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toeplitz.m
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1999-12-24
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## Copyright (C) 1996, 1997 John W. Eaton
##
## This file is part of Octave.
##
## Octave is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## Octave is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING. If not, write to the Free
## Software Foundation, 59 Temple Place - Suite 330, Boston, MA
## 02111-1307, USA.
## -*- texinfo -*-
## @deftypefn {Function File} {} toeplitz (@var{c}, @var{r})
## Return the Toeplitz matrix constructed given the first column @var{c},
## and (optionally) the first row @var{r}. If the first element of @var{c}
## is not the same as the first element of @var{r}, the first element of
## @var{c} is used. If the second argument is omitted, the first row is
## taken to be the same as the first column.
##
## A square Toeplitz matrix has the form
## @iftex
## @tex
## $$
## \left[\matrix{c_0 & r_1 & r_2 & \ldots & r_n\cr
## c_1 & c_0 & r_1 & & c_{n-1}\cr
## c_2 & c_1 & c_0 & & c_{n-2}\cr
## \vdots & & & & \vdots\cr
## c_n & c_{n-1} & c_{n-2} & \ldots & c_0}\right].
## $$
## @end tex
## @end iftex
## @ifinfo
##
## @example
## @group
## c(0) r(1) r(2) ... r(n)
## c(1) c(0) r(1) r(n-1)
## c(2) c(1) c(0) r(n-2)
## . .
## . .
## . .
##
## c(n) c(n-1) c(n-2) ... c(0)
## @end group
## @end example
## @end ifinfo
## @end deftypefn
## See also: hankel, vander, sylv_mat, hilb, invhib
## Author: jwe
function retval = toeplitz (c, r)
if (nargin == 1)
r = c;
elseif (nargin != 2)
usage ("toeplitz (c, r)");
endif
[c_nr, c_nc] = size (c);
[r_nr, r_nc] = size (r);
if ((c_nr != 1 && c_nc != 1) || (r_nr != 1 && r_nc != 1))
error ("toeplitz: expecting vector arguments");
endif
if (c_nc != 1)
c = c.';
endif
if (r_nr != 1)
r = r.';
endif
if (r (1) != c (1))
warning ("toeplitz: column wins diagonal conflict");
endif
## If we have a single complex argument, we want to return a
## Hermitian-symmetric matrix (actually, this will really only be
## Hermitian-symmetric if the first element of the vector is real).
if (nargin == 1)
c = conj (c);
c(1) = conj (c(1));
endif
## This should probably be done with the colon operator...
nc = length (r);
nr = length (c);
retval = zeros (nr, nc);
for i = 1:min (nc, nr)
retval (i:nr, i) = c (1:nr-i+1);
endfor
for i = 1:min (nr, nc-1)
retval (i, i+1:nc) = r (2:nc-i+1);
endfor
endfunction