Mercurial > octave-nkf
annotate scripts/general/curl.m @ 12256:7cc26ca98b00 release-3-4-x
curl.m: fix thinko in previous change
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Thu, 27 Jan 2011 00:12:30 -0500 |
| parents | 1f14586af94c |
| children | ad05e1547398 |
| rev | line source |
|---|---|
| 11523 | 1 ## Copyright (C) 2009-2011 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{cx}, @var{cy}, @var{cz}, @var{v}] =} curl (@var{x}, @var{y}, @var{z}, @var{fx}, @var{fy}, @var{fz}) |
| 11428 | 21 ## @deftypefnx {Function File} {[@var{cz}, @var{v}] =} curl (@var{x}, @var{y}, @var{fx}, @var{fy}) |
| 22 ## @deftypefnx {Function File} {[@dots{}] =} curl (@var{fx}, @var{fy}, @var{fz}) | |
| 23 ## @deftypefnx {Function File} {[@dots{}] =} curl (@var{fx}, @var{fy}) | |
| 24 ## @deftypefnx {Function File} {@var{v} =} curl (@dots{}) | |
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25 ## Calculate curl of vector field given by the arrays @var{fx}, @var{fy}, and |
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26 ## @var{fz} or @var{fx}, @var{fy} respectively. |
| 11428 | 27 ## @tex |
| 28 ## $$ curl F(x,y,z) = \left( {\partial{d} \over \partial{y}} F_z - {\partial{d} \over \partial{z}} F_y, {\partial{d} \over \partial{z}} F_x - {\partial{d} \over \partial{x}} F_z, {\partial{d} \over \partial{x}} F_y - {\partial{d} \over \partial{y}} F_x \right)$$ | |
| 29 ## @end tex | |
| 30 ## @ifnottex | |
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31 ## |
| 11428 | 32 ## @example |
| 33 ## @group | |
| 34 ## / d d d d d d \ | |
| 35 ## curl F(x,y,z) = | -- Fz - -- Fy, -- Fx - -- Fz, -- Fy - -- Fx | | |
| 36 ## \ dy dz dz dx dx dy / | |
| 37 ## @end group | |
| 38 ## @end example | |
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39 ## |
| 11428 | 40 ## @end ifnottex |
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41 ## The coordinates of the vector field can be given by the arguments @var{x}, |
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42 ## @var{y}, @var{z} or @var{x}, @var{y} respectively. @var{v} calculates the |
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43 ## scalar component of the angular velocity vector in direction of the z-axis |
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44 ## for two-dimensional input. For three-dimensional input the scalar |
| 11428 | 45 ## rotation is calculated at each grid point in direction of the vector field |
| 46 ## at that point. | |
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47 ## @seealso{divergence, gradient, del2, cross, dot} |
| 11428 | 48 ## @end deftypefn |
| 49 | |
| 50 ## Author: Kai Habel <kai.habel@gmx.de> | |
| 51 | |
| 52 function varargout = curl (varargin) | |
| 53 | |
| 54 fidx = 1; | |
| 55 if (nargin == 2) | |
| 56 sz = size (varargin{fidx}); | |
| 57 dx = (1:sz(2))(:); | |
| 58 dy = (1:sz(1))(:); | |
| 59 elseif (nargin == 3) | |
| 60 sz = size (varargin{fidx}); | |
| 61 dx = (1:sz(2))(:); | |
| 62 dy = (1:sz(1))(:); | |
| 63 dz = (1:sz(3))(:); | |
| 64 elseif (nargin == 4) | |
| 65 fidx = 3; | |
| 66 dx = varargin{1}(1,:); | |
| 67 dy = varargin{2}(:,1); | |
| 68 elseif (nargin == 6) | |
| 69 fidx = 4; | |
| 70 dx = varargin{1}(1,:,1)(:); | |
| 71 dy = varargin{2}(:,1,1)(:); | |
| 72 dz = varargin{3}(1,1,:)(:); | |
| 73 else | |
| 74 print_usage(); | |
| 75 endif | |
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76 |
| 11428 | 77 if ((nargin == 4) || (nargin == 2)) |
| 78 if (!size_equal (varargin{fidx}, varargin{fidx + 1})) | |
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79 error ("curl: size of X and Y must match"); |
| 11428 | 80 elseif (ndims (varargin{fidx}) != 2) |
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parents:
