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version 1.8, 2011/07/22 07:38:21 version 1.19, 2023/08/07 08:39:40
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   *> \brief \b ZTGEXC
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZTGEXC + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgexc.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztgexc.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgexc.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZTGEXC( 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*16         A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
   *      $                   Z( LDZ, * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> 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
   *> \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*16 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*16 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*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.
   *> \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*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.
   *> \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 complex16GEcomputational
   *
   *> \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 ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,        SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
      $                   LDZ, IFST, ILST, INFO )       $                   LDZ, IFST, ILST, INFO )
 *  *
 *  -- LAPACK routine (version 3.3.1) --  *  -- LAPACK computational routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *  -- April 2011                                                      --  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       LOGICAL            WANTQ, WANTZ        LOGICAL            WANTQ, WANTZ
Line 15 Line 211
      $                   Z( LDZ, * )       $                   Z( LDZ, * )
 *     ..  *     ..
 *  *
 *  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  
 *  
 *  Arguments  
 *  =========  
 *  
 *  WANTQ   (input) LOGICAL  
 *          .TRUE. : update the left transformation matrix Q;  
 *          .FALSE.: do not update Q.  
 *  
 *  WANTZ   (input) LOGICAL  
 *          .TRUE. : update the right transformation matrix Z;  
 *          .FALSE.: do not update Z.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrices A and B. N >= 0.  
 *  
 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)  
 *          On entry, the upper triangular matrix A in the pair (A, B).  
 *          On exit, the updated matrix A.  
 *  
 *  LDA     (input)  INTEGER  
 *          The leading dimension of the array A. LDA >= max(1,N).  
 *  
 *  B       (input/output) COMPLEX*16 array, dimension (LDB,N)  
 *          On entry, the upper triangular matrix B in the pair (A, B).  
 *          On exit, the updated matrix B.  
 *  
 *  LDB     (input)  INTEGER  
 *          The leading dimension of the array B. LDB >= max(1,N).  
 *  
 *  Q       (input/output) COMPLEX*16 array, dimension (LDZ,N)  
 *          On entry, if WANTQ = .TRUE., the unitary 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) 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.  
 *  
 *  LDZ     (input) INTEGER  
 *          The leading dimension of the array Z. LDZ >= 1;  
 *          If WANTZ = .TRUE., LDZ >= N.  
 *  
 *  IFST    (input) 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.  
 *  
 *  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.  
 *  
 *  [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.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
Removed from v.1.8  
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  Added in v.1.19

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