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version 1.7, 2010/12/21 13:53:26 version 1.8, 2011/11/21 20:42:52
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   *> \brief \b DGGBAK
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DGGBAK + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dggbak.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dggbak.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dggbak.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
   *                          LDV, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          JOB, SIDE
   *       INTEGER            IHI, ILO, INFO, LDV, M, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   LSCALE( * ), RSCALE( * ), V( LDV, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DGGBAK forms the right or left eigenvectors of a real generalized
   *> eigenvalue problem A*x = lambda*B*x, by backward transformation on
   *> the computed eigenvectors of the balanced pair of matrices output by
   *> DGGBAL.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] JOB
   *> \verbatim
   *>          JOB is CHARACTER*1
   *>          Specifies the type of backward transformation required:
   *>          = 'N':  do nothing, return immediately;
   *>          = 'P':  do backward transformation for permutation only;
   *>          = 'S':  do backward transformation for scaling only;
   *>          = 'B':  do backward transformations for both permutation and
   *>                  scaling.
   *>          JOB must be the same as the argument JOB supplied to DGGBAL.
   *> \endverbatim
   *>
   *> \param[in] SIDE
   *> \verbatim
   *>          SIDE is CHARACTER*1
   *>          = 'R':  V contains right eigenvectors;
   *>          = 'L':  V contains left eigenvectors.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The number of rows of the matrix V.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] ILO
   *> \verbatim
   *>          ILO is INTEGER
   *> \endverbatim
   *>
   *> \param[in] IHI
   *> \verbatim
   *>          IHI is INTEGER
   *>          The integers ILO and IHI determined by DGGBAL.
   *>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
   *> \endverbatim
   *>
   *> \param[in] LSCALE
   *> \verbatim
   *>          LSCALE is DOUBLE PRECISION array, dimension (N)
   *>          Details of the permutations and/or scaling factors applied
   *>          to the left side of A and B, as returned by DGGBAL.
   *> \endverbatim
   *>
   *> \param[in] RSCALE
   *> \verbatim
   *>          RSCALE is DOUBLE PRECISION array, dimension (N)
   *>          Details of the permutations and/or scaling factors applied
   *>          to the right side of A and B, as returned by DGGBAL.
   *> \endverbatim
   *>
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of columns of the matrix V.  M >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] V
   *> \verbatim
   *>          V is DOUBLE PRECISION array, dimension (LDV,M)
   *>          On entry, the matrix of right or left eigenvectors to be
   *>          transformed, as returned by DTGEVC.
   *>          On exit, V is overwritten by the transformed eigenvectors.
   *> \endverbatim
   *>
   *> \param[in] LDV
   *> \verbatim
   *>          LDV is INTEGER
   *>          The leading dimension of the matrix V. LDV >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit.
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleGBcomputational
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  See R.C. Ward, Balancing the generalized eigenvalue problem,
   *>                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,        SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
      $                   LDV, INFO )       $                   LDV, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational 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..--
 *     November 2006  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOB, SIDE        CHARACTER          JOB, SIDE
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       DOUBLE PRECISION   LSCALE( * ), RSCALE( * ), V( LDV, * )        DOUBLE PRECISION   LSCALE( * ), RSCALE( * ), V( LDV, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DGGBAK forms the right or left eigenvectors of a real generalized  
 *  eigenvalue problem A*x = lambda*B*x, by backward transformation on  
 *  the computed eigenvectors of the balanced pair of matrices output by  
 *  DGGBAL.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  JOB     (input) CHARACTER*1  
 *          Specifies the type of backward transformation required:  
 *          = 'N':  do nothing, return immediately;  
 *          = 'P':  do backward transformation for permutation only;  
 *          = 'S':  do backward transformation for scaling only;  
 *          = 'B':  do backward transformations for both permutation and  
 *                  scaling.  
 *          JOB must be the same as the argument JOB supplied to DGGBAL.  
 *  
 *  SIDE    (input) CHARACTER*1  
 *          = 'R':  V contains right eigenvectors;  
 *          = 'L':  V contains left eigenvectors.  
 *  
 *  N       (input) INTEGER  
 *          The number of rows of the matrix V.  N >= 0.  
 *  
 *  ILO     (input) INTEGER  
 *  IHI     (input) INTEGER  
 *          The integers ILO and IHI determined by DGGBAL.  
 *          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.  
 *  
 *  LSCALE  (input) DOUBLE PRECISION array, dimension (N)  
 *          Details of the permutations and/or scaling factors applied  
 *          to the left side of A and B, as returned by DGGBAL.  
 *  
 *  RSCALE  (input) DOUBLE PRECISION array, dimension (N)  
 *          Details of the permutations and/or scaling factors applied  
 *          to the right side of A and B, as returned by DGGBAL.  
 *  
 *  M       (input) INTEGER  
 *          The number of columns of the matrix V.  M >= 0.  
 *  
 *  V       (input/output) DOUBLE PRECISION array, dimension (LDV,M)  
 *          On entry, the matrix of right or left eigenvectors to be  
 *          transformed, as returned by DTGEVC.  
 *          On exit, V is overwritten by the transformed eigenvectors.  
 *  
 *  LDV     (input) INTEGER  
 *          The leading dimension of the matrix V. LDV >= max(1,N).  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit.  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  See R.C. Ward, Balancing the generalized eigenvalue problem,  
 *                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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