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/* eigen/gensymmv.c
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*
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* Copyright (C) 2007 Patrick Alken
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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#include <stdlib.h>
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#include <config.h>
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#include <gsl/gsl_eigen.h>
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#include <gsl/gsl_linalg.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_blas.h>
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#include <gsl/gsl_vector.h>
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#include <gsl/gsl_matrix.h>
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/*
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* This module computes the eigenvalues and eigenvectors of a real
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* generalized symmetric-definite eigensystem A x = \lambda B x, where
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* A and B are symmetric, and B is positive-definite.
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*/
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static void gensymmv_normalize_eigenvectors(gsl_matrix *evec);
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/*
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gsl_eigen_gensymmv_alloc()
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Allocate a workspace for solving the generalized symmetric-definite
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eigenvalue problem. The size of this workspace is O(4n).
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Inputs: n - size of matrices
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Return: pointer to workspace
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*/
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gsl_eigen_gensymmv_workspace *
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gsl_eigen_gensymmv_alloc(const size_t n)
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{
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gsl_eigen_gensymmv_workspace *w;
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if (n == 0)
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{
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GSL_ERROR_NULL ("matrix dimension must be positive integer",
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GSL_EINVAL);
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}
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w = (gsl_eigen_gensymmv_workspace *) calloc (1, sizeof (gsl_eigen_gensymmv_workspace));
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if (w == 0)
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{
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GSL_ERROR_NULL ("failed to allocate space for workspace", GSL_ENOMEM);
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}
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w->size = n;
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w->symmv_workspace_p = gsl_eigen_symmv_alloc(n);
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if (!w->symmv_workspace_p)
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{
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gsl_eigen_gensymmv_free(w);
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GSL_ERROR_NULL("failed to allocate space for symmv workspace", GSL_ENOMEM);
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}
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return (w);
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} /* gsl_eigen_gensymmv_alloc() */
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/*
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gsl_eigen_gensymmv_free()
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Free workspace w
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*/
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void
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gsl_eigen_gensymmv_free (gsl_eigen_gensymmv_workspace * w)
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{
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RETURN_IF_NULL (w);
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if (w->symmv_workspace_p)
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gsl_eigen_symmv_free(w->symmv_workspace_p);
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free(w);
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} /* gsl_eigen_gensymmv_free() */
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/*
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gsl_eigen_gensymmv()
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Solve the generalized symmetric-definite eigenvalue problem
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A x = \lambda B x
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for the eigenvalues \lambda and eigenvectors x.
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Inputs: A - real symmetric matrix
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B - real symmetric and positive definite matrix
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eval - where to store eigenvalues
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evec - where to store eigenvectors
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w - workspace
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Return: success or error
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*/
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int
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gsl_eigen_gensymmv (gsl_matrix * A, gsl_matrix * B, gsl_vector * eval,
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gsl_matrix * evec, gsl_eigen_gensymmv_workspace * w)
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{
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const size_t N = A->size1;
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/* check matrix and vector sizes */
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if (N != A->size2)
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{
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GSL_ERROR ("matrix must be square to compute eigenvalues", GSL_ENOTSQR);
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}
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else if ((N != B->size1) || (N != B->size2))
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{
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GSL_ERROR ("B matrix dimensions must match A", GSL_EBADLEN);
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}
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else if (eval->size != N)
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{
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GSL_ERROR ("eigenvalue vector must match matrix size", GSL_EBADLEN);
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}
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else if (evec->size1 != evec->size2)
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{
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GSL_ERROR ("eigenvector matrix must be square", GSL_ENOTSQR);
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}
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else if (evec->size1 != N)
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{
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GSL_ERROR ("eigenvector matrix has wrong size", GSL_EBADLEN);
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}
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else if (w->size != N)
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{
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GSL_ERROR ("matrix size does not match workspace", GSL_EBADLEN);
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}
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else
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{
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int s;
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/* compute Cholesky factorization of B */
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s = gsl_linalg_cholesky_decomp1(B);
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if (s != GSL_SUCCESS)
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return s; /* B is not positive definite */
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/* transform to standard symmetric eigenvalue problem */
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gsl_eigen_gensymm_standardize(A, B);
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/* compute eigenvalues and eigenvectors */
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s = gsl_eigen_symmv(A, eval, evec, w->symmv_workspace_p);
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if (s != GSL_SUCCESS)
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return s;
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/* backtransform eigenvectors: evec -> L^{-T} evec */
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gsl_blas_dtrsm(CblasLeft,
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CblasLower,
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CblasTrans,
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CblasNonUnit,
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1.0,
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B,
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evec);
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/* the blas call destroyed the normalization - renormalize */
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gensymmv_normalize_eigenvectors(evec);
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return GSL_SUCCESS;
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}
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} /* gsl_eigen_gensymmv() */
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/********************************************
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* INTERNAL ROUTINES *
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********************************************/
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/*
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gensymmv_normalize_eigenvectors()
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Normalize eigenvectors so that their Euclidean norm is 1
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Inputs: evec - eigenvectors
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*/
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static void
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gensymmv_normalize_eigenvectors(gsl_matrix *evec)
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{
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const size_t N = evec->size1;
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size_t i; /* looping */
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for (i = 0; i < N; ++i)
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{
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gsl_vector_view vi = gsl_matrix_column(evec, i);
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double scale = 1.0 / gsl_blas_dnrm2(&vi.vector);
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gsl_blas_dscal(scale, &vi.vector);
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}
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} /* gensymmv_normalize_eigenvectors() */
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