add numerical recipes library

lib/nr/cpp/recipes/golden.cpp

@@ -0,0 +1,53 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+namespace {
+	inline void shft2(DP &a, DP &b, const DP c)
+	{
+		a=b;
+		b=c;
+	}
+
+	inline void shft3(DP &a, DP &b, DP &c, const DP d)
+	{
+		a=b;
+		b=c;
+		c=d;
+	}
+}
+
+DP NR::golden(const DP ax, const DP bx, const DP cx, DP f(const DP),
+	const DP tol, DP &xmin)
+{
+	const DP R=0.61803399,C=1.0-R;
+	DP 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*x2+C*x3);
+			shft2(f1,f2,f(x2));
+		} else {
+			shft3(x3,x2,x1,R*x1+C*x0);
+			shft2(f2,f1,f(x1));
+		}
+	}
+	if (f1 < f2) {
+		xmin=x1;
+		return f1;
+	} else {
+		xmin=x2;
+		return f2;
+	}
+}