Mercurial > octave
view scripts/general/curl.m @ 30893:e1788b1a315f
maint: Use "fcn" as preferred abbreviation for "function" in m-files.
* accumarray.m, accumdim.m, quadl.m, quadv.m, randi.m, structfun.m,
__is_function__.m, uigetfile.m, uimenu.m, uiputfile.m, doc_cache_create.m,
colorspace_conversion_input_check.m, imageIO.m, argnames.m, vectorize.m,
vectorize.m, normest1.m, inputname.m, nthargout.m, display_info_file.m,
decic.m, ode15i.m, ode15s.m, ode23.m, ode23s.m, ode45.m, odeset.m,
check_default_input.m, integrate_adaptive.m, ode_event_handler.m,
runge_kutta_23.m, runge_kutta_23s.m, runge_kutta_45_dorpri.m,
runge_kutta_interpolate.m, starting_stepsize.m, __all_opts__.m, fminbnd.m,
fminsearch.m, fminunc.m, fsolve.m, fzero.m, sqp.m, fplot.m, plotyy.m,
__bar__.m, __ezplot__.m, flat_entry.html, profexport.m, movfun.m, bicg.m,
bicgstab.m, cgs.m, eigs.m, gmres.m, pcg.m, __alltohandles__.m, __sprand__.m,
qmr.m, tfqmr.m, dump_demos.m:
Replace "func", "fun", "fn" in documentation and variable names with "fcn".
author | Rik <rik@octave.org> |
---|---|
date | Mon, 04 Apr 2022 18:14:56 -0700 |
parents | 796f54d4ddbf |
children | e54a36a82537 |
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######################################################################## ## ## Copyright (C) 2009-2022 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{cx}, @var{cy}, @var{cz}, @var{v}] =} curl (@var{x}, @var{y}, @var{z}, @var{fx}, @var{fy}, @var{fz}) ## @deftypefnx {} {[@var{cz}, @var{v}] =} curl (@var{x}, @var{y}, @var{fx}, @var{fy}) ## @deftypefnx {} {[@dots{}] =} curl (@var{fx}, @var{fy}, @var{fz}) ## @deftypefnx {} {[@dots{}] =} curl (@var{fx}, @var{fy}) ## @deftypefnx {} {@var{v} =} curl (@dots{}) ## Calculate curl of vector field given by the arrays @var{fx}, @var{fy}, and ## @var{fz} or @var{fx}, @var{fy} respectively. ## @tex ## $$ curl F(x,y,z) = \left( {\partial{d} \over \partial{y}} F_z - {\partial{d} \over \partial{z}} F_y, {\partial{d} \over \partial{z}} F_x - {\partial{d} \over \partial{x}} F_z, {\partial{d} \over \partial{x}} F_y - {\partial{d} \over \partial{y}} F_x \right)$$ ## @end tex ## @ifnottex ## ## @example ## @group ## / d d d d d d \ ## curl F(x,y,z) = | -- Fz - -- Fy, -- Fx - -- Fz, -- Fy - -- Fx | ## \ dy dz dz dx dx dy / ## @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. @var{v} calculates the ## scalar component of the angular velocity vector in direction of the z-axis ## for two-dimensional input. For three-dimensional input the scalar ## rotation is calculated at each grid point in direction of the vector field ## at that point. ## @seealso{divergence, gradient, del2, cross} ## @end deftypefn function varargout = curl (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 ("curl: size of X and Y must match"); elseif (ndims (varargin{fidx}) != 2) error ("curl: X and Y must be 2-D matrices"); elseif ((length (dx) != columns (varargin{fidx})) || (length (dy) != rows (varargin{fidx}))) error ("curl: size of dx and dy must match the respective dimension of X and Y"); endif dFx_dy = gradient (varargin{fidx}.', dy, dx).'; dFy_dx = gradient (varargin{fidx + 1}, dx, dy); rot_z = dFy_dx - dFx_dy; av = rot_z / 2; if (nargout == 0 || nargout == 1) varargout{1} = av; else varargout{1} = rot_z; varargout{2} = av; endif elseif (nargin == 6 || nargin == 3) if (! size_equal (varargin{fidx}, varargin{fidx + 1}, varargin{fidx + 2})) error ("curl: size of X, Y, and Z must match"); elseif (ndims (varargin{fidx}) != 3) error ("curl: 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 ("curl: size of dx, dy, and dz must match the respective dimesion of X, Y, and Z"); endif [~, dFx_dy, dFx_dz] = gradient (varargin{fidx}, dx, dy, dz); [dFy_dx, ~, dFy_dz] = gradient (varargin{fidx + 1}, dx, dy, dz); [dFz_dx, dFz_dy] = gradient (varargin{fidx + 2}, dx, dy, dz); rot_x = dFz_dy - dFy_dz; rot_y = dFx_dz - dFz_dx; rot_z = dFy_dx - dFx_dy; l = sqrt(varargin{fidx}.^2 + varargin{fidx + 1}.^2 + varargin{fidx + 2}.^2); av = (rot_x .* varargin{fidx} + rot_y .* varargin{fidx + 1} + rot_z .* varargin{fidx + 2}) ./ (2 * l); if (nargout == 0 || nargout == 1) varargout{1} = av; else varargout{1} = rot_x; varargout{2} = rot_y; varargout{3} = rot_z; varargout{4} = av; endif endif endfunction %!test %! [X,Y] = meshgrid (-20:20,-22:22); %! av = curl (2*(X-Y), Y); %! assert (all (av(:) == 1)); %! [cz,av] = curl (2*(X-Y), Y); %! assert (all (cz(:) == 2)); %! assert (all (av(:) == 1)); %! [cz,av] = curl (X/2, Y/2, 2*(X-Y), Y); %! assert (all (cz(:) == 4)); %! assert (all (av(:) == 2)); %! assert (size_equal (X,Y,cz,av));