% -*- texinfo -*-
% @deftypefn {Function File} {[@var{aa}, @var{bb}, @var{q}, @var{z}] =} qzhess (@var{a}, @var{b})
% Compute the Hessenberg-triangular decomposition of the matrix pencil
% @code{(@var{a}, @var{b})}, returning
% @code{@var{aa} = @var{q} * @var{a} * @var{z}},
% @code{@var{bb} = @var{q} * @var{b} * @var{z}}, with @var{q} and @var{z}
% orthogonal. For example,
%
% @example
% @group
% [aa, bb, q, z] = qzhess ([1, 2; 3, 4], [5, 6; 7, 8])
% @result{} aa = [ -3.02244, -4.41741; 0.92998, 0.69749 ]
% @result{} bb = [ -8.60233, -9.99730; 0.00000, -0.23250 ]
% @result{} q = [ -0.58124, -0.81373; -0.81373, 0.58124 ]
% @result{} z = [ 1, 0; 0, 1 ]
% @end group
% @end example
%
% The Hessenberg-triangular decomposition is the first step in
% Moler and Stewart's QZ decomposition algorithm.
%
% Algorithm taken from Golub and Van Loan, @cite{Matrix Computations, 2nd
% edition}.
% @end deftypefn