Čech complex

Čech complex


This program computes the persistent homology with coefficient field Z/pZ of a Čech complex defined on a set of input points, using Euclidean distance. 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).


cech_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 Čech complex construction.
  • -d [ --cpx-dimension ] (default = 1) Maximal dimension of the Čech 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

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

Example 2 with Z/3Z coefficients

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