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version 1.9, 2011/11/21 22:19:53 version 1.18, 2020/05/21 21:46:09
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 *> \brief \b ZLAQR4  *> \brief \b ZLAQR4 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition.
 *  *
 *  =========== 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 ZLAQR4 + dependencies   *> Download ZLAQR4 + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqr4.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqr4.f">
 *> [TGZ]</a>   *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqr4.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqr4.f">
 *> [ZIP]</a>   *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqr4.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqr4.f">
 *> [TXT]</a>  *> [TXT]</a>
 *> \endhtmlonly   *> \endhtmlonly
 *  *
 *  Definition:  *  Definition:
 *  ===========  *  ===========
 *  *
 *       SUBROUTINE ZLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,  *       SUBROUTINE ZLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
 *                          IHIZ, Z, LDZ, WORK, LWORK, INFO )  *                          IHIZ, Z, LDZ, WORK, LWORK, INFO )
 *   *
 *       .. Scalar Arguments ..  *       .. Scalar Arguments ..
 *       INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N  *       INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N
 *       LOGICAL            WANTT, WANTZ  *       LOGICAL            WANTT, WANTZ
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 *       .. Array Arguments ..  *       .. Array Arguments ..
 *       COMPLEX*16         H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )  *       COMPLEX*16         H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )
 *       ..  *       ..
 *    *
 *  *
 *> \par Purpose:  *> \par Purpose:
 *  =============  *  =============
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 *> \param[in] N  *> \param[in] N
 *> \verbatim  *> \verbatim
 *>          N is INTEGER  *>          N is INTEGER
 *>           The order of the matrix H.  N .GE. 0.  *>           The order of the matrix H.  N >= 0.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] ILO  *> \param[in] ILO
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 *> \verbatim  *> \verbatim
 *>          IHI is INTEGER  *>          IHI is INTEGER
 *>           It is assumed that H is already upper triangular in rows  *>           It is assumed that H is already upper triangular in rows
 *>           and columns 1:ILO-1 and IHI+1:N and, if ILO.GT.1,  *>           and columns 1:ILO-1 and IHI+1:N and, if ILO > 1,
 *>           H(ILO,ILO-1) is zero. ILO and IHI are normally set by a  *>           H(ILO,ILO-1) is zero. ILO and IHI are normally set by a
 *>           previous call to ZGEBAL, and then passed to ZGEHRD when the  *>           previous call to ZGEBAL, and then passed to ZGEHRD when the
 *>           matrix output by ZGEBAL is reduced to Hessenberg form.  *>           matrix output by ZGEBAL is reduced to Hessenberg form.
 *>           Otherwise, ILO and IHI should be set to 1 and N,  *>           Otherwise, ILO and IHI should be set to 1 and N,
 *>           respectively.  If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N.  *>           respectively.  If N > 0, then 1 <= ILO <= IHI <= N.
 *>           If N = 0, then ILO = 1 and IHI = 0.  *>           If N = 0, then ILO = 1 and IHI = 0.
 *> \endverbatim  *> \endverbatim
 *>  *>
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 *>           contains the upper triangular matrix T from the Schur  *>           contains the upper triangular matrix T from the Schur
 *>           decomposition (the Schur form). If INFO = 0 and WANT is  *>           decomposition (the Schur form). If INFO = 0 and WANT is
 *>           .FALSE., then the contents of H are unspecified on exit.  *>           .FALSE., then the contents of H are unspecified on exit.
 *>           (The output value of H when INFO.GT.0 is given under the  *>           (The output value of H when INFO > 0 is given under the
 *>           description of INFO below.)  *>           description of INFO below.)
 *>  *>
 *>           This subroutine may explicitly set H(i,j) = 0 for i.GT.j and  *>           This subroutine may explicitly set H(i,j) = 0 for i > j and
 *>           j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N.  *>           j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] LDH  *> \param[in] LDH
 *> \verbatim  *> \verbatim
 *>          LDH is INTEGER  *>          LDH is INTEGER
 *>           The leading dimension of the array H. LDH .GE. max(1,N).  *>           The leading dimension of the array H. LDH >= max(1,N).
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[out] W  *> \param[out] W
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 *>          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..  *>           applied if WANTZ is .TRUE..
 *>           1 .LE. ILOZ .LE. ILO; IHI .LE. IHIZ .LE. N.  *>           1 <= ILOZ <= ILO; IHI <= IHIZ <= N.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in,out] Z  *> \param[in,out] Z
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 *>           If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is  *>           If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is
 *>           replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the  *>           replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the
 *>           orthogonal Schur factor of H(ILO:IHI,ILO:IHI).  *>           orthogonal Schur factor of H(ILO:IHI,ILO:IHI).
 *>           (The output value of Z when INFO.GT.0 is given under  *>           (The output value of Z when INFO > 0 is given under
 *>           the description of INFO below.)  *>           the description of INFO below.)
