/* eigen/gsl_eigen.h
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2006, 2007 Gerard Jungman, Brian Gough, Patrick Alken
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#ifndef __GSL_EIGEN_H__
#define __GSL_EIGEN_H__
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#undef __BEGIN_DECLS
#undef __END_DECLS
#ifdef __cplusplus
# define __BEGIN_DECLS extern "C" {
# define __END_DECLS }
#else
# define __BEGIN_DECLS /* empty */
# define __END_DECLS /* empty */
#endif
__BEGIN_DECLS
typedef struct {
size_t size;
double * d;
double * sd;
} gsl_eigen_symm_workspace;
gsl_eigen_symm_workspace * gsl_eigen_symm_alloc (const size_t n);
void gsl_eigen_symm_free (gsl_eigen_symm_workspace * w);
int gsl_eigen_symm (gsl_matrix * A, gsl_vector * eval, gsl_eigen_symm_workspace * w);
typedef struct {
size_t size;
double * d;
double * sd;
double * gc;
double * gs;
} gsl_eigen_symmv_workspace;
gsl_eigen_symmv_workspace * gsl_eigen_symmv_alloc (const size_t n);
void gsl_eigen_symmv_free (gsl_eigen_symmv_workspace * w);
int gsl_eigen_symmv (gsl_matrix * A, gsl_vector * eval, gsl_matrix * evec, gsl_eigen_symmv_workspace * w);
typedef struct {
size_t size;
double * d;
double * sd;
double * tau;
} gsl_eigen_herm_workspace;
gsl_eigen_herm_workspace * gsl_eigen_herm_alloc (const size_t n);
void gsl_eigen_herm_free (gsl_eigen_herm_workspace * w);
int gsl_eigen_herm (gsl_matrix_complex * A, gsl_vector * eval,
gsl_eigen_herm_workspace * w);
typedef struct {
size_t size;
double * d;
double * sd;
double * tau;
double * gc;
double * gs;
} gsl_eigen_hermv_workspace;
gsl_eigen_hermv_workspace * gsl_eigen_hermv_alloc (const size_t n);
void gsl_eigen_hermv_free (gsl_eigen_hermv_workspace * w);
int gsl_eigen_hermv (gsl_matrix_complex * A, gsl_vector * eval,
gsl_matrix_complex * evec,
gsl_eigen_hermv_workspace * w);
typedef struct {
size_t size; /* matrix size */
size_t max_iterations; /* max iterations since last eigenvalue found */
size_t n_iter; /* number of iterations since last eigenvalue found */
size_t n_evals; /* number of eigenvalues found so far */
int compute_t; /* compute Schur form T = Z^t A Z */
gsl_matrix *H; /* pointer to Hessenberg matrix */
gsl_matrix *Z; /* pointer to Schur vector matrix */
} gsl_eigen_francis_workspace;
gsl_eigen_francis_workspace * gsl_eigen_francis_alloc (void);
void gsl_eigen_francis_free (gsl_eigen_francis_workspace * w);
void gsl_eigen_francis_T (const int compute_t,
gsl_eigen_francis_workspace * w);
int gsl_eigen_francis (gsl_matrix * H, gsl_vector_complex * eval,
gsl_eigen_francis_workspace * w);
int gsl_eigen_francis_Z (gsl_matrix * H, gsl_vector_complex * eval,
gsl_matrix * Z,
gsl_eigen_francis_workspace * w);
typedef struct {
size_t size; /* size of matrices */
gsl_vector *diag; /* diagonal matrix elements from balancing */
gsl_vector *tau; /* Householder coefficients */
gsl_matrix *Z; /* pointer to Z matrix */
int do_balance; /* perform balancing transformation? */
size_t n_evals; /* number of eigenvalues found */
gsl_eigen_francis_workspace *francis_workspace_p;
} gsl_eigen_nonsymm_workspace;
gsl_eigen_nonsymm_workspace * gsl_eigen_nonsymm_alloc (const size_t n);
void gsl_eigen_nonsymm_free (gsl_eigen_nonsymm_workspace * w);
void gsl_eigen_nonsymm_params (const int compute_t, const int balance,
gsl_eigen_nonsymm_workspace *w);
int gsl_eigen_nonsymm (gsl_matrix * A, gsl_vector_complex * eval,
gsl_eigen_nonsymm_workspace * w);
int gsl_eigen_nonsymm_Z (gsl_matrix * A, gsl_vector_complex * eval,
gsl_matrix * Z, gsl_eigen_nonsymm_workspace * w);
typedef struct {
size_t size; /* size of matrices */
gsl_vector *work; /* scratch workspace */
gsl_vector *work2; /* scratch workspace */
gsl_vector *work3; /* scratch workspace */
gsl_matrix *Z; /* pointer to Schur vectors */
gsl_eigen_nonsymm_workspace *nonsymm_workspace_p;
} gsl_eigen_nonsymmv_workspace;
gsl_eigen_nonsymmv_workspace * gsl_eigen_nonsymmv_alloc (const size_t n);
void gsl_eigen_nonsymmv_free (gsl_eigen_nonsymmv_workspace * w);
void gsl_eigen_nonsymmv_params (const int balance,
gsl_eigen_nonsymmv_workspace *w);
int gsl_eigen_nonsymmv (gsl_matrix * A, gsl_vector_complex * eval,
gsl_matrix_complex * evec,
gsl_eigen_nonsymmv_workspace * w);
int gsl_eigen_nonsymmv_Z (gsl_matrix * A, gsl_vector_complex * eval,
gsl_matrix_complex * evec, gsl_matrix * Z,
gsl_eigen_nonsymmv_workspace * w);
typedef struct {
size_t size; /* size of matrices */
gsl_eigen_symm_workspace *symm_workspace_p;
} gsl_eigen_gensymm_workspace;
gsl_eigen_gensymm_workspace * gsl_eigen_gensymm_alloc (const size_t n);
void gsl_eigen_gensymm_free (gsl_eigen_gensymm_workspace * w);
int gsl_eigen_gensymm (gsl_matrix * A, gsl_matrix * B,
gsl_vector * eval, gsl_eigen_gensymm_workspace * w);
int gsl_eigen_gensymm_standardize (gsl_matrix * A, const gsl_matrix * B);
typedef struct {
size_t size; /* size of matrices */
gsl_eigen_symmv_workspace *symmv_workspace_p;
} gsl_eigen_gensymmv_workspace;
gsl_eigen_gensymmv_workspace * gsl_eigen_gensymmv_alloc (const size_t n);
void gsl_eigen_gensymmv_free (gsl_eigen_gensymmv_workspace * w);
int gsl_eigen_gensymmv (gsl_matrix * A, gsl_matrix * B,
gsl_vector * eval, gsl_matrix * evec,
gsl_eigen_gensymmv_workspace * w);
typedef struct {
size_t size; /* size of matrices */
gsl_eigen_herm_workspace *herm_workspace_p;
} gsl_eigen_genherm_workspace;
gsl_eigen_genherm_workspace * gsl_eigen_genherm_alloc (const size_t n);
void gsl_eigen_genherm_free (gsl_eigen_genherm_workspace * w);
int gsl_eigen_genherm (gsl_matrix_complex * A, gsl_matrix_complex * B,
gsl_vector * eval, gsl_eigen_genherm_workspace * w);
int gsl_eigen_genherm_standardize (gsl_matrix_complex * A,
const gsl_matrix_complex * B);
typedef struct {
size_t size; /* size of matrices */
gsl_eigen_hermv_workspace *hermv_workspace_p;
} gsl_eigen_genhermv_workspace;
gsl_eigen_genhermv_workspace * gsl_eigen_genhermv_alloc (const size_t n);
void gsl_eigen_genhermv_free (gsl_eigen_genhermv_workspace * w);
int gsl_eigen_genhermv (gsl_matrix_complex * A, gsl_matrix_complex * B,
gsl_vector * eval, gsl_matrix_complex * evec,
gsl_eigen_genhermv_workspace * w);
typedef struct {
size_t size; /* size of matrices */
gsl_vector *work; /* scratch workspace */
size_t n_evals; /* number of eigenvalues found */
size_t max_iterations; /* maximum QZ iterations allowed */
size_t n_iter; /* number of iterations since last eigenvalue found */
double eshift; /* exceptional shift counter */
int needtop; /* need to compute top index? */
double atol; /* tolerance for splitting A matrix */
double btol; /* tolerance for splitting B matrix */
double ascale; /* scaling factor for shifts */
double bscale; /* scaling factor for shifts */
gsl_matrix *H; /* pointer to hessenberg matrix */
gsl_matrix *R; /* pointer to upper triangular matrix */
int compute_s; /* compute generalized Schur form S */
int compute_t; /* compute generalized Schur form T */
gsl_matrix *Q; /* pointer to left Schur vectors */
gsl_matrix *Z; /* pointer to right Schur vectors */
