/* eigen/symm.c

 * 

 * Copyright (C) 2001, 2007 Brian Gough

 * 

 * 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 <config.h>

#include <stdlib.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_vector.h>

#include <gsl/gsl_matrix.h>

#include <gsl/gsl_linalg.h>

#include <gsl/gsl_eigen.h>

/* Compute eigenvalues/eigenvectors of real symmetric matrix using

   reduction to tridiagonal form, followed by QR iteration with

   implicit shifts.

   See Golub & Van Loan, "Matrix Computations" (3rd ed), Section 8.3

   */

#include "qrstep.c"

gsl_eigen_symm_workspace *

gsl_eigen_symm_alloc (const size_t n)

{

  gsl_eigen_symm_workspace *w;

  if (n == 0)

    {

      GSL_ERROR_NULL ("matrix dimension must be positive integer",

                      GSL_EINVAL);

    }

  w = ((gsl_eigen_symm_workspace *)

       malloc (sizeof (gsl_eigen_symm_workspace)));

  if (w == 0)

    {

      GSL_ERROR_NULL ("failed to allocate space for workspace", GSL_ENOMEM);

    }

  w->d = (double *) malloc (n * sizeof (double));

  if (w->d == 0)

    {

      GSL_ERROR_NULL ("failed to allocate space for diagonal", GSL_ENOMEM);

    }

  w->sd = (double *) malloc (n * sizeof (double));

  if (w->sd == 0)

    {

      GSL_ERROR_NULL ("failed to allocate space for subdiagonal", GSL_ENOMEM);

    }

  w->size = n;

  return w;

}

void

gsl_eigen_symm_free (gsl_eigen_symm_workspace * w)

{

  RETURN_IF_NULL (w);

  free (w->sd);

  free (w->d);

  free (w);

}

int

gsl_eigen_symm (gsl_matrix * A, gsl_vector * eval,

                gsl_eigen_symm_workspace * w)

{

  if (A->size1 != A->size2)

    {

      GSL_ERROR ("matrix must be square to compute eigenvalues", GSL_ENOTSQR);

    }

  else if (eval->size != A->size1)

    {

      GSL_ERROR ("eigenvalue vector must match matrix size", GSL_EBADLEN);

    }

  else if (A->size1 != w->size)

    {

      GSL_ERROR ("matrix does not match workspace", GSL_EBADLEN);

    }

  else

    {

      const size_t N = A->size1;

      double *const d = w->d;

      double *const sd = w->sd;

      size_t a, b;

      /* handle special case */

      if (N == 1)

        {

          double A00 = gsl_matrix_get (A, 0, 0);

          gsl_vector_set (eval, 0, A00);

          return GSL_SUCCESS;

        }

      /* use sd as the temporary workspace for the decomposition,

         since we can discard the tau result immediately if we are not

         computing eigenvectors */

      {

        gsl_vector_view d_vec = gsl_vector_view_array (d, N);

        gsl_vector_view sd_vec = gsl_vector_view_array (sd, N - 1);

        gsl_vector_view tau = gsl_vector_view_array (sd, N - 1);

        gsl_linalg_symmtd_decomp (A, &tau.vector);

        gsl_linalg_symmtd_unpack_T (A, &d_vec.vector, &sd_vec.vector);

      }

      /* Make an initial pass through the tridiagonal decomposition

         to remove off-diagonal elements which are effectively zero */

      chop_small_elements (N, d, sd);

      /* Progressively reduce the matrix until it is diagonal */

      b = N - 1;

      while (b > 0)

        {

          if (sd[b - 1] == 0.0 || isnan(sd[b - 1]))

            {

              b--;

              continue;

            }

          /* Find the largest unreduced block (a,b) starting from b

             and working backwards */

          a = b - 1;

          while (a > 0)

            {

              if (sd[a - 1] == 0.0)

                {

                  break;

                }

              a--;

            }

          {

            const size_t n_block = b - a + 1;

            double *d_block = d + a;

            double *sd_block = sd + a;

            /* apply QR reduction with implicit deflation to the

               unreduced block */

            qrstep (n_block, d_block, sd_block, NULL, NULL);

            /* remove any small off-diagonal elements */

            chop_small_elements (n_block, d_block, sd_block);

          }

        }

      {

        gsl_vector_view d_vec = gsl_vector_view_array (d, N);

        gsl_vector_memcpy (eval, &d_vec.vector);

      }

      return GSL_SUCCESS;

    }

}