Periodic cubical complex reference manual¶
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class
gudhi.
PeriodicCubicalComplex
¶ Bases:
object
The PeriodicCubicalComplex is an example of a structured complex useful in computational mathematics (specially rigorous numerics) and image analysis.
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__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.
- periodic_dimensions (list of boolean) – A list of top dimensional cells periodicity value.
Or
Parameters: perseus_file (string) – A Perseus-style file name.
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betti_numbers
()¶ This function returns the Betti numbers of the complex.
Returns: list of int – The Betti numbers ([B0, B1, …, Bn]). Note: betti_numbers function requires persistence function to be launched first. Note: betti_numbers function always returns [1, 0, 0, …] as infinity filtration cubes are not removed from the complex.
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dimension
()¶ This function returns the dimension of the complex.
Returns: int – the complex dimension.
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num_simplices
()¶ This function returns the number of all cubes in the complex.
Returns: int – the number of all cubes in the complex.
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persistence
()¶ This function returns the persistence of the 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 complex.
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persistence_intervals_in_dimension
()¶ This function returns the persistence intervals of the complex in a specific dimension.
Parameters: dimension (int.) – The specific dimension. Returns: The persistence intervals. Return type: numpy array of dimension 2 Note: intervals_in_dim function requires persistence function to be launched first.
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persistent_betti_numbers
()¶ This function returns the persistent Betti numbers of the 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.
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