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version 1.8, 2010/12/21 13:53:31 version 1.9, 2011/11/21 20:42:56
Line 1 Line 1
   *> \brief \b DLAQR2
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLAQR2 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqr2.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqr2.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqr2.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
   *                          IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T,
   *                          LDT, NV, WV, LDWV, WORK, LWORK )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV,
   *      $                   LDZ, LWORK, N, ND, NH, NS, NV, NW
   *       LOGICAL            WANTT, WANTZ
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   H( LDH, * ), SI( * ), SR( * ), T( LDT, * ),
   *      $                   V( LDV, * ), WORK( * ), WV( LDWV, * ),
   *      $                   Z( LDZ, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *>    DLAQR2 is identical to DLAQR3 except that it avoids
   *>    recursion by calling DLAHQR instead of DLAQR4.
   *>
   *>    Aggressive early deflation:
   *>
   *>    This subroutine accepts as input an upper Hessenberg matrix
   *>    H and performs an orthogonal similarity transformation
   *>    designed to detect and deflate fully converged eigenvalues from
   *>    a trailing principal submatrix.  On output H has been over-
   *>    written by a new Hessenberg matrix that is a perturbation of
   *>    an orthogonal similarity transformation of H.  It is to be
   *>    hoped that the final version of H has many zero subdiagonal
   *>    entries.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] WANTT
   *> \verbatim
   *>          WANTT is LOGICAL
   *>          If .TRUE., then the Hessenberg matrix H is fully updated
   *>          so that the quasi-triangular Schur factor may be
   *>          computed (in cooperation with the calling subroutine).
   *>          If .FALSE., then only enough of H is updated to preserve
   *>          the eigenvalues.
   *> \endverbatim
   *>
   *> \param[in] WANTZ
   *> \verbatim
   *>          WANTZ is LOGICAL
   *>          If .TRUE., then the orthogonal matrix Z is updated so
   *>          so that the orthogonal Schur factor may be computed
   *>          (in cooperation with the calling subroutine).
   *>          If .FALSE., then Z is not referenced.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix H and (if WANTZ is .TRUE.) the
   *>          order of the orthogonal matrix Z.
   *> \endverbatim
   *>
   *> \param[in] KTOP
   *> \verbatim
   *>          KTOP is INTEGER
   *>          It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0.
   *>          KBOT and KTOP together determine an isolated block
   *>          along the diagonal of the Hessenberg matrix.
   *> \endverbatim
   *>
   *> \param[in] KBOT
   *> \verbatim
   *>          KBOT is INTEGER
   *>          It is assumed without a check that either
   *>          KBOT = N or H(KBOT+1,KBOT)=0.  KBOT and KTOP together
   *>          determine an isolated block along the diagonal of the
   *>          Hessenberg matrix.
   *> \endverbatim
   *>
   *> \param[in] NW
   *> \verbatim
   *>          NW is INTEGER
   *>          Deflation window size.  1 .LE. NW .LE. (KBOT-KTOP+1).
   *> \endverbatim
   *>
   *> \param[in,out] H
   *> \verbatim
   *>          H is DOUBLE PRECISION array, dimension (LDH,N)
   *>          On input the initial N-by-N section of H stores the
   *>          Hessenberg matrix undergoing aggressive early deflation.
   *>          On output H has been transformed by an orthogonal
   *>          similarity transformation, perturbed, and the returned
   *>          to Hessenberg form that (it is to be hoped) has some
   *>          zero subdiagonal entries.
   *> \endverbatim
   *>
   *> \param[in] LDH
   *> \verbatim
   *>          LDH is integer
   *>          Leading dimension of H just as declared in the calling
   *>          subroutine.  N .LE. LDH
   *> \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 DOUBLE PRECISION array, dimension (LDZ,N)
   *>          IF WANTZ is .TRUE., then on output, the orthogonal
   *>          similarity transformation mentioned above has been
   *>          accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right.
   *>          If WANTZ is .FALSE., then Z is unreferenced.
   *> \endverbatim
   *>
   *> \param[in] LDZ
   *> \verbatim
   *>          LDZ is integer
   *>          The leading dimension of Z just as declared in the
   *>          calling subroutine.  1 .LE. LDZ.
   *> \endverbatim
   *>
   *> \param[out] NS
   *> \verbatim
   *>          NS is integer
   *>          The number of unconverged (ie approximate) eigenvalues
   *>          returned in SR and SI that may be used as shifts by the
   *>          calling subroutine.
   *> \endverbatim
   *>
   *> \param[out] ND
   *> \verbatim
   *>          ND is integer
   *>          The number of converged eigenvalues uncovered by this
   *>          subroutine.
