sggesx.f

          SUBROUTINE SGGESX( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, LDA,
         $                   B, LDB, SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL,
         $                   VSR, LDVSR, RCONDE, RCONDV, WORK, LWORK, IWORK,
         $                   LIWORK, 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, SENSE, SORT
          INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LIWORK, LWORK, N,
         $                   SDIM
    *     ..
    *     .. Array Arguments ..
          LOGICAL            BWORK( * )
          INTEGER            IWORK( * )
          REAL               A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
         $                   B( LDB, * ), BETA( * ), RCONDE( 2 ),
         $                   RCONDV( 2 ), VSL( LDVSL, * ), VSR( LDVSR, * ),
         $                   WORK( * )
    *     ..
    *     .. Function Arguments ..
          LOGICAL            SELCTG
          EXTERNAL           SELCTG
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SGGESX computes for a pair of N-by-N real nonsymmetric matrices
    *  (A,B), the generalized eigenvalues, the real Schur form (S,T), and,
    *  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; computes
    *  a reciprocal condition number for the average of the selected
    *  eigenvalues (RCONDE); and computes a reciprocal condition number for
    *  the right and left deflating subspaces corresponding to the selected
    *  eigenvalues (RCONDV). The leading columns of VSL and VSR then form
    *  an orthonormal basis for the corresponding left and right eigenspaces
    *  (deflating subspaces).
    *
    *  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 for 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 SELCTG).
    *
    *  SELCTG  (external procedure) LOGICAL FUNCTION of three REAL 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 (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if
    *          SELCTG(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 a selected complex eigenvalue may no longer satisfy
    *          SELCTG(ALPHAR(j),ALPHAI(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+3.
    *
    *  SENSE   (input) CHARACTER*1
    *          Determines which reciprocal condition numbers are computed.
    *          = 'N' : None are computed;
    *          = 'E' : Computed for average of selected eigenvalues only;
    *          = 'V' : Computed for selected deflating subspaces only;
    *          = 'B' : Computed for both.
    *          If SENSE = 'E', 'V', or 'B', SORT must equal 'S'.
    *
    *  N       (input) INTEGER
    *          The order of the matrices A, B, VSL, and VSR.  N >= 0.
    *
    *  A       (input/output) REAL 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) REAL 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.  (Complex conjugate pairs for which
    *          SELCTG is true for either eigenvalue count as 2.)
    *
    *  ALPHAR  (output) REAL array, dimension (N)
    *  ALPHAI  (output) REAL array, dimension (N)
    *  BETA    (output) REAL 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) REAL 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) REAL 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.
    *
    *  RCONDE  (output) REAL array, dimension ( 2 )
    *          If SENSE = 'E' or 'B', RCONDE(1) and RCONDE(2) contain the
    *          reciprocal condition numbers for the average of the selected
    *          eigenvalues.
    *          Not referenced if SENSE = 'N' or 'V'.
    *
    *  RCONDV  (output) REAL array, dimension ( 2 )
    *          If SENSE = 'V' or 'B', RCONDV(1) and RCONDV(2) contain the
    *          reciprocal condition numbers for the selected deflating
    *          subspaces.
    *          Not referenced if SENSE = 'N' or 'E'.
    *
    *  WORK    (workspace/output) REAL 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.
    *          If N = 0, LWORK >= 1, else if SENSE = 'E', 'V', or 'B',
    *          LWORK >= max( 8*N, 6*N+16, 2*SDIM*(N-SDIM) ), else
    *          LWORK >= max( 8*N, 6*N+16 ).
    *          Note that 2*SDIM*(N-SDIM) <= N*N/2.
    *          Note also that an error is only returned if
    *          LWORK < max( 8*N, 6*N+16), but if SENSE = 'E' or 'V' or 'B'
    *          this may not be large enough.
    *
    *          If LWORK = -1, then a workspace query is assumed; the routine
    *          only calculates the bound on the optimal size of the WORK
    *          array and the minimum size of the IWORK array, returns these
    *          values as the first entries of the WORK and IWORK arrays, and
    *          no error message related to LWORK or LIWORK is issued by
    *          XERBLA.
    *
    *  IWORK   (workspace) INTEGER array, dimension (MAX(1,LIWORK))
    *          On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK.
    *
    *  LIWORK  (input) INTEGER
    *          The dimension of the array IWORK.
    *          If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise
    *          LIWORK >= N+6.
    *
    *          If LIWORK = -1, then a workspace query is assumed; the
    *          routine only calculates the bound on the optimal size of the
    *          WORK array and the minimum size of the IWORK array, returns
    *          these values as the first entries of the WORK and IWORK
    *          arrays, and no error message related to LWORK or LIWORK 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 SHGEQZ
    *                =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 failed in STGSEN.
    *
    *  Further details
    *  ===============
    *
    *  An approximate (asymptotic) bound on the average absolute error of
    *  the selected eigenvalues is
    *
    *       EPS * norm((A, B)) / RCONDE( 1 ).
    *
    *  An approximate (asymptotic) bound on the maximum angular error in
    *  the computed deflating subspaces is
    *
    *       EPS * norm((A, B)) / RCONDV( 2 ).
    *
    *  See LAPACK User's Guide, section 4.11 for more information.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ZERO, ONE
          PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
         $                   LQUERY, LST2SL, WANTSB, WANTSE, WANTSN, WANTST,
         $                   WANTSV
          INTEGER            I, ICOLS, IERR, IHI, IJOB, IJOBVL, IJOBVR,
         $                   ILEFT, ILO, IP, IRIGHT, IROWS, ITAU, IWRK,
         $                   LIWMIN, LWRK, MAXWRK, MINWRK
          REAL               ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PL,
         $                   PR, SAFMAX, SAFMIN, SMLNUM
    *     ..
    *     .. Local Arrays ..
          REAL               DIF( 2 )
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SGEQRF, SGGBAK, SGGBAL, SGGHRD, SHGEQZ, SLABAD,
         $                   SLACPY, SLASCL, SLASET, SORGQR, SORMQR, STGSEN,
         $                   XERBLA
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          REAL               SLAMCH, SLANGE
          EXTERNAL           LSAME, ILAENV, SLAMCH, SLANGE
    *     ..
    *     .. 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' )
          WANTSN = LSAME( SENSE, 'N' )
          WANTSE = LSAME( SENSE, 'E' )
          WANTSV = LSAME( SENSE, 'V' )
          WANTSB = LSAME( SENSE, 'B' )
          LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
          IF( WANTSN ) THEN
             IJOB = 0
          ELSE IF( WANTSE ) THEN
             IJOB = 1
          ELSE IF( WANTSV ) THEN
             IJOB = 2
          ELSE IF( WANTSB ) THEN
             IJOB = 4
          END IF
    *
    *     Test the input arguments
    *
          INFO = 0
          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( .NOT.( WANTSN .OR. WANTSE .OR. WANTSV .OR. WANTSB ) .OR.
         $         ( .NOT.WANTST .AND. .NOT.WANTSN ) ) THEN
             INFO = -5
          ELSE IF( N.LT.0 ) THEN
             INFO = -6
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -8
          ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
             INFO = -10
          ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
             INFO = -16
          ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
             INFO = -18
          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
             IF( N.GT.0) THEN
                MINWRK = MAX( 8*N, 6*N + 16 )
                MAXWRK = MINWRK - N +
         $               N*ILAENV( 1, 'SGEQRF', ' ', N, 1, N, 0 )
                MAXWRK = MAX( MAXWRK, MINWRK - N +
         $               N*ILAENV( 1, 'SORMQR', ' ', N, 1, N, -1 ) )
                IF( ILVSL ) THEN
                   MAXWRK = MAX( MAXWRK, MINWRK - N +
         $                  N*ILAENV( 1, 'SORGQR', ' ', N, 1, N, -1 ) )
                END IF
                LWRK = MAXWRK
                IF( IJOB.GE.1 )
         $         LWRK = MAX( LWRK, N*N/2 )
             ELSE
                MINWRK = 1
                MAXWRK = 1
                LWRK   = 1
             END IF
             WORK( 1 ) = LWRK
             IF( WANTSN .OR. N.EQ.0 ) THEN
                LIWMIN = 1
             ELSE
                LIWMIN = N + 6
             END IF
             IWORK( 1 ) = LIWMIN
    *
             IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
                INFO = -22
             ELSE IF( LIWORK.LT.LIWMIN  .AND. .NOT.LQUERY ) THEN
                INFO = -24
             END IF
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'SGGESX', -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' )
          SAFMIN = SLAMCH( 'S' )
          SAFMAX = ONE / SAFMIN
          CALL SLABAD( SAFMIN, SAFMAX )
          SMLNUM = SQRT( SAFMIN ) / EPS
          BIGNUM = ONE / SMLNUM
    *
    *     Scale A if max element outside range [SMLNUM,BIGNUM]
    *
          ANRM = SLANGE( 'M', N, N, A, LDA, WORK )
          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 SLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
    *
    *     Scale B if max element outside range [SMLNUM,BIGNUM]
    *
          BNRM = SLANGE( 'M', N, N, B, LDB, WORK )
          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 SLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
    *
    *     Permute the matrix to make it more nearly triangular
    *     (Workspace: need 6*N + 2*N for permutation parameters)
    *
          ILEFT = 1
          IRIGHT = N + 1
          IWRK = IRIGHT + N
          CALL SGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, WORK( ILEFT ),
         $             WORK( IRIGHT ), WORK( IWRK ), IERR )
    *
    *     Reduce B to triangular form (QR decomposition of B)
    *     (Workspace: need N, prefer N*NB)
    *
          IROWS = IHI + 1 - ILO
          ICOLS = N + 1 - ILO
          ITAU = IWRK
          IWRK = ITAU + IROWS
          CALL SGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
         $             WORK( IWRK ), LWORK+1-IWRK, IERR )
    *
    *     Apply the orthogonal transformation to matrix A
    *     (Workspace: need N, prefer N*NB)
    *
          CALL SORMQR( 'L', 'T', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
         $             WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
         $             LWORK+1-IWRK, IERR )
    *
    *     Initialize VSL
    *     (Workspace: need N, prefer N*NB)
    *
          IF( ILVSL ) THEN
             CALL SLASET( 'Full', N, N, ZERO, ONE, VSL, LDVSL )
             IF( IROWS.GT.1 ) THEN
                CALL SLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
         $                   VSL( ILO+1, ILO ), LDVSL )
             END IF
             CALL SORGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
         $                WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
          END IF
    *
    *     Initialize VSR
    *
          IF( ILVSR )
         $   CALL SLASET( 'Full', N, N, ZERO, ONE, VSR, LDVSR )
    *
    *     Reduce to generalized Hessenberg form
    *     (Workspace: none needed)
    *
          CALL SGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
         $             LDVSL, VSR, LDVSR, IERR )
    *
          SDIM = 0
    *
    *     Perform QZ algorithm, computing Schur vectors if desired
    *     (Workspace: need N)
    *
          IWRK = ITAU
          CALL SHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
         $             ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR,
         $             WORK( IWRK ), LWORK+1-IWRK, 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 50
          END IF
    *
    *     Sort eigenvalues ALPHA/BETA and compute the reciprocal of
    *     condition number(s)
    *     (Workspace: If IJOB >= 1, need MAX( 8*(N+1), 2*SDIM*(N-SDIM) )
    *                 otherwise, need 8*(N+1) )
    *
          IF( WANTST ) THEN
    *
    *        Undo scaling on eigenvalues before SELCTGing
    *
             IF( ILASCL ) THEN
                CALL SLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N,
         $                   IERR )
                CALL SLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N,
         $                   IERR )
             END IF
             IF( ILBSCL )
         $      CALL SLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
    *
    *        Select eigenvalues
    *
             DO 10 I = 1, N
                BWORK( I ) = SELCTG( ALPHAR( I ), ALPHAI( I ), BETA( I ) )
       10    CONTINUE
    *
    *        Reorder eigenvalues, transform Generalized Schur vectors, and
    *        compute reciprocal condition numbers
    *
             CALL STGSEN( IJOB, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB,
         $                ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR,
         $                SDIM, PL, PR, DIF, WORK( IWRK ), LWORK-IWRK+1,
         $                IWORK, LIWORK, IERR )
    *
             IF( IJOB.GE.1 )
         $      MAXWRK = MAX( MAXWRK, 2*SDIM*( N-SDIM ) )
             IF( IERR.EQ.-22 ) THEN
    *
    *            not enough real workspace
    *
                INFO = -22
             ELSE
                IF( IJOB.EQ.1 .OR. IJOB.EQ.4 ) THEN
                   RCONDE( 1 ) = PL
                   RCONDE( 2 ) = PR
                END IF
                IF( IJOB.EQ.2 .OR. IJOB.EQ.4 ) THEN
                   RCONDV( 1 ) = DIF( 1 )
                   RCONDV( 2 ) = DIF( 2 )
                END IF
                IF( IERR.EQ.1 )
         $         INFO = N + 3
             END IF
    *
          END IF
    *
    *     Apply permutation to VSL and VSR
    *     (Workspace: none needed)
    *
          IF( ILVSL )
         $   CALL SGGBAK( 'P', 'L', N, ILO, IHI, WORK( ILEFT ),
         $                WORK( IRIGHT ), N, VSL, LDVSL, IERR )
    *
          IF( ILVSR )
         $   CALL SGGBAK( 'P', 'R', N, ILO, IHI, WORK( ILEFT ),
         $                WORK( IRIGHT ), N, VSR, LDVSR, IERR )
    *
    *     Check if unscaling would cause over/underflow, if so, rescale
    *     (ALPHAR(I),ALPHAI(I),BETA(I)) so BETA(I) is on the order of
    *     B(I,I) and ALPHAR(I) and ALPHAI(I) are on the order of A(I,I)
    *
          IF( ILASCL ) THEN
             DO 20 I = 1, N
                IF( ALPHAI( I ).NE.ZERO ) THEN
                   IF( ( ALPHAR( I ) / SAFMAX ).GT.( ANRMTO / ANRM ) .OR.
         $             ( SAFMIN / ALPHAR( I ) ).GT.( ANRM / ANRMTO ) )
         $            THEN
                      WORK( 1 ) = ABS( A( I, I ) / ALPHAR( I ) )
                      BETA( I ) = BETA( I )*WORK( 1 )
                      ALPHAR( I ) = ALPHAR( I )*WORK( 1 )
                      ALPHAI( I ) = ALPHAI( I )*WORK( 1 )
                   ELSE IF( ( ALPHAI( I ) / SAFMAX ).GT.( ANRMTO / ANRM )
         $            .OR. ( SAFMIN / ALPHAI( I ) ).GT.( ANRM / ANRMTO ) )
         $            THEN
                      WORK( 1 ) = ABS( A( I, I+1 ) / ALPHAI( I ) )
                      BETA( I ) = BETA( I )*WORK( 1 )
                      ALPHAR( I ) = ALPHAR( I )*WORK( 1 )
                      ALPHAI( I ) = ALPHAI( I )*WORK( 1 )
                   END IF
                END IF
       20    CONTINUE
          END IF
    *
          IF( ILBSCL ) THEN
             DO 25 I = 1, N
                IF( ALPHAI( I ).NE.ZERO ) THEN
                   IF( ( BETA( I ) / SAFMAX ).GT.( BNRMTO / BNRM ) .OR.
         $             ( SAFMIN / BETA( I ) ).GT.( BNRM / BNRMTO ) ) THEN
                      WORK( 1 ) = ABS( B( I, I ) / BETA( I ) )
                      BETA( I ) = BETA( I )*WORK( 1 )
                      ALPHAR( I ) = ALPHAR( I )*WORK( 1 )
                      ALPHAI( I ) = ALPHAI( I )*WORK( 1 )
                   END IF
                END IF
       25    CONTINUE
          END IF
    *
    *     Undo scaling
    *
          IF( ILASCL ) THEN
             CALL SLASCL( 'H', 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR )
             CALL SLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N, IERR )
             CALL SLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N, IERR )
          END IF
    *
          IF( ILBSCL ) THEN
             CALL SLASCL( 'U', 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR )
             CALL SLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
          END IF
    *
          IF( WANTST ) THEN
    *
    *        Check if reordering is correct
    *
             LASTSL = .TRUE.
             LST2SL = .TRUE.
             SDIM = 0
             IP = 0
             DO 40 I = 1, N
                CURSL = SELCTG( ALPHAR( I ), ALPHAI( I ), BETA( I ) )
                IF( ALPHAI( I ).EQ.ZERO ) THEN
                   IF( CURSL )
         $            SDIM = SDIM + 1
                   IP = 0
                   IF( CURSL .AND. .NOT.LASTSL )
         $            INFO = N + 2
                ELSE
                   IF( IP.EQ.1 ) THEN
    *
    *                 Last eigenvalue of conjugate pair
    *
                      CURSL = CURSL .OR. LASTSL
                      LASTSL = CURSL
                      IF( CURSL )
         $               SDIM = SDIM + 2
                      IP = -1
                      IF( CURSL .AND. .NOT.LST2SL )
         $               INFO = N + 2
                   ELSE
    *
    *                 First eigenvalue of conjugate pair
    *
                      IP = 1
                   END IF
                END IF
                LST2SL = LASTSL
                LASTSL = CURSL
       40    CONTINUE
    *
          END IF
    *
       50 CONTINUE
    *
          WORK( 1 ) = MAXWRK
          IWORK( 1 ) = LIWMIN
    *
          RETURN
    *
    *     End of SGGESX
    *
          END