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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 DTGEXC
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DTGEXC + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtgexc.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtgexc.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtgexc.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
   *                          LDZ, IFST, ILST, WORK, LWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       LOGICAL            WANTQ, WANTZ
   *       INTEGER            IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, LWORK, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
   *      $                   WORK( * ), Z( LDZ, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DTGEXC reorders the generalized real Schur decomposition of a real
   *> matrix pair (A,B) using an orthogonal equivalence transformation
   *>
   *>                (A, B) = Q * (A, B) * Z**T,
   *>
   *> so that the diagonal block of (A, B) with row index IFST is moved
   *> to row ILST.
   *>
   *> (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, dimension (LDA,N)
   *>          On entry, the matrix A in generalized real Schur canonical
   *>          form.
   *>          On exit, the updated matrix A, again in generalized
   *>          real Schur canonical form.
   *> \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, dimension (LDB,N)
   *>          On entry, the matrix B in generalized real Schur canonical
   *>          form (A,B).
   *>          On exit, the updated matrix B, again in generalized
   *>          real Schur canonical form (A,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.
   *>          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 DOUBLE PRECISION array, dimension (LDZ,N)
   *>          On entry, if WANTZ = .TRUE., the orthogonal 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,out] 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.
   *>          On exit, if IFST pointed on entry to the second row of
   *>          a 2-by-2 block, it is changed to point to the first row;
   *>          ILST always points to the first row of the block in its
   *>          final position (which may differ from its input value by
   *>          +1 or -1). 1 <= IFST, ILST <= N.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
   *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is INTEGER
   *>          The dimension of the array WORK.
   *>          LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16.
   *>
   *>          If LWORK = -1, then a workspace query is assumed; the routine
   *>          only calculates the optimal size of the WORK array, returns
   *>          this value as the first entry of the WORK array, and no error
   *>          message related to LWORK is issued by XERBLA.
   *> \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. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleGEcomputational
   *
   *> \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.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,        SUBROUTINE DTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
      $                   LDZ, IFST, ILST, WORK, LWORK, INFO )       $                   LDZ, IFST, ILST, WORK, LWORK, INFO )
 *  *
 *  -- LAPACK routine (version 3.3.1) --  *  -- LAPACK computational 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 234
      $                   WORK( * ), Z( LDZ, * )       $                   WORK( * ), Z( LDZ, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DTGEXC reorders the generalized real Schur decomposition of a real  
 *  matrix pair (A,B) using an orthogonal equivalence transformation  
 *  
 *                 (A, B) = Q * (A, B) * Z**T,  
 *  
 *  so that the diagonal block of (A, B) with row index IFST is moved  
 *  to row ILST.  
 *  
 *  (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, dimension (LDA,N)  
 *          On entry, the matrix A in generalized real Schur canonical  
 *          form.  
 *          On exit, the updated matrix A, again in generalized  
 *          real Schur canonical form.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A. LDA >= max(1,N).  
 *  
 *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,N)  
 *          On entry, the matrix B in generalized real Schur canonical  
 *          form (A,B).  
 *          On exit, the updated matrix B, again in generalized  
 *          real Schur canonical form (A,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.  
 *          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) DOUBLE PRECISION array, dimension (LDZ,N)  
 *          On entry, if WANTZ = .TRUE., the orthogonal 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/output) 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.  
 *          On exit, if IFST pointed on entry to the second row of  
 *          a 2-by-2 block, it is changed to point to the first row;  
 *          ILST always points to the first row of the block in its  
 *          final position (which may differ from its input value by  
 *          +1 or -1). 1 <= IFST, ILST <= N.  
 *  
 *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))  
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.  
 *  
 *  LWORK   (input) INTEGER  
 *          The dimension of the array WORK.  
 *          LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16.  
 *  
 *          If LWORK = -1, then a workspace query is assumed; the routine  
 *          only calculates the optimal size of the WORK array, returns  
 *          this value as the first entry of the WORK array, and no error  
 *          message related to LWORK is issued by XERBLA.  
 *  
 *  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.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.9  
changed lines
  Added in v.1.10

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