add numerical recipes library

lib/nr/cpp/recipes/toeplz.cpp

@@ -0,0 +1,56 @@
+#include "nr.h"
+
+void NR::toeplz(Vec_I_DP &r, Vec_O_DP &x, Vec_I_DP &y)
+{
+	int j,k,m,m1,m2,n,n1;
+	DP pp,pt1,pt2,qq,qt1,qt2,sd,sgd,sgn,shn,sxn;
+
+	n=y.size();
+	n1=n-1;
+	if (r[n1] == 0.0) nrerror("toeplz-1 singular principal minor");
+	x[0]=y[0]/r[n1];
+	if (n1 == 0) return;
+	Vec_DP g(n1),h(n1);
+	g[0]=r[n1-1]/r[n1];
+	h[0]=r[n1+1]/r[n1];
+	for (m=0;m<n;m++) {
+		m1=m+1;
+		sxn = -y[m1];
+		sd = -r[n1];
+		for (j=0;j<m+1;j++) {
+			sxn += r[n1+m1-j]*x[j];
+			sd += r[n1+m1-j]*g[m-j];
+		}
+		if (sd == 0.0) nrerror("toeplz-2 singular principal minor");
+		x[m1]=sxn/sd;
+		for (j=0;j<m+1;j++)
+			x[j] -= x[m1]*g[m-j];
+		if (m1 == n1) return;
+		sgn = -r[n1-m1-1];
+		shn = -r[n1+m1+1];
+		sgd = -r[n1];
+		for (j=0;j<m+1;j++) {
+			sgn += r[n1+j-m1]*g[j];
+			shn += r[n1+m1-j]*h[j];
+			sgd += r[n1+j-m1]*h[m-j];
+		}
+		if (sgd == 0.0) nrerror("toeplz-3 singular principal minor");
+		g[m1]=sgn/sgd;
+		h[m1]=shn/sd;
+		k=m;
+		m2=(m+2) >> 1;
+		pp=g[m1];
+		qq=h[m1];
+		for (j=0;j<m2;j++) {
+			pt1=g[j];
+			pt2=g[k];
+			qt1=h[j];
+			qt2=h[k];
+			g[j]=pt1-pp*qt2;
+			g[k]=pt2-pp*qt1;
+			h[j]=qt1-qq*pt2;
+			h[k--]=qt2-qq*pt1;
+		}
+	}
+	nrerror("toeplz - should not arrive here!");
+}