*> \brief \b SGGBAK
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE SGGBAK( 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 ..
*       REAL               LSCALE( * ), RSCALE( * ), V( LDV, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SGGBAK 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
*> SGGBAL.
*> \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 SGGBAL.
*> \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 SGGBAL.
*>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
*> \endverbatim
*>
*> \param[in] LSCALE
*> \verbatim
*>          LSCALE is REAL array, dimension (N)
*>          Details of the permutations and/or scaling factors applied
*>          to the left side of A and B, as returned by SGGBAL.
*> \endverbatim
*>
*> \param[in] RSCALE
*> \verbatim
*>          RSCALE is REAL array, dimension (N)
*>          Details of the permutations and/or scaling factors applied
*>          to the right side of A and B, as returned by SGGBAL.
*> \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 REAL array, dimension (LDV,M)
*>          On entry, the matrix of right or left eigenvectors to be
*>          transformed, as returned by STGEVC.
*>          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.
*
*> \ingroup realGBcomputational
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*>
*>  See R.C. Ward, Balancing the generalized eigenvalue problem,
*>                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE SGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
     $                   LDV, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          JOB, SIDE
      INTEGER            IHI, ILO, INFO, LDV, M, N
*     ..
*     .. Array Arguments ..
      REAL               LSCALE( * ), RSCALE( * ), V( LDV, * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            LEFTV, RIGHTV
      INTEGER            I, K
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           SSCAL, SSWAP, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters
*
      RIGHTV = LSAME( SIDE, 'R' )
      LEFTV = LSAME( SIDE, 'L' )
*
      INFO = 0
      IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND.
     $    .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN
         INFO = -1
      ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( ILO.LT.1 ) THEN
         INFO = -4
      ELSE IF( N.EQ.0 .AND. IHI.EQ.0 .AND. ILO.NE.1 ) THEN
         INFO = -4
      ELSE IF( N.GT.0 .AND. ( IHI.LT.ILO .OR. IHI.GT.MAX( 1, N ) ) )
     $   THEN
         INFO = -5
      ELSE IF( N.EQ.0 .AND. ILO.EQ.1 .AND. IHI.NE.0 ) THEN
         INFO = -5
      ELSE IF( M.LT.0 ) THEN
         INFO = -8
      ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
         INFO = -10
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'SGGBAK', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
      IF( M.EQ.0 )
     $   RETURN
      IF( LSAME( JOB, 'N' ) )
     $   RETURN
*
      IF( ILO.EQ.IHI )
     $   GO TO 30
*
*     Backward balance
*
      IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN
*
*        Backward transformation on right eigenvectors
*
         IF( RIGHTV ) THEN
            DO 10 I = ILO, IHI
               CALL SSCAL( M, RSCALE( I ), V( I, 1 ), LDV )
   10       CONTINUE
         END IF
*
*        Backward transformation on left eigenvectors
*
         IF( LEFTV ) THEN
            DO 20 I = ILO, IHI
               CALL SSCAL( M, LSCALE( I ), V( I, 1 ), LDV )
   20       CONTINUE
         END IF
      END IF
*
*     Backward permutation
*
   30 CONTINUE
      IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN
*
*        Backward permutation on right eigenvectors
*
         IF( RIGHTV ) THEN
            IF( ILO.EQ.1 )
     $         GO TO 50
*
            DO 40 I = ILO - 1, 1, -1
               K = INT( RSCALE( I ) )
               IF( K.EQ.I )
     $            GO TO 40
               CALL SSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
   40       CONTINUE
*
   50       CONTINUE
            IF( IHI.EQ.N )
     $         GO TO 70
            DO 60 I = IHI + 1, N
               K = INT( RSCALE( I ) )
               IF( K.EQ.I )
     $            GO TO 60
               CALL SSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
   60       CONTINUE
         END IF
*
*        Backward permutation on left eigenvectors
*
   70    CONTINUE
         IF( LEFTV ) THEN
            IF( ILO.EQ.1 )
     $         GO TO 90
            DO 80 I = ILO - 1, 1, -1
               K = INT( LSCALE( I ) )
               IF( K.EQ.I )
     $            GO TO 80
               CALL SSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
   80       CONTINUE
*
   90       CONTINUE
            IF( IHI.EQ.N )
     $         GO TO 110
            DO 100 I = IHI + 1, N
               K = INT( LSCALE( I ) )
               IF( K.EQ.I )
     $            GO TO 100
               CALL SSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
  100       CONTINUE
         END IF
      END IF
*
  110 CONTINUE
*
      RETURN
*
*     End of SGGBAK
*
      END
