          SUBROUTINE CHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
         $                   ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK,
         $                   IWORK, IFAIL, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBZ, RANGE, UPLO
          INTEGER            IL, INFO, IU, LDA, LDZ, LWORK, M, N
          REAL               ABSTOL, VL, VU
    *     ..
    *     .. Array Arguments ..
          INTEGER            IFAIL( * ), IWORK( * )
          REAL               RWORK( * ), W( * )
          COMPLEX            A( LDA, * ), WORK( * ), Z( LDZ, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CHEEVX computes selected eigenvalues and, optionally, eigenvectors
    *  of a complex Hermitian matrix A.  Eigenvalues and eigenvectors can
    *  be selected by specifying either a range of values or a range of
    *  indices for the desired eigenvalues.
    *
    *  Arguments
    *  =========
    *
    *  JOBZ    (input) CHARACTER*1
    *          = 'N':  Compute eigenvalues only;
    *          = 'V':  Compute eigenvalues and eigenvectors.
    *
    *  RANGE   (input) CHARACTER*1
    *          = 'A': all eigenvalues will be found.
    *          = 'V': all eigenvalues in the half-open interval (VL,VU]
    *                 will be found.
    *          = 'I': the IL-th through IU-th eigenvalues will be found.
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U':  Upper triangle of A is stored;
    *          = 'L':  Lower triangle of A is stored.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  A       (input/output) COMPLEX array, dimension (LDA, N)
    *          On entry, the Hermitian matrix A.  If UPLO = 'U', the
    *          leading N-by-N upper triangular part of A contains the
    *          upper triangular part of the matrix A.  If UPLO = 'L',
    *          the leading N-by-N lower triangular part of A contains
    *          the lower triangular part of the matrix A.
    *          On exit, the lower triangle (if UPLO='L') or the upper
    *          triangle (if UPLO='U') of A, including the diagonal, is
    *          destroyed.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,N).
    *
    *  VL      (input) REAL
    *  VU      (input) REAL
    *          If RANGE='V', the lower and upper bounds of the interval to
    *          be searched for eigenvalues. VL < VU.
    *          Not referenced if RANGE = 'A' or 'I'.
    *
    *  IL      (input) INTEGER
    *  IU      (input) INTEGER
    *          If RANGE='I', the indices (in ascending order) of the
    *          smallest and largest eigenvalues to be returned.
    *          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
    *          Not referenced if RANGE = 'A' or 'V'.
    *
    *  ABSTOL  (input) REAL
    *          The absolute error tolerance for the eigenvalues.
    *          An approximate eigenvalue is accepted as converged
    *          when it is determined to lie in an interval [a,b]
    *          of width less than or equal to
    *
    *                  ABSTOL + EPS *   max( |a|,|b| ) ,
    *
    *          where EPS is the machine precision.  If ABSTOL is less than
    *          or equal to zero, then  EPS*|T|  will be used in its place,
    *          where |T| is the 1-norm of the tridiagonal matrix obtained
    *          by reducing A to tridiagonal form.
    *
    *          Eigenvalues will be computed most accurately when ABSTOL is
    *          set to twice the underflow threshold 2*SLAMCH('S'), not zero.
    *          If this routine returns with INFO>0, indicating that some
    *          eigenvectors did not converge, try setting ABSTOL to
    *          2*SLAMCH('S').
    *
    *          See "Computing Small Singular Values of Bidiagonal Matrices
    *          with Guaranteed High Relative Accuracy," by Demmel and
    *          Kahan, LAPACK Working Note #3.
    *
    *  M       (output) INTEGER
    *          The total number of eigenvalues found.  0 <= M <= N.
    *          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
    *
    *  W       (output) REAL array, dimension (N)
    *          On normal exit, the first M elements contain the selected
    *          eigenvalues in ascending order.
    *
    *  Z       (output) COMPLEX array, dimension (LDZ, max(1,M))
    *          If JOBZ = 'V', then if INFO = 0, the first M columns of Z
    *          contain the orthonormal eigenvectors of the matrix A
    *          corresponding to the selected eigenvalues, with the i-th
    *          column of Z holding the eigenvector associated with W(i).
    *          If an eigenvector fails to converge, then that column of Z
    *          contains the latest approximation to the eigenvector, and the
    *          index of the eigenvector is returned in IFAIL.
    *          If JOBZ = 'N', then Z is not referenced.
    *          Note: the user must ensure that at least max(1,M) columns are
    *          supplied in the array Z; if RANGE = 'V', the exact value of M
    *          is not known in advance and an upper bound must be used.
    *
    *  LDZ     (input) INTEGER
    *          The leading dimension of the array Z.  LