add numerical recipes library

lib/nr/cpp/recipes/rtsafe.cpp

@@ -0,0 +1,52 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+DP NR::rtsafe(void funcd(const DP, DP &, DP &), const DP x1, const DP x2,
+	const DP xacc)
+{
+	const int MAXIT=100;
+	int j;
+	DP df,dx,dxold,f,fh,fl,temp,xh,xl,rts;
+
+	funcd(x1,fl,df);
+	funcd(x2,fh,df);
+	if ((fl > 0.0 && fh > 0.0) || (fl < 0.0 && fh < 0.0))
+		nrerror("Root must be bracketed in rtsafe");
+	if (fl == 0.0) return x1;
+	if (fh == 0.0) return x2;
+	if (fl < 0.0) {
+		xl=x1;
+		xh=x2;
+	} else {
+		xh=x1;
+		xl=x2;
+	}
+	rts=0.5*(x1+x2);
+	dxold=fabs(x2-x1);
+	dx=dxold;
+	funcd(rts,f,df);
+	for (j=0;j<MAXIT;j++) {
+		if ((((rts-xh)*df-f)*((rts-xl)*df-f) > 0.0)
+			|| (fabs(2.0*f) > fabs(dxold*df))) {
+			dxold=dx;
+			dx=0.5*(xh-xl);
+			rts=xl+dx;
+			if (xl == rts) return rts;
+		} else {
+			dxold=dx;
+			dx=f/df;
+			temp=rts;
+			rts -= dx;
+			if (temp == rts) return rts;
+		}
+		if (fabs(dx) < xacc) return rts;
+		funcd(rts,f,df);
+		if (f < 0.0)
+			xl=rts;
+		else
+			xh=rts;
+	}
+	nrerror("Maximum number of iterations exceeded in rtsafe");
+	return 0.0;
+}