Module smartcore::linalg::traits::cholesky

Cholesky Decomposition

every positive definite matrix \(A \in R^{n \times n}\) can be factored as

\[A = R^TR\]

where \(R\) is upper triangular matrix with positive diagonal elements

Example:

use smartcore::linalg::basic::matrix::DenseMatrix;
use smartcore::linalg::traits::cholesky::*;

let A = DenseMatrix::from_2d_array(&[
                &[25., 15., -5.],
                &[15., 18., 0.],
                &[-5., 0., 11.]
        ]);

let cholesky = A.cholesky().unwrap();
let lower_triangular: DenseMatrix<f64> = cholesky.L();
let upper_triangular: DenseMatrix<f64> = cholesky.U();

References:

• “No bullshit guide to linear algebra”, Ivan Savov, 2016, 7.6 Matrix decompositions
• “Numerical Recipes: The Art of Scientific Computing”, Press W.H., Teukolsky S.A., Vetterling W.T, Flannery B.P, 3rd ed., 2.9 Cholesky Decomposition

Structs

• Cholesky
  Results of Cholesky decomposition.

Traits

• CholeskyDecomposable
  Trait that implements Cholesky decomposition routine for any matrix.