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## ztgexc()

subroutine ztgexc | ( | logical | wantq,
|  | logical | wantz,
|  | integer | n,
|  | complex*16, dimension( lda, * ) | a,
|  | integer | lda,
|  | complex*16, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | complex*16, dimension( ldq, * ) | q,
|  | integer | ldq,
|  | complex*16, dimension( ldz, * ) | z,
|  | integer | ldz,
|  | integer | ifst,
|  | integer | ilst,
|  | integer | info )

ZTGEXC

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

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**H, 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)**H = Q(out) * A(out) * Z(out)**H
      !>        Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
      !>

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 COMPLEX*16 array, dimension (LDA,N)
      !>          On entry, the upper triangular matrix A in the pair (A, B).
      !>          On exit, the updated matrix A.
      !>

  [in]

  LDA

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

  [in,out]

  B

      !>          B is COMPLEX*16 array, dimension (LDB,N)
      !>          On entry, the upper triangular matrix B in the pair (A, B).
      !>          On exit, the updated matrix B.
      !>

  [in]

  LDB

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

  [in,out]

  Q

      !>          Q is COMPLEX*16 array, dimension (LDQ,N)
      !>          On entry, if WANTQ = .TRUE., the unitary 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 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.
      !>

  [in]

  LDZ

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

  [in]

  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.
      !>

  [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.
  [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.