Module smartcore::linalg::svd

Singular value decomposition.

SVD Decomposition

Any m by n matrix \(A\) can be factored into:

\[A = U \Sigma V^T\]

Where columns of \(U\) are eigenvectors of \(AA^T\) (left-singular vectors of A), \(V\) are eigenvectors of \(A^TA\) (right-singular vectors of A), and the diagonal values in the \(\Sigma\) matrix are known as the singular values of the original matrix.

Example:

use smartcore::linalg::naive::dense_matrix::*;
use smartcore::linalg::svd::*;

let A = DenseMatrix::from_2d_array(&[
                &[0.9, 0.4, 0.7],
                &[0.4, 0.5, 0.3],
                &[0.7, 0.3, 0.8]
        ]);

let svd = A.svd().unwrap();
let u: DenseMatrix<f64> = svd.U;
let v: DenseMatrix<f64> = svd.V;
let s: Vec<f64> = svd.s;

References:

• "Linear Algebra and Its Applications", Gilbert Strang, 5th ed., 6.3 Singular Value Decomposition
• "Numerical Recipes: The Art of Scientific Computing", Press W.H., Teukolsky S.A., Vetterling W.T, Flannery B.P, 3rd ed., 2.6 Singular Value Decomposition

Structs

SVD	Results of SVD decomposition

Traits

SVDDecomposableMatrix

Trait that implements SVD decomposition routine for any matrix.