pax_global_header00006660000000000000000000000064140270675410014520gustar00rootroot0000000000000052 comment=eacd8ce28682b53227ac62c3a807686d8b5d0e1c ripser-1.2.1/000077500000000000000000000000001402706754100130255ustar00rootroot00000000000000ripser-1.2.1/.clang-format000066400000000000000000000004441402706754100154020ustar00rootroot00000000000000BasedOnStyle: LLVM IndentWidth: 4 TabWidth: 4 ColumnLimit: 100 AccessModifierOffset: -4 AllowShortIfStatementsOnASingleLine: true AllowShortLoopsOnASingleLine: true AllowShortBlocksOnASingleLine: true AllowShortFunctionsOnASingleLine: true DerivePointerAlignment: true UseTab: ForIndentation ripser-1.2.1/.gitignore000066400000000000000000000000541402706754100150140ustar00rootroot00000000000000DerivedData ripser.dSYM ripser ripser-coeff ripser-1.2.1/.gitmodules000066400000000000000000000001661402706754100152050ustar00rootroot00000000000000[submodule "robin-hood-hashing"] path = robin-hood-hashing url = https://github.com/martinus/robin-hood-hashing.git ripser-1.2.1/CONTRIBUTING.txt000066400000000000000000000012341402706754100154750ustar00rootroot00000000000000You are under no obligation whatsoever to provide any bug fixes, patches, or upgrades to the features, functionality or performance of the source code ("Enhancements") to anyone; however, if you choose to make your Enhancements available either publicly, or directly to the author of this software, without imposing a separate written license agreement for such Enhancements, then you hereby grant the following license: a non-exclusive, royalty-free perpetual license to install, use, modify, prepare derivative works, incorporate into other computer software, distribute, and sublicense such enhancements or derivative works thereof, in binary and source code form. ripser-1.2.1/COPYING.txt000066400000000000000000000020641402706754100147000ustar00rootroot00000000000000MIT License Copyright (c) 2015–2018 Ulrich Bauer Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. ripser-1.2.1/Makefile000066400000000000000000000005601402706754100144660ustar00rootroot00000000000000build: ripser all: ripser ripser-coeff ripser-debug ripser: ripser.cpp c++ -std=c++11 -Wall ripser.cpp -o ripser -O3 -D NDEBUG ripser-coeff: ripser.cpp c++ -std=c++11 -Wall ripser.cpp -o ripser-coeff -O3 -D NDEBUG -D USE_COEFFICIENTS ripser-debug: ripser.cpp c++ -std=c++11 -Wall ripser.cpp -o ripser-debug -g clean: rm -f ripser ripser-coeff ripser-debug ripser-1.2.1/README.md000066400000000000000000000164461402706754100143170ustar00rootroot00000000000000# Ripser Copyright © 2015–2021 [Ulrich Bauer]. ### Description Ripser is a lean C++ code for the computation of Vietoris–Rips persistence barcodes. It can do just this one thing, but does it extremely well. To see a live demo of Ripser's capabilities, go to [live.ripser.org]. The computation happens inside the browser (using [Emscripten] to compile Ripser to [WebAssembly], supported on recent browsers). The main features of Ripser: - time- and memory-efficient - only about 1000 lines of code in a single C++ file - support for coefficients in prime finite fields - no external dependencies (optional support for Google's [sparsehash]) Currently, Ripser outperforms other codes ([Dionysus], [DIPHA], [GUDHI], [Perseus], [PHAT]) by a factor of more than 40 in computation time and a factor of more than 15 in memory efficiency (for the example linked at [live.ripser.org]). (Note that [PHAT] does not contain code for generating Vietoris–Rips filtrations). Input formats currently supported by Ripser: - comma-separated values lower triangular distance matrix - comma-separated values upper triangular distance matrix (MATLAB output from the function `pdist`) - comma-separated values full distance matrix - [DIPHA] distance matrix data - sparse distance matrix in sparse triplet format - binary lower triangular distance matrix - point cloud data Ripser's efficiency is based on a few important concepts and principles, building on key previous and concurrent developments by other researchers in computational topology: - Compute persistent *co*homology (as suggested by [Vin de Silva, Dmitriy Morozov, and Mikael Vejdemo-Johansson](https://doi.org/10.1088/0266-5611/27/12/124003)) - Use the chain complex property that boundaries are cycles (employ the *clearing* optimization, aka *persistence with a twist*, as suggested by [Chao Chen and Michael Kerber](http://www.geometrie.tugraz.at/kerber/kerber_papers/ck-phcwat-11.pdf)) - If no threshold is specified, choose the *enclosing radius* as the threshold, from which on homology is guaranteed to be trivial (as suggested by [Greg Henselman-Petrusek](https://github.com/Eetion/Eirene.jl)) - Don't store information that can be readily recomputed (in particular, the original and the reduced boundary matrix) - Take computational shortcuts (*apparent* and *emergent persistence pairs*) ### Version [Latest release][latest-release]: 1.2.1 (March 2021) ### Building Ripser requires a C++11 compiler. Here is how to obtain, build, and run Ripser: ```sh git clone https://github.com/Ripser/ripser.git cd ripser make ./ripser examples/sphere_3_192.lower_distance_matrix ``` ### Options Ripser supports several compile-time options. They are switched on by defining the C preprocessor macros listed below, either using `#define` in the code or by passing an argument to the compiler. The following options are supported: - `USE_COEFFICIENTS`: enable support for coefficients in a prime field - `INDICATE_PROGRESS`: indicate the current progress in the console - `PRINT_PERSISTENCE_PAIRS`: output the computed persistence pairs (enabled by default in the code; comment out to disable) - `USE_ROBINHOOD_HASHMAP`: enable support for Martin Ankerl's [robinhoodhash] data structure; may further reduce memory footprint For example, to build Ripser with support for Martin Ankerl's robin hood hashmap: ```sh $ c++ -std=c++11 ripser.cpp -o ripser -O3 -D NDEBUG -D USE_ROBINHOOD_HASHMAP ``` A Makefile is provided with some variants of the above options. Use `make all` to build them. The default `make` builds a binary with the default options. The input is given either in a file whose name is passed as an argument, or through stdin. The following options are supported at the command line: - `--format`: use the specified file format for the input. The following formats are supported: - `lower-distance`: lower triangular distance matrix; a comma (or whitespace, or other non-numerical character) separated list of the distance matrix entries below the diagonal, sorted lexicographically by row index, then column index. - `upper-distance`: upper triangular distance matrix; similar to the previous, but for the entries above the diagonal; suitable for output from the MATLAB functions `pdist` or `seqpdist`, exported to a CSV file. - `distance` (default if no format is specified): full distance matrix; similar to the above, but for all entries of the distance matrix. One line per row of the matrix; only the part below the diagonal is actually read. - `dipha`: DIPHA distance matrix as described on the [DIPHA] website. - `point-cloud`: point cloud; a comma (or whitespace, or other non-numerical character) separated list of coordinates of the points in some Euclidean space, one point per line. - `binary`: lower distance matrix in binary file format; a sequence of the distance matrix entries below the diagonal in 32 bit float format (IEEE 754, single, little endian). - `sparse`: sparse triplet format; a whitespace separated list of entries of a sparse distance matrix, one entry per line, each of the form *i j d(i,j)* specifying the distance between points *i* and *j*. Each pair of points should appear in the file at most once. - `--dim k`: compute persistent homology up to dimension *k*. - `--threshold t`: compute Rips complexes up to diameter *t*. - `--modulus p`: compute homology with coefficients in the prime field Z/*p*Z (only available when built with the option `USE_COEFFICIENTS`). - `--ratio r`: only show persistence pairs with death/birth ratio > *r*. ### Experimental features The following experimental features are currently available in separate branches: - `representative-cocycles`: output of representative cocycles for persistent cohomology. - `representative-cycles`: computation and output of representative cycles for persistent homology (in the standard version, only *co*cycles are computed). - `simple`: a simplified version of Ripser, without support for sparse distance matrices and coefficients. This might be a good starting point for exploring the code. ### Citing If you use Ripser in your research or if you want to give a reference to Ripser in a paper, you may use the following bibtex entry (will be updated with complete publication data): ``` @misc{1908.02518, Author = {Ulrich Bauer}, Title = {Ripser: efficient computation of Vietoris-Rips persistence barcodes}, Month = Feb, Year = {2021}, Eprint = {1908.02518v2}, Note = {Preprint} } ``` ### License Ripser is licensed under the [MIT] license (`COPYING.txt`), with an extra clause (`CONTRIBUTING.txt`) clarifying the license for modifications released without an explicit written license agreement. Please contact the author if you want to use Ripser in your software under a different license. 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1.81899,0.23879,0.744896,0.169115,1.26997,1.24651,1.88787,1.53299,1.24773,0.910244,1.48149,1.35674,0.980719,1.71058,1.82557,0.381084,1.79646,1.27526,1.4816,1.35382,0.717499,0.949433, 1.37801,0.738307,1.41981,0.971098,0.74155,0.783719,1.50016,1.23885,1.10743,0.881203,1.29683,0.727244,1.58421,1.89793,1.35117,0.706576,1.77673,1.62702,1.85533,1.8164,1.285,1.3182,0.824956, 1.4044,1.7395,1.7487,1.81715,1.31777,1.87771,1.29388,1.79261,1.04072,1.34123,1.83505,1.36818,1.38307,1.40954,1.01536,1.94114,0.0633425,1.77332,1.48835,1.49215,1.88925,1.21449,1.82164,1.77992, 1.98864,0.670627,0.559498,0.532104,1.48061,1.67029,1.99927,1.80996,1.202,0.96984,1.73913,1.60973,0.387245,1.54612,1.91138,0.951241,1.51459,1.23804,1.23016,1.03696,0.823293,0.586931,0.635738,1.3188,1.55508, 0.0853842,1.81734,1.91663,1.87754,1.25864,0.96398,0.174111,0.770854,1.57158,1.69834,0.930954,1.08286,1.98887,1.36374,0.576485,1.67628,1.39775,1.59273,1.64746,1.77037,1.79701,1.91076,1.83316,1.38086,1.35273,1.99196, 0.643286,1.66572,1.9839,1.82971,0.820147,1.15236,0.671768,1.19085,1.15441,1.35246,1.34403,0.657854,1.93019,1.68011,0.176636,1.68417,1.1828,1.87027,1.87583,1.93918,1.92466,1.66451,1.75491,1.21926,1.14426,1.89707,0.569394, 1.22781,1.91925,1.44557,1.78492,1.90951,1.63416,1.10699,1.27522,1.84287,1.94034,1.21708,1.86805,1.43328,0.336643,1.43536,1.81484,1.19566,0.986907,0.688818,0.874996,1.47401,1.7381,1.85233,1.95515,1.17456,1.65826,1.24569,1.52981, 0.530267,1.66573,1.96926,1.81556,0.874587,1.03477,0.592646,1.06754,1.24947,1.41135,1.23036,0.688519,1.96286,1.65189,0.288354,1.63695,1.29118,1.81939,1.85912,1.93233,1.88381,1.72937,1.74003,1.17993,1.25246,1.91935,0.46308,0.151879,1.52115, 1.9076,1.29638,1.08394,1.25828,1.55521,1.97062,1.84717,1.9645,1.11742,1.16135,1.92198,1.68256,0.520655,1.36797,1.70007,1.57502,0.90726,1.43578,1.14541,0.996814,1.36438,0.637788,1.32893,1.72726,0.959764,0.799539,1.88926,1.7586,1.33209,1.82551, 0.912694,1.38513,1.44422,1.34365,1.41623,0.252863,1.04807,0.341855,1.75755,1.651,0.379453,1.28162,1.79906,1.37773,1.35781,0.991016,1.91796,1.14838,1.48822,1.56814,1.17645,1.85673,1.30288,0.984825,1.8994,1.67949,0.975594,1.26652,1.49507,1.14702,1.96342, 1.70927,0.574945,1.34503,0.914817,0.64864,1.4077,1.76476,1.73043,0.54433,0.168587,1.76468,0.837278,1.21831,1.96656,1.43749,1.00662,1.43207,1.78187,1.83901,1.73392,1.4001,0.705239,0.799471,0.738915,1.45823,0.96645,1.68621,1.36642,1.97239,1.40875,1.2601,1.55628, 0.0814685,1.81725,1.91551,1.87683,1.26064,0.961788,0.173684,0.767349,1.57375,1.69975,0.927511,1.0848,1.98889,1.36213,0.580209,1.67507,1.40009,1.59052,1.64606,1.76922,1.79533,1.91184,1.83259,1.38076,1.35512,1.99189,0.00391946,0.572785,1.24481,0.466103,1.89016,0.972731,1.68734, 0.946102,1.34291,1.86437,1.5735,0.433403,0.997242,1.03923,1.24982,0.955549,1.04677,1.39133,0.208851,1.85105,1.87712,0.649351,1.39854,1.39384,1.8961,1.98074,1.99885,1.78782,1.49762,1.46348,0.807349,1.37491,1.72161,0.902445,0.49478,1.797,0.500744,1.7655,1.18739,1.01997,0.904429, 1.61165,1.16831,1.62736,1.40777,0.693378,1.69707,1.60279,1.87062,0.162738,0.542064,1.92845,0.877326,1.2903,1.88131,1.14246,1.54029,0.871347,1.93807,1.82939,1.75299,1.75155,0.732709,1.34704,1.23613,0.900116,1.23716,1.56212,1.1475,1.77353,1.25401,1.04196,1.81711,0.690588,1.56446,1.01836, 0.273482,1.79315,1.78381,1.79154,1.44391,0.799694,0.368834,0.453052,1.7512,1.81095,0.606549,1.27495,1.95754,1.20354,0.909006,1.55464,1.58914,1.36335,1.49409,1.63668,1.61734,1.98127,1.76319,1.38566,1.54989,1.95562,0.357629,0.886081,1.1632,0.766912,1.93944,0.729943,1.77653,0.353776,1.11008,1.75443, 1.51252,0.621256,1.09899,0.675514,1.14546,0.763446,1.6265,1.16454,1.3776,1.09586,1.15089,1.1411,1.42303,1.73512,1.62805,0.276383,1.92258,1.32031,1.62989,1.57882,0.899073,1.3487,0.561628,0.46675,1.93031,1.14154,1.53744,1.5191,1.86971,1.46322,1.6933,0.869752,0.951758,1.53635,1.19526,1.49045,1.43845, 0.988645,1.95269,1.56153,1.83941,1.85396,1.46217,0.870207,1.05397,1.88003,1.97774,1.01812,1.77728,1.61842,0.461814,1.30073,1.79574,1.30008,1.03425,0.874937,1.07425,1.52609,1.86517,1.88724,1.87788,1.26844,1.79124,1.0163,1.38445,0.301331,1.35304,1.53781,1.3159,1.99447,1.01493,1.67717,1.82357,0.90487,1.81366, 1.98648,0.735528,0.820882,0.735347,1.35829,1.75871,1.9863,1.90676,0.989125,0.802004,1.86074,1.51396,0.437096,1.63472,1.81542,1.12033,1.3396,1.43092,1.35618,1.17291,1.07648,0.310257,0.788926,1.3406,1.38586,0.287316,1.97747,1.81092,1.69091,1.85483,0.646305,1.7933,0.843697,1.97797,1.64214,1.01075,1.99259,1.26205,1.83065, 