zerosec.C

/*
 * Search for a zero of a function in a given interval, by means of a
 *  secant method.
 *
 */

/*
 *   Copyright (c) 1999-2001 Eric Gourgoulhon
 *
 *   This file is part of LORENE.
 *
 *   LORENE 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.
 *
 *   LORENE 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 LORENE; if not, write to the Free Software
 *   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 *
 */


char zerosec_C[] = "$Header: /cvsroot/Lorene/C++/Source/Non_class_members/Utilities/zerosec.C,v 1.4 2002/10/16 14:37:12 j_novak Exp $" ;

/*
 * $Id: zerosec.C,v 1.4 2002/10/16 14:37:12 j_novak Exp $
 * $Log: zerosec.C,v $
 * Revision 1.4  2002/10/16 14:37:12  j_novak
 * Reorganization of #include instructions of standard C++, in order to
 * use experimental version 3 of gcc.
 *
 * Revision 1.3  2002/04/11 09:19:46  j_novak
 * Back to old version of zerosec
 *
 * Revision 1.1.1.1  2001/11/20 15:19:29  e_gourgoulhon
 * LORENE
 *
 * Revision 1.6  2001/10/17  08:16:47  eric
 * In case there is not a single zero in the interval, the found
 * zero is displayed in the warning message.
 *
 * Revision 1.5  2000/01/04  13:20:34  eric
 * Test final f0 != double(0) remplace par fabs(f0) > 1.e-15 .
 *
 * Revision 1.4  1999/12/20  09:46:08  eric
 * Anglicisation des messages.
 *
 * Revision 1.3  1999/12/17  10:08:46  eric
 * Le test final fabs(f0) > 1.e-14 est remplace par f0 != 0.
 *
 * Revision 1.2  1999/12/17  09:37:40  eric
 * Ajout de assert(df != 0).
 *
 * Revision 1.1  1999/12/15  09:41:34  eric
 * Initial revision
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Non_class_members/Utilities/zerosec.C,v 1.4 2002/10/16 14:37:12 j_novak Exp $
 *
 */

// Headers C
#include <stdlib.h>
#include <math.h>
#include <assert.h>

// Headers Lorene 
#include "headcpp.h"
#include "param.h"
//****************************************************************************

double zerosec(double (*f)(double, const Param&), const Param& parf, 
    double x1, double x2, double precis, int nitermax, int& niter) {
    
    double f0_prec, f0, x0, x0_prec, dx, df ;

// Teste si un zero unique existe dans l'intervalle [x_1,x_2]

    bool warning = false ; 
    
    f0_prec = f(x1, parf) ;
    f0 = f(x2, parf) ;
    if ( f0*f0_prec > 0.) {
    warning = true ; 
    cout << 
      "WARNING: zerosec: there does not exist a unique zero of the function" 
    << endl ;
    cout << "  between x1 = " << x1 << " ( f(x1)=" << f0_prec << " )" << endl ; 
    cout << "      and x2 = " << x2 << " ( f(x2)=" << f0 << " )" << endl ;
    }

// Choisit la borne avec la plus petite valeur de |f(x)| comme la valeur la
//  "plus recente" de x0

    if ( fabs(f0) < fabs(f0_prec) ) {  // On a bien choisi f0_prec et f0
    x0_prec = x1 ;
    x0 = x2 ;
    }
    else {  // il faut interchanger f0_prec et f0
    x0_prec = x2 ;
    x0 = x1 ;
    double swap = f0_prec ;
    f0_prec = f0 ;
    f0 = swap ; 
    }

// Debut des iterations de la methode de la secante
    
    niter = 0 ;
    do {
    df = f0 - f0_prec ;
    assert(df != double(0)) ; 
    dx = (x0_prec - x0) * f0 / df ;
    x0_prec = x0 ;
    f0_prec = f0 ;
    x0 += dx ;
    f0 = f(x0, parf) ;
    niter++ ;
    if (niter > nitermax) {
        cout << "zerosec: Maximum number of iterations has been reached ! " 
        << endl ;
        abort () ;
    }
    }
    while ( ( fabs(dx) > precis ) && ( fabs(f0) > 1.e-15 ) ) ;

    if (warning) {
    cout << "      A zero has been found at x0 = " << x0 << endl ; 
    }

    return x0 ;
}  

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