add numerical recipes library

lib/nr/cpp/recipes/pearsn.cpp

@@ -0,0 +1,32 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::pearsn(Vec_I_DP &x, Vec_I_DP &y, DP &r, DP &prob, DP &z)
+{
+	const DP TINY=1.0e-20;
+	int j;
+	DP yt,xt,t,df;
+	DP syy=0.0,sxy=0.0,sxx=0.0,ay=0.0,ax=0.0;
+
+	int n=x.size();
+	for (j=0;j<n;j++) {
+		ax += x[j];
+		ay += y[j];
+	}
+	ax /= n;
+	ay /= n;
+	for (j=0;j<n;j++) {
+		xt=x[j]-ax;
+		yt=y[j]-ay;
+		sxx += xt*xt;
+		syy += yt*yt;
+		sxy += xt*yt;
+	}
+	r=sxy/(sqrt(sxx*syy)+TINY);
+	z=0.5*log((1.0+r+TINY)/(1.0-r+TINY));
+	df=n-2;
+	t=r*sqrt(df/((1.0-r+TINY)*(1.0+r+TINY)));
+	prob=betai(0.5*df,0.5,df/(df+t*t));
+	// prob=erfcc(fabs(z*sqrt(n-1.0))/1.4142136);
+}