Mercurial > octave-nkf
view scripts/special-matrix/toeplitz.m @ 6975:0d11a12643f1
[project @ 2007-10-08 18:23:44 by jwe]
author | jwe |
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date | Mon, 08 Oct 2007 18:23:44 +0000 |
parents | 34f96dd5441b |
children | 93c65f2a5668 |
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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, Inc., 51 Franklin Street, Fifth Floor, Boston, MA ## 02110-1301, 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 ## $$ ## \left[\matrix{c_0 & r_1 & r_2 & \cdots & r_n\cr ## c_1 & c_0 & r_1 & \cdots & r_{n-1}\cr ## c_2 & c_1 & c_0 & \cdots & r_{n-2}\cr ## \vdots & \vdots & \vdots & \ddots & \vdots\cr ## c_n & c_{n-1} & c_{n-2} & \ldots & c_0}\right] ## $$ ## @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 ## @seealso{hankel, vander, sylvester_matrix, hilb, invhilb} ## @end deftypefn ## Author: jwe function retval = toeplitz (c, r) if (nargin == 1) r = c; elseif (nargin != 2) print_usage (); 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 = resize (resize (c, 0), 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