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version 1.9, 2011/07/22 07:38:06 version 1.10, 2011/11/21 20:42:55
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   *> \brief \b DLAEIN
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLAEIN + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaein.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaein.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaein.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B,
   *                          LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO )
   * 
   *       .. Scalar Arguments ..
   *       LOGICAL            NOINIT, RIGHTV
   *       INTEGER            INFO, LDB, LDH, N
   *       DOUBLE PRECISION   BIGNUM, EPS3, SMLNUM, WI, WR
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   B( LDB, * ), H( LDH, * ), VI( * ), VR( * ),
   *      $                   WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLAEIN uses inverse iteration to find a right or left eigenvector
   *> corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg
   *> matrix H.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] RIGHTV
   *> \verbatim
   *>          RIGHTV is LOGICAL
   *>          = .TRUE. : compute right eigenvector;
   *>          = .FALSE.: compute left eigenvector.
   *> \endverbatim
   *>
   *> \param[in] NOINIT
   *> \verbatim
   *>          NOINIT is LOGICAL
   *>          = .TRUE. : no initial vector supplied in (VR,VI).
   *>          = .FALSE.: initial vector supplied in (VR,VI).
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix H.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] H
   *> \verbatim
   *>          H is DOUBLE PRECISION array, dimension (LDH,N)
   *>          The upper Hessenberg matrix H.
   *> \endverbatim
   *>
   *> \param[in] LDH
   *> \verbatim
   *>          LDH is INTEGER
   *>          The leading dimension of the array H.  LDH >= max(1,N).
   *> \endverbatim
   *>
   *> \param[in] WR
   *> \verbatim
   *>          WR is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[in] WI
   *> \verbatim
   *>          WI is DOUBLE PRECISION
   *>          The real and imaginary parts of the eigenvalue of H whose
   *>          corresponding right or left eigenvector is to be computed.
   *> \endverbatim
   *>
   *> \param[in,out] VR
   *> \verbatim
   *>          VR is DOUBLE PRECISION array, dimension (N)
   *> \endverbatim
   *>
   *> \param[in,out] VI
   *> \verbatim
   *>          VI is DOUBLE PRECISION array, dimension (N)
   *>          On entry, if NOINIT = .FALSE. and WI = 0.0, VR must contain
   *>          a real starting vector for inverse iteration using the real
   *>          eigenvalue WR; if NOINIT = .FALSE. and WI.ne.0.0, VR and VI
   *>          must contain the real and imaginary parts of a complex
   *>          starting vector for inverse iteration using the complex
   *>          eigenvalue (WR,WI); otherwise VR and VI need not be set.
   *>          On exit, if WI = 0.0 (real eigenvalue), VR contains the
   *>          computed real eigenvector; if WI.ne.0.0 (complex eigenvalue),
   *>          VR and VI contain the real and imaginary parts of the
   *>          computed complex eigenvector. The eigenvector is normalized
   *>          so that the component of largest magnitude has magnitude 1;
   *>          here the magnitude of a complex number (x,y) is taken to be
   *>          |x| + |y|.
   *>          VI is not referenced if WI = 0.0.
   *> \endverbatim
   *>
   *> \param[out] B
   *> \verbatim
   *>          B is DOUBLE PRECISION array, dimension (LDB,N)
   *> \endverbatim
   *>
   *> \param[in] LDB
   *> \verbatim
   *>          LDB is INTEGER
   *>          The leading dimension of the array B.  LDB >= N+1.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (N)
   *> \endverbatim
   *>
   *> \param[in] EPS3
   *> \verbatim
   *>          EPS3 is DOUBLE PRECISION
   *>          A small machine-dependent value which is used to perturb
   *>          close eigenvalues, and to replace zero pivots.
   *> \endverbatim
   *>
   *> \param[in] SMLNUM
   *> \verbatim
   *>          SMLNUM is DOUBLE PRECISION
   *>          A machine-dependent value close to the underflow threshold.
   *> \endverbatim
   *>
   *> \param[in] BIGNUM
   *> \verbatim
   *>          BIGNUM is DOUBLE PRECISION
   *>          A machine-dependent value close to the overflow threshold.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          = 1:  inverse iteration did not converge; VR is set to the
   *>                last iterate, and so is VI if WI.ne.0.0.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleOTHERauxiliary
   *
   *  =====================================================================
       SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B,        SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B,
      $                   LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO )       $                   LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO )
 *  *
 *  -- LAPACK auxiliary routine (version 3.3.1) --  *  -- LAPACK auxiliary routine (version 3.4.0) --
 *  -- 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..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       LOGICAL            NOINIT, RIGHTV        LOGICAL            NOINIT, RIGHTV
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      $                   WORK( * )       $                   WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLAEIN uses inverse iteration to find a right or left eigenvector  
 *  corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg  
 *  matrix H.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  RIGHTV  (input) LOGICAL  
 *          = .TRUE. : compute right eigenvector;  
 *          = .FALSE.: compute left eigenvector.  
 *  
 *  NOINIT  (input) LOGICAL  
 *          = .TRUE. : no initial vector supplied in (VR,VI).  
 *          = .FALSE.: initial vector supplied in (VR,VI).  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix H.  N >= 0.  
 *  
 *  H       (input) DOUBLE PRECISION array, dimension (LDH,N)  
 *          The upper Hessenberg matrix H.  
 *  
 *  LDH     (input) INTEGER  
 *          The leading dimension of the array H.  LDH >= max(1,N).  
 *  
 *  WR      (input) DOUBLE PRECISION  
 *  WI      (input) DOUBLE PRECISION  
 *          The real and imaginary parts of the eigenvalue of H whose  
 *          corresponding right or left eigenvector is to be computed.  
 *  
 *  VR      (input/output) DOUBLE PRECISION array, dimension (N)  
 *  VI      (input/output) DOUBLE PRECISION array, dimension (N)  
 *          On entry, if NOINIT = .FALSE. and WI = 0.0, VR must contain  
 *          a real starting vector for inverse iteration using the real  
 *          eigenvalue WR; if NOINIT = .FALSE. and WI.ne.0.0, VR and VI  
 *          must contain the real and imaginary parts of a complex  
 *          starting vector for inverse iteration using the complex  
 *          eigenvalue (WR,WI); otherwise VR and VI need not be set.  
 *          On exit, if WI = 0.0 (real eigenvalue), VR contains the  
 *          computed real eigenvector; if WI.ne.0.0 (complex eigenvalue),  
 *          VR and VI contain the real and imaginary parts of the  
 *          computed complex eigenvector. The eigenvector is normalized  
 *          so that the component of largest magnitude has magnitude 1;  
 *          here the magnitude of a complex number (x,y) is taken to be  
 *          |x| + |y|.  
 *          VI is not referenced if WI = 0.0.  
 *  
 *  B       (workspace) DOUBLE PRECISION array, dimension (LDB,N)  
 *  
 *  LDB     (input) INTEGER  
 *          The leading dimension of the array B.  LDB >= N+1.  
 *  
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (N)  
 *  
 *  EPS3    (input) DOUBLE PRECISION  
 *          A small machine-dependent value which is used to perturb  
 *          close eigenvalues, and to replace zero pivots.  
 *  
 *  SMLNUM  (input) DOUBLE PRECISION  
 *          A machine-dependent value close to the underflow threshold.  
 *  
 *  BIGNUM  (input) DOUBLE PRECISION  
 *          A machine-dependent value close to the overflow threshold.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          = 1:  inverse iteration did not converge; VR is set to the  
 *                last iterate, and so is VI if WI.ne.0.0.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.9  
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  Added in v.1.10

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