*> \brief \b DGGBAK * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DGGBAK + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DGGBAK( 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 .. * DOUBLE PRECISION LSCALE( * ), RSCALE( * ), V( LDV, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGGBAK 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 *> DGGBAL. *> \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 DGGBAL. *> \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 DGGBAL. *> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. *> \endverbatim *> *> \param[in] LSCALE *> \verbatim *> LSCALE is DOUBLE PRECISION array, dimension (N) *> Details of the permutations and/or scaling factors applied *> to the left side of A and B, as returned by DGGBAL. *> \endverbatim *> *> \param[in] RSCALE *> \verbatim *> RSCALE is DOUBLE PRECISION array, dimension (N) *> Details of the permutations and/or scaling factors applied *> to the right side of A and B, as returned by DGGBAL. *> \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 DTGEVC. *> 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. * *> \ingroup doubleGBcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> See R.C. Ward, Balancing the generalized eigenvalue problem, *> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152. *> \endverbatim *> * ===================================================================== SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, 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 LSCALE( * ), RSCALE( * ), V( LDV, * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL LEFTV, RIGHTV INTEGER I, K * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DSCAL, DSWAP, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, INT * .. * .. 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( 'DGGBAK', -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 DSCAL( 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 DSCAL( 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 = INT(RSCALE( I )) IF( K.EQ.I ) $ GO TO 40 CALL DSWAP( 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 = INT(RSCALE( I )) IF( K.EQ.I ) $ GO TO 60 CALL DSWAP( 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 = INT(LSCALE( I )) IF( K.EQ.I ) $ GO TO 80 CALL DSWAP( 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 = INT(LSCALE( I )) IF( K.EQ.I ) $ GO TO 100 CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV ) 100 CONTINUE END IF END IF * 110 CONTINUE * RETURN * * End of DGGBAK * END