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version 1.9, 2011/07/22 07:38:21 version 1.10, 2011/11/21 20:43:22
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   *> \brief \b ZTGEX2
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZTGEX2 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgex2.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztgex2.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgex2.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
   *                          LDZ, J1, INFO )
   * 
   *       .. Scalar Arguments ..
   *       LOGICAL            WANTQ, WANTZ
   *       INTEGER            INFO, J1, LDA, LDB, LDQ, LDZ, N
   *       ..
   *       .. Array Arguments ..
   *       COMPLEX*16         A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
   *      $                   Z( LDZ, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
   *> in an upper triangular matrix pair (A, B) by an unitary equivalence
   *> transformation.
   *>
   *> (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 arrays, dimensions (LDA,N)
   *>          On entry, the 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 arrays, dimensions (LDB,N)
   *>          On entry, the 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 (LDZ,N)
   *>          If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,
   *>          the updated matrix Q.
   *>          Not referenced if WANTQ = .FALSE..
   *> \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)
   *>          If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit,
   *>          the updated matrix Z.
   *>          Not referenced if WANTZ = .FALSE..
   *> \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] J1
   *> \verbatim
   *>          J1 is INTEGER
   *>          The index to the first block (A11, B11).
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>           =0:  Successful exit.
   *>           =1:  The transformed matrix pair (A, B) would be too far
   *>                from generalized Schur form; the problem is ill-
   *>                conditioned. 
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16GEauxiliary
   *
   *> \par Further Details:
   *  =====================
   *>
   *>  In the current code both weak and strong stability tests are
   *>  performed. The user can omit the strong stability test by changing
   *>  the internal logical parameter WANDS to .FALSE.. See ref. [2] for
   *>  details.
   *
   *> \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.
   *>
   *  =====================================================================
       SUBROUTINE ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,        SUBROUTINE ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
      $                   LDZ, J1, INFO )       $                   LDZ, J1, INFO )
 *  *
 *  -- LAPACK auxiliary routine (version 3.3.1) --  *  -- LAPACK auxiliary routine (version 3.4.0) --
 *  -- 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                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       LOGICAL            WANTQ, WANTZ        LOGICAL            WANTQ, WANTZ
Line 15 Line 204
      $                   Z( LDZ, * )       $                   Z( LDZ, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)  
 *  in an upper triangular matrix pair (A, B) by an unitary equivalence  
 *  transformation.  
 *  
 *  (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 arrays, dimensions (LDA,N)  
 *          On entry, the 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 arrays, dimensions (LDB,N)  
 *          On entry, the 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)  
 *          If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,  
 *          the updated matrix Q.  
 *          Not referenced if WANTQ = .FALSE..  
 *  
 *  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)  
 *          If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit,  
 *          the updated matrix Z.  
 *          Not referenced if WANTZ = .FALSE..  
 *  
 *  LDZ     (input) INTEGER  
 *          The leading dimension of the array Z. LDZ >= 1;  
 *          If WANTZ = .TRUE., LDZ >= N.  
 *  
 *  J1      (input) INTEGER  
 *          The index to the first block (A11, B11).  
 *  
 *  INFO    (output) INTEGER  
 *           =0:  Successful exit.  
 *           =1:  The transformed matrix pair (A, B) would be too far  
 *                from generalized Schur form; the problem is ill-  
 *                conditioned.   
 *  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Based on contributions by  
 *     Bo Kagstrom and Peter Poromaa, Department of Computing Science,  
 *     Umea University, S-901 87 Umea, Sweden.  
 *  
 *  In the current code both weak and strong stability tests are  
 *  performed. The user can omit the strong stability test by changing  
 *  the internal logical parameter WANDS to .FALSE.. See ref. [2] for  
 *  details.  
 *  
 *  [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.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.9  
changed lines
  Added in v.1.10

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