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   *> \brief \b ZLAQR5
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZLAQR5 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqr5.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqr5.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqr5.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S,
   *                          H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV,
   *                          WV, LDWV, NH, WH, LDWH )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV,
   *      $                   LDWH, LDWV, LDZ, N, NH, NSHFTS, NV
   *       LOGICAL            WANTT, WANTZ
   *       ..
   *       .. Array Arguments ..
   *       COMPLEX*16         H( LDH, * ), S( * ), U( LDU, * ), V( LDV, * ),
   *      $                   WH( LDWH, * ), WV( LDWV, * ), Z( LDZ, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *>    ZLAQR5, called by ZLAQR0, performs a
   *>    single small-bulge multi-shift QR sweep.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] WANTT
   *> \verbatim
   *>          WANTT is logical scalar
   *>             WANTT = .true. if the triangular Schur factor
   *>             is being computed.  WANTT is set to .false. otherwise.
   *> \endverbatim
   *>
   *> \param[in] WANTZ
   *> \verbatim
   *>          WANTZ is logical scalar
   *>             WANTZ = .true. if the unitary Schur factor is being
   *>             computed.  WANTZ is set to .false. otherwise.
   *> \endverbatim
   *>
   *> \param[in] KACC22
   *> \verbatim
   *>          KACC22 is integer with value 0, 1, or 2.
   *>             Specifies the computation mode of far-from-diagonal
   *>             orthogonal updates.
   *>        = 0: ZLAQR5 does not accumulate reflections and does not
   *>             use matrix-matrix multiply to update far-from-diagonal
   *>             matrix entries.
   *>        = 1: ZLAQR5 accumulates reflections and uses matrix-matrix
   *>             multiply to update the far-from-diagonal matrix entries.
   *>        = 2: ZLAQR5 accumulates reflections, uses matrix-matrix
   *>             multiply to update the far-from-diagonal matrix entries,
   *>             and takes advantage of 2-by-2 block structure during
   *>             matrix multiplies.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is integer scalar
   *>             N is the order of the Hessenberg matrix H upon which this
   *>             subroutine operates.
   *> \endverbatim
   *>
   *> \param[in] KTOP
   *> \verbatim
   *>          KTOP is integer scalar
   *> \endverbatim
   *>
   *> \param[in] KBOT
   *> \verbatim
   *>          KBOT is integer scalar
   *>             These are the first and last rows and columns of an
   *>             isolated diagonal block upon which the QR sweep is to be
   *>             applied. It is assumed without a check that
   *>                       either KTOP = 1  or   H(KTOP,KTOP-1) = 0
   *>             and
   *>                       either KBOT = N  or   H(KBOT+1,KBOT) = 0.
   *> \endverbatim
   *>
   *> \param[in] NSHFTS
   *> \verbatim
   *>          NSHFTS is integer scalar
   *>             NSHFTS gives the number of simultaneous shifts.  NSHFTS
   *>             must be positive and even.
   *> \endverbatim
   *>
   *> \param[in,out] S
   *> \verbatim
   *>          S is COMPLEX*16 array of size (NSHFTS)
   *>             S contains the shifts of origin that define the multi-
   *>             shift QR sweep.  On output S may be reordered.
   *> \endverbatim
   *>
   *> \param[in,out] H
   *> \verbatim
   *>          H is COMPLEX*16 array of size (LDH,N)
   *>             On input H contains a Hessenberg matrix.  On output a
   *>             multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied
   *>             to the isolated diagonal block in rows and columns KTOP
   *>             through KBOT.
   *> \endverbatim
   *>
   *> \param[in] LDH
   *> \verbatim
   *>          LDH is integer scalar
   *>             LDH is the leading dimension of H just as declared in the
   *>             calling procedure.  LDH.GE.MAX(1,N).
   *> \endverbatim
   *>
   *> \param[in] ILOZ
   *> \verbatim
   *>          ILOZ is INTEGER
   *> \endverbatim
   *>
   *> \param[in] IHIZ
   *> \verbatim
   *>          IHIZ is INTEGER
   *>             Specify the rows of Z to which transformations must be
   *>             applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N
   *> \endverbatim
   *>
   *> \param[in,out] Z
   *> \verbatim
   *>          Z is COMPLEX*16 array of size (LDZ,IHI)
   *>             If WANTZ = .TRUE., then the QR Sweep unitary
   *>             similarity transformation is accumulated into
   *>             Z(ILOZ:IHIZ,ILO:IHI) from the right.
   *>             If WANTZ = .FALSE., then Z is unreferenced.