} gsl_eigen_gen_workspace;
gsl_eigen_gen_workspace * gsl_eigen_gen_alloc (const size_t n);
void gsl_eigen_gen_free (gsl_eigen_gen_workspace * w);
void gsl_eigen_gen_params (const int compute_s, const int compute_t,
const int balance, gsl_eigen_gen_workspace * w);
int gsl_eigen_gen (gsl_matrix * A, gsl_matrix * B,
gsl_vector_complex * alpha, gsl_vector * beta,
gsl_eigen_gen_workspace * w);
int gsl_eigen_gen_QZ (gsl_matrix * A, gsl_matrix * B,
gsl_vector_complex * alpha, gsl_vector * beta,
gsl_matrix * Q, gsl_matrix * Z,
gsl_eigen_gen_workspace * w);
typedef struct {
size_t size; /* size of matrices */
gsl_vector *work1; /* 1-norm of columns of A */
gsl_vector *work2; /* 1-norm of columns of B */
gsl_vector *work3; /* real part of eigenvector */
gsl_vector *work4; /* imag part of eigenvector */
gsl_vector *work5; /* real part of back-transformed eigenvector */
gsl_vector *work6; /* imag part of back-transformed eigenvector */
gsl_matrix *Q; /* pointer to left Schur vectors */
gsl_matrix *Z; /* pointer to right Schur vectors */
gsl_eigen_gen_workspace *gen_workspace_p;
} gsl_eigen_genv_workspace;
gsl_eigen_genv_workspace * gsl_eigen_genv_alloc (const size_t n);
void gsl_eigen_genv_free (gsl_eigen_genv_workspace * w);
int gsl_eigen_genv (gsl_matrix * A, gsl_matrix * B,
gsl_vector_complex * alpha, gsl_vector * beta,
gsl_matrix_complex * evec,
gsl_eigen_genv_workspace * w);
int gsl_eigen_genv_QZ (gsl_matrix * A, gsl_matrix * B,
gsl_vector_complex * alpha, gsl_vector * beta,
gsl_matrix_complex * evec,
gsl_matrix * Q, gsl_matrix * Z,
gsl_eigen_genv_workspace * w);
typedef enum {
GSL_EIGEN_SORT_VAL_ASC,
GSL_EIGEN_SORT_VAL_DESC,
GSL_EIGEN_SORT_ABS_ASC,
GSL_EIGEN_SORT_ABS_DESC
}
gsl_eigen_sort_t;
/* Sort eigensystem results based on eigenvalues.
* Sorts in order of increasing value or increasing
* absolute value.
*
* exceptions: GSL_EBADLEN
*/
int gsl_eigen_symmv_sort(gsl_vector * eval, gsl_matrix * evec,
gsl_eigen_sort_t sort_type);
int gsl_eigen_hermv_sort(gsl_vector * eval, gsl_matrix_complex * evec,
gsl_eigen_sort_t sort_type);
int gsl_eigen_nonsymmv_sort(gsl_vector_complex * eval,
gsl_matrix_complex * evec,
gsl_eigen_sort_t sort_type);
int gsl_eigen_gensymmv_sort (gsl_vector * eval, gsl_matrix * evec,
gsl_eigen_sort_t sort_type);
int gsl_eigen_genhermv_sort (gsl_vector * eval, gsl_matrix_complex * evec,
gsl_eigen_sort_t sort_type);
int gsl_eigen_genv_sort (gsl_vector_complex * alpha, gsl_vector * beta,
gsl_matrix_complex * evec,
gsl_eigen_sort_t sort_type);
/* Prototypes for the schur module */
int gsl_schur_gen_eigvals(const gsl_matrix *A, const gsl_matrix *B,
double *wr1, double *wr2, double *wi,
double *scale1, double *scale2);
int gsl_schur_solve_equation(double ca, const gsl_matrix *A, double z,
double d1, double d2, const gsl_vector *b,
gsl_vector *x, double *s, double *xnorm,
double smin);
int gsl_schur_solve_equation_z(double ca, const gsl_matrix *A,
gsl_complex *z, double d1, double d2,
const gsl_vector_complex *b,
gsl_vector_complex *x, double *s,
double *xnorm, double smin);
/* The following functions are obsolete: */
/* Eigensolve by Jacobi Method
*
* The data in the matrix input is destroyed.
*
* exceptions:
*/
int
gsl_eigen_jacobi(gsl_matrix * matrix,
gsl_vector * eval,
gsl_matrix * evec,
unsigned int max_rot,
unsigned int * nrot);
/* Invert by Jacobi Method
*
* exceptions:
*/
int
gsl_eigen_invert_jacobi(const gsl_matrix * matrix,
gsl_matrix * ainv,
unsigned int max_rot);
__END_DECLS
#endif /* __GSL_EIGEN_H__ */