Struct SparsityMetrics 

pub struct SparsityMetrics;

Metrics for quantifying signal sparsity and dictionary coherence.

Implementations

impl SparsityMetrics

pub fn l0_norm(x: &[f64], threshold: f64) -> usize

Count the number of elements whose absolute value exceeds threshold (ℓ₀ norm).

pub fn l1_norm(x: &[f64]) -> f64

Compute the ℓ₁ norm (sum of absolute values).

pub fn l2_norm(x: &[f64]) -> f64

Compute the ℓ₂ norm.

pub fn gini(x: &[f64]) -> f64

Compute the Gini coefficient of |x| as a sparsity measure.

Returns a value in [0, 1]; 1 = maximally sparse, 0 = maximally spread.

pub fn coherence(a: &[Vec<f64>]) -> f64

Compute the mutual coherence of a matrix a.

Defined as the maximum normalised inner product between distinct columns: μ(A) = max_{i≠j} |a_i^T a_j| / (||a_i|| ||a_j||).

pub fn babel_function(a: &[Vec<f64>], k: usize) -> f64

Compute the Babel function μ_1(k) of a dictionary.

μ_1(k) = max_i sum_{j in S, |S|=k, j≠i} |a_i^T a_j| / (||a_i|| ||a_j||). A small Babel function implies better sparse recovery guarantees.