1.95655,0.673864,0.957653,0.768004,1.21719,1.72828,1.96376,1.91285,0.835253,0.630279,1.88485,1.38777,0.612634,1.73185,1.74161,1.1178,1.3148,1.54384,1.48574,1.31729,1.17619,0.193804,0.781909,1.24623,1.36043,0.428368,1.94213,1.72863,1.76775,1.77877,0.728846,1.78828,0.682559,1.94287,1.53049,0.872265,1.982,1.22517,1.8884,0.184757, 0.531651,1.52437,1.80359,1.62376,1.03794,0.525224,0.704872,0.656598,1.48683,1.50296,0.836064,0.837086,1.96891,1.60041,0.819273,1.33201,1.66101,1.59649,1.78274,1.86276,1.62646,1.83339,1.54413,0.94609,1.63096,1.86628,0.549429,0.691322,1.57764,0.552645,1.97608,0.657677,1.4409,0.548424,0.669371,1.53474,0.571566,1.13395,1.37516,1.88045,1.82399, 0.924244,1.7759,1.41648,1.63017,1.82421,1.04407,0.916287,0.582372,1.97799,1.97079,0.474843,1.7182,1.6911,0.672219,1.43364,1.46691,1.69525,0.786668,0.957368,1.14175,1.24722,1.95116,1.66671,1.62103,1.66996,1.75434,0.991309,1.44481,0.807317,1.35978,1.77653,0.834812,1.93575,0.988227,1.61044,1.97111,0.698602,1.47248,0.606907,1.86497,1.91917,1.13414, 0.709904,1.93093,1.94945,1.99439,1.3311,1.48074,0.560484,1.28067,1.41338,1.65723,1.37909,1.23919,1.82947,1.28246,0.523358,1.93594,0.872074,1.70155,1.5584,1.66485,1.94566,1.73479,1.97538,1.68398,0.814681,1.93228,0.651037,0.680288,1.03283,0.726882,1.57273,1.48249,1.70864,0.653632,1.12132,1.33749,0.901659,1.85303,0.916574,1.85071,1.82266,1.11005,1.24383, 1.71779,0.740853,0.559643,0.445398,1.56687,1.10379,1.7855,1.27276,1.60923,1.3389,1.1651,1.59064,1.07477,1.42728,1.90039,0.374531,1.92612,0.866331,1.20342,1.11674,0.297386,1.30078,0.516885,1.04286,1.94179,0.856509,1.754,1.8396,1.64223,1.79285,1.47505,1.06241,1.23921,1.75241,1.63627,1.68247,1.58891,0.624693,1.6576,1.08946,1.14771,1.49907,1.33348,1.96473, 0.780627,1.84964,1.98167,1.9596,1.1378,1.4802,0.67683,1.36924,1.23129,1.50334,1.48241,1.05467,1.82863,1.46473,0.344005,1.90561,0.814987,1.82147,1.6944,1.77271,1.9871,1.64022,1.92334,1.57895,0.760821,1.89943,0.706865,0.516661,1.23237,0.608727,1.55483,1.5241,1.56199,0.710235,0.949682,1.1576,1.00721,1.80358,1.13598,1.79095,1.73874,1.07904,1.412,0.255364,1.97646, 1.20992,1.6118,1.90008,1.79155,0.849319,1.64116,1.15586,1.67777,0.754764,1.1046,1.77301,0.880018,1.6256,1.71057,0.630948,1.82284,0.610961,1.96004,1.8122,1.81762,1.97085,1.26396,1.74147,1.45677,0.58991,1.66274,1.14087,0.716832,1.51198,0.856401,1.30087,1.73478,1.20481,1.14408,0.889363,0.655113,1.41521,1.73324,1.50249,1.48627,1.39604,1.31105,1.75253,0.777786,1.93442,0.561426, 1.34176,1.43408,0.967133,1.19999,1.84003,1.00485,1.37917,0.7951,1.95254,1.82659,0.607973,1.78024,1.42124,0.867835,1.75438,1.04527,1.89127,0.400365,0.852719,0.943223,0.716108,1.76479,1.26381,1.44338,1.88512,1.41093,1.4036,1.73013,1.13517,1.65136,1.6807,0.797431,1.76114,1.40082,1.73057,1.97818,1.12637,1.13699,1.07318,1.59851,1.67614,1.33027,0.611541,1.66312,0.821859,1.77449,1.96183, 1.97801,1.10126,0.758667,0.983663,1.62433,1.8815,1.94241,1.90449,1.24737,1.16884,1.83406,1.74826,0.154095,1.34761,1.86132,1.34594,1.22152,1.24402,1.03501,0.837441,1.07393,0.628115,1.08567,1.63467,1.26771,0.495773,1.97352,1.8932,1.40259,1.93634,0.370337,1.86062,1.22631,1.97379,1.83745,1.21674,1.96555,1.51159,1.599,0.45635,0.613874,1.98529,1.72428,1.76605,1.201,1.7608,1.54027,1.50483, 0.614648,1.47253,1.81955,1.6032,0.914746,0.583043,0.776416,0.783334,1.38961,1.40987,0.954395,0.707129,1.9573,1.67869,0.775264,1.32162,1.62972,1.66832,1.84211,1.90791,1.65686,1.77475,1.51288,0.86915,1.60169,1.84087,0.614992,0.62862,1.64643,0.501447,1.95277,0.750125,1.34847,0.614813,0.538428,1.44412,0.692725,1.11085,1.45924,1.83924,1.77016,0.141103,1.24752,1.12338,1.51545,1.06017,1.24142,1.41682,1.96997, 1.72684,0.795785,0.503301,0.481755,1.61459,1.14073,1.78809,1.27721,1.64124,1.38101,1.16021,1.63795,1.04408,1.37384,1.91908,0.453047,1.91795,0.799517,1.13841,1.05053,0.218561,1.31158,0.571655,1.11015,1.93378,0.849552,1.76425,1.86464,1.59785,1.81853,1.45205,1.08376,1.28828,1.76261,1.67973,1.70795,1.59244,0.698633,1.62121,1.09064,1.16064,1.5309,1.30329,1.96195,0.0802451,1.98253,1.94983,0.779401,1.17239,1.55215, 1.57784,1.77952,1.33911,1.67551,1.82545,1.91198,1.46021,1.69262,1.56943,1.69607,1.64342,1.85824,1.06775,0.779394,1.53567,1.84659,0.84172,1.21506,0.77945,0.806586,1.50897,1.35097,1.7537,1.98799,0.850288,1.37478,1.56983,1.6428,0.62495,1.68539,0.81335,1.82959,1.77045,1.5702,1.84914,1.47111,1.58301,1.93488,0.888712,1.33471,1.4199,1.84776,1.32639,1.18076,1.68377,1.29253,1.34339,1.46536,0.982965,1.87333,1.64169, 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Ripser: a lean C++ code for computation of Vietoris-Rips persistence barcodes MIT License Copyright (c) 2015–2021 Ulrich Bauer Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. You are under no obligation whatsoever to provide any bug fixes, patches, or upgrades to the features, functionality or performance of the source code ("Enhancements") to anyone; however, if you choose to make your Enhancements available either publicly, or directly to the author of this software, without imposing a separate written license agreement for such Enhancements, then you hereby grant the following license: a non-exclusive, royalty-free perpetual license to install, use, modify, prepare derivative works, incorporate into other computer software, distribute, and sublicense such enhancements or derivative works thereof, in binary and source code form. */ //#define USE_COEFFICIENTS //#define INDICATE_PROGRESS #define PRINT_PERSISTENCE_PAIRS //#define USE_ROBINHOOD_HASHMAP #include #include #include #include #include #include #include #include #include #include #ifdef USE_ROBINHOOD_HASHMAP #include "robin-hood-hashing/src/include/robin_hood.h" template using hash_map = robin_hood::unordered_map; template using hash = robin_hood::hash; #else template using hash_map = std::unordered_map; template using hash = std::hash; #endif typedef float value_t; typedef int64_t index_t; typedef uint16_t coefficient_t; #ifdef INDICATE_PROGRESS static const std::chrono::milliseconds time_step(40); #endif static const std::string clear_line("\r\033[K"); static const size_t num_coefficient_bits = 8; static const index_t max_simplex_index = (1l << (8 * sizeof(index_t) - 1 - num_coefficient_bits)) - 1; void check_overflow(index_t i) { if #ifdef USE_COEFFICIENTS (i > max_simplex_index) #else (i < 0) #endif throw std::overflow_error("simplex index " + std::to_string((uint64_t)i) + " in filtration is larger than maximum index " + std::to_string(max_simplex_index)); } class binomial_coeff_table { std::vector> B; public: binomial_coeff_table(index_t n, index_t k) : B(n + 1) { for (index_t i = 0; i <= n; ++i) { B[i].resize(k + 1, 0); B[i][0] = 1; for (index_t j = 1; j < std::min(i, k + 1); ++j) B[i][j] = B[i - 1][j - 1] + B[i - 1][j]; if (i <= k) B[i][i] = 1; check_overflow(B[i][std::min(i >> 1, k)]); } } index_t operator()(index_t n, index_t k) const { assert(n < B.size() && k < B[n].size() && n >= k - 1); return B[n][k]; } }; bool is_prime(const coefficient_t n) { if (!(n & 1) || n < 2) return n == 2; for (coefficient_t p = 3; p <= n / p; p += 2) if (!