Mercurial > octave-nkf
annotate scripts/general/divergence.m @ 19867:9fc020886ae9
maint: Clean up m-files to follow Octave coding conventions.
Try to trim long lines to < 80 chars.
Use '##' for single line comments.
Use '(...)' around tests for if/elseif/switch/while.
Abut cell indexing operator '{' next to variable.
Abut array indexing operator '(' next to variable.
Use space between negation operator '!' and following expression.
Use two newlines between endfunction and start of %!test or %!demo code.
Remove unnecessary parens grouping between short-circuit operators.
Remove stray extra spaces (typos) between variables and assignment operators.
Remove stray extra spaces from ends of lines.
| author | Rik <rik@octave.org> |
|---|---|
| date | Mon, 23 Feb 2015 14:54:39 -0800 |
| parents | 4197fc428c7d |
| children | 7503499a252b |
| rev | line source |
|---|---|
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1 ## Copyright (C) 2009-2015 Kai Habel |
| 11428 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7 ## the Free Software Foundation; either version 3 of the License, or (at | |
| 8 ## your option) any later version. | |
| 9 ## | |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 16 ## along with Octave; see the file COPYING. If not, see | |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 18 | |
| 19 ## -*- texinfo -*- | |
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20 ## @deftypefn {Function File} {@var{div} =} divergence (@var{x}, @var{y}, @var{z}, @var{fx}, @var{fy}, @var{fz}) |
| 11428 | 21 ## @deftypefnx {Function File} {@var{div} =} divergence (@var{fx}, @var{fy}, @var{fz}) |
| 22 ## @deftypefnx {Function File} {@var{div} =} divergence (@var{x}, @var{y}, @var{fx}, @var{fy}) | |
| 23 ## @deftypefnx {Function File} {@var{div} =} divergence (@var{fx}, @var{fy}) | |
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24 ## Calculate divergence of a vector field given by the arrays @var{fx}, |
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25 ## @var{fy}, and @var{fz} or @var{fx}, @var{fy} respectively. |
| 11428 | 26 ## @tex |
| 27 ## $$ | |
| 28 ## div F(x,y,z) = \partial_x{F} + \partial_y{F} + \partial_z{F} | |
| 29 ## $$ | |
| 30 ## @end tex | |
| 31 ## @ifnottex | |
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32 ## |
| 11428 | 33 ## @example |
| 34 ## @group | |
| 35 ## d d d | |
| 36 ## div F(x,y,z) = -- F(x,y,z) + -- F(x,y,z) + -- F(x,y,z) | |
| 37 ## dx dy dz | |
| 38 ## @end group | |
| 39 ## @end example | |
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40 ## |
| 11428 | 41 ## @end ifnottex |
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42 ## The coordinates of the vector field can be given by the arguments @var{x}, |
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43 ## @var{y}, @var{z} or @var{x}, @var{y} respectively. |
| 11428 | 44 ## |
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45 ## @seealso{curl, gradient, del2, dot} |
| 11428 | 46 ## @end deftypefn |
| 47 | |
| 48 ## Author: Kai Habel <kai.habel@gmx.de> | |
| 49 | |
| 50 function retval = divergence (varargin) | |
| 51 | |
| 52 fidx = 1; | |
| 53 if (nargin == 2) | |
| 54 sz = size (varargin{fidx}); | |
| 55 dx = (1:sz(2))(:); | |
| 56 dy = (1:sz(1))(:); | |
| 57 elseif (nargin == 3) | |
| 58 sz = size (varargin{fidx}); | |
| 59 dx = 1:sz(2); | |
| 60 dy = 1:sz(1); | |
| 61 dz = 1:sz(3); | |
| 62 elseif (nargin == 4) | |
| 63 fidx = 3; | |
| 64 dx = varargin{1}(1,:); | |
| 65 dy = varargin{2}(:,1); | |
| 66 elseif (nargin == 6) | |
| 67 fidx = 4; | |
| 68 dx = varargin{1}(1,:,1)(:); | |
| 69 dy = varargin{2}(:,1,1)(:); | |
| 70 dz = varargin{3}(1,1,:)(:); | |
| 71 else | |
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72 print_usage (); |
| 11428 | 73 endif |
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74 |
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75 if (nargin == 4 || nargin == 2) |
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76 if (! size_equal (varargin{fidx},varargin{fidx + 1})) |
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77 error ("divergence: size of X and Y must match"); |
| 11428 | 78 elseif (ndims (varargin{fidx}) != 2) |
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79 error ("divergence: expected two-dimensional matrices X and Y"); |
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80 elseif (length (dx) != columns (varargin{fidx}) |
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81 || length (dy) != rows (varargin{fidx})) |
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82 error ("divergence: size of dx and dy must match the respective dimension of X and Y"); |
| 11428 | 83 endif |
| 84 | |
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85 retval = gradient (varargin{fidx}, dx, dy); |
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86 retval += gradient (varargin{fidx + 1}.', dy, dx).'; |
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87 |
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88 elseif (nargin == 6 || nargin == 3) |
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89 if (! size_equal (varargin{fidx},varargin{fidx + 1},varargin{fidx + 2})) |
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90 error ("divergence: size of X, Y, and Z must match"); |
| 11428 | 91 elseif (ndims (varargin{fidx}) != 3) |
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parents:
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diff
changeset
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92 error ("divergence: expected two-dimensional matrices X, Y, and Z"); |
| 11428 | 93 elseif ((length (dx) != size (varargin{fidx}, 2)) |
| 94 || (length (dy) != size (varargin{fidx}, 1)) | |
| 95 || (length (dz) != size (varargin{fidx}, 3))) | |
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parents:
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96 error ("divergence: size of dx, dy, and dz must match the respective dimesion of X, Y, and Z"); |
| 11428 | 97 endif |
| 98 | |
| 99 ## x-direction | |
| 100 retval = gradient (varargin{fidx}, dx, dy, dz); | |
| 101 ## y-direction | |
| 102 retval += shiftdim (gradient (shiftdim (varargin{fidx + 1}, 2), dy), 1); | |
| 103 ## z-direction | |
| 104 retval += shiftdim (gradient (shiftdim (varargin{fidx + 2}, 1), dz), 2); | |
| 105 endif | |
| 106 | |
| 107 endfunction | |
| 108 | |
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109 |
| 11428 | 110 %!test |
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111 %! [X,Y] = meshgrid (-20:20,-22:22); |
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112 %! div = divergence (X-Y,Y); |
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113 %! assert (all (div(:) == 2)); |
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114 %! assert (size_equal (X,Y,div)); |
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115 |