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Exchanging eigenvalues of a complex 2-by-2 skew-Hamiltonian/Hamiltonian pencil in structured Schur form

**[Specification]**
**[Arguments]**
**[Method]**
**[References]**
**[Comments]**
**[Example]**
**Purpose**

To compute a unitary matrix Q for a complex regular 2-by-2
skew-Hamiltonian/Hamiltonian pencil aS - bH with
( S11 S12 ) ( H11 H12 )
S = ( ), H = ( ),
( 0 S11' ) ( 0 -H11' )
such that J Q' J' (aS - bH) Q is upper triangular but the
eigenvalues are in reversed order. The matrix Q is represented by
( CO SI )
Q = ( ).
( -SI' CO )
The notation M' denotes the conjugate transpose of the matrix M.

**Arguments**
**Input/Output Parameters**

S11 (input) COMPLEX*16
Upper left element of the skew-Hamiltonian matrix S.
S12 (input) COMPLEX*16
Upper right element of the skew-Hamiltonian matrix 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.
CO (output) DOUBLE PRECISION
Upper left element of Q.
SI (output) COMPLEX*16
Upper right element of Q.

**Method**
The algorithm uses unitary transformations as described on page 43
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**
None

**Example**
**Program Text**

None

**Program Data**
None

**Program Results**
None

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