add numerical recipes library

lib/nr/k_and_r/recipes/qroot.c

@@ -0,0 +1,46 @@
+
+#include <math.h>
+#include "nrutil.h"
+#define ITMAX 20
+#define TINY 1.0e-6
+
+void qroot(p,n,b,c,eps)
+float *b,*c,eps,p[];
+int n;
+{
+	void poldiv();
+	int iter;
+	float sc,sb,s,rc,rb,r,dv,delc,delb;
+	float *q,*qq,*rem;
+	float d[3];
+
+	q=vector(0,n);
+	qq=vector(0,n);
+	rem=vector(0,n);
+	d[2]=1.0;
+	for (iter=1;iter<=ITMAX;iter++) {
+		d[1]=(*b);
+		d[0]=(*c);
+		poldiv(p,n,d,2,q,rem);
+		s=rem[0];
+		r=rem[1];
+		poldiv(q,(n-1),d,2,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)) {
+			free_vector(rem,0,n);
+			free_vector(qq,0,n);
+			free_vector(q,0,n);
+			return;
+		}
+	}
+	nrerror("Too many iterations in routine qroot");
+}
+#undef ITMAX
+#undef TINY