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version 1.7, 2010/12/21 13:53:49 version 1.8, 2011/11/21 20:43:15
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   *> \brief \b ZLAHQR
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZLAHQR + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlahqr.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlahqr.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlahqr.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
   *                          IHIZ, Z, LDZ, INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
   *       LOGICAL            WANTT, WANTZ
   *       ..
   *       .. Array Arguments ..
   *       COMPLEX*16         H( LDH, * ), W( * ), Z( LDZ, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *>    ZLAHQR is an auxiliary routine called by CHSEQR to update the
   *>    eigenvalues and Schur decomposition already computed by CHSEQR, by
   *>    dealing with the Hessenberg submatrix in rows and columns ILO to
   *>    IHI.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] WANTT
   *> \verbatim
   *>          WANTT is LOGICAL
   *>          = .TRUE. : the full Schur form T is required;
   *>          = .FALSE.: only eigenvalues are required.
   *> \endverbatim
   *>
   *> \param[in] WANTZ
   *> \verbatim
   *>          WANTZ is LOGICAL
   *>          = .TRUE. : the matrix of Schur vectors Z is required;
   *>          = .FALSE.: Schur vectors are not required.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix H.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] ILO
   *> \verbatim
   *>          ILO is INTEGER
   *> \endverbatim
   *>
   *> \param[in] IHI
   *> \verbatim
   *>          IHI is INTEGER
   *>          It is assumed that H is already upper triangular in rows and
   *>          columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1).
   *>          ZLAHQR works primarily with the Hessenberg submatrix in rows
   *>          and columns ILO to IHI, but applies transformations to all of
   *>          H if WANTT is .TRUE..
   *>          1 <= ILO <= max(1,IHI); IHI <= N.
   *> \endverbatim
   *>
   *> \param[in,out] H
   *> \verbatim
   *>          H is COMPLEX*16 array, dimension (LDH,N)
   *>          On entry, the upper Hessenberg matrix H.
   *>          On exit, if INFO is zero and if WANTT is .TRUE., then H
   *>          is upper triangular in rows and columns ILO:IHI.  If INFO
   *>          is zero and if WANTT is .FALSE., then the contents of H
   *>          are unspecified on exit.  The output state of H in case
   *>          INF is positive is below under the description of INFO.
   *> \endverbatim
   *>
   *> \param[in] LDH
   *> \verbatim
   *>          LDH is INTEGER
   *>          The leading dimension of the array H. LDH >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] W
   *> \verbatim
   *>          W is COMPLEX*16 array, dimension (N)
   *>          The computed eigenvalues ILO to IHI are stored in the
   *>          corresponding elements of W. If WANTT is .TRUE., the
   *>          eigenvalues are stored in the same order as on the diagonal
   *>          of the Schur form returned in H, with W(i) = H(i,i).
   *> \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 <= ILOZ <= ILO; IHI <= IHIZ <= N.
   *> \endverbatim
   *>
   *> \param[in,out] Z
   *> \verbatim
   *>          Z is COMPLEX*16 array, dimension (LDZ,N)
   *>          If WANTZ is .TRUE., on entry Z must contain the current
   *>          matrix Z of transformations accumulated by CHSEQR, and on
   *>          exit Z has been updated; transformations are applied only to
   *>          the submatrix Z(ILOZ:IHIZ,ILO:IHI).
   *>          If WANTZ is .FALSE., Z is not referenced.
   *> \endverbatim
   *>
   *> \param[in] LDZ
   *> \verbatim
   *>          LDZ is INTEGER
   *>          The leading dimension of the array Z. LDZ >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>           =   0: successful exit
   *>          .GT. 0: if INFO = i, ZLAHQR failed to compute all the
   *>                  eigenvalues ILO to IHI in a total of 30 iterations
   *>                  per eigenvalue; elements i+1:ihi of W contain
   *>                  those eigenvalues which have been successfully
   *>                  computed.
   *>
   *>                  If INFO .GT. 0 and WANTT is .FALSE., then on exit,
   *>                  the remaining unconverged eigenvalues are the
   *>                  eigenvalues of the upper Hessenberg matrix
   *>                  rows and columns ILO thorugh INFO of the final,
   *>                  output value of H.
   *>
   *>                  If INFO .GT. 0 and WANTT is .TRUE., then on exit
   *>          (*)       (initial value of H)*U  = U*(final value of H)
   *>                  where U is an orthognal matrix.    The final
   *>                  value of H is upper Hessenberg and triangular in
   *>                  rows and columns INFO+1 through IHI.
   *>
   *>                  If INFO .GT. 0 and WANTZ is .TRUE., then on exit
   *>                      (final value of Z)  = (initial value of Z)*U
   *>                  where U is the orthogonal matrix in (*)
   *>                  (regardless of the value of WANTT.)
   *> \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:
   *  ==================
   *>
   *> \verbatim
   *>
   *>     02-96 Based on modifications by
   *>     David Day, Sandia National Laboratory, USA
   *>
   *>     12-04 Further modifications by
   *>     Ralph Byers, University of Kansas, USA
   *>     This is a modified version of ZLAHQR from LAPACK version 3.0.
   *>     It is (1) more robust against overflow and underflow and
   *>     (2) adopts the more conservative Ahues & Tisseur stopping
   *>     criterion (LAWN 122, 1997).
