add numerical recipes library

lib/nr/k_and_r/recipes/voltra.c

@@ -0,0 +1,36 @@
+
+#include "nrutil.h"
+
+void voltra(n,m,t0,h,t,f,g,ak)
+float (*ak)(),(*g)(),**f,*t,h,t0;
+int m,n;
+{
+	void lubksb(),ludcmp();
+	int i,j,k,l,*indx;
+	float d,sum,**a,*b;
+
+	indx=ivector(1,m);
+	a=matrix(1,m,1,m);
+	b=vector(1,m);
+	t[1]=t0;
+	for (k=1;k<=m;k++) f[k][1]=(*g)(k,t[1]);
+	for (i=2;i<=n;i++) {
+		t[i]=t[i-1]+h;
+		for (k=1;k<=m;k++) {
+			sum=(*g)(k,t[i]);
+			for (l=1;l<=m;l++) {
+				sum += 0.5*h*(*ak)(k,l,t[i],t[1])*f[l][1];
+				for (j=2;j<i;j++)
+					sum += h*(*ak)(k,l,t[i],t[j])*f[l][j];
+				a[k][l]=(k == l)-0.5*h*(*ak)(k,l,t[i],t[i]);
+			}
+			b[k]=sum;
+		}
+		ludcmp(a,m,indx,&d);
+		lubksb(a,m,indx,b);
+		for (k=1;k<=m;k++) f[k][i]=b[k];
+	}
+	free_vector(b,1,m);
+	free_matrix(a,1,m,1,m);
+	free_ivector(indx,1,m);
+}