add numerical recipes library

lib/nr/k_and_r/recipes/odeint.c

@@ -0,0 +1,56 @@
+
+#include <math.h>
+#include "nrutil.h"
+#define MAXSTP 10000
+#define TINY 1.0e-30
+
+extern int kmax,kount;
+extern float *xp,**yp,dxsav;
+
+void odeint(ystart,nvar,x1,x2,eps,h1,hmin,nok,nbad,derivs,rkqs)
+float eps,h1,hmin,x1,x2,ystart[];
+int *nbad,*nok,nvar;
+void (*derivs)(),(*rkqs)();
+{
+	int nstp,i;
+	float xsav,x,hnext,hdid,h;
+	float *yscal,*y,*dydx;
+
+	yscal=vector(1,nvar);
+	y=vector(1,nvar);
+	dydx=vector(1,nvar);
+	x=x1;
+	h=SIGN(h1,x2-x1);
+	*nok = (*nbad) = kount = 0;
+	for (i=1;i<=nvar;i++) y[i]=ystart[i];
+	if (kmax > 0) xsav=x-dxsav*2.0;
+	for (nstp=1;nstp<=MAXSTP;nstp++) {
+		(*derivs)(x,y,dydx);
+		for (i=1;i<=nvar;i++)
+			yscal[i]=fabs(y[i])+fabs(dydx[i]*h)+TINY;
+		if (kmax > 0 && kount < kmax-1 && fabs(x-xsav) > fabs(dxsav)) {
+			xp[++kount]=x;
+			for (i=1;i<=nvar;i++) yp[i][kount]=y[i];
+			xsav=x;
+		}
+		if ((x+h-x2)*(x+h-x1) > 0.0) h=x2-x;
+		(*rkqs)(y,dydx,nvar,&x,h,eps,yscal,&hdid,&hnext,derivs);
+		if (hdid == h) ++(*nok); else ++(*nbad);
+		if ((x-x2)*(x2-x1) >= 0.0) {
+			for (i=1;i<=nvar;i++) ystart[i]=y[i];
+			if (kmax) {
+				xp[++kount]=x;
+				for (i=1;i<=nvar;i++) yp[i][kount]=y[i];
+			}
+			free_vector(dydx,1,nvar);
+			free_vector(y,1,nvar);
+			free_vector(yscal,1,nvar);
+			return;
+		}
+		if (fabs(hnext) <= hmin) nrerror("Step size too small in odeint");
+		h=hnext;
+	}
+	nrerror("Too many steps in routine odeint");
+}
+#undef MAXSTP
+#undef TINY