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version 1.11, 2011/11/21 22:19:58 version 1.21, 2023/08/07 08:39:40
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 *> \brief \b ZTGEX2  *> \brief \b ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.
 *  *
 *  =========== DOCUMENTATION ===========  *  =========== DOCUMENTATION ===========
 *  *
 * Online html documentation available at   * Online html documentation available at
 *            http://www.netlib.org/lapack/explore-html/   *            http://www.netlib.org/lapack/explore-html/
 *  *
 *> \htmlonly  *> \htmlonly
 *> Download ZTGEX2 + dependencies   *> Download ZTGEX2 + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgex2.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgex2.f">
 *> [TGZ]</a>   *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztgex2.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztgex2.f">
 *> [ZIP]</a>   *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgex2.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgex2.f">
 *> [TXT]</a>  *> [TXT]</a>
 *> \endhtmlonly   *> \endhtmlonly
 *  *
 *  Definition:  *  Definition:
 *  ===========  *  ===========
 *  *
 *       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 )
 *   *
 *       .. Scalar Arguments ..  *       .. Scalar Arguments ..
 *       LOGICAL            WANTQ, WANTZ  *       LOGICAL            WANTQ, WANTZ
 *       INTEGER            INFO, J1, LDA, LDB, LDQ, LDZ, N  *       INTEGER            INFO, J1, LDA, LDB, LDQ, LDZ, N
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 *       COMPLEX*16         A( LDA, * ), B( LDB, * ), Q( LDQ, * ),  *       COMPLEX*16         A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
 *      $                   Z( LDZ, * )  *      $                   Z( LDZ, * )
 *       ..  *       ..
 *    *
 *  *
 *> \par Purpose:  *> \par Purpose:
 *  =============  *  =============
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 *>  *>
 *> \param[in,out] A  *> \param[in,out] A
 *> \verbatim  *> \verbatim
 *>          A is COMPLEX*16 arrays, dimensions (LDA,N)  *>          A is COMPLEX*16 array, dimensions (LDA,N)
 *>          On entry, the matrix A in the pair (A, B).  *>          On entry, the matrix A in the pair (A, B).
 *>          On exit, the updated matrix A.  *>          On exit, the updated matrix A.
 *> \endverbatim  *> \endverbatim
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 *>  *>
 *> \param[in,out] B  *> \param[in,out] B
 *> \verbatim  *> \verbatim
 *>          B is COMPLEX*16 arrays, dimensions (LDB,N)  *>          B is COMPLEX*16 array, dimensions (LDB,N)
 *>          On entry, the matrix B in the pair (A, B).  *>          On entry, the matrix B in the pair (A, B).
 *>          On exit, the updated matrix B.  *>          On exit, the updated matrix B.
 *> \endverbatim  *> \endverbatim
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 *>  *>
 *> \param[in,out] Q  *> \param[in,out] Q
 *> \verbatim  *> \verbatim
 *>          Q is COMPLEX*16 array, dimension (LDZ,N)  *>          Q is COMPLEX*16 array, dimension (LDQ,N)
 *>          If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,  *>          If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,
 *>          the updated matrix Q.  *>          the updated matrix Q.
 *>          Not referenced if WANTQ = .FALSE..  *>          Not referenced if WANTQ = .FALSE..
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 *>           =0:  Successful exit.  *>           =0:  Successful exit.
 *>           =1:  The transformed matrix pair (A, B) would be too far  *>           =1:  The transformed matrix pair (A, B) would be too far
 *>                from generalized Schur form; the problem is ill-  *>                from generalized Schur form; the problem is ill-
 *>                conditioned.   *>                conditioned.
 *> \endverbatim  *> \endverbatim
 *  *
 *  Authors:  *  Authors:
 *  ========  *  ========
 *  *
 *> \author Univ. of Tennessee   *> \author Univ. of Tennessee
 *> \author Univ. of California Berkeley   *> \author Univ. of California Berkeley
 *> \author Univ. of Colorado Denver   *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.   *> \author NAG Ltd.
