add numerical recipes library

lib/nr/ansi/recipes/zbrent.c

@@ -0,0 +1,73 @@
+
+#include <math.h>
+#define NRANSI
+#include "nrutil.h"
+#define ITMAX 100
+#define EPS 3.0e-8
+
+float zbrent(float (*func)(float), float x1, float x2, float tol)
+{
+	int iter;
+	float a=x1,b=x2,c=x2,d,e,min1,min2;
+	float fa=(*func)(a),fb=(*func)(b),fc,p,q,r,s,tol1,xm;
+
+	if ((fa > 0.0 && fb > 0.0) || (fa < 0.0 && fb < 0.0))
+		nrerror("Root must be bracketed in zbrent");
+	fc=fb;
+	for (iter=1;iter<=ITMAX;iter++) {
+		if ((fb > 0.0 && fc > 0.0) || (fb < 0.0 && fc < 0.0)) {
+			c=a;
+			fc=fa;
+			e=d=b-a;
+		}
+		if (fabs(fc) < fabs(fb)) {
+			a=b;
+			b=c;
+			c=a;
+			fa=fb;
+			fb=fc;
+			fc=fa;
+		}
+		tol1=2.0*EPS*fabs(b)+0.5*tol;
+		xm=0.5*(c-b);
+		if (fabs(xm) <= tol1 || fb == 0.0) return b;
+		if (fabs(e) >= tol1 && fabs(fa) > fabs(fb)) {
+			s=fb/fa;
+			if (a == c) {
+				p=2.0*xm*s;
+				q=1.0-s;
+			} else {
+				q=fa/fc;
+				r=fb/fc;
+				p=s*(2.0*xm*q*(q-r)-(b-a)*(r-1.0));
+				q=(q-1.0)*(r-1.0)*(s-1.0);
+			}
+			if (p > 0.0) q = -q;
+			p=fabs(p);
+			min1=3.0*xm*q-fabs(tol1*q);
+			min2=fabs(e*q);
+			if (2.0*p < (min1 < min2 ? min1 : min2)) {
+				e=d;
+				d=p/q;
+			} else {
+				d=xm;
+				e=d;
+			}
+		} else {
+			d=xm;
+			e=d;
+		}
+		a=b;
+		fa=fb;
+		if (fabs(d) > tol1)
+			b += d;
+		else
+			b += SIGN(tol1,xm);
+		fb=(*func)(b);
+	}
+	nrerror("Maximum number of iterations exceeded in zbrent");
+	return 0.0;
+}
+#undef ITMAX
+#undef EPS
+#undef NRANSI