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/* eigen/genhermv.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 <config.h>
#include <gsl/gsl_eigen.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_complex.h>
#include <gsl/gsl_complex_math.h>
/*
* This module computes the eigenvalues and eigenvectors of a complex
* generalized hermitian-definite eigensystem A x = \lambda B x, where
* A and B are hermitian, and B is positive-definite.
*/
static void genhermv_normalize_eigenvectors(gsl_matrix_complex *evec);
/*
gsl_eigen_genhermv_alloc()
Allocate a workspace for solving the generalized hermitian-definite
eigenvalue problem. The size of this workspace is O(5n).
Inputs: n - size of matrices
Return: pointer to workspace
*/
gsl_eigen_genhermv_workspace *
gsl_eigen_genhermv_alloc(const size_t n)
{
gsl_eigen_genhermv_workspace *w;
if (n == 0)
{
GSL_ERROR_NULL ("matrix dimension must be positive integer",
GSL_EINVAL);
}
w = (gsl_eigen_genhermv_workspace *) calloc (1, sizeof (gsl_eigen_genhermv_workspace));
if (w == 0)
{
GSL_ERROR_NULL ("failed to allocate space for workspace", GSL_ENOMEM);
}
w->size = n;
w->hermv_workspace_p = gsl_eigen_hermv_alloc(n);
if (!w->hermv_workspace_p)
{
gsl_eigen_genhermv_free(w);
GSL_ERROR_NULL("failed to allocate space for hermv workspace", GSL_ENOMEM);
}
return (w);
} /* gsl_eigen_genhermv_alloc() */
/*
gsl_eigen_genhermv_free()
Free workspace w
*/
void
gsl_eigen_genhermv_free (gsl_eigen_genhermv_workspace * w)
{
RETURN_IF_NULL (w);
if (w->hermv_workspace_p)
gsl_eigen_hermv_free(w->hermv_workspace_p);
free(w);
} /* gsl_eigen_genhermv_free() */
/*
gsl_eigen_genhermv()
Solve the generalized hermitian-definite eigenvalue problem
A x = \lambda B x
for the eigenvalues \lambda and eigenvectors x.
Inputs: A - complex hermitian matrix
B - complex hermitian and positive definite matrix
eval - where to store eigenvalues
evec - where to store eigenvectors
w - workspace
Return: success or error
*/
int
gsl_eigen_genhermv (gsl_matrix_complex * A, gsl_matrix_complex * B,
gsl_vector * eval, gsl_matrix_complex * evec,
gsl_eigen_genhermv_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_complex_cholesky_decomp(B);
if (s != GSL_SUCCESS)
return s; /* B is not positive definite */
/* transform to standard hermitian eigenvalue problem */
gsl_eigen_genherm_standardize(A, B);
/* compute eigenvalues and eigenvectors */
s = gsl_eigen_hermv(A, eval, evec, w->hermv_workspace_p);
if (s != GSL_SUCCESS)
return s;
/* backtransform eigenvectors: evec -> L^{-H} evec */
gsl_blas_ztrsm(CblasLeft,
CblasLower,
CblasConjTrans,
CblasNonUnit,
GSL_COMPLEX_ONE,
B,
evec);
/* the blas call destroyed the normalization - renormalize */
genhermv_normalize_eigenvectors(evec);
return GSL_SUCCESS;
}
} /* gsl_eigen_genhermv() */
/********************************************
* INTERNAL ROUTINES *
********************************************/
/*
genhermv_normalize_eigenvectors()
Normalize eigenvectors so that their Euclidean norm is 1
Inputs: evec - eigenvectors
*/
static void
genhermv_normalize_eigenvectors(gsl_matrix_complex *evec)
{
const size_t N = evec->size1;
size_t i; /* looping */
for (i = 0; i < N; ++i)
{
gsl_vector_complex_view vi = gsl_matrix_complex_column(evec, i);
double scale = 1.0 / gsl_blas_dznrm2(&vi.vector);
gsl_blas_zdscal(scale, &vi.vector);
}
} /* genhermv_normalize_eigenvectors() */
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