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diff --git a/utilities/Cech_complex/cechcomplex.md b/utilities/Cech_complex/cechcomplex.md new file mode 100644 index 00000000..f7817dbb --- /dev/null +++ b/utilities/Cech_complex/cechcomplex.md @@ -0,0 +1,38 @@ + + +# Čech complex # + +## cech_persistence ## +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` |