1.5. Lower Star Filtration for Simplicial Complexes

This is the Lower Star Filtration class for Simplicial Complexes. It is built on top of Gudhi’s SimplexTree structure. It allows for the assignment of a lower star filtration based on a function defined on the vertices of the simplicial complex.

Note that this class can be imported as:

import cereeberus
T = cereeberus.LowerStarSC()

class cereeberus.reeb.lowerstarSC.LowerStarSC

Class to create a simplicial compex that has a lower star filtration, based on Gudhi’s SimplexTree.

Inherits from:

SimplexTree: A simplex tree structure from the Gudhi library.

__init__()

Initializes the simplex tree.

__init__()

Initialize class. Due to SimplexTree C++ weirdness, this does nothing but initialize the instance.

assign_filtration(vertex, value)

Sets the filtration value for a given vertex. Vertex can be provided either as an integer, or as a single integer in a list representing the integer label of the vertex.

Parameters:

• vertex (Union[int, tuple]) – Name of the vertex (an integer or a single-element list).

• value (float) – Filtration value to set.

max_filtration()

Returns the maximum filtration value among all simplices in the torus.

Returns:

Maximum filtration value.

Return type:

float

min_filtration()

Returns the minimum filtration value among all simplices in the torus.

Returns:

Minimum filtration value.

Return type:

float

assign_random_values(min, max, seed=None)

Assign uniform random filtrations sampled in (min, max) for all vertices.

Parameters:

• min (float) – Minimum value for random function values

• max (float) – Maximum value for random function value

• seed (int, optional) – Random seed for reproducibility. Default is None.

num_vertices()

Return the number of vertices (0-simplices) in the simplex tree.

iter_vertices()

Yield the names (tuples) of all vertices (0-simplices) in the simplex tree.