sggbak.f

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*> \brief \b SGGBAK
*
*  =========== DOCUMENTATION ===========
*
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*            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. 
*
*> \date November 2011
*
*> \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 (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. 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 = 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 = 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 = 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 = 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