(n % p)) return false; return true; } std::vector multiplicative_inverse_vector(const coefficient_t m) { std::vector inverse(m); inverse[1] = 1; // m = a * (m / a) + m % a // Multipying with inverse(a) * inverse(m % a): // 0 = inverse(m % a) * (m / a) + inverse(a) (mod m) for (coefficient_t a = 2; a < m; ++a) inverse[a] = m - (inverse[m % a] * (m / a)) % m; return inverse; } #ifdef USE_COEFFICIENTS struct __attribute__((packed)) entry_t { index_t index : 8 * sizeof(index_t) - num_coefficient_bits; coefficient_t coefficient : num_coefficient_bits; entry_t(index_t _index, coefficient_t _coefficient) : index(_index), coefficient(_coefficient) {} entry_t(index_t _index) : index(_index), coefficient(0) {} entry_t() : index(0), coefficient(0) {} }; static_assert(sizeof(entry_t) == sizeof(index_t), "size of entry_t is not the same as index_t"); entry_t make_entry(index_t i, coefficient_t c) { return entry_t(i, c); } index_t get_index(const entry_t& e) { return e.index; } index_t get_coefficient(const entry_t& e) { return e.coefficient; } void set_coefficient(entry_t& e, const coefficient_t c) { e.coefficient = c; } std::ostream& operator<<(std::ostream& stream, const entry_t& e) { stream << get_index(e) << ":" << get_coefficient(e); return stream; } #else typedef index_t entry_t; const index_t get_index(const entry_t& i) { return i; } index_t get_coefficient(const entry_t& i) { return 1; } entry_t make_entry(index_t _index, coefficient_t _value) { return entry_t(_index); } void set_coefficient(entry_t& e, const coefficient_t c) {} #endif const entry_t& get_entry(const entry_t& e) { return e; } typedef std::pair diameter_index_t; value_t get_diameter(const diameter_index_t& i) { return i.first; } index_t get_index(const diameter_index_t& i) { return i.second; } typedef std::pair index_diameter_t; index_t get_index(const index_diameter_t& i) { return i.first; } value_t get_diameter(const index_diameter_t& i) { return i.second; } struct diameter_entry_t : std::pair { using std::pair::pair; diameter_entry_t(value_t _diameter, index_t _index, coefficient_t _coefficient) : diameter_entry_t(_diameter, make_entry(_index, _coefficient)) {} diameter_entry_t(const diameter_index_t& _diameter_index, coefficient_t _coefficient) : diameter_entry_t(get_diameter(_diameter_index), make_entry(get_index(_diameter_index), _coefficient)) {} diameter_entry_t(const diameter_index_t& _diameter_index) : diameter_entry_t(get_diameter(_diameter_index), make_entry(get_index(_diameter_index), 0)) {} diameter_entry_t(const index_t& _index) : diameter_entry_t(0, _index, 0) {} }; const entry_t& get_entry(const diameter_entry_t& p) { return p.second; } entry_t& get_entry(diameter_entry_t& p) { return p.second; } const index_t get_index(const diameter_entry_t& p) { return get_index(get_entry(p)); } const coefficient_t get_coefficient(const diameter_entry_t& p) { return get_coefficient(get_entry(p)); } const value_t& get_diameter(const diameter_entry_t& p) { return p.first; } void set_coefficient(diameter_entry_t& p, const coefficient_t c) { set_coefficient(get_entry(p), c); } template struct greater_diameter_or_smaller_index_comp { bool operator()(const Entry& a, const Entry& b) { return greater_diameter_or_smaller_index(a, b); } }; template bool greater_diameter_or_smaller_index(const Entry& a, const Entry& b) { return (get_diameter(a) > get_diameter(b)) || ((get_diameter(a) == get_diameter(b)) && (get_index(a) < get_index(b))); } enum compressed_matrix_layout { LOWER_TRIANGULAR, UPPER_TRIANGULAR }; template struct compressed_distance_matrix { std::vector distances; std::vector rows; compressed_distance_matrix(std::vector&& _distances) : distances(std::move(_distances)), rows((1 + std::sqrt(1 + 8 * distances.size())) / 2) { assert(distances.size() == size() * (size() - 1) / 2); init_rows(); } template compressed_distance_matrix(const DistanceMatrix& mat) : distances(mat.size() * (mat.size() - 1) / 2), rows(mat.size()) { init_rows(); for (size_t i = 1; i < size(); ++i) for (size_t j = 0; j < i; ++j) rows[i][j] = mat(i, j); } value_t operator()(const index_t i, const index_t j) const; size_t size() const { return rows.size(); } void init_rows(); }; typedef compressed_distance_matrix compressed_lower_distance_matrix; typedef compressed_distance_matrix compressed_upper_distance_matrix; template <> void compressed_lower_distance_matrix::init_rows() { value_t* pointer = &distances[0]; for (size_t i = 1; i < size(); ++i) { rows[i] = pointer; pointer += i; } } template <> void compressed_upper_distance_matrix::init_rows() { value_t* pointer = &distances[0] - 1; for (size_t i = 0; i < size() - 1; ++i) { rows[i] = pointer; pointer += size() - i - 2; } } template <> value_t compressed_lower_distance_matrix::operator()(const index_t i, const index_t j) const { return i == j ? 0 : i < j ? rows[j][i] : rows[i][j]; } template <> value_t compressed_upper_distance_matrix::operator()(const index_t i, const index_t j) const { return i == j ? 0 : i > j ? rows[j][i] : rows[i][j]; } struct sparse_distance_matrix { std::vector> neighbors; index_t num_edges; sparse_distance_matrix(std::vector>&& _neighbors, index_t _num_edges) : neighbors(std::move(_neighbors)), num_edges(_num_edges) {} template sparse_distance_matrix(const DistanceMatrix& mat, const value_t threshold) : neighbors(mat.size()), num_edges(0) { for (size_t i = 0; i < size(); ++i) for (size_t j = 0; j < size(); ++j) if (i != j) { auto d = mat(i, j); if (d <= threshold) { ++num_edges; neighbors[i].push_back({j, d}); } } } value_t operator()(const index_t i, const index_t j) const { auto neighbor = std::lower_bound(neighbors[i].begin(), neighbors[i].end(), index_diameter_t{j, 0}); return (neighbor != neighbors[i].end() && get_index(*neighbor) == j) ? get_diameter(*neighbor) : std::numeric_limits::infinity(); } size_t size() const { return neighbors.size(); } }; struct euclidean_distance_matrix { std::vector> points; euclidean_distance_matrix(std::vector>&& _points) : points(std::move(_points)) { for (auto p : points) { assert(p.size() == points.front().size()); } } value_t operator()(const index_t i, const index_t j) const { assert(i < points.size()); assert(j < points.size()); return std::sqrt(std::inner_product( points[i].begin(), points[i].end(), points[j].begin(), value_t(), std::plus(), [](value_t u, value_t v) { return (u - v) * (u - v); })); } size_t size() const { return points.size(); } }; class union_find { std::vector parent; std::vector rank; public: union_find(const index_t n) : parent(n), rank(n, 0) { for (index_t i = 0; i < n; ++i) parent[i] = i; } index_t find(index_t x) { index_t y = x, z; while ((z = parent[y]) != y) y = z; while ((z = parent[x]) != y) { parent[x] = y; x = z; } return z; } void link(index_t x, index_t y) { if ((x = find(x)) == (y = find(y))) return; if (rank[x] > rank[y]) parent[y] = x; else { parent[x] = y; if (rank[x] == rank[y]) ++rank[y]; } } }; template T begin(std::pair& p) { return p.first; } template T end(std::pair& p) { return p.second; } template class compressed_sparse_matrix { std::vector bounds; std::vector entries; typedef typename std::vector::iterator iterator; typedef std::pair iterator_pair; public: size_t size() const { return bounds.size(); } iterator_pair subrange(const index_t index) { return {entries.begin() + (index == 0 ? 