zggevx.f

          SUBROUTINE ZGGEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB,
         $                   ALPHA, BETA, VL, LDVL, VR, LDVR, ILO, IHI,
         $                   LSCALE, RSCALE, ABNRM, BBNRM, RCONDE, RCONDV,
         $                   WORK, LWORK, RWORK, IWORK, BWORK, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          BALANC, JOBVL, JOBVR, SENSE
          INTEGER            IHI, ILO, INFO, LDA, LDB, LDVL, LDVR, LWORK, N
          DOUBLE PRECISION   ABNRM, BBNRM
    *     ..
    *     .. Array Arguments ..
          LOGICAL            BWORK( * )
          INTEGER            IWORK( * )
          DOUBLE PRECISION   LSCALE( * ), RCONDE( * ), RCONDV( * ),
         $                   RSCALE( * ), RWORK( * )
          COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
         $                   BETA( * ), VL( LDVL, * ), VR( LDVR, * ),
         $                   WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZGGEVX computes for a pair of N-by-N complex nonsymmetric matrices
    *  (A,B) the generalized eigenvalues, and optionally, the left and/or
    *  right generalized eigenvectors.
    *
    *  Optionally, it also computes a balancing transformation to improve
    *  the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
    *  LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for
    *  the eigenvalues (RCONDE), and reciprocal condition numbers for the
    *  right eigenvectors (RCONDV).
    *
    *  A generalized eigenvalue for a pair of matrices (A,B) is a scalar
    *  lambda or a ratio alpha/beta = lambda, such that A - lambda*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.
    *
    *  The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
    *  of (A,B) satisfies
    *                   A * v(j) = lambda(j) * B * v(j) .
    *  The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
    *  of (A,B) satisfies
    *                   u(j)**H * A  = lambda(j) * u(j)**H * B.
    *  where u(j)**H is the conjugate-transpose of u(j).
    *
    *
    *  Arguments
    *  =========
    *
    *  BALANC  (input) CHARACTER*1
    *          Specifies the balance option to be performed:
    *          = 'N':  do not diagonally scale or permute;
    *          = 'P':  permute only;
    *          = 'S':  scale only;
    *          = 'B':  both permute and scale.
    *          Computed reciprocal condition numbers will be for the
    *          matrices after permuting and/or balancing. Permuting does
    *          not change condition numbers (in exact arithmetic), but
    *          balancing does.
    *
    *  JOBVL   (input) CHARACTER*1
    *          = 'N':  do not compute the left generalized eigenvectors;
    *          = 'V':  compute the left generalized eigenvectors.
    *
    *  JOBVR   (input) CHARACTER*1
    *          = 'N':  do not compute the right generalized eigenvectors;
    *          = 'V':  compute the right generalized eigenvectors.
    *
    *  SENSE   (input) CHARACTER*1
    *          Determines which reciprocal condition numbers are computed.
    *          = 'N': none are computed;
    *          = 'E': computed for eigenvalues only;
    *          = 'V': computed for eigenvectors only;
    *          = 'B': computed for eigenvalues and eigenvectors.
    *
    *  N       (input) INTEGER
    *          The order of the matrices A, B, VL, and VR.  N >= 0.
    *
    *  A       (input/output) COMPLEX*16 array, dimension (LDA, N)
    *          On entry, the matrix A in the pair (A,B).
    *          On exit, A has been overwritten. If JOBVL='V' or JOBVR='V'
    *          or both, then A contains the first part of the complex Schur
    *          form of the "balanced" versions of the input A and B.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of A.  LDA >= max(1,N).
    *
    *  B       (input/output) COMPLEX*16 array, dimension (LDB, N)
    *          On entry, the matrix B in the pair (A,B).
    *          On exit, B has been overwritten. If JOBVL='V' or JOBVR='V'
    *          or both, then B contains the second part of the complex
    *          Schur form of the "balanced" versions of the input A and B.
    *
    *  LDB     (input) INTEGER
    *          The leading dimension of B.  LDB >= max(1,N).
    *
    *  ALPHA   (output) COMPLEX*16 array, dimension (N)
    *  BETA    (output) COMPLEX*16 array, dimension (N)
    *          On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the generalized
    *          eigenvalues.
    *
    *          Note: the quotient 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).
    *
    *  VL      (output) COMPLEX*16 array, dimension (LDVL,N)
    *          If JOBVL = 'V', the left generalized eigenvectors u(j) are
    *          stored one after another in the columns of VL, in the same
    *          order as their eigenvalues.
    *          Each eigenvector will be scaled so the largest component
    *          will have abs(real part) + abs(imag. part) = 1.
    *          Not referenced if JOBVL = 'N'.
    *
    *  LDVL    (input) INTEGER
    *          The leading dimension of the matrix VL. LDVL >= 1, and
    *          if JOBVL = 'V', LDVL >= N.
    *
    *  VR      (output) COMPLEX*16 array, dimension (LDVR,N)
    *          If JOBVR = 'V', the right generalized eigenvectors v(j) are
    *          stored one after another in the columns of VR, in the same
    *          order as their eigenvalues.
    *          Each eigenvector will be scaled so the largest component
    *          will have abs(real part) + abs(imag. part) = 1.
    *          Not referenced if JOBVR = 'N'.
    *
    *  LDVR    (input) INTEGER
    *          The leading dimension of the matrix VR. LDVR >= 1, and
    *          if JOBVR = 'V', LDVR >= N.
    *
    *  ILO     (output) INTEGER
    *  IHI     (output) INTEGER
    *          ILO and IHI are integer values such that on exit
    *          A(i,j) = 0 and B(i,j) = 0 if i > j and
    *          j = 1,...,ILO-1 or i = IHI+1,...,N.
    *          If BALANC = 'N' or 'S', ILO = 1 and IHI = N.
    *
    *  LSCALE  (output) DOUBLE PRECISION array, dimension (N)
    *          Details of the permutations and scaling factors applied
    *          to the left side of A and B.  If PL(j) is the index of the
    *          row interchanged with row j, and DL(j) is the scaling
    *          factor applied to row j, then
    *            LSCALE(j) = PL(j)  for j = 1,...,ILO-1
    *                      = DL(j)  for j = ILO,...,IHI
    *                      = PL(j)  for j = IHI+1,...,N.
    *          The order in which the interchanges are made is N to IHI+1,
    *          then 1 to ILO-1.
    *
    *  RSCALE  (output) DOUBLE PRECISION array, dimension (N)
    *          Details of the permutations and scaling factors applied
    *          to the right side of A and B.  If PR(j) is the index of the
    *          column interchanged with column j, and DR(j) is the scaling
    *          factor applied to column j, then
    *            RSCALE(j) = PR(j)  for j = 1,...,ILO-1
    *                      = DR(j)  for j = ILO,...,IHI
    *                      = PR(j)  for j = IHI+1,...,N
    *          The order in which the interchanges are made is N to IHI+1,
    *          then 1 to ILO-1.
    *
    *  ABNRM   (output) DOUBLE PRECISION
    *          The one-norm of the balanced matrix A.
    *
    *  BBNRM   (output) DOUBLE PRECISION
    *          The one-norm of the balanced matrix B.
    *
    *  RCONDE  (output) DOUBLE PRECISION array, dimension (N)
    *          If SENSE = 'E' or 'B', the reciprocal condition numbers of
    *          the eigenvalues, stored in consecutive elements of the array.
    *          If SENSE = 'N' or 'V', RCONDE is not referenced.
    *
    *  RCONDV  (output) DOUBLE PRECISION array, dimension (N)
    *          If JOB = 'V' or 'B', the estimated reciprocal condition
    *          numbers of the eigenvectors, stored in consecutive elements
    *          of the array. If the eigenvalues cannot be reordered to
    *          compute RCONDV(j), RCONDV(j) is set to 0; this can only occur
    *          when the true value would be very small anyway.
    *          If SENSE = 'N' or 'E', RCONDV is not referenced.
    *
    *  WORK    (workspace/output) COMPLEX*16 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).
    *          If SENSE = 'E', LWORK >= max(1,4*N).
    *          If SENSE = 'V' or 'B', LWORK >= max(1,2*N*N+2*N).
    *
    *          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 (lrwork)
    *          lrwork must be at least max(1,6*N) if BALANC = 'S' or 'B',
    *          and at least max(1,2*N) otherwise.
    *          Real workspace.
    *
    *  IWORK   (workspace) INTEGER array, dimension (N+2)
    *          If SENSE = 'E', IWORK is not referenced.
    *
    *  BWORK   (workspace) LOGICAL array, dimension (N)
    *          If SENSE = 'N', BWORK is not referenced.
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value.
    *          = 1,...,N:
    *                The QZ iteration failed.  No eigenvectors have been
    *                calculated, but ALPHA(j) and BETA(j) should be correct
    *                for j=INFO+1,...,N.
    *          > N:  =N+1: other than QZ iteration failed in ZHGEQZ.
    *                =N+2: error return from ZTGEVC.
    *
    *  Further Details
    *  ===============
    *
    *  Balancing a matrix pair (A,B) includes, first, permuting rows and
    *  columns to isolate eigenvalues, second, applying diagonal similarity
    *  transformation to the rows and columns to make the rows and columns
    *  as close in norm as possible. The computed reciprocal condition
    *  numbers correspond to the balanced matrix. Permuting rows and columns
    *  will not change the condition numbers (in exact arithmetic) but
    *  diagonal scaling will.  For further explanation of balancing, see
    *  section 4.11.1.2 of LAPACK Users' Guide.
    *
    *  An approximate error bound on the chordal distance between the i-th
    *  computed generalized eigenvalue w and the corresponding exact
    *  eigenvalue lambda is
    *
    *       chord(w, lambda) <= EPS * norm(ABNRM, BBNRM) / RCONDE(I)
    *
    *  An approximate error bound for the angle between the i-th computed
    *  eigenvector VL(i) or VR(i) is given by
    *
    *       EPS * norm(ABNRM, BBNRM) / DIF(i).
    *
    *  For further explanation of the reciprocal condition numbers RCONDE
    *  and RCONDV, see section 4.11 of LAPACK User's Guide.
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ZERO, ONE
          PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
          COMPLEX*16         CZERO, CONE
          PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
         $                   CONE = ( 1.0D+0, 0.0D+0 ) )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY, NOSCL,
         $                   WANTSB, WANTSE, WANTSN, WANTSV
          CHARACTER          CHTEMP
          INTEGER            I, ICOLS, IERR, IJOBVL, IJOBVR, IN, IROWS,
         $                   ITAU, IWRK, IWRK1, J, JC, JR, M, MAXWRK, MINWRK
          DOUBLE PRECISION   ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
         $                   SMLNUM, TEMP
          COMPLEX*16         X
    *     ..
    *     .. Local Arrays ..
          LOGICAL            LDUMMA( 1 )
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DLABAD, DLASCL, XERBLA, ZGEQRF, ZGGBAK, ZGGBAL,
         $                   ZGGHRD, ZHGEQZ, ZLACPY, ZLASCL, ZLASET, ZTGEVC,
         $                   ZTGSNA, ZUNGQR, ZUNMQR
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          DOUBLE PRECISION   DLAMCH, ZLANGE
          EXTERNAL           LSAME, ILAENV, DLAMCH, ZLANGE
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, DBLE, DIMAG, MAX, SQRT
    *     ..
    *     .. Statement Functions ..
          DOUBLE PRECISION   ABS1
    *     ..
    *     .. Statement Function definitions ..
          ABS1( X ) = ABS( DBLE( X ) ) + ABS( DIMAG( X ) )
    *     ..
    *     .. Executable Statements ..
    *
    *     Decode the input arguments
    *
          IF( LSAME( JOBVL, 'N' ) ) THEN
             IJOBVL = 1
             ILVL = .FALSE.
          ELSE IF( LSAME( JOBVL, 'V' ) ) THEN
             IJOBVL = 2
             ILVL = .TRUE.
          ELSE
             IJOBVL = -1
             ILVL = .FALSE.
          END IF
    *
          IF( LSAME( JOBVR, 'N' ) ) THEN
             IJOBVR = 1
             ILVR = .FALSE.
          ELSE IF( LSAME( JOBVR, 'V' ) ) THEN
             IJOBVR = 2
             ILVR = .TRUE.
          ELSE
             IJOBVR = -1
             ILVR = .FALSE.
          END IF
          ILV = ILVL .OR. ILVR
    *
          NOSCL  = LSAME( BALANC, 'N' ) .OR. LSAME( BALANC, 'P' )
          WANTSN = LSAME( SENSE, 'N' )
          WANTSE = LSAME( SENSE, 'E' )
          WANTSV = LSAME( SENSE, 'V' )
          WANTSB = LSAME( SENSE, 'B' )
    *
    *     Test the input arguments
    *
          INFO = 0
          LQUERY = ( LWORK.EQ.-1 )
          IF( .NOT.( NOSCL .OR. LSAME( BALANC,'S' ) .OR.
         $    LSAME( BALANC, 'B' ) ) ) THEN
             INFO = -1
          ELSE IF( IJOBVL.LE.0 ) THEN
             INFO = -2
          ELSE IF( IJOBVR.LE.0 ) THEN
             INFO = -3
          ELSE IF( .NOT.( WANTSN .OR. WANTSE .OR. WANTSB .OR. WANTSV ) )
         $          THEN
             INFO = -4
          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( LDVL.LT.1 .OR. ( ILVL .AND. LDVL.LT.N ) ) THEN
             INFO = -13
          ELSE IF( LDVR.LT.1 .OR. ( ILVR .AND. LDVR.LT.N ) ) THEN
             INFO = -15
          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. The workspace is
    *       computed assuming ILO = 1 and IHI = N, the worst case.)
    *
          IF( INFO.EQ.0 ) THEN
             IF( N.EQ.0 ) THEN
                MINWRK = 1
                MAXWRK = 1
             ELSE
                MINWRK = 2*N
                IF( WANTSE ) THEN
                   MINWRK = 4*N
                ELSE IF( WANTSV .OR. WANTSB ) THEN
                   MINWRK = 2*N*( N + 1)
                END IF
                MAXWRK = MINWRK
                MAXWRK = MAX( MAXWRK,
         $                    N + N*ILAENV( 1, 'ZGEQRF', ' ', N, 1, N, 0 ) )
                MAXWRK = MAX( MAXWRK,
         $                    N + N*ILAENV( 1, 'ZUNMQR', ' ', N, 1, N, 0 ) )
                IF( ILVL ) THEN
                   MAXWRK = MAX( MAXWRK, N +
         $                       N*ILAENV( 1, 'ZUNGQR', ' ', N, 1, N, 0 ) )
                END IF
             END IF
             WORK( 1 ) = MAXWRK
    *
             IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
                INFO = -25
             END IF
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZGGEVX', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
    *     Get machine constants
    *
          EPS = DLAMCH( 'P' )
          SMLNUM = DLAMCH( 'S' )
          BIGNUM = ONE / SMLNUM
          CALL DLABAD( SMLNUM, BIGNUM )
          SMLNUM = SQRT( SMLNUM ) / EPS
          BIGNUM = ONE / SMLNUM
    *
    *     Scale A if max element outside range [SMLNUM,BIGNUM]
    *
          ANRM = ZLANGE( '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 ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
    *
    *     Scale B if max element outside range [SMLNUM,BIGNUM]
    *
          BNRM = ZLANGE( '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 ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
    *
    *     Permute and/or balance the matrix pair (A,B)
    *     (Real Workspace: need 6*N if BALANC = 'S' or 'B', 1 otherwise)
    *
          CALL ZGGBAL( BALANC, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE,
         $             RWORK, IERR )
    *
    *     Compute ABNRM and BBNRM
    *
          ABNRM = ZLANGE( '1', N, N, A, LDA, RWORK( 1 ) )
          IF( ILASCL ) THEN
             RWORK( 1 ) = ABNRM
             CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, 1, 1, RWORK( 1 ), 1,
         $                IERR )
             ABNRM = RWORK( 1 )
          END IF
    *
          BBNRM = ZLANGE( '1', N, N, B, LDB, RWORK( 1 ) )
          IF( ILBSCL ) THEN
             RWORK( 1 ) = BBNRM
             CALL DLASCL( 'G', 0, 0, BNRMTO, BNRM, 1, 1, RWORK( 1 ), 1,
         $                IERR )
             BBNRM = RWORK( 1 )
          END IF
    *
    *     Reduce B to triangular form (QR decomposition of B)
    *     (Complex Workspace: need N, prefer N*NB )
    *
          IROWS = IHI + 1 - ILO
          IF( ILV .OR. .NOT.WANTSN ) THEN
             ICOLS = N + 1 - ILO
          ELSE
             ICOLS = IROWS
          END IF
          ITAU = 1
          IWRK = ITAU + IROWS
          CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
         $             WORK( IWRK ), LWORK+1-IWRK, IERR )
    *
    *     Apply the unitary transformation to A
    *     (Complex Workspace: need N, prefer N*NB)
    *
          CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
         $             WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
         $             LWORK+1-IWRK, IERR )
    *
    *     Initialize VL and/or VR
    *     (Workspace: need N, prefer N*NB)
    *
          IF( ILVL ) THEN
             CALL ZLASET( 'Full', N, N, CZERO, CONE, VL, LDVL )
             IF( IROWS.GT.1 ) THEN
                CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
         $                   VL( ILO+1, ILO ), LDVL )
             END IF
             CALL ZUNGQR( IROWS, IROWS, IROWS, VL( ILO, ILO ), LDVL,
         $                WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
          END IF
    *
          IF( ILVR )
         $   CALL ZLASET( 'Full', N, N, CZERO, CONE, VR, LDVR )
    *
    *     Reduce to generalized Hessenberg form
    *     (Workspace: none needed)
    *
          IF( ILV .OR. .NOT.WANTSN ) THEN
    *
    *        Eigenvectors requested -- work on whole matrix.
    *
             CALL ZGGHRD( JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB, VL,
         $                LDVL, VR, LDVR, IERR )
          ELSE
             CALL ZGGHRD( 'N', 'N', IROWS, 1, IROWS, A( ILO, ILO ), LDA,
         $                B( ILO, ILO ), LDB, VL, LDVL, VR, LDVR, IERR )
          END IF
    *
    *     Perform QZ algorithm (Compute eigenvalues, and optionally, the
    *     Schur forms and Schur vectors)
    *     (Complex Workspace: need N)
    *     (Real Workspace: need N)
    *
          IWRK = ITAU
          IF( ILV .OR. .NOT.WANTSN ) THEN
             CHTEMP = 'S'
          ELSE
             CHTEMP = 'E'
          END IF
    *
          CALL ZHGEQZ( CHTEMP, JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB,
         $             ALPHA, BETA, VL, LDVL, VR, LDVR, WORK( IWRK ),
         $             LWORK+1-IWRK, RWORK, 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 90
          END IF
    *
    *     Compute Eigenvectors and estimate condition numbers if desired
    *     ZTGEVC: (Complex Workspace: need 2*N )
    *             (Real Workspace:    need 2*N )
    *     ZTGSNA: (Complex Workspace: need 2*N*N if SENSE='V' or 'B')
    *             (Integer Workspace: need N+2 )
    *
          IF( ILV .OR. .NOT.WANTSN ) THEN
             IF( ILV ) THEN
                IF( ILVL ) THEN
                   IF( ILVR ) THEN
                      CHTEMP = 'B'
                   ELSE
                      CHTEMP = 'L'
                   END IF
                ELSE
                   CHTEMP = 'R'
                END IF
    *
                CALL ZTGEVC( CHTEMP, 'B', LDUMMA, N, A, LDA, B, LDB, VL,
         $                   LDVL, VR, LDVR, N, IN, WORK( IWRK ), RWORK,
         $                   IERR )
                IF( IERR.NE.0 ) THEN
                   INFO = N + 2
                   GO TO 90
                END IF
             END IF
    *
             IF( .NOT.WANTSN ) THEN
    *
    *           compute eigenvectors (DTGEVC) and estimate condition
    *           numbers (DTGSNA). Note that the definition of the condition
    *           number is not invariant under transformation (u,v) to
    *           (Q*u, Z*v), where (u,v) are eigenvectors of the generalized
    *           Schur form (S,T), Q and Z are orthogonal matrices. In order
    *           to avoid using extra 2*N*N workspace, we have to
    *           re-calculate eigenvectors and estimate the condition numbers
    *           one at a time.
    *
                DO 20 I = 1, N
    *
                   DO 10 J = 1, N
                      BWORK( J ) = .FALSE.
       10          CONTINUE
                   BWORK( I ) = .TRUE.
    *
                   IWRK = N + 1
                   IWRK1 = IWRK + N
    *
                   IF( WANTSE .OR. WANTSB ) THEN
                      CALL ZTGEVC( 'B', 'S', BWORK, N, A, LDA, B, LDB,
         $                         WORK( 1 ), N, WORK( IWRK ), N, 1, M,
         $                         WORK( IWRK1 ), RWORK, IERR )
                      IF( IERR.NE.0 ) THEN
                         INFO = N + 2
                         GO TO 90
                      END IF
                   END IF
    *
                   CALL ZTGSNA( SENSE, 'S', BWORK, N, A, LDA, B, LDB,
         $                      WORK( 1 ), N, WORK( IWRK ), N, RCONDE( I ),
         $                      RCONDV( I ), 1, M, WORK( IWRK1 ),
         $                      LWORK-IWRK1+1, IWORK, IERR )
    *
       20       CONTINUE
             END IF
          END IF
    *
    *     Undo balancing on VL and VR and normalization
    *     (Workspace: none needed)
    *
          IF( ILVL ) THEN
             CALL ZGGBAK( BALANC, 'L', N, ILO, IHI, LSCALE, RSCALE, N, VL,
         $                LDVL, IERR )
    *
             DO 50 JC = 1, N
                TEMP = ZERO
                DO 30 JR = 1, N
                   TEMP = MAX( TEMP, ABS1( VL( JR, JC ) ) )
       30       CONTINUE
                IF( TEMP.LT.SMLNUM )
         $         GO TO 50
                TEMP = ONE / TEMP
                DO 40 JR = 1, N
                   VL( JR, JC ) = VL( JR, JC )*TEMP
       40       CONTINUE
       50    CONTINUE
          END IF
    *
          IF( ILVR ) THEN
             CALL ZGGBAK( BALANC, 'R', N, ILO, IHI, LSCALE, RSCALE, N, VR,
         $                LDVR, IERR )
             DO 80 JC = 1, N
                TEMP = ZERO
                DO 60 JR = 1, N
                   TEMP = MAX( TEMP, ABS1( VR( JR, JC ) ) )
       60       CONTINUE
                IF( TEMP.LT.SMLNUM )
         $         GO TO 80
                TEMP = ONE / TEMP
                DO 70 JR = 1, N
                   VR( JR, JC ) = VR( JR, JC )*TEMP
       70       CONTINUE
       80    CONTINUE
          END IF
    *
    *     Undo scaling if necessary
    *
          IF( ILASCL )
         $   CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )
    *
          IF( ILBSCL )
         $   CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
    *
       90 CONTINUE
          WORK( 1 ) = MAXWRK
    *
          RETURN
    *
    *     End of ZGGEVX
    *
          END