add numerical recipes library

lib/nr/ansi/recipes/toeplz.c

@@ -0,0 +1,60 @@
+
+#define NRANSI
+#include "nrutil.h"
+#define FREERETURN {free_vector(h,1,n);free_vector(g,1,n);return;}
+
+void toeplz(float r[], float x[], float y[], int n)
+{
+	int j,k,m,m1,m2;
+	float pp,pt1,pt2,qq,qt1,qt2,sd,sgd,sgn,shn,sxn;
+	float *g,*h;
+
+	if (r[n] == 0.0) nrerror("toeplz-1 singular principal minor");
+	g=vector(1,n);
+	h=vector(1,n);
+	x[1]=y[1]/r[n];
+	if (n == 1) FREERETURN
+	g[1]=r[n-1]/r[n];
+	h[1]=r[n+1]/r[n];
+	for (m=1;m<=n;m++) {
+		m1=m+1;
+		sxn = -y[m1];
+		sd = -r[n];
+		for (j=1;j<=m;j++) {
+			sxn += r[n+m1-j]*x[j];
+			sd += r[n+m1-j]*g[m-j+1];
+		}
+		if (sd == 0.0) nrerror("toeplz-2 singular principal minor");
+		x[m1]=sxn/sd;
+		for (j=1;j<=m;j++) x[j] -= x[m1]*g[m-j+1];
+		if (m1 == n) FREERETURN
+		sgn = -r[n-m1];
+		shn = -r[n+m1];
+		sgd = -r[n];
+		for (j=1;j<=m;j++) {
+			sgn += r[n+j-m1]*g[j];
+			shn += r[n+m1-j]*h[j];
+			sgd += r[n+j-m1]*h[m-j+1];
+		}
+		if (sgd == 0.0) nrerror("toeplz-3 singular principal minor");
+		g[m1]=sgn/sgd;
+		h[m1]=shn/sd;
+		k=m;
+		m2=(m+1) >> 1;
+		pp=g[m1];
+		qq=h[m1];
+		for (j=1;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!");
+}
+#undef FREERETURN
+#undef NRANSI