layout: page title: "Čech complex" meta_title: "Čech complex" teaser: ""
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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).
Usage
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
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