dtgexc.f(3)

NAME
dtgexc.f -

SYNOPSIS

  Functions/Subroutines

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

Function/Subroutine Documentation

  subroutine dtgexc (logicalWANTQ, logicalWANTZ, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldq, * )Q, integerLDQ, double precision, dimension( ldz, * )Z, integerLDZ, integerIFST, integerILST, double precision, dimension( * )WORK, integerLWORK, integerINFO)

DTGEXC

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**T,

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

Parameters:
    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, 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

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

    B

              B is 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

              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.
              If WANTQ = .FALSE., Q is not referenced.

    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.
              If WANTZ = .FALSE., Z is not referenced.

    LDZ

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

    IFST

              IFST is INTEGER

    ILST

              ILST is 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

              WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              LWORK >= 1 when N <= 1, otherwise 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

              INFO is 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.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

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

References:

      [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.

Definition at line 220 of file dtgexc.f.

Author

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