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@@ -1,13 +1,13 @@ # Ripser -Copyright © 2015–2016 [Ulrich Bauer]. +Copyright © 2015–2018 [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 [PNaCl] on Chrome and JavaScript via [Emscripten] on other browsers). +To see a live demo of Ripser's capabilities, go to [live.ripser.org]. The computation happens inside the browser (using [PNaCl] on Chrome and JavaScript via [Emscripten] on other browsers). The main features of Ripser: @@ -20,19 +20,20 @@ Currently, Ripser outperforms other codes ([Dionysus], [DIPHA], [GUDHI], [Perseu Input formats currently supported by Ripser: - - comma-separated values lower triangular distance matrix (preferred) + - 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 - point cloud data -Ripser's efficiency is based on a few important concepts and principles: +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 + - 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)) - Don't compute information that is never needed - (for the experts: employ the *clearing* optimization, aka *persistence with a twist*) - - Don't store information that can be readily recomputed - - Take obvious shortcuts (*apparent persistence pairs*) + (for the experts: 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)) + - Don't store information that can be readily recomputed (in particular, the boundary matrix and the reduced boundary matrix) + - Take computational shortcuts (*apparent* and *emergent persistence pairs*) + - 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)) ### Version @@ -72,14 +73,14 @@ A Makefile is provided with some variants of the above options. Use `make all` t 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` (default if no format is specified): 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`: full distance matrix; similar to the above, but for all entries of the distance matrix - - `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 - - `--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`) + - `lower-distance` (default if no format is specified): 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`: 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. + - `--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`). @@ -96,7 +97,7 @@ Prototype implementations are already avaliable; please contact the author if on ### License -Ripser is licensed under the [LGPL] 3.0. Please contact the author if you want to use Ripser in your software under a different 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. [Ulrich Bauer]: <http://ulrich-bauer.org> [live.ripser.org]: <http://live.ripser.org> @@ -109,4 +110,4 @@ Ripser is licensed under the [LGPL] 3.0. Please contact the author if you want t [Perseus]: <http://www.sas.upenn.edu/~vnanda/perseus/> [GUDHI]: <http://gudhi.gforge.inria.fr> [sparsehash]: <https://github.com/sparsehash/sparsehash> -[LGPL]: <https://www.gnu.org/licenses/lgpl>
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