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,        SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
      $                   IHIZ, Z, LDZ, INFO )       $                   IHIZ, Z, LDZ, INFO )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2) --  *  -- 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 2006  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N        INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
Line 13 Line 208
       COMPLEX*16         H( LDH, * ), W( * ), Z( LDZ, * )        COMPLEX*16         H( LDH, * ), W( * ), Z( LDZ, * )
 *     ..  *     ..
 *  *
 *     Purpose  *  =========================================================
 *     =======  
 *  
 *     ZLAHQR is an auxiliary routine called by CHSEQR to update the  
 *     eigenvalues and Schur decomposition already computed by CHSEQR, by  
 *     dealing with the Hessenberg submatrix in rows and columns ILO to  
 *     IHI.  
 *  
 *     Arguments  
 *     =========  
 *  
 *     WANTT   (input) LOGICAL  
 *          = .TRUE. : the full Schur form T is required;  
 *          = .FALSE.: only eigenvalues are required.  
 *  
 *     WANTZ   (input) LOGICAL  
 *          = .TRUE. : the matrix of Schur vectors Z is required;  
 *          = .FALSE.: Schur vectors are not required.  
 *  
 *     N       (input) INTEGER  
 *          The order of the matrix H.  N >= 0.  
 *  
 *     ILO     (input) INTEGER  
 *     IHI     (input) INTEGER  
 *          It is assumed that H is already upper triangular in rows and  
 *          columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1).  
 *          ZLAHQR works primarily with the Hessenberg submatrix in rows  
 *          and columns ILO to IHI, but applies transformations to all of  
 *          H if WANTT is .TRUE..  
 *          1 <= ILO <= max(1,IHI); IHI <= N.  
 *  
 *     H       (input/output) COMPLEX*16 array, dimension (LDH,N)  
 *          On entry, the upper Hessenberg matrix H.  
 *          On exit, if INFO is zero and if WANTT is .TRUE., then H  
 *          is upper triangular in rows and columns ILO:IHI.  If INFO  
 *          is zero and if WANTT is .FALSE., then the contents of H  
 *          are unspecified on exit.  The output state of H in case  
 *          INF is positive is below under the description of INFO.  
 *  
 *     LDH     (input) INTEGER  
 *          The leading dimension of the array H. LDH >= max(1,N).  
 *  
 *     W       (output) COMPLEX*16 array, dimension (N)  
 *          The computed eigenvalues ILO to IHI are stored in the  
 *          corresponding elements of W. If WANTT is .TRUE., the  
 *          eigenvalues are stored in the same order as on the diagonal  
 *          of the Schur form returned in H, with W(i) = H(i,i).  
 *  
 *     ILOZ    (input) INTEGER  
 *     IHIZ    (input) INTEGER  
 *          Specify the rows of Z to which transformations must be  
 *          applied if WANTZ is .TRUE..  
 *          1 <= ILOZ <= ILO; IHI <= IHIZ <= N.  
 *  
 *     Z       (input/output) COMPLEX*16 array, dimension (LDZ,N)  
 *          If WANTZ is .TRUE., on entry Z must contain the current  
 *          matrix Z of transformations accumulated by CHSEQR, and on  
 *          exit Z has been updated; transformations are applied only to  
 *          the submatrix Z(ILOZ:IHIZ,ILO:IHI).  
 *          If WANTZ is .FALSE., Z is not referenced.  
 *  
 *     LDZ     (input) INTEGER  
 *          The leading dimension of the array Z. LDZ >= max(1,N).  
 *  
 *     INFO    (output) INTEGER  
 *           =   0: successful exit  
 *          .GT. 0: if INFO = i, ZLAHQR failed to compute all the  
 *                  eigenvalues ILO to IHI in a total of 30 iterations  
 *                  per eigenvalue; elements i+1:ihi of W contain  
 *                  those eigenvalues which have been successfully  
 *                  computed.  
 *  
 *                  If INFO .GT. 0 and WANTT is .FALSE., then on exit,  
 *                  the remaining unconverged eigenvalues are the  
 *                  eigenvalues of the upper Hessenberg matrix  
 *                  rows and columns ILO thorugh INFO of the final,  
 *                  output value of H.  
 *  
 *                  If INFO .GT. 0 and WANTT is .TRUE., then on exit  
 *          (*)       (initial value of H)*U  = U*(final value of H)  
 *                  where U is an orthognal matrix.    The final  
 *                  value of H is upper Hessenberg and triangular in  
 *                  rows and columns INFO+1 through IHI.  
 *  
 *                  If INFO .GT. 0 and WANTZ is .TRUE., then on exit  
 *                      (final value of Z)  = (initial value of Z)*U  
 *                  where U is the orthogonal matrix in (*)  
 *                  (regardless of the value of WANTT.)  
 *  
 *     Further Details  
 *     ===============  
 *  
 *     02-96 Based on modifications by  
 *     David Day, Sandia National Laboratory, USA  
 *  
 *     12-04 Further modifications by  
 *     Ralph Byers, University of Kansas, USA  
 *     This is a modified version of ZLAHQR from LAPACK version 3.0.  
 *     It is (1) more robust against overflow and underflow and  
 *     (2) adopts the more conservative Ahues & Tisseur stopping  
 *     criterion (LAWN 122, 1997).  
 *  
 *     =========================================================  
 *  *
 *     .. Parameters ..  *     .. Parameters ..
       INTEGER            ITMAX        INTEGER            ITMAX
Removed from v.1.7  
changed lines
  Added in v.1.8

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