add numerical recipes library

lib/nr/cpp/recipes/zroots.cpp

@@ -0,0 +1,41 @@
+#include <cmath>
+#include <complex>
+#include "nr.h"
+using namespace std;
+
+void NR::zroots(Vec_I_CPLX_DP &a, Vec_O_CPLX_DP &roots, const bool &polish)
+{
+	const DP EPS=1.0e-14;
+	int i,its,j,jj;
+	complex<DP> x,b,c;
+
+	int m=a.size()-1;
+	Vec_CPLX_DP ad(m+1);
+	for (j=0;j<=m;j++) ad[j]=a[j];
+	for (j=m-1;j>=0;j--) {
+		x=0.0;
+		Vec_CPLX_DP ad_v(j+2);
+		for (jj=0;jj<j+2;jj++) ad_v[jj]=ad[jj];
+		laguer(ad_v,x,its);
+		if (fabs(imag(x)) <= 2.0*EPS*fabs(real(x)))
+			x=complex<DP>(real(x),0.0);
+		roots[j]=x;
+		b=ad[j+1];
+		for (jj=j;jj>=0;jj--) {
+			c=ad[jj];
+			ad[jj]=b;
+			b=x*b+c;
+		}
+	}
+	if (polish)
+		for (j=0;j<m;j++)
+			laguer(a,roots[j],its);
+	for (j=1;j<m;j++) {
+		x=roots[j];
+		for (i=j-1;i>=0;i--) {
+			if (real(roots[i]) <= real(x)) break;
+			roots[i+1]=roots[i];
+		}
+		roots[i+1]=x;
+	}
+}