dtgexc(3S)

NAME
     DTGEXC - reorder the generalized real Schur decomposition of a real
     matrix pair (A,B) using an orthogonal equivalence transformation  (A, B)
     = Q * (A, B) * Z',

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

         LOGICAL        WANTQ, WANTZ

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

         DOUBLE         PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ), WORK(
                        * ), 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
     DTGEXC reorders the generalized real Schur decomposition of a real matrix
     pair (A,B) using an orthogonal 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 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)' = 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) DOUBLE PRECISION array, dimension (LDA,N)
             On entry, the matrix A in generalized real Schur canonical form.
             On exit, the updated matrix A, again in generalized real Schur
             canonical form.

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

     B       (input/output) DOUBLE PRECISION array, dimension (LDB,N)
             On entry, the matrix B in generalized real Schur canonical form
             (A,B).  On exit, the updated matrix B, again in generalized real
             Schur canonical form (A,B).

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

     Q       (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
             On entry, if WANTQ = .TRUE., the orthogonal 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) DOUBLE PRECISION array, dimension (LDZ,N)
             On entry, if WANTZ = .TRUE., the orthogonal 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.  On exit, if IFST pointed on entry to the second row of a
             2-by-2 block, it is changed to point to the first row; ILST
             always points to the first row of the block in its final position
             (which may differ from its input value by +1 or -1). 1 <= IFST,
             ILST <= N.

     WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
             On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
     LWORK   (input) INTEGER
             The dimension of the array WORK. LWORK >= 4*N + 16.

             If LWORK = -1, then a workspace query is assumed; the routine
             only calculates the optimal size of the WORK array, returns this
             value as the first entry of the WORK array, and no error message
             related to LWORK is issued by XERBLA.

     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.


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

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