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)[source]¶ 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
- G (
-
permaviss.simplicial_complexes.vietoris_rips.
vietoris_rips
(Dist, max_r, max_dim)[source]¶ 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 aNumpy 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 1DNumpy Array
containing each of the birth radii for each i simplex in C.
- Dist (