DowkerComplex

This construction of the Dowker complex builds a Gudhi SimplexTree object based on a potentially asymmetric distance matrix and is taken directly from Niklas Hellmer and Jan Spalinski’s pyDowker, nihell/pyDowker. The DowkerComplex can then be fed into Gudhi’s persistent homology algorithm.

Usage:

complex = DowkerComplex(D)

D is the distance matrix, or more generally, the relation used to build the Dowker complex. In our case, this will be the distance matrix for the directed graph formed by binning the dynamical system.

class cactis.DowkerComplex(rel_matrix, max_filtration=inf)

Class MNeighborComplex. Constructs Dowker’s simplicial complex for a relation. Filtrations can be added using filtered relations, or total weight, or combining both into a bifiltration.

__init__(rel_matrix, max_filtration=inf) → None

_summary_ Constructor for the filtered Dowker complex from the relations given by sublevels of the matrix rel_matrix. The vertices in the complex will correspond to the rows of the matrix.

Parameters:

rel_matrix (Sequence[Sequence[float]]): distance matrix (full square or lower triangular).

max_filtration (float): specifies the maximal filtration value to be considered.