add numerical recipes library

lib/nr/cpp/recipes/realft.cpp

@@ -0,0 +1,46 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::realft(Vec_IO_DP &data, const int isign)
+{
+	int i,i1,i2,i3,i4;
+	DP c1=0.5,c2,h1r,h1i,h2r,h2i,wr,wi,wpr,wpi,wtemp,theta;
+
+	int n=data.size();
+	theta=3.141592653589793238/DP(n>>1);
+	if (isign == 1) {
+		c2 = -0.5;
+		four1(data,1);
+	} else {
+		c2=0.5;
+		theta = -theta;
+	}
+	wtemp=sin(0.5*theta);
+	wpr = -2.0*wtemp*wtemp;
+	wpi=sin(theta);
+	wr=1.0+wpr;
+	wi=wpi;
+	for (i=1;i<(n>>2);i++) {
+		i2=1+(i1=i+i);
+		i4=1+(i3=n-i1);
+		h1r=c1*(data[i1]+data[i3]);
+		h1i=c1*(data[i2]-data[i4]);
+		h2r= -c2*(data[i2]+data[i4]);
+		h2i=c2*(data[i1]-data[i3]);
+		data[i1]=h1r+wr*h2r-wi*h2i;
+		data[i2]=h1i+wr*h2i+wi*h2r;
+		data[i3]=h1r-wr*h2r+wi*h2i;
+		data[i4]= -h1i+wr*h2i+wi*h2r;
+		wr=(wtemp=wr)*wpr-wi*wpi+wr;
+		wi=wi*wpr+wtemp*wpi+wi;
+	}
+	if (isign == 1) {
+		data[0] = (h1r=data[0])+data[1];
+		data[1] = h1r-data[1];
+	} else {
+		data[0]=c1*((h1r=data[0])+data[1]);
+		data[1]=c1*(h1r-data[1]);
+		four1(data,-1);
+	}
+}