach,no,5.223882314791547 DENI031,DENI031,DE,Germany,Jadebusen,1984-06-01,,Background,rural,rural,unknown,,8.09059,53.59617,2,,,3405000,"Wilhelmshaven, Stadt",no,10.450504669281006 DEHE060,DEHE060,DE,Germany,Kellerwald,2005-10-09,,Background,rural,rural,regional,,9.031753,51.154842,483,,,6635009,Edertal,no,6.500547300478271 DEHE052,DEHE052,DE,Germany,Kleiner Feldberg,1992-03-12,,Background,rural,rural,unknown,,8.446078,50.221943,811,,,6434003,Glashütten,no,6.913817430801052 DEBY004,DEBY004,DE,Germany,Kleinwallstadt/Hofstetter Straße,1978-08-01,,Background,suburban,rural,near city,,9.171545,49.869419,124,KLEINWALLSTADT,96765630,,"Kleinwallstadt, M",no,17.107523426602675 DEMV024,DEMV024,DE,Germany,Leizen,2010-06-16,,Background,rural,rural,unknown,,12.463929,53.396348,116,,130565621,,Leizen,no,6.520525826751615 DEHE042,DEHE042,DE,Germany,Linden/Leihgestern,1995-04-05,,Background,rural,rural,unknown,,8.684398,50.532963,172,,,6531012,"Linden, Stadt",no,17.19400233075487 DEMV012,DEMV012,DE,Germany,Löcknitz,1994-01-15,,Background,rural,rural,unknown,,14.257408,53.520458,17,MEWEGEN,130625212,,Rothenklempenow,no,6.572471710102648 DEBB065,DEBB065,DE,Germany,Lütte (Belzig),2003-02-14,,Background,rural,rural,regional,,12.561389,52.194225,111,,,,,no,6.5688081305907895 DEBY013,DEBY013,DE,Germany,Mehring/Sportplatz,1977-03-01,,Background,rural,rural,regional,,12.781385,48.182835,415,MEHRING,91715101,,Mehring,no,14.525675711369342 DENW065,DENW065,DE,Germany,Netphen (Rothaargebirge),1985-12-01,,Background,rural,rural,regional,,8.191934,50.930328,635,,,5970032,"Netphen, Stadt",no,5.5828906369949856 DENW066,DENW066,DE,Germany,Nettetal-Kaldenkirchen,1987-12-01,,Background,rural,rural,near city,,6.195867,51.326939,49,NETTETAL,,5166016,"Nettetal, Stadt",no,19.60067672326852 DEUB030,DEUB030,DE,Germany,Neuglobsow,1991-11-01,,Background,rural,rural,regional,,13.031661,53.141304,65,NEUGLOBSOW,120655502,,Stechlin,yes,4.248033122879065 DETH027,DETH027,DE,Germany,Neuhaus,1991-08-12,,Background,rural background,rural,remote,Unknown,11.134591,50.499954,840,,160725051,,"Neuhaus am Rennweg, Stadt",no,5.4560661043846945 DEBY049,DEBY049,DE,Germany,Neustadt a.d. Donau/Eining,1977-03-01,,Background,rural,rural,regional,,11.777817,48.85321,359,NEUSTADT A.D.DONAU,,9273152,"Neustadt a.d.Donau, St",no,11.463016348388106 DESN079,DESN079,DE,Germany,Niesky,2003-05-05,,Background,rural,rural,regional,,14.749731,51.285355,148,,146265502,,Quitzdorf am See,no,8.341097323821916 DENI058,DENI058,DE,Germany,Ostfries. Inseln,1996-02-01,,Background,rural,rural,unknown,,7.21398,53.715302,5,,,3452020,"Norderney, Stadt",no,8.455727814497608 DERP017,DERP017,DE,Germany,Pfälzerwald-Hortenkopf,1986-01-01,,Background,rural,rural,unknown,,7.826522,49.270264,606,HORTENKOPF,73405004,,Merzalben,no,4.996870112175138 DETH042,DETH042,DE,Germany,Possen,1996-01-12,,Background,rural