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# Witness_complex #
For more details about the witness complex, please read the [user manual of the package](http://gudhi.gforge.inria.fr/doc/latest/group__witness__complex.html).
## `weak_witness_persistence` ##
This program computes the persistent homology with coefficient field *Z/pZ* of a Weak witness 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.
*Usage*
`weak_witness_persistence [options] <OFF input file>`
*Allowed options*
* `-h [ --help ]` Produce help message
* `-l [ --landmarks ]` Number of landmarks to choose from the point cloud.
* `-o [ --output-file ]` Name of file in which the persistence diagram is written. By default, print in std::cout.
* `-a [ --max-sq-alpha ]` (default = inf) Maximal squared relaxation parameter.
* `-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.
* `-d [ --cpx-dimension ]` (default = 2147483647) Maximal dimension of the weak witness complex we want to compute.
*Example*
`weak_witness_persistence data/points/tore3D_1307.off -l 20 -a 0.5 -m 0.006`
outputs:
```
Successfully read 1307 points.
Ambient dimension is 3.
The complex contains 732 simplices and has dimension 8
11 0 0 inf
11 1 0 inf
11 2 0.0275251 0.0534586
11 1 0 0.0239952
```
N.B.: output is random as the 20 landmarks are chosen randomly.
## `strong_witness_persistence` ##
This program computes the persistent homology with coefficient field *Z/pZ* of a Strong witness 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.
*Usage*
`strong_witness_persistence [options] <OFF input file>`
*Allowed options*
* `-h [ --help ]` Produce help message
* `-l [ --landmarks ]` Number of landmarks to choose from the point cloud.
* `-o [ --output-file ]` Name of file in which the persistence diagram is written. By default, print in std::cout.
* `-a [ --max-sq-alpha ]` (default = inf) Maximal squared relaxation parameter.
* `-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.
* `-d [ --cpx-dimension ]` (default = 2147483647) Maximal dimension of the weak witness complex we want to compute.
*Example*
`strong_witness_persistence data/points/tore3D_1307.off -l 20 -a 0.5 -m 0.06`
outputs:
```
Successfully read 1307 points.
Ambient dimension is 3.
The complex contains 1836 simplices and has dimension 8
11 0 0 inf
11 1 0.00674748 inf
11 2 0.0937751 0.235354
```
N.B.: output is random as the 20 landmarks are chosen randomly.
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