add numerical recipes library

lib/nr/cpp/recipes/rkqs.cpp

@@ -0,0 +1,31 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::rkqs(Vec_IO_DP &y, Vec_IO_DP &dydx, DP &x, const DP htry,
+	const DP eps, Vec_I_DP &yscal, DP &hdid, DP &hnext,
+	void derivs(const DP, Vec_I_DP &, Vec_O_DP &))
+{
+	const DP SAFETY=0.9, PGROW=-0.2, PSHRNK=-0.25, ERRCON=1.89e-4;
+	int i;
+	DP errmax,h,htemp,xnew;
+
+	int n=y.size();
+	h=htry;
+	Vec_DP yerr(n),ytemp(n);
+	for (;;) {
+		rkck(y,dydx,x,h,ytemp,yerr,derivs);
+		errmax=0.0;
+		for (i=0;i<n;i++) errmax=MAX(errmax,fabs(yerr[i]/yscal[i]));
+		errmax /= eps;
+		if (errmax <= 1.0) break;
+		htemp=SAFETY*h*pow(errmax,PSHRNK);
+		h=(h >= 0.0 ? MAX(htemp,0.1*h) : MIN(htemp,0.1*h));
+		xnew=x+h;
+		if (xnew == x) nrerror("stepsize underflow in rkqs");
+	}
+	if (errmax > ERRCON) hnext=SAFETY*h*pow(errmax,PGROW);
+	else hnext=5.0*h;
+	x += (hdid=h);
+	for (i=0;i<n;i++) y[i]=ytemp[i];
+}