add numerical recipes library

lib/nr/cpp/recipes/newt.cpp

@@ -0,0 +1,79 @@
+#include <cmath>
+#include <limits>
+#include "nr.h"
+using namespace std;
+
+Vec_DP *fvec_p;
+void (*nrfuncv)(Vec_I_DP &v, Vec_O_DP &f);
+
+void NR::newt(Vec_IO_DP &x, bool &check, void vecfunc(Vec_I_DP &, Vec_O_DP &))
+{
+	const int MAXITS=200;
+	const DP TOLF=1.0e-8,TOLMIN=1.0e-12,STPMX=100.0;
+	const DP TOLX=numeric_limits<DP>::epsilon();
+	int i,j,its;
+	DP d,den,f,fold,stpmax,sum,temp,test;
+
+	int n=x.size();
+	Vec_INT indx(n);
+	Vec_DP g(n),p(n),xold(n);
+	Mat_DP fjac(n,n);
+	fvec_p=new Vec_DP(n);
+	nrfuncv=vecfunc;
+	Vec_DP &fvec=*fvec_p;
+	f=fmin(x);
+	test=0.0;
+	for (i=0;i<n;i++)
+		if (fabs(fvec[i]) > test) test=fabs(fvec[i]);
+	if (test < 0.01*TOLF) {
+		check=false;
+		delete fvec_p;
+		return;
+	}
+	sum=0.0;
+	for (i=0;i<n;i++) sum += SQR(x[i]);
+	stpmax=STPMX*MAX(sqrt(sum),DP(n));
+	for (its=0;its<MAXITS;its++) {
+		fdjac(x,fvec,fjac,vecfunc);
+		for (i=0;i<n;i++) {
+			sum=0.0;
+			for (j=0;j<n;j++) sum += fjac[j][i]*fvec[j];
+			g[i]=sum;
+		}
+		for (i=0;i<n;i++) xold[i]=x[i];
+		fold=f;
+		for (i=0;i<n;i++) p[i] = -fvec[i];
+		ludcmp(fjac,indx,d);
+		lubksb(fjac,indx,p);
+		lnsrch(xold,fold,g,p,x,f,stpmax,check,fmin);
+		test=0.0;
+		for (i=0;i<n;i++)
+			if (fabs(fvec[i]) > test) test=fabs(fvec[i]);
+		if (test < TOLF) {
+			check=false;
+			delete fvec_p;
+			return;
+		}
+		if (check) {
+			test=0.0;
+			den=MAX(f,0.5*n);
+			for (i=0;i<n;i++) {
+				temp=fabs(g[i])*MAX(fabs(x[i]),1.0)/den;
+				if (temp > test) test=temp;
+			}
+			check=(test < TOLMIN);
+			delete fvec_p;
+			return;
+		}
+		test=0.0;
+		for (i=0;i<n;i++) {
+			temp=(fabs(x[i]-xold[i]))/MAX(fabs(x[i]),1.0);
+			if (temp > test) test=temp;
+		}
+		if (test < TOLX) {
+			delete fvec_p;
+			return;
+		}
+	}
+	nrerror("MAXITS exceeded in newt");
+}