Mercurial > octave
annotate scripts/general/divergence.m @ 23220:092078913d54
maint: Merge stable to default.
| author | John W. Eaton <jwe@octave.org> |
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| date | Wed, 22 Feb 2017 12:58:07 -0500 |
| parents | ef4d915df748 3ac9f9ecfae5 |
| children | 194eb4bd202b |
| rev | line source |
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1 ## Copyright (C) 2009-2017 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 | |
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7 ## the Free Software Foundation; either version 3 of the License, or |
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8 ## (at your option) any later version. |
| 11428 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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13 ## GNU General Public License for more details. |
| 11428 | 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 {} {@var{div} =} divergence (@var{x}, @var{y}, @var{z}, @var{fx}, @var{fy}, @var{fz}) |
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21 ## @deftypefnx {} {@var{div} =} divergence (@var{fx}, @var{fy}, @var{fz}) |
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22 ## @deftypefnx {} {@var{div} =} divergence (@var{x}, @var{y}, @var{fx}, @var{fy}) |
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23 ## @deftypefnx {} {@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. |
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26 ## |
| 11428 | 27 ## @tex |
| 28 ## $$ | |
| 29 ## div F(x,y,z) = \partial_x{F} + \partial_y{F} + \partial_z{F} | |
| 30 ## $$ | |
| 31 ## @end tex | |
| 32 ## @ifnottex | |
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33 ## |
| 11428 | 34 ## @example |
| 35 ## @group | |
| 36 ## d d d | |
| 37 ## div F(x,y,z) = -- F(x,y,z) + -- F(x,y,z) + -- F(x,y,z) | |
| 38 ## dx dy dz | |
| 39 ## @end group | |
| 40 ## @end example | |
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41 ## |
| 11428 | 42 ## @end ifnottex |
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43 ## The coordinates of the vector field can be given by the arguments @var{x}, |
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44 ## @var{y}, @var{z} or @var{x}, @var{y} respectively. |
| 11428 | 45 ## |
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46 ## @seealso{curl, gradient, del2, dot} |
| 11428 | 47 ## @end deftypefn |
| 48 | |
| 49 ## Author: Kai Habel <kai.habel@gmx.de> | |
| 50 | |
| 51 function retval = divergence (varargin) | |
| 52 | |
| 53 fidx = 1; | |
| 54 if (nargin == 2) | |
| 55 sz = size (varargin{fidx}); | |
| 56 dx = (1:sz(2))(:); | |
| 57 dy = (1:sz(1))(:); | |
| 58 elseif (nargin == 3) | |
| 59 sz = size (varargin{fidx}); | |
| 60 dx = 1:sz(2); | |
| 61 dy = 1:sz(1); | |
| 62 dz = 1:sz(3); | |
| 63 elseif (nargin == 4) | |
| 64 fidx = 3; | |
| 65 dx = varargin{1}(1,:); | |
| 66 dy = varargin{2}(:,1); | |
| 67 elseif (nargin == 6) | |
| 68 fidx = 4; | |
| 69 dx = varargin{1}(1,:,1)(:); | |
| 70 dy = varargin{2}(:,1,1)(:); | |
| 71 dz = varargin{3}(1,1,:)(:); | |
| 72 else | |
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73 print_usage (); |
| 11428 | 74 endif |
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75 |
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76 if (nargin == 4 || nargin == 2) |
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77 if (! size_equal (varargin{fidx},varargin{fidx + 1})) |
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78 error ("divergence: size of X and Y must match"); |
| 11428 | 79 elseif (ndims (varargin{fidx}) != 2) |
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80 error ("divergence: X and Y must be 2-D matrices"); |
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81 elseif (length (dx) != columns (varargin{fidx}) |
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82 || length (dy) != rows (varargin{fidx})) |
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83 error ("divergence: size of dx and dy must match the respective dimension of X and Y"); |
| 11428 | 84 endif |
| 85 | |
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86 retval = gradient (varargin{fidx}, dx, dy); |
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87 retval += gradient (varargin{fidx + 1}.', dy, dx).'; |
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88 |
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89 elseif (nargin == 6 || nargin == 3) |
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90 if (! size_equal (varargin{fidx},varargin{fidx + 1},varargin{fidx + 2})) |
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91 error ("divergence: size of X, Y, and Z must match"); |
| 11428 | 92 elseif (ndims (varargin{fidx}) != 3) |
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| 11428 | 94 elseif ((length (dx) != size (varargin{fidx}, 2)) |
| 95 || (length (dy) != size (varargin{fidx}, 1)) | |
| 96 || (length (dz) != size (varargin{fidx}, 3))) | |
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97 error ("divergence: size of dx, dy, and dz must match the respective dimesion of X, Y, and Z"); |
| 11428 | 98 endif |
| 99 | |
| 100 ## x-direction | |
| 101 retval = gradient (varargin{fidx}, dx, dy, dz); | |
| 102 ## y-direction | |
| 103 retval += shiftdim (gradient (shiftdim (varargin{fidx + 1}, 2), dy), 1); | |
| 104 ## z-direction | |
| 105 retval += shiftdim (gradient (shiftdim (varargin{fidx + 2}, 1), dz), 2); | |
| 106 endif | |
| 107 | |
| 108 endfunction | |
| 109 | |
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110 |
| 11428 | 111 %!test |
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112 %! [X,Y] = meshgrid (-20:20,-22:22); |
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113 %! div = divergence (X-Y,Y); |
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114 %! assert (all (div(:) == 2)); |
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115 %! assert (size_equal (X,Y,div)); |