 *  
 *> \date November 2011  
 *  *
 *> \ingroup complex16GEauxiliary  *> \ingroup complex16GEauxiliary
 *  *
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       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 3.4.0) --  *  -- LAPACK auxiliary 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..--
 *     November 2011  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       LOGICAL            WANTQ, WANTZ        LOGICAL            WANTQ, WANTZ
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       PARAMETER          ( WANDS = .TRUE. )        PARAMETER          ( WANDS = .TRUE. )
 *     ..  *     ..
 *     .. Local Scalars ..  *     .. Local Scalars ..
       LOGICAL            DTRONG, WEAK        LOGICAL            STRONG, WEAK
       INTEGER            I, M        INTEGER            I, M
       DOUBLE PRECISION   CQ, CZ, EPS, SA, SB, SCALE, SMLNUM, SS, SUM,        DOUBLE PRECISION   CQ, CZ, EPS, SA, SB, SCALE, SMLNUM, SUM,
      $                   THRESH, WS       $                   THRESHA, THRESHB
       COMPLEX*16         CDUM, F, G, SQ, SZ        COMPLEX*16         CDUM, F, G, SQ, SZ
 *     ..  *     ..
 *     .. Local Arrays ..  *     .. Local Arrays ..
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 *  *
       M = LDST        M = LDST
       WEAK = .FALSE.        WEAK = .FALSE.
       DTRONG = .FALSE.        STRONG = .FALSE.
 *  *
 *     Make a local copy of selected block in (A, B)  *     Make a local copy of selected block in (A, B)
 *  *
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       SUM = DBLE( CONE )        SUM = DBLE( CONE )
       CALL ZLACPY( 'Full', M, M, S, LDST, WORK, M )        CALL ZLACPY( 'Full', M, M, S, LDST, WORK, M )
       CALL ZLACPY( 'Full', M, M, T, LDST, WORK( M*M+1 ), M )        CALL ZLACPY( 'Full', M, M, T, LDST, WORK( M*M+1 ), M )
       CALL ZLASSQ( 2*M*M, WORK, 1, SCALE, SUM )        CALL ZLASSQ( M*M, WORK, 1, SCALE, SUM )
       SA = SCALE*SQRT( SUM )        SA = SCALE*SQRT( SUM )
         SCALE = DBLE( CZERO )
         SUM = DBLE( CONE )
         CALL ZLASSQ( M*M, WORK(M*M+1), 1, SCALE, SUM )
         SB = SCALE*SQRT( SUM )
 *  *
 *     THRES has been changed from   *     THRES has been changed from
 *        THRESH = MAX( TEN*EPS*SA, SMLNUM )  *        THRESH = MAX( TEN*EPS*SA, SMLNUM )
 *     to  *     to
 *        THRESH = MAX( TWENTY*EPS*SA, SMLNUM )  *        THRESH = MAX( TWENTY*EPS*SA, SMLNUM )
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 *     "Bug" reported by Ondra Kamenik, confirmed by Julie Langou, fixed by  *     "Bug" reported by Ondra Kamenik, confirmed by Julie Langou, fixed by
 *     Jim Demmel and Guillaume Revy. See forum post 1783.  *     Jim Demmel and Guillaume Revy. See forum post 1783.
 *  *
       THRESH = MAX( TWENTY*EPS*SA, SMLNUM )        THRESHA = MAX( TWENTY*EPS*SA, SMLNUM )
         THRESHB = MAX( TWENTY*EPS*SB, SMLNUM )
 *  *
 *     Compute unitary QL and RQ that swap 1-by-1 and 1-by-1 blocks  *     Compute unitary QL and RQ that swap 1-by-1 and 1-by-1 blocks
 *     using Givens rotations and perform the swap tentatively.  *     using Givens rotations and perform the swap tentatively.
