add numerical recipes library

lib/nr/cpp/recipes/period.cpp

@@ -0,0 +1,70 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::period(Vec_I_DP &x, Vec_I_DP &y, const DP ofac, const DP hifac,
+	Vec_O_DP &px, Vec_O_DP &py, int &nout, int &jmax, DP &prob)
+{
+	const DP TWOPI=6.283185307179586476;
+	int i,j;
+	DP ave,c,cc,cwtau,effm,expy,pnow,pymax,s,ss,sumc,sumcy,sums,sumsh,
+		sumsy,swtau,var,wtau,xave,xdif,xmax,xmin,yy,arg,wtemp;
+
+	int n=x.size();
+	int np=px.size();
+	Vec_DP wi(n),wpi(n),wpr(n),wr(n);
+	nout=0.5*ofac*hifac*n;
+	if (nout > np) nrerror("output arrays too short in period");
+	avevar(y,ave,var);
+	if (var == 0.0) nrerror("zero variance in period");
+	xmax=xmin=x[0];
+	for (j=0;j<n;j++) {
+		if (x[j] > xmax) xmax=x[j];
+		if (x[j] < xmin) xmin=x[j];
+	}
+	xdif=xmax-xmin;
+	xave=0.5*(xmax+xmin);
+	pymax=0.0;
+	pnow=1.0/(xdif*ofac);
+	for (j=0;j<n;j++) {
+		arg=TWOPI*((x[j]-xave)*pnow);
+		wpr[j]= -2.0*SQR(sin(0.5*arg));
+		wpi[j]=sin(arg);
+		wr[j]=cos(arg);
+		wi[j]=wpi[j];
+	}
+	for (i=0;i<nout;i++) {
+		px[i]=pnow;
+		sumsh=sumc=0.0;
+		for (j=0;j<n;j++) {
+			c=wr[j];
+			s=wi[j];
+			sumsh += s*c;
+			sumc += (c-s)*(c+s);
+		}
+		wtau=0.5*atan2(2.0*sumsh,sumc);
+		swtau=sin(wtau);
+		cwtau=cos(wtau);
+		sums=sumc=sumsy=sumcy=0.0;
+		for (j=0;j<n;j++) {
+			s=wi[j];
+			c=wr[j];
+			ss=s*cwtau-c*swtau;
+			cc=c*cwtau+s*swtau;
+			sums += ss*ss;
+			sumc += cc*cc;
+			yy=y[j]-ave;
+			sumsy += yy*ss;
+			sumcy += yy*cc;
+			wr[j]=((wtemp=wr[j])*wpr[j]-wi[j]*wpi[j])+wr[j];
+			wi[j]=(wi[j]*wpr[j]+wtemp*wpi[j])+wi[j];
+		}
+		py[i]=0.5*(sumcy*sumcy/sumc+sumsy*sumsy/sums)/var;
+		if (py[i] >= pymax) pymax=py[jmax=i];
+		pnow += 1.0/(ofac*xdif);
+	}
+	expy=exp(-pymax);
+	effm=2.0*nout/ofac;
+	prob=effm*expy;
+	if (prob > 0.01) prob=1.0-pow(1.0-expy,effm);
+}