add numerical recipes library

lib/nr/ansi/recipes/fasper.c

@@ -0,0 +1,70 @@
+
+#include <math.h>
+#define NRANSI
+#include "nrutil.h"
+#define MOD(a,b) 	while(a >= b) a -= b;
+#define MACC 4
+
+void fasper(float x[], float y[], unsigned long n, float ofac, float hifac,
+	float wk1[], float wk2[], unsigned long nwk, unsigned long *nout,
+	unsigned long *jmax, float *prob)
+{
+	void avevar(float data[], unsigned long n, float *ave, float *var);
+	void realft(float data[], unsigned long n, int isign);
+	void spread(float y, float yy[], unsigned long n, float x, int m);
+	unsigned long j,k,ndim,nfreq,nfreqt;
+	float ave,ck,ckk,cterm,cwt,den,df,effm,expy,fac,fndim,hc2wt;
+	float hs2wt,hypo,pmax,sterm,swt,var,xdif,xmax,xmin;
+
+	*nout=0.5*ofac*hifac*n;
+	nfreqt=ofac*hifac*n*MACC;
+	nfreq=64;
+	while (nfreq < nfreqt) nfreq <<= 1;
+	ndim=nfreq << 1;
+	if (ndim > nwk) nrerror("workspaces too small in fasper");
+	avevar(y,n,&ave,&var);
+	if (var == 0.0) nrerror("zero variance in fasper");
+	xmin=x[1];
+	xmax=xmin;
+	for (j=2;j<=n;j++) {
+		if (x[j] < xmin) xmin=x[j];
+		if (x[j] > xmax) xmax=x[j];
+	}
+	xdif=xmax-xmin;
+	for (j=1;j<=ndim;j++) wk1[j]=wk2[j]=0.0;
+	fac=ndim/(xdif*ofac);
+	fndim=ndim;
+	for (j=1;j<=n;j++) {
+		ck=(x[j]-xmin)*fac;
+		MOD(ck,fndim)
+		ckk=2.0*(ck++);
+		MOD(ckk,fndim)
+		++ckk;
+		spread(y[j]-ave,wk1,ndim,ck,MACC);
+		spread(1.0,wk2,ndim,ckk,MACC);
+	}
+	realft(wk1,ndim,1);
+	realft(wk2,ndim,1);
+	df=1.0/(xdif*ofac);
+	pmax = -1.0;
+	for (k=3,j=1;j<=(*nout);j++,k+=2) {
+		hypo=sqrt(wk2[k]*wk2[k]+wk2[k+1]*wk2[k+1]);
+		hc2wt=0.5*wk2[k]/hypo;
+		hs2wt=0.5*wk2[k+1]/hypo;
+		cwt=sqrt(0.5+hc2wt);
+		swt=SIGN(sqrt(0.5-hc2wt),hs2wt);
+		den=0.5*n+hc2wt*wk2[k]+hs2wt*wk2[k+1];
+		cterm=SQR(cwt*wk1[k]+swt*wk1[k+1])/den;
+		sterm=SQR(cwt*wk1[k+1]-swt*wk1[k])/(n-den);
+		wk1[j]=j*df;
+		wk2[j]=(cterm+sterm)/(2.0*var);
+		if (wk2[j] > pmax) pmax=wk2[(*jmax=j)];
+	}
+	expy=exp(-pmax);
+	effm=2.0*(*nout)/ofac;
+	*prob=effm*expy;
+	if (*prob > 0.01) *prob=1.0-pow(1.0-expy,effm);
+}
+#undef MOD
+#undef MACC
+#undef NRANSI