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*> \brief \b SGGBAK
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SGGBAK + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sggbak.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sggbak.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sggbak.f">
*> [TXT]</a>
*> \endhtmlonly
*
* 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
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