add numerical recipes library

lib/nr/cpp/recipes/four1.cpp

@@ -0,0 +1,49 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::four1(Vec_IO_DP &data, const int isign)
+{
+	int n,mmax,m,j,istep,i;
+	DP wtemp,wr,wpr,wpi,wi,theta,tempr,tempi;
+
+	int nn=data.size()/2;
+	n=nn << 1;
+	j=1;
+	for (i=1;i<n;i+=2) {
+		if (j > i) {
+			SWAP(data[j-1],data[i-1]);
+			SWAP(data[j],data[i]);
+		}
+		m=nn;
+		while (m >= 2 && j > m) {
+			j -= m;
+			m >>= 1;
+		}
+		j += m;
+	}
+	mmax=2;
+	while (n > mmax) {
+		istep=mmax << 1;
+		theta=isign*(6.28318530717959/mmax);
+		wtemp=sin(0.5*theta);
+		wpr = -2.0*wtemp*wtemp;
+		wpi=sin(theta);
+		wr=1.0;
+		wi=0.0;
+		for (m=1;m<mmax;m+=2) {
+			for (i=m;i<=n;i+=istep) {
+				j=i+mmax;
+				tempr=wr*data[j-1]-wi*data[j];
+				tempi=wr*data[j]+wi*data[j-1];
+				data[j-1]=data[i-1]-tempr;
+				data[j]=data[i]-tempi;
+				data[i-1] += tempr;
+				data[i] += tempi;
+			}
+			wr=(wtemp=wr)*wpr-wi*wpi+wr;
+			wi=wi*wpr+wtemp*wpi+wi;
+		}
+		mmax=istep;
+	}
+}