add numerical recipes library

lib/nr/k_and_r/recipes/golden.c

@@ -0,0 +1,44 @@
+
+#include <math.h>
+#define R 0.61803399
+#define C (1.0-R)
+#define SHFT2(a,b,c) (a)=(b);(b)=(c);
+#define SHFT3(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);
+
+float golden(ax,bx,cx,f,tol,xmin)
+float (*f)(),*xmin,ax,bx,cx,tol;
+{
+	float f1,f2,x0,x1,x2,x3;
+
+	x0=ax;
+	x3=cx;
+	if (fabs(cx-bx) > fabs(bx-ax)) {
+		x1=bx;
+		x2=bx+C*(cx-bx);
+	} else {
+		x2=bx;
+		x1=bx-C*(bx-ax);
+	}
+	f1=(*f)(x1);
+	f2=(*f)(x2);
+	while (fabs(x3-x0) > tol*(fabs(x1)+fabs(x2))) {
+		if (f2 < f1) {
+			SHFT3(x0,x1,x2,R*x1+C*x3)
+			SHFT2(f1,f2,(*f)(x2))
+		} else {
+			SHFT3(x3,x2,x1,R*x2+C*x0)
+			SHFT2(f2,f1,(*f)(x1))
+		}
+	}
+	if (f1 < f2) {
+		*xmin=x1;
+		return f1;
+	} else {
+		*xmin=x2;
+		return f2;
+	}
+}
+#undef C
+#undef R
+#undef SHFT2
+#undef SHFT3