Module ndarray_linalg::cholesky

Cholesky decomposition of Hermitian (or real symmetric) positive definite matrices

See the Wikipedia page about Cholesky decomposition for more information.

Example

Using the Cholesky decomposition of A for various operations, where A is a Hermitian (or real symmetric) positive definite matrix:

#[macro_use]
extern crate ndarray;
extern crate ndarray_linalg;

use ndarray::prelude::*;
use ndarray_linalg::cholesky::*;

let a: Array2<f64> = array![
    [  4.,  12., -16.],
    [ 12.,  37., -43.],
    [-16., -43.,  98.]
];

// Obtain `L`
let lower = a.cholesky(UPLO::Lower).unwrap();
assert!(lower.abs_diff_eq(&array![
    [ 2., 0., 0.],
    [ 6., 1., 0.],
    [-8., 5., 3.]
], 1e-9));

// Find the determinant of `A`
let det = a.detc().unwrap();
assert!((det - 36.).abs() < 1e-9);

// Solve `A * x = b`
let b = array![4., 13., -11.];
let x = a.solvec(&b).unwrap();
assert!(x.abs_diff_eq(&array![-2., 1., 0.], 1e-9));

Structs

• CholeskyFactorized
  Cholesky decomposition of Hermitian (or real symmetric) positive definite matrix

Enums

• UPLO
  Upper/Lower specification for seveal usages

Traits

• Cholesky
  Cholesky decomposition of Hermitian (or real symmetric) positive definite matrix reference
• CholeskyInplace
  Cholesky decomposition of Hermitian (or real symmetric) positive definite mutable reference of matrix
• CholeskyInto
  Cholesky decomposition of Hermitian (or real symmetric) positive definite matrix
• DeterminantC
  Determinant of Hermitian (or real symmetric) positive definite matrix ref
• DeterminantCInto
  Determinant of Hermitian (or real symmetric) positive definite matrix
• FactorizeC
  Cholesky decomposition of Hermitian (or real symmetric) positive definite matrix reference
• FactorizeCInto
  Cholesky decomposition of Hermitian (or real symmetric) positive definite matrix
• InverseC
  Inverse of Hermitian (or real symmetric) positive definite matrix ref
• InverseCInto
  Inverse of Hermitian (or real symmetric) positive definite matrix
• SolveC
  Solve systems of linear equations with Hermitian (or real symmetric) positive definite coefficient matrices