add numerical recipes library

lib/nr/cpp/recipes/mmid.cpp

@@ -0,0 +1,31 @@
+#include "nr.h"
+
+void NR::mmid(Vec_I_DP &y, Vec_I_DP &dydx, const DP xs, const DP htot,
+	const int nstep, Vec_O_DP &yout,
+	void derivs(const DP, Vec_I_DP &, Vec_O_DP &))
+{
+	int i,n;
+	DP x,swap,h2,h;
+
+	int nvar=y.size();
+	Vec_DP ym(nvar),yn(nvar);
+	h=htot/nstep;
+	for (i=0;i<nvar;i++) {
+		ym[i]=y[i];
+		yn[i]=y[i]+h*dydx[i];
+	}
+	x=xs+h;
+	derivs(x,yn,yout);
+	h2=2.0*h;
+	for (n=1;n<nstep;n++) {
+		for (i=0;i<nvar;i++) {
+			swap=ym[i]+h2*yout[i];
+			ym[i]=yn[i];
+			yn[i]=swap;
+		}
+		x += h;
+		derivs(x,yn,yout);
+	}
+	for (i=0;i<nvar;i++)
+		yout[i]=0.5*(ym[i]+yn[i]+h*yout[i]);
+}