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
dim is the dimension of the homological feature,
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>
-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