add numerical recipes library

lib/nr/cpp/recipes/fitexy.cpp

@@ -0,0 +1,75 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+Vec_DP *xx_p,*yy_p,*sx_p,*sy_p,*ww_p;
+DP aa,offs;
+
+void NR::fitexy(Vec_I_DP &x, Vec_I_DP &y, Vec_I_DP &sigx, Vec_I_DP &sigy,
+	DP &a, DP &b, DP &siga, DP &sigb, DP &chi2, DP &q)
+{
+	int j;
+	const DP POTN=1.571000,BIG=1.0e30,ACC=1.0e-3;
+	const DP PI=3.141592653589793238;
+	DP amx,amn,varx,vary,ang[7],ch[7],scale,bmn,bmx,d1,d2,r2,
+		dum1,dum2,dum3,dum4,dum5;
+
+	int ndat=x.size();
+	xx_p=new Vec_DP(ndat);
+	yy_p=new Vec_DP(ndat);
+	sx_p=new Vec_DP(ndat);
+	sy_p=new Vec_DP(ndat);
+	ww_p=new Vec_DP(ndat);
+	Vec_DP &xx=*xx_p, &yy=*yy_p;
+	Vec_DP &sx=*sx_p, &sy=*sy_p, &ww=*ww_p;
+	avevar(x,dum1,varx);
+	avevar(y,dum1,vary);
+	scale=sqrt(varx/vary);
+	for (j=0;j<ndat;j++) {
+		xx[j]=x[j];
+		yy[j]=y[j]*scale;
+		sx[j]=sigx[j];
+		sy[j]=sigy[j]*scale;
+		ww[j]=sqrt(SQR(sx[j])+SQR(sy[j]));
+	}
+	fit(xx,yy,ww,true,dum1,b,dum2,dum3,dum4,dum5);
+	offs=ang[0]=0.0;
+	ang[1]=atan(b);
+	ang[3]=0.0;
+	ang[4]=ang[1];
+	ang[5]=POTN;
+	for (j=3;j<6;j++) ch[j]=chixy(ang[j]);
+	mnbrak(ang[0],ang[1],ang[2],ch[0],ch[1],ch[2],chixy);
+	chi2=brent(ang[0],ang[1],ang[2],chixy,ACC,b);
+	chi2=chixy(b);
+	a=aa;
+	q=gammq(0.5*(ndat-2),chi2*0.5);
+	r2=0.0;
+	for (j=0;j<ndat;j++) r2 += ww[j];
+	r2=1.0/r2;
+	bmx=BIG;
+	bmn=BIG;
+	offs=chi2+1.0;
+	for (j=0;j<6;j++) {
+		if (ch[j] > offs) {
+			d1=fabs(ang[j]-b);
+			while (d1 >= PI) d1 -= PI;
+			d2=PI-d1;
+			if (ang[j] < b)
+				SWAP(d1,d2);
+			if (d1 < bmx) bmx=d1;
+			if (d2 < bmn) bmn=d2;
+		}
+	}
+	if (bmx < BIG) {
+		bmx=zbrent(chixy,b,b+bmx,ACC)-b;
+		amx=aa-a;
+		bmn=zbrent(chixy,b,b-bmn,ACC)-b;
+		amn=aa-a;
+		sigb=sqrt(0.5*(bmx*bmx+bmn*bmn))/(scale*SQR(cos(b)));
+		siga=sqrt(0.5*(amx*amx+amn*amn)+r2)/scale;
+	} else sigb=siga=BIG;
+	a /= scale;
+	b=tan(b)/scale;
+	delete ww_p; delete sy_p; delete sx_p; delete yy_p; delete xx_p;
+}