permaviss.simplicial_complexes.vietoris_rips

vietoris_rips.py

Functions

vietoris_rips(Dist, max_r, max_dim)

This computes the Vietoris-Rips complex with simplexes of dimension less or equal to max_dim, and with maximum radius specified by max_r

permaviss.simplicial_complexes.vietoris_rips._lower_neighbours(G, u)

Given a graph G and a vertex u in G, we return a list with the vertices in G that are lower than u and are connected to u by an edge in G.

Parameters:

• G (Numpy Array(no. of edges, 2)) – Matrix storing the edges of the graph.
• u (int) – Vertex of the graph.

Returns:

lower_neighbours – List of lower neighbours of u in G.

Return type:

list

permaviss.simplicial_complexes.vietoris_rips.vietoris_rips(Dist, max_r, max_dim)

This computes the Vietoris-Rips complex with simplexes of dimension less or equal to max_dim, and with maximum radius specified by max_r

Parameters:

• Dist (Numpy Array(no. of points, no. of points)) – Distance matrix of points.
• max_r (float) – Maximum radius of filtration.
• max_dim (int) – Maximum dimension of computed Rips complex.

Returns:

• C (list(Numpy Array)) – Vietoris Rips complex generated for the given parameters. List where the first entry stores the number of vertices, and all other entries contain a Numpy Array with the list of simplices in C.
• R (list(Numpy Array)) – List with radius of birth for the simplices in C. The i entry contains a 1D Numpy Array containing each of the birth radii for each i simplex in C.