add numerical recipes library

lib/nr/cpp/recipes/qroot.cpp

@@ -0,0 +1,36 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::qroot(Vec_I_DP &p, DP &b, DP &c, const DP eps)
+{
+	const int ITMAX=20;
+	const DP TINY=1.0e-14;
+	int iter;
+	DP sc,sb,s,rc,rb,r,dv,delc,delb;
+	Vec_DP d(3);
+
+	int n=p.size()-1;
+	Vec_DP q(n+1),qq(n+1),rem(n+1);
+	d[2]=1.0;
+	for (iter=0;iter<ITMAX;iter++) {
+		d[1]=b;
+		d[0]=c;
+		poldiv(p,d,q,rem);
+		s=rem[0];
+		r=rem[1];
+		poldiv(q,d,qq,rem);
+		sb = -c*(rc = -rem[1]);
+		rb = -b*rc+(sc = -rem[0]);
+		dv=1.0/(sb*rc-sc*rb);
+		delb=(r*sc-s*rc)*dv;
+		delc=(-r*sb+s*rb)*dv;
+		b += (delb=(r*sc-s*rc)*dv);
+		c += (delc=(-r*sb+s*rb)*dv);
+		if ((fabs(delb) <= eps*fabs(b) || fabs(b) < TINY)
+			&& (fabs(delc) <= eps*fabs(c) || fabs(c) < TINY)) {
+			return;
+		}
+	}
+	nrerror("Too many iterations in routine qroot");
+}