add numerical recipes library

lib/nr/cpp/recipes/spline.cpp

@@ -0,0 +1,33 @@
+#include "nr.h"
+
+void NR::spline(Vec_I_DP &x, Vec_I_DP &y, const DP yp1, const DP ypn,
+	Vec_O_DP &y2)
+{
+	int i,k;
+	DP p,qn,sig,un;
+
+	int n=y2.size();
+	Vec_DP u(n-1);
+	if (yp1 > 0.99e30)
+		y2[0]=u[0]=0.0;
+	else {
+		y2[0] = -0.5;
+		u[0]=(3.0/(x[1]-x[0]))*((y[1]-y[0])/(x[1]-x[0])-yp1);
+	}
+	for (i=1;i<n-1;i++) {
+		sig=(x[i]-x[i-1])/(x[i+1]-x[i-1]);
+		p=sig*y2[i-1]+2.0;
+		y2[i]=(sig-1.0)/p;
+		u[i]=(y[i+1]-y[i])/(x[i+1]-x[i]) - (y[i]-y[i-1])/(x[i]-x[i-1]);
+		u[i]=(6.0*u[i]/(x[i+1]-x[i-1])-sig*u[i-1])/p;
+	}
+	if (ypn > 0.99e30)
+		qn=un=0.0;
+	else {
+		qn=0.5;
+		un=(3.0/(x[n-1]-x[n-2]))*(ypn-(y[n-1]-y[n-2])/(x[n-1]-x[n-2]));
+	}
+	y2[n-1]=(un-qn*u[n-2])/(qn*y2[n-2]+1.0);
+	for (k=n-2;k>=0;k--)
+		y2[k]=y2[k]*y2[k+1]+u[k];
+}