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+---
+layout: page
+title: "Collapse"
+meta_title: "Edge collapse"
+teaser: ""
+permalink: /collapse/
+---
+{::comment}
+Leave the lines above as it is required by the web site generator 'Jekyll'
+{:/comment}
+
+
+## point_cloud_edge_collapse_rips_persistence ##
+This program computes the Rips graph defined on a set of input points, using Euclidean distance, and collapses edges.
+This program finally computes persistent homology with coefficient field *Z/pZ* of the Rips complex built on top of these collapse edges.
+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**
+
+`point_cloud_edge_collapse_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.
+* `-i [ --edge-collapse-iterations ]` (default = 1) Number of iterations edge collapse is performed.
+
+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**
+
+`point_cloud_edge_collapse_rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 2`
+
+**Example 2 with Z/3Z coefficients**
+
+`point_cloud_edge_collapse_rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3`
+
+
+## distance_matrix_edge_collapse_rips_persistence ##
+
+Same as `point_cloud_edge_collapse_rips_persistence` but taking a distance matrix as input.
+
+**Usage**
+
+`distance_matrix_edge_collapse_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 ';'.
+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**
+
+`distance_matrix_edge_collapse_rips_persistence data/distance_matrix/full_square_distance_matrix.csv -r 15 -d 3 -p 3 -m 0`
+