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diff --git a/src/Rips_complex/utilities/README b/src/Rips_complex/utilities/README new file mode 100644 index 00000000..390e31f8 --- /dev/null +++ b/src/Rips_complex/utilities/README @@ -0,0 +1,110 @@ +# Rips_complex # + +## `rips_persistence` ## +This program computes the persistent homology with coefficient field *Z/pZ* of a Rips complex defined on a set of input points. 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** +`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. + +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** +`rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 2` + +outputs: +``` +2 0 0 inf +2 1 0.0983494 inf +2 1 0.104347 inf +2 2 0.138335 inf +``` + +**Example 2 with Z/3Z coefficients** + +rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3 + +outputs: +``` +3 0 0 inf +3 1 0.0983494 inf +3 1 0.104347 inf +3 2 0.138335 inf +``` + + + + +## `rips_distance_matrix_persistence` ## +Same as `rips_persistence` but taking a distance matrix as input.
+
+**Usage** +`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 ';'. + +**Example** +`rips_distance_matrix_persistence data/distance_matrix/full_square_distance_matrix.csv -r 15 -d 3 -p 3 -m 0` + +outputs: +``` +The complex contains 46 simplices + and has dimension 3 +3 0 0 inf +3 0 0 8.94427 +3 0 0 7.28011 +3 0 0 6.08276 +3 0 0 5.83095 +3 0 0 5.38516 +3 0 0 5 +3 1 11 12.0416 +3 1 6.32456 6.7082 +``` + + + + +## `rips_persistence` ## +This program computes the persistent homology with coefficient field *Z/pZ* +of a sparse (1+epsilon)-approximation of the Rips complex defined on a set of input points. 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** +`sparse_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. +* `-e [ --approximation ]` (default = .5) Epsilon, where the sparse Rips complex is a (1+epsilon)-approximation of the Rips complex. +* `-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. + +**Example with Z/2Z coefficients** +`rips_persistence ../../data/points/tore3D_1307.off -e .5 -m .2 -d 3 -p 2` + +may output (there is randomness involved): +``` +The complex contains 17002096 simplices + and has dimension 3 +2 0 0 inf +2 1 0.104347 1.29343 +2 2 0.138335 0.577743 +2 1 0.0983494 0.529708 +``` |