ctgexc.f

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*> \brief \b CTGEXC
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE CTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
*                          LDZ, IFST, ILST, INFO )
*
*       .. Scalar Arguments ..
*       LOGICAL            WANTQ, WANTZ
*       INTEGER            IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
*       ..
*       .. Array Arguments ..
*       COMPLEX            A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
*      $                   Z( LDZ, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CTGEXC 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
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] WANTQ
*> \verbatim
*>          WANTQ is LOGICAL
*>          .TRUE. : update the left transformation matrix Q;
*>          .FALSE.: do not update Q.
*> \endverbatim
*>
*> \param[in] WANTZ
*> \verbatim
*>          WANTZ is LOGICAL
*>          .TRUE. : update the right transformation matrix Z;
*>          .FALSE.: do not update Z.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrices A and B. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is COMPLEX array, dimension (LDA,N)
*>          On entry, the upper triangular matrix A in the pair (A, B).
*>          On exit, the updated matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is COMPLEX array, dimension (LDB,N)
*>          On entry, the upper triangular matrix B in the pair (A, B).
*>          On exit, the updated matrix B.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] Q
*> \verbatim
*>          Q is COMPLEX 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.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*>          LDQ is INTEGER
*>          The leading dimension of the array Q. LDQ >= 1;
*>          If WANTQ = .TRUE., LDQ >= N.
*> \endverbatim
*>
*> \param[in,out] Z
*> \verbatim
*>          Z is COMPLEX 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.
*> \endverbatim
*>
*> \param[in] LDZ
*> \verbatim
*>          LDZ is INTEGER
*>          The leading dimension of the array Z. LDZ >= 1;
*>          If WANTZ = .TRUE., LDZ >= N.
*> \endverbatim
*>
*> \param[in] IFST
*> \verbatim
*>          IFST is INTEGER
*> \endverbatim
*>
*> \param[in,out] ILST
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          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.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup tgexc
*
*> \par Contributors:
*  ==================
*>
*>     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*>     Umea University, S-901 87 Umea, Sweden.
*
*> \par 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.
*> \n
*>  [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.
*> \n
*>  [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.
*>
*  =====================================================================
      SUBROUTINE ctgexc( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, IFST, ILST, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      LOGICAL            WANTQ, WANTZ
      INTEGER            IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
*     ..
*     .. Array Arguments ..
      COMPLEX            A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
     $                   z( ldz, * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      INTEGER            HERE
*     ..
*     .. External Subroutines ..
      EXTERNAL           ctgex2, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Decode and test input arguments.
      info = 0
      IF( n.LT.0 ) THEN
         info = -3
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -5
      ELSE IF( ldb.LT.max( 1, n ) ) THEN
         info = -7
      ELSE IF( ldq.LT.1 .OR. wantq .AND. ( ldq.LT.max( 1, n ) ) ) THEN
         info = -9
      ELSE IF( ldz.LT.1 .OR. wantz .AND. ( ldz.LT.max( 1, n ) ) ) THEN
         info = -11
      ELSE IF( ifst.LT.1 .OR. ifst.GT.n ) THEN
         info = -12
      ELSE IF( ilst.LT.1 .OR. ilst.GT.n ) THEN
         info = -13
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'CTGEXC', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.LE.1 )
     $   RETURN
      IF( ifst.EQ.ilst )
     $   RETURN
*
      IF( ifst.LT.ilst ) THEN
*
         here = ifst
*
   10    CONTINUE
*
*        Swap with next one below
*
         CALL ctgex2( wantq, wantz, n, a, lda, b, ldb, q, ldq, z,
     $                ldz,
     $                here, info )
         IF( info.NE.0 ) THEN
            ilst = here
            RETURN
         END IF
         here = here + 1
         IF( here.LT.ilst )
     $      GO TO 10
         here = here - 1
      ELSE
         here = ifst - 1
*
   20    CONTINUE
*
*        Swap with next one above
*
         CALL ctgex2( wantq, wantz, n, a, lda, b, ldb, q, ldq, z,
     $                ldz,
     $                here, info )
         IF( info.NE.0 ) THEN
            ilst = here
            RETURN
         END IF
         here = here - 1
         IF( here.GE.ilst )
     $      GO TO 20
         here = here + 1
      END IF
      ilst = here
      RETURN
*
*     End of CTGEXC
*
      SUBROUTINE ctgexc( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, …
      END