add numerical recipes library

lib/nr/cpp/recipes/lnsrch.cpp

@@ -0,0 +1,63 @@
+#include <cmath>
+#include <limits>
+#include "nr.h"
+using namespace std;
+
+void NR::lnsrch(Vec_I_DP &xold, const DP fold, Vec_I_DP &g, Vec_IO_DP &p,
+	Vec_O_DP &x, DP &f, const DP stpmax, bool &check, DP func(Vec_I_DP &))
+{
+	const DP ALF=1.0e-4, TOLX=numeric_limits<DP>::epsilon();
+	int i;
+	DP a,alam,alam2=0.0,alamin,b,disc,f2=0.0;
+	DP rhs1,rhs2,slope,sum,temp,test,tmplam;
+
+	int n=xold.size();
+	check=false;
+	sum=0.0;
+	for (i=0;i<n;i++) sum += p[i]*p[i];
+	sum=sqrt(sum);
+	if (sum > stpmax)
+		for (i=0;i<n;i++) p[i] *= stpmax/sum;
+	slope=0.0;
+	for (i=0;i<n;i++)
+		slope += g[i]*p[i];
+	if (slope >= 0.0) nrerror("Roundoff problem in lnsrch.");
+	test=0.0;
+	for (i=0;i<n;i++) {
+		temp=fabs(p[i])/MAX(fabs(xold[i]),1.0);
+		if (temp > test) test=temp;
+	}
+	alamin=TOLX/test;
+	alam=1.0;
+	for (;;) {
+		for (i=0;i<n;i++) x[i]=xold[i]+alam*p[i];
+		f=func(x);
+		if (alam < alamin) {
+			for (i=0;i<n;i++) x[i]=xold[i];
+			check=true;
+			return;
+		} else if (f <= fold+ALF*alam*slope) return;
+		else {
+			if (alam == 1.0)
+				tmplam = -slope/(2.0*(f-fold-slope));
+			else {
+				rhs1=f-fold-alam*slope;
+				rhs2=f2-fold-alam2*slope;
+				a=(rhs1/(alam*alam)-rhs2/(alam2*alam2))/(alam-alam2);
+				b=(-alam2*rhs1/(alam*alam)+alam*rhs2/(alam2*alam2))/(alam-alam2);
+				if (a == 0.0) tmplam = -slope/(2.0*b);
+				else {
+					disc=b*b-3.0*a*slope;
+					if (disc < 0.0) tmplam=0.5*alam;
+					else if (b <= 0.0) tmplam=(-b+sqrt(disc))/(3.0*a);
+					else tmplam=-slope/(b+sqrt(disc));
+				}
+				if (tmplam>0.5*alam)
+					tmplam=0.5*alam;
+			}
+		}
+		alam2=alam;
+		f2 = f;
+		alam=MAX(tmplam,0.1*alam);
+	}
+}