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version 1.4, 2010/08/06 15:32:36 version 1.9, 2011/11/21 22:19:42
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   *> \brief \b DTREXC
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DTREXC + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrexc.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrexc.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrexc.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK,
   *                          INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          COMPQ
   *       INTEGER            IFST, ILST, INFO, LDQ, LDT, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   Q( LDQ, * ), T( LDT, * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DTREXC reorders the real Schur factorization of a real matrix
   *> A = Q*T*Q**T, so that the diagonal block of T with row index IFST is
   *> moved to row ILST.
   *>
   *> The real Schur form T is reordered by an orthogonal similarity
   *> transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors
   *> is updated by postmultiplying it with Z.
   *>
   *> T must be in Schur canonical form (as returned by DHSEQR), that is,
   *> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
   *> 2-by-2 diagonal block has its diagonal elements equal and its
   *> off-diagonal elements of opposite sign.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] COMPQ
   *> \verbatim
   *>          COMPQ is CHARACTER*1
   *>          = 'V':  update the matrix Q of Schur vectors;
   *>          = 'N':  do not update Q.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix T. N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] T
   *> \verbatim
   *>          T is DOUBLE PRECISION array, dimension (LDT,N)
   *>          On entry, the upper quasi-triangular matrix T, in Schur
   *>          Schur canonical form.
   *>          On exit, the reordered upper quasi-triangular matrix, again
   *>          in Schur canonical form.
   *> \endverbatim
   *>
   *> \param[in] LDT
   *> \verbatim
   *>          LDT is INTEGER
   *>          The leading dimension of the array T. LDT >= max(1,N).
   *> \endverbatim
   *>
   *> \param[in,out] Q
   *> \verbatim
   *>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
   *>          On entry, if COMPQ = 'V', the matrix Q of Schur vectors.
   *>          On exit, if COMPQ = 'V', Q has been postmultiplied by the
   *>          orthogonal transformation matrix Z which reorders T.
   *>          If COMPQ = 'N', Q is not referenced.
   *> \endverbatim
   *>
   *> \param[in] LDQ
   *> \verbatim
   *>          LDQ is INTEGER
   *>          The leading dimension of the array Q.  LDQ >= max(1,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 T.
   *>          The block with row index IFST is moved to row ILST, by a
   *>          sequence of transpositions 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 <= N; 1 <= ILST <= N.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (N)
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   *>          = 1:  two adjacent blocks were too close to swap (the problem
   *>                is very ill-conditioned); T 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 doubleOTHERcomputational
   *
   *  =====================================================================
       SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK,        SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK,
      $                   INFO )       $                   INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- 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..--
 *     November 2006  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          COMPQ        CHARACTER          COMPQ
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       DOUBLE PRECISION   Q( LDQ, * ), T( LDT, * ), WORK( * )        DOUBLE PRECISION   Q( LDQ, * ), T( LDT, * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DTREXC reorders the real Schur factorization of a real matrix  
 *  A = Q*T*Q**T, so that the diagonal block of T with row index IFST is  
 *  moved to row ILST.  
 *  
 *  The real Schur form T is reordered by an orthogonal similarity  
 *  transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors  
 *  is updated by postmultiplying it with Z.  
 *  
 *  T must be in Schur canonical form (as returned by DHSEQR), that is,  
 *  block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each  
 *  2-by-2 diagonal block has its diagonal elements equal and its  
 *  off-diagonal elements of opposite sign.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  COMPQ   (input) CHARACTER*1  
 *          = 'V':  update the matrix Q of Schur vectors;  
 *          = 'N':  do not update Q.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix T. N >= 0.  
 *  
 *  T       (input/output) DOUBLE PRECISION array, dimension (LDT,N)  
 *          On entry, the upper quasi-triangular matrix T, in Schur  
 *          Schur canonical form.  
 *          On exit, the reordered upper quasi-triangular matrix, again  
 *          in Schur canonical form.  
 *  
 *  LDT     (input) INTEGER  
 *          The leading dimension of the array T. LDT >= max(1,N).  
 *  
 *  Q       (input/output) DOUBLE PRECISION array, dimension (LDQ,N)  
 *          On entry, if COMPQ = 'V', the matrix Q of Schur vectors.  
 *          On exit, if COMPQ = 'V', Q has been postmultiplied by the  
 *          orthogonal transformation matrix Z which reorders T.  
 *          If COMPQ = 'N', Q is not referenced.  
 *  
 *  LDQ     (input) INTEGER  
 *          The leading dimension of the array Q.  LDQ >= max(1,N).  
 *  
 *  IFST    (input/output) INTEGER  
 *  ILST    (input/output) INTEGER  
 *          Specify the reordering of the diagonal blocks of T.  
 *          The block with row index IFST is moved to row ILST, by a  
 *          sequence of transpositions 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 <= N; 1 <= ILST <= N.  
 *  
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (N)  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *          = 1:  two adjacent blocks were too close to swap (the problem  
 *                is very ill-conditioned); T may have been partially  
 *                reordered, and ILST points to the first row of the  
 *                current position of the block being moved.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.4  
changed lines
  Added in v.1.9

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