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########################################################################
##
## Copyright (C) 1995-2025 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{z} =} cross (@var{x}, @var{y})
## @deftypefnx {} {@var{z} =} 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 arrays, 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. An error will be produced if the specified
## dimension is not three elements in size.
##
## In the case of a complex output, orthogonality of the output with respect
## to the inputs is also satisfied, and the condition
## @example
## @code{dot (conj (@var{z}), @var{x}) @equiv{} dot (conj (@var{z}), @var{y}) = 0}
## @end example
## is met. @code{dot (@var{z}, @var{x}) = 0} and
## @code{dot (@var{z}, @var{y}) = 0} will not hold. Also note that instead of
## using the @code{dot} function, the inner product
## @example
## @code{@var{z}(:).' * @var{x}(:) @equiv{} @var{z}(:).' * @var{y}(:) = 0}
## @end example
## will meet the orthogonality condition for vector input.
##
## Example Code:
##
## @example
## @group
## cross ([1, 1, 0], [0, 1, 1])
## @result{}
## 1 -1 1
## @end group
## @end example
##
## @example
## @group
## cross (magic (3), eye (3), 2)
## @result{}
## 0 6 -1
## -7 0 3
## 9 -4 0
## @end group
## @end example
##
## @seealso{dot, curl, divergence, conj}
## @end deftypefn
function z = cross (x, y, dim)
if (nargin < 2)
print_usage ();
endif
nd = ndims (x);
if (nargin < 3 && nd < 3 && ndims (y) < 3)
## Matlab Compatibility: mixed row/column vector inputs.
## Transpose x and y in the assignments below to get row output to match
## Matlab behavior (verified version: 2023b).
## Recommend instead that programmers change calling code to use matched
## vectors to remove any ambiguity in output form.
if (columns (x) == 1 && rows (y) == 1)
warning ("cross: cross product of column by row produces row output");
x = x.';
elseif (rows (x) == 1 && columns (y) == 1)
warning ("cross: cross product of row by column produces row output");
y = y.';
endif
endif
sz = size (x);
if (nargin == 2)
dim = find (sz == 3, 1);
if (isempty (dim))
error ("cross: must have at least one dimension with 3 elements");
endif
else
if (! (isnumeric (dim) && dim > 0 && isreal (dim) && ...
isscalar (dim) && dim == fix (dim)))
error ("cross: DIM must be a positive scalar whole number");
endif
if (dim > nd || sz(dim) != 3 || ...
dim > ndims (y) || size (y, dim) != 3)
error ("cross: X and Y must have three elements in dimension DIM");
endif
endif
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, eps);
%!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, eps);
%!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, eps);
%! assert (cross (x, y, 1), -r, eps);
%!test
%! x = [1, 0, 0; 0, 1, 0; 0, 0, 1];
%! x = cat (3, x, x);
%! y = [0, 1, 0; 0, 0, 1; 1, 0, 0];
%! y = cat (3, y, y);
%! r = [0, 0, 1; 1, 0, 0; 0, 1, 0];
%! r = cat (3, r, r);
%! assert (cross (x, y, 2), r, eps);
%! assert (cross (x, y, 1), -r, eps);
%! fail ("cross (x, y, 3)", "X and Y must have three elements");
## Test mixed vector inputs
%!test <*61295>
%! x = [1, 0, 0];
%! y = [0, 1, 0];
%! r = [0, 0, 1];
%! warning ("off", "all", "local");
%! assert (cross (x, y), r, eps);
%! assert (cross (x', y'), r', eps);
%! assert (cross (x', y), r, eps);
%! assert (cross (x, y'), r, eps);
## Test input validation
%!error <Invalid call> cross ()
%!error <Invalid call> cross (1)
%!error <must have at least one dimension with 3 elements> cross (0, 0)
%!error <must have at least one dimension with 3 elements> cross ([1, 2], [3, 4])
%!error <must have at least one dimension with 3 elements> cross ([1, 2], [3, 4, 5])
%!error <X and Y must have three elements in dimension DIM> cross (0, 0, 1)
%!error <X and Y must have three elements in dimension DIM> cross ([1, 2, 3], [1, 2, 3], 1)
%!error <X and Y must have three elements in dimension DIM> cross ([1, 2, 3], [1, 2, 3], 9)
%!error <X and Y must have three elements in dimension DIM> cross (magic (3), magic (3), 4)
%!error <DIM must be a positive scalar whole number> cross ([1, 2, 3], [4, 5, 6], {1})
%!error <DIM must be a positive scalar whole number> cross ([1, 2, 3], [4, 5, 6], "a")
%!error <DIM must be a positive scalar whole number> cross ([1, 2, 3], [4, 5, 6], true)
%!error <DIM must be a positive scalar whole number> cross ([1, 2, 3], [4, 5, 6], [1, 2])
%!error <DIM must be a positive scalar whole number> cross ([1, 2, 3], [4, 5, 6], 0)
%!error <DIM must be a positive scalar whole number> cross ([1, 2, 3], [4, 5, 6], -1)
%!error <DIM must be a positive scalar whole number> cross ([1, 2, 3], [4, 5, 6], 1.5)
%!error <DIM must be a positive scalar whole number> cross ([1, 2, 3], [4, 5, 6], 2i)
%!error <X and Y must have the same dimensions> cross ([1, 2, 3], [3, 4])
%!warning <cross product of column by row> cross ([1, 2, 3]', [4, 5, 6]);
%!warning <cross product of row by column> cross ([1, 2, 3], [4, 5, 6]');
%!test
%! x = cat (3, [1, 1, 1]', [1, 1, 1]');
%! y = cat (3, [1, 0, 0], [1, 0, 0]);
%! fail ("cross (x, y)", "X and Y must have the same dimensions");
%! fail ("cross (y, x)", "X and Y must have the same dimensions");
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