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########################################################################
##
## Copyright (C) 2007-2022 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 {} {} mode (@var{x})
## @deftypefnx {} {} mode (@var{x}, @var{dim})
## @deftypefnx {} {[@var{m}, @var{f}, @var{c}] =} mode (@dots{})
## Compute the most frequently occurring value in a dataset (mode).
##
## @code{mode} determines the frequency of values along the first non-singleton
## dimension and returns the value with the highest frequency. If two, or
## more, values have the same frequency @code{mode} returns the smallest.
##
## If the optional argument @var{dim} is given, operate along this dimension.
##
## The return variable @var{f} is the number of occurrences of the mode in
## the dataset.
##
## The cell array @var{c} contains all of the elements with the maximum
## frequency.
## @seealso{mean, median}
## @end deftypefn
function [m, f, c] = mode (x, dim)
if (nargin < 1)
print_usage ();
endif
if (! (isnumeric (x) || islogical (x)))
error ("mode: X must be a numeric vector or matrix");
endif
nd = ndims (x);
sz = size (x);
if (nargin < 2)
## Find the first non-singleton dimension.
(dim = find (sz > 1, 1)) || (dim = 1);
else
if (! (isscalar (dim) && dim == fix (dim) && dim > 0))
error ("mode: DIM must be an integer and a valid dimension");
endif
endif
if (dim > nd)
## Special case of mode over non-existent dimension.
m = x;
f = ones (size (x));
c = num2cell (x);
return;
endif
sz2 = sz;
sz2(dim) = 1;
sz3 = ones (1, nd);
sz3(dim) = sz(dim);
if (issparse (x))
t2 = sparse (sz(1), sz(2));
else
t2 = zeros (sz);
endif
if (dim != 1)
perm = [dim, 1:dim-1, dim+1:nd];
t2 = permute (t2, perm);
endif
xs = sort (x, dim);
t = cat (dim, true (sz2), diff (xs, 1, dim) != 0);
if (dim != 1)
t2(permute (t != 0, perm)) = diff ([find(permute (t, perm))(:); prod(sz)+1]);
f = max (ipermute (t2, perm), [], dim);
xs = permute (xs, perm);
else
t2(t) = diff ([find(t)(:); prod(sz)+1]);
f = max (t2, [], dim);
endif
c = cell (sz2);
if (issparse (x))
m = sparse (sz2(1), sz2(2));
else
m = zeros (sz2, class (x));
endif
for i = 1 : prod (sz2)
c{i} = xs(t2(:, i) == f(i), i);
m(i) = c{i}(1);
endfor
endfunction
%!test
%! [m, f, c] = mode (toeplitz (1:5));
%! assert (m, [1,2,2,2,1]);
%! assert (f, [1,2,2,2,1]);
%! assert (c, {[1;2;3;4;5],[2],[2;3],[2],[1;2;3;4;5]});
%!test
%! [m, f, c] = mode (toeplitz (1:5), 2);
%! assert (m, [1;2;2;2;1]);
%! assert (f, [1;2;2;2;1]);
%! assert (c, {[1;2;3;4;5];[2];[2;3];[2];[1;2;3;4;5]});
%!test
%! a = sprandn (32, 32, 0.05);
%! sp0 = sparse (0);
%! [m, f, c] = mode (a);
%! [m2, f2, c2] = mode (full (a));
%! assert (m, sparse (m2));
%! assert (f, sparse (f2));
%! c_exp(1:length (a)) = { sp0 };
%! assert (c ,c_exp);
%! assert (c2,c_exp);
%!assert (mode ([2,3,1,2,3,4],1),[2,3,1,2,3,4])
%!assert (mode ([2,3,1,2,3,4],2),2)
%!assert (mode ([2,3,1,2,3,4]),2)
%!assert (mode (single ([2,3,1,2,3,4])), single (2))
%!assert (mode (int8 ([2,3,1,2,3,4])), int8 (2))
%!assert (mode ([2;3;1;2;3;4],1),2)
%!assert (mode ([2;3;1;2;3;4],2),[2;3;1;2;3;4])
%!assert (mode ([2;3;1;2;3;4]),2)
%!test
%! x = magic (3);
%! [m, f, c] = mode (x, 3);
%! assert (m, x);
%! assert (f, ones (3,3));
%! assert (c, num2cell (x));
%!shared x
%! x(:,:,1) = toeplitz (1:3);
%! x(:,:,2) = circshift (toeplitz (1:3), 1);
%! x(:,:,3) = circshift (toeplitz (1:3), 2);
%!test
%! [m, f, c] = mode (x, 1);
%! assert (reshape (m, [3, 3]), [1 1 1; 2 2 2; 1 1 1]);
%! assert (reshape (f, [3, 3]), [1 1 1; 2 2 2; 1 1 1]);
%! c = reshape (c, [3, 3]);
%! assert (c{1}, [1; 2; 3]);
%! assert (c{2}, 2);
%! assert (c{3}, [1; 2; 3]);
%!test
%! [m, f, c] = mode (x, 2);
%! assert (reshape (m, [3, 3]), [1 1 2; 2 1 1; 1 2 1]);
%! assert (reshape (f, [3, 3]), [1 1 2; 2 1 1; 1 2 1]);
%! c = reshape (c, [3, 3]);
%! assert (c{1}, [1; 2; 3]);
%! assert (c{2}, 2);
%! assert (c{3}, [1; 2; 3]);
%!test
%! [m, f, c] = mode (x, 3);
%! assert (reshape (m, [3, 3]), [1 2 1; 1 2 1; 1 2 1]);
%! assert (reshape (f, [3, 3]), [1 2 1; 1 2 1; 1 2 1]);
%! c = reshape (c, [3, 3]);
%! assert (c{1}, [1; 2; 3]);
%! assert (c{2}, [1; 2; 3]);
%! assert (c{3}, [1; 2; 3]);
## Test input validation
%!error <Invalid call> mode ()
%!error <X must be a numeric> mode ({1 2 3})
%!error <DIM must be an integer> mode (1, ones (2,2))
%!error <DIM must be an integer> mode (1, 1.5)
%!error <DIM must be .* a valid dimension> mode (1, 0)
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