Struct SimplicialComplex 

pub struct SimplicialComplex {
    pub simplices: Vec<Vec<usize>>,
    pub n_vertices: usize,
}

A simplicial complex defined by a collection of simplices over a vertex set.

A simplex is a list of vertex indices; e.g., [0,1,2] is a triangle. The complex automatically includes all faces (sub-simplices) when a simplex is added.

Fields

simplices: Vec<Vec<usize>>

All simplices stored as sorted vertex-index lists.

n_vertices: usize

Number of vertices (0-simplices) in the complex.

Implementations

impl SimplicialComplex

pub fn new(n_vertices: usize) -> Self

Create an empty simplicial complex with n_vertices vertices.

pub fn add_simplex(&mut self, simplex: &[usize])

Add a simplex (and all its faces) to the complex.

simplex is a slice of vertex indices. Duplicate simplices are ignored.

pub fn k_simplices(&self, k: usize) -> Vec<&Vec<usize>>

Return all k-simplices (simplices of dimension k).

pub fn boundary_operator(&self, k: usize) -> Vec<Vec<i32>>

Compute the boundary operator matrix ∂_k as a matrix over ℤ.

Rows index (k-1)-simplices, columns index k-simplices. Entry [i][j] is ±1 if the i-th (k-1)-simplex is the i-th face of the j-th k-simplex (with the appropriate sign), or 0 otherwise.

pub fn betti_numbers(&self) -> Vec<usize>

Compute Betti numbers β_0, β_1, … via Smith normal form over ℤ.

β_k = dim(ker ∂_k) − dim(im ∂_{k+1}).

pub fn euler_characteristic(&self) -> i32

Euler characteristic χ = Σ_k (-1)^k * #(k-simplices).

pub fn is_manifold(&self) -> bool

Check if the complex is a (combinatorial) manifold.

Every (n-1)-simplex must be shared by exactly 1 or 2 n-simplices, and the link of every vertex must be a sphere or a ball.

pub fn skeleton(&self, k: usize) -> Self

Return the k-skeleton (sub-complex of all simplices of dimension ≤ k).

pub fn link(&self, v: usize) -> Self

Return the link of vertex v.

lk(v) = { τ ∈ K | v ∉ τ, {v} ∪ τ ∈ K }.

pub fn star(&self, v: usize) -> Self

Return the star of vertex v.

st(v) = { σ ∈ K | v ∈ σ }.

Trait Implementations

impl Clone for SimplicialComplex

fn clone(&self) -> SimplicialComplex

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SimplicialComplex

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

Formats the value using the given formatter.