add numerical recipes library

lib/nr/k_and_r/recipes/mmid.c

@@ -0,0 +1,35 @@
+
+#include "nrutil.h"
+
+void mmid(y,dydx,nvar,xs,htot,nstep,yout,derivs)
+float dydx[],htot,xs,y[],yout[];
+int nstep,nvar;
+void (*derivs)();
+{
+	int n,i;
+	float x,swap,h2,h,*ym,*yn;
+
+	ym=vector(1,nvar);
+	yn=vector(1,nvar);
+	h=htot/nstep;
+	for (i=1;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=2;n<=nstep;n++) {
+		for (i=1;i<=nvar;i++) {
+			swap=ym[i]+h2*yout[i];
+			ym[i]=yn[i];
+			yn[i]=swap;
+		}
+		x += h;
+		(*derivs)(x,yn,yout);
+	}
+	for (i=1;i<=nvar;i++)
+		yout[i]=0.5*(ym[i]+yn[i]+h*yout[i]);
+	free_vector(yn,1,nvar);
+	free_vector(ym,1,nvar);
+}