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# Ripser
Copyright © 2015–2016 [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.
The main features of Ripser:
- time- and memory-efficient
- support for coefficients in prime finite fields
- less than 1000 lines of code in a single C++ file
- no external dependencies (optional support for Google's [sparsehash])
Currently, Ripser outperforms other codes ([Dionysus], [DIPHA], [GUDHI], [Perseus], [PHAT]) by a factor of at least 40 in computation time and a factor of at least 15 in memory efficiency. (Note that [PHAT] does not contain code for generating Vietoris–Rips filtrations).
Input formats currently supported by Ripser:
- comma-separated lower triangular distance matrix (preferred)
- comma-separated lower triangular distance matrix (MATLAB output from the function `pdist`)
- [DIPHA] distance matrix data
Ripser's efficiency is based on a few important concepts and principles:
- Compute persistent *co*homology
- 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*)
### Version
[Latest release][latest-release]: 1.0 (July 2016)
### 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:
- `ASSEMBLE_REDUCTION_MATRIX`: store the reduction matrix; may speed up computation but will also increase memory usage
- `USE_COEFFICIENTS`: enable support for coeffitients in a prime field
- `INDICATE_PROGRESS`: indicate the current progress in the console
- `PRINT_PERSISTENCE_PAIRS`: output the computed persistence pairs (enabled by default)
- `USE_GOOGLE_HASHMAP`: enable support for Google's [sparsehash] data structure; may further reducue memory footprint
Furthermore, one of the following options needs to be chosen to specify the format for the input files:
- `FILE_FORMAT_LOWER_TRIANGULAR_CSV`: lower triangular distance matrix; a comma separated list of the distance matrix entries below the diagonal, sorted lexicographically by row index and column index
- `FILE_FORMAT_UPPER_TRIANGULAR_CSV`: upper triangular distance matrix; similar to the previous, but for the entries above the diagonal; suitable for output from the MATLAB function `pdist`, saved in a CSV file
- `FILE_FORMAT_DIPHA`: DIPHA distance matrix as described on the [DIPHA] website
For example, to build with support for coefficients:
```sh
$ c++ -std=c++11 ripser.cpp -o ripser -Ofast -D NDEBUG -D FILE_FORMAT_LOWER_TRIANGULAR_CSV -D USE_COEFFICIENTS
```
The following options are supported at the command line:
- `--top_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 build with the option `USE_COEFFICIENTS`)
### Planned features
The following features are currently planned for future versions:
- support for point clouds
- computation of representative cycles for persistent homology (currenly only *co*cycles are computed)
- support for sparse distance matrices
### License
[LGPL] 3.0
[Ulrich Bauer]: <http://ulrich-bauer.org>
[latest-release]: <https://github.com/Ripser/ripser/releases/latest>
[Dionysus]: <http://www.mrzv.org/software/dionysus/>
[DIPHA]: <http://git.io/dipha>
[PHAT]: <http://git.io/dipha>
[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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