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## -*- 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)