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## -*- texinfo -*-
## @deftypefn {} {@var{v} =} vech (@var{x})
## Return the vector obtained by eliminating all superdiagonal elements of
## the square matrix @var{x} and stacking the result one column above the
## other.
##
## This has uses in matrix calculus where the underlying matrix is symmetric
## and it would be pointless to keep values above the main diagonal.
## @seealso{vec}
## @end deftypefn

## See Magnus and Neudecker, Matrix differential calculus with applications in
## statistics and econometrics, 1988.

function v = vech (x)

  if (nargin < 1)
    print_usage ();
  endif

  if (! issquare (x))
    error ("vech: X must be square");
  endif

  n = rows (x);
  slices = cellslices (x(:), (1:n) + n*(0:n-1), n*(1:n));
  v = vertcat (slices{:});

endfunction


%!assert (vech ([1, 2, 3; 4, 5, 6; 7, 8, 9]), [1; 4; 7; 5; 8; 9])

## Test input validation
%!error <Invalid call> vech ()
%!error <X must be square> vech ([1,2,3;4,5,6])
