Mercurial > octave
view scripts/general/cart2pol.m @ 23219:3ac9f9ecfae5 stable
maint: Update copyright dates.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 22 Feb 2017 12:39:29 -0500 |
parents | e9a0469dedd9 |
children | 092078913d54 |
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## Copyright (C) 2000-2017 Kai Habel ## ## 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 ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {} {[@var{theta}, @var{r}] =} cart2pol (@var{x}, @var{y}) ## @deftypefnx {} {[@var{theta}, @var{r}, @var{z}] =} cart2pol (@var{x}, @var{y}, @var{z}) ## @deftypefnx {} {[@var{theta}, @var{r}] =} cart2pol (@var{C}) ## @deftypefnx {} {[@var{theta}, @var{r}, @var{z}] =} cart2pol (@var{C}) ## @deftypefnx {} {@var{P} =} cart2pol (@dots{}) ## ## Transform Cartesian coordinates to polar or cylindrical coordinates. ## ## The inputs @var{x}, @var{y} (, and @var{z}) must be the same shape, or ## scalar. If called with a single matrix argument then each row of @var{C} ## represents the Cartesian coordinate (@var{x}, @var{y} (, @var{z})). ## ## @var{theta} describes the angle relative to the positive x-axis. ## ## @var{r} is the distance to the z-axis @w{(0, 0, z)}. ## ## If only a single return argument is requested then return a matrix @var{P} ## where each row represents one polar/(cylindrical) coordinate ## (@var{theta}, @var{phi} (, @var{z})). ## @seealso{pol2cart, cart2sph, sph2cart} ## @end deftypefn ## Author: Kai Habel <kai.habel@gmx.de> ## Adapted-by: jwe function [theta, r, z] = cart2pol (x, y, z = []) if (nargin < 1 || nargin > 3) print_usage (); endif if (nargin == 1) if (! (isnumeric (x) && ismatrix (x) && (columns (x) == 2 || columns (x) == 3))) error ("cart2pol: matrix input must have 2 or 3 columns [X, Y (, Z)]"); endif if (columns (x) == 3) z = x(:,3); endif y = x(:,2); x = x(:,1); elseif (nargin == 2) if (! isnumeric (x) || ! isnumeric (y)) error ("cart2pol: X, Y must be numeric arrays of the same size, or scalar"); endif [err, x, y] = common_size (x, y); if (err) error ("cart2pol: X, Y must be numeric arrays of the same size, or scalar"); endif elseif (nargin == 3) if (! isnumeric (x) || ! isnumeric (y) || ! isnumeric (z)) error ("cart2pol: X, Y, Z must be numeric arrays of the same size, or scalar"); endif [err, x, y, z] = common_size (x, y, z); if (err) error ("cart2pol: X, Y, Z must be numeric arrays of the same size, or scalar"); endif endif theta = atan2 (y, x); r = sqrt (x .^ 2 + y .^ 2); if (nargout <= 1) if (isempty (z)) theta = [theta(:), r(:)]; else theta = [theta(:), r(:), z(:)]; endif endif endfunction %!test %! x = [0, 1, 2]; %! y = 0; %! [t, r] = cart2pol (x, y); %! assert (t, [0, 0, 0]); %! assert (r, x); %!test %! x = [0, 1, 2]; %! y = [0, 1, 2]; %! P = cart2pol (x, y); %! assert (P(:,1), [0; pi/4; pi/4], sqrt (eps)); %! assert (P(:,2), sqrt (2)*[0; 1; 2], sqrt (eps)); %!test %! x = [0, 1, 2]; %! y = [0, 1, 2]; %! z = [0, 1, 2]; %! [t, r, z2] = cart2pol (x, y, z); %! assert (t, [0, pi/4, pi/4], sqrt (eps)); %! assert (r, sqrt (2)*[0, 1, 2], sqrt (eps)); %! assert (z2, z); %!test %! x = [0, 1, 2]; %! y = 0; %! z = 0; %! [t, r, z2] = cart2pol (x, y, z); %! assert (t, [0, 0, 0], eps); %! assert (r, x, eps); %! assert (z2, [0, 0, 0]); %!test %! x = 0; %! y = [0, 1, 2]; %! z = 0; %! [t, r, z2] = cart2pol (x, y, z); %! assert (t, [0, 1, 1]*pi/2, eps); %! assert (r, y, eps); %! assert (z2, [0, 0, 0]); %!test %! x = 0; %! y = 0; %! z = [0, 1, 2]; %! [t, r, z2] = cart2pol (x, y, z); %! assert (t, [0, 0, 0]); %! assert (r, [0, 0, 0]); %! assert (z2, z); %!test %! C = [0, 0; 1, 1; 2, 2]; %! P = [0, 0; pi/4, sqrt(2); pi/4, 2*sqrt(2)]; %! assert (cart2pol (C), P, sqrt (eps)); %!test %! C = [0, 0, 0; 1, 1, 1; 2, 2, 2]; %! P = [0, 0, 0; pi/4, sqrt(2), 1; pi/4, 2*sqrt(2), 2]; %! assert (cart2pol (C), P, sqrt (eps)); %!test %! x = zeros (1, 1, 1, 2); %! x(1, 1, 1, 2) = sqrt (2); %! y = x; %! [t, r] = cart2pol (x, y); %! T = zeros (1, 1, 1, 2); %! T(1, 1, 1, 2) = pi/4; %! R = zeros (1, 1, 1, 2); %! R(1, 1, 1, 2) = 2; %! assert (t, T, eps); %! assert (r, R, eps); %!test %! [x, y, Z] = meshgrid ([0, 1], [0, 1], [0, 1]); %! [t, r, z] = cart2pol (x, y, Z); %! T(:, :, 1) = [0, 0; pi/2, pi/4]; %! T(:, :, 2) = T(:, :, 1); %! R = sqrt (x.^2 + y.^2); %! assert (t, T, eps); %! assert (r, R, eps); %! assert (z, Z); ## Test input validation %!error cart2pol () %!error cart2pol (1,2,3,4) %!error <matrix input must have 2 or 3 columns> cart2pol ({1,2,3}) %!error <matrix input must have 2 or 3 columns> cart2pol (ones (3,3,2)) %!error <matrix input must have 2 or 3 columns> cart2pol ([1]) %!error <matrix input must have 2 or 3 columns> cart2pol ([1,2,3,4]) %!error <numeric arrays of the same size> cart2pol ({1,2,3}, [1,2,3]) %!error <numeric arrays of the same size> cart2pol ([1,2,3], {1,2,3}) %!error <numeric arrays of the same size> cart2pol (ones (3,3,3), ones (3,2,3)) %!error <numeric arrays of the same size> cart2pol ({1,2,3}, [1,2,3], [1,2,3]) %!error <numeric arrays of the same size> cart2pol ([1,2,3], {1,2,3}, [1,2,3]) %!error <numeric arrays of the same size> cart2pol ([1,2,3], [1,2,3], {1,2,3}) %!error <numeric arrays of the same size> cart2pol (ones (3,3,3), 1, ones (3,2,3)) %!error <numeric arrays of the same size> cart2pol (ones (3,3,3), ones (3,2,3), 1)