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81 error ("curl: expected two-dimensional matrices X and Y"); |
| 11428 | 82 elseif ((length (dx) != columns (varargin{fidx})) |
| 83 || (length (dy) != rows (varargin{fidx}))) | |
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84 error ("curl: size of dx and dy must match the respective dimension of X and Y"); |
| 11428 | 85 endif |
| 86 | |
| 87 dFx_dy = gradient (varargin{fidx}.', dy, dx).'; | |
| 88 dFy_dx = gradient (varargin{fidx + 1}, dx, dy); | |
| 89 rot_z = dFy_dx - dFx_dy; | |
| 90 av = rot_z / 2; | |
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91 if (nargout == 0 || nargout == 1) |
| 11428 | 92 varargout{1} = av; |
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curl.m: fix thinko in previous change
John W. Eaton <jwe@octave.org>
parents:
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93 else |
| 11428 | 94 varargout{1} = rot_z; |
| 95 varargout{2} = av; | |
| 96 endif | |
| 97 | |
| 98 elseif ((nargin == 6) || (nargin == 3)) | |
| 99 if (!size_equal (varargin{fidx}, varargin{fidx + 1}, varargin{fidx + 2})) | |
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100 error ("curl: size of X, Y, and Z must match"); |
| 11428 | 101 elseif (ndims (varargin{fidx}) != 3) |
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11588
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style fixes for warning and error messages in script files
John W. Eaton <jwe@octave.org>
parents:
11587
diff
changeset
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102 error ("curl: expected two-dimensional matrices X, Y, and Z"); |
| 11428 | 103 elseif ((length (dx) != size (varargin{fidx}, 2)) |
| 104 || (length (dy) != size (varargin{fidx}, 1)) | |
| 105 || (length (dz) != size (varargin{fidx}, 3))) | |
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style fixes for warning and error messages in script files
John W. Eaton <jwe@octave.org>
parents:
11587
diff
changeset
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106 error ("curl: size of dx, dy, and dz must match the respective dimesion of X, Y, and Z"); |
| 11428 | 107 endif |
| 108 | |
| 109 [~, dFx_dy, dFx_dz] = gradient (varargin{fidx}, dx, dy, dz); | |
| 110 [dFy_dx, ~, dFy_dz] = gradient (varargin{fidx + 1}, dx, dy, dz); | |
| 111 [dFz_dx, dFz_dy] = gradient (varargin{fidx + 2}, dx, dy, dz); | |
| 112 rot_x = dFz_dy - dFy_dz; | |
| 113 rot_y = dFx_dz - dFz_dx; | |
| 114 rot_z = dFy_dx - dFx_dy; | |
| 115 l = sqrt(varargin{fidx}.^2 + varargin{fidx + 1}.^2 + varargin{fidx + 2}.^2); | |
| 116 av = (rot_x .* varargin{fidx} + | |
| 117 rot_y .* varargin{fidx + 1} + | |
| 118 rot_z .* varargin{fidx + 2}) ./ (2 * l); | |
| 119 | |
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curl: simplify processing of output values
John W. Eaton <jwe@octave.org>
parents:
11589
diff
changeset
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120 if (nargout == 0 || nargout == 1) |
| 11428 | 121 varargout{1} = av; |
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parents:
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changeset
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122 else |
| 11428 | 123 varargout{1} = rot_x; |
| 124 varargout{2} = rot_y; | |
| 125 varargout{3} = rot_z; | |
| 126 varargout{4} = av; | |
| 127 endif | |
| 128 endif | |
| 129 | |
| 130 endfunction | |
| 131 | |
| 132 %!test | |
| 133 %! [X,Y]=meshgrid(-20:20,-22:22); | |
| 134 %! av = curl(2*(X-Y),Y); | |
| 135 %! assert(all(av(:)==1)); | |
| 136 %! [cz,av] = curl(2*(X-Y),Y); | |
| 137 %! assert(all(cz(:)==2)); | |
| 138 %! assert(all(av(:)==1)); | |
| 139 %! [cz,av] = curl(X/2,Y/2,2*(X-Y),Y); | |
| 140 %! assert(all(cz(:)==4)); | |
| 141 %! assert(all(av(:)==2)); | |
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142 %! assert(size_equal(X,Y,cz,av)); |