text: /* 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;
  