dgebak.F90 Source File


Source Code

#include "ESMF_LapackBlas.inc"
!> \brief \b DGEBAK
!
!  =========== DOCUMENTATION ===========
!
! Online html documentation available at
!            http://www.netlib.org/lapack/explore-html/
!
!> \htmlonly
!> Download DGEBAK + dependencies
!> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgebak.f">
!> [TGZ]</a>
!> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgebak.f">
!> [ZIP]</a>
!> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgebak.f">
!> [TXT]</a>
!> \endhtmlonly
!
!  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.
!
!> \date December 2016
!
!> \ingroup doubleGEcomputational
!
!  =====================================================================
      SUBROUTINE DGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, &
                         INFO )
!
!  -- LAPACK computational routine (version 3.7.0) --
!  -- LAPACK is a software package provided by Univ. of Tennessee,    --
!  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
!     December 2016
!
!     .. 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 = 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 = 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