Collapse

point_cloud_edge_collapse_rips_persistence

This program computes the Rips graph defined on a set of input points, using Euclidean distance, and collapses edges. This program finally computes persistent homology with coefficient field Z/pZ of the Rips complex built on top of these collapse edges. 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

point_cloud_edge_collapse_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.
  • -i [ --edge-collapse-iterations ] (default = 1) Number of iterations edge collapse is performed.

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

point_cloud_edge_collapse_rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 2

Example 2 with Z/3Z coefficients

point_cloud_edge_collapse_rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3

distance_matrix_edge_collapse_rips_persistence

Same as point_cloud_edge_collapse_rips_persistence but taking a distance matrix as input.

Usage

distance_matrix_edge_collapse_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 ‘;’. The code do not check if it is dealing with a distance matrix. It is the user responsibility to provide a valid input. Please refer to data/distance_matrix/lower_triangular_distance_matrix.csv for an example of a file.

Example

distance_matrix_edge_collapse_rips_persistence data/distance_matrix/full_square_distance_matrix.csv -r 15 -d 3 -p 3 -m 0

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