/*  ----------------------------------------------------------------	Speech Signal Processing Toolkit (SPTK): version 3.0			 SPTK Working Group		   Department of Computer Science		   Nagoya Institute of Technology				and    Interdisciplinary Graduate School of Science and Engineering		   Tokyo Institute of Technology		      Copyright (c) 1984-2000			All Rights Reserved.  Permission is hereby granted, free of charge, to use and  distribute this software and its documentation without  restriction, including without limitation the rights to use,  copy, modify, merge, publish, distribute, sublicense, and/or  sell copies of this work, and to permit persons to whom this  work is furnished to do so, subject to the following conditions:    1. The code must retain the above copyright notice, this list       of conditions and the following disclaimer.    2. Any modifications must be clearly marked as such.  NAGOYA INSTITUTE OF TECHNOLOGY, TOKYO INSITITUTE OF TECHNOLOGY,  SPTK WORKING GROUP, AND THE CONTRIBUTORS TO THIS WORK DISCLAIM  ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING ALL  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT  SHALL NAGOYA INSTITUTE OF TECHNOLOGY, TOKYO INSITITUTE OF  TECHNOLOGY, SPTK WORKING GROUP, NOR THE CONTRIBUTORS BE LIABLE  FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY  DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,  WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS  ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR  PERFORMANCE OF THIS SOFTWARE. ----------------------------------------------------------------*//****************************************************************    $Id: toeplitz.c,v 1.2 2002/12/25 05:34:54 sako Exp $    Solve a Synmetric Toeplitz Set of Linear Equations		int toeplitz(t, a, b, n, eps)	< Ta=b >	double *t  : Toeplitz elements -> T(i,j) = t(|i-j|) t[0]..t[n-1]	double *a  : solution vector of equation	double *b  : known vector	int    n   : system order	double eps : singular check (eps(if -1., 1.0e-6 is assumed))	return value : 	0  -> normally completed			-1 -> abnormally completed****************************************************************/#include <stdio.h>#include <SPTK.h>int toeplitz(t, a, b, n, eps)double *t, *a, *b, eps;int n;{    register int 	l, k;    static double 	*c = NULL, *cc;    static int		size;    double 	  	rmd, mue, mue2;        if (c == NULL){	c = dgetmem(n+n+2);	cc = c + n;	size = n;    }    if (n > size){	free(c);	c = dgetmem(n+n+2);	cc = c + n;	size = n;    }        if (eps < 0.0) eps = 1.0e-6;    fillz(c, sizeof(*c), n+1);    rmd = t[0];    if (((rmd < 0.0) ? -rmd : rmd) <= eps) return(-1);        a[0] = b[0] / rmd;    for (l=1; l<n; l++){	mue = -t[l];	for (k=1; k<l; k++)	    mue -= c[k] * t[l-k];	mue /= rmd;	for (k=1; k<l; k++)	    cc[k] = c[k] + mue * c[l-k];	cc[l] = mue;	rmd = (1.0 - mue*mue) * rmd;	if (((rmd < 0.0) ? -rmd : rmd) <= eps) return(-1);	for (k=1; k<=l; k++) c[k] = cc[k];	mue2 = b[l];	for (k=0; k<=l-1; k++)	    mue2 += c[l-k] * b[k];	mue2 /= rmd;	for (k=0; k<l; k++)	    a[k] += mue2 * c[l-k];	a[l] = mue2;    }    return(0);}