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+# Witness_complex #
+
+## `weak_witness_persistence` ##
+This program computes the persistent homology with coefficient field *Z/pZ* of a Weak witness complex defined on a set of input points. The output diagram contains one bar per line, written with the convention:
+
+`p dim b d`
+
+where `dim` is the dimension of the homological feature, `b` and `d` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients.
+
+*Usage*
+`weak_witness_persistence [options] <OFF input file>`
+
+*Allowed options*
+
+* `-h [ --help ]` Produce help message
+* `-l [ --landmarks ]` Number of landmarks to choose from the point cloud.
+* `-o [ --output-file ]` Name of file in which the persistence diagram is written. By default, print in std::cout.
+* `-a [ --max-sq-alpha ]` (default = inf) Maximal squared relaxation parameter.
+* `-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.
+* `-d [ --cpx-dimension ]` (default = 2147483647) Maximal dimension of the weak witness complex we want to compute.
+
+*Example*
+`weak_witness_persistence data/points/tore3D_1307.off -l 20 -a 0.5 -m 0.006`
+
+outputs:
+```
+Successfully read 1307 points.
+Ambient dimension is 3.
+The complex contains 732 simplices and has dimension 8 
+11  0 0 inf 
+11  1 0 inf 
+11  2 0.0275251 0.0534586 
+11  1 0 0.0239952 
+```
+
+N.B.: output is random as the 20 landmarks are chosen randomly.
+
+## `strong_witness_persistence` ##
+This program computes the persistent homology with coefficient field *Z/pZ* of a Strong witness complex defined on a set of input points. The output diagram contains one bar per line, written with the convention:
+
+`p dim b d`
+
+where `dim` is the dimension of the homological feature, `b` and `d` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients.
+
+*Usage*
+`strong_witness_persistence [options] <OFF input file>`
+
+*Allowed options*
+
+* `-h [ --help ]` Produce help message
+* `-l [ --landmarks ]` Number of landmarks to choose from the point cloud.
+* `-o [ --output-file ]` Name of file in which the persistence diagram is written. By default, print in std::cout.
+* `-a [ --max-sq-alpha ]` (default = inf) Maximal squared relaxation parameter.
+* `-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.
+* `-d [ --cpx-dimension ]` (default = 2147483647) Maximal dimension of the weak witness complex we want to compute.
+
+*Example*
+`strong_witness_persistence data/points/tore3D_1307.off -l 20 -a 0.5 -m 0.06`
+
+outputs:
+```
+Successfully read 1307 points.
+Ambient dimension is 3.
+The complex contains 1836 simplices and has dimension 8 
+11  0 0 inf 
+11  1 0.00674748 inf 
+11  2 0.0937751 0.235354 
+```
+
+N.B.: output is random as the 20 landmarks are chosen randomly.