add numerical recipes library

lib/nr/cpp/recipes/medfit.cpp

@@ -0,0 +1,64 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+DP aa,abdevt;
+const Vec_DP *xt_p,*yt_p;
+
+void NR::medfit(Vec_I_DP &x, Vec_I_DP &y, DP &a, DP &b, DP &abdev)
+{
+	int j;
+	DP bb,b1,b2,del,f,f1,f2,sigb,temp;
+	DP sx=0.0,sy=0.0,sxy=0.0,sxx=0.0,chisq=0.0;
+
+	int ndata=x.size();
+	xt_p= &x;
+	yt_p= &y;
+	for (j=0;j<ndata;j++) {
+		sx += x[j];
+		sy += y[j];
+		sxy += x[j]*y[j];
+		sxx += x[j]*x[j];
+	}
+	del=ndata*sxx-sx*sx;
+	aa=(sxx*sy-sx*sxy)/del;
+	bb=(ndata*sxy-sx*sy)/del;
+	for (j=0;j<ndata;j++)
+		chisq += (temp=y[j]-(aa+bb*x[j]),temp*temp);
+	sigb=sqrt(chisq/del);
+	b1=bb;
+	f1=rofunc(b1);
+	if (sigb > 0.0) {
+		b2=bb+SIGN(3.0*sigb,f1);
+		f2=rofunc(b2);
+		if (b2 == b1) {
+			a=aa;
+			b=bb;
+			abdev=abdevt/ndata;
+			return;
+		}
+		while (f1*f2 > 0.0) {
+			bb=b2+1.6*(b2-b1);
+			b1=b2;
+			f1=f2;
+			b2=bb;
+			f2=rofunc(b2);
+		}
+		sigb=0.01*sigb;
+		while (fabs(b2-b1) > sigb) {
+			bb=b1+0.5*(b2-b1);
+			if (bb == b1 || bb == b2) break;
+			f=rofunc(bb);
+			if (f*f1 >= 0.0) {
+				f1=f;
+				b1=bb;
+			} else {
+				f2=f;
+				b2=bb;
+			}
+		}
+	}
+	a=aa;
+	b=bb;
+	abdev=abdevt/ndata;
+}