# 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] ` *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] ` *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.