SVD

Singular value decomposition factors any rows x cols matrix a as u * diag(sigma) * vᵗ, where u has orthonormal columns, sigma is a length-cols vector of non-negative singular values sorted in descending order, and v is a cols x cols orthogonal matrix. Unlike LU or Cholesky, a doesn’t need to be square — the SVD exists for any matrix.

rustebra computes it via svd_qr_iteration: it eigendecomposes aᵗ * a using a fixed-iteration QR algorithm (100 iterations, rather than convergence-checked, so behavior stays predictable in no_std contexts) to get v and sigma, then recovers u from a * v scaled by sigma. svd is the general-purpose entry point, delegating to svd_qr_iteration with an automatically-computed tolerance so callers don’t have to pick one. Both are shown below, alongside the ergonomic StaticMatrix/DynamicMatrix::svd() method used in Matrix Operations.

#![allow(unused)]
fn main() {
use rustebra::algorithm::matrix::{svd, svd_qr_iteration};
use rustebra::storage::StaticStorage;

pub(crate) fn run() {
    println!("\n== Singular Value Decomposition (SVD) ==");
    // [[2, 0], [0, 1]].
    let a = StaticStorage::new([2.0, 0.0, 0.0, 1.0]);
    let mut scratch = [0.0; 5 * 2 * 2 + 2 + 2];

    let mut u = [0.0; 4];
    let mut sigma = [0.0; 2];
    let mut v = [0.0; 4];
    svd(&a, 2, 2, &mut u, &mut sigma, &mut v, &mut scratch).unwrap();
    println!("sigma = {sigma:?}, u = {u:?}, v = {v:?}");

    let mut sigma_explicit = [0.0; 2];
    svd_qr_iteration(
        &a,
        2,
        2,
        &mut u,
        &mut sigma_explicit,
        &mut v,
        &mut scratch,
        1e-9,
    )
    .unwrap();
    println!("sigma (explicit QR iteration) = {sigma_explicit:?}");
}
}

Gotchas

• svd/svd_qr_iteration need a caller-provided scratch buffer sized 5 * cols * cols + cols + rows — get the length wrong and you get Err(DimensionMismatch) back, not a panic. DynamicMatrix::svd() allocates this internally and doesn’t expose the parameter.
• The QR iteration count inside svd_qr_iteration is fixed (100), not convergence-checked — for matrices with closely clustered singular values, more iterations might be needed for full precision than this budget provides.