Struct VietorisRipsComplex 

pub struct VietorisRipsComplex {
    pub points: Vec<Vec<f64>>,
    pub epsilon: f64,
    pub simplices: Vec<Vec<usize>>,
}

A Vietoris-Rips simplicial complex at a fixed scale epsilon.

Unlike VietorisRips (which computes the full persistent homology across all scales), this struct stores the explicit list of simplices formed when all pairwise distances ≤ epsilon.

Example

use scirs2_transform::tda_ext::VietorisRipsComplex;

let pts = vec![
    vec![0.0, 0.0],
    vec![1.0, 0.0],
    vec![1.0, 1.0],
    vec![0.0, 1.0],
];
let vrc = VietorisRipsComplex::new(&pts, 1.5).expect("should succeed");
assert!(vrc.n_simplices(0) == 4); // four 0-simplices (vertices)
assert!(vrc.euler_characteristic() != 0); // non-trivial topology

Fields

points: Vec<Vec<f64>>

Input point cloud

epsilon: f64

Scale parameter (all edges with length ≤ epsilon are included)

simplices: Vec<Vec<usize>>

All simplices (sorted by dimension then by vertex tuple)

Implementations

impl VietorisRipsComplex

pub fn new(points: &[Vec<f64>], epsilon: f64) -> Result<Self>

Construct the Vietoris-Rips complex for the given point cloud at scale epsilon.

Only simplices up to dimension 2 (triangles) are computed for tractability.

Arguments

• points — slice of point vectors (all of equal length)
• epsilon — maximum edge length to include

pub fn n_simplices(&self, dim: usize) -> usize

Count the number of simplices of a given dimension.

Dimension 0 = vertices, 1 = edges, 2 = triangles.

pub fn euler_characteristic(&self) -> i64

Compute the Euler characteristic χ = Σ_k (-1)^k * C_k, where C_k is the number of k-simplices.

pub fn are_connected(&self, u: usize, v: usize) -> bool

Check whether two vertices are connected by an edge in the complex.

pub fn edges(&self) -> Vec<(usize, usize)>

List all edges (1-simplices) as pairs (u, v).

Trait Implementations

impl Clone for VietorisRipsComplex

fn clone(&self) -> VietorisRipsComplex

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for VietorisRipsComplex

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

Formats the value using the given formatter.