ctgex2(3S)

NAME
     CTGEX2 - swap adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)

SYNOPSIS
     SUBROUTINE CTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1,
                        INFO )

         LOGICAL        WANTQ, WANTZ

         INTEGER        INFO, J1, LDA, LDB, LDQ, LDZ, N

         COMPLEX        A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     CTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22) in
     an upper triangular matrix pair (A, B) by an unitary equivalence
     transformation.

     (A, B) must be in generalized Schur canonical form, that is, A and B are
     both upper triangular.

     Optionally, the matrices Q and Z of generalized Schur vectors are
     updated.

            Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
            Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'



ARGUMENTS
     WANTQ   (input) LOGICAL

     WANTZ   (input) LOGICAL

     N       (input) INTEGER
             The order of the matrices A and B. N >= 0.

     A       (input/output) COMPLEX arrays, dimensions (LDA,N)
             On entry, the matrix A in the pair (A, B).  On exit, the updated
             matrix A.

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

     B       (input/output) COMPLEX arrays, dimensions (LDB,N)
             On entry, the matrix B in the pair (A, B).  On exit, the updated
             matrix B.

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

     Q       (input/output) COMPLEX array, dimension (LDZ,N)
             If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit, the
             updated matrix Q.  Not referenced if WANTQ = .FALSE..

     LDQ     (input) INTEGER
             The leading dimension of the array Q. LDQ >= 1; If WANTQ =
             .TRUE., LDQ >= N.

     Z       (input/output) COMPLEX array, dimension (LDZ,N)
             If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit, the
             updated matrix Z.  Not referenced if WANTZ = .FALSE..

     LDZ     (input) INTEGER
             The leading dimension of the array Z. LDZ >= 1; If WANTZ =
             .TRUE., LDZ >= N.

     J1      (input) INTEGER
             The index to the first block (A11, B11).

     INFO    (output) INTEGER
             =0:  Successful exit.
             =1:  The transformed matrix pair (A, B) would be too far from
             generalized Schur form; the problem is ill- conditioned. (A, B)
             may have been partially reordered, and ILST points to the first
             row of the current position of the block being moved.

FURTHER DETAILS
     Based on contributions by
        Bo Kagstrom and Peter Poromaa, Department of Computing Science,
        Umea University, S-901 87 Umea, Sweden.

     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.

     [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.


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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