ztgexc(3S)

NAME
     ZTGEXC - reorder the generalized Schur decomposition of a complex matrix
     pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A,
     B) * Z', so that the diagonal block of (A, B) with row index IFST is
     moved to row ILST

SYNOPSIS
     SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST,
                        ILST, INFO )

         LOGICAL        WANTQ, WANTZ

         INTEGER        IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N

         COMPLEX*16     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
     ZTGEXC reorders the generalized Schur decomposition of a complex matrix
     pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A,
     B) * Z', so that the diagonal block of (A, B) with row index IFST is
     moved to row ILST. (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*16 array, dimension (LDA,N)
             On entry, the upper triangular 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*16 array, dimension (LDB,N)
             On entry, the upper triangular 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*16 array, dimension (LDZ,N)
             On entry, if WANTQ = .TRUE., the unitary matrix Q.  On exit, the
             updated matrix Q.  If WANTQ = .FALSE., Q is not referenced.

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

     Z       (input/output) COMPLEX*16 array, dimension (LDZ,N)
             On entry, if WANTZ = .TRUE., the unitary matrix Z.  On exit, the
             updated matrix Z.  If WANTZ = .FALSE., Z is not referenced.

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

     IFST    (input/output) INTEGER
             ILST    (input/output) INTEGER Specify the reordering of the
             diagonal blocks of (A, B).  The block with row index IFST is
             moved to row ILST, by a sequence of swapping between adjacent
             blocks.

     INFO    (output) INTEGER
             =0:  Successful exit.
             <0:  if INFO = -i, the i-th argument had an illegal value.
             =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.

     [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.

     [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
         for Solving the Generalized Sylvester Equation and Estimating the
         Separation between Regular Matrix Pairs, Report UMINF - 93.23,
         Department of Computing Science, Umea University, S-901 87 Umea,
         Sweden, December 1993, Revised April 1994, Also as LAPACK working
         Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
         1996.


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

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