add numerical recipes library

lib/nr/k_and_r/recipes/simpr.c

@@ -0,0 +1,48 @@
+
+#include "nrutil.h"
+
+void simpr(y,dydx,dfdx,dfdy,n,xs,htot,nstep,yout,derivs)
+float **dfdy,dfdx[],dydx[],htot,xs,y[],yout[];
+int n,nstep;
+void (*derivs)();
+{
+	void lubksb(),ludcmp();
+	int i,j,nn,*indx;
+	float d,h,x,**a,*del,*ytemp;
+
+	indx=ivector(1,n);
+	a=matrix(1,n,1,n);
+	del=vector(1,n);
+	ytemp=vector(1,n);
+	h=htot/nstep;
+	for (i=1;i<=n;i++) {
+		for (j=1;j<=n;j++) a[i][j] = -h*dfdy[i][j];
+		++a[i][i];
+	}
+	ludcmp(a,n,indx,&d);
+	for (i=1;i<=n;i++)
+		yout[i]=h*(dydx[i]+h*dfdx[i]);
+	lubksb(a,n,indx,yout);
+	for (i=1;i<=n;i++)
+		ytemp[i]=y[i]+(del[i]=yout[i]);
+	x=xs+h;
+	(*derivs)(x,ytemp,yout);
+	for (nn=2;nn<=nstep;nn++) {
+		for (i=1;i<=n;i++)
+			yout[i]=h*yout[i]-del[i];
+		lubksb(a,n,indx,yout);
+		for (i=1;i<=n;i++)
+			ytemp[i] += (del[i] += 2.0*yout[i]);
+		x += h;
+		(*derivs)(x,ytemp,yout);
+	}
+	for (i=1;i<=n;i++)
+		yout[i]=h*yout[i]-del[i];
+	lubksb(a,n,indx,yout);
+	for (i=1;i<=n;i++)
+		yout[i] += ytemp[i];
+	free_vector(ytemp,1,n);
+	free_vector(del,1,n);
+	free_matrix(a,1,n,1,n);
+	free_ivector(indx,1,n);
+}