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########################################################################
##
## Copyright (C) 2009-2024 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{cx}, @var{cy}, @var{cz}, @var{v}] =} curl (@var{x}, @var{y}, @var{z}, @var{fx}, @var{fy}, @var{fz})
## @deftypefnx {} {[@var{cz}, @var{v}] =} curl (@var{x}, @var{y}, @var{fx}, @var{fy})
## @deftypefnx {} {[@dots{}] =} curl (@var{fx}, @var{fy}, @var{fz})
## @deftypefnx {} {[@dots{}] =} curl (@var{fx}, @var{fy})
## @deftypefnx {} {@var{v} =} curl (@dots{})
## Calculate curl of vector field given by the arrays @var{fx}, @var{fy}, and
## @var{fz} or @var{fx}, @var{fy} respectively.
## @tex
## $$ curl F(x,y,z) = \left( {\partial{F_z} \over \partial{y}} - {\partial{F_y} \over \partial{z}}, {\partial{F_x} \over \partial{z}} - {\partial{F_z} \over \partial{x}}, {\partial{F_y} \over \partial{x}} - {\partial{F_x} \over \partial{y}} \right)$$
## @end tex
## @ifnottex
##
## @example
## @group
## / d d d d d d \
## curl F(x,y,z) = | -- Fz - -- Fy, -- Fx - -- Fz, -- Fy - -- Fx |
## \ dy dz dz dx dx dy /
## @end group
## @end example
##
## @end ifnottex
## The coordinates of the vector field can be given by the arguments @var{x},
## @var{y}, @var{z} or @var{x}, @var{y} respectively. @var{v} calculates the
## scalar component of the angular velocity vector in direction of the z-axis
## for two-dimensional input. For three-dimensional input the scalar
## rotation is calculated at each grid point in direction of the vector field
## at that point.
## @seealso{divergence, gradient, del2, cross}
## @end deftypefn
function varargout = curl (varargin)
fidx = 1;
if (nargin == 2)
sz = size (varargin{fidx});
dx = (1:sz(2))(:);
dy = (1:sz(1))(:);
elseif (nargin == 3)
sz = size (varargin{fidx});
dx = (1:sz(2))(:);
dy = (1:sz(1))(:);
dz = (1:sz(3))(:);
elseif (nargin == 4)
fidx = 3;
dx = varargin{1}(1,:);
dy = varargin{2}(:,1);
elseif (nargin == 6)
fidx = 4;
dx = varargin{1}(1,:,1)(:);
dy = varargin{2}(:,1,1)(:);
dz = varargin{3}(1,1,:)(:);
else
print_usage ();
endif
if (nargin == 4 || nargin == 2)
if (! size_equal (varargin{fidx}, varargin{fidx + 1}))
error ("curl: size of X and Y must match");
elseif (ndims (varargin{fidx}) != 2)
error ("curl: X and Y must be 2-D matrices");
elseif ((length (dx) != columns (varargin{fidx}))
|| (length (dy) != rows (varargin{fidx})))
error ("curl: size of dx and dy must match the respective dimension of X and Y");
endif
dFx_dy = gradient (varargin{fidx}.', dy, dx).';
dFy_dx = gradient (varargin{fidx + 1}, dx, dy);
rot_z = dFy_dx - dFx_dy;
av = rot_z / 2;
if (nargout == 0 || nargout == 1)
varargout{1} = av;
else
varargout{1} = rot_z;
varargout{2} = av;
endif
elseif (nargin == 6 || nargin == 3)
if (! size_equal (varargin{fidx}, varargin{fidx + 1}, varargin{fidx + 2}))
error ("curl: size of X, Y, and Z must match");
elseif (ndims (varargin{fidx}) != 3)
error ("curl: X, Y, and Z must be 2-D matrices");
elseif ((length (dx) != size (varargin{fidx}, 2))
|| (length (dy) != size (varargin{fidx}, 1))
|| (length (dz) != size (varargin{fidx}, 3)))
error ("curl: size of dx, dy, and dz must match the respective dimesion of X, Y, and Z");
endif
[~, dFx_dy, dFx_dz] = gradient (varargin{fidx}, dx, dy, dz);
[dFy_dx, ~, dFy_dz] = gradient (varargin{fidx + 1}, dx, dy, dz);
[dFz_dx, dFz_dy] = gradient (varargin{fidx + 2}, dx, dy, dz);
rot_x = dFz_dy - dFy_dz;
rot_y = dFx_dz - dFz_dx;
rot_z = dFy_dx - dFx_dy;
l = sqrt(varargin{fidx}.^2 + varargin{fidx + 1}.^2 + varargin{fidx + 2}.^2);
av = (rot_x .* varargin{fidx} +
rot_y .* varargin{fidx + 1} +
rot_z .* varargin{fidx + 2}) ./ (2 * l);
if (nargout == 0 || nargout == 1)
varargout{1} = av;
else
varargout{1} = rot_x;
varargout{2} = rot_y;
varargout{3} = rot_z;
varargout{4} = av;
endif
endif
endfunction
%!test
%! [X,Y] = meshgrid (-20:20,-22:22);
%! av = curl (2*(X-Y), Y);
%! assert (all (av(:) == 1));
%! [cz,av] = curl (2*(X-Y), Y);
%! assert (all (cz(:) == 2));
%! assert (all (av(:) == 1));
%! [cz,av] = curl (X/2, Y/2, 2*(X-Y), Y);
%! assert (all (cz(:) == 4));
%! assert (all (av(:) == 2));
%! assert (size_equal (X,Y,cz,av));
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