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version 1.9, 2011/11/21 20:42:57 version 1.22, 2023/08/07 08:38:56
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 *> \brief \b DLAQR3  *> \brief \b DLAQR3 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).
 *  *
 *  =========== 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 DLAQR3 + dependencies   *> Download DLAQR3 + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqr3.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqr3.f">
 *> [TGZ]</a>   *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqr3.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqr3.f">
 *> [ZIP]</a>   *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqr3.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqr3.f">
 *> [TXT]</a>  *> [TXT]</a>
 *> \endhtmlonly   *> \endhtmlonly
 *  *
 *  Definition:  *  Definition:
 *  ===========  *  ===========
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 *       SUBROUTINE DLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,  *       SUBROUTINE DLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
 *                          IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T,  *                          IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T,
 *                          LDT, NV, WV, LDWV, WORK, LWORK )  *                          LDT, NV, WV, LDWV, WORK, LWORK )
 *   *
 *       .. Scalar Arguments ..  *       .. Scalar Arguments ..
 *       INTEGER            IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV,  *       INTEGER            IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV,
 *      $                   LDZ, LWORK, N, ND, NH, NS, NV, NW  *      $                   LDZ, LWORK, N, ND, NH, NS, NV, NW
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 *      $                   V( LDV, * ), WORK( * ), WV( LDWV, * ),  *      $                   V( LDV, * ), WORK( * ), WV( LDWV, * ),
 *      $                   Z( LDZ, * )  *      $                   Z( LDZ, * )
 *       ..  *       ..
 *    *
 *  *
 *> \par Purpose:  *> \par Purpose:
 *  =============  *  =============
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 *> \param[in] NW  *> \param[in] NW
 *> \verbatim  *> \verbatim
 *>          NW is INTEGER  *>          NW is INTEGER
 *>          Deflation window size.  1 .LE. NW .LE. (KBOT-KTOP+1).  *>          Deflation window size.  1 <= NW <= (KBOT-KTOP+1).
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in,out] H  *> \param[in,out] H
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 *>  *>
 *> \param[in] LDH  *> \param[in] LDH
 *> \verbatim  *> \verbatim
 *>          LDH is integer  *>          LDH is INTEGER
 *>          Leading dimension of H just as declared in the calling  *>          Leading dimension of H just as declared in the calling
 *>          subroutine.  N .LE. LDH  *>          subroutine.  N <= LDH
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] ILOZ  *> \param[in] ILOZ
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 *> \verbatim  *> \verbatim
 *>          IHIZ is INTEGER  *>          IHIZ is INTEGER
 *>          Specify the rows of Z to which transformations must be  *>          Specify the rows of Z to which transformations must be
 *>          applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N.  *>          applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in,out] Z  *> \param[in,out] Z
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 *>          Z is DOUBLE PRECISION array, dimension (LDZ,N)  *>          Z is DOUBLE PRECISION array, dimension (LDZ,N)
 *>          IF WANTZ is .TRUE., then on output, the orthogonal  *>          IF WANTZ is .TRUE., then on output, the orthogonal
 *>          similarity transformation mentioned above has been  *>          similarity transformation mentioned above has been
 *>          accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right.  *>          accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right.
 *>          If WANTZ is .FALSE., then Z is unreferenced.  *>          If WANTZ is .FALSE., then Z is unreferenced.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] LDZ  *> \param[in] LDZ
 *> \verbatim  *> \verbatim
 *>          LDZ is integer  *>          LDZ is INTEGER
 *>          The leading dimension of Z just as declared in the  *>          The leading dimension of Z just as declared in the
 *>          calling subroutine.  1 .LE. LDZ.  *>          calling subroutine.  1 <= LDZ.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[out] NS  *> \param[out] NS
 *> \verbatim  *> \verbatim
 *>          NS is integer  *>          NS is INTEGER
 *>          The number of unconverged (ie approximate) eigenvalues  *>          The number of unconverged (ie approximate) eigenvalues
 *>          returned in SR and SI that may be used as shifts by the  *>          returned in SR and SI that may be used as shifts by the
 *>          calling subroutine.  *>          calling subroutine.
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 *>  *>
 *> \param[out] ND  *> \param[out] ND
 *> \verbatim  *> \verbatim
 *>          ND is integer  *>          ND is INTEGER
 *>          The number of converged eigenvalues uncovered by this  *>          The number of converged eigenvalues uncovered by this
 *>          subroutine.  *>          subroutine.
 *> \endverbatim  *> \endverbatim
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 *>  *>
 *> \param[in] LDV  *> \param[in] LDV
 *> \verbatim  *> \verbatim
 *>          LDV is integer scalar  *>          LDV is INTEGER
 *>          The leading dimension of V just as declared in the  *>          The leading dimension of V just as declared in the
 *>          calling subroutine.  NW .LE. LDV  *>          calling subroutine.  NW <= LDV
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] NH  *> \param[in] NH
 *> \verbatim  *> \verbatim
 *>          NH is integer scalar  *>          NH is INTEGER
 *>          The number of columns of T.  NH.GE.NW.  *>          The number of columns of T.  NH >= NW.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[out] T  *> \param[out] T
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 *>  *>
 *> \param[in] LDT  *> \param[in] LDT
 *> \verbatim  *> \verbatim
 *>          LDT is integer  *>          LDT is INTEGER
 *>          The leading dimension of T just as declared in the  *>          The leading dimension of T just as declared in the
 *>          calling subroutine.  NW .LE. LDT  *>          calling subroutine.  NW <= LDT
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] NV  *> \param[in] NV
 *> \verbatim  *> \verbatim
 *>          NV is integer  *>          NV is INTEGER
 *>          The number of rows of work array WV available for  *>          The number of rows of work array WV available for
 *>          workspace.  NV.GE.NW.  *>          workspace.  NV >= NW.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[out] WV  *> \param[out] WV
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 *>  *>
 *> \param[in] LDWV  *> \param[in] LDWV
 *> \verbatim  *> \verbatim
 *>          LDWV is integer  *>          LDWV is INTEGER
 *>          The leading dimension of W just as declared in the  *>          The leading dimension of W just as declared in the
 *>          calling subroutine.  NW .LE. LDV  *>          calling subroutine.  NW <= LDV
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[out] WORK  *> \param[out] WORK
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 *>  *>
 *> \param[in] LWORK  *> \param[in] LWORK
 *> \verbatim  *> \verbatim
 *>          LWORK is integer  *>          LWORK is INTEGER
 *>          The dimension of the work array WORK.  LWORK = 2*NW  *>          The dimension of the work array WORK.  LWORK = 2*NW
 *>          suffices, but greater efficiency may result from larger  *>          suffices, but greater efficiency may result from larger
 *>          values of LWORK.  *>          values of LWORK.
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 *  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 doubleOTHERauxiliary  *> \ingroup doubleOTHERauxiliary
 *  *
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      $                   IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T,       $                   IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T,
      $                   LDT, NV, WV, LDWV, WORK, LWORK )       $                   LDT, NV, WV, LDWV, WORK, LWORK )
 *  *
 *  -- 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 ..
       INTEGER            IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV,        INTEGER            IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV,
Removed from v.1.9  
changed lines
  Added in v.1.22

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