 *  *
       F = S( 2, 2 )*T( 1, 1 ) - T( 2, 2 )*S( 1, 1 )        F = S( 2, 2 )*T( 1, 1 ) - T( 2, 2 )*S( 1, 1 )
       G = S( 2, 2 )*T( 1, 2 ) - T( 2, 2 )*S( 1, 2 )        G = S( 2, 2 )*T( 1, 2 ) - T( 2, 2 )*S( 1, 2 )
       SA = ABS( S( 2, 2 ) )        SA = ABS( S( 2, 2 ) ) * ABS( T( 1, 1 ) )
       SB = ABS( T( 2, 2 ) )        SB = ABS( S( 1, 1 ) ) * ABS( T( 2, 2 ) )
       CALL ZLARTG( G, F, CZ, SZ, CDUM )        CALL ZLARTG( G, F, CZ, SZ, CDUM )
       SZ = -SZ        SZ = -SZ
       CALL ZROT( 2, S( 1, 1 ), 1, S( 1, 2 ), 1, CZ, DCONJG( SZ ) )        CALL ZROT( 2, S( 1, 1 ), 1, S( 1, 2 ), 1, CZ, DCONJG( SZ ) )
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       CALL ZROT( 2, S( 1, 1 ), LDST, S( 2, 1 ), LDST, CQ, SQ )        CALL ZROT( 2, S( 1, 1 ), LDST, S( 2, 1 ), LDST, CQ, SQ )
       CALL ZROT( 2, T( 1, 1 ), LDST, T( 2, 1 ), LDST, CQ, SQ )        CALL ZROT( 2, T( 1, 1 ), LDST, T( 2, 1 ), LDST, CQ, SQ )
 *  *
 *     Weak stability test: |S21| + |T21| <= O(EPS F-norm((S, T)))  *     Weak stability test: |S21| <= O(EPS F-norm((A)))
   *                          and  |T21| <= O(EPS F-norm((B)))
 *  *
       WS = ABS( S( 2, 1 ) ) + ABS( T( 2, 1 ) )        WEAK = ABS( S( 2, 1 ) ).LE.THRESHA .AND. 
       WEAK = WS.LE.THRESH       $ ABS( T( 2, 1 ) ).LE.THRESHB
       IF( .NOT.WEAK )        IF( .NOT.WEAK )
      $   GO TO 20       $   GO TO 20
 *  *
       IF( WANDS ) THEN        IF( WANDS ) THEN
 *  *
 *        Strong stability test:  *        Strong stability test:
 *           F-norm((A-QL**H*S*QR, B-QL**H*T*QR)) <= O(EPS*F-norm((A, B)))  *           F-norm((A-QL**H*S*QR)) <= O(EPS*F-norm((A)))
   *           and
   *           F-norm((B-QL**H*T*QR)) <= O(EPS*F-norm((B)))
 *  *
          CALL ZLACPY( 'Full', M, M, S, LDST, WORK, M )           CALL ZLACPY( 'Full', M, M, S, LDST, WORK, M )
          CALL ZLACPY( 'Full', M, M, T, LDST, WORK( M*M+1 ), M )           CALL ZLACPY( 'Full', M, M, T, LDST, WORK( M*M+1 ), M )
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    10    CONTINUE     10    CONTINUE
          SCALE = DBLE( CZERO )           SCALE = DBLE( CZERO )
          SUM = DBLE( CONE )           SUM = DBLE( CONE )
          CALL ZLASSQ( 2*M*M, WORK, 1, SCALE, SUM )           CALL ZLASSQ( M*M, WORK, 1, SCALE, SUM )
          SS = SCALE*SQRT( SUM )           SA = SCALE*SQRT( SUM )
          DTRONG = SS.LE.THRESH           SCALE = DBLE( CZERO )
          IF( .NOT.DTRONG )           SUM = DBLE( CONE )
            CALL ZLASSQ( M*M, WORK(M*M+1), 1, SCALE, SUM )
            SB = SCALE*SQRT( SUM )
            STRONG = SA.LE.THRESHA .AND. SB.LE.THRESHB
            IF( .NOT.STRONG )
      $      GO TO 20       $      GO TO 20
       END IF        END IF
 *  *
Removed from v.1.11  
changed lines
  Added in v.1.21

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