add numerical recipes library

lib/nr/cpp/recipes/odeint.cpp

@@ -0,0 +1,54 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+extern DP dxsav;
+extern int kmax,kount;
+extern Vec_DP *xp_p;
+extern Mat_DP *yp_p;
+
+void NR::odeint(Vec_IO_DP &ystart, const DP x1, const DP x2, const DP eps,
+	const DP h1, const DP hmin, int &nok, int &nbad,
+	void derivs(const DP, Vec_I_DP &, Vec_O_DP &),
+	void rkqs(Vec_IO_DP &, Vec_IO_DP &, DP &, const DP, const DP,
+	Vec_I_DP &, DP &, DP &, void (*)(const DP, Vec_I_DP &, Vec_O_DP &)))
+{
+	const int MAXSTP=10000;
+	const DP TINY=1.0e-30;
+	int i,nstp;
+	DP xsav,x,hnext,hdid,h;
+
+	int nvar=ystart.size();
+	Vec_DP yscal(nvar),y(nvar),dydx(nvar);
+	Vec_DP &xp=*xp_p;
+	Mat_DP &yp=*yp_p;
+	x=x1;
+	h=SIGN(h1,x2-x1);
+	nok = nbad = kount = 0;
+	for (i=0;i<nvar;i++) y[i]=ystart[i];
+	if (kmax > 0) xsav=x-dxsav*2.0;
+	for (nstp=0;nstp<MAXSTP;nstp++) {
+		derivs(x,y,dydx);
+		for (i=0;i<nvar;i++)
+			yscal[i]=fabs(y[i])+fabs(dydx[i]*h)+TINY;
+		if (kmax > 0 && kount < kmax-1 && fabs(x-xsav) > fabs(dxsav)) {
+			for (i=0;i<nvar;i++) yp[i][kount]=y[i];
+			xp[kount++]=x;
+			xsav=x;
+		}
+		if ((x+h-x2)*(x+h-x1) > 0.0) h=x2-x;
+		rkqs(y,dydx,x,h,eps,yscal,hdid,hnext,derivs);
+		if (hdid == h) ++nok; else ++nbad;
+		if ((x-x2)*(x2-x1) >= 0.0) {
+			for (i=0;i<nvar;i++) ystart[i]=y[i];
+			if (kmax != 0) {
+				for (i=0;i<nvar;i++) yp[i][kount]=y[i];
+				xp[kount++]=x;
+			}
+			return;
+		}
+		if (fabs(hnext) <= hmin) nrerror("Step size too small in odeint");
+		h=hnext;
+	}
+	nrerror("Too many steps in routine odeint");
+}