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/*
* 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 1.6 2014/10/13 08:53:32 j_novak Exp $" ;
/*
* $Id: zerosec.C,v 1.6 2014/10/13 08:53:32 j_novak Exp $
* $Log: zerosec.C,v $
* Revision 1.6 2014/10/13 08:53:32 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.5 2014/07/04 12:09:06 j_novak
* New argument in zerosec(): a boolean (false by default) for aborting if the number of iteration is greater than the max.
*
* 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 1.6 2014/10/13 08:53:32 j_novak Exp $
*
*/
// Headers C
#include <cstdlib>
#include <cmath>
#include <cassert>
// Headers C++
#include <exception>
// Headers Lorene
#include "headcpp.h"
#include "param.h"
//****************************************************************************
namespace Lorene {
double zerosec(double (*f)(double, const Param&), const Param& parf,
double x1, double x2, double precis, int nitermax, int& niter,
bool abor) {
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 ;
if (abor)
abort () ;
else {
warning = true ;
f0 = 0. ;
}
}
}
while ( ( fabs(dx) > precis ) && ( fabs(f0) > 1.e-15 ) ) ;
if (warning) {
cout << " A zero may have been found at x0 = " << x0 << endl ;
}
return x0 ;
}
}
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