123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201 |
- /* eigen/gensymmv.c
- *
- * Copyright (C) 2007 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.
- */
- #include <stdlib.h>
- #include "gsl__config.h"
- #include "gsl_eigen.h"
- #include "gsl_linalg.h"
- #include "gsl_math.h"
- #include "gsl_blas.h"
- #include "gsl_vector.h"
- #include "gsl_matrix.h"
- /*
- * This module computes the eigenvalues and eigenvectors of a real
- * generalized symmetric-definite eigensystem A x = \lambda B x, where
- * A and B are symmetric, and B is positive-definite.
- */
- static void gensymmv_normalize_eigenvectors(gsl_matrix *evec);
- /*
- gsl_eigen_gensymmv_alloc()
- Allocate a workspace for solving the generalized symmetric-definite
- eigenvalue problem. The size of this workspace is O(4n).
- Inputs: n - size of matrices
- Return: pointer to workspace
- */
- gsl_eigen_gensymmv_workspace *
- gsl_eigen_gensymmv_alloc(const size_t n)
- {
- gsl_eigen_gensymmv_workspace *w;
- if (n == 0)
- {
- GSL_ERROR_NULL ("matrix dimension must be positive integer",
- GSL_EINVAL);
- }
- w = (gsl_eigen_gensymmv_workspace *)calloc (1, sizeof (gsl_eigen_gensymmv_workspace));
- if (w == 0)
- {
- GSL_ERROR_NULL ("failed to allocate space for workspace", GSL_ENOMEM);
- }
- w->size = n;
- w->symmv_workspace_p = gsl_eigen_symmv_alloc(n);
- if (!w->symmv_workspace_p)
- {
- gsl_eigen_gensymmv_free(w);
- GSL_ERROR_NULL("failed to allocate space for symmv workspace", GSL_ENOMEM);
- }
- return (w);
- } /* gsl_eigen_gensymmv_alloc() */
- /*
- gsl_eigen_gensymmv_free()
- Free workspace w
- */
- void
- gsl_eigen_gensymmv_free (gsl_eigen_gensymmv_workspace * w)
- {
- if (w->symmv_workspace_p)
- gsl_eigen_symmv_free(w->symmv_workspace_p);
- free(w);
- } /* gsl_eigen_gensymmv_free() */
- /*
- gsl_eigen_gensymmv()
- Solve the generalized symmetric-definite eigenvalue problem
- A x = \lambda B x
- for the eigenvalues \lambda and eigenvectors x.
- Inputs: A - real symmetric matrix
- B - real symmetric and positive definite matrix
- eval - where to store eigenvalues
- evec - where to store eigenvectors
- w - workspace
- Return: success or error
- */
- int
- gsl_eigen_gensymmv (gsl_matrix * A, gsl_matrix * B, gsl_vector * eval,
- gsl_matrix * evec, gsl_eigen_gensymmv_workspace * w)
- {
- const size_t N = A->size1;
- /* check matrix and vector sizes */
- if (N != A->size2)
- {
- GSL_ERROR ("matrix must be square to compute eigenvalues", GSL_ENOTSQR);
- }
- else if ((N != B->size1) || (N != B->size2))
- {
- GSL_ERROR ("B matrix dimensions must match A", GSL_EBADLEN);
- }
- else if (eval->size != N)
- {
- GSL_ERROR ("eigenvalue vector must match matrix size", GSL_EBADLEN);
- }
- else if (evec->size1 != evec->size2)
- {
- GSL_ERROR ("eigenvector matrix must be square", GSL_ENOTSQR);
- }
- else if (evec->size1 != N)
- {
- GSL_ERROR ("eigenvector matrix has wrong size", GSL_EBADLEN);
- }
- else if (w->size != N)
- {
- GSL_ERROR ("matrix size does not match workspace", GSL_EBADLEN);
- }
- else
- {
- int s;
- /* compute Cholesky factorization of B */
- s = gsl_linalg_cholesky_decomp(B);
- if (s != GSL_SUCCESS)
- return s; /* B is not positive definite */
- /* transform to standard symmetric eigenvalue problem */
- gsl_eigen_gensymm_standardize(A, B);
- /* compute eigenvalues and eigenvectors */
- s = gsl_eigen_symmv(A, eval, evec, w->symmv_workspace_p);
- if (s != GSL_SUCCESS)
- return s;
- /* backtransform eigenvectors: evec -> L^{-T} evec */
- gsl_blas_dtrsm(CblasLeft,
- CblasLower,
- CblasTrans,
- CblasNonUnit,
- 1.0,
- B,
- evec);
- /* the blas call destroyed the normalization - renormalize */
- gensymmv_normalize_eigenvectors(evec);
- return GSL_SUCCESS;
- }
- } /* gsl_eigen_gensymmv() */
- /********************************************
- * INTERNAL ROUTINES *
- ********************************************/
- /*
- gensymmv_normalize_eigenvectors()
- Normalize eigenvectors so that their Euclidean norm is 1
- Inputs: evec - eigenvectors
- */
- static void
- gensymmv_normalize_eigenvectors(gsl_matrix *evec)
- {
- const size_t N = evec->size1;
- size_t i; /* looping */
- for (i = 0; i < N; ++i)
- {
- gsl_vector_view vi = gsl_matrix_column(evec, i);
- double scale = 1.0 / gsl_blas_dnrm2(&vi.vector);
- gsl_blas_dscal(scale, &vi.vector);
- }
- } /* gensymmv_normalize_eigenvectors() */
|