add numerical recipes library

lib/nr/cpp/recipes/powell.cpp

@@ -0,0 +1,51 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::powell(Vec_IO_DP &p, Mat_IO_DP &xi, const DP ftol, int &iter,
+	DP &fret, DP func(Vec_I_DP &))
+{
+	const int ITMAX=200;
+	const DP TINY=1.0e-25;
+	int i,j,ibig;
+	DP del,fp,fptt,t;
+
+	int n=p.size();
+	Vec_DP pt(n),ptt(n),xit(n);
+	fret=func(p);
+	for (j=0;j<n;j++) pt[j]=p[j];
+	for (iter=0;;++iter) {
+		fp=fret;
+		ibig=0;
+		del=0.0;
+		for (i=0;i<n;i++) {
+			for (j=0;j<n;j++) xit[j]=xi[j][i];
+			fptt=fret;
+			linmin(p,xit,fret,func);
+			if (fptt-fret > del) {
+				del=fptt-fret;
+				ibig=i+1;
+			}
+		}
+		if (2.0*(fp-fret) <= ftol*(fabs(fp)+fabs(fret))+TINY) {
+			return;
+		}
+		if (iter == ITMAX) nrerror("powell exceeding maximum iterations.");
+		for (j=0;j<n;j++) {
+			ptt[j]=2.0*p[j]-pt[j];
+			xit[j]=p[j]-pt[j];
+			pt[j]=p[j];
+		}
+		fptt=func(ptt);
+		if (fptt < fp) {
+			t=2.0*(fp-2.0*fret+fptt)*SQR(fp-fret-del)-del*SQR(fp-fptt);
+			if (t < 0.0) {
+				linmin(p,xit,fret,func);
+				for (j=0;j<n;j++) {
+					xi[j][ibig-1]=xi[j][n-1];
+					xi[j][n-1]=xit[j];
+				}
+			}
+		}
+	}
+}