1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
|
/*
* Search for a zero of a function in a given interval, by means of a
* secant method. The input parameters x1 and x2 must be such that
* f(x1)*f(x2) < 0 . The obtained root is then necessarily in the
* interval [x1,x2].
*
*/
/*
* Copyright (c) 2002 Jerome Novak
*
* 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_borne_C[] = "$Header: /cvsroot/Lorene/C++/Source/Non_class_members/Utilities/zerosec_borne.C,v 1.7 2014/10/13 08:53:32 j_novak Exp $" ;
/*
* $Id: zerosec_borne.C,v 1.7 2014/10/13 08:53:32 j_novak Exp $
* $Log: zerosec_borne.C,v $
* Revision 1.7 2014/10/13 08:53:32 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.6 2014/10/06 15:16:11 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.5 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 1.4 2002/05/02 15:16:22 j_novak
* Added functions for more general bi-fluid EOS
*
* Revision 1.3 2002/04/18 09:17:17 j_novak
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Source/Non_class_members/Utilities/zerosec_borne.C,v 1.7 2014/10/13 08:53:32 j_novak Exp $
*
*/
// Headers C
#include <cstdlib>
#include <cmath>
#include <cassert>
// Headers Lorene
#include "headcpp.h"
#include "param.h"
//****************************************************************************
namespace Lorene {
double zerosec_b(double (*f)(double, const Param&), const Param& parf,
double x1, double x2, double precis, int nitermax, int& niter) {
double f0_moins, f0, x0, x0_moins, dx, df , fnew, xnew;
// Teste si un zero unique existe dans l'intervalle [x_1,x_2]
f0_moins = f(x1, parf) ;
f0 = f(x2, parf) ;
if ( f0*f0_moins > 0.) {
cout <<
"WARNING: zerosec: there may not exist a zero of the function"
<< endl ;
cout << " between x1 = " << x1 << " ( f(x1)=" << f0_moins << " )" << endl ;
cout << " and x2 = " << x2 << " ( f(x2)=" << f0 << " )" << endl ;
}
// Choisit la borne avec la plus grande valeur de f(x) (borne positive)
// comme la valeur la de x0
if ( f0_moins < f0) { // On a bien choisi f0_moins et f0
x0_moins = x1 ;
x0 = x2 ;
}
else { // il faut interchanger f0_moins et f0
x0_moins = x2 ;
x0 = x1 ;
double swap = f0_moins ;
f0_moins = f0 ;
f0 = swap ;
}
// Debut des iterations de la methode de la secante
niter = 0 ;
do {
df = f0 - f0_moins ;
assert(df != double(0)) ;
xnew = (x0_moins*f0 - x0*f0_moins)/df ; ;
fnew = f(xnew, parf) ;
if (fnew < 0.) {
dx = x0_moins - xnew ;
x0_moins = xnew ;
f0_moins = fnew ;
}
else {
dx = x0 - xnew ;
x0 = xnew ;
f0 = fnew ;
}
niter++ ;
if (niter > nitermax) {
//cout << "zerosec: Maximum number of iterations has been reached ! "
// << endl ;
//cout << x0_moins << ", " << xnew << ", " << x0 << endl ;
//cout << f0_moins << ", " << fnew << ", " << f0 << endl ;
return xnew ;
}
}
while ( ( fabs(dx) > precis ) && ( fabs(fnew) > 1.e-15 ) ) ;
return xnew ;
}
}
|
