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## Copyright (C) 1996-2013 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 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
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} sylvester_matrix (@var{k})
## Return the Sylvester matrix of order
## @tex
## $n = 2^k$.
## @end tex
## @ifnottex
## n = 2^@var{k}.
## @end ifnottex
##
## @seealso{toeplitz, hankel}
## @end deftypefn
## Author: jwe
function retval = sylvester_matrix (k)
persistent warned = false;
if (! warned)
warned = true;
warning ("Octave:deprecated-function",
"sylvester_matrix is obsolete and will be removed from a future version of Octave; please use hadamard(2^k) instead");
endif
if (nargin != 1)
print_usage ();
endif
if (isscalar (k))
if (k < 1)
retval = 1;
else
tmp = sylvester_matrix (k-1);
retval = [tmp, tmp; tmp, -tmp];
endif
else
error ("sylvester_matrix: expecting scalar argument");
endif
endfunction
%!assert((sylvester_matrix (1) == [1, 1; 1, -1]
%! && (sylvester_matrix (2)
%! == [1, 1, 1, 1; 1, -1, 1, -1; 1, 1, -1, -1; 1, -1, -1, 1])));
%!error sylvester_matrix ([1, 2; 3, 4]);
%!error sylvester_matrix ();
%!error sylvester_matrix (1, 2);
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