#include <cmath>
#include <complex>
#include <vector>
#include "Utilities/GSLComplex.h"
#include "Utilities/GSLMatrix.h"

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Classes
struct	gsl_eigen_nonsymm_workspace
	Workspace for nonsymmetric eigenvalue computation. More...

struct	gsl_eigen_nonsymmv_workspace
	Workspace for nonsymmetric eigenvalues/eigenvectors. More...

Functions
gsl_eigen_nonsymm_workspace *	gsl_eigen_nonsymm_alloc (size_t n)
	Allocate a nonsymmetric eigenvalue workspace for \(n \times n\) matrices.

void	gsl_eigen_nonsymm_params (int, int, gsl_eigen_nonsymm_workspace *)
	Accept GSL-style parameters (no-op in this implementation).

void	gsl_eigen_nonsymm_free (gsl_eigen_nonsymm_workspace *w)
	Free a workspace allocated by `gsl_eigen_nonsymm_alloc`.

gsl_eigen_nonsymmv_workspace *	gsl_eigen_nonsymmv_alloc (size_t n)
	Allocate a nonsymmetric eigenvalue/vector workspace for \(n \times n\) matrices.

void	gsl_eigen_nonsymmv_free (gsl_eigen_nonsymmv_workspace *w)
	Free a workspace allocated by `gsl_eigen_nonsymmv_alloc`.

int	gsl_eigen_nonsymm (gsl_matrix A, gsl_vector_complex eval, gsl_eigen_nonsymm_workspace *)
	Compute eigenvalues of a real nonsymmetric matrix.

int	gsl_eigen_nonsymmv (gsl_matrix A, gsl_vector_complex eval, gsl_matrix_complex evec, gsl_eigen_nonsymmv_workspace w)
	Compute eigenvalues and a simplified set of eigenvectors.

Function Documentation

◆ gsl_eigen_nonsymm()

int gsl_eigen_nonsymm	(	gsl_matrix *	A,
		gsl_vector_complex *	eval,
		gsl_eigen_nonsymm_workspace *
	)

inline

Compute eigenvalues of a real nonsymmetric matrix.

See also: https://www.gnu.org/software/gsl/doc/html/eigen.html

Uses a basic QR iteration to approximate eigenvalues for small matrices.

Parameters

A	Input: matrix (read-only; may be modified by algorithm).
eval	Output: vector of eigenvalues (complex).
w	Input: workspace (unused).

Returns: Output: 0 on success, -1 on size mismatch.

Definition at line 94 of file GSLEigen.h.

References dot(), gsl_matrix_ptr(), gsl_vector_complex_ptr(), gsl_vector_complex::size, gsl_matrix::size1, and gsl_matrix::size2.

Referenced by interpolation::MMatrix< Tmplt >::eigenvalues(), gsl_eigen_nonsymmv(), TEST_F(), TEST_F(), and TEST_F().

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◆ gsl_eigen_nonsymm_alloc()

gsl_eigen_nonsymm_workspace * gsl_eigen_nonsymm_alloc ( size_t n )

inline

Allocate a nonsymmetric eigenvalue workspace for \(n \times n\) matrices.

See also: https://www.gnu.org/software/gsl/doc/html/eigen.html

Parameters

n	Input: matrix dimension.

Returns: Output: workspace pointer.

Definition at line 49 of file GSLEigen.h.

References gsl_eigen_nonsymm_workspace::n, and gsl_eigen_nonsymm_workspace::work.

Referenced by interpolation::MMatrix< Tmplt >::eigenvalues(), TEST_F(), TEST_F(), TEST_F(), and TEST_F().

◆ gsl_eigen_nonsymm_free()

void gsl_eigen_nonsymm_free ( gsl_eigen_nonsymm_workspace * w )

inline

Free a workspace allocated by gsl_eigen_nonsymm_alloc.

See also: https://www.gnu.org/software/gsl/doc/html/eigen.html

Parameters

w	Input: workspace to release (can be null).

Definition at line 69 of file GSLEigen.h.

Referenced by interpolation::MMatrix< Tmplt >::eigenvalues(), TEST_F(), TEST_F(), TEST_F(), and TEST_F().

◆ gsl_eigen_nonsymm_params()

void gsl_eigen_nonsymm_params	(	int	,
		int	,
		gsl_eigen_nonsymm_workspace *
	)

inline

Accept GSL-style parameters (no-op in this implementation).

See also: https://www.gnu.org/software/gsl/doc/html/eigen.html

Parameters

balance	Input: balancing flag (unused).
compute_shur	Input: Schur computation flag (unused).
w	Input: workspace (unused).

Definition at line 61 of file GSLEigen.h.

Referenced by interpolation::MMatrix< Tmplt >::eigenvalues().

◆ gsl_eigen_nonsymmv()

int gsl_eigen_nonsymmv	(	gsl_matrix *	A,
		gsl_vector_complex *	eval,
		gsl_matrix_complex *	evec,
		gsl_eigen_nonsymmv_workspace *	w
	)

inline

Compute eigenvalues and a simplified set of eigenvectors.

See also: https://www.gnu.org/software/gsl/doc/html/eigen.html

Eigenvectors are approximated with a basic heuristic per eigenvalue.

Parameters

A	Input: matrix (read-only; may be modified by algorithm).
eval	Output: vector of eigenvalues (complex).
evec	Output: matrix of eigenvectors in columns.
w	Input: workspace (unused aside from type).