X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?a=blobdiff_plain;ds=sidebyside;f=octave_packages%2Fm%2Fgeneral%2Fdivergence.m;fp=octave_packages%2Fm%2Fgeneral%2Fdivergence.m;h=67e55ac61983df1e115869e4f9b30ff3bc05cd8c;hb=1c0469ada9531828709108a4882a751d2816994a;hp=0000000000000000000000000000000000000000;hpb=63de9f36673d49121015e3695f2c336ea92bc278;p=CreaPhase.git diff --git a/octave_packages/m/general/divergence.m b/octave_packages/m/general/divergence.m new file mode 100644 index 0000000..67e55ac --- /dev/null +++ b/octave_packages/m/general/divergence.m @@ -0,0 +1,112 @@ +## Copyright (C) 2009-2012 Kai Habel +## +## 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 +## . + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{div} =} divergence (@var{x}, @var{y}, @var{z}, @var{fx}, @var{fy}, @var{fz}) +## @deftypefnx {Function File} {@var{div} =} divergence (@var{fx}, @var{fy}, @var{fz}) +## @deftypefnx {Function File} {@var{div} =} divergence (@var{x}, @var{y}, @var{fx}, @var{fy}) +## @deftypefnx {Function File} {@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 + +## Author: Kai Habel + +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: expected two-dimensional matrices X and Y"); + 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: expected two-dimensional matrices X, Y, and Z"); + 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));