Struct Eigen 

pub struct Eigen<R> { /* private fields */ }

The eigendecomposition A·V = V·Λ of a square matrix: its eigenvalues, the diagonal of Λ, and its eigenvectors, the columns of V, complex in general, each of length 1. When A has a full set of independent eigenvectors, A = V·Λ·V⁻¹. From Matrix::eigen.

Examples

use a::math::complex::Complex;
use a::math::matrix::Matrix;

let a: Matrix<f64> = Matrix::from_rows(&[[2.0, 1.0], [1.0, 2.0]]);
let e = a.eigen();
let (v, w) = (e.vectors(), e.values());
// Each column is an eigenvector: A·v = λ·v.
let a = a.map(|&x| Complex::from(x));
for (j, &w) in w.iter().enumerate() {
    let v = Matrix::from_columns(&[v.column(j)]);
    let d = &(&a * &v) - &(&v * w);
    assert!(d.as_slice().iter().all(|x| x.abs() < 1e-14));
}

Implementations

impl<R: Float> Eigen<R>

pub fn values(&self) -> &[Complex<R>]

The eigenvalues, in the order of the columns of vectors.

pub fn vectors(&self) -> &Matrix<Complex<R>>

The eigenvectors, each a column of length 1 in the 2-norm.

Trait Implementations

impl<R: Clone> Clone for Eigen<R>

fn clone(&self) -> Self

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<R: Debug> Debug for Eigen<R>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.