Struct BasisPursuit 

pub struct BasisPursuit;

Basis Pursuit via iterative shrinkage-thresholding (ISTA and FISTA).

Solves the LASSO problem: argmin_x 0.5 ||Ax - b||^2 + lambda ||x||_1.

FISTA adds Nesterov momentum for faster O(1/k²) convergence versus O(1/k) for plain ISTA.

Implementations

impl BasisPursuit

pub fn solve_lasso( a: &[Vec<f64>], b: &[f64], lambda: f64, max_iter: usize, ) -> Vec<f64>

Solve the LASSO problem using ISTA.

• a — measurement matrix (m × n, row-major)
• b — measurement vector (length m)
• lambda — sparsity regularisation weight
• max_iter — maximum number of iterations

Returns the recovered sparse signal of length n.

pub fn solve_fista( a: &[Vec<f64>], b: &[f64], lambda: f64, max_iter: usize, ) -> Vec<f64>

Solve the LASSO problem using FISTA (Fast ISTA with Nesterov momentum).

• a — measurement matrix (m × n, row-major)
• b — measurement vector (length m)
• lambda — sparsity regularisation weight
• max_iter — maximum number of iterations

Returns the recovered sparse signal of length n.

pub fn objective(a: &[Vec<f64>], b: &[f64], x: &[f64], lambda: f64) -> f64

Compute the objective value 0.5 ||Ax - b||^2 + lambda ||x||_1.

Useful for monitoring convergence.