add numerical recipes library

lib/nr/cpp/recipes/laguer.cpp

@@ -0,0 +1,49 @@
+#include <cmath>
+#include <complex>
+#include <limits>
+#include "nr.h"
+using namespace std;
+
+void NR::laguer(Vec_I_CPLX_DP &a, complex<DP> &x, int &its)
+{
+	const int MR=8,MT=10,MAXIT=MT*MR;
+	const DP EPS=numeric_limits<DP>::epsilon();
+	static const DP frac[MR+1]=
+		{0.0,0.5,0.25,0.75,0.13,0.38,0.62,0.88,1.0};
+	int iter,j;
+	DP abx,abp,abm,err;
+	complex<DP> dx,x1,b,d,f,g,h,sq,gp,gm,g2;
+
+	int m=a.size()-1;
+	for (iter=1;iter<=MAXIT;iter++) {
+		its=iter;
+		b=a[m];
+		err=abs(b);
+		d=f=0.0;
+		abx=abs(x);
+		for (j=m-1;j>=0;j--) {
+			f=x*f+d;
+			d=x*d+b;
+			b=x*b+a[j];
+			err=abs(b)+abx*err;
+		}
+		err *= EPS;
+		if (abs(b) <= err) return;
+		g=d/b;
+		g2=g*g;
+		h=g2-2.0*f/b;
+		sq=sqrt(DP(m-1)*(DP(m)*h-g2));
+		gp=g+sq;
+		gm=g-sq;
+		abp=abs(gp);
+		abm=abs(gm);
+		if (abp < abm) gp=gm;
+		dx=MAX(abp,abm) > 0.0 ? DP(m)/gp : polar(1+abx,DP(iter));
+		x1=x-dx;
+		if (x == x1) return;
+		if (iter % MT != 0) x=x1;
+		else x -= frac[iter/MT]*dx;
+	}
+	nrerror("too many iterations in laguer");
+	return;
+}