add numerical recipes library

lib/nr/cpp/recipes/cosft2.cpp

@@ -0,0 +1,64 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::cosft2(Vec_IO_DP &y, const int isign)
+{
+	const DP PI=3.141592653589793238;
+	int i;
+	DP sum,sum1,y1,y2,ytemp,theta,wi=0.0,wi1,wpi,wpr,wr=1.0,wr1,wtemp;
+
+	int n=y.size();
+	theta=0.5*PI/n;
+	wr1=cos(theta);
+	wi1=sin(theta);
+	wpr = -2.0*wi1*wi1;
+	wpi=sin(2.0*theta);
+	if (isign == 1) {
+		for (i=0;i<n/2;i++) {
+			y1=0.5*(y[i]+y[n-1-i]);
+			y2=wi1*(y[i]-y[n-1-i]);
+			y[i]=y1+y2;
+			y[n-1-i]=y1-y2;
+			wr1=(wtemp=wr1)*wpr-wi1*wpi+wr1;
+			wi1=wi1*wpr+wtemp*wpi+wi1;
+		}
+		realft(y,1);
+		for (i=2;i<n;i+=2) {
+			wr=(wtemp=wr)*wpr-wi*wpi+wr;
+			wi=wi*wpr+wtemp*wpi+wi;
+			y1=y[i]*wr-y[i+1]*wi;
+			y2=y[i+1]*wr+y[i]*wi;
+			y[i]=y1;
+			y[i+1]=y2;
+		}
+		sum=0.5*y[1];
+		for (i=n-1;i>0;i-=2) {
+			sum1=sum;
+			sum += y[i];
+			y[i]=sum1;
+		}
+	} else if (isign == -1) {
+		ytemp=y[n-1];
+		for (i=n-1;i>2;i-=2)
+			y[i]=y[i-2]-y[i];
+		y[1]=2.0*ytemp;
+		for (i=2;i<n;i+=2) {
+			wr=(wtemp=wr)*wpr-wi*wpi+wr;
+			wi=wi*wpr+wtemp*wpi+wi;
+			y1=y[i]*wr+y[i+1]*wi;
+			y2=y[i+1]*wr-y[i]*wi;
+			y[i]=y1;
+			y[i+1]=y2;
+		}
+		realft(y,-1);
+		for (i=0;i<n/2;i++) {
+			y1=y[i]+y[n-1-i];
+			y2=(0.5/wi1)*(y[i]-y[n-1-i]);
+			y[i]=0.5*(y1+y2);
+			y[n-1-i]=0.5*(y1-y2);
+			wr1=(wtemp=wr1)*wpr-wi1*wpi+wr1;
+			wi1=wi1*wpr+wtemp*wpi+wi1;
+		}
+	}
+}