Trait GeneralisedEigenvalueSolvable

pub trait GeneralisedEigenvalueSolvable {
    type NumType;
    type RealType;

    // Required methods
    fn solve_generalised_eigenvalue_problem_with_canonical_orthogonalisation(
        &self,
        complex_symmetric: bool,
        thresh_offdiag: Self::RealType,
        thresh_zeroov: Self::RealType,
        eigenvalue_comparison_mode: EigenvalueComparisonMode,
    ) -> Result<GeneralisedEigenvalueResult<Self::NumType>, Error>;
    fn solve_generalised_eigenvalue_problem_with_ggev(
        &self,
        complex_symmetric: bool,
        thresh_offdiag: Self::RealType,
        thresh_zeroov: Self::RealType,
        eigenvalue_comparison_mode: EigenvalueComparisonMode,
    ) -> Result<GeneralisedEigenvalueResult<Self::NumType>, Error>;
}

Trait to solve the generalised eigenvalue equation for a pair of square matrices $\mathbf{A}$ and $\mathbf{B}$:

    \mathbf{A} \mathbf{v} = \lambda \mathbf{B} \mathbf{v},

where $\mathbf{A}$ and $\mathbf{B}$ are in general non-Hermitian and non-positive-definite.

Required Associated Types

type NumType

Numerical type of the matrix elements constituting the generalised eigenvalue problem.

type RealType

Numerical type of the various thresholds for comparison.

Required Methods

fn solve_generalised_eigenvalue_problem_with_canonical_orthogonalisation( &self, complex_symmetric: bool, thresh_offdiag: Self::RealType, thresh_zeroov: Self::RealType, eigenvalue_comparison_mode: EigenvalueComparisonMode, ) -> Result<GeneralisedEigenvalueResult<Self::NumType>, Error>

Solves the auxiliary generalised eigenvalue problem

    \tilde{\mathbf{A}} \tilde{\mathbf{v}} = \tilde{\lambda} \tilde{\mathbf{B}} \tilde{\mathbf{v}},

where $\tilde{\mathbf{B}}$ is the canonical-orthogonalised version of $\mathbf{B}$. If $\mathbf{B}$ is not of full rank, then the two eigenvalue problems are different.

Arguments

• complex_symmetric - Boolean indicating whether the provided pair of matrices are complex-symmetric.
• thresh_offdiag - Threshold for checking if any off-diagonal elements are non-zero when verifying orthogonality.
• thresh_zeroov - Threshold for determining zero eigenvalues of $\mathbf{B}$.
• eigenvalue_comparison_mode - Comparison mode for sorting eigenvalues and their corresponding eigenvectors.

Returns

The generalised eigenvalue result.

fn solve_generalised_eigenvalue_problem_with_ggev( &self, complex_symmetric: bool, thresh_offdiag: Self::RealType, thresh_zeroov: Self::RealType, eigenvalue_comparison_mode: EigenvalueComparisonMode, ) -> Result<GeneralisedEigenvalueResult<Self::NumType>, Error>

Solves the generalised eigenvalue problem using LAPACK’s ?ggev generalised eigensolver.

Note that this can be numerically unstable if $\mathbf{B}$ is not of full rank.

Arguments

• complex_symmetric - Boolean indicating whether the provided pair of matrices are complex-symmetric.
• thresh_offdiag - Threshold for checking if any off-diagonal elements are non-zero when verifying orthogonality.
• thresh_zeroov - Threshold for determining zero eigenvalues of $\mathbf{B}$.
• eigenvalue_comparison_mode - Comparison mode for sorting eigenvalues and their corresponding eigenvectors.

Returns

The generalised eigenvalue result.

Implementations on Foreign Types

impl GeneralisedEigenvalueSolvable for (&ArrayView2<'_, f32>, &ArrayView2<'_, f32>)

type NumType = f32

type RealType = f32

fn solve_generalised_eigenvalue_problem_with_canonical_orthogonalisation( &self, _: bool, thresh_offdiag: f32, thresh_zeroov: f32, eigenvalue_comparison_mode: EigenvalueComparisonMode, ) -> Result<GeneralisedEigenvalueResult<Self::NumType>, Error>

fn solve_generalised_eigenvalue_problem_with_ggev( &self, _: bool, thresh_offdiag: f32, thresh_zeroov: f32, eigenvalue_comparison_mode: EigenvalueComparisonMode, ) -> Result<GeneralisedEigenvalueResult<Self::NumType>, Error>

impl GeneralisedEigenvalueSolvable for (&ArrayView2<'_, f64>, &ArrayView2<'_, f64>)

type NumType = f64

type RealType = f64

fn solve_generalised_eigenvalue_problem_with_canonical_orthogonalisation( &self, _: bool, thresh_offdiag: f64, thresh_zeroov: f64, eigenvalue_comparison_mode: EigenvalueComparisonMode, ) -> Result<GeneralisedEigenvalueResult<Self::NumType>, Error>

fn solve_generalised_eigenvalue_problem_with_ggev( &self, _: bool, thresh_offdiag: f64, thresh_zeroov: f64, eigenvalue_comparison_mode: EigenvalueComparisonMode, ) -> Result<GeneralisedEigenvalueResult<Self::NumType>, Error>

impl<T> GeneralisedEigenvalueSolvable for (&ArrayView2<'_, Complex<T>>, &ArrayView2<'_, Complex<T>>)

where T: Float + FloatConst + Scalar<Complex = Complex<T>>, Complex<T>: ComplexFloat<Real = T> + Scalar<Real = T, Complex = Complex<T>> + Lapack, for<'a> ArrayView2<'a, Complex<T>>: CanonicalOrthogonalisable<NumType = Complex<T>, RealType = T>,

type NumType = Complex<T>

type RealType = T

fn solve_generalised_eigenvalue_problem_with_canonical_orthogonalisation( &self, complex_symmetric: bool, thresh_offdiag: T, thresh_zeroov: T, eigenvalue_comparison_mode: EigenvalueComparisonMode, ) -> Result<GeneralisedEigenvalueResult<Complex<T>>, Error>

fn solve_generalised_eigenvalue_problem_with_ggev( &self, complex_symmetric: bool, thresh_offdiag: T, thresh_zeroov: T, eigenvalue_comparison_mode: EigenvalueComparisonMode, ) -> Result<GeneralisedEigenvalueResult<Self::NumType>, Error>

Implementors