!>
!> DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
!> of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
!> (A, B) by an orthogonal equivalence transformation.
!>
!> (A, B) must be in generalized real Schur canonical form (as returned
!> by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2
!> diagonal blocks. B is upper triangular.
!>
!> Optionally, the matrices Q and Z of generalized Schur vectors are
!> updated.
!>
!>        Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
!>        Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
!>
!> 

WANTQ

!>          WANTQ is LOGICAL
!>          .TRUE. : update the left transformation matrix Q;
!>          .FALSE.: do not update Q.
!> 

WANTZ

!>          WANTZ is LOGICAL
!>          .TRUE. : update the right transformation matrix Z;
!>          .FALSE.: do not update Z.
!> 

N

!>          N is INTEGER
!>          The order of the matrices A and B. N >= 0.
!> 

A

!>          A is DOUBLE PRECISION array, dimensions (LDA,N)
!>          On entry, the matrix A in the pair (A, B).
!>          On exit, the updated matrix A.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A. LDA >= max(1,N).
!> 

B

!>          B is DOUBLE PRECISION array, dimensions (LDB,N)
!>          On entry, the matrix B in the pair (A, B).
!>          On exit, the updated matrix B.
!> 

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B. LDB >= max(1,N).
!> 

Q

!>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
!>          On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
!>          On exit, the updated matrix Q.
!>          Not referenced if WANTQ = .FALSE..
!> 

LDQ

!>          LDQ is INTEGER
!>          The leading dimension of the array Q. LDQ >= 1.
!>          If WANTQ = .TRUE., LDQ >= N.
!> 

Z

!>          Z is DOUBLE PRECISION array, dimension (LDZ,N)
!>          On entry, if WANTZ =.TRUE., the orthogonal matrix Z.
!>          On exit, the updated matrix Z.
!>          Not referenced if WANTZ = .FALSE..
!> 

LDZ

!>          LDZ is INTEGER
!>          The leading dimension of the array Z. LDZ >= 1.
!>          If WANTZ = .TRUE., LDZ >= N.
!> 

J1

!>          J1 is INTEGER
!>          The index to the first block (A11, B11). 1 <= J1 <= N.
!> 

N1

!>          N1 is INTEGER
!>          The order of the first block (A11, B11). N1 = 0, 1 or 2.
!> 

N2

!>          N2 is INTEGER
!>          The order of the second block (A22, B22). N2 = 0, 1 or 2.
!> 

WORK

!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>          LWORK >=  MAX( 1, N*(N2+N1), (N2+N1)*(N2+N1)*2 )
!> 

INFO

!>          INFO is INTEGER
!>            =0: Successful exit
!>            >0: If INFO = 1, the transformed matrix (A, B) would be
!>                too far from generalized Schur form; the blocks are
!>                not swapped and (A, B) and (Q, Z) are unchanged.
!>                The problem of swapping is too ill-conditioned.
!>            <0: If INFO = -16: LWORK is too small. Appropriate value
!>                for LWORK is returned in WORK(1).
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

In the current code both weak and strong stability tests are performed. The user can omit the strong stability test by changing the internal logical parameter WANDS to .FALSE.. See ref. [2] for details.

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

!>
!>  [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
!>      Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
!>      M.S. Moonen et al (eds), Linear Algebra for Large Scale and
!>      Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
!>
!>  [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
!>      Eigenvalues of a Regular Matrix Pair (A, B) and Condition
!>      Estimation: Theory, Algorithms and Software,
!>      Report UMINF - 94.04, Department of Computing Science, Umea
!>      University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working
!>      Note 87. To appear in Numerical Algorithms, 1996.
!>