Purpose
  To compute a unitary matrix Q and a unitary symplectic matrix U
  for a complex regular 2-by-2 skew-Hamiltonian/Hamiltonian pencil
  aS - bH with S = J Z' J' Z, where
         (  Z11  Z12  )         (  H11  H12  )
     Z = (            ) and H = (            ),
         (   0   Z22  )         (   0  -H11' )
  such that U' Z Q, (J Q J' )' H Q are both upper triangular, but the  
  eigenvalues of (J Q J')' ( aS - bH ) Q are in reversed order.
  The matrices Q and U are represented by
         (  CO1  SI1  )         (  CO2  SI2  )
     Q = (            ) and U = (            ), respectively.
         ( -SI1' CO1  )         ( -SI2' CO2  )
  The notation M' denotes the conjugate transpose of the matrix M.
Specification
      SUBROUTINE MB03GZ( Z11, Z12, Z22, H11, H12, CO1, SI1, CO2, SI2 )
C     .. Scalar Arguments ..
      DOUBLE PRECISION   CO1, CO2
      COMPLEX*16         H11, H12, SI1, SI2, Z11, Z12, Z22
Arguments
Input/Output Parameters
  Z11     (input) COMPLEX*16
          Upper left element of the non-trivial factor Z in the
          factorization of S.
  Z12     (input) COMPLEX*16
          Upper right element of the non-trivial factor Z in the
          factorization of S.
  Z22     (input) COMPLEX*16
          Lower right element of the non-trivial factor Z in the
          factorization of S.
  H11     (input) COMPLEX*16
          Upper left element of the Hamiltonian matrix H.
  H12     (input) COMPLEX*16
          Upper right element of the Hamiltonian matrix H.
  CO1     (output) DOUBLE PRECISION
          Upper left element of Q.
  SI1     (output) COMPLEX*16
          Upper right element of Q.
  CO2     (output) DOUBLE PRECISION
          Upper left element of U.
  SI2     (output) COMPLEX*16
          Upper right element of U.
Method
The algorithm uses unitary and unitary symplectic transformations as described on page 37 in [1].References
  [1] Benner, P., Byers, R., Mehrmann, V. and Xu, H.
      Numerical Computation of Deflating Subspaces of Embedded
      Hamiltonian Pencils.
      Tech. Rep. SFB393/99-15, Technical University Chemnitz,
      Germany, June 1999.
Numerical Aspects
The algorithm is numerically backward stable.Further Comments
NoneExample
Program Text
NoneProgram Data
NoneProgram Results
None