zgegv.f

          SUBROUTINE ZGEGV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA,
         $                  VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBVL, JOBVR
          INTEGER            INFO, LDA, LDB, LDVL, LDVR, LWORK, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   RWORK( * )
          COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
         $                   BETA( * ), VL( LDVL, * ), VR( LDVR, * ),
         $                   WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  This routine is deprecated and has been replaced by routine ZGGEV.
    *
    *  ZGEGV computes the eigenvalues and, optionally, the left and/or right
    *  eigenvectors of a complex matrix pair (A,B).
    *  Given two square matrices A and B,
    *  the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
    *  eigenvalues lambda and corresponding (non-zero) eigenvectors x such
    *  that
    *     A*x = lambda*B*x.
    *
    *  An alternate form is to find the eigenvalues mu and corresponding
    *  eigenvectors y such that
    *     mu*A*y = B*y.
    *
    *  These two forms are equivalent with mu = 1/lambda and x = y if
    *  neither lambda nor mu is zero.  In order to deal with the case that
    *  lambda or mu is zero or small, two values alpha and beta are returned
    *  for each eigenvalue, such that lambda = alpha/beta and
    *  mu = beta/alpha.
    *
    *  The vectors x and y in the above equations are right eigenvectors of
    *  the matrix pair (A,B).  Vectors u and v satisfying
    *     u**H*A = lambda*u**H*B  or  mu*v**H*A = v**H*B
    *  are left eigenvectors of (A,B).
    *
    *  Note: this routine performs "full balancing" on A and B -- see
    *  "Further Details", below.
    *
    *  Arguments
    *  =========
    *
    *  JOBVL   (input) CHARACTER*1
    *          = 'N':  do not compute the left generalized eigenvectors;
    *          = 'V':  compute the left generalized eigenvectors (returned
    *                  in VL).
    *
    *  JOBVR   (input) CHARACTER*1
    *          = 'N':  do not compute the right generalized eigenvectors;
    *          = 'V':  compute the right generalized eigenvectors (returned
    *                  in VR).
    *
    *  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.
    *          If JOBVL = 'V' or JOBVR = 'V', then on exit A
    *          contains the Schur form of A from the generalized Schur
    *          factorization of the pair (A,B) after balancing.  If no
    *          eigenvectors were computed, then only the diagonal elements
    *          of the Schur form will be correct.  See ZGGHRD and ZHGEQZ
    *          for details.
    *
    *  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.
    *          If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the
    *          upper triangular matrix obtained from B in the generalized
    *          Schur factorization of the pair (A,B) after balancing.
    *          If no eigenvectors were computed, then only the diagonal
    *          elements of B will be correct.  See ZGGHRD and ZHGEQZ for
    *          details.
    *
    *  LDB     (input) INTEGER
    *          The leading dimension of B.  LDB >= max(1,N).
    *
    *  ALPHA   (output) COMPLEX*16 array, dimension (N)
    *          The complex scalars alpha that define the eigenvalues of
    *          GNEP.
    *
    *  BETA    (output) COMPLEX*16 array, dimension (N)
    *          The complex scalars beta that define the eigenvalues of GNEP.
    *
    *          Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
    *          represent the j-th eigenvalue of the matrix pair (A,B), in
    *          one of the forms lambda = alpha/beta or mu = beta/alpha.
    *          Since either lambda or mu may overflow, they should not,
    *          in general, be computed.
    *
    *  VL      (output) COMPLEX*16 array, dimension (LDVL,N)
    *          If JOBVL = 'V', the left eigenvectors u(j) are stored
    *          in the columns of VL, in the same order as their eigenvalues.
    *          Each eigenvector is scaled so that its largest component has
    *          abs(real part) + abs(imag. part) = 1, except for eigenvectors
    *          corresponding to an eigenvalue with alpha = beta = 0, which
    *          are set to zero.
    *          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 eigenvectors x(j) are stored
    *          in the columns of VR, in the same order as their eigenvalues.
    *          Each eigenvector is scaled so that its largest component has
    *          abs(real part) + abs(imag. part) = 1, except for eigenvectors
    *          corresponding to an eigenvalue with alpha = beta = 0, which
    *          are set to zero.
    *          Not referenced if JOBVR = 'N'.
    *
    *  LDVR    (input) INTEGER
    *          The leading dimension of the matrix VR. LDVR >= 1, and
    *          if JOBVR = 'V', LDVR >= N.
    *
    *  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).
    *          For good performance, LWORK must generally be larger.
    *          To compute the optimal value of LWORK, call ILAENV to get
    *          blocksizes (for ZGEQRF, ZUNMQR, and ZUNGQR.)  Then compute:
    *          NB  -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and ZUNGQR;
    *          The optimal LWORK is  MAX( 2*N, N*(NB+1) ).
    *
    *          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/output) DOUBLE PRECISION array, dimension (8*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.  No eigenvectors have been
    *                calculated, but ALPHA(j) and BETA(j) should be
    *                correct for j=INFO+1,...,N.
    *          > N:  errors that usually indicate LAPACK problems:
    *                =N+1: error return from ZGGBAL
    *                =N+2: error return from ZGEQRF
    *                =N+3: error return from ZUNMQR
    *                =N+4: error return from ZUNGQR
    *                =N+5: error return from ZGGHRD
    *                =N+6: error return from ZHGEQZ (other than failed
    *                                               iteration)
    *                =N+7: error return from ZTGEVC
    *                =N+8: error return from ZGGBAK (computing VL)
    *                =N+9: error return from ZGGBAK (computing VR)
    *                =N+10: error return from ZLASCL (various calls)
    *
    *  Further Details
    *  ===============
    *
    *  Balancing
    *  ---------
    *
    *  This driver calls ZGGBAL to both permute and scale rows and columns
    *  of A and B.  The permutations PL and PR are chosen so that PL*A*PR
    *  and PL*B*R will be upper triangular except for the diagonal blocks
    *  A(i:j,i:j) and B(i:j,i:j), with i and j as close together as
    *  possible.  The diagonal scaling matrices DL and DR are chosen so
    *  that the pair  DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to
    *  one (except for the elements that start out zero.)
    *
    *  After the eigenvalues and eigenvectors of the balanced matrices
    *  have been computed, ZGGBAK transforms the eigenvectors back to what
    *  they would have been (in perfect arithmetic) if they had not been
    *  balanced.
    *
    *  Contents of A and B on Exit
    *  -------- -- - --- - -- ----
    *
    *  If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or
    *  both), then on exit the arrays A and B will contain the complex Schur
    *  form[*] of the "balanced" versions of A and B.  If no eigenvectors
    *  are computed, then only the diagonal blocks will be correct.
    *
    *  [*] In other words, upper triangular form.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ZERO, ONE
          PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
          COMPLEX*16         CZERO, CONE
          PARAMETER          ( CZERO = ( 0.0D0, 0.0D0 ),
         $                   CONE = ( 1.0D0, 0.0D0 ) )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            ILIMIT, ILV, ILVL, ILVR, LQUERY
          CHARACTER          CHTEMP
          INTEGER            ICOLS, IHI, IINFO, IJOBVL, IJOBVR, ILEFT, ILO,
         $                   IN, IRIGHT, IROWS, IRWORK, ITAU, IWORK, JC, JR,
         $                   LOPT, LWKMIN, LWKOPT, NB, NB1, NB2, NB3
          DOUBLE PRECISION   ABSAI, ABSAR, ABSB, ANRM, ANRM1, ANRM2, BNRM,
         $                   BNRM1, BNRM2, EPS, SAFMAX, SAFMIN, SALFAI,
         $                   SALFAR, SBETA, SCALE, TEMP
          COMPLEX*16         X
    *     ..
    *     .. Local Arrays ..
          LOGICAL            LDUMMA( 1 )
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHRD, ZHGEQZ,
         $                   ZLACPY, ZLASCL, ZLASET, ZTGEVC, ZUNGQR, ZUNMQR
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          DOUBLE PRECISION   DLAMCH, ZLANGE
          EXTERNAL           LSAME, ILAENV, DLAMCH, ZLANGE
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, DBLE, DCMPLX, DIMAG, INT, MAX
    *     ..
    *     .. 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
    *
    *     Test the input arguments
    *
          LWKMIN = MAX( 2*N, 1 )
          LWKOPT = LWKMIN
          WORK( 1 ) = LWKOPT
          LQUERY = ( LWORK.EQ.-1 )
          INFO = 0
          IF( IJOBVL.LE.0 ) THEN
             INFO = -1
          ELSE IF( IJOBVR.LE.0 ) THEN
             INFO = -2
          ELSE IF( N.LT.0 ) THEN
             INFO = -3
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -5
          ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
             INFO = -7
          ELSE IF( LDVL.LT.1 .OR. ( ILVL .AND. LDVL.LT.N ) ) THEN
             INFO = -11
          ELSE IF( LDVR.LT.1 .OR. ( ILVR .AND. LDVR.LT.N ) ) THEN
             INFO = -13
          ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
             INFO = -15
          END IF
    *
          IF( INFO.EQ.0 ) THEN
             NB1 = ILAENV( 1, 'ZGEQRF', ' ', N, N, -1, -1 )
             NB2 = ILAENV( 1, 'ZUNMQR', ' ', N, N, N, -1 )
             NB3 = ILAENV( 1, 'ZUNGQR', ' ', N, N, N, -1 )
             NB = MAX( NB1, NB2, NB3 )
             LOPT = MAX( 2*N, N*( NB+1 ) )
             WORK( 1 ) = LOPT
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZGEGV ', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
    *     Get machine constants
    *
          EPS = DLAMCH( 'E' )*DLAMCH( 'B' )
          SAFMIN = DLAMCH( 'S' )
          SAFMIN = SAFMIN + SAFMIN
          SAFMAX = ONE / SAFMIN
    *
    *     Scale A
    *
          ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
          ANRM1 = ANRM
          ANRM2 = ONE
          IF( ANRM.LT.ONE ) THEN
             IF( SAFMAX*ANRM.LT.ONE ) THEN
                ANRM1 = SAFMIN
                ANRM2 = SAFMAX*ANRM
             END IF
          END IF
    *
          IF( ANRM.GT.ZERO ) THEN
             CALL ZLASCL( 'G', -1, -1, ANRM, ONE, N, N, A, LDA, IINFO )
             IF( IINFO.NE.0 ) THEN
                INFO = N + 10
                RETURN
             END IF
          END IF
    *
    *     Scale B
    *
          BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
          BNRM1 = BNRM
          BNRM2 = ONE
          IF( BNRM.LT.ONE ) THEN
             IF( SAFMAX*BNRM.LT.ONE ) THEN
                BNRM1 = SAFMIN
                BNRM2 = SAFMAX*BNRM
             END IF
          END IF
    *
          IF( BNRM.GT.ZERO ) THEN
             CALL ZLASCL( 'G', -1, -1, BNRM, ONE, N, N, B, LDB, IINFO )
             IF( IINFO.NE.0 ) THEN
                INFO = N + 10
                RETURN
             END IF
          END IF
    *
    *     Permute the matrix to make it more nearly triangular
    *     Also "balance" the matrix.
    *
          ILEFT = 1
          IRIGHT = N + 1
          IRWORK = IRIGHT + N
          CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
         $             RWORK( IRIGHT ), RWORK( IRWORK ), IINFO )
          IF( IINFO.NE.0 ) THEN
             INFO = N + 1
             GO TO 80
          END IF
    *
    *     Reduce B to triangular form, and initialize VL and/or VR
    *
          IROWS = IHI + 1 - ILO
          IF( ILV ) THEN
             ICOLS = N + 1 - ILO
          ELSE
             ICOLS = IROWS
          END IF
          ITAU = 1
          IWORK = ITAU + IROWS
          CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
         $             WORK( IWORK ), LWORK+1-IWORK, IINFO )
          IF( IINFO.GE.0 )
         $   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
          IF( IINFO.NE.0 ) THEN
             INFO = N + 2
             GO TO 80
          END IF
    *
          CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
         $             WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWORK ),
         $             LWORK+1-IWORK, IINFO )
          IF( IINFO.GE.0 )
         $   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
          IF( IINFO.NE.0 ) THEN
             INFO = N + 3
             GO TO 80
          END IF
    *
          IF( ILVL ) THEN
             CALL ZLASET( 'Full', N, N, CZERO, CONE, VL, LDVL )
             CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
         $                VL( ILO+1, ILO ), LDVL )
             CALL ZUNGQR( IROWS, IROWS, IROWS, VL( ILO, ILO ), LDVL,
         $                WORK( ITAU ), WORK( IWORK ), LWORK+1-IWORK,
         $                IINFO )
             IF( IINFO.GE.0 )
         $      LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
             IF( IINFO.NE.0 ) THEN
                INFO = N + 4
                GO TO 80
             END IF
          END IF
    *
          IF( ILVR )
         $   CALL ZLASET( 'Full', N, N, CZERO, CONE, VR, LDVR )
    *
    *     Reduce to generalized Hessenberg form
    *
          IF( ILV ) THEN
    *
    *        Eigenvectors requested -- work on whole matrix.
    *
             CALL ZGGHRD( JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB, VL,
         $                LDVL, VR, LDVR, IINFO )
          ELSE
             CALL ZGGHRD( 'N', 'N', IROWS, 1, IROWS, A( ILO, ILO ), LDA,
         $                B( ILO, ILO ), LDB, VL, LDVL, VR, LDVR, IINFO )
          END IF
          IF( IINFO.NE.0 ) THEN
             INFO = N + 5
             GO TO 80
          END IF
    *
    *     Perform QZ algorithm
    *
          IWORK = ITAU
          IF( ILV ) 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( IWORK ),
         $             LWORK+1-IWORK, RWORK( IRWORK ), IINFO )
          IF( IINFO.GE.0 )
         $   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
          IF( IINFO.NE.0 ) THEN
             IF( IINFO.GT.0 .AND. IINFO.LE.N ) THEN
                INFO = IINFO
             ELSE IF( IINFO.GT.N .AND. IINFO.LE.2*N ) THEN
                INFO = IINFO - N
             ELSE
                INFO = N + 6
             END IF
             GO TO 80
          END IF
    *
          IF( ILV ) THEN
    *
    *        Compute Eigenvectors
    *
             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( IWORK ), RWORK( IRWORK ),
         $                IINFO )
             IF( IINFO.NE.0 ) THEN
                INFO = N + 7
                GO TO 80
             END IF
    *
    *        Undo balancing on VL and VR, rescale
    *
             IF( ILVL ) THEN
                CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
         $                   RWORK( IRIGHT ), N, VL, LDVL, IINFO )
                IF( IINFO.NE.0 ) THEN
                   INFO = N + 8
                   GO TO 80
                END IF
                DO 30 JC = 1, N
                   TEMP = ZERO
                   DO 10 JR = 1, N
                      TEMP = MAX( TEMP, ABS1( VL( JR, JC ) ) )
       10          CONTINUE
                   IF( TEMP.LT.SAFMIN )
         $            GO TO 30
                   TEMP = ONE / TEMP
                   DO 20 JR = 1, N
                      VL( JR, JC ) = VL( JR, JC )*TEMP
       20          CONTINUE
       30       CONTINUE
             END IF
             IF( ILVR ) THEN
                CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
         $                   RWORK( IRIGHT ), N, VR, LDVR, IINFO )
                IF( IINFO.NE.0 ) THEN
                   INFO = N + 9
                   GO TO 80
                END IF
                DO 60 JC = 1, N
                   TEMP = ZERO
                   DO 40 JR = 1, N
                      TEMP = MAX( TEMP, ABS1( VR( JR, JC ) ) )
       40          CONTINUE
                   IF( TEMP.LT.SAFMIN )
         $            GO TO 60
                   TEMP = ONE / TEMP
                   DO 50 JR = 1, N
                      VR( JR, JC ) = VR( JR, JC )*TEMP
       50          CONTINUE
       60       CONTINUE
             END IF
    *
    *        End of eigenvector calculation
    *
          END IF
    *
    *     Undo scaling in alpha, beta
    *
    *     Note: this does not give the alpha and beta for the unscaled
    *     problem.
    *
    *     Un-scaling is limited to avoid underflow in alpha and beta
    *     if they are significant.
    *
          DO 70 JC = 1, N
             ABSAR = ABS( DBLE( ALPHA( JC ) ) )
             ABSAI = ABS( DIMAG( ALPHA( JC ) ) )
             ABSB = ABS( DBLE( BETA( JC ) ) )
             SALFAR = ANRM*DBLE( ALPHA( JC ) )
             SALFAI = ANRM*DIMAG( ALPHA( JC ) )
             SBETA = BNRM*DBLE( BETA( JC ) )
             ILIMIT = .FALSE.
             SCALE = ONE
    *
    *        Check for significant underflow in imaginary part of ALPHA
    *
             IF( ABS( SALFAI ).LT.SAFMIN .AND. ABSAI.GE.
         $       MAX( SAFMIN, EPS*ABSAR, EPS*ABSB ) ) THEN
                ILIMIT = .TRUE.
                SCALE = ( SAFMIN / ANRM1 ) / MAX( SAFMIN, ANRM2*ABSAI )
             END IF
    *
    *        Check for significant underflow in real part of ALPHA
    *
             IF( ABS( SALFAR ).LT.SAFMIN .AND. ABSAR.GE.
         $       MAX( SAFMIN, EPS*ABSAI, EPS*ABSB ) ) THEN
                ILIMIT = .TRUE.
                SCALE = MAX( SCALE, ( SAFMIN / ANRM1 ) /
         $              MAX( SAFMIN, ANRM2*ABSAR ) )
             END IF
    *
    *        Check for significant underflow in BETA
    *
             IF( ABS( SBETA ).LT.SAFMIN .AND. ABSB.GE.
         $       MAX( SAFMIN, EPS*ABSAR, EPS*ABSAI ) ) THEN
                ILIMIT = .TRUE.
                SCALE = MAX( SCALE, ( SAFMIN / BNRM1 ) /
         $              MAX( SAFMIN, BNRM2*ABSB ) )
             END IF
    *
    *        Check for possible overflow when limiting scaling
    *
             IF( ILIMIT ) THEN
                TEMP = ( SCALE*SAFMIN )*MAX( ABS( SALFAR ), ABS( SALFAI ),
         $             ABS( SBETA ) )
                IF( TEMP.GT.ONE )
         $         SCALE = SCALE / TEMP
                IF( SCALE.LT.ONE )
         $         ILIMIT = .FALSE.
             END IF
    *
    *        Recompute un-scaled ALPHA, BETA if necessary.
    *
             IF( ILIMIT ) THEN
                SALFAR = ( SCALE*DBLE( ALPHA( JC ) ) )*ANRM
                SALFAI = ( SCALE*DIMAG( ALPHA( JC ) ) )*ANRM
                SBETA = ( SCALE*BETA( JC ) )*BNRM
             END IF
             ALPHA( JC ) = DCMPLX( SALFAR, SALFAI )
             BETA( JC ) = SBETA
       70 CONTINUE
    *
       80 CONTINUE
          WORK( 1 ) = LWKOPT
    *
          RETURN
    *
    *     End of ZGEGV
    *
          END