add numerical recipes library

lib/nr/cpp/recipes/brent.cpp

@@ -0,0 +1,79 @@
+#include <cmath>
+#include <limits>
+#include "nr.h"
+using namespace std;
+
+namespace {
+	inline void shft3(DP &a, DP &b, DP &c, const DP d)
+	{
+		a=b;
+		b=c;
+		c=d;
+	}
+}
+
+DP NR::brent(const DP ax, const DP bx, const DP cx, DP f(const DP),
+	const DP tol, DP &xmin)
+{
+	const int ITMAX=100;
+	const DP CGOLD=0.3819660;
+	const DP ZEPS=numeric_limits<DP>::epsilon()*1.0e-3;
+	int iter;
+	DP a,b,d=0.0,etemp,fu,fv,fw,fx;
+	DP p,q,r,tol1,tol2,u,v,w,x,xm;
+	DP e=0.0;
+
+	a=(ax < cx ? ax : cx);
+	b=(ax > cx ? ax : cx);
+	x=w=v=bx;
+	fw=fv=fx=f(x);
+	for (iter=0;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;
+			shft3(v,w,x,u);
+			shft3(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;
+}