/* multiroots/gnewton.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.

 */

#include <config.h>

#include <stddef.h>

#include <stdlib.h>

#include <stdio.h>

#include <math.h>

#include <float.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_multiroots.h>

#include <gsl/gsl_linalg.h>

#include "enorm.c"

/* Simple globally convergent Newton method (rejects uphill steps) */

typedef struct

  {

    double phi;

    gsl_vector * x_trial;

    gsl_vector * d;

    gsl_matrix * lu;

    gsl_permutation * permutation;

  }

gnewton_state_t;

static int gnewton_alloc (void * vstate, size_t n);

static int gnewton_set (void * vstate, gsl_multiroot_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx);

static int gnewton_iterate (void * vstate, gsl_multiroot_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx);

static void gnewton_free (void * vstate);

static int

gnewton_alloc (void * vstate, size_t n)

{

  gnewton_state_t * state = (gnewton_state_t *) vstate;

  gsl_vector * d, * x_trial ;

  gsl_permutation * p;

  gsl_matrix * m;

  m = gsl_matrix_calloc (n,n);

  if (m == 0) 

    {

      GSL_ERROR ("failed to allocate space for lu", GSL_ENOMEM);

    }

  state->lu = m ;

  p = gsl_permutation_calloc (n);

  if (p == 0)

    {

      gsl_matrix_free(m);

      GSL_ERROR ("failed to allocate space for permutation", GSL_ENOMEM);

    }

  state->permutation = p ;

  d = gsl_vector_calloc (n);

  if (d == 0)

    {

      gsl_permutation_free(p);

      gsl_matrix_free(m);

      GSL_ERROR ("failed to allocate space for d", GSL_ENOMEM);

    }

  state->d = d;

  x_trial = gsl_vector_calloc (n);

  if (x_trial == 0)

    {

      gsl_vector_free(d);

      gsl_permutation_free(p);

      gsl_matrix_free(m);

      GSL_ERROR ("failed to allocate space for x_trial", GSL_ENOMEM);

    }

  state->x_trial = x_trial;

  return GSL_SUCCESS;

}

static int

gnewton_set (void * vstate, gsl_multiroot_function_fdf * FDF, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx)

{

  gnewton_state_t * state = (gnewton_state_t *) vstate;

  size_t i, n = FDF->n ;

  GSL_MULTIROOT_FN_EVAL_F_DF (FDF, x, f, J);

  for (i = 0; i < n; i++)

    {

      gsl_vector_set (dx, i, 0.0);

    }

  state->phi = enorm(f);

  return GSL_SUCCESS;

}

static int

gnewton_iterate (void * vstate, gsl_multiroot_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx)

{

  gnewton_state_t * state = (gnewton_state_t *) vstate;

  int signum ;

  double t, phi0, phi1;

  size_t i;

  size_t n = fdf->n ;

  gsl_matrix_memcpy (state->lu, J);

  gsl_linalg_LU_decomp (state->lu, state->permutation, &signum);

  {

    int status = gsl_linalg_LU_solve (state->lu, state->permutation, f, state->d);

    if (status)

      return status;

  }

  t = 1;

  phi0 = state->phi;

new_step:

  for (i = 0; i < n; i++)

    {

      double di = gsl_vector_get (state->d, i);

      double xi = gsl_vector_get (x, i);

      gsl_vector_set (state->x_trial, i, xi - t*di);

    }

  { 

    int status = GSL_MULTIROOT_FN_EVAL_F (fdf, state->x_trial, f);

    if (status != GSL_SUCCESS)

      {

        return GSL_EBADFUNC;

      }

  }

  phi1 = enorm (f);

  if (phi1 > phi0 && t > GSL_DBL_EPSILON)  

    {

      /* full step goes uphill, take a reduced step instead */

      double theta = phi1 / phi0;

      double u = (sqrt(1.0 + 6.0 * theta) - 1.0) / (3.0 * theta);

      t *= u ;

      goto new_step;

    }

  /* copy x_trial into x */

  gsl_vector_memcpy (x, state->x_trial);

  for (i = 0; i < n; i++)

    {

      double di = gsl_vector_get (state->d, i);

      gsl_vector_set (dx, i, -t*di);

    }

  { 

    int status = GSL_MULTIROOT_FN_EVAL_DF (fdf, x, J);

    if (status != GSL_SUCCESS)

      {

        return GSL_EBADFUNC;

      }

  }

  state->phi = phi1;

  return GSL_SUCCESS;

}

static void

gnewton_free (void * vstate)

{

  gnewton_state_t * state = (gnewton_state_t *) vstate;

  gsl_vector_free(state->d);

  gsl_vector_free(state->x_trial);

  gsl_matrix_free(state->lu);

  gsl_permutation_free(state->permutation);

}

static const gsl_multiroot_fdfsolver_type gnewton_type =

{"gnewton",                             /* name */

 sizeof (gnewton_state_t),

 &gnewton_alloc,

 &gnewton_set,

 &gnewton_iterate,

 &gnewton_free};

const gsl_multiroot_fdfsolver_type  * gsl_multiroot_fdfsolver_gnewton = &gnewton_type;