add numerical recipes library

lib/nr/cpp/recipes/dftint.cpp

@@ -0,0 +1,53 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::dftint(DP func(const DP), const DP a, const DP b, const DP w,
+	DP &cosint, DP &sinint)
+{
+	static int init=0;
+	static DP (*funcold)(const DP);
+	static DP aold = -1.e30,bold = -1.e30,delta;
+	const int M=64,NDFT=1024,MPOL=6;
+	const DP TWOPI=6.283185307179586476;
+	int j,nn;
+	DP c,cdft,cerr,corfac,corim,corre,en,s,sdft,serr;
+	static Vec_DP data(NDFT),endpts(8);
+	Vec_DP cpol(MPOL),spol(MPOL),xpol(MPOL);
+
+	if (init != 1 || a != aold || b != bold || func != funcold) {
+		init=1;
+		aold=a;
+		bold=b;
+		funcold=func;
+		delta=(b-a)/M;
+		for (j=0;j<M+1;j++)
+			data[j]=func(a+j*delta);
+		for (j=M+1;j<NDFT;j++)
+			data[j]=0.0;
+		for (j=0;j<4;j++) {
+			endpts[j]=data[j];
+			endpts[j+4]=data[M-3+j];
+		}
+		realft(data,1);
+		data[1]=0.0;
+	}
+	en=w*delta*NDFT/TWOPI+1.0;
+	nn=MIN(MAX(int(en-0.5*MPOL+1.0),1),NDFT/2-MPOL+1);
+	for (j=0;j<MPOL;j++,nn++) {
+		cpol[j]=data[2*nn-2];
+		spol[j]=data[2*nn-1];
+		xpol[j]=nn;
+	}
+	polint(xpol,cpol,en,cdft,cerr);
+	polint(xpol,spol,en,sdft,serr);
+	dftcor(w,delta,a,b,endpts,corre,corim,corfac);
+	cdft *= corfac;
+	sdft *= corfac;
+	cdft += corre;
+	sdft += corim;
+	c=delta*cos(w*a);
+	s=delta*sin(w*a);
+	cosint=c*cdft-s*sdft;
+	sinint=s*cdft+c*sdft;
+}