update packages

[CreaPhase.git] / octave_packages / m / general / cart2pol.m

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+## Copyright (C) 2000-2012 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  {Function File} {[@var{theta}, @var{r}] =} cart2pol (@var{x}, @var{y})
+## @deftypefnx {Function File} {[@var{theta}, @var{r}, @var{z}] =} cart2pol (@var{x}, @var{y}, @var{z})
+## @deftypefnx {Function File} {[@var{theta}, @var{r}] =} cart2pol (@var{c})
+## @deftypefnx {Function File} {[@var{theta}, @var{r}, @var{z}] =} cart2pol (@var{c})
+## @deftypefnx {Function File} {@var{p} =} cart2pol (@dots{})
+##
+## Transform Cartesian to polar or cylindrical coordinates.
+##
+## @var{theta} describes the angle relative to the positive x-axis.
+## @var{r} is the distance to the z-axis @w{(0, 0, z)}.
+## @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})).
+##
+## 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 (ismatrix (x) && (columns (x) == 2 || columns (x) == 3))
+      if (columns (x) == 3)
+        z = x(:,3);
+      else
+        z = [];
+      endif
+      y = x(:,2);
+      x = x(:,1);
+    else
+      error ("cart2pol: matrix input must have 2 or 3 columns [X, Y (, Z)]");
+    endif
+  elseif (nargin == 2)
+    if (! ((ismatrix (x) && ismatrix (y))
+            && (size_equal (x, y) || isscalar (x) || isscalar (y))))
+      error ("cart2pol: arguments must be matrices of same size, or scalar");
+    endif
+  elseif (nargin == 3)
+    if (! ((ismatrix (x) && ismatrix (y) && ismatrix (z))
+            && (size_equal (x, y) || isscalar (x) || isscalar (y))
+            && (size_equal (x, z) || isscalar (x) || isscalar (z))
+            && (size_equal (y, z) || isscalar (y) || isscalar (z))))
+      error ("cart2pol: arguments must be matrices of same size, or scalar");
+    endif
+  endif
+
+  theta = atan2 (y, x);
+  r = sqrt (x .^ 2 + y .^ 2);
+
+  if (nargout <= 1)
+    theta = [theta, r, z];
+  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];
+%! [t, r] = cart2pol (x, y);
+%! assert (t, [0, pi/4, pi/4], sqrt(eps));
+%! assert (r, 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 (z, z2);
+
+%!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 (z, z2);
+
+%!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 (z, z2);
+
+%!test
+%! x = 0;
+%! y = 0;
+%! z = [0, 1, 2];
+%! [t, r, z2] = cart2pol (x, y, z);
+%! assert (t, 0);
+%! assert (r, 0);
+%! assert (z, z2);
+
+%!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));
+