/* poly/zsolve.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 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.

 */

/* zsolve.c - finds the complex roots of  = 0 */

#include <config.h>

#include <math.h>

#include <stdlib.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_complex.h>

#include <gsl/gsl_poly.h>

/* C-style matrix elements */

#define MAT(m,i,j,n) ((m)[(i)*(n) + (j)])

/* Fortran-style matrix elements */

#define FMAT(m,i,j,n) ((m)[((i)-1)*(n) + ((j)-1)])

#include "companion.c"

#include "balance.c"

#include "qr.c"

int

gsl_poly_complex_solve (const double *a, size_t n,

                        gsl_poly_complex_workspace * w,

                        gsl_complex_packed_ptr z)

{

  int status;

  double *m;

  if (n == 0)

    {

      GSL_ERROR ("number of terms must be a positive integer", GSL_EINVAL);

    }

  if (n == 1)

    {

      GSL_ERROR ("cannot solve for only one term", GSL_EINVAL);

    }

  if (a[n - 1] == 0)

    {

      GSL_ERROR ("leading term of polynomial must be non-zero", GSL_EINVAL) ;

    }

  if (w->nc != n - 1)

    {

      GSL_ERROR ("size of workspace does not match polynomial", GSL_EINVAL);

    }

  m = w->matrix;

  set_companion_matrix (a, n - 1, m);

  balance_companion_matrix (m, n - 1);

  status = qr_companion (m, n - 1, z);

  if (status)

    {

      GSL_ERROR("root solving qr method failed to converge", GSL_EFAILED);

    }

  return GSL_SUCCESS;

}