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/* ----------------------------------------------------------------- */
/* The Speech Signal Processing Toolkit (SPTK) */
/* developed by SPTK Working Group */
/* http://sp-tk.sourceforge.net/ */
/* ----------------------------------------------------------------- */
/* */
/* Copyright (c) 1984-2007 Tokyo Institute of Technology */
/* Interdisciplinary Graduate School of */
/* Science and Engineering */
/* */
/* 1996-2015 Nagoya Institute of Technology */
/* Department of Computer Science */
/* */
/* All rights reserved. */
/* */
/* Redistribution and use in source and binary forms, with or */
/* without modification, are permitted provided that the following */
/* conditions are met: */
/* */
/* - Redistributions of source code must retain the above copyright */
/* notice, this list of conditions and the following disclaimer. */
/* - Redistributions in binary form must reproduce the above */
/* copyright notice, this list of conditions and the following */
/* disclaimer in the documentation and/or other materials provided */
/* with the distribution. */
/* - Neither the name of the SPTK working group nor the names of its */
/* contributors may be used to endorse or promote products derived */
/* from this software without specific prior written permission. */
/* */
/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */
/* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */
/* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */
/* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */
/* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS */
/* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, */
/* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED */
/* TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, */
/* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON */
/* ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, */
/* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY */
/* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE */
/* POSSIBILITY OF SUCH DAMAGE. */
/* ----------------------------------------------------------------- */
/****************************************************************
$Id: toeplitz.c,v 1.15 2015/12/14 01:14:25 uratec 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 <stdlib.h>
#if defined(WIN32)
#include "SPTK.h"
#else
#include <SPTK.h>
#endif
int toeplitz(double *t, double *a, double *b, const int n, double eps)
{
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);
}
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