add numerical recipes library

lib/nr/ansi/recipes/zroots.c

@@ -0,0 +1,39 @@
+
+#include <math.h>
+#include "complex.h"
+#define EPS 2.0e-6
+#define MAXM 100
+
+void zroots(fcomplex a[], int m, fcomplex roots[], int polish)
+{
+	void laguer(fcomplex a[], int m, fcomplex *x, int *its);
+	int i,its,j,jj;
+	fcomplex x,b,c,ad[MAXM];
+
+	for (j=0;j<=m;j++) ad[j]=a[j];
+	for (j=m;j>=1;j--) {
+		x=Complex(0.0,0.0);
+		laguer(ad,j,&x,&its);
+		if (fabs(x.i) <= 2.0*EPS*fabs(x.r)) x.i=0.0;
+		roots[j]=x;
+		b=ad[j];
+		for (jj=j-1;jj>=0;jj--) {
+			c=ad[jj];
+			ad[jj]=b;
+			b=Cadd(Cmul(x,b),c);
+		}
+	}
+	if (polish)
+		for (j=1;j<=m;j++)
+			laguer(a,m,&roots[j],&its);
+	for (j=2;j<=m;j++) {
+		x=roots[j];
+		for (i=j-1;i>=1;i--) {
+			if (roots[i].r <= x.r) break;
+			roots[i+1]=roots[i];
+		}
+		roots[i+1]=x;
+	}
+}
+#undef EPS
+#undef MAXM