 *> \endverbatim  *> \endverbatim
 *>  *>
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 *> \verbatim  *> \verbatim
 *>          LDZ is INTEGER  *>          LDZ is INTEGER
 *>           The leading dimension of the array Z.  if WANTZ is .TRUE.  *>           The leading dimension of the array Z.  if WANTZ is .TRUE.
 *>           then LDZ.GE.MAX(1,IHIZ).  Otherwize, LDZ.GE.1.  *>           then LDZ >= MAX(1,IHIZ).  Otherwise, LDZ >= 1.
 *> \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 array WORK.  LWORK .GE. max(1,N)  *>           The dimension of the array WORK.  LWORK >= max(1,N)
 *>           is sufficient, but LWORK typically as large as 6*N may  *>           is sufficient, but LWORK typically as large as 6*N may
 *>           be required for optimal performance.  A workspace query  *>           be required for optimal performance.  A workspace query
 *>           to determine the optimal workspace size is recommended.  *>           to determine the optimal workspace size is recommended.
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 *> \verbatim  *> \verbatim
 *>          INFO is INTEGER  *>          INFO is INTEGER
 *>             =  0:  successful exit  *>             =  0:  successful exit
 *>           .GT. 0:  if INFO = i, ZLAQR4 failed to compute all of  *>             > 0:  if INFO = i, ZLAQR4 failed to compute all of
 *>                the eigenvalues.  Elements 1:ilo-1 and i+1:n of WR  *>                the eigenvalues.  Elements 1:ilo-1 and i+1:n of WR
 *>                and WI contain those eigenvalues which have been  *>                and WI contain those eigenvalues which have been
 *>                successfully computed.  (Failures are rare.)  *>                successfully computed.  (Failures are rare.)
 *>  *>
 *>                If INFO .GT. 0 and WANT is .FALSE., then on exit,  *>                If INFO > 0 and WANT is .FALSE., then on exit,
 *>                the remaining unconverged eigenvalues are the eigen-  *>                the remaining unconverged eigenvalues are the eigen-
 *>                values of the upper Hessenberg matrix rows and  *>                values of the upper Hessenberg matrix rows and
 *>                columns ILO through INFO of the final, output  *>                columns ILO through INFO of the final, output
 *>                value of H.  *>                value of H.
 *>  *>
 *>                If INFO .GT. 0 and WANTT is .TRUE., then on exit  *>                If INFO > 0 and WANTT is .TRUE., then on exit
 *>  *>
 *>           (*)  (initial value of H)*U  = U*(final value of H)  *>           (*)  (initial value of H)*U  = U*(final value of H)
 *>  *>
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 *>                value of  H is upper Hessenberg and triangular in  *>                value of  H is upper Hessenberg and triangular in
 *>                rows and columns INFO+1 through IHI.  *>                rows and columns INFO+1 through IHI.
 *>  *>
 *>                If INFO .GT. 0 and WANTZ is .TRUE., then on exit  *>                If INFO > 0 and WANTZ is .TRUE., then on exit
 *>  *>
 *>                  (final value of Z(ILO:IHI,ILOZ:IHIZ)  *>                  (final value of Z(ILO:IHI,ILOZ:IHIZ)
 *>                   =  (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U  *>                   =  (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U
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 *>                where U is the unitary matrix in (*) (regard-  *>                where U is the unitary matrix in (*) (regard-
 *>                less of the value of WANTT.)  *>                less of the value of WANTT.)
 *>  *>
 *>                If INFO .GT. 0 and WANTZ is .FALSE., then Z is not  *>                If INFO > 0 and WANTZ is .FALSE., then Z is not
 *>                accessed.  *>                accessed.
 *> \endverbatim  *> \endverbatim
 *  *
 *  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  *> \date December 2016
 *  *
 *> \ingroup complex16OTHERauxiliary  *> \ingroup complex16OTHERauxiliary
 *  *
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       SUBROUTINE ZLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,        SUBROUTINE ZLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
      $                   IHIZ, Z, LDZ, WORK, LWORK, INFO )       $                   IHIZ, Z, LDZ, WORK, LWORK, INFO )
 *  *
 *  -- LAPACK auxiliary routine (version 3.4.0) --  *  -- LAPACK auxiliary routine (version 3.7.0) --
 *  -- 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 2011  *     December 2016
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N        INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N
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                   END IF                    END IF
                END IF                 END IF
 *  *
 *              ==== Use up to NS of the the smallest magnatiude  *              ==== Use up to NS of the the smallest magnitude
 *              .    shifts.  If there aren't NS shifts available,  *              .    shifts.  If there aren't NS shifts available,
 *              .    then use them all, possibly dropping one to  *              .    then use them all, possibly dropping one to
 *              .    make the number of shifts even. ====  *              .    make the number of shifts even. ====
Removed from v.1.9  
changed lines
  Added in v.1.18

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