   *> \endverbatim
   *>
   *> \param[in] LDZ
   *> \verbatim
   *>          LDZ is integer scalar
   *>             LDA is the leading dimension of Z just as declared in
   *>             the calling procedure. LDZ.GE.N.
   *> \endverbatim
   *>
   *> \param[out] V
   *> \verbatim
   *>          V is COMPLEX*16 array of size (LDV,NSHFTS/2)
   *> \endverbatim
   *>
   *> \param[in] LDV
   *> \verbatim
   *>          LDV is integer scalar
   *>             LDV is the leading dimension of V as declared in the
   *>             calling procedure.  LDV.GE.3.
   *> \endverbatim
   *>
   *> \param[out] U
   *> \verbatim
   *>          U is COMPLEX*16 array of size
   *>             (LDU,3*NSHFTS-3)
   *> \endverbatim
   *>
   *> \param[in] LDU
   *> \verbatim
   *>          LDU is integer scalar
   *>             LDU is the leading dimension of U just as declared in the
   *>             in the calling subroutine.  LDU.GE.3*NSHFTS-3.
   *> \endverbatim
   *>
   *> \param[in] NH
   *> \verbatim
   *>          NH is integer scalar
   *>             NH is the number of columns in array WH available for
   *>             workspace. NH.GE.1.
   *> \endverbatim
   *>
   *> \param[out] WH
   *> \verbatim
   *>          WH is COMPLEX*16 array of size (LDWH,NH)
   *> \endverbatim
   *>
   *> \param[in] LDWH
   *> \verbatim
   *>          LDWH is integer scalar
   *>             Leading dimension of WH just as declared in the
   *>             calling procedure.  LDWH.GE.3*NSHFTS-3.
   *> \endverbatim
   *>
   *> \param[in] NV
   *> \verbatim
   *>          NV is integer scalar
   *>             NV is the number of rows in WV agailable for workspace.
   *>             NV.GE.1.
   *> \endverbatim
   *>
   *> \param[out] WV
   *> \verbatim
   *>          WV is COMPLEX*16 array of size
   *>             (LDWV,3*NSHFTS-3)
   *> \endverbatim
   *>
   *> \param[in] LDWV
   *> \verbatim
   *>          LDWV is integer scalar
   *>             LDWV is the leading dimension of WV as declared in the
   *>             in the calling subroutine.  LDWV.GE.NV.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16OTHERauxiliary
   *
   *> \par Contributors:
   *  ==================
   *>
   *>       Karen Braman and Ralph Byers, Department of Mathematics,
   *>       University of Kansas, USA
   *
   *> \par References:
   *  ================
   *>
   *>       K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
   *>       Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
   *>       Performance, SIAM Journal of Matrix Analysis, volume 23, pages
   *>       929--947, 2002.
   *>
   *  =====================================================================
       SUBROUTINE ZLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S,        SUBROUTINE ZLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S,
      $                   H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV,       $                   H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV,
      $                   WV, LDWV, NH, WH, LDWH )       $                   WV, LDWV, NH, WH, LDWH )
 *  *
 *  -- LAPACK auxiliary routine (version 3.3.0) --  *  -- LAPACK auxiliary routine (version 3.4.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *     November 2010  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV,        INTEGER            IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV,
Line 16 Line 266
      $                   WH( LDWH, * ), WV( LDWV, * ), Z( LDZ, * )       $                   WH( LDWH, * ), WV( LDWV, * ), Z( LDZ, * )
 *     ..  *     ..
 *  *
 *     This auxiliary subroutine called by ZLAQR0 performs a  *  ================================================================
 *     single small-bulge multi-shift QR sweep.  
 *  
 *      WANTT  (input) logical scalar  
 *             WANTT = .true. if the triangular Schur factor  
 *             is being computed.  WANTT is set to .false. otherwise.  
 *  
 *      WANTZ  (input) logical scalar  
 *             WANTZ = .true. if the unitary Schur factor is being  
 *             computed.  WANTZ is set to .false. otherwise.  
 *  
 *      KACC22 (input) integer with value 0, 1, or 2.  
 *             Specifies the computation mode of far-from-diagonal  
 *             orthogonal updates.  
 *        = 0: ZLAQR5 does not accumulate reflections and does not  
 *             use matrix-matrix multiply to update far-from-diagonal  
 *             matrix entries.  
 *        = 1: ZLAQR5 accumulates reflections and uses matrix-matrix  
 *             multiply to update the far-from-diagonal matrix entries.  