0 : bounds[index - 1]), entries.begin() + bounds[index]}; } void append_column() { bounds.push_back(entries.size()); } void push_back(const ValueType e) { assert(0 < size()); entries.push_back(e); ++bounds.back(); } }; template index_t get_max(index_t top, const index_t bottom, const Predicate pred) { if (!pred(top)) { index_t count = top - bottom; while (count > 0) { index_t step = count >> 1, mid = top - step; if (!pred(mid)) { top = mid - 1; count -= step + 1; } else count = step; } } return top; } template class ripser { const DistanceMatrix dist; const index_t n, dim_max; const value_t threshold; const float ratio; const coefficient_t modulus; const binomial_coeff_table binomial_coeff; const std::vector multiplicative_inverse; mutable std::vector cofacet_entries; mutable std::vector vertices; struct entry_hash { std::size_t operator()(const entry_t& e) const { return hash()(::get_index(e)); } }; struct equal_index { bool operator()(const entry_t& e, const entry_t& f) const { return ::get_index(e) == ::get_index(f); } }; typedef hash_map entry_hash_map; public: ripser(DistanceMatrix&& _dist, index_t _dim_max, value_t _threshold, float _ratio, coefficient_t _modulus) : dist(std::move(_dist)), n(dist.size()), dim_max(std::min(_dim_max, index_t(dist.size() - 2))), threshold(_threshold), ratio(_ratio), modulus(_modulus), binomial_coeff(n, dim_max + 2), multiplicative_inverse(multiplicative_inverse_vector(_modulus)) {} index_t get_max_vertex(const index_t idx, const index_t k, const index_t n) const { return get_max(n, k - 1, [&](index_t w) -> bool { return (binomial_coeff(w, k) <= idx); }); } index_t get_edge_index(const index_t i, const index_t j) const { return binomial_coeff(i, 2) + j; } template OutputIterator get_simplex_vertices(index_t idx, const index_t dim, index_t n, OutputIterator out) const { --n; for (index_t k = dim + 1; k > 0; --k) { n = get_max_vertex(idx, k, n); *out++ = n; idx -= binomial_coeff(n, k); } return out; } value_t compute_diameter(const index_t index, const index_t dim) const { value_t diam = -std::numeric_limits::infinity(); vertices.resize(dim + 1); get_simplex_vertices(index, dim, dist.size(), vertices.rbegin()); for (index_t i = 0; i <= dim; ++i) for (index_t j = 0; j < i; ++j) { diam = std::max(diam, dist(vertices[i], vertices[j])); } return diam; } class simplex_coboundary_enumerator; class simplex_boundary_enumerator { private: index_t idx_below, idx_above, j, k; diameter_entry_t simplex; index_t dim; const coefficient_t modulus; const binomial_coeff_table& binomial_coeff; const ripser& parent; public: simplex_boundary_enumerator(const diameter_entry_t _simplex, const index_t _dim, const ripser& _parent) : idx_below(get_index(_simplex)), idx_above(0), j(_parent.n - 1), k(_dim), simplex(_simplex), modulus(_parent.modulus), binomial_coeff(_parent.binomial_coeff), parent(_parent) {} simplex_boundary_enumerator(const index_t _dim, const ripser& _parent) : simplex_boundary_enumerator(-1, _dim, _parent) {} void set_simplex(const diameter_entry_t _simplex, const index_t _dim) { idx_below = get_index(_simplex); idx_above = 0; j = parent.n - 1; k = _dim; simplex = _simplex; dim = _dim; } bool has_next() { return (k >= 0); } diameter_entry_t next() { j = parent.get_max_vertex(idx_below, k + 1, j); index_t face_index = idx_above - binomial_coeff(j, k + 1) + idx_below; value_t face_diameter = parent.compute_diameter(face_index, dim - 1); coefficient_t face_coefficient = (k & 1 ? -1 + modulus : 1) * get_coefficient(simplex) % modulus; idx_below -= binomial_coeff(j, k + 1); idx_above += binomial_coeff(j, k); --k; return diameter_entry_t(face_diameter, face_index, face_coefficient); } }; diameter_entry_t get_zero_pivot_facet(const diameter_entry_t simplex, const index_t dim) { static simplex_boundary_enumerator facets(0, *this); facets.set_simplex(simplex, dim); while (facets.has_next()) { diameter_entry_t facet = facets.next(); if (get_diameter(facet) == get_diameter(simplex)) return facet; } return diameter_entry_t(-1); } diameter_entry_t get_zero_pivot_cofacet(const diameter_entry_t simplex, const index_t dim) { static simplex_coboundary_enumerator cofacets(*this); cofacets.set_simplex(simplex, dim); while (cofacets.has_next()) { diameter_entry_t cofacet = cofacets.next(); if (get_diameter(cofacet) == get_diameter(simplex)) return cofacet; } return diameter_entry_t(-1); } diameter_entry_t get_zero_apparent_facet(const diameter_entry_t simplex, const index_t dim) { diameter_entry_t facet = get_zero_pivot_facet(simplex, dim); return ((get_index(facet) != -1) && (get_index(get_zero_pivot_cofacet(facet, dim - 1)) == get_index(simplex))) ? facet : diameter_entry_t(-1); } diameter_entry_t get_zero_apparent_cofacet(const diameter_entry_t simplex, const index_t dim) { diameter_entry_t cofacet = get_zero_pivot_cofacet(simplex, dim); return ((get_index(cofacet) != -1) && (get_index(get_zero_pivot_facet(cofacet, dim + 1)) == get_index(simplex))) ? cofacet : diameter_entry_t(-1); } bool is_in_zero_apparent_pair(const diameter_entry_t simplex, const index_t dim) { return (get_index(get_zero_apparent_cofacet(simplex, dim)) != -1) || (get_index(get_zero_apparent_facet(simplex, dim)) != -1); } void assemble_columns_to_reduce(std::vector& simplices, std::vector& columns_to_reduce, entry_hash_map& pivot_column_index, index_t dim) { #ifdef INDICATE_PROGRESS std::cerr << clear_line << "assembling columns" << std::flush; std::chrono::steady_clock::time_point next = std::chrono::steady_clock::now() + time_step; #endif columns_to_reduce.clear(); std::vector next_simplices; simplex_coboundary_enumerator cofacets(*this); for (diameter_index_t& simplex : simplices) { cofacets.set_simplex(diameter_entry_t(simplex, 1), dim - 1); while (cofacets.has_next(false)) { #ifdef INDICATE_PROGRESS if (std::chrono::steady_clock::now() > next) { std::cerr << clear_line << "assembling " << next_simplices.size() << " columns (processing " << std::distance(&simplices[0], &simplex) << "/" << simplices.size() << " simplices)" << std::flush; next = std::chrono::steady_clock::now() + time_step; } #endif auto cofacet = cofacets.next(); if (get_diameter(cofacet) <= threshold) { next_simplices.push_back({get_diameter(cofacet), get_index(cofacet)}); if (!is_in_zero_apparent_pair(cofacet, dim) && (pivot_column_index.find(get_entry(cofacet)) == pivot_column_index.end())) columns_to_reduce.push_back({get_diameter(cofacet), get_index(cofacet)}); } } } simplices.swap(next_simplices); #ifdef INDICATE_PROGRESS std::cerr << clear_line << "sorting " << columns_to_reduce.size() << " columns" << std::flush; #endif