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304 lines
8.1 KiB
304 lines
8.1 KiB
*> \brief \b CGGBAK
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download CGGBAK + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cggbak.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cggbak.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cggbak.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
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* LDV, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER JOB, SIDE
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* INTEGER IHI, ILO, INFO, LDV, M, N
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* ..
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* .. Array Arguments ..
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* REAL LSCALE( * ), RSCALE( * )
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* COMPLEX V( LDV, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> CGGBAK forms the right or left eigenvectors of a complex generalized
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*> eigenvalue problem A*x = lambda*B*x, by backward transformation on
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*> the computed eigenvectors of the balanced pair of matrices output by
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*> CGGBAL.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] JOB
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*> \verbatim
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*> JOB is CHARACTER*1
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*> Specifies the type of backward transformation required:
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*> = 'N': do nothing, return immediately;
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*> = 'P': do backward transformation for permutation only;
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*> = 'S': do backward transformation for scaling only;
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*> = 'B': do backward transformations for both permutation and
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*> scaling.
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*> JOB must be the same as the argument JOB supplied to CGGBAL.
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*> \endverbatim
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*>
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*> \param[in] SIDE
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*> \verbatim
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*> SIDE is CHARACTER*1
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*> = 'R': V contains right eigenvectors;
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*> = 'L': V contains left eigenvectors.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of rows of the matrix V. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] ILO
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*> \verbatim
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*> ILO is INTEGER
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*> \endverbatim
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*>
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*> \param[in] IHI
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*> \verbatim
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*> IHI is INTEGER
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*> The integers ILO and IHI determined by CGGBAL.
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*> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
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*> \endverbatim
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*>
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*> \param[in] LSCALE
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*> \verbatim
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*> LSCALE is REAL array, dimension (N)
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*> Details of the permutations and/or scaling factors applied
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*> to the left side of A and B, as returned by CGGBAL.
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*> \endverbatim
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*>
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*> \param[in] RSCALE
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*> \verbatim
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*> RSCALE is REAL array, dimension (N)
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*> Details of the permutations and/or scaling factors applied
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*> to the right side of A and B, as returned by CGGBAL.
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*> \endverbatim
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*>
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of columns of the matrix V. M >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] V
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*> \verbatim
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*> V is COMPLEX array, dimension (LDV,M)
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*> On entry, the matrix of right or left eigenvectors to be
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*> transformed, as returned by CTGEVC.
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*> On exit, V is overwritten by the transformed eigenvectors.
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*> \endverbatim
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*>
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*> \param[in] LDV
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*> \verbatim
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*> LDV is INTEGER
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*> The leading dimension of the matrix V. LDV >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit.
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*> < 0: if INFO = -i, the i-th argument had an illegal value.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complexGBcomputational
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> See R.C. Ward, Balancing the generalized eigenvalue problem,
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*> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE CGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
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$ LDV, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER JOB, SIDE
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INTEGER IHI, ILO, INFO, LDV, M, N
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* ..
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* .. Array Arguments ..
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REAL LSCALE( * ), RSCALE( * )
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COMPLEX V( LDV, * )
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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LOGICAL LEFTV, RIGHTV
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INTEGER I, K
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL CSSCAL, CSWAP, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters
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*
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RIGHTV = LSAME( SIDE, 'R' )
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LEFTV = LSAME( SIDE, 'L' )
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*
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INFO = 0
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IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND.
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$ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( ILO.LT.1 ) THEN
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INFO = -4
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ELSE IF( N.EQ.0 .AND. IHI.EQ.0 .AND. ILO.NE.1 ) THEN
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INFO = -4
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ELSE IF( N.GT.0 .AND. ( IHI.LT.ILO .OR. IHI.GT.MAX( 1, N ) ) )
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$ THEN
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INFO = -5
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ELSE IF( N.EQ.0 .AND. ILO.EQ.1 .AND. IHI.NE.0 ) THEN
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INFO = -5
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ELSE IF( M.LT.0 ) THEN
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INFO = -8
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ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
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INFO = -10
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CGGBAK', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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IF( M.EQ.0 )
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$ RETURN
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IF( LSAME( JOB, 'N' ) )
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$ RETURN
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*
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IF( ILO.EQ.IHI )
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$ GO TO 30
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*
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* Backward balance
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*
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IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN
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*
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* Backward transformation on right eigenvectors
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*
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IF( RIGHTV ) THEN
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DO 10 I = ILO, IHI
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CALL CSSCAL( M, RSCALE( I ), V( I, 1 ), LDV )
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10 CONTINUE
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END IF
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*
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* Backward transformation on left eigenvectors
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*
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IF( LEFTV ) THEN
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DO 20 I = ILO, IHI
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CALL CSSCAL( M, LSCALE( I ), V( I, 1 ), LDV )
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20 CONTINUE
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END IF
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END IF
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*
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* Backward permutation
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*
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30 CONTINUE
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IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN
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*
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* Backward permutation on right eigenvectors
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*
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IF( RIGHTV ) THEN
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IF( ILO.EQ.1 )
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$ GO TO 50
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DO 40 I = ILO - 1, 1, -1
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K = INT( RSCALE( I ) )
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IF( K.EQ.I )
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$ GO TO 40
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CALL CSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
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40 CONTINUE
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*
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50 CONTINUE
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IF( IHI.EQ.N )
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$ GO TO 70
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DO 60 I = IHI + 1, N
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K = INT( RSCALE( I ) )
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IF( K.EQ.I )
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$ GO TO 60
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CALL CSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
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60 CONTINUE
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END IF
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*
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* Backward permutation on left eigenvectors
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*
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70 CONTINUE
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IF( LEFTV ) THEN
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IF( ILO.EQ.1 )
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$ GO TO 90
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DO 80 I = ILO - 1, 1, -1
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K = INT( LSCALE( I ) )
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IF( K.EQ.I )
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$ GO TO 80
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CALL CSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
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80 CONTINUE
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*
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90 CONTINUE
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IF( IHI.EQ.N )
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$ GO TO 110
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DO 100 I = IHI + 1, N
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K = INT( LSCALE( I ) )
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IF( K.EQ.I )
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$ GO TO 100
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CALL CSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
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100 CONTINUE
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END IF
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END IF
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*
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110 CONTINUE
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*
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RETURN
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*
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* End of CGGBAK
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*
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END
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