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gsl_newt.cpp

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    gsl_newt.cpp 3.26 KiB
    // $Id: gsl_newt.cpp,v 1.15 2006-11-27 22:22:17 geuzaine Exp $
    //
    // Copyright (C) 1997-2007 C. Geuzaine, J.-F. Remacle
    //
    // 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 2 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307
    // USA.
    // 
    // Please report all bugs and problems to <gmsh@geuz.org>.
    //
    // Contributor(s):
    //   Nicolas Tardieu
    //
    
    // This implements a Newton method using the GSL.
    
    #if defined(HAVE_GSL)
    
    #include "Gmsh.h"
    #include "Numeric.h"
    
    #include <gsl/gsl_math.h>
    #include <gsl/gsl_errno.h>
    #include <gsl/gsl_multiroots.h>
    #include <gsl/gsl_linalg.h>
    
    #define MAX_DIM_NEWT 10
    #define MAXITER 10000
    #define PREC 1.e-8
    
    int nrdim;
    double nru[MAX_DIM_NEWT], nrv[MAX_DIM_NEWT];
    static void (*nrfunc) (int n, double x[], double y[]);
    struct gsl_dummy{ int i; };
    
    void convert_vector_from_gsl(const gsl_vector * gv, double *v)
    {
      int i, m;
      m = gv->size;
      for(i = 0; i < m; i++) {
        v[i + 1] = gsl_vector_get(gv, i);
      }
    }
    
    void convert_vector_to_gsl(double *v, int n, gsl_vector * gv)
    {
      int i;
      for(i = 0; i < n; i++) {
        gsl_vector_set(gv, i, v[i + 1]);
      }
    }
    
    int gslfunc(const gsl_vector * xx, void *params, gsl_vector * f)
    {
      convert_vector_from_gsl(xx, nru);
      (*nrfunc) (nrdim, nru, nrv);
      // Msg(INFO, "f(%lf,%lf) = %lf %lf\n",nru[1],nru[2],nrv[1],nrv[2]);
      convert_vector_to_gsl(nrv, nrdim, f);
      return GSL_SUCCESS;
    }
    
    // Warning: for compatibility with the old newt from NR, x[] and the
    // arguments of func() are indexed from 1 to n...
    
    void newt(double x[], int n, int *check,
              void (*func) (int, double[], double[]))
    {
      const gsl_multiroot_fsolver_type *T;
      gsl_multiroot_fsolver *s;
      int status;
      size_t iter = 0;
      struct gsl_dummy p = { 1 };
      gsl_multiroot_function f = { &gslfunc, n, &p };
      gsl_vector *xx = gsl_vector_alloc(n);
    
      if(n > MAX_DIM_NEWT - 1)
        Msg(FATAL, "Maximum Newton dimension exceeded\n");
      nrdim = n;
    
      nrfunc = func;
      convert_vector_to_gsl(x, n, xx);
    
      T = gsl_multiroot_fsolver_hybrid;
      s = gsl_multiroot_fsolver_alloc(T, 2);
      gsl_multiroot_fsolver_set(s, &f, xx);
    
      do {
        iter++;
        status = gsl_multiroot_fsolver_iterate(s);
        // Msg(INFO, "status %d %d %d %lf %lf\n",
        //     status,n,iter,gsl_vector_get(s->x,0),gsl_vector_get(s->x,1));
        if(status)
          break;    // solver problem
        status = gsl_multiroot_test_residual(s->f, n * PREC);
      }
      while(status == GSL_CONTINUE && iter < MAXITER);
    
      if(status == GSL_CONTINUE) {
        *check = 1; // problem !!!
      }
      else {
        // Msg(INFO, "status %d %d %d %lf %lf\n",
        //     status,n,iter,gsl_vector_get(s->x,0),gsl_vector_get(s->x,1));
        convert_vector_from_gsl(s->x, x);
        *check = 0; // converged
      }
    
      gsl_multiroot_fsolver_free(s);
      gsl_vector_free(xx);
    }
    
    #endif