persist_spatial.topology_utils

Functions

diagram_to_array(→ numpy.ndarray)

Converts a persistence diagram to a numpy array.

p_norm(→ float)

Computes the p-norm of a diagram given in array form. To be called upon by compute_persistence.run_persistence().

function_filtration(→ dionysus.Filtration)

Computes the upper star filtration given am adjacency structure and values at each vertex.

Module Contents

persist_spatial.topology_utils.diagram_to_array(diagram, dimension=0) → numpy.ndarray

Converts a persistence diagram to a numpy array.

Takes in a dionysus diagram object and returns a m x 2 numpy array with the birth and death times of each persistence feature of a given dimension in the diagram. Of the form

feature_1 feature_2 … feature_n

birth time . . … . death time . . … . To be called upon by compute_persistence.run_persistence().

Parameters:

  • diagram (List[d.Diagram]) – List of dionysus diagrams, one for each dimension.

  • dimension (int, default=0) – Which homology dimension to take the persistent features from.

Returns:

Array containing birth and death features for each feature in the specified dimension of the diagram. Dimensions 2 x n_features.

Return type:

np.ndarray

persist_spatial.topology_utils.p_norm(diagram: numpy.ndarray, p: int = 2) → float

Computes the p-norm of a diagram given in array form. To be called upon by compute_persistence.run_persistence().

Parameters:

  • diagram (np.ndarray) –

    Array containing birth and death times of features from a persistence diagram. Of the form

    feature_1 feature_2 … feature_n

    birth time . . … . death time . . … .

  • p (int, default=2:) – Which norm to compute.

Returns:

p-norm of the given diagram.

Return type:

float

persist_spatial.topology_utils.function_filtration(values: numpy.ndarray, edges: numpy.ndarray) → dionysus.Filtration

Computes the upper star filtration given am adjacency structure and values at each vertex.

Takes in an adjacency structure (which vertices are adjacent to each other) a list of function values at a set of vertices, and computes the upper star filtration for this function on the given network structure. In the resulting filtration,

  • index of each vertex = value of the function at that vertex

  • index of an edge = value of the function on the lowest vertex of the edge

Higher dimensional faces not included as they do not affect the 0D PH. To be called upon by compute_persistence.run_persistence().

Parameters:

  • values (np.ndarray) – Values of the function at each vertex. Dimensions n_vertices x 1

  • edges (np.ndarray) – A 2d matrix specfying which vertices are adjacent. Each row [a,b] specfies that a and b are adjacent, and adds the edge [a,b] to the simplex. Dimensions n_edges x 2.

Returns:

Simplex representing the function filtration.

Return type:

d.Filtration