cechmate.filtrations.Extended

class cechmate.filtrations.Extended(simplices, f)

This class computed the extended persistence of a simplicial complex. It requires input as a simplicial complex and a mapping on each vertex in the complex. It returns a dictionary storing the associated diagrams in each homology class.

The basic steps are to:

• convert an abstract simplicial complex to the correct boundary matrix, using the lower-star up pass and upper-star down pass

• read the reduced boundary matrix into birth-death pairs.

• partition pairs into respective Ordinary/Extended/Relative diagrams.

References

Cohen-Steiner, David, Herbert Edelsbrunner, and John Harer. “Extending persistence using Poincaré and Lefschetz duality.” Foundations of Computational Mathematics 9.1 (2009): 79-103.

__init__(simplices, f)

Initialize Extended persistence class.

Parameters

• simplices (List[List]) – Simplices

• f (dictionary mapping name of vertex to value.) –

Methods

__init__(simplices, f)	Initialize Extended persistence class.
diagrams()	Compute diagrams of extended persistent homology for a simplicial complex simplices and function f.
from_kmapper(graph, f)	Construct Extended object from a Kepler Mapper graph output
from_nx(graph, f)	Construct Extended object from an nx.Graph object.