# 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. [Ulrich Bauer]: [live.ripser.org]: [Emscripten]: [WebAssembly]: [latest-release]: [Dionysus]: [DIPHA]: [PHAT]: [Perseus]: [GUDHI]: [robinhoodhash]: [MIT]: