SUBROUTINE DGGES( JOBVSL, JOBVSR, SORT, DELCTG, N, A, LDA, B, LDB,
     $                  SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR,
     $                  LDVSR, WORK, LWORK, BWORK, INFO )
*
*  -- LAPACK driver routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          JOBVSL, JOBVSR, SORT
      INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
*     ..
*     .. Array Arguments ..
      LOGICAL            BWORK( * )
      DOUBLE PRECISION   A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
     $                   B( LDB, * ), BETA( * ), VSL( LDVSL, * ),
     $                   VSR( LDVSR, * ), WORK( * )
*     ..
*     .. Function Arguments ..
      LOGICAL            DELCTG
      EXTERNAL           DELCTG
*     ..
*
*  Purpose
*  =======
*
*  DGGES computes for a pair of N-by-N real nonsymmetric matrices (A,B),
*  the generalized eigenvalues, the generalized real Schur form (S,T),
*  optionally, the left and/or right matrices of Schur vectors (VSL and
*  VSR). This gives the generalized Schur factorization
*
*           (A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T )
*
*  Optionally, it also orders the eigenvalues so that a selected cluster
*  of eigenvalues appears in the leading diagonal blocks of the upper
*  quasi-triangular matrix S and the upper triangular matrix T.The
*  leading columns of VSL and VSR then form an orthonormal basis for the
*  corresponding left and right eigenspaces (deflating subspaces).
*
*  (If only the generalized eigenvalues are needed, use the driver
*  DGGEV 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 or both being zero.
*
*  A pair of matrices (S,T) is in generalized real Schur form if T is
*  upper triangular with non-negative diagonal and S is block upper
*  triangular with 1-by-1 and 2-by-2 blocks.  1-by-1 blocks correspond
*  to real generalized eigenvalues, while 2-by-2 blocks of S will be
*  "standardized" by making the corresponding elements of T have the
*  form:
*          [  a  0  ]
*          [  0  b  ]
*
*  and the pair of corresponding 2-by-2 blocks in S and T will have a
*  complex conjugate pair of generalized eigenvalues.
*
*
*  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 DELZTG);
*
*  DELZTG  (input) LOGICAL FUNCTION of three DOUBLE PRECISION arguments
*          DELZTG must be declared EXTERNAL in the calling subroutine.
*          If SORT = 'N', DELZTG is not referenced.
*          If SORT = 'S', DELZTG is used to select eigenvalues to sort
*          to the top left of the Schur form.
*          An eigenvalue (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if
*          DELZTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either
*          one of a complex conjugate pair of eigenvalues is selected,
*          then both complex eigenvalues are selected.
*
*          Note that in the ill-conditioned case, a selected complex
*          eigenvalue may no longer satisfy DELZTG(ALPHAR(j),ALPHAI(j),
*          BETA(j)) = .TRUE. after ordering. INFO is to be set to N+2
*          in this case.
*
*  N       (input) INTEGER
*          The order of the matrices A, B, VSL, and VSR.  N >= 0.
*
*  A       (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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 DELZTG is true.  (Complex conjugate pairs for which
*          DELZTG is true for either eigenvalue count as 2.)
*
*  ALPHAR  (output) DOUBLE PRECISION array, dimension (N)
*  ALPHAI  (output) DOUBLE PRECISION array, dimension (N)
*  BETA    (output) DOUBLE PRECISION array, dimension (N)
*          On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
*          be the generalized eigenvalues.  ALPHAR(j) + ALPHAI(j)*i,
*          and  BETA(j),j=1,...,N are the diagonals of the complex Schur
*          form (S,T) that would result if the 2-by-2 diagonal blocks of
*          the real Schur form of (A,B) were further reduced to
*          triangular form using 2-by-2 complex unitary transformations.
*          If ALPHAI(j) is zero, then the j-th eigenvalue is real; if
*          positive, then the j-th and (j+1)-st eigenvalues are a
*          complex conjugate pair, with ALPHAI(j+1) negative.
*
*          Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
*          may easily over- or underflow, and BETA(j) may even be zero.
*          Thus, the user should avoid naively computing the ratio.
*          However, ALPHAR and ALPHAI 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.  LWORK >= 8*N+16.
*
*          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.
*
*  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 ALPHAR(j), ALPHAI(j), and BETA(j) should
*                be correct for j=INFO+1,...,N.
*          > N:  =N+1: other than QZ iteration failed in DHGEQZ.
*                =N+2: after reordering, roundoff changed values of
*                      some complex eigenvalues so that leading
*                      eigenvalues in the Generalized Schur form no
*                      longer satisfy DELZTG=.TRUE.  This could also
*                      be caused due to scaling.
*                =N+3: reordering failed in DTGSEN.
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
     $                   LQUERY, LST2SL, WANTST
      INTEGER            I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT,
     $                   ILO, IP, IRIGHT, IROWS, ITAU, IWRK, MAXWRK,
     $                   MINWRK
      DOUBLE PRECISION   ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL,
     $                   PVSR, SAFMAX, SAFMIN, SMLNUM
*     ..
*     .. Local Arrays ..
      INTEGER            IDUM( 1 )
      DOUBLE PRECISION   DIF( 2 )
*     ..
*     .. External Subroutines ..
      EXTERNAL           DGEQRF, DGGBAK, DGGBAL, DGGHRD, DHGEQZ, DLABAD,
     $                   DLACPY, DLASCL, DLASET, DORGQR, DORMQR, DTGSEN,
     $                   XERBLA
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      DOUBLE PRECISION   DLAMCH, DLANGE
      EXTERNAL           LSAME, ILAENV, DLAMCH, DLANGE
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, 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 = -15
      ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
         INFO = -17
      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.)
*
      MINWRK = 1
      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
         MINWRK = 7*( N+1 ) + 16