Module topological_data 

Topological Data Analysis (TDA) — persistent homology utilities.

Provides Vietoris–Rips filtration for 0- and 1-dimensional persistent homology, bottleneck and Wasserstein distances between persistence diagrams, Betti numbers, Euler characteristic, cubical complexes, and persistence entropy.

Structured types: VietorisRips, SimplexTree, PersistenceDiagram, BarcodeSummary, and MapperGraph.

Structs

BarcodeSummary

Summary statistics derived from a persistence barcode.

BettiNumbers

Betti numbers β₀, β₁, β₂ of a topological space.

FilteredSimplex

A simplex with its filtration value.

MapperGraph

Mapper graph: nodes (clusters) connected when adjacent cover intervals share common points.

MapperNode

A node in a Mapper graph.

PersistenceDiagram

A persistence diagram: a collection of birth-death pairs.

PersistentInterval

A bar in a persistence diagram: [birth, death) for homology class H_k.

SimplexEdge

A weighted undirected edge in a simplicial filtration.

SimplexTree

Simplex tree data structure for filtration-based TDA.

UnionFind

Union–Find (disjoint-set) data structure for Kruskal’s algorithm.

VietorisRips

Vietoris–Rips complex construction from a 2-D point cloud.

Functions

bottleneck_distance

Bottleneck distance between two persistence diagrams.

cubical_complex_1d

Compute Betti numbers of the sublevel set {x : signal[i] ≤ threshold}.

euler_characteristic

Euler characteristic χ = β₀ − β₁ + β₂.

persistence_entropy

Entropy of a persistence diagram.

vietoris_rips_h0

Compute 0-dimensional persistent homology of the Vietoris–Rips filtration up to max_r using Kruskal’s algorithm.

vietoris_rips_h1_approx

Approximate 1-dimensional persistent homology (loops) of the Vietoris–Rips filtration.

wasserstein_distance_1

1-Wasserstein (Earth Mover’s) distance between two persistence diagrams.