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/* 1 dimentional root finding code */
/* inspired by the Van Wijngaarden-Dekker-Brent */
/* method algorithm presented in */
/* "Numerical Recipes in C", by W.H.Press, */
/* B.P.Flannery, S.A.Teukolsky & W.T.Vetterling. */
/*
* Copyright 2000 Graeme W. Gill
* All rights reserved.
*
* This material is licenced under the GNU AFFERO GENERAL PUBLIC LICENSE Version 3 :-
* see the License.txt file for licencing details.
*/
#include "numsup.h"
#include "zbrent.h"
#undef DEBUG
#define ZBRACK_MAXTRY 40 /* Maximum tries to bracket */
#define ZBRACK_GOLD 1.618034 /* Golden ratio */
/* Bracket search function */
/* return 0 on sucess */
/* -1 on no range */
/* -2 on too many itterations */
int zbrac(
double *x1p, /* Input and output bracket values */
double *x2p, /* Min and Max */
double (*func)(void *fdata, double tp), /* function to evaluate */
void *fdata /* Opaque data pointer */
) {
int i;
double x1, x2; /* Bracket under consideration */
double f1, f2; /* Function values at points x1 and x2 */
x1 = *x1p;
x2 = *x2p;
if (x1 == x2) /* Nowhere to go */
return -1;
f1 = (*func)(fdata, x1); /* Initial function values */
f2 = (*func)(fdata, x2);
for (i = 0; i < ZBRACK_MAXTRY; i++) {
if ((f1 * f2) < 0.0) {
*x1p = x1;
*x2p = x2;
return 0; /* If signs are opposite, we're done */
}
if (fabs(f2) > fabs(f1)) { /* Move smaller in direction away from larger */
x1 += ZBRACK_GOLD * (x1 - x2);
f1 = (*func)(fdata, x1);
} else {
x2 += ZBRACK_GOLD * (x2 - x1);
f2 = (*func)(fdata, x2);
}
}
return -2;
}
#undef ZBRACK_GOLD
#undef ZBRACK_MAXTRY
#define ZBRENT_MAXIT 100
/* Root finder */
/* return 0 on sucess */
/* -1 on root not bracketed */
/* -2 on too many itterations */
int zbrent(
double *rv, /* Return value */
double ax, /* Bracket to search */
double bx, /* (Min, Max) */
double tol, /* Desired tollerance */
double (*func)(void *fdata, double tp), /* function to evaluate */
void *fdata /* Opaque data pointer */
) {
int i;
double cx; /* Trial points, bx = best current */
double af ,bf, cf; /* Function values at those points */
af = (*func)(fdata, ax);
bf = (*func)(fdata, bx);
/* Sanity check bracketing */
if (af * bf > 0.0)
return -1; /* No good */
cx = bx; /* Force bisection for first itter */
cf = bf;
for (i = 0; i < ZBRENT_MAXIT; i++) {
double xdel; /* Bisection delta to bx */
double del = 1e80; /* Delta to be applied to bx */
double pdel = 1e80; /* Last del from interpolation step */
double tol1; /* Minimum reasonable change in bx */
/* Make bx and cx straddle root */
if (bf * cf > 0.0) { /* bx and cx don't straddle root */
cx = ax; /* ax must, so make cx = ax */
cf = af;
pdel = del = bx - ax;
}
/* Make bx be point closest to solution */
if (fabs(cf) < fabs(bf)) {
ax = bx; /* swap bx & cx, and make ax == new cx */
af = bf;
bx = cx;
bf = cf;
cx = ax;
cf = af;
}
tol1 = (0.5 * tol) + (2.0 * DBL_EPSILON * fabs(bx)); /* Minimum tollerable bx move */
xdel = 0.5 * (cx - bx); /* Delta to bx for bisection move */
if (bf == 0.0 || fabs(xdel) <= tol1) { /* If exact soln, or last was min move */
*rv = bx;
return 0;
}
if (fabs(pdel) >= tol1 && fabs(af) > fabs(bf)) { /* Try inv. quadratic interpolation */
double P, Q;
if (ax == cx) { /* Only have 2 points, use extrapolation */
double R;
R = bf / cf;
P = (cx - bx) * R;
Q = R - 1.0;
} else { /* Brent's interpolation of 3 points */
double R, S, T;
R = bf / cf;
S = bf / af;
T = af / cf;
P = S * ((T * (R - T) * (cx - bx)) - ((1.0 - R) * (bx - ax)));
Q = (T - 1.0) * (R - 1.0) * (S - 1.0);
}
if (P < 0.0) /* Keep sign of P/Q with abs(P) */
Q = -Q;
P = fabs(P);
{
double min1, min2;
min1 = (3.0 * xdel * Q) - (tol1 * fabs(Q));
min2 = fabs(pdel * Q);
if (min2 < min1)
min1 = min2;
if ((2.0 * P) < min1) { /* Interpolation looks OK */
pdel = del; /* Remember last delta */
del = P / Q; /* Next delta */
} else {
pdel = del = xdel; /* Use bisection */
}
}
} else {
pdel = del = xdel; /* Use bisection */
}
ax = bx; /* a keeps previous best point */
af = bf;
if (fabs(del) > tol1) /* Delta looks reasonable */
bx += del;
else
bx += (xdel > 0.0 ? tol1 : -tol1); /* Do minimum move in direction of bisection */
bf = (*func)(fdata, bx);
}
return -2; /* Too many iterations */
}
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