std::sort(columns_to_reduce.begin(), columns_to_reduce.end(), greater_diameter_or_smaller_index); #ifdef INDICATE_PROGRESS std::cerr << clear_line << std::flush; #endif } void compute_dim_0_pairs(std::vector& edges, std::vector& columns_to_reduce) { #ifdef PRINT_PERSISTENCE_PAIRS std::cout << "persistence intervals in dim 0:" << std::endl; #endif union_find dset(n); edges = get_edges(); std::sort(edges.rbegin(), edges.rend(), greater_diameter_or_smaller_index); std::vector vertices_of_edge(2); for (auto e : edges) { get_simplex_vertices(get_index(e), 1, n, vertices_of_edge.rbegin()); index_t u = dset.find(vertices_of_edge[0]), v = dset.find(vertices_of_edge[1]); if (u != v) { #ifdef PRINT_PERSISTENCE_PAIRS if (get_diameter(e) != 0) std::cout << " [0," << get_diameter(e) << ")" << std::endl; #endif dset.link(u, v); } else if (get_index(get_zero_apparent_cofacet(e, 1)) == -1) columns_to_reduce.push_back(e); } std::reverse(columns_to_reduce.begin(), columns_to_reduce.end()); #ifdef PRINT_PERSISTENCE_PAIRS for (index_t i = 0; i < n; ++i) if (dset.find(i) == i) std::cout << " [0, )" << std::endl; #endif } template diameter_entry_t pop_pivot(Column& column) { diameter_entry_t pivot(-1); #ifdef USE_COEFFICIENTS while (!column.empty()) { if (get_coefficient(pivot) == 0) pivot = column.top(); else if (get_index(column.top()) != get_index(pivot)) return pivot; else set_coefficient(pivot, (get_coefficient(pivot) + get_coefficient(column.top())) % modulus); column.pop(); } return (get_coefficient(pivot) == 0) ? -1 : pivot; #else while (!column.empty()) { pivot = column.top(); column.pop(); if (column.empty() || get_index(column.top()) != get_index(pivot)) return pivot; column.pop(); } return -1; #endif } template diameter_entry_t get_pivot(Column& column) { diameter_entry_t result = pop_pivot(column); if (get_index(result) != -1) column.push(result); return result; } template diameter_entry_t init_coboundary_and_get_pivot(const diameter_entry_t simplex, Column& working_coboundary, const index_t& dim, entry_hash_map& pivot_column_index) { static simplex_coboundary_enumerator cofacets(*this); bool check_for_emergent_pair = true; cofacet_entries.clear(); cofacets.set_simplex(simplex, dim); while (cofacets.has_next()) { diameter_entry_t cofacet = cofacets.next(); if (get_diameter(cofacet) <= threshold) { cofacet_entries.push_back(cofacet); if (check_for_emergent_pair && (get_diameter(simplex) == get_diameter(cofacet))) { if ((pivot_column_index.find(get_entry(cofacet)) == pivot_column_index.end()) && (get_index(get_zero_apparent_facet(cofacet, dim + 1)) == -1)) return cofacet; check_for_emergent_pair = false; } } } for (auto cofacet : cofacet_entries) working_coboundary.push(cofacet); return get_pivot(working_coboundary); } template void add_simplex_coboundary(const diameter_entry_t simplex, const index_t& dim, Column& working_reduction_column, Column& working_coboundary) { static simplex_coboundary_enumerator cofacets(*this); working_reduction_column.push(simplex); cofacets.set_simplex(simplex, dim); while (cofacets.has_next()) { diameter_entry_t cofacet = cofacets.next(); if (get_diameter(cofacet) <= threshold) working_coboundary.push(cofacet); } } template void add_coboundary(compressed_sparse_matrix& reduction_matrix, const std::vector& columns_to_reduce, const size_t index_column_to_add, const coefficient_t factor, const size_t& dim, Column& working_reduction_column, Column& working_coboundary) { diameter_entry_t column_to_add(columns_to_reduce[index_column_to_add], factor); add_simplex_coboundary(column_to_add, dim, working_reduction_column, working_coboundary); for (diameter_entry_t simplex : reduction_matrix.subrange(index_column_to_add)) { set_coefficient(simplex, get_coefficient(simplex) * factor % modulus); add_simplex_coboundary(simplex, dim, working_reduction_column, working_coboundary); } } void compute_pairs(const std::vector& columns_to_reduce, entry_hash_map& pivot_column_index, const index_t dim) { #ifdef PRINT_PERSISTENCE_PAIRS std::cout << "persistence intervals in dim " << dim << ":" << std::endl; #endif compressed_sparse_matrix reduction_matrix; #ifdef INDICATE_PROGRESS std::chrono::steady_clock::time_point next = std::chrono::steady_clock::now() + time_step; #endif for (size_t index_column_to_reduce = 0; index_column_to_reduce < columns_to_reduce.size(); ++index_column_to_reduce) { diameter_entry_t column_to_reduce(columns_to_reduce[index_column_to_reduce], 1); value_t diameter = get_diameter(column_to_reduce); reduction_matrix.append_column(); std::priority_queue, greater_diameter_or_smaller_index_comp> working_reduction_column, working_coboundary; diameter_entry_t e, pivot = init_coboundary_and_get_pivot( column_to_reduce, working_coboundary, dim, pivot_column_index); while (true) { #ifdef INDICATE_PROGRESS if (std::chrono::steady_clock::now() > next) { std::cerr << clear_line << "reducing column " << index_column_to_reduce + 1 << "/" << columns_to_reduce.size() << " (diameter " << diameter << ")" << std::flush; next = std::chrono::steady_clock::now() + time_step; } #endif if (get_index(pivot) != -1) { auto pair = pivot_column_index.find(get_entry(pivot)); if (pair != pivot_column_index.end()) { entry_t other_pivot = pair->first; index_t index_column_to_add = pair->second; coefficient_t factor = modulus - get_coefficient(pivot) * multiplicative_inverse[get_coefficient(other_pivot)] % modulus; add_coboundary(reduction_matrix, columns_to_reduce, index_column_to_add, factor, dim, working_reduction_column, working_coboundary); pivot = get_pivot(working_coboundary); } else if (get_index(e = get_zero_apparent_facet(pivot, dim + 1)) != -1) { set_coefficient(e, modulus - get_coefficient(e)); add_simplex_coboundary(e, dim, working_reduction_column, working_coboundary); pivot = get_pivot(working_coboundary); } else { #ifdef PRINT_PERSISTENCE_PAIRS value_t death = get_diameter(pivot); if (death > diameter * ratio) { #ifdef INDICATE_PROGRESS std::cerr << clear_line << std::flush; #endif std::cout << " [" << diameter << "," << death << ")" << std::endl; } #endif pivot_column_index.insert({get_entry(pivot), index_column_to_reduce}); while (true) { diameter_entry_t e = pop_pivot(working_reduction_column); if (get_index(e) == -1) break; assert(get_coefficient(e) > 0); reduction_matrix.push_back(e); } break; } } else { #ifdef PRINT_PERSISTENCE_PAIRS #ifdef INDICATE_PROGRESS std::cerr << clear_line << std::flush; #endif std::cout << " [" << diameter << ", )" << std::endl; #endif break; } } } #ifdef INDICATE_PROGRESS std::cerr << clear_line << std::flush; #endif } std::vector get_edges(); void compute_barcodes() { std::vector simplices, columns_to_reduce; compute_dim_0_pairs(simplices, columns_to_reduce); for (index_t dim = 1; dim <= dim_max; ++dim) { entry_hash_map pivot_column_index; pivot_column_index.reserve(columns_to_reduce.size()); compute_pairs(columns_to_reduce, pivot_column_index, dim); if (dim < dim_max) assemble_columns_to_reduce(simplices, columns_to_reduce, pivot_column_index, dim + 1); } } }; template <> class ripser::simplex_coboundary_enumerator { index_t idx_below, idx_above, j, k; std::vector vertices; diameter_entry_t simplex; const coefficient_t modulus; const compressed_lower_distance_matrix& dist; const binomial_coeff_table& binomial_coeff; const ripser& parent; public: simplex_coboundary_enumerator(const diameter_entry_t _simplex, const index_t _dim, const ripser& _parent) : modulus(_parent.modulus), dist(_parent.dist), binomial_coeff(_parent.binomial_coeff), parent(_parent) { if (get_index(_simplex) != -1) parent.get_simplex_vertices(get_index(_simplex), _dim, parent.n, vertices.rbegin()); } simplex_coboundary_enumerator(const ripser& _parent) : modulus(_parent.modulus), dist(_parent.dist), binomial_coeff(_parent.binomial_coeff), parent(_parent) {} void set_simplex(const diameter_entry_t _simplex, const index_t _dim) { idx_below = get_index(_simplex); idx_above = 0; j = parent.n - 1; k = _dim + 1; simplex = _simplex; vertices.resize(_dim + 1); parent.get_simplex_vertices(get_index(_simplex), _dim, parent.n, vertices.rbegin()); } bool has_next(bool all_cofacets = true) { return (j >= k && (all_cofacets || binomial_coeff(j, k) > idx_below)); } diameter_entry_t next() { while ((binomial_coeff(j, k) <= idx_below)) { idx_below -= binomial_coeff(j, k); idx_above += binomial_coeff(j, k + 1); --j; --k; assert(k != -1); } value_t cofacet_diameter = get_diameter(simplex); for (index_t i : vertices) cofacet_diameter = std::max(cofacet_diameter, dist(j, i)); index_t cofacet_index = idx_above + binomial_coeff(j--, k + 1) + idx_below; coefficient_t cofacet_coefficient = (k & 1 ? modulus - 1 : 1) * get_coefficient(simplex) % modulus; return diameter_entry_t(cofacet_diameter, cofacet_index, cofacet_coefficient); } }; template <> class ripser::simplex_coboundary_enumerator { index_t idx_below, idx_above, k; std::vector vertices; diameter_entry_t simplex; const coefficient_t modulus; const sparse_distance_matrix& dist; const binomial_coeff_table& binomial_coeff; std::vector::const_reverse_iterator> neighbor_it; std::vector::const_reverse_iterator> neighbor_end; index_diameter_t neighbor; const ripser& parent; public: simplex_coboundary_enumerator(const diameter_entry_t _simplex, const index_t _dim, const ripser& _parent) : modulus(_parent.modulus), dist(_parent.dist), binomial_coeff(_parent.binomial_coeff), parent(_parent) { if (get_index(_simplex) != -1) set_simplex(_simplex, _dim); } simplex_coboundary_enumerator(const ripser& _parent) : modulus(_parent.modulus), dist(_parent.dist), binomial_coeff(_parent.binomial_coeff), parent(_parent) {} void set_simplex(const diameter_entry_t _simplex, const index_t _dim) { idx_below = get_index(_simplex); idx_above = 0; k = _dim + 1; simplex = _simplex; vertices.resize(_dim + 1); parent.get_simplex_vertices(idx_below, _dim, parent.n, vertices.rbegin()); neighbor_it.resize(_dim + 1); neighbor_end.resize(_dim + 1); for (index_t i = 0; i <= _dim; ++i) { auto v = vertices[i]; neighbor_it[i] = dist.neighbors[v].rbegin(); neighbor_end[i] = dist.neighbors[v].rend(); } } bool has_next(bool all_cofacets = true) { for (auto &it0 = neighbor_it[0], &end0 = neighbor_end[0]; it0 != end0; ++it0) { neighbor = *it0; for (size_t idx = 1; idx < neighbor_it.size(); ++idx) { auto &it = neighbor_it[idx], end = neighbor_end[idx]; while (get_index(*it) > get_index(neighbor)) if (++it == end) return false; if (get_index(*it) != get_index(neighbor)) goto continue_outer; else neighbor = std::max(neighbor, *it); } while (k > 0 && vertices[k - 1] > get_index(neighbor)) { if (!all_cofacets) return false; idx_below -= binomial_coeff(vertices[k - 1], k); idx_above += binomial_coeff(vertices[k - 1], k + 1); --k; } return true; continue_outer:; } return false; } diameter_entry_t next() { ++neighbor_it[0]; value_t cofacet_diameter = std::max(get_diameter(simplex), get_diameter(neighbor)); index_t cofacet_index = idx_above + binomial_coeff(get_index(neighbor), k + 1) + idx_below; coefficient_t cofacet_coefficient = (k & 1 ? modulus - 1 : 1) * get_coefficient(simplex) % modulus; return diameter_entry_t(cofacet_diameter, cofacet_index, cofacet_coefficient); } }; template <> std::vector ripser::get_edges() { std::vector edges; std::vector vertices(2); for (index_t index = binomial_coeff(n, 2); index-- > 0;) { get_simplex_vertices(index, 1, dist.size(), vertices.rbegin()); value_t length = dist(vertices[0], vertices[1]); if (length <= threshold) edges.push_back({length, index}); } return edges; } template <> std::vector ripser::get_edges() { std::vector edges; for (index_t i = 0; i < n; ++i) for (auto n : dist.neighbors[i]) { index_t j = get_index(n); if (i > j) edges.push_back({get_diameter(n), get_edge_index(i, j)}); } return edges; } enum file_format { LOWER_DISTANCE_MATRIX, UPPER_DISTANCE_MATRIX, DISTANCE_MATRIX, POINT_CLOUD, DIPHA, SPARSE, BINARY }; static const uint16_t endian_check(0xff00); static const bool is_big_endian = *reinterpret_cast(&endian_check); template T read(std::istream& input_stream) { T result; char* p = reinterpret_cast(&result); if (input_stream.read(p, sizeof(T)).gcount() != sizeof(T)) return T(); if (is_big_endian) std::reverse(p, p + sizeof(T)); return result; } euclidean_distance_matrix read_point_cloud(std::istream& input_stream) { std::vector> points; std::string line; value_t value; while (std::getline(input_stream, line)) { std::vector point; std::istringstream s(line); while (s >> value) { point.push_back(value); s.ignore(); } if (!point.empty()) points.push_back(point); assert(point.size() == points.front().size()); } euclidean_distance_matrix eucl_dist(std::move(points)); index_t n = eucl_dist.size(); std::cout << "point cloud with " << n << " points in dimension " << eucl_dist.points.front().size() << std::endl; return eucl_dist; } sparse_distance_matrix read_sparse_distance_matrix(std::istream& input_stream) { std::vector> neighbors; index_t num_edges = 0; std::string line; while (std::getline(input_stream, line)) { std::istringstream s(line); size_t i, j; value_t value; s >> i; s >> j; s >> value; if (i != j) { neighbors.resize(std::max({neighbors.size(), i + 1, j + 1})); neighbors[i].push_back({j, value}); neighbors[j].push_back({i, value}); ++num_edges; } } for (size_t i = 0; i < neighbors.size(); ++i) std::sort(neighbors[i].begin(), neighbors[i].end()); return sparse_distance_matrix(std::move(neighbors), num_edges); } compressed_lower_distance_matrix read_lower_distance_matrix(std::istream& input_stream) { std::vector distances; value_t value; while (input_stream >> value) { distances.push_back(value); input_stream.ignore(); } return compressed_lower_distance_matrix(std::move(distances)); } compressed_lower_distance_matrix read_upper_distance_matrix(std::istream& input_stream) { std::vector distances; value_t value; while (input_stream >> value) { distances.push_back(value); input_stream.ignore(); } return