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guma_minimize.cpp

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/* LIBGUL - Geometry Utility Library
 * Copyright (C) 1998-1999 Norbert Irmer
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Library General Public
 * License as published by the Free Software Foundation; either
 * version 2 of the License, or (at your option) any later version.
 *
 * This library 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
 * Library General Public License for more details.
 *
 * You should have received a copy of the GNU Library General Public
 * License along with this library; if not, write to the
 * Free Software Foundation, Inc., 59 Temple Place - Suite 330,
 * Boston, MA 02111-1307, USA.
 */

#include "stdafx.h"
#include "gul_types.h"

namespace guma {

using gul::rtr;

/*-------------------------------------------------------------------------*//**
  Searches the minimum of a function, defined over an intervall.
  uses Golden Section search (a three point bracketing method),
  see "Numerical recipes in C",
  intervall:          ax  <   bx  <   cx,
  function values:  f(ax) > f(bx) < f(cx)                                     */
/*----------------------------------------------------------------------------*/
template< class T >
bool GoldenSectionSearch( T ax, T bx, T cx, T (*func)( T, void * ), void *fdat,
                          T tol, int max_iterations, T *xmin, T *fmin )
{
  T x0,x1,x2,x3,f1,f2;
  int iteration;
    
  x0 = ax;
  x3 = cx;
  
  if( rtr<T>::fabs(cx-bx) > rtr<T>::fabs(bx-ax) )
  {
    x1 = bx;
    x2 = bx + rtr<T>::golden_c()*(cx-bx);
  }
  else
  {
    x2 = bx;
    x1 = bx - rtr<T>::golden_c()*(bx-ax);
  }    
  f1 = func( x1, fdat );
  f2 = func( x2, fdat );

  for( iteration = 0; iteration < max_iterations; iteration++ )
  {
    if( f2 < f1 )
    {
      x0 = x1;
      x1 = x2;
      x2 = rtr<T>::golden_r() * x2 + rtr<T>::golden_c() * x3;
      f1 = f2;
      f2 = func( x2, fdat );
    }
    else
    {
      x3 = x2;
      x2 = x1;
      x1 = rtr<T>::golden_r() * x2 + rtr<T>::golden_c() * x0;
      f2 = f1;
      f1 = func( x1, fdat );
    }    
    if( rtr<T>::fabs(x3-x0) <= tol*(rtr<T>::fabs(x1)+rtr<T>::fabs(x2)) )
      break;
  }
  if( f1 < f2 )
  {
    *xmin = x1;
    *fmin = f1;  
  }
  else
  {
    *xmin = x2;
    *fmin = f2;
  }
  if( iteration == max_iterations ) return false;
  return true;
}
template bool GoldenSectionSearch( 
      float ax, float bx, float cx, float (*func)( float, void * ), void *,
      float tol, int max_iterations, float *xmin, float *fmin );
template bool GoldenSectionSearch( 
      double ax, double bx, double cx, double (*func)( double, void * ), void *,
      double tol, int max_iterations, double *xmin, double *fmin );

}

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