```      SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, 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, LDVL, LDVR, LWORK, N
*     ..
*     .. Array Arguments ..
DOUBLE PRECISION   RWORK( * )
COMPLEX*16         A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
\$                   W( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  ZGEEV computes for an N-by-N complex 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 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) COMPLEX*16 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).
*
*  W       (output) COMPLEX*16 array, dimension (N)
*          W contains the computed eigenvalues.
*
*  VL      (output) COMPLEX*16 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.
*          u(j) = VL(:,j), the j-th column of VL.
*
*  LDVL    (input) INTEGER
*          The leading dimension of the array VL.  LDVL >= 1; if
*          JOBVL = 'V', LDVL >= N.
*
*  VR      (output) COMPLEX*16 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.
*          v(j) = VR(:,j), the j-th column of VR.
*
*  LDVR    (input) INTEGER
*          The leading dimension of the array VR.  LDVR >= 1; 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.
*
*          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) DOUBLE PRECISION array, dimension (2*N)
*
*  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 and i+1:N of W contain eigenvalues which have
*                converged.
*
*  =====================================================================
*
*     .. Parameters ..
DOUBLE PRECISION   ZERO, ONE
PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
*     ..
*     .. Local Scalars ..
LOGICAL            LQUERY, SCALEA, WANTVL, WANTVR
CHARACTER          SIDE
INTEGER            HSWORK, I, IBAL, IERR, IHI, ILO, IRWORK, ITAU,
\$                   IWRK, K, MAXWRK, MINWRK, NOUT
DOUBLE PRECISION   ANRM, BIGNUM, CSCALE, EPS, SCL, SMLNUM
COMPLEX*16         TMP
*     ..
*     .. Local Arrays ..
LOGICAL            SELECT( 1 )
DOUBLE PRECISION   DUM( 1 )
*     ..
*     .. External Subroutines ..
EXTERNAL           DLABAD, XERBLA, ZDSCAL, ZGEBAK, ZGEBAL, ZGEHRD,
\$                   ZHSEQR, ZLACPY, ZLASCL, ZSCAL, ZTREVC, ZUNGHR
*     ..
*     .. External Functions ..
LOGICAL            LSAME
INTEGER            IDAMAX, ILAENV
DOUBLE PRECISION   DLAMCH, DZNRM2, ZLANGE
EXTERNAL           LSAME, IDAMAX, ILAENV, DLAMCH, DZNRM2, ZLANGE
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          DBLE, DCMPLX, DCONJG, DIMAG, 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 = -8
ELSE IF( LDVR.LT.1 .OR. ( WANTVR .AND. LDVR.LT.N ) ) THEN
INFO = -10
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.
*       CWorkspace refers to complex workspace, and RWorkspace to real
*       workspace. NB refers to the optimal block size for the
*       immediately following subroutine, as returned by ILAENV.
*       HSWORK refers to the workspace preferred by ZHSEQR, 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 = N + N*ILAENV( 1, 'ZGEHRD', ' ', N, 1, N, 0 )
MINWRK = 2*N
IF( WANTVL ) THEN
MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'ZUNGHR',
\$                       ' ', N, 1, N, -1 ) )
CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VL, LDVL,
\$                WORK, -1, INFO )
ELSE IF( WANTVR ) THEN
MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'ZUNGHR',
\$                       ' ', N, 1, N, -1 ) )
CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VR, LDVR,
\$                WORK, -1, INFO )
ELSE
CALL ZHSEQR( 'E', 'N', N, 1, N, A, LDA, W, VR, LDVR,
\$                WORK, -1, INFO )
END IF
HSWORK = WORK( 1 )
MAXWRK = MAX( MAXWRK, HSWORK, MINWRK )
END IF
WORK( 1 ) = MAXWRK
*
IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
INFO = -12
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZGEEV ', -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, 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 ZLASCL( 'G', 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR )
*
*     Balance the matrix
*     (CWorkspace: none)
*     (RWorkspace: need N)
*
IBAL = 1
CALL ZGEBAL( 'B', N, A, LDA, ILO, IHI, RWORK( IBAL ), IERR )
*
*     Reduce to upper Hessenberg form
*     (CWorkspace: need 2*N, prefer N+N*NB)
*     (RWorkspace: none)
*
ITAU = 1
IWRK = ITAU + N
CALL ZGEHRD( 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 ZLACPY( 'L', N, N, A, LDA, VL, LDVL )
*
*        Generate unitary matrix in VL
*        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
*        (RWorkspace: none)
*
CALL ZUNGHR( N, ILO, IHI, VL, LDVL, WORK( ITAU ), WORK( IWRK ),
\$                LWORK-IWRK+1, IERR )
*
*        Perform QR iteration, accumulating Schur vectors in VL
*        (CWorkspace: need 1, prefer HSWORK (see comments) )
*        (RWorkspace: none)
*
IWRK = ITAU
CALL ZHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VL, LDVL,
\$                WORK( IWRK ), LWORK-IWRK+1, INFO )
*
IF( WANTVR ) THEN
*
*           Want left and right eigenvectors
*           Copy Schur vectors to VR
*
SIDE = 'B'
CALL ZLACPY( 'F', N, N, VL, LDVL, VR, LDVR )
END IF
*
ELSE IF( WANTVR ) THEN
*
*        Want right eigenvectors
*        Copy Householder vectors to VR
*
SIDE = 'R'
CALL ZLACPY( 'L', N, N, A, LDA, VR, LDVR )
*
*        Generate unitary matrix in VR
*        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
*        (RWorkspace: none)
*
CALL ZUNGHR( N, ILO, IHI, VR, LDVR, WORK( ITAU ), WORK( IWRK ),
\$                LWORK-IWRK+1, IERR )
*
*        Perform QR iteration, accumulating Schur vectors in VR
*        (CWorkspace: need 1, prefer HSWORK (see comments) )
*        (RWorkspace: none)
*
IWRK = ITAU
CALL ZHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VR, LDVR,
\$                WORK( IWRK ), LWORK-IWRK+1, INFO )
*
ELSE
*
*        Compute eigenvalues only
*        (CWorkspace: need 1, prefer HSWORK (see comments) )
*        (RWorkspace: none)
*
IWRK = ITAU
CALL ZHSEQR( 'E', 'N', N, ILO, IHI, A, LDA, W, VR, LDVR,
\$                WORK( IWRK ), LWORK-IWRK+1, INFO )
END IF
*
*     If INFO > 0 from ZHSEQR, then quit
*
IF( INFO.GT.0 )
\$   GO TO 50
*
IF( WANTVL .OR. WANTVR ) THEN
*
*        Compute left and/or right eigenvectors
*        (CWorkspace: need 2*N)
*        (RWorkspace: need 2*N)
*
IRWORK = IBAL + N
CALL ZTREVC( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR,
\$                N, NOUT, WORK( IWRK ), RWORK( IRWORK ), IERR )
END IF
*
IF( WANTVL ) THEN
*
*        Undo balancing of left eigenvectors
*        (CWorkspace: none)
*        (RWorkspace: need N)
*
CALL ZGEBAK( 'B', 'L', N, ILO, IHI, RWORK( IBAL ), N, VL, LDVL,
\$                IERR )
*
*        Normalize left eigenvectors and make largest component real
*
DO 20 I = 1, N
SCL = ONE / DZNRM2( N, VL( 1, I ), 1 )
CALL ZDSCAL( N, SCL, VL( 1, I ), 1 )
DO 10 K = 1, N
RWORK( IRWORK+K-1 ) = DBLE( VL( K, I ) )**2 +
\$                               DIMAG( VL( K, I ) )**2
10       CONTINUE
K = IDAMAX( N, RWORK( IRWORK ), 1 )
TMP = DCONJG( VL( K, I ) ) / SQRT( RWORK( IRWORK+K-1 ) )
CALL ZSCAL( N, TMP, VL( 1, I ), 1 )
VL( K, I ) = DCMPLX( DBLE( VL( K, I ) ), ZERO )
20    CONTINUE
END IF
*
IF( WANTVR ) THEN
*
*        Undo balancing of right eigenvectors
*        (CWorkspace: none)
*        (RWorkspace: need N)
*
CALL ZGEBAK( 'B', 'R', N, ILO, IHI, RWORK( IBAL ), N, VR, LDVR,
\$                IERR )
*
*        Normalize right eigenvectors and make largest component real
*
DO 40 I = 1, N
SCL = ONE / DZNRM2( N, VR( 1, I ), 1 )
CALL ZDSCAL( N, SCL, VR( 1, I ), 1 )
DO 30 K = 1, N
RWORK( IRWORK+K-1 ) = DBLE( VR( K, I ) )**2 +
\$                               DIMAG( VR( K, I ) )**2
30       CONTINUE
K = IDAMAX( N, RWORK( IRWORK ), 1 )
TMP = DCONJG( VR( K, I ) ) / SQRT( RWORK( IRWORK+K-1 ) )
CALL ZSCAL( N, TMP, VR( 1, I ), 1 )
VR( K, I ) = DCMPLX( DBLE( VR( K, I ) ), ZERO )
40    CONTINUE
END IF
*
*     Undo scaling if necessary
*
50 CONTINUE
IF( SCALEA ) THEN
CALL ZLASCL( 'G', 0, 0, CSCALE, ANRM, N-INFO, 1, W( INFO+1 ),
\$                MAX( N-INFO, 1 ), IERR )
IF( INFO.GT.0 ) THEN
CALL ZLASCL( 'G', 0, 0, CSCALE, ANRM, ILO-1, 1, W, N, IERR )
END IF
END IF
*
WORK( 1 ) = MAXWRK
RETURN
*
*     End of ZGEEV
*
END

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