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