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[CreaPhase.git] / octave_packages / m / linear-algebra / cross.m

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+## Copyright (C) 1995-2012 Kurt Hornik
+##
+## 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} {} cross (@var{x}, @var{y})
+## @deftypefnx {Function File} {} cross (@var{x}, @var{y}, @var{dim})
+## Compute the vector cross product of two 3-dimensional vectors
+## @var{x} and @var{y}.
+##
+## @example
+## @group
+## cross ([1,1,0], [0,1,1])
+##      @result{} [ 1; -1; 1 ]
+## @end group
+## @end example
+##
+## If @var{x} and @var{y} are matrices, the cross product is applied
+## along the first dimension with 3 elements.  The optional argument
+## @var{dim} forces the cross product to be calculated along
+## the specified dimension.
+## @seealso{dot, curl, divergence}
+## @end deftypefn
+
+## Author: Kurt Hornik <Kurt.Hornik@wu-wien.ac.at>
+## Created: 15 October 1994
+## Adapted-By: jwe
+
+function z = cross (x, y, dim)
+
+  if (nargin != 2 && nargin != 3)
+    print_usage ();
+  endif
+
+  if (ndims (x) < 3 && ndims (y) < 3 && nargin < 3)
+    ## COMPATIBILITY -- opposite behaviour for cross(row,col)
+    ## Swap x and y in the assignments below to get the matlab behaviour.
+    ## Better yet, fix the calling code so that it uses conformant vectors.
+    if (columns (x) == 1 && rows (y) == 1)
+      warning ("cross: taking cross product of column by row");
+      y = y.';
+    elseif (rows (x) == 1 && columns (y) == 1)
+      warning ("cross: taking cross product of row by column");
+      x = x.';
+    endif
+  endif
+
+  if (nargin == 2)
+     dim = find (size (x) == 3, 1);
+     if (isempty (dim))
+       error ("cross: must have at least one dimension with 3 elements");
+     endif
+   else
+     if (size (x, dim) != 3)
+       error ("cross: dimension DIM must have 3 elements");
+     endif
+  endif
+
+  nd = ndims (x);
+  sz = size (x);
+  idx2 = idx3 = idx1 = {':'}(ones (1, nd));
+  idx1(dim) = 1;
+  idx2(dim) = 2;
+  idx3(dim) = 3;
+
+  if (size_equal (x, y))
+    x1 = x(idx1{:});
+    x2 = x(idx2{:});
+    x3 = x(idx3{:});
+    y1 = y(idx1{:});
+    y2 = y(idx2{:});
+    y3 = y(idx3{:});
+    z = cat (dim, (x2.*y3 - x3.*y2), (x3.*y1 - x1.*y3), (x1.*y2 - x2.*y1));
+  else
+    error ("cross: X and Y must have the same dimensions");
+  endif
+
+endfunction
+
+%!test
+%! x = [1 0 0];
+%! y = [0 1 0];
+%! r = [0 0 1];
+%! assert(cross(x, y), r, 2e-8);
+
+%!test
+%! x = [1 2 3];
+%! y = [4 5 6];
+%! r = [(2*6-3*5) (3*4-1*6) (1*5-2*4)];
+%! assert(cross(x, y), r, 2e-8);
+
+%!test
+%! x = [1 0 0; 0 1 0; 0 0 1];
+%! y = [0 1 0; 0 0 1; 1 0 0];
+%! r = [0 0 1; 1 0 0; 0 1 0];
+%! assert(cross(x, y, 2), r, 2e-8);
+%! assert(cross(x, y, 1), -r, 2e-8);
+
+%!error cross(0,0);
+%!error cross();
+