layout: page title: "Witness complex" meta_title: "Witness complex" teaser: ""
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For more details about the witness complex, please read the user manual of the package.
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 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.
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::clog.-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
N.B.: output is random as the 20 landmarks are chosen randomly.
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 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.
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::clog.-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
N.B.: output is random as the 20 landmarks are chosen randomly.
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