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########################################################################
##
## Copyright (C) 2010-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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 {} {@var{p} =} powerset (@var{a})
## @deftypefnx {} {@var{p} =} powerset (@var{a}, "rows")
## Compute the powerset (all subsets) of the set @var{a}.
##
## The set @var{a} must be a numerical matrix or a cell array of strings. The
## output will always be a cell array of either vectors or strings.
##
## With the optional argument @qcode{"rows"}, each row of the set @var{a} is
## considered one element of the set. The input must be a 2-D numeric matrix
## to use this argument.
##
## @seealso{unique, union, intersect, setdiff, setxor, ismember}
## @end deftypefn
function p = powerset (a, byrows_arg)
if (nargin < 1)
print_usage ();
endif
byrows = false;
if (nargin == 2)
if (! strcmpi (byrows_arg, "rows"))
error ('powerset: optional second argument must be "rows"');
elseif (iscell (a))
error ('powerset: "rows" not valid for cell arrays');
else
byrows = true;
endif
endif
if (iscell (a) && ! iscellstr (a))
error ("powerset: cell arrays can only be used for character strings");
endif
if (byrows)
a = unique (a, "rows");
n = rows (a);
else
a = unique (a);
n = numel (a);
endif
if (n == 0)
p = {};
else
if (n > 32)
error ("powerset: not implemented for more than 32 elements");
endif
## Logical rep
m = uint32 (0:2^n-1);
## FIXME: better test for endianness?
if (bitunpack (uint16 (1))(1) == 0)
m = swapbytes (m);
endif
b = reshape (bitunpack (m), 32, 2^n)(1:n,:);
## Convert to indices and lengths.
[i, k] = find (b);
k = sum (b, 1);
## Index and split.
if (byrows)
p = mat2cell (a(i,:), k, columns (a));
else
if (rows (a) == 1)
p = mat2cell (a(i), 1, k);
else
p = mat2cell (a(i), k, 1);
endif
endif
endif
endfunction
%!test
%! c = sort (cellstr ({[], [1], [2], [3], [1, 2], [1, 3], [2, 3], [1, 2, 3]}));
%! p = sort (cellstr (powerset ([1, 2, 3])));
%! assert (p, c);
%!test
%! c = sort (cellstr ({ [], [1:3], [2:4], [3:5], [1:3; 2:4], [1:3; 3:5], [2:4; 3:5], [1:3; 2:4; 3:5]}));
%! p = sort (cellstr (powerset ([1:3;2:4;3:5], "rows")));
%! assert (p,c);
%!assert (powerset([]), {}); # always return a cell array
## Test input validation
%!error <Invalid call> powerset ()
%!error <second argument must be "rows"> powerset (1, "cols")
%!error <"rows" not valid for cell arrays> powerset ({1}, "rows")
%!error <cell arrays can only be used for character> powerset ({1})
%!error <not implemented for more than 32 elements> powerset (1:33)
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