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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{div} =} divergence (@var{x}, @var{y}, @var{z}, @var{fx}, @var{fy}, @var{fz})
## @deftypefnx {} {@var{div} =} divergence (@var{fx}, @var{fy}, @var{fz})
## @deftypefnx {} {@var{div} =} divergence (@var{x}, @var{y}, @var{fx}, @var{fy})
## @deftypefnx {} {@var{div} =} divergence (@var{fx}, @var{fy})
## Calculate divergence of a vector field given by the arrays @var{fx},
## @var{fy}, and @var{fz} or @var{fx}, @var{fy} respectively.
##
## @tex
## $$
## div F(x,y,z) = \partial_x{F} + \partial_y{F} + \partial_z{F}
## $$
## @end tex
## @ifnottex
##
## @example
## @group
## d d d
## div F(x,y,z) = -- F(x,y,z) + -- F(x,y,z) + -- F(x,y,z)
## dx dy dz
## @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.
##
## @seealso{curl, gradient, del2, dot}
## @end deftypefn
function retval = divergence (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 ("divergence: size of X and Y must match");
elseif (ndims (varargin{fidx}) != 2)
error ("divergence: X and Y must be 2-D matrices");
elseif (length (dx) != columns (varargin{fidx})
|| length (dy) != rows (varargin{fidx}))
error ("divergence: size of dx and dy must match the respective dimension of X and Y");
endif
retval = gradient (varargin{fidx}, dx, dy);
retval += gradient (varargin{fidx + 1}.', dy, dx).';
elseif (nargin == 6 || nargin == 3)
if (! size_equal (varargin{fidx},varargin{fidx + 1},varargin{fidx + 2}))
error ("divergence: size of X, Y, and Z must match");
elseif (ndims (varargin{fidx}) != 3)
error ("divergence: 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 ("divergence: size of dx, dy, and dz must match the respective dimesion of X, Y, and Z");
endif
## x-direction
retval = gradient (varargin{fidx}, dx, dy, dz);
## y-direction
retval += shiftdim (gradient (shiftdim (varargin{fidx + 1}, 2), dy), 1);
## z-direction
retval += shiftdim (gradient (shiftdim (varargin{fidx + 2}, 1), dz), 2);
endif
endfunction
%!test
%! [X,Y] = meshgrid (-20:20,-22:22);
%! div = divergence (X-Y,Y);
%! assert (all (div(:) == 2));
%! assert (size_equal (X,Y,div));
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