background,rural,remote,,10.867189,51.33308,420,POSSEN,,16065067,"Sondershausen, Stadt",no,5.731506017470791 DESN051,DESN051,DE,Germany,Radebeul-Wahnsdorf,1967-12-01,,Background,rural,rural,near city,Unknown,13.675006,51.119511,246,RADEBEUL,,14627210,"Radebeul, Stadt",no,12.431592385265933 DEHE043,DEHE043,DE,Germany,Riedstadt,1996-03-20,,Background,rural,rural,near city,,8.516797,49.825165,87,RIEDSTADT,,6433011,"Riedstadt, Stadt",no,16.680100143239645 DEUB004,DEUB004,DE,Germany,Schauinsland,1968-01-01,,Background,rural,rural,regional,,7.908036,47.913254,1205,OBERRIED-HOFSGRUND,83155003,,Oberried,yes,2.069317908430549 DEUB029,DEUB029,DE,Germany,Schmücke,1991-06-01,,Background,rural,rural,unknown,,10.769533,50.654068,937,GEHLBERG,,,,yes,4.390458645846876 DESN074,DESN074,DE,Germany,Schwartenberg,1998-02-06,,Background,rural,rural,regional,,13.465077,50.6591,785,NEUHAUSEN,,14522400,Neuhausen/Erzgeb.,no,7.68523284266574 DEBW031,DEBW031,DE,Germany,Schwarzwald-Süd,1984-01-01,,Background,rural,rural,regional,,7.764528,47.809892,904,,83155012,,"Sulzburg, Stadt",no,3.4389926002665256 DEBW087,DEBW087,DE,Germany,Schwäbische_Alb,1994-04-27,,Background,rural,rural,regional,,9.207639,48.345778,798,ERPFINGEN,,8415091,Sonnenbühl,no,6.540338979727645 DENW064,DENW064,DE,Germany,Simmerath (Eifel),1983-09-01,,Background,rural,rural,regional,,6.28107,50.653236,572,SIMMERATH,,5334028,Simmerath,no,5.509009866414982 DENW068,DENW068,DE,Germany,Soest-Ost,1989-03-01,,Background,rural,rural,near city,,8.148061,51.57066,110,SOEST,,5974040,"Soest, Stadt",no,12.670414585555143 DENI077,DENI077,DE,Germany,Solling-Süd,2010-01-01,,Background,rural,rural,unknown,,9.55462,51.708839,295,,31559501,,"Solling (Landkreis Northeim), gemfr. Geb.",no,8.40113799392387 DEHE026,DEHE026,DE,Germany,Spessart,1986-01-01,,Background,rural,rural,regional,,9.399442,50.164433,502,SPESSART,,6435016,Jossgrund,no,7.538232128849274 DEBB066,DEBB066,DE,Germany,Spreewald,2003-04-17,,Background,rural,rural,regional,,14.057064,51.897598,52,,120615113,,Neu Zauche,no,6.242489303806773 DEBY072,DEBY072,DE,Germany,Tiefenbach/Altenschneeberg,1983-10-01,,Background,rural,rural,regional,,12.54887,49.438465,755,TIEFENBACH,93725308,,Tiefenbach,no,6.55314033706656 DEST098,DEST098,DE,Germany,Unterharz / Friedrichsbrunn,2003-06-24,,Background,rural,rural,regional,,11.043384,51.662453,410,,,,,no,4.3249722250585805 DEUB005,DEUB005,DE,Germany,Waldhof,1970-01-01,,Background,rural,rural,unknown,,10.756733,52.800774,74,ZELLA-MEHLIS,33605402,,Lüder,yes,6.637390724799518 DEHE051,DEHE051,DE,Germany,Wasserkuppe,2000-07-05,,Background,rural,rural,unknown,,9.935862,50.497711,931,WASSERKUPPE,,6631010,"Gersfeld (Rhön), Stadt",no,5.258516400704886 DENI060,DENI060,DE,Germany,Wendland,1998-04-01,,Background,rural,rural,unknown,,11.16705,52.95702,16,,33545407,,"Lüchow (Wendland), Stadt",no,9.88399812585395 DERP015,DERP015,DE,Germany,Westeifel Wascheid,1984-01-01,,Background,rural,rural,unknown,,6.3781,50.2665,680,WASCHEID,72325006,,Gondenbrett,no,5.270283853346025 DEUB001,DEUB001,DE,Germany,Westerland,1968-01-01,,Background,rural,rural,unknown,,8.308208,54.924969,12,WESTERLAND,,1054168,Sylt,yes,5.123743401705111 DERP016,DERP016,DE,Germany,Westerwald-Herdorf,1984-01-01,,Background,rural,rural,unknown,,7.9735,50.76675,480,HERDORF,,7132050,"Herdorf, Stadt",no,7.5608887467047445 DERP028,DERP028,DE,Germany,Westerwald-Neuhäusel,1994-01-01,,Background,rural,rural,unknown,,7.7299,50.4243,546,NEUSTADT,71435004,,"Montabaur, Stadt",no,8.176328171592356 DERP013,DERP013,DE,Germany,Westpfalz-Waldmohr,1984-01-01,,Background,rural,rural,unknown,,7.293522,49.423138,455,DUNZWEILER,73365006,,Dunzweiler,no,7.241496239470168 DEHE024,DEHE024,DE,Germany,Witzenhausen/Wald,1983-05-01,,Background,rural,rural,unknown,,9.774589,51.291759,610,WITZENHAUSEN/WALD,66369200,,"Gutsbezirk Kaufunger Wald, gemfr. Gebiet",no,6.34763255724478 DENI051,DENI051,DE,Germany,Wurmberg,1991-06-06,,Background,rural,rural,unknown,,10.612481,51.758163,939,,,3153003,"Braunlage, Stadt",no,5.652281144348398 DEST089,DEST089,DE,Germany,Zartau/Waldstation,1997-12-01,,Background,rural,rural,regional,,11.17235,52.59317,95,BITTERFELD,,,,no,6.349581619662699 DEHE050,DEHE050,DE,Germany,Zierenberg,2000-05-01,,Background,rural,rural,unknown,,9.271233,51.360752,489,ZIERENBERG,,6633029,"Zierenberg, Stadt",no,8.549351783351376 DEUB028,DEUB028,DE,Germany,Zingst,1991-09-01,,Background,rural,rural,unknown,,12.721938,54.436989,1,ZINGST,,13057096,Zingst,yes,5.197794008346108 DESN052,DESN052,DE,Germany,Zinnwald,1978-05-01,,Background,rural,rural,regional,,13.75145,50.731476,877,ZINNWALD,146285201,,"Altenberg, Stadt",no,6.719808983782324 gstat/inst/external/oxford.jpg0000644000176200001440000017505113777370515016226 0ustar liggesusersJFIFC   %# , #&')*)-0-(0%()(C   ((((((((((((((((((((((((((((((((((((((((((((((((((('" }!1AQa"q2#BR$3br %&'()*456789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz w!1AQaq"2B #3Rbr $4%&'()*56789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz ?(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((cVr5)Vh촻:c l&7'?)]7J ?(/)d6׭rUJ!fTe)\0İW|R:}S[kMr݈S#eH I9+y〹'XƯkx?zI s<ʁ@Rp=:+iʱ]4,B@Hx6Wg* #!RGU=b~#h-GƞoZYOt9H.cpq joe]~ѻ>Am6zPE|cJ&Y^!ti6gKXò#,Y6 ƽ;ǚ{vʶ22DCnB2hQ^uwށD3[B~e'8Va߇.O; ,ѩ\Up @+[N x?`o6JAֺ(_Y<׳~nڑWn|G_e;g}?n۴[d}޼^kwⵯ]Wje"Ou$h}`^~WXK_5 yz̍mC:+H *4ƯAm Z2"+TF$fÎ/q}ou+`I ȿ#A x |bOgWnnol/EzMM%e#Rqx/Z>:n^^Ep8!BoF9#:o#> g_Yյ=ե~dɈ.Ðp:kxþv滇OCʮK+-Z+4ͦ:VKCe@%@`7劁(((((((((((t*~!.몮WM>((((((+g]7J ꨢ(((((((((+|ATkVi"'c"b]`=]yW/7)tx?U񞕶;{"IG61 s&| ih%#H'ses7QA>O|2^L&Ucc["ez|t_WM6Oytb vǵFު4rvjR麄^u%+7XdFA< ;Xml hQc(*F0@ ? 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