Category : C Source Code
Archive   : RECIPEX.ZIP
Filename : BRENT.C
#define ITMAX 100
#define CGOLD 0.3819660
#define ZEPS 1.0e-10
#define SIGN(a,b) ((b) > 0.0 ? fabs(a) : -fabs(a))
#define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);
float brent(ax,bx,cx,f,tol,xmin)
float ax,bx,cx,tol,*xmin;
float (*f)(); /* ANSI: float (*f)(float); */
{
int iter;
float a,b,d,etemp,fu,fv,fw,fx,p,q,r,tol1,tol2,u,v,w,x,xm;
float e=0.0;
void nrerror();
a=((ax < cx) ? ax : cx);
b=((ax > cx) ? ax : cx);
x=w=v=bx;
fw=fv=fx=(*f)(x);
for (iter=1;iter<=ITMAX;iter++) {
xm=0.5*(a+b);
tol2=2.0*(tol1=tol*fabs(x)+ZEPS);
if (fabs(x-xm) <= (tol2-0.5*(b-a))) {
*xmin=x;
return fx;
}
if (fabs(e) > tol1) {
r=(x-w)*(fx-fv);
q=(x-v)*(fx-fw);
p=(x-v)*q-(x-w)*r;
q=2.0*(q-r);
if (q > 0.0) p = -p;
q=fabs(q);
etemp=e;
e=d;
if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))
d=CGOLD*(e=(x >= xm ? a-x : b-x));
else {
d=p/q;
u=x+d;
if (u-a < tol2 || b-u < tol2)
d=SIGN(tol1,xm-x);
}
} else {
d=CGOLD*(e=(x >= xm ? a-x : b-x));
}
u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));
fu=(*f)(u);
if (fu <= fx) {
if (u >= x) a=x; else b=x;
SHFT(v,w,x,u)
SHFT(fv,fw,fx,fu)
} else {
if (u < x) a=u; else b=u;
if (fu <= fw || w == x) {
v=w;
w=u;
fv=fw;
fw=fu;
} else if (fu <= fv || v == x || v == w) {
v=u;
fv=fu;
}
}
}
nrerror("Too many iterations in BRENT");
*xmin=x;
return fx;
}
#undef ITMAX
#undef CGOLD
#undef ZEPS
#undef SIGN
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