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diff --git a/src/Rips_complex/utilities/ripscomplex.md b/src/Rips_complex/utilities/ripscomplex.md new file mode 100644 index 00000000..6df49310 --- /dev/null +++ b/src/Rips_complex/utilities/ripscomplex.md @@ -0,0 +1,109 @@ +--- +layout: page +title: "Rips complex" +meta_title: "Rips complex" +teaser: "" +permalink: /ripscomplex/ +--- +{::comment} +Leave the lines above as it is required by the web site generator 'Jekyll' +{:/comment} + + +## rips_persistence ## +This program computes the persistent homology with coefficient field *Z/pZ* of a Rips 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** + +`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` + +**Example 2 with Z/3Z coefficients** + +`rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3` + + +## rips_distance_matrix_persistence ## + +Same as `rips_persistence` but taking a distance matrix as input. + +**Usage** + +`rips_distance_matrix_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 ';'. +The code do not check if it is dealing with a distance matrix. It is the user responsibility to provide a valid input. +Please refer to data/distance_matrix/lower_triangular_distance_matrix.csv for an example of a file. + +**Example** + +`rips_distance_matrix_persistence data/distance_matrix/full_square_distance_matrix.csv -r 15 -d 3 -p 3 -m 0` + + +## rips_correlation_matrix_persistence ## + +Same as `rips_distance_matrix_persistence` but taking a correlation matrix as input. + +**Usage** + +`rips_correlation_matrix_persistence [options] <CSV input file>` + +where +`<CSV input file>` is the path to the file containing a correlation matrix. Can be square or lower triangular matrix. Separator is ';'. +Note that no check is performed if the matrix given as the input is a correlation matrix. +It is the user responsibility to ensure that this is the case. +Please refer to data/correlation_matrix/lower_triangular_correlation_matrix.csv for an example of a file. + +**Example** + +`rips_correlation_matrix_persistence data/distance_matrix/full_square_distance_matrix.csv -r 15 -d 3 -p 3 -m 0` + +**Warning** + +As persistence diagrams points will be under the diagonal, bottleneck distance and persistence graphical tool will not work +properly, this is a known issue. + + +## sparse_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 Euclidean 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** + +`sparse_rips_persistence ../../data/points/tore3D_1307.off -e .5 -m .2 -d 3 -p 2` |