Module eigh

Eigendecomposition for Hermitian matrices.

For a Hermitian matrix A, this solves the eigenvalue problem A V = V D for D and V, where D is the diagonal matrix of eigenvalues in ascending order and V is the orthonormal matrix of corresponding eigenvectors.

For a pair of Hermitian matrices A and B where B is also positive definite, this solves the generalized eigenvalue problem A V = B V D, where D is the diagonal matrix of generalized eigenvalues in ascending order and V is the matrix of corresponding generalized eigenvectors. The matrix V is normalized such that V^H B V = I.

Example

Find the eigendecomposition of a Hermitian (or real symmetric) matrix.

use approx::assert_abs_diff_eq;
use ndarray::{array, Array2};
use ndarray_linalg::{Eigh, UPLO};

let a: Array2<f64> = array![
    [2., 1.],
    [1., 2.],
];
let (eigvals, eigvecs) = a.eigh(UPLO::Lower)?;
assert_abs_diff_eq!(eigvals, array![1., 3.]);
assert_abs_diff_eq!(
    a.dot(&eigvecs),
    eigvecs.dot(&Array2::from_diag(&eigvals)),
);

Traits

EigValsh

Calculate eigenvalues without eigenvectors

EigValshInplace

Calculate eigenvalues without eigenvectors

EigValshInto

Calculate eigenvalues without eigenvectors

Eigh

Eigenvalue decomposition of Hermite matrix reference

EighInplace

Eigenvalue decomposition of mutable reference of Hermite matrix

EighInto

Eigenvalue decomposition of Hermite matrix

SymmetricSqrt

Calculate symmetric square-root matrix using eigh

SymmetricSqrtInto

Calculate symmetric square-root matrix using eigh