add numerical recipes library

lib/nr/cpp/recipes/cosft1.cpp

@@ -0,0 +1,37 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::cosft1(Vec_IO_DP &y)
+{
+	const DP PI=3.141592653589793238;
+	int j;
+	DP sum,y1,y2,theta,wi=0.0,wpi,wpr,wr=1.0,wtemp;
+
+	int n=y.size()-1;
+	Vec_DP yy(n);
+	theta=PI/n;
+	wtemp=sin(0.5*theta);
+	wpr = -2.0*wtemp*wtemp;
+	wpi=sin(theta);
+	sum=0.5*(y[0]-y[n]);
+	yy[0]=0.5*(y[0]+y[n]);
+	for (j=1;j<n/2;j++) {
+		wr=(wtemp=wr)*wpr-wi*wpi+wr;
+		wi=wi*wpr+wtemp*wpi+wi;
+		y1=0.5*(y[j]+y[n-j]);
+		y2=(y[j]-y[n-j]);
+		yy[j]=y1-wi*y2;
+		yy[n-j]=y1+wi*y2;
+		sum += wr*y2;
+	}
+	yy[n/2]=y[n/2];
+	realft(yy,1);
+	for (j=0;j<n;j++) y[j]=yy[j];
+	y[n]=y[1];
+	y[1]=sum;
+	for (j=3;j<n;j+=2) {
+		sum += y[j];
+		y[j]=sum;
+	}
+}