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version 1.9, 2011/07/22 07:38:12 version 1.10, 2011/11/21 20:43:06
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   *> \brief \b DTGEX2
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DTGEX2 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtgex2.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtgex2.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtgex2.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
   *                          LDZ, J1, N1, N2, WORK, LWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       LOGICAL            WANTQ, WANTZ
   *       INTEGER            INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
   *      $                   WORK( * ), Z( LDZ, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
   *> of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
   *> (A, B) by an orthogonal equivalence transformation.
   *>
   *> (A, B) must be in generalized real Schur canonical form (as returned
   *> by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2
   *> diagonal blocks. B is upper triangular.
   *>
   *> Optionally, the matrices Q and Z of generalized Schur vectors are
   *> updated.
   *>
   *>        Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
   *>        Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
   *>
   *> \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 DOUBLE PRECISION array, 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 DOUBLE PRECISION array, 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 DOUBLE PRECISION array, dimension (LDQ,N)
   *>          On entry, if WANTQ = .TRUE., the orthogonal 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 DOUBLE PRECISION array, dimension (LDZ,N)
   *>          On entry, if WANTZ =.TRUE., the orthogonal 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). 1 <= J1 <= N.
   *> \endverbatim
   *>
   *> \param[in] N1
   *> \verbatim
   *>          N1 is INTEGER
   *>          The order of the first block (A11, B11). N1 = 0, 1 or 2.
   *> \endverbatim
   *>
   *> \param[in] N2
   *> \verbatim
   *>          N2 is INTEGER
   *>          The order of the second block (A22, B22). N2 = 0, 1 or 2.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is INTEGER
   *>          The dimension of the array WORK.
   *>          LWORK >=  MAX( 1, N*(N2+N1), (N2+N1)*(N2+N1)*2 )
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>            =0: Successful exit
   *>            >0: If INFO = 1, the transformed matrix (A, B) would be
   *>                too far from generalized Schur form; the blocks are
   *>                not swapped and (A, B) and (Q, Z) are unchanged.
   *>                The problem of swapping is too ill-conditioned.
   *>            <0: If INFO = -16: LWORK is too small. Appropriate value
   *>                for LWORK is returned in WORK(1).
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleGEauxiliary
   *
   *> \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:
   *  ================
   *>
   *> \verbatim
   *>
   *>  [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.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,        SUBROUTINE DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
      $                   LDZ, J1, N1, N2, WORK, LWORK, INFO )       $                   LDZ, J1, N1, N2, WORK, LWORK, 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 235
      $                   WORK( * ), Z( LDZ, * )       $                   WORK( * ), Z( LDZ, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)  
 *  of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair  
 *  (A, B) by an orthogonal equivalence transformation.  
 *  
 *  (A, B) must be in generalized real Schur canonical form (as returned  
 *  by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2  
 *  diagonal blocks. B is upper triangular.  
 *  
 *  Optionally, the matrices Q and Z of generalized Schur vectors are  
 *  updated.  
 *  
 *         Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T  
 *         Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T  
 *  
 *  
 *  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) DOUBLE PRECISION array, 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) DOUBLE PRECISION array, 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) DOUBLE PRECISION array, dimension (LDQ,N)  
 *          On entry, if WANTQ = .TRUE., the orthogonal 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) DOUBLE PRECISION array, dimension (LDZ,N)  
 *          On entry, if WANTZ =.TRUE., the orthogonal 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). 1 <= J1 <= N.  
 *  
 *  N1      (input) INTEGER  
 *          The order of the first block (A11, B11). N1 = 0, 1 or 2.  
 *  
 *  N2      (input) INTEGER  
 *          The order of the second block (A22, B22). N2 = 0, 1 or 2.  
 *  
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)).  
 *  
 *  LWORK   (input) INTEGER  
 *          The dimension of the array WORK.  
 *          LWORK >=  MAX( 1, N*(N2+N1), (N2+N1)*(N2+N1)*2 )  
 *  
 *  INFO    (output) INTEGER  
 *            =0: Successful exit  
 *            >0: If INFO = 1, the transformed matrix (A, B) would be  
 *                too far from generalized Schur form; the blocks are  
 *                not swapped and (A, B) and (Q, Z) are unchanged.  
 *                The problem of swapping is too ill-conditioned.  
 *            <0: If INFO = -16: LWORK is too small. Appropriate value  
 *                for LWORK is returned in WORK(1).  
 *  
 *  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.  
 *  
 *  =====================================================================  *  =====================================================================
 *  Replaced various illegal calls to DCOPY by calls to DLASET, or by DO  *  Replaced various illegal calls to DCOPY by calls to DLASET, or by DO
 *  loops. Sven Hammarling, 1/5/02.  *  loops. Sven Hammarling, 1/5/02.
Removed from v.1.9  
changed lines
  Added in v.1.10

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