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########################################################################
##
## Copyright (C) 1993-2024 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{t} =} trace (@var{A})
## Compute the trace of @var{A}, the sum of the elements along the main
## diagonal.
##
## The implementation is straightforward: @code{sum (diag (@var{A}))}.
## @seealso{eig}
## @end deftypefn
function t = trace (A)
if (nargin < 1)
print_usage ();
endif
if (ndims (A) > 2)
error ("trace: only valid on 2-D objects");
elseif (isempty (A))
t = 0;
elseif (isvector (A))
t = A(1);
else
t = sum (diag (A));
endif
endfunction
%!assert (trace ([1, 2; 3, 4]), 5)
%!assert (trace ([1, 2; 3, 4; 5, 6]), 5)
%!assert (trace ([1, 3, 5; 2, 4, 6]), 5)
%!assert (trace ([]), 0)
%!assert (trace (rand (1,0)), 0)
%!assert (trace ([3:10]), 3)
%!error <Invalid call> trace ()
%!error <only valid on 2-D objects> trace (reshape (1:9,[1,3,3]))
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