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########################################################################
##
## Copyright (C) 2006-2024 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{y1}, @var{y2}, @dots{}, @var{y}n] =} ndgrid (@var{x1}, @var{x2}, @dots{}, @var{x}n)
## @deftypefnx {} {[@var{y1}, @var{y2}, @dots{}, @var{y}n] =} ndgrid (@var{x})
## Given n vectors @var{x1}, @dots{}, @var{x}n, @code{ndgrid} returns n
## arrays of dimension n.
##
## The elements of the i-th output argument contains the elements of the
## vector @var{x}i repeated over all dimensions different from the i-th
## dimension. Calling ndgrid with only one input argument @var{x} is
## equivalent to calling ndgrid with all n input arguments equal to @var{x}:
##
## [@var{y1}, @var{y2}, @dots{}, @var{y}n] = ndgrid (@var{x}, @dots{}, @var{x})
##
## Programming Note: @code{ndgrid} is very similar to the function
## @code{meshgrid} except that the first two dimensions are transposed in
## comparison to @code{meshgrid}. Some core functions expect @code{meshgrid}
## input and others expect @code{ndgrid} input. Check the documentation for
## the function in question to determine the proper input format.
## @seealso{meshgrid}
## @end deftypefn
function varargout = ndgrid (varargin)
if (nargin == 0)
print_usage ();
elseif (nargin == 1)
nd = max (nargout, 1);
## If only one input argument is given, repeat it nd-times
varargin(1:nd) = varargin(1);
elseif (nargin >= nargout)
nd = max (nargin, 1);
else
error ("ndgrid: wrong number of input arguments");
endif
## Determine the size of the output arguments
shape = zeros (1, nd);
for i = 1:nd
if (! isvector (varargin{i}) && ! isempty (varargin{i}))
error ("ndgrid: arguments must be vectors");
endif
shape(i) = length (varargin{i});
endfor
if (nd == 1)
## Special case, single input vector
varargout{1} = varargin{1}(:);
else
for i = 1:nd
## size for reshape
r = ones (1, nd+1);
r(i) = shape(i);
## size for repmat
s = shape;
s(i) = 1;
varargout{i} = repmat (reshape (varargin{i}, r), s);
endfor
endif
endfunction
%!test
%! x = 1:3;
%! assert (isequal (ndgrid (x), x(:)));
%!test
%! x = 1:3;
%! [XX, YY] = ndgrid (x);
%! assert (size_equal (XX, YY));
%! assert (isequal (XX, repmat (x(:), 1, numel (x))));
%! assert (isequal (YY, repmat (x, numel (x), 1)));
%!test
%! x = 1:2;
%! y = 1:3;
%! z = 1:4;
%! [XX, YY, ZZ] = ndgrid (x, y, z);
%! assert (size_equal (XX, YY, ZZ));
%! assert (ndims (XX), 3);
%! assert (size (XX), [2, 3, 4]);
%! assert (XX(1) * YY(1) * ZZ(1), x(1) * y(1) * z(1));
%! assert (XX(end) * YY(end) * ZZ(end), x(end) * y(end) * z(end));
%!test
%! x = 1:2;
%! y = 1:3;
%! [XX1, YY1] = meshgrid (x, y);
%! [XX2, YY2] = ndgrid (x, y);
%! assert (size_equal (XX1, YY1));
%! assert (size_equal (XX2, YY2));
%! assert (ndims (XX1), 2);
%! assert (size (XX1), [3, 2]);
%! assert (size (XX2), [2, 3]);
%! assert (XX2(1) * YY2(1), x(1) * y(1));
%! assert (XX2(end) * YY2(end), x(end) * y(end));
%! assert (XX1, XX2.');
%! assert (YY1, YY2.');
%!assert (ndgrid ([]), zeros (0,1))
%!assert (ndgrid ([], []), zeros(0,0))
## Test input validation
%!error <Invalid call> ndgrid ()
%!error <wrong number of input arguments> [a,b,c] = ndgrid (1:3,1:3)
%!error <arguments must be vectors> ndgrid (ones (2,2))
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