   *> \endverbatim
   *>
   *> \param[out] SR
   *> \verbatim
   *>          SR is DOUBLE PRECISION array, dimension (KBOT)
   *> \endverbatim
   *>
   *> \param[out] SI
   *> \verbatim
   *>          SI is DOUBLE PRECISION array, dimension (KBOT)
   *>          On output, the real and imaginary parts of approximate
   *>          eigenvalues that may be used for shifts are stored in
   *>          SR(KBOT-ND-NS+1) through SR(KBOT-ND) and
   *>          SI(KBOT-ND-NS+1) through SI(KBOT-ND), respectively.
   *>          The real and imaginary parts of converged eigenvalues
   *>          are stored in SR(KBOT-ND+1) through SR(KBOT) and
   *>          SI(KBOT-ND+1) through SI(KBOT), respectively.
   *> \endverbatim
   *>
   *> \param[out] V
   *> \verbatim
   *>          V is DOUBLE PRECISION array, dimension (LDV,NW)
   *>          An NW-by-NW work array.
   *> \endverbatim
   *>
   *> \param[in] LDV
   *> \verbatim
   *>          LDV is integer scalar
   *>          The leading dimension of V just as declared in the
   *>          calling subroutine.  NW .LE. LDV
   *> \endverbatim
   *>
   *> \param[in] NH
   *> \verbatim
   *>          NH is integer scalar
   *>          The number of columns of T.  NH.GE.NW.
   *> \endverbatim
   *>
   *> \param[out] T
   *> \verbatim
   *>          T is DOUBLE PRECISION array, dimension (LDT,NW)
   *> \endverbatim
   *>
   *> \param[in] LDT
   *> \verbatim
   *>          LDT is integer
   *>          The leading dimension of T just as declared in the
   *>          calling subroutine.  NW .LE. LDT
   *> \endverbatim
   *>
   *> \param[in] NV
   *> \verbatim
   *>          NV is integer
   *>          The number of rows of work array WV available for
   *>          workspace.  NV.GE.NW.
   *> \endverbatim
   *>
   *> \param[out] WV
   *> \verbatim
   *>          WV is DOUBLE PRECISION array, dimension (LDWV,NW)
   *> \endverbatim
   *>
   *> \param[in] LDWV
   *> \verbatim
   *>          LDWV is integer
   *>          The leading dimension of W just as declared in the
   *>          calling subroutine.  NW .LE. LDV
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (LWORK)
   *>          On exit, WORK(1) is set to an estimate of the optimal value
   *>          of LWORK for the given values of N, NW, KTOP and KBOT.
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is integer
   *>          The dimension of the work array WORK.  LWORK = 2*NW
   *>          suffices, but greater efficiency may result from larger
   *>          values of LWORK.
   *>
   *>          If LWORK = -1, then a workspace query is assumed; DLAQR2
   *>          only estimates the optimal workspace size for the given
   *>          values of N, NW, KTOP and KBOT.  The estimate is returned
   *>          in WORK(1).  No error message related to LWORK is issued
   *>          by XERBLA.  Neither H nor Z are accessed.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleOTHERauxiliary
   *
   *> \par Contributors:
   *  ==================
   *>
   *>       Karen Braman and Ralph Byers, Department of Mathematics,
   *>       University of Kansas, USA
   *>
   *  =====================================================================
       SUBROUTINE DLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,        SUBROUTINE DLAQR2( 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 )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2.2)                        --  *  -- 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,    --
 *  -- June 2010                                                       --  *  -- 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,
Line 17 Line 294
      $                   Z( LDZ, * )       $                   Z( LDZ, * )
 *     ..  *     ..
 *  *
 *     This subroutine is identical to DLAQR3 except that it avoids  *  ================================================================
 *     recursion by calling DLAHQR instead of DLAQR4.  
 *  
 *  
 *     ******************************************************************  
 *     Aggressive early deflation:  
 *  
 *     This subroutine accepts as input an upper Hessenberg matrix  
 *     H and performs an orthogonal similarity transformation  
 *     designed to detect and deflate fully converged eigenvalues from  
 *     a trailing principal submatrix.  On output H has been over-  
 *     written by a new Hessenberg matrix that is a perturbation of  
 *     an orthogonal similarity transformation of H.  It is to be  
 *     hoped that the final version of H has many zero subdiagonal  
 *     entries.  
 *  
 *     ******************************************************************  
 *     WANTT   (input) LOGICAL  
 *          If .TRUE., then the Hessenberg matrix H is fully updated  
 *          so that the quasi-triangular Schur factor may be  
 *          computed (in cooperation with the calling subroutine).  
 *          If .FALSE., then only enough of H is updated to preserve  
 *          the eigenvalues.  
 *  
 *     WANTZ   (input) LOGICAL  
 *          If .TRUE., then the orthogonal matrix Z is updated so  
 *          so that the orthogonal Schur factor may be computed  
 *          (in cooperation with the calling subroutine).  
 *          If .FALSE., then Z is not referenced.  
 *  
 *     N       (input) INTEGER  
 *          The order of the matrix H and (if WANTZ is .TRUE.) the  
 *          order of the orthogonal matrix Z.  
 *  
 *     KTOP    (input) INTEGER  
 *          It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0.  
