Witness complex

For more details about the witness complex, please read the user manual of the package.

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

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

N.B.: output is random as the 20 landmarks are chosen randomly.