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/*
freesteam - IAPWS-IF97 steam tables library
Copyright (C) 2004-2009 John Pye
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.
*/
#define FREESTEAM_BUILDING_LIB
#include "zeroin.h"
#include <math.h>
#include <stdio.h>
#ifndef DBL_EPSILON
#define DBL_EPSILON 2e-16
#endif
char zeroin_solve(ZeroInSubjectFunction *func, void *user_data, double lowerbound, double upperbound, double tol, double *solution, double *error){
double a, b, c; /* Abscissae, descr. see above. */
double fa;
double fb;
double fc;
a = lowerbound;
b = upperbound;
fa = (*func)(a,user_data);
fb = (*func)(b,user_data);
c = a;
fc = fa;
if(fa == 0.){
*error = 0.; /* used by getError */
*solution = a;
return 0;
}
/* Main iteration loop */
for (;;) {
double prev_step = b - a; /* Distance from the last but one to the last approximation */
double tol_act; /* Actual tolerance */
double p; /* Interpolation step is calculated in the form p/q; division */
double q; /* operations is delayed until the last moment */
double new_step; /* Step at this iteration */
if (fabs(fc) < fabs(fb)) {
a = b;
b = c;
c = a; /* Swap data for b to be the best approximation */
fa = fb;
fb = fc;
fc = fa;
}
/* DBL_EPSILON is defined in math.h */
tol_act = 2.0* DBL_EPSILON * fabs(b) + tol / 2.0;
new_step = (c - b) / 2.0;
if (fabs(new_step) <= tol_act || fb == 0.) {
*error = fb;
*solution = b;
return 0;
}
/* Decide if the interpolation can be tried */
if (fabs(prev_step) >= tol_act /* If prev_step was large enough and was in true direction, */
&& fabs(fa) > fabs(fb)) /* Interpolatiom may be tried */
{
register double t1, t2;
double cb;
cb = c - b;
if (a == c) {
/* If we have only two distinct points
then only linear interpolation can be applied */
t1 = fb / fa;
p = cb * t1;
q = 1.0 - t1;
} else {
/* Quadric inverse interpolation */
q = fa / fc;
t1 = fb / fc;
t2 = fb / fa;
p = t2 * (cb * q * (q - t1) - (b - a) * (t1 - 1.0));
q = (q - 1.0) * (t1 - 1.0) * (t2 - 1.0);
}
if (p > 0.) {
/* p was calculated with the opposite sign; make p positive- */
q = -q; /* and assign possible minus to q */
} else {
p = -p;
}
if (p < (0.75 * cb * q - fabs(tol_act * q) / 2.0)
&& p < fabs(prev_step * q / 2.0)
) {
/* If b+p/q falls in [b,c] and
isn't too large it is accepted */
new_step = p / q;
}
/* If p/q is too large then the bissection procedure can
reduce [b,c] range to more extent */
}
if (fabs(new_step) < tol_act) { /* Adjust the step to be not less */
if (new_step > 0.) /* than tolerance */
new_step = tol_act;
else
new_step = -tol_act;
}
a = b;
fa = fb; /* Save the previous approx. */
b += new_step;
fb = (*func)(b,user_data); /* Do step to a new approxim. */
if ((fb > 0. && fc > 0.)
|| (fb < 0. && fc < 0.)) {
c = a;
fc = fa; /* Adjust c for it to have a sign opposite to that of b */
}
}
/* (((we never arrive here))) */
}
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