Purpose
  To compute an orthogonal matrix Q and an orthogonal symplectic
  matrix U for a real regular 2-by-2 or 4-by-4 skew-Hamiltonian/
  Hamiltonian pencil a J B' J' B - b D with
        ( B11  B12 )      (  D11  D12  )
    B = (          ), D = (            ),
        (  0   B22 )      (   0  -D11' )
  such that J Q' J' D Q and U' B Q keep block triangular form, but
  the eigenvalues are reordered.
Specification
      SUBROUTINE MB03GD( N, B, LDB, D, LDD, MACPAR, Q, LDQ, U, LDU,
     $                   DWORK, LDWORK, INFO )
C     .. Scalar Arguments ..
      INTEGER            INFO, LDB, LDD, LDQ, LDU, LDWORK, N
C     .. Array Arguments ..
      DOUBLE PRECISION   B( LDB, * ), D( LDD, * ), DWORK( * ),
     $                   MACPAR( * ), Q( LDQ, * ), U( LDU, * )
Arguments
Input/Output Parameters
  N       (input) INTEGER
          The order of the pencil a J B' J' B - b D. N = 2 or N = 4.
  B       (input) DOUBLE PRECISION array, dimension (LDB, N)
          The leading N-by-N part of this array must contain the
          non-trivial factor of the decomposition of the
          skew-Hamiltonian input matrix J B' J' B. The (2,1) block
          is not referenced.
  LDB     INTEGER
          The leading dimension of the array B.  LDB >= N.
  D       (input) DOUBLE PRECISION array, dimension (LDD, N)
          The leading N/2-by-N part of this array must contain the
          first block row of the second matrix of a J B' J' B - b D.
          The matrix D has to be Hamiltonian. The strict lower
          triangle of the (1,2) block is not referenced.
  LDD     INTEGER
          The leading dimension of the array D.  LDD >= N/2.
  MACPAR  (input)  DOUBLE PRECISION array, dimension (2)
          Machine parameters:
          MACPAR(1)  (machine precision)*base, DLAMCH( 'P' );
          MACPAR(2)  safe minimum,             DLAMCH( 'S' ).
          This argument is not used for N = 2.
  Q       (output) DOUBLE PRECISION array, dimension (LDQ, N)
          The leading N-by-N part of this array contains the
          orthogonal transformation matrix Q.
  LDQ     INTEGER
          The leading dimension of the array Q.  LDQ >= N.
  U       (output) DOUBLE PRECISION array, dimension (LDU, N)
          The leading N-by-N part of this array contains the
          orthogonal symplectic transformation matrix U.
  LDU     INTEGER
          The leading dimension of the array U.  LDU >= N.
Workspace
  DWORK   DOUBLE PRECISION array, dimension (LDWORK)
          If N = 2 then DWORK is not referenced.
  LDWORK  INTEGER
          The length of the array DWORK.
          If N = 2 then LDWORK >= 0; if N = 4 then LDWORK >= 12.
Error Indicator
  INFO    INTEGER
          = 0: succesful exit;
          = 1: B11 or B22 is a (numerically) singular matrix.
Method
The algorithm uses orthogonal transformations as described on page 22 in [1], but with an improved implementation.References
  [1] Benner, P., Byers, R., Losse, P., Mehrmann, V. and Xu, H.
      Numerical Solution of Real Skew-Hamiltonian/Hamiltonian
      Eigenproblems.
      Tech. Rep., Technical University Chemnitz, Germany,
      Nov. 2007.
Numerical Aspects
The algorithm is numerically backward stable.Further Comments
NoneExample
Program Text
NoneProgram Data
NoneProgram Results
None