add numerical recipes library

lib/nr/k_and_r/recipes/period.c

@@ -0,0 +1,79 @@
+
+#include <math.h>
+#include "nrutil.h"
+#define TWOPID 6.2831853071795865
+
+void period(x,y,n,ofac,hifac,px,py,np,nout,jmax,prob)
+float *prob,hifac,ofac,px[],py[],x[],y[];
+int *jmax,*nout,n,np;
+{
+	void avevar();
+	int i,j;
+	float ave,c,cc,cwtau,effm,expy,pnow,pymax,s,ss,sumc,sumcy,sums,sumsh,
+		sumsy,swtau,var,wtau,xave,xdif,xmax,xmin,yy;
+	double arg,wtemp,*wi,*wpi,*wpr,*wr;
+
+	wi=dvector(1,n);
+	wpi=dvector(1,n);
+	wpr=dvector(1,n);
+	wr=dvector(1,n);
+	*nout=0.5*ofac*hifac*n;
+	if (*nout > np) nrerror("output arrays too short in period");
+	avevar(y,n,&ave,&var);
+	if (var == 0.0) nrerror("zero variance in period");
+	xmax=xmin=x[1];
+	for (j=1;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=1;j<=n;j++) {
+		arg=TWOPID*((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=1;i<=(*nout);i++) {
+		px[i]=pnow;
+		sumsh=sumc=0.0;
+		for (j=1;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=1;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);
+	free_dvector(wr,1,n);
+	free_dvector(wpr,1,n);
+	free_dvector(wpi,1,n);
+	free_dvector(wi,1,n);
+}
+#undef TWOPID