          SUBROUTINE SGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR,
         $                  LDVR, WORK, LWORK, 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, LDVL, LDVR, LWORK, N
    *     ..
    *     .. Array Arguments ..
          REAL               A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
         $                   WI( * ), WORK( * ), WR( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SGEEV computes for an N-by-N real nonsymmetric matrix A, the
    *  eigenvalues and, optionally, the left and/or right eigenvectors.
    *
    *  The right eigenvector v(j) of A satisfies
    *                   A * v(j) = lambda(j) * v(j)
    *  where lambda(j) is its eigenvalue.
    *  The left eigenvector u(j) of A satisfies
    *                u(j)**H * A = lambda(j) * u(j)**H
    *  where u(j)**H denotes the conjugate transpose of u(j).
    *
    *  The computed eigenvectors are normalized to have Euclidean norm
    *  equal to 1 and largest component real.
    *
    *  Arguments
    *  =========
    *
    *  JOBVL   (input) CHARACTER*1
    *          = 'N': left eigenvectors of A are not computed;
    *          = 'V': left eigenvectors of A are computed.
    *
    *  JOBVR   (input) CHARACTER*1
    *          = 'N': right eigenvectors of A are not computed;
    *          = 'V': right eigenvectors of A are computed.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A. N >= 0.
    *
    *  A       (input/output) REAL array, dimension (LDA,N)
    *          On entry, the N-by-N matrix A.
    *          On exit, A has been overwritten.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,N).
    *
    *  WR      (output) REAL array, dimension (N)
    *  WI      (output) REAL array, dimension (N)
    *          WR and WI contain the real and imaginary parts,
    *          respectively, of the computed eigenvalues.  Complex
    *          conjugate pairs of eigenvalues appear consecutively
    *          with the eigenvalue having the positive imaginary part
    *          first.
    *
    *  VL      (output) REAL array, dimension (LDVL,N)
    *          If JOBVL = 'V', the left eigenvectors u(j) are stored one
    *          after another in the columns of VL, in the same order
    *          as their eigenvalues.
    *          If JOBVL = 'N', VL is not referenced.
    *          If the j-th eigenvalue is real, then u(j) = VL(:,j),
    *          the j-th column of VL.
    *          If the j-th and (j+1)-st eigenvalues form a complex
    *          conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and
    *          u(j+1) = VL(:,j) - i*VL(:,j+1).
    *
    *  LDVL    (input) INTEGER
    *          The leading dimension of the array VL.  LDVL >= 1; if
    *          JOBVL = 'V', LDVL >= N.
    *
    *  VR      (output) REAL array, dimension (LDVR,N)
    *          If JOBVR = 'V', the right eigenvectors v(j) are stored one
    *          after another in the columns of VR, in the same order
    *          as their eigenvalues.
    *          If JOBVR = 'N', VR is not referenced.
    *          If the j-th eigenvalue is real, then v(j) = VR(:,j),
    *          the j-th column of VR.
    *          If the j-th and (j+1)-st eigenvalues form a complex
    *          conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and
    *          v(j+1) = VR(:,j) - i*VR(:,j+1).
    *
    *  LDVR    (input) INTEGER
    *          The leading dimension of the array VR.  LDVR >= 1; if
    *          JOBVR = 'V', LDVR >= N.
    *
    *  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.  LWORK >= max(1,3*N), and
    *          if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*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.
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value.
    *          > 0:  if INFO = i, the QR algorithm failed to compute all the
    *                eigenvalues, and no eigenvectors have been computed;
    *                elements i+1:N of WR and WI contain eigenvalues which
    *                have converged.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ZERO, ONE
          PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            LQUERY, SCALEA, WANTVL, WANTVR
          CHARACTER          SIDE
          INTEGER            HSWORK, I, IBAL, IERR, IHI, ILO, ITAU, IWRK, K,
         $                   MAXWRK, MINWRK, NOUT
          REAL               ANRM, BIGNUM, CS, CSCALE, EPS, R, SCL, SMLNUM,
         $                   SN
    *     ..
    *     .. Local Arrays ..
          LOGICAL            SELECT( 1 )
          REAL               DUM( 1 )
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SGEBAK, SGEBAL, SGEHRD, SHSEQR, SLABAD, SLACPY,
         $                   SLARTG, SLASCL, SORGHR, SROT, SSCAL, STREVC,
         $                   XERBLA
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV, ISAMAX
          REAL               SLAMCH, SLANGE, SLAPY2, SNRM2
          EXTERNAL           LSAME, ILAENV, ISAMAX, SLAMCH, SLANGE, SLAPY2,
         $                   SNRM2
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, SQRT
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input arguments
    *
          INFO = 0
          LQUERY = ( LWORK.EQ.-1 )
          WANTVL = LSAME( JOBVL, 'V' )
          WANTVR = LSAME( JOBVR, 'V' )
          IF( ( .NOT.WANTVL ) .AND. ( .NOT.LSAME( JOBVL, 'N' ) ) ) THEN
             INFO = -1
          ELSE IF( ( .NOT.WANTVR ) .AND. ( .NOT.LSAME( JOBVR, 'N' ) ) ) THEN
             INFO = -2
          ELSE IF( N.LT.0 ) THEN
             INFO = -3
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -5
          ELSE IF( LDVL.LT.1 .OR. ( WANTVL .AND. LDVL.LT.N ) ) THEN
             INFO = -9
          ELSE IF( LDVR.LT.1 .OR. ( WANTVR .AND. LDVR.LT.N ) ) THEN
             INFO = -11
          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.
