add numerical recipes library

lib/nr/cpp/recipes/ratint.cpp

@@ -0,0 +1,41 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::ratint(Vec_I_DP &xa, Vec_I_DP &ya, const DP x, DP &y, DP &dy)
+{
+	const DP TINY=1.0e-25;
+	int m,i,ns=0;
+	DP w,t,hh,h,dd;
+
+	int n=xa.size();
+	Vec_DP c(n),d(n);
+	hh=fabs(x-xa[0]);
+	for (i=0;i<n;i++) {
+		h=fabs(x-xa[i]);
+		if (h == 0.0) {
+			y=ya[i];
+			dy=0.0;
+			return;
+		} else if (h < hh) {
+			ns=i;
+			hh=h;
+		}
+		c[i]=ya[i];
+		d[i]=ya[i]+TINY;
+	}
+	y=ya[ns--];
+	for (m=1;m<n;m++) {
+		for (i=0;i<n-m;i++) {
+			w=c[i+1]-d[i];
+			h=xa[i+m]-x;
+			t=(xa[i]-x)*d[i]/h;
+			dd=t-c[i+1];
+			if (dd == 0.0) nrerror("Error in routine ratint");
+			dd=w/dd;
+			d[i]=c[i+1]*dd;
+			c[i]=t*dd;
+		}
+		y += (dy=(2*(ns+1) < (n-m) ? c[ns+1] : d[ns--]));
+	}
+}