 symplectic scaling on the Hamiltonian matrix

           ( A    G  )
       H = (       T ),                                          (1)
           ( Q   -A  )

  i.e., perform either the symplectic scaling transformation

                                -1
              ( A'   G'  )   ( D   0 ) ( A   G  ) ( D  0   )
       H' &lt;-- (        T ) = (       ) (      T ) (     -1 ),    (2)
              ( Q'  -A'  )   ( 0   D ) ( Q  -A  ) ( 0  D   )

  where D is a diagonal scaling matrix, or the symplectic