add numerical recipes library

lib/nr/k_and_r/recipes/laguer.c

@@ -0,0 +1,55 @@
+
+#include <math.h>
+#include "complex.h"
+#include "nrutil.h"
+#define EPSS 1.0e-7
+#define MR 8
+#define MT 10
+#define MAXIT (MT*MR)
+
+void laguer(a,m,x,its)
+fcomplex *x,a[];
+int *its,m;
+{
+	int iter,j;
+	float abx,abp,abm,err;
+	fcomplex dx,x1,b,d,f,g,h,sq,gp,gm,g2;
+	static float frac[MR+1] = {0.0,0.5,0.25,0.75,0.13,0.38,0.62,0.88,1.0};
+
+	for (iter=1;iter<=MAXIT;iter++) {
+		*its=iter;
+		b=a[m];
+		err=Cabs(b);
+		d=f=Complex(0.0,0.0);
+		abx=Cabs(*x);
+		for (j=m-1;j>=0;j--) {
+			f=Cadd(Cmul(*x,f),d);
+			d=Cadd(Cmul(*x,d),b);
+			b=Cadd(Cmul(*x,b),a[j]);
+			err=Cabs(b)+abx*err;
+		}
+		err *= EPSS;
+		if (Cabs(b) <= err) return;
+		g=Cdiv(d,b);
+		g2=Cmul(g,g);
+		h=Csub(g2,RCmul(2.0,Cdiv(f,b)));
+		sq=Csqrt(RCmul((float) (m-1),Csub(RCmul((float) m,h),g2)));
+		gp=Cadd(g,sq);
+		gm=Csub(g,sq);
+		abp=Cabs(gp);
+		abm=Cabs(gm);
+		if (abp < abm) gp=gm;
+		dx=((FMAX(abp,abm) > 0.0 ? Cdiv(Complex((float) m,0.0),gp)
+			: RCmul(1+abx,Complex(cos((float)iter),sin((float)iter)))));
+		x1=Csub(*x,dx);
+		if (x->r == x1.r && x->i == x1.i) return;
+		if (iter % MT) *x=x1;
+		else *x=Csub(*x,RCmul(frac[iter/MT],dx));
+	}
+	nrerror("too many iterations in laguer");
+	return;
+}
+#undef EPSS
+#undef MR
+#undef MT
+#undef MAXIT