/usr/share/octave/packages/signal-1.3.0/fwht.m is in octave-signal 1.3.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 | ## Copyright (C) 2013 Mike Miller <mtmiller@ieee.org>
##
## This program 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.
##
## This program 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
## this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} fwht (@var{x})
## @deftypefnx {Function File} {} fwht (@var{x}, @var{n})
## @deftypefnx {Function File} {} fwht (@var{x}, @var{n}, @var{order})
## Compute the Walsh-Hadamard transform of @var{x} using the Fast
## Walsh-Hadamard Transform (FWHT) algorithm. If the input is a matrix,
## the FWHT is calculated along the columns of @var{x}.
##
## The number of elements of @var{x} must be a power of 2; if not, the
## input will be extended and filled with zeros. If a second argument
## is given, the input is truncated or extended to have length @var{n}.
##
## The third argument specifies the @var{order} in which the returned
## Walsh-Hadamard transform coefficients should be arranged. The
## @var{order} may be any of the following strings:
##
## @table @asis
## @item "sequency"
## The coefficients are returned in sequency order. This is the default
## if @var{order} is not given.
##
## @item "hadamard"
## The coefficients are returned in Hadamard order.
##
## @item "dyadic"
## The coefficients are returned in Gray code order.
## @end table
##
## @seealso{ifwht}
## @end deftypefn
## Author: Mike Miller
function y = fwht (x, n, order)
if (nargin < 1 || nargin > 3)
print_usage ();
elseif (nargin == 1)
n = order = [];
elseif (nargin == 2)
order = [];
endif
[y, n] = __fwht_opts__ ("fwht", x, n, order);
y /= n;
endfunction
%!assert (isempty (fwht ([])));
%!assert (fwht (zeros (16)), zeros (16));
%!assert (fwht (ones (16, 1)), [1; (zeros (15, 1))]);
%!assert (fwht (zeros (17, 1)), zeros (32, 1));
%!assert (fwht ([1 -1 1 -1 1 -1 1 -1]), [0 0 0 0 0 0 0 1]);
%!test
%! x = randi (16, 16);
%! assert (ifwht (fwht (x)), x);
%!test
%! x = randi (16, 16);
%! assert (ifwht (fwht (x, [], "sequency"), [], "sequency"), x);
%!test
%! x = randi (16, 16);
%! assert (ifwht (fwht (x, [], "hadamard"), [], "hadamard"), x);
%!test
%! x = randi (16, 16);
%! assert (ifwht (fwht (x, [], "dyadic"), [], "dyadic"), x);
%% Test input validation
%!error fwht ();
%!error fwht (1, 2, 3, 4);
%!error fwht (0, 0);
%!error fwht (0, 5);
%!error fwht (0, [], "invalid");
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