dgebak.f

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*> \brief \b DGEBAK
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
*                          INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          JOB, SIDE
*       INTEGER            IHI, ILO, INFO, LDV, M, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   SCALE( * ), V( LDV, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DGEBAK forms the right or left eigenvectors of a real general matrix
*> by backward transformation on the computed eigenvectors of the
*> balanced matrix output by DGEBAL.
*> \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 DGEBAL.
*> \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 DGEBAL.
*>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
*> \endverbatim
*>
*> \param[in] SCALE
*> \verbatim
*>          SCALE is DOUBLE PRECISION array, dimension (N)
*>          Details of the permutation and scaling factors, as returned
*>          by DGEBAL.
*> \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 DHSEIN or DTREVC.
*>          On exit, V is overwritten by the transformed eigenvectors.
*> \endverbatim
*>
*> \param[in] LDV
*> \verbatim
*>          LDV is INTEGER
*>          The leading dimension of the array 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 gebak
*
*  =====================================================================
      SUBROUTINE dgebak( JOB, SIDE, N, ILO, IHI, SCALE, 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 ..
      DOUBLE PRECISION   SCALE( * ), V( LDV, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE
      parameter( one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LEFTV, RIGHTV
      INTEGER            I, II, K
      DOUBLE PRECISION   S
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           dscal, dswap, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Decode and 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 .OR. ilo.GT.max( 1, n ) ) THEN
         info = -4
      ELSE IF( ihi.LT.min( ilo, n ) .OR. ihi.GT.n ) THEN
         info = -5
      ELSE IF( m.LT.0 ) THEN
         info = -7
      ELSE IF( ldv.LT.max( 1, n ) ) THEN
         info = -9
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DGEBAK', -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
*
         IF( rightv ) THEN
            DO 10 i = ilo, ihi
               s = scale( i )
               CALL dscal( m, s, v( i, 1 ), ldv )
   10       CONTINUE
         END IF
*
         IF( leftv ) THEN
            DO 20 i = ilo, ihi
               s = one / scale( i )
               CALL dscal( m, s, v( i, 1 ), ldv )
   20       CONTINUE
         END IF
*
      END IF
*
*     Backward permutation
*
*     For  I = ILO-1 step -1 until 1,
*              IHI+1 step 1 until N do --
*
   30 CONTINUE
      IF( lsame( job, 'P' ) .OR. lsame( job, 'B' ) ) THEN
         IF( rightv ) THEN
            DO 40 ii = 1, n
               i = ii
               IF( i.GE.ilo .AND. i.LE.ihi )
     $            GO TO 40
               IF( i.LT.ilo )
     $            i = ilo - ii
               k = int( scale( i ) )
               IF( k.EQ.i )
     $            GO TO 40
               CALL dswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
   40       CONTINUE
         END IF
*
         IF( leftv ) THEN
            DO 50 ii = 1, n
               i = ii
               IF( i.GE.ilo .AND. i.LE.ihi )
     $            GO TO 50
               IF( i.LT.ilo )
     $            i = ilo - ii
               k = int( scale( i ) )
               IF( k.EQ.i )
     $            GO TO 50
               CALL dswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
   50       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of DGEBAK
*
      END