add numerical recipes library

lib/nr/cpp/recipes/ratlsq.cpp

@@ -0,0 +1,64 @@
+#include <iostream>
+#include <iomanip>
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::ratlsq(DP fn(const DP), const DP a, const DP b, const int mm,
+	const int kk, Vec_O_DP &cof, DP &dev)
+{
+	const int NPFAC=8,MAXIT=5;
+	const DP BIG=1.0e30,PIO2=1.570796326794896619;
+	int i,it,j,ncof,npt;
+	DP devmax,e,hth,power,sum;
+
+	ncof=mm+kk+1;
+	npt=NPFAC*ncof;
+	Vec_DP bb(npt),coff(ncof),ee(npt),fs(npt),w(ncof),wt(npt),xs(npt);
+	Mat_DP u(npt,ncof),v(ncof,ncof);
+	dev=BIG;
+	for (i=0;i<npt;i++) {
+		if (i < (npt/2)-1) {
+			hth=PIO2*i/(npt-1.0);
+			xs[i]=a+(b-a)*SQR(sin(hth));
+		} else {
+			hth=PIO2*(npt-i)/(npt-1.0);
+			xs[i]=b-(b-a)*SQR(sin(hth));
+		}
+		fs[i]=fn(xs[i]);
+		wt[i]=1.0;
+		ee[i]=1.0;
+	}
+	e=0.0;
+	for (it=0;it<MAXIT;it++) {
+		for (i=0;i<npt;i++) {
+			power=wt[i];
+			bb[i]=power*(fs[i]+SIGN(e,ee[i]));
+			for (j=0;j<mm+1;j++) {
+				u[i][j]=power;
+				power *= xs[i];
+			}
+			power = -bb[i];
+			for (j=mm+1;j<ncof;j++) {
+				power *= xs[i];
+				u[i][j]=power;
+			}
+		}
+		svdcmp(u,w,v);
+		svbksb(u,w,v,bb,coff);
+		devmax=sum=0.0;
+		for (j=0;j<npt;j++) {
+			ee[j]=ratval(xs[j],coff,mm,kk)-fs[j];
+			wt[j]=fabs(ee[j]);
+			sum += wt[j];
+			if (wt[j] > devmax) devmax=wt[j];
+		}
+		e=sum/npt;
+		if (devmax <= dev) {
+			for (j=0;j<ncof;j++) cof[j]=coff[j];
+			dev=devmax;
+		}
+		cout << " ratlsq iteration= " << it;
+		cout << "  max error= " << setw(10) << devmax << endl;
+	}
+}