 *          KBOT and KTOP together determine an isolated block  
 *          along the diagonal of the Hessenberg matrix.  
 *  
 *     KBOT    (input) INTEGER  
 *          It is assumed without a check that either  
 *          KBOT = N or H(KBOT+1,KBOT)=0.  KBOT and KTOP together  
 *          determine an isolated block along the diagonal of the  
 *          Hessenberg matrix.  
 *  
 *     NW      (input) INTEGER  
 *          Deflation window size.  1 .LE. NW .LE. (KBOT-KTOP+1).  
 *  
 *     H       (input/output) DOUBLE PRECISION array, dimension (LDH,N)  
 *          On input the initial N-by-N section of H stores the  
 *          Hessenberg matrix undergoing aggressive early deflation.  
 *          On output H has been transformed by an orthogonal  
 *          similarity transformation, perturbed, and the returned  
 *          to Hessenberg form that (it is to be hoped) has some  
 *          zero subdiagonal entries.  
 *  
 *     LDH     (input) integer  
 *          Leading dimension of H just as declared in the calling  
 *          subroutine.  N .LE. LDH  
 *  
 *     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) DOUBLE PRECISION array, dimension (LDZ,N)  
 *          IF WANTZ is .TRUE., then on output, the orthogonal  
 *          similarity transformation mentioned above has been  
 *          accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right.  
 *          If WANTZ is .FALSE., then Z is unreferenced.  
 *  
 *     LDZ     (input) integer  
 *          The leading dimension of Z just as declared in the  
 *          calling subroutine.  1 .LE. LDZ.  
 *  
 *     NS      (output) integer  
 *          The number of unconverged (ie approximate) eigenvalues  
 *          returned in SR and SI that may be used as shifts by the  
 *          calling subroutine.  
 *  
 *     ND      (output) integer  
 *          The number of converged eigenvalues uncovered by this  
 *          subroutine.  
 *  
 *     SR      (output) DOUBLE PRECISION array, dimension (KBOT)  
 *     SI      (output) DOUBLE PRECISION array, dimension (KBOT)  
 *          On output, the real and imaginary parts of approximate  
 *          eigenvalues that may be used for shifts are stored in  
 *          SR(KBOT-ND-NS+1) through SR(KBOT-ND) and  
 *          SI(KBOT-ND-NS+1) through SI(KBOT-ND), respectively.  
 *          The real and imaginary parts of converged eigenvalues  
 *          are stored in SR(KBOT-ND+1) through SR(KBOT) and  
 *          SI(KBOT-ND+1) through SI(KBOT), respectively.  
 *  
 *     V       (workspace) DOUBLE PRECISION array, dimension (LDV,NW)  
 *          An NW-by-NW work array.  
 *  
 *     LDV     (input) integer scalar  
 *          The leading dimension of V just as declared in the  
 *          calling subroutine.  NW .LE. LDV  
 *  
 *     NH      (input) integer scalar  
 *          The number of columns of T.  NH.GE.NW.  
 *  
 *     T       (workspace) DOUBLE PRECISION array, dimension (LDT,NW)  
 *  
 *     LDT     (input) integer  
 *          The leading dimension of T just as declared in the  
 *          calling subroutine.  NW .LE. LDT  
 *  
 *     NV      (input) integer  
 *          The number of rows of work array WV available for  
 *          workspace.  NV.GE.NW.  
 *  
 *     WV      (workspace) DOUBLE PRECISION array, dimension (LDWV,NW)  
 *  
 *     LDWV    (input) integer  
 *          The leading dimension of W just as declared in the  
 *          calling subroutine.  NW .LE. LDV  
 *  
 *     WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK)  
 *          On exit, WORK(1) is set to an estimate of the optimal value  
 *          of LWORK for the given values of N, NW, KTOP and KBOT.  
 *  
 *     LWORK   (input) integer  
 *          The dimension of the work array WORK.  LWORK = 2*NW  
 *          suffices, but greater efficiency may result from larger  
 *          values of LWORK.  
 *  
 *          If LWORK = -1, then a workspace query is assumed; DLAQR2  
 *          only estimates the optimal workspace size for the given  
 *          values of N, NW, KTOP and KBOT.  The estimate is returned  
 *          in WORK(1).  No error message related to LWORK is issued  
 *          by XERBLA.  Neither H nor Z are accessed.  
 *  
 *     ================================================================  
 *     Based on contributions by  
 *        Karen Braman and Ralph Byers, Department of Mathematics,  
 *        University of Kansas, USA  
 *  
 *     ================================================================  
 *     .. Parameters ..  *     .. Parameters ..
       DOUBLE PRECISION   ZERO, ONE        DOUBLE PRECISION   ZERO, ONE
       PARAMETER          ( ZERO = 0.0d0, ONE = 1.0d0 )        PARAMETER          ( ZERO = 0.0d0, ONE = 1.0d0 )
Removed from v.1.8  
changed lines
  Added in v.1.9

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