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########################################################################
##
## Copyright (C) 1995-2022 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 {} {} cross (@var{x}, @var{y})
## @deftypefnx {} {} cross (@var{x}, @var{y}, @var{dim})
## Compute the vector cross product of two 3-dimensional vectors @var{x} and
## @var{y}.
##
## If @var{x} and @var{y} are matrices, the cross product is applied along the
## first dimension with three elements.
##
## The optional argument @var{dim} forces the cross product to be calculated
## along the specified dimension.
##
## Example Code:
##
## @example
## @group
## cross ([1, 1, 0], [0, 1, 1])
## @result{}
## 1 -1 1
## @end group
## @end example
##
## @seealso{dot, curl, divergence}
## @end deftypefn
function z = cross (x, y, dim)
if (nargin < 2)
print_usage ();
endif
if (ndims (x) < 3 && ndims (y) < 3 && nargin < 3)
## COMPATIBILITY -- opposite behavior for cross(row,col)
## Swap x and y in the assignments below to get the matlab behavior.
## Better yet, fix the calling code so that it uses conformant vectors.
if (columns (x) == 1 && rows (y) == 1)
warning ("cross: taking cross product of column by row");
y = y.';
elseif (rows (x) == 1 && columns (y) == 1)
warning ("cross: taking cross product of row by column");
x = x.';
endif
endif
if (nargin == 2)
dim = find (size (x) == 3, 1);
if (isempty (dim))
error ("cross: must have at least one dimension with 3 elements");
endif
else
if (size (x, dim) != 3)
error ("cross: dimension DIM must have 3 elements");
endif
endif
nd = ndims (x);
sz = size (x);
idx2 = idx3 = idx1 = {':'}(ones (1, nd));
idx1(dim) = 1;
idx2(dim) = 2;
idx3(dim) = 3;
if (size_equal (x, y))
x1 = x(idx1{:});
x2 = x(idx2{:});
x3 = x(idx3{:});
y1 = y(idx1{:});
y2 = y(idx2{:});
y3 = y(idx3{:});
z = cat (dim, (x2.*y3 - x3.*y2), (x3.*y1 - x1.*y3), (x1.*y2 - x2.*y1));
else
error ("cross: X and Y must have the same dimensions");
endif
endfunction
%!test
%! x = [1 0 0];
%! y = [0 1 0];
%! r = [0 0 1];
%! assert (cross (x, y), r, 2e-8);
%!test
%! x = [1 2 3];
%! y = [4 5 6];
%! r = [(2*6-3*5) (3*4-1*6) (1*5-2*4)];
%! assert (cross (x, y), r, 2e-8);
%!test
%! x = [1 0 0; 0 1 0; 0 0 1];
%! y = [0 1 0; 0 0 1; 1 0 0];
%! r = [0 0 1; 1 0 0; 0 1 0];
%! assert (cross (x, y, 2), r, 2e-8);
%! assert (cross (x, y, 1), -r, 2e-8);
## Test input validation
%!error <Invalid call> cross ()
%!error <Invalid call> cross (1)
## FIXME: Need tests for other error() conditions and warning() calls.
%!error <must have at least one dimension with 3 elements> cross (0,0)
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