/* 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() */