add numerical recipes library

lib/nr/cpp/recipes/tqli.cpp

@@ -0,0 +1,56 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::tqli(Vec_IO_DP &d, Vec_IO_DP &e, Mat_IO_DP &z)
+{
+	int m,l,iter,i,k;
+	DP s,r,p,g,f,dd,c,b;
+
+	int n=d.size();
+	for (i=1;i<n;i++) e[i-1]=e[i];
+	e[n-1]=0.0;
+	for (l=0;l<n;l++) {
+		iter=0;
+		do {
+			for (m=l;m<n-1;m++) {
+				dd=fabs(d[m])+fabs(d[m+1]);
+				if (fabs(e[m])+dd == dd) break;
+			}
+			if (m != l) {
+				if (iter++ == 30) nrerror("Too many iterations in tqli");
+				g=(d[l+1]-d[l])/(2.0*e[l]);
+				r=pythag(g,1.0);
+				g=d[m]-d[l]+e[l]/(g+SIGN(r,g));
+				s=c=1.0;
+				p=0.0;
+				for (i=m-1;i>=l;i--) {
+					f=s*e[i];
+					b=c*e[i];
+					e[i+1]=(r=pythag(f,g));
+					if (r == 0.0) {
+						d[i+1] -= p;
+						e[m]=0.0;
+						break;
+					}
+					s=f/r;
+					c=g/r;
+					g=d[i+1]-p;
+					r=(d[i]-g)*s+2.0*c*b;
+					d[i+1]=g+(p=s*r);
+					g=c*r-b;
+					// Next loop can be omitted if eigenvectors not wanted
+					for (k=0;k<n;k++) {
+						f=z[k][i+1];
+						z[k][i+1]=s*z[k][i]+c*f;
+						z[k][i]=c*z[k][i]-s*f;
+					}
+				}
+				if (r == 0.0 && i >= l) continue;
+				d[l] -= p;
+				e[l]=g;
+				e[m]=0.0;
+			}
+		} while (m != l);
+	}
+}