add numerical recipes library

lib/nr/cpp/recipes/simpr.cpp

@@ -0,0 +1,40 @@
+#include "nr.h"
+
+void NR::simpr(Vec_I_DP &y, Vec_I_DP &dydx, Vec_I_DP &dfdx, Mat_I_DP &dfdy,
+	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,j,nn;
+	DP d,h,x;
+
+	int n=y.size();
+	Mat_DP a(n,n);
+	Vec_INT indx(n);
+	Vec_DP del(n),ytemp(n);
+	h=htot/nstep;
+	for (i=0;i<n;i++) {
+		for (j=0;j<n;j++) a[i][j] = -h*dfdy[i][j];
+		++a[i][i];
+	}
+	ludcmp(a,indx,d);
+	for (i=0;i<n;i++)
+		yout[i]=h*(dydx[i]+h*dfdx[i]);
+	lubksb(a,indx,yout);
+	for (i=0;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=0;i<n;i++)
+			yout[i]=h*yout[i]-del[i];
+		lubksb(a,indx,yout);
+		for (i=0;i<n;i++) ytemp[i] += (del[i] += 2.0*yout[i]);
+		x += h;
+		derivs(x,ytemp,yout);
+	}
+	for (i=0;i<n;i++)
+		yout[i]=h*yout[i]-del[i];
+	lubksb(a,indx,yout);
+	for (i=0;i<n;i++)
+		yout[i] += ytemp[i];
+}