Trait EigGeneralized

pub trait EigGeneralized {
    type EigVal;
    type EigVec;
    type Real;

    // Required method
    fn eig_generalized(
        &self,
        thresh_opt: Option<Self::Real>,
    ) -> Result<(Self::EigVal, Self::EigVec)>;
}

Eigenvalue decomposition of general matrix reference

Required Associated Types

type EigVal

EigVec is the right eivenvector

type EigVec

type Real

Required Methods

fn eig_generalized( &self, thresh_opt: Option<Self::Real>, ) -> Result<(Self::EigVal, Self::EigVec)>

Calculate eigenvalues with the right eigenvector

$$ A u_i = \lambda_i B u_i $$

use ndarray::*;
use ndarray_linalg::*;

let a: Array2<f64> = array![
    [-1.01,  0.86, -4.60,  3.31, -4.81],
    [ 3.98,  0.53, -7.04,  5.29,  3.55],
    [ 3.30,  8.26, -3.89,  8.20, -1.51],
    [ 4.43,  4.96, -7.66, -7.33,  6.18],
    [ 7.31, -6.43, -6.16,  2.47,  5.58],
];
let b: Array2<f64> = array![
    [ 1.23, -4.56,  7.89,  0.12, -3.45],
    [ 6.78, -9.01,  2.34, -5.67,  8.90],
    [-1.11,  3.33, -6.66,  9.99, -2.22],
    [ 4.44, -7.77,  0.00,  1.11,  5.55],
    [-8.88,  6.66, -3.33,  2.22, -9.99],
];
let (geneigs, vecs) = (a.clone(), b.clone()).eig_generalized(None).unwrap();

let a = a.map(|v| v.as_c());
let b = b.map(|v| v.as_c());
for (ge, vec) in geneigs.iter().zip(vecs.axis_iter(Axis(1))) {
    if let GeneralizedEigenvalue::Finite(e, _) = ge {
        let ebv = b.dot(&vec).map(|v| v * e);
        let av = a.dot(&vec);
        assert_close_l2!(&av, &ebv, 1e-5);
    }
}

Arguments

• thresh_opt - An optional threshold for determining approximate zero |β| values when computing the eigenvalues as α/β. If None, no approximate comparisons to zero will be made.

Implementations on Foreign Types

impl<A, S> EigGeneralized for (ArrayBase<S, Ix2>, ArrayBase<S, Ix2>)

where A: Scalar + Lapack, S: Data<Elem = A>,

type EigVal = ArrayBase<OwnedRepr<GeneralizedEigenvalue<<A as Scalar>::Complex>>, Dim<[usize; 1]>>

type EigVec = ArrayBase<OwnedRepr<<A as Scalar>::Complex>, Dim<[usize; 2]>>

type Real = <A as Scalar>::Real

fn eig_generalized( &self, thresh_opt: Option<Self::Real>, ) -> Result<(Self::EigVal, Self::EigVec)>

Implementors