add numerical recipes library

lib/nr/k_and_r/recipes/fit.c

@@ -0,0 +1,60 @@
+
+#include <math.h>
+#include "nrutil.h"
+
+void fit(x,y,ndata,sig,mwt,a,b,siga,sigb,chi2,q)
+float *a,*b,*chi2,*q,*siga,*sigb,sig[],x[],y[];
+int mwt,ndata;
+{
+	float gammq();
+	int i;
+	float wt,t,sxoss,sx=0.0,sy=0.0,st2=0.0,ss,sigdat;
+
+	*b=0.0;
+	if (mwt) {
+		ss=0.0;
+		for (i=1;i<=ndata;i++) {
+			wt=1.0/SQR(sig[i]);
+			ss += wt;
+			sx += x[i]*wt;
+			sy += y[i]*wt;
+		}
+	} else {
+		for (i=1;i<=ndata;i++) {
+			sx += x[i];
+			sy += y[i];
+		}
+		ss=ndata;
+	}
+	sxoss=sx/ss;
+	if (mwt) {
+		for (i=1;i<=ndata;i++) {
+			t=(x[i]-sxoss)/sig[i];
+			st2 += t*t;
+			*b += t*y[i]/sig[i];
+		}
+	} else {
+		for (i=1;i<=ndata;i++) {
+			t=x[i]-sxoss;
+			st2 += t*t;
+			*b += t*y[i];
+		}
+	}
+	*b /= st2;
+	*a=(sy-sx*(*b))/ss;
+	*siga=sqrt((1.0+sx*sx/(ss*st2))/ss);
+	*sigb=sqrt(1.0/st2);
+	*chi2=0.0;
+	*q=1.0;
+	if (mwt == 0) {
+		for (i=1;i<=ndata;i++)
+			*chi2 += SQR(y[i]-(*a)-(*b)*x[i]);
+		sigdat=sqrt((*chi2)/(ndata-2));
+		*siga *= sigdat;
+		*sigb *= sigdat;
+	} else {
+		for (i=1;i<=ndata;i++)
+			*chi2 += SQR((y[i]-(*a)-(*b)*x[i])/sig[i]);
+		if (ndata>2) *q=gammq(0.5*(ndata-2),0.5*(*chi2));
+	}
+}