compressed_lower_distance_matrix(compressed_upper_distance_matrix(std::move(distances))); } compressed_lower_distance_matrix read_distance_matrix(std::istream& input_stream) { std::vector distances; std::string line; value_t value; for (int i = 0; std::getline(input_stream, line); ++i) { std::istringstream s(line); for (int j = 0; j < i && s >> value; ++j) { distances.push_back(value); s.ignore(); } } return compressed_lower_distance_matrix(std::move(distances)); } compressed_lower_distance_matrix read_dipha(std::istream& input_stream) { if (read(input_stream) != 8067171840) { std::cerr << "input is not a Dipha file (magic number: 8067171840)" << std::endl; exit(-1); } if (read(input_stream) != 7) { std::cerr << "input is not a Dipha distance matrix (file type: 7)" << std::endl; exit(-1); } index_t n = read(input_stream); std::vector distances; for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j) if (i > j) distances.push_back(read(input_stream)); else read(input_stream); return compressed_lower_distance_matrix(std::move(distances)); } compressed_lower_distance_matrix read_binary(std::istream& input_stream) { std::vector distances; while (!input_stream.eof()) distances.push_back(read(input_stream)); return compressed_lower_distance_matrix(std::move(distances)); } compressed_lower_distance_matrix read_file(std::istream& input_stream, const file_format format) { switch (format) { case LOWER_DISTANCE_MATRIX: return read_lower_distance_matrix(input_stream); case UPPER_DISTANCE_MATRIX: return read_upper_distance_matrix(input_stream); case DISTANCE_MATRIX: return read_distance_matrix(input_stream); case POINT_CLOUD: return read_point_cloud(input_stream); case DIPHA: return read_dipha(input_stream); default: return read_binary(input_stream); } } void print_usage_and_exit(int exit_code) { std::cerr << "Usage: " << "ripser " << "[options] [filename]" << std::endl << std::endl << "Options:" << std::endl << std::endl << " --help print this screen" << std::endl << " --format use the specified file format for the input. Options are:" << std::endl << " lower-distance (lower triangular distance matrix; default)" << std::endl << " upper-distance (upper triangular distance matrix)" << std::endl << " distance (full distance matrix)" << std::endl << " point-cloud (point cloud in Euclidean space)" << std::endl << " dipha (distance matrix in DIPHA file format)" << std::endl << " sparse (sparse distance matrix in sparse triplet format)" << std::endl << " binary (lower triangular distance matrix in binary format)" << std::endl << " --dim compute persistent homology up to dimension k" << std::endl << " --threshold compute Rips complexes up to diameter t" << std::endl #ifdef USE_COEFFICIENTS << " --modulus

compute homology with coefficients in the prime field Z/pZ" << std::endl #endif << " --ratio only show persistence pairs with death/birth ratio > r" << std::endl << std::endl; exit(exit_code); } int main(int argc, char** argv) { const char* filename = nullptr; file_format format = DISTANCE_MATRIX; index_t dim_max = 1; value_t threshold = std::numeric_limits::max(); float ratio = 1; coefficient_t modulus = 2; for (index_t i = 1; i < argc; ++i) { const std::string arg(argv[i]); if (arg == "--help") { print_usage_and_exit(0); } else if (arg == "--dim") { std::string parameter = std::string(argv[++i]); size_t next_pos; dim_max = std::stol(parameter, &next_pos); if (next_pos != parameter.size()) print_usage_and_exit(-1); } else if (arg == "--threshold") { std::string parameter = std::string(argv[++i]); size_t next_pos; threshold = std::stof(parameter, &next_pos); if (next_pos != parameter.size()) print_usage_and_exit(-1); } else if (arg == "--ratio") { std::string parameter = std::string(argv[++i]); size_t next_pos; ratio = std::stof(parameter, &next_pos); if (next_pos != parameter.size()) print_usage_and_exit(-1); } else if (arg == "--format") { std::string parameter = std::string(argv[++i]); if (parameter.rfind("lower", 0) == 0) format = LOWER_DISTANCE_MATRIX; else if (parameter.rfind("upper", 0) == 0) format = UPPER_DISTANCE_MATRIX; else if (parameter.rfind("dist", 0) == 0) format = DISTANCE_MATRIX; else if (parameter.rfind("point", 0) == 0) format = POINT_CLOUD; else if (parameter == "dipha") format = DIPHA; else if (parameter == "sparse") format = SPARSE; else if (parameter == "binary") format = BINARY; else print_usage_and_exit(-1); #ifdef USE_COEFFICIENTS } else if (arg == "--modulus") { std::string parameter = std::string(argv[++i]); size_t next_pos; modulus = std::stol(parameter, &next_pos); if (next_pos != parameter.size() || !is_prime(modulus)) print_usage_and_exit(-1); #endif } else { if (filename) { print_usage_and_exit(-1); } filename = argv[i]; } } std::ifstream file_stream(filename); if (filename && file_stream.fail()) { std::cerr << "couldn't open file " << filename << std::endl; exit(-1); } if (format == SPARSE) { sparse_distance_matrix dist = read_sparse_distance_matrix(filename ? file_stream : std::cin); std::cout << "sparse distance matrix with " << dist.size() << " points and " << dist.num_edges << "/" << (dist.size() * (dist.size() - 1)) / 2 << " entries" << std::endl; ripser(std::move(dist), dim_max, threshold, ratio, modulus) .compute_barcodes(); } else if (format == POINT_CLOUD && threshold < std::numeric_limits::max()) { sparse_distance_matrix dist(read_point_cloud(filename ? file_stream : std::cin), threshold); ripser(std::move(dist), dim_max, threshold, ratio, modulus) .compute_barcodes(); } else { compressed_lower_distance_matrix dist = read_file(filename ? file_stream : std::cin, format); value_t min = std::numeric_limits::infinity(), max = -std::numeric_limits::infinity(), max_finite = max; int num_edges = 0; value_t enclosing_radius = std::numeric_limits::infinity(); if (threshold == std::numeric_limits::max()) { for (size_t i = 0; i < dist.size(); ++i) { value_t r_i = -std::numeric_limits::infinity(); for (size_t j = 0; j < dist.size(); ++j) r_i = std::max(r_i, dist(i, j)); enclosing_radius = std::min(enclosing_radius, r_i); } } for (auto d : dist.distances) { min = std::min(min, d); max = std::max(max, d); if (d != std::numeric_limits::infinity()) max_finite = std::max(max_finite, d); if (d <= threshold) ++num_edges; } std::cout << "value range: [" << min << "," << max_finite << "]" << std::endl; if (threshold == std::numeric_limits::max()) { std::cout << "distance matrix with " << dist.size() << " points, using threshold at enclosing radius " << enclosing_radius << std::endl; ripser(std::move(dist), dim_max, enclosing_radius, ratio, modulus) .compute_barcodes(); } else { std::cout << "sparse distance matrix with " << dist.size() << " points and " << num_edges << "/" << (dist.size() * dist.size() - 1) / 2 << " entries" << std::endl; ripser(sparse_distance_matrix(std::move(dist), threshold), dim_max, threshold, ratio, modulus) .compute_barcodes(); } exit(0); } } ripser-1.2.1/robin-hood-hashing/000077500000000000000000000000001402706754100165045ustar00rootroot00000000000000