Rips complex reference manual#

class gudhi.RipsComplex#

Bases: object

The data structure is a one skeleton graph, or Rips graph, containing edges when the edge length is less or equal to a given threshold. Edge length is computed from a user given point cloud with a given distance function, or a distance matrix.

__init__()#

RipsComplex constructor.

Parameters:: points¶ (List[List[float]]) – A list of points in d-Dimension.

Or

Parameters:: distance_matrix¶ (List[List[float]]) – A distance matrix (full square or lower triangular).

And in both cases

Parameters:

max_edge_length¶ (float) – Maximal edge length. All edges of the graph strictly greater than threshold are not inserted in the graph.
sparse¶ (float) – If this is not None, it switches to building a sparse Rips and represents the approximation parameter epsilon.

__new__(**kwargs)#

create_simplex_tree()#

Parameters:: max_dimension¶ (int) – graph expansion for Rips until this given maximal dimension.
Returns:: A simplex tree encoding the Vietoris–Rips filtration.
Return type:: SimplexTree

Weighted Rips complex reference manual#

class gudhi.weighted_rips_complex.WeightedRipsComplex[source]#

Bases: object

Class to generate a weighted Rips complex from a distance matrix and weights on vertices, in the way described in [1] with p=1. The filtration value of vertex i is 2*weights[i], and the filtration value of edge ij is distance_matrix[i][j]+weights[i]+weights[j], or the maximum of the filtrations of its extremities, whichever is largest. Remark that all the filtration values are doubled compared to the definition in the paper for consistency with RipsComplex.

__init__(distance_matrix, weights=None, max_filtration=inf)[source]#

Parameters:

distance_matrix¶ (Sequence[Sequence[float]]) – distance matrix (full square or lower triangular).
weights¶ (Sequence[float]) – (one half of) weight for each vertex.
max_filtration¶ (float) – specifies the maximal filtration value to be considered.

create_simplex_tree(max_dimension)[source]#

Parameters:: max_dimension¶ (int) – graph expansion until this given dimension.

DTM Rips complex reference manual#

class gudhi.dtm_rips_complex.DTMRipsComplex[source]#

Bases: WeightedRipsComplex

Class to generate a DTM Rips complex from a distance matrix or a point set, in the way described in [1]. Remark that all the filtration values are doubled compared to the definition in the paper for the consistency with RipsComplex.

Requires:: SciPy

__init__(points=None, distance_matrix=None, k=1, q=2, max_filtration=inf)[source]#

Parameters:

points¶ (numpy.ndarray) – array of points.
distance_matrix¶ (numpy.ndarray) – full distance matrix.
k¶ (int) – number of neighbors for the computation of DTM. Defaults to 1, which is equivalent to the usual Rips complex.
q¶ (float) – order used to compute the distance to measure. Defaults to 2.
max_filtration¶ (float) – specifies the maximal filtration value to be considered.