 *        = 2: ZLAQR5 accumulates reflections, uses matrix-matrix  
 *             multiply to update the far-from-diagonal matrix entries,  
 *             and takes advantage of 2-by-2 block structure during  
 *             matrix multiplies.  
 *  
 *      N      (input) integer scalar  
 *             N is the order of the Hessenberg matrix H upon which this  
 *             subroutine operates.  
 *  
 *      KTOP   (input) integer scalar  
 *      KBOT   (input) integer scalar  
 *             These are the first and last rows and columns of an  
 *             isolated diagonal block upon which the QR sweep is to be  
 *             applied. It is assumed without a check that  
 *                       either KTOP = 1  or   H(KTOP,KTOP-1) = 0  
 *             and  
 *                       either KBOT = N  or   H(KBOT+1,KBOT) = 0.  
 *  
 *      NSHFTS (input) integer scalar  
 *             NSHFTS gives the number of simultaneous shifts.  NSHFTS  
 *             must be positive and even.  
 *  
 *      S      (input/output) COMPLEX*16 array of size (NSHFTS)  
 *             S contains the shifts of origin that define the multi-  
 *             shift QR sweep.  On output S may be reordered.  
 *  
 *      H      (input/output) COMPLEX*16 array of size (LDH,N)  
 *             On input H contains a Hessenberg matrix.  On output a  
 *             multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied  
 *             to the isolated diagonal block in rows and columns KTOP  
 *             through KBOT.  
 *  
 *      LDH    (input) integer scalar  
 *             LDH is the leading dimension of H just as declared in the  
 *             calling procedure.  LDH.GE.MAX(1,N).  
 *  
 *      ILOZ   (input) INTEGER  
 *      IHIZ   (input) INTEGER  
 *             Specify the rows of Z to which transformations must be  
 *             applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N  
 *  
 *      Z      (input/output) COMPLEX*16 array of size (LDZ,IHI)  
 *             If WANTZ = .TRUE., then the QR Sweep unitary  
 *             similarity transformation is accumulated into  
 *             Z(ILOZ:IHIZ,ILO:IHI) from the right.  
 *             If WANTZ = .FALSE., then Z is unreferenced.  
 *  
 *      LDZ    (input) integer scalar  
 *             LDA is the leading dimension of Z just as declared in  
 *             the calling procedure. LDZ.GE.N.  
 *  
 *      V      (workspace) COMPLEX*16 array of size (LDV,NSHFTS/2)  
 *  
 *      LDV    (input) integer scalar  
 *             LDV is the leading dimension of V as declared in the  
 *             calling procedure.  LDV.GE.3.  
 *  
 *      U      (workspace) COMPLEX*16 array of size  
 *             (LDU,3*NSHFTS-3)  
 *  
 *      LDU    (input) integer scalar  
 *             LDU is the leading dimension of U just as declared in the  
 *             in the calling subroutine.  LDU.GE.3*NSHFTS-3.  
 *  
 *      NH     (input) integer scalar  
 *             NH is the number of columns in array WH available for  
 *             workspace. NH.GE.1.  
 *  
 *      WH     (workspace) COMPLEX*16 array of size (LDWH,NH)  
 *  
 *      LDWH   (input) integer scalar  
 *             Leading dimension of WH just as declared in the  
 *             calling procedure.  LDWH.GE.3*NSHFTS-3.  
 *  
 *      NV     (input) integer scalar  
 *             NV is the number of rows in WV agailable for workspace.  
 *             NV.GE.1.  
 *  
 *      WV     (workspace) COMPLEX*16 array of size  
 *             (LDWV,3*NSHFTS-3)  
 *  
 *      LDWV   (input) integer scalar  
 *             LDWV is the leading dimension of WV as declared in the  
 *             in the calling subroutine.  LDWV.GE.NV.  
 *  
 *     ================================================================  
 *     Based on contributions by  
 *        Karen Braman and Ralph Byers, Department of Mathematics,  
 *        University of Kansas, USA  
 *  
 *     ================================================================  
 *     Reference:  
 *  
 *     K. Braman, R. Byers and R. Mathias, The Multi-Shift QR  
 *     Algorithm Part I: Maintaining Well Focused Shifts, and  
 *     Level 3 Performance, SIAM Journal of Matrix Analysis,  
 *     volume 23, pages 929--947, 2002.  
 *  
 *     ================================================================  
 *     .. Parameters ..  *     .. Parameters ..
       COMPLEX*16         ZERO, ONE        COMPLEX*16         ZERO, ONE
       PARAMETER          ( ZERO = ( 0.0d0, 0.0d0 ),        PARAMETER          ( ZERO = ( 0.0d0, 0.0d0 ),
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