add numerical recipes library

lib/nr/cpp/recipes/voltra.cpp

@@ -0,0 +1,36 @@
+#include "nr.h"
+
+void NR::voltra(const DP t0, const DP h, Vec_O_DP &t, Mat_O_DP &f,
+	DP g(const int, const DP),
+	DP ak(const int, const int, const DP, const DP))
+{
+	int i,j,k,l;
+	DP d,sum;
+
+	int m=f.nrows();
+	int n=f.ncols();
+	Vec_INT indx(m);
+	Vec_DP b(m);
+	Mat_DP a(m,m);
+	t[0]=t0;
+	for (k=0;k<m;k++) f[k][0]=g(k,t[0]);
+	for (i=1;i<n;i++) {
+		t[i]=t[i-1]+h;
+		for (k=0;k<m;k++) {
+			sum=g(k,t[i]);
+			for (l=0;l<m;l++) {
+				sum += 0.5*h*ak(k,l,t[i],t[0])*f[l][0];
+				for (j=1;j<i;j++)
+					sum += h*ak(k,l,t[i],t[j])*f[l][j];
+				if (k == l)
+					a[k][l]=1.0-0.5*h*ak(k,l,t[i],t[i]);
+				else
+					a[k][l] = -0.5*h*ak(k,l,t[i],t[i]);
+			}
+			b[k]=sum;
+		}
+		ludcmp(a,indx,d);
+		lubksb(a,indx,b);
+		for (k=0;k<m;k++) f[k][i]=b[k];
+	}
+}