    *       HSWORK refers to the workspace preferred by SHSEQR, as
    *       calculated below. HSWORK 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
                MAXWRK = 2*N + N*ILAENV( 1, 'SGEHRD', ' ', N, 1, N, 0 )
                IF( WANTVL ) THEN
                   MINWRK = 4*N
                   MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*ILAENV( 1,
         $                       'SORGHR', ' ', N, 1, N, -1 ) )
                   CALL SHSEQR( 'S', 'V', N, 1, N, A, LDA, WR, WI, VL, LDVL,
         $                WORK, -1, INFO )
                   HSWORK = WORK( 1 )
                   MAXWRK = MAX( MAXWRK, N + 1, N + HSWORK )
                   MAXWRK = MAX( MAXWRK, 4*N )
                ELSE IF( WANTVR ) THEN
                   MINWRK = 4*N
                   MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*ILAENV( 1,
         $                       'SORGHR', ' ', N, 1, N, -1 ) )
                   CALL SHSEQR( 'S', 'V', N, 1, N, A, LDA, WR, WI, VR, LDVR,
         $                WORK, -1, INFO )
                   HSWORK = WORK( 1 )
                   MAXWRK = MAX( MAXWRK, N + 1, N + HSWORK )
                   MAXWRK = MAX( MAXWRK, 4*N )
                ELSE
                   MINWRK = 3*N
                   CALL SHSEQR( 'E', 'N', N, 1, N, A, LDA, WR, WI, VR, LDVR,
         $                WORK, -1, INFO )
                   HSWORK = WORK( 1 )
                   MAXWRK = MAX( MAXWRK, N + 1, N + HSWORK )
                END IF
                MAXWRK = MAX( MAXWRK, MINWRK )
             END IF
             WORK( 1 ) = MAXWRK
    *
             IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
                INFO = -13
             END IF
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'SGEEV ', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
    *     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 = SLANGE( 'M', N, N, A, LDA, DUM )
          SCALEA = .FALSE.
          IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
             SCALEA = .TRUE.
             CSCALE = SMLNUM
          ELSE IF( ANRM.GT.BIGNUM ) THEN
             SCALEA = .TRUE.
             CSCALE = BIGNUM
          END IF
          IF( SCALEA )
         $   CALL SLASCL( 'G', 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR )
    *
    *     Balance the matrix
    *     (Workspace: need N)
    *
          IBAL = 1
          CALL SGEBAL( 'B', N, A, LDA, ILO, IHI, WORK( IBAL ), IERR )
    *
    *     Reduce to upper Hessenberg form
    *     (Workspace: need 3*N, prefer 2*N+N*NB)
    *
          ITAU = IBAL + N
          IWRK = ITAU + N
          CALL SGEHRD( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ),
         $             LWORK-IWRK+1, IERR )
    *
          IF( WANTVL ) THEN
    *
    *        Want left eigenvectors
    *        Copy Householder vectors to VL
    *
             SIDE = 'L'
             CALL SLACPY( 'L', N, N, A, LDA, VL, LDVL )
    *
    *        Generate orthogonal matrix in VL
    *        (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB)
    *
             CALL SORGHR( N, ILO, IHI, VL, LDVL, WORK( ITAU ), WORK( IWRK ),
         $                LWORK-IWRK+1, IERR )
    *
    *        Perform QR iteration, accumulating Schur vectors in VL
    *        (Workspace: need N+1, prefer N+HSWORK (see comments) )
    *
             IWRK = ITAU
             CALL SHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, WR, WI, VL, LDVL,
         $                WORK( IWRK ), LWORK-IWRK+1, INFO )
    *
             IF( WANTVR ) THEN
    *
    *           Want left and right eigenvectors
    *           Copy Schur vectors to VR
    *
                SIDE = 'B'
                CALL SLACPY( 'F', N, N, VL, LDVL, VR, LDVR )
             END IF
    *
          ELSE IF( WANTVR ) THEN
    *
    *        Want right eigenvectors
    *        Copy Householder vectors to VR
    *
             SIDE = 'R'
             CALL SLACPY( 'L', N, N, A, LDA, VR, LDVR )
    *
    *        Generate orthogonal matrix in VR
    *        (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB)
    *
             CALL SORGHR( N, ILO, IHI, VR, LDVR, WORK( ITAU ), WORK( IWRK ),
         $                LWORK-IWRK+1, IERR )
    *
    *        Perform QR iteration, accumulating Schur vectors in VR
    *        (Workspace: need N+1, prefer N+HSWORK (see comments) )
    *
             IWRK = ITAU
             CALL SHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, WR, WI, VR, LDVR,
         $                WORK( IWRK ), LWORK-IWRK+1, INFO )
    *
          ELSE
    *
    *        Compute eigenvalues only
    *        (Workspace: need N+1, prefer N+HSWORK (see comments) )
    *
             IWRK = ITAU
             CALL SHSEQR( 'E', 'N', N, ILO, IHI, A, LDA, WR, WI, VR, LDVR,
         $                WORK( IWRK ), LWORK-IWRK+1, INFO )
          END IF
    *
    *     If INFO > 0 from SHSEQR, then quit
    *
          IF( INFO.GT.0 )
         $   GO TO 50
    *
          IF( WANTVL .OR. WANTVR ) THEN
    *
    *        Compute left and/or right eigenvectors
    *        (Workspace: need 4*N)
    *
             CALL STREVC( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR,
         $                N, NOUT, WORK( IWRK ), IERR )
          END IF
    *
          IF( WANTVL ) THEN
    *
    *        Undo balancing of left eigenvectors
    *        (Workspace: need N)
    *
             CALL SGEBAK( 'B', 'L', N, ILO, IHI, WORK( IBAL ), N, VL, LDVL,
         $                IERR )
    *
    *        Normalize left eigenvectors and make largest component real
    *
             DO 20 I = 1, N
                IF( WI( I ).EQ.ZERO ) THEN
                   SCL = ONE / SNRM2( N, VL( 1, I ), 1 )
                   CALL SSCAL( N, SCL, VL( 1, I ), 1 )
                ELSE IF( WI( I ).GT.ZERO ) THEN
                   SCL = ONE / SLAPY2( SNRM2( N, VL( 1, I ), 1 ),
         $               SNRM2( N, VL( 1, I+1 ), 1 ) )
                   CALL SSCAL( N, SCL, VL( 1, I ), 1 )
                   CALL SSCAL( N, SCL, VL( 1, I+1 ), 1 )
                   DO 10 K = 1, N
                      WORK( IWRK+K-1 ) = VL( K, I )**2 + VL( K, I+1 )**2
       10          CONTINUE
                   K = ISAMAX( N, WORK( IWRK ), 1 )
                   CALL SLARTG( VL( K, I ), VL( K, I+1 ), CS, SN, R )
                   CALL SROT( N, VL( 1, I ), 1, VL( 1, I+1 ), 1, CS, SN )
                   VL( K, I+1 ) = ZERO
                END IF
       20    CONTINUE
          END IF
    *
          IF( WANTVR ) THEN
    *
    *        Undo balancing of right eigenvectors
    *        (Workspace: need N)
    *
             CALL SGEBAK( 'B', 'R', N, ILO, IHI, WORK( IBAL ), N, VR, LDVR,
         $                IERR )
    *
    *        Normalize right eigenvectors and make largest component real
    *
             DO 40 I = 1, N
                IF( WI( I ).EQ.ZERO ) THEN
                   SCL = ONE / SNRM2( N, VR( 1, I ), 1 )
                   CALL SSCAL( N, SCL, VR( 1, I ), 1 )
                ELSE IF( WI( I ).GT.ZERO ) THEN
                   SCL = ONE / SLAPY2( SNRM2( N, VR( 1, I ), 1 ),
         $               SNRM2( N, VR( 1, I+1 ), 1 ) )
                   CALL SSCAL( N, SCL, VR( 1, I ), 1 )
                   CALL SSCAL( N, SCL, VR( 1, I+1 ), 1 )
                   DO 30 K = 1, N
                      WORK( IWRK+K-1 ) = VR( K, I )**2 + VR( K, I+1 )**2
       30          CONTINUE
                   K = ISAMAX( N, WORK( IWRK ), 1 )
                   CALL SLARTG( VR( K, I ), VR( K, I+1 ), CS, SN, R )
                   CALL SROT( N, VR( 1, I ), 1, VR( 1, I+1 ), 1, CS, SN )
                   VR( K, I+1 ) = ZERO
                END IF
       40    CONTINUE
          END IF
    *
    *     Undo scaling if necessary
    *
       50 CONTINUE
          IF( SCALEA ) THEN
             CALL SLASCL( 'G', 0, 0, CSCALE, ANRM, N-INFO, 1, WR( INFO+1 ),
         $                MAX( N-INFO, 1 ), IERR )
             CALL SLASCL( 'G', 0, 0, CSCALE, ANRM, N-INFO, 1, WI( INFO+1 ),
         $                MAX( N-INFO, 1 ), IERR )
             IF( INFO.GT.0 ) THEN
                CALL SLASCL( 'G', 0, 0, CSCALE, ANRM, ILO-1, 1, WR, N,
         $                   IERR )
                CALL SLASCL( 'G', 0, 0, CSCALE, ANRM, ILO-1, 1, WI, N,
         $                   IERR )
             END IF
          END IF
    *
          WORK( 1 ) = MAXWRK
          RETURN
    *
    *     End of SGEEV
    *
          END