Periodic cubical complex reference manual

class gudhi.PeriodicCubicalComplex

Bases: object

The PeriodicCubicalComplex is an example of a structured complex useful in computational mathematics (specially rigorous numerics) and image analysis.

__init__()

PeriodicCubicalComplex constructor from dimensions and top_dimensional_cells or from a Perseus-style file name.

Parameters:

• dimensions (list of int) – A list of number of top dimensional cells.
• top_dimensional_cells (list of double) – A list of cells filtration values.

Or

Parameters:perseus_file (string) – A Perseus-style file name.

betti_numbers()

This function returns the Betti numbers of the simplicial complex.

Returns:list of int – The Betti numbers ([B0, B1, ..., Bn]). Note:betti_numbers function requires persistence function to be launched first.

dimension()

This function returns the dimension of the simplicial complex.

Returns:int – the simplicial complex dimension.

num_simplices()

This function returns the number of simplices of the simplicial complex.

Returns:int – the simplicial complex number of simplices.

persistence()

This function returns the persistence of the simplicial complex.

Parameters:

• homology_coeff_field (int.) – The homology coefficient field. Must be a prime number
• min_persistence (float.) – The minimum persistence value to take into account (strictly greater than min_persistence). Default value is 0.0. Sets min_persistence to -1.0 to see all values.

Returns:

list of pairs(dimension, pair(birth, death)) – the persistence of the simplicial complex.

persistence_intervals_in_dimension()

This function returns the persistence intervals of the simplicial complex in a specific dimension.

Parameters:dimension – The specific dimension. Returns:The persistence intervals. Return type:list of pair of float Note:intervals_in_dim function requires persistence function to be launched first.

persistent_betti_numbers()

This function returns the persistent Betti numbers of the simplicial complex.

Parameters:

• from_value (float.) – The persistence birth limit to be added in the numbers (persistent birth <= from_value).
• to_value (float.) – The persistence death limit to be added in the numbers (persistent death > to_value).

Returns:

list of int – The persistent Betti numbers ([B0, B1, ..., Bn]).

Note:

persistent_betti_numbers function requires persistence function to be launched first.