Struct TopologicalDataAnalysis 

pub struct TopologicalDataAnalysis {
    pub point_cloud: Vec<Vec<f64>>,
}

Topological Data Analysis tools for point clouds.

Provides Vietoris–Rips and Čech complex construction, and Wasserstein distance between persistence diagrams.

Fields

point_cloud: Vec<Vec<f64>>

Input point cloud: list of d-dimensional points.

Implementations

impl TopologicalDataAnalysis

pub fn new(point_cloud: Vec<Vec<f64>>) -> Self

Create a new TDA object from a point cloud.

pub fn vietoris_rips(&self, epsilon: f64) -> SimplicialComplex

Build the Vietoris–Rips complex at scale epsilon.

An edge is added between two points whose distance is ≤ epsilon. Higher-dimensional simplices are added as cliques.

pub fn cech_complex(&self, epsilon: f64) -> SimplicialComplex

Build the Čech complex at scale epsilon.

A k-simplex {v_0,…,v_k} is included if the minimum enclosing ball of the k+1 points has radius ≤ epsilon.

pub fn wasserstein_distance(d1: &[(f64, f64)], d2: &[(f64, f64)]) -> f64

Compute the p=1 Wasserstein distance between two persistence diagrams.

d1 and d2 are lists of (birth, death) points. Uses linear assignment heuristic for matching.

Trait Implementations

impl Clone for TopologicalDataAnalysis

fn clone(&self) -> TopologicalDataAnalysis

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for TopologicalDataAnalysis

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.