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## dtgexc()

subroutine dtgexc | ( | logical | wantq,
|  | logical | wantz,
|  | integer | n,
|  | double precision, dimension( lda, * ) | a,
|  | integer | lda,
|  | double precision, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | double precision, dimension( ldq, * ) | q,
|  | integer | ldq,
|  | double precision, dimension( ldz, * ) | z,
|  | integer | ldz,
|  | integer | ifst,
|  | integer | ilst,
|  | double precision, dimension( * ) | work,
|  | integer | lwork,
|  | integer | info )

DTGEXC

Download DTGEXC + dependencies [TGZ] [ZIP] [TXT]

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

  [in]

  WANTQ

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

  [in]

  WANTZ

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

  [in]

  N

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

  [in,out]

  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.
      !>

  [in]

  LDA

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

  [in,out]

  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).
      !>

  [in]

  LDB

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

  [in,out]

  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.
      !>

  [in]

  LDQ

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

  [in,out]

  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.
      !>

  [in]

  LDZ

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

  [in,out]

  IFST

      !>          IFST is INTEGER
      !>

  [in,out]

  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.
      !>

  [out]

  WORK

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

  [in]

  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.
      !>

  [out]

  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.

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.
      !>