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# Rips_complex #
## `rips_persistence` ##
This program computes the persistent homology with coefficient field *Z/pZ* of a Rips complex defined on a set of input points. The output diagram contains one bar per line, written with the convention:
`p dim birth death`
where `dim` is the dimension of the homological feature, `birth` and `death` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p` must be a prime number).
**Usage**
`rips_persistence [options] <OFF input file>`
**Allowed options**
* `-h [ --help ]` Produce help message
* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
* `-r [ --max-edge-length ]` (default = inf) Maximal length of an edge for the Rips complex construction.
* `-d [ --cpx-dimension ]` (default = 1) Maximal dimension of the Rips complex we want to compute.
* `-p [ --field-charac ]` (default = 11) Characteristic p of the coefficient field Z/pZ for computing homology.
* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.
Beware: this program may use a lot of RAM and take a lot of time if `max-edge-length` is set to a large value.
**Example 1 with Z/2Z coefficients**
`rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 2`
outputs:
```
2 0 0 inf
2 1 0.0983494 inf
2 1 0.104347 inf
2 2 0.138335 inf
```
**Example 2 with Z/3Z coefficients**
rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3
outputs:
```
3 0 0 inf
3 1 0.0983494 inf
3 1 0.104347 inf
3 2 0.138335 inf
```
## `rips_distance_matrix_persistence` ##
Same as `rips_persistence` but taking a distance matrix as input.
**Usage**
`rips_persistence [options] <CSV input file>`
where
`<CSV input file>` is the path to the file containing a distance matrix. Can be square or lower triangular matrix. Separator is ';'.
**Example**
`rips_distance_matrix_persistence data/distance_matrix/full_square_distance_matrix.csv -r 15 -d 3 -p 3 -m 0`
outputs:
```
The complex contains 46 simplices
and has dimension 3
3 0 0 inf
3 0 0 8.94427
3 0 0 7.28011
3 0 0 6.08276
3 0 0 5.83095
3 0 0 5.38516
3 0 0 5
3 1 11 12.0416
3 1 6.32456 6.7082
```
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