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view scripts/plot/draw/stream2.m @ 27919:1891570abac8
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2020.
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 06 Jan 2020 22:29:51 -0500 |
parents | b442ec6dda5c |
children | bd51beb6205e |
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## Copyright (C) 2019-2020 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this distribution ## or <https://octave.org/COPYRIGHT.html/>. ## ## ## 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{xy} =} stream2 (@var{x}, @var{y}, @var{u}, @var{v}, @var{sx}, @var{sy}) ## @deftypefnx {} {@var{xy} =} stream2 (@var{u}, @var{v}, @var{sx}, @var{sy}) ## @deftypefnx {} {@var{xy} =} stream2 (@dots{}, @var{options}) ## Compute 2-D streamline data. ## ## Calculates streamlines of a vector field given by @code{[@var{u}, @var{v}]}. ## The vector field is defined over a rectangular grid given by ## @code{[@var{x}, @var{y}]}. The streamlines start at the seed points ## @code{[@var{sx}, @var{sy}]}. The returned value @var{xy} contains a cell ## array of vertex arrays. If the starting point is outside the vector field, ## @code{[]} is returned. ## ## The input parameter @var{options} is a 2-D vector of the form ## @code{[@var{stepsize}, @var{max_vertices}]}. The first parameter ## specifies the step size used for trajectory integration (default 0.1). A ## negative value is allowed which will reverse the direction of integration. ## The second parameter specifies the maximum number of segments used to ## create a streamline (default 10,000). ## ## The return value @var{xy} is a @nospell{nverts x 2} matrix containing the ## coordinates of the field line segments. ## ## Example: ## ## @example ## @group ## [x, y] = meshgrid (0:3); ## u = 2 * x; ## v = y; ## xy = stream2 (x, y, u, v, 1.0, 0.5); ## @end group ## @end example ## ## @seealso{streamline, stream3} ## @end deftypefn ## References: ## ## @article{ ## title = {Particle Tracing Algorithms for 3D Curvilinear Grids}, ## year = {2000}, ## author = {Nielson, Gregory and Uller, H. and Sadarjoen, I. and Walsum, Theo and Hin, Andrea and Post, Frits} ## } ## ## @article{ ## title = {Sources of error in the graphical analysis of CFD results}, ## publisher = {Journal of Scientific Computing}, ## year = {1988}, ## volume = {3}, ## number = {2}, ## pages = {149--164}, ## author = {Buning, Pieter G.}, ## } function xy = stream2 (varargin) options = []; switch (numel (varargin)) case 0 print_usage (); case {4,5} if (numel (varargin) == 4) [u, v, spx, spy] = varargin{:}; else [u, v, spx, spy, options] = varargin{:}; endif [m, n] = size (u); [x, y] = meshgrid (1:n, 1:m); case 6 [x, y, u, v, spx, spy] = varargin{:}; case 7 [x, y, u, v, spx, spy, options] = varargin{:}; otherwise error ("stream2: invalid number of inputs"); endswitch stepsize = 0.1; max_vertices = 10_000; if (! isempty (options)) switch (numel (options)) case 1 stepsize = options(1); case 2 stepsize = options(1); max_vertices = options(2); otherwise error ("stream2: invalid number of OPTIONS elements"); endswitch if (! isreal (stepsize) || stepsize == 0) error ("stream2: STEPSIZE must be a real scalar != 0"); endif if (! isreal (max_vertices) || max_vertices < 1) error ("stream2: MAX_VERTICES must be an integer > 0"); endif max_vertices = fix (max_vertices); endif if (! (size_equal (u, v, x, y) && size_equal (spx, spy))) error ("stream2: matrix dimensions must match"); endif if (iscomplex (u) || iscomplex (v) || iscomplex (x) || iscomplex (y) || iscomplex (spx) || iscomplex (spy)) error ("stream2: all inputs must be real-valued"); endif gx = x(1,:); gy = y(:,1).'; ## Jacobian Matrix dx = diff (gx); dy = diff (gy); ## "<" used to check if the mesh is ascending if (any (dx <= 0) || any (dy <= 0) || any (isnan (dx)) || any (isnan (dy))) error ("stream2: non-monotonically increasing or NaN values found in mesh"); endif tx = 1 ./ dx; ty = 1 ./ dy; ## "Don't cares" used for handling points located on the border tx(end + 1) = 0; ty(end + 1) = 0; dx(end + 1) = 0; dy(end + 1) = 0; px = spx(:); py = spy(:); for nseed = 1 : numel (px) xp = px(nseed); yp = py(nseed); idx = find (diff (gx <= xp), 1); if (gx(end) == xp) idx = numel (gx); endif idy = find (diff (gy <= yp), 1); if (gy(end) == yp) idy = numel (gy); endif if (isempty (idx) || isempty (idy)) xy{nseed} = []; else ## Transform seed from P coordinates to C coordinates zeta = (idx - 1) + (xp - gx(idx)) * tx(idx); xi = (idy - 1) + (yp - gy(idy)) * ty(idy); C = __streameuler2d__ (u, v, tx, ty, zeta, xi, stepsize, max_vertices); ## Transform from C coordinates to P coordinates idu = floor (C(:,1)); idv = floor (C(:,2)); xy{nseed} = [gx(idu + 1).' + (C(:,1) - idu).*(dx(idu + 1).'), ... gy(idv + 1).' + (C(:,2) - idv).*(dy(idv + 1).')]; endif endfor endfunction %!demo %! clf; %! [x, y] = meshgrid (-5:5, -4:4); %! u = x - 2 * y; %! v = 2 * x - 3 * y; %! sx = [3, 0, -1, -2, -3, 0, 1, 2]; %! sy = [3, 3, 3, 3, -3, -3, -3, -3]; %! h = streamline (x, y, u, v, sx, sy, 0.05); %! set (h, "color", "r"); %! hold on; %! quiver (x, y, u, v); %! scatter (sx(:), sy(:), 20, "filled", "o", "markerfacecolor", "r"); %! grid on; %! title ("Asymptotically Stable Equilibrium"); %! axis equal; %!test %! xy = stream2 ([1,1,1;2,2,2;3,3,3], [1,1,1;2,2,2;3,3,3], 1, 1, [0.01,5]); %! assert (numel (xy{:}), 10); ## Test input validation %!error stream2 () %!error <invalid number of inputs> stream2 (1) %!error <invalid number of inputs> stream2 (1,2) %!error <invalid number of inputs> stream2 (1,2,3) %!error <invalid number of OPTIONS> stream2 (1,2,3,4, [1,2,3]) %!error <STEPSIZE must be a real scalar != 0> stream2 (1,2,3,4, [1i]) %!error <STEPSIZE must be a real scalar != 0> stream2 (1,2,3,4, [0]) %!error <MAX_VERTICES must be an integer> stream2 (1,2,3,4, [1, 1i]) %!error <MAX_VERTICES must be an integer> stream2 (1,2,3,4, [1, 0]) %!error <matrix dimensions must match> stream2 ([1 1],2,3,4) %!error <matrix dimensions must match> stream2 (1,[2 2],3,4) %!error <matrix dimensions must match> stream2 (1,2,[3 3],4) %!error <matrix dimensions must match> stream2 (1,2,3,[4 4]) %!error <all inputs must be real-valued> stream2 (1i,2,3,4) %!error <all inputs must be real-valued> stream2 (1,2i,3,4) %!error <all inputs must be real-valued> stream2 (1,2,3i,4) %!error <all inputs must be real-valued> stream2 (1,2,3,4i) %!error <non-monotonically increasing or NaN values found in mesh> %! stream2 ([2 1], [1 2], [1 1], [2 2], [3 3], [4 4]); %!error <non-monotonically increasing or NaN values found in mesh> %! stream2 ([1 NaN], [1 2], [1 1], [2 2], [3 3], [4 4]); ## FIXME: vectors representing x, y mesh are not accepted. %#!error <non-monotonically increasing or NaN values found in mesh> %! stream2 ([1 2], [2 1], [1 1], [2 2], [3 3], [4 4]); %#!error <non-monotonically increasing or NaN values found in mesh> %! stream2 ([1 2], [1 NaN], [1 1], [2 2], [3 3], [4 4]);