          SUBROUTINE CGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
         $                  SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
         $                  LWORK, RWORK, BWORK, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBVSL, JOBVSR, SORT
          INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
    *     ..
    *     .. Array Arguments ..
          LOGICAL            BWORK( * )
          REAL               RWORK( * )
          COMPLEX            A( LDA, * ), ALPHA( * ), B( LDB, * ),
         $                   BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
         $                   WORK( * )
    *     ..
    *     .. Function Arguments ..
          LOGICAL            SELCTG
          EXTERNAL           SELCTG
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CGGES computes for a pair of N-by-N complex nonsymmetric matrices
    *  (A,B), the generalized eigenvalues, the generalized complex Schur
    *  form (S, T), and optionally left and/or right Schur vectors (VSL
    *  and VSR). This gives the generalized Schur factorization
    *
    *          (A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )
    *
    *  where (VSR)**H is the conjugate-transpose of VSR.
    *
    *  Optionally, it also orders the eigenvalues so that a selected cluster
    *  of eigenvalues appears in the leading diagonal blocks of the upper
    *  triangular matrix S and the upper triangular matrix T. The leading
    *  columns of VSL and VSR then form an unitary basis for the
    *  corresponding left and right eigenspaces (deflating subspaces).
    *
    *  (If only the generalized eigenvalues are needed, use the driver
    *  CGGEV instead, which is faster.)
    *
    *  A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
    *  or a ratio alpha/beta = w, such that  A - w*B is singular.  It is
    *  usually represented as the pair (alpha,beta), as there is a
    *  reasonable interpretation for beta=0, and even for both being zero.
    *
    *  A pair of matrices (S,T) is in generalized complex Schur form if S
    *  and T are upper triangular and, in addition, the diagonal elements
    *  of T are non-negative real numbers.
    *
    *  Arguments
    *  =========
    *
    *  JOBVSL  (input) CHARACTER*1
    *          = 'N':  do not compute the left Schur vectors;
    *          = 'V':  compute the left Schur vectors.
    *
    *  JOBVSR  (input) CHARACTER*1
    *          = 'N':  do not compute the right Schur vectors;
    *          = 'V':  compute the right Schur vectors.
    *
    *  SORT    (input) CHARACTER*1
    *          Specifies whether or not to order the eigenvalues on the
    *          diagonal of the generalized Schur form.
    *          = 'N':  Eigenvalues are not ordered;
    *          = 'S':  Eigenvalues are ordered (see SELCTG).
    *
    *  SELCTG  (external procedure) LOGICAL FUNCTION of two COMPLEX arguments
    *          SELCTG must be declared EXTERNAL in the calling subroutine.
    *          If SORT = 'N', SELCTG is not referenced.
    *          If SORT = 'S', SELCTG is used to select eigenvalues to sort
    *          to the top left of the Schur form.
    *          An eigenvalue ALPHA(j)/BETA(j) is selected if
    *          SELCTG(ALPHA(j),BETA(j)) is true.
    *
    *          Note that a selected complex eigenvalue may no longer satisfy
    *          SELCTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since
    *          ordering may change the value of complex eigenvalues
    *          (especially if the eigenvalue is ill-conditioned), in this
    *          case INFO is set to N+2 (See INFO below).
    *
    *  N       (input) INTEGER
    *          The order of the matrices A, B, VSL, and VSR.  N >= 0.
    *
    *  A       (input/output) COMPLEX array, dimension (LDA, N)
    *          On entry, the first of the pair of matrices.
    *          On exit, A has been overwritten by its generalized Schur
    *          form S.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of A.  LDA >= max(1,N).
    *
    *  B       (input/output) COMPLEX array, dimension (LDB, N)
    *          On entry, the second of the pair of matrices.
    *          On exit, B has been overwritten by its generalized Schur
    *          form T.
    *
    *  LDB     (input) INTEGER
    *          The leading dimension of B.  LDB >= max(1,N).
    *
    *  SDIM    (output) INTEGER
    *          If SORT = 'N', SDIM = 0.
    *          If SORT = 'S', SDIM = number of eigenvalues (after sorting)
    *          for which SELCTG is true.
    *
    *  ALPHA   (output) COMPLEX array, dimension (N)
    *  BETA    (output) COMPLEX array, dimension (N)
    *          On exit,  ALPHA(j)/BETA(j), j=1,...,N, will be the
    *          generalized eigenvalues.  ALPHA(j), j=1,...,N  and  BETA(j),
    *          j=1,...,N  are the diagonals of the complex Schur form (A,B)
    *          output by CGGES. The  BETA(j) will be non-negative real.
    *
    *          Note: the quotients ALPHA(j)/BETA(j) may easily over- or
    *          underflow, and BETA(j) may even be zero.  Thus, the user
    *          should avoid naively computing the ratio alpha/beta.
    *          However, ALPHA will be always less than and usually
    *          comparable with norm(A) in magnitude, and BETA always less
    *          than and usually comparable with norm(B).
    *
    *  VSL     (output) COMPLEX array, dimension (LDVSL,N)
    *          If JOBVSL = 'V', VSL will contain the left Schur vectors.
    *          Not referenced if JOBVSL = 'N'.
    *
    *  LDVSL   (input) INTEGER
    *          The leading dimension of the matrix VSL. LDVSL >= 1, and
    *          if JOBVSL = 'V', LDVSL >= N.
    *
    *  VSR     (output) COMPLEX array, dimension (LDVSR,N)
    *          If JOBVSR = 'V', VSR will contain the right Schur vectors.
    *          Not referenced if JOBVSR = 'N'.
    *
    *  LDVSR   (input) INTEGER
    *          The leading dimension of the matrix VSR. LDVSR >= 1, and
    *          if JOBVSR = 'V', LDVSR >= N.
    *
    *  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) INTEGER
    *          The dimension of the array WORK.  LWORK >= max(1,2*N).
    *          For good performance, LWORK must generally be larger.
    *
    *          If LWORK = -1, then a workspace query is assumed; the routine
    *          only calculates the optimal size of the WORK array, returns
    *          this value as the first entry of the WORK array, and no error
    *          message related to LWORK is issued by XERBLA.
    *
    *  RWORK   (workspace) REAL array, dimension (8*N)
    *
    *  BWORK   (workspace) LOGICAL array, dimension (N)
    *          Not referenced if SORT = 'N'.
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value.
    *          =1,...,N:
    *                The QZ iteration failed.  (A,B) are not in Schur
    *                form, but ALPHA(j) and BETA(j) should be correct for
    *                j=INFO+1,...,N.
    *          > N:  =N+1: other than QZ iteration failed in CHGEQZ
    *                =N+2: after reordering, roundoff changed values of
    *                      some complex eigenvalues so that leading
    *                      eigenvalues in the Generalized Schur form no
    *                      longer satisfy SELCTG=.TRUE.  This could also
    *                      be caused due to scaling.
    *                =N+3: reordering falied in CTGSEN.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ZERO, ONE
          PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
          COMPLEX            CZERO, CONE
          PARAMETER          ( CZERO = ( 0.0E0, 0.0E0 ),
         $                   CONE = ( 1.0E0, 0.0E0 ) )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
         $                   LQUERY, WANTST
          INTEGER            I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT,
         $                   ILO, IRIGHT, IROWS, IRWRK, ITAU, IWRK, LWKMIN,
         $                   LWKOPT
          REAL               ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL,
         $                   PVSR, SMLNUM
    *     ..
    *     .. Local Arrays ..
          INTEGER            IDUM( 1 )
          REAL               DIF( 2 )
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CGEQRF, CGGBAK, CGGBAL, CGGHRD, CHGEQZ, CLACPY,
         $                   CLASCL, CLASET, CTGSEN, CUNGQR, CUNMQR, SLABAD,
         $                   XERBLA
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          REAL               CLANGE, SLAMCH
          EXTERNAL           LSAME, ILAENV, CLANGE, SLAMCH
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, SQRT
    *     ..
    *     .. Executable Statements ..
    *
    *     Decode the input arguments
    *
          IF( LSAME( JOBVSL, 'N' ) ) THEN
             IJOBVL = 1
             ILVSL = .FALSE.
          ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN
             IJOBVL = 2
             ILVSL = .TRUE.
          ELSE
             IJOBVL = -1
             ILVSL = .FALSE.
          END IF
    *
          IF( LSAME( JOBVSR, 'N' ) ) THEN
             IJOBVR = 1
             ILVSR = .FALSE.
          ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN
             IJOBVR = 2
             ILVSR = .TRUE.
          ELSE
             IJOBVR = -1
             ILVSR = .FALSE.
          END IF
    *
          WANTST = LSAME( SORT, 'S' )
    *
    *     Test the input arguments
    *
          INFO = 0
          LQUERY = ( LWORK.EQ.-1 )
          IF( IJOBVL.LE.0 ) THEN
             INFO = -1
          ELSE IF( IJOBVR.LE.0 ) THEN
             INFO = -2
          ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.LSAME( SORT, 'N' ) ) ) THEN
             INFO = -3
          ELSE IF( N.LT.0 ) THEN
             INFO = -5
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -7
          ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
             INFO = -9
          ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
             INFO = -14
          ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
             INFO = -16
          END IF
    *
    *     Compute workspace
    *      (Note: Comments in the code beginning "Workspace:" describe the
    *       minimal amount of workspace needed at that point in the code,
    *       as well as the preferred amount for good performance.
    *       NB refers to the optimal block size for the immediately
    *       following subroutine, as returned by ILAENV.)
    *
          IF( INFO.EQ.0 ) THEN
             LWKMIN = MAX( 1, 2*N )
             LWKOPT = MAX( 1, N + N*ILAENV( 1, 'CGEQRF', ' ', N, 1, N, 0 ) )
             LWKOPT = MAX( LWKOPT, N +
         $                 N*ILAENV( 1, 'CUNMQR', ' ', N, 1, N, -1 ) )
             IF( ILVSL ) THEN
                LWKOPT = MAX( LWKOPT, N +
         $                    N*ILAENV( 1, 'CUNGQR', ' ', N, 1, N, -1 ) )
             END IF
             WORK( 1 ) = LWKOPT
    *
             IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY )
         $      INFO = -18
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'CGGES ', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 ) THEN
             SDIM = 0
             RETURN
          END IF
    *
    *     Get machine constants
    *
          EPS = SLAMCH( 'P' )
          SMLNUM = SLAMCH( 'S' )
          BIGNUM = ONE / SMLNUM
          CALL SLABAD( SMLNUM, BIGNUM )
          SMLNUM = SQRT( SMLNUM ) / EPS
          BIGNUM = ONE / SMLNUM
    *
    *     Scale A if max element outside range [SMLNUM,BIGNUM]
    *
          ANRM = CLANGE( 'M', N, N, A, LDA, RWORK )
          ILASCL = .FALSE.
          IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
             ANRMTO = SMLNUM
             ILASCL = .TRUE.
          ELSE IF( ANRM.GT.BIGNUM ) THEN
             ANRMTO = BIGNUM
             ILASCL = .TRUE.
          END IF
    *
          IF( ILASCL )
         $   CALL CLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
    *
    *     Scale B if max element outside range [SMLNUM,BIGNUM]
    *
          BNRM = CLANGE( 'M', N, N, B, LDB, RWORK )
          ILBSCL = .FALSE.
          IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
             BNRMTO = SMLNUM
             ILBSCL = .TRUE.
          ELSE IF( BNRM.GT.BIGNUM ) THEN
             BNRMTO = BIGNUM
             ILBSCL = .TRUE.
          END IF
    *
          IF( ILBSCL )
         $   CALL CLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
    *
    *     Permute the matrix to make it more nearly triangular
    *     (Real Workspace: need 6*N)
    *
          ILEFT = 1
          IRIGHT = N + 1
          IRWRK = IRIGHT + N
          CALL CGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
         $             RWORK( IRIGHT ), RWORK( IRWRK ), IERR )
    *
    *     Reduce B to triangular form (QR decomposition of B)
    *     (Complex Workspace: need N, prefer N*NB)
    *
          IROWS = IHI + 1 - ILO
          ICOLS = N + 1 - ILO
          ITAU = 1
          IWRK = ITAU + IROWS
          CALL CGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
         $             WORK( IWRK ), LWORK+1-IWRK, IERR )
    *
    *     Apply the orthogonal transformation to matrix A
    *     (Complex Workspace: need N, prefer N*NB)
    *
          CALL CUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
         $             WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
         $             LWORK+1-IWRK, IERR )
    *
    *     Initialize VSL
    *     (Complex Workspace: need N, prefer N*NB)
    *
          IF( ILVSL ) THEN
             CALL CLASET( 'Full', N, N, CZERO, CONE, VSL, LDVSL )
             IF( IROWS.GT.1 ) THEN
                CALL CLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
         $                   VSL( ILO+1, ILO ), LDVSL )
             END IF
             CALL CUNGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
         $                WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
          END IF
    *
    *     Initialize VSR
    *
          IF( ILVSR )
         $   CALL CLASET( 'Full', N, N, CZERO, CONE, VSR, LDVSR )
    *
    *     Reduce to generalized Hessenberg form
    *     (Workspace: none needed)
    *
          CALL CGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
         $             LDVSL, VSR, LDVSR, IERR )
    *
          SDIM = 0
    *
    *     Perform QZ algorithm, computing Schur vectors if desired
    *     (Complex Workspace: need N)
    *     (Real Workspace: need N)
    *
          IWRK = ITAU
          CALL CHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
         $             ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK( IWRK ),
         $             LWORK+1-IWRK, RWORK( IRWRK ), IERR )
          IF( IERR.NE.0 ) THEN
             IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
                INFO = IERR
             ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
                INFO = IERR - N
             ELSE
                INFO = N + 1
             END IF
             GO TO 30
          END IF
    *
    *     Sort eigenvalues ALPHA/BETA if desired
    *     (Workspace: none needed)
    *
          IF( WANTST ) THEN
    *
    *        Undo scaling on eigenvalues before selecting
    *
             IF( ILASCL )
         $      CALL CLASCL( 'G', 0, 0, ANRM, ANRMTO, N, 1, ALPHA, N, IERR )
             IF( ILBSCL )
         $      CALL CLASCL( 'G', 0, 0, BNRM, BNRMTO, N, 1, BETA, N, IERR )
    *
    *        Select eigenvalues
    *
             DO 10 I = 1, N
                BWORK( I ) = SELCTG( ALPHA( I ), BETA( I ) )
       10    CONTINUE
    *
             CALL CTGSEN( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB, ALPHA,
         $                BETA, VSL, LDVSL, VSR, LDVSR, SDIM, PVSL, PVSR,
         $                DIF, WORK( IWRK ), LWORK-IWRK+1, IDUM, 1, IERR )
             IF( IERR.EQ.1 )
         $      INFO = N + 3
    *
          END IF
    *
    *     Apply back-permutation to VSL and VSR
    *     (Workspace: none needed)
    *
          IF( ILVSL )
         $   CALL CGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
         $                RWORK( IRIGHT ), N, VSL, LDVSL, IERR )
          IF( ILVSR )
         $   CALL CGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
         $                RWORK( IRIGHT ), N, VSR, LDVSR, IERR )
    *
    *     Undo scaling
    *
          IF( ILASCL ) THEN
             CALL CLASCL( 'U', 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR )
             CALL CLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )
          END IF
    *
          IF( ILBSCL ) THEN
             CALL CLASCL( 'U', 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR )
             CALL CLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
          END IF
    *
          IF( WANTST ) THEN
    *
    *        Check if reordering is correct
    *
             LASTSL = .TRUE.
             SDIM = 0
             DO 20 I = 1, N
                CURSL = SELCTG( ALPHA( I ), BETA( I ) )
                IF( CURSL )
         $         SDIM = SDIM + 1
                IF( CURSL .AND. .NOT.LASTSL )
         $         INFO = N + 2
                LASTSL = CURSL
       20    CONTINUE
    *
          END IF
    *
       30 CONTINUE
    *
          WORK( 1 ) = LWKOPT
    *
          RETURN
    *
    *     End of CGGES
    *
          END