Struct nalgebra_lapack::GeneralizedEigen

pub struct GeneralizedEigen<T: Scalar, D: Dim>where
    DefaultAllocator: Allocator<T, D> + Allocator<T, D, D>,{ /* private fields */ }

Generalized eigenvalues and generalized eigenvectors (left and right) of a pair of N*N real square matrices.

Each generalized eigenvalue (lambda) satisfies determinant(A - lambda*B) = 0

The right eigenvector v(j) corresponding to the eigenvalue lambda(j) of (A,B) satisfies

A * v(j) = lambda(j) * B * v(j).

The left eigenvector u(j) corresponding to the eigenvalue lambda(j) of (A,B) satisfies

u(j)**H * A = lambda(j) * u(j)**H * B . where u(j)**H is the conjugate-transpose of u(j).

Implementations

impl<T: GeneralizedEigenScalar + RealField + Copy, D: Dim> GeneralizedEigen<T, D>where
    DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,

pub fn new(a: OMatrix<T, D, D>, b: OMatrix<T, D, D>) -> Self

Attempts to compute the generalized eigenvalues, and left and right associated eigenvectors via the raw returns from LAPACK’s dggev and sggev routines

Panics if the method did not converge.

pub fn try_new(a: OMatrix<T, D, D>, b: OMatrix<T, D, D>) -> Option<Self>

Attempts to compute the generalized eigenvalues (and eigenvectors) via the raw returns from LAPACK’s dggev and sggev routines

Returns None if the method did not converge.

pub fn eigenvectors(
    &self
) -> (OMatrix<Complex<T>, D, D>, OMatrix<Complex<T>, D, D>)where
    DefaultAllocator: Allocator<Complex<T>, D, D> + Allocator<Complex<T>, D> + Allocator<(Complex<T>, T), D>,

Calculates the generalized eigenvectors (left and right) associated with the generalized eigenvalues

Outputs two matrices. The first output matrix contains the left eigenvectors of the generalized eigenvalues as columns. The second matrix contains the right eigenvectors of the generalized eigenvalues as columns.

pub fn raw_eigenvalues(&self) -> OVector<(Complex<T>, T), D>where
    DefaultAllocator: Allocator<(Complex<T>, T), D>,

Outputs the unprocessed (almost) version of generalized eigenvalues ((alphar, alphai), beta) straight from LAPACK

Trait Implementations

impl<T: Clone + Scalar, D: Clone + Dim> Clone for GeneralizedEigen<T, D>where
    DefaultAllocator: Allocator<T, D> + Allocator<T, D, D>,

fn clone(&self) -> GeneralizedEigen<T, D>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Debug + Scalar, D: Debug + Dim> Debug for GeneralizedEigen<T, D>where
    DefaultAllocator: Allocator<T, D> + Allocator<T, D, D>,

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

Formats the value using the given formatter.

impl<T: Scalar + Copy, D: Dim> Copy for GeneralizedEigen<T, D>where
    DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
    OMatrix<T, D, D>: Copy,
    OVector<T, D>: Copy,