Mercurial > octave
view scripts/special-matrix/toeplitz.m @ 27919:1891570abac8
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2020.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Mon, 06 Jan 2020 22:29:51 -0500 |
parents | b442ec6dda5c |
children | bd51beb6205e |
line wrap: on
line source
## Copyright (C) 1993-2020 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this distribution ## or <https://octave.org/COPYRIGHT.html/>. ## ## ## 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 3 of the License, 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, see ## <https://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {} {} toeplitz (@var{c}) ## @deftypefnx {} {} toeplitz (@var{c}, @var{r}) ## Return the Toeplitz matrix constructed from the first column @var{c}, ## and optionally the first row @var{r}. ## ## If the second argument is omitted, the first row is taken to be the ## same as the first column. If the first element of @var{r} is not the same ## as the first element of @var{c}, the first element of @var{c} is used. ## ## A Toeplitz, or diagonal-constant, matrix has the same value along each ## diagonal. Although it need not be square, it often is. An @nospell{MxN} ## Toeplitz matrix has the form: ## @tex ## $$ ## \left[\matrix{c_1 & r_2 & r_3 & \cdots & r_n\cr ## c_2 & c_1 & r_2 & \cdots & r_{n-1}\cr ## c_3 & c_2 & c_1 & \cdots & r_{n-2}\cr ## \vdots & \vdots & \vdots & \ddots & \vdots\cr ## c_m & c_{m-1} & c_{m-2} & \ldots & c{m-n+1}}\right] ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## c(1) r(2) r(3) @dots{} r(n) ## c(2) c(1) r(2) @dots{} r(n-1) ## c(3) c(2) c(1) @dots{} r(n-2) ## . . . . . ## . . . . . ## . . . . . ## c(m) c(m-1) c(m-2) @dots{} c(m-n+1) ## @end group ## @end example ## ## @end ifnottex ## @seealso{hankel} ## @end deftypefn ## Author: jwe && jh function retval = toeplitz (c, r) if (nargin < 1 || nargin > 2) print_usage (); endif if (nargin == 1) if (! isvector (c)) error ("toeplitz: C must be a vector"); endif r = c; nr = length (c); nc = nr; else if (! (isvector (c) && isvector (r))) error ("toeplitz: C and R must be vectors"); elseif (r(1) != c(1)) warning ("toeplitz: column wins diagonal conflict"); endif nr = length (c); nc = length (r); endif if (nr == 0 || nc == 0) ## Empty matrix. retval = zeros (nr, nc, class (c)); return; 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 && iscomplex (c)) c = conj (c); c(1) = conj (c(1)); endif if (issparse (c) && issparse (r)) c = c(:).'; # enforce row vector r = r(:).'; # enforce row vector cidx = find (c); ridx = find (r); ## Ignore the first element in r. ridx = ridx(ridx > 1); ## Form matrix. retval = spdiags (repmat (c(cidx),nr,1),1-cidx,nr,nc) + ... spdiags (repmat (r(ridx),nr,1),ridx-1,nr,nc); else ## Concatenate data into a single column vector. data = [r(end:-1:2)(:); c(:)]; ## Get slices. slices = cellslices (data, nc:-1:1, nc+nr-1:-1:nr); ## Form matrix. retval = horzcat (slices{:}); endif endfunction %!assert (toeplitz (1), [1]) %!assert (toeplitz ([1, 2, 3], [1; -3; -5]), [1, -3, -5; 2, 1, -3; 3, 2, 1]) %!assert (toeplitz ([1, 2, 3], [1; -3i; -5i]), [1, -3i, -5i; 2, 1, -3i; 3, 2, 1]) ## Test input validation %!error toeplitz () %!error toeplitz (1, 2, 3) %!error <C must be a vector> toeplitz ([1, 2; 3, 4]) %!error <C and R must be vectors> toeplitz ([1, 2; 3, 4], 1) %!error <C and R must be vectors> toeplitz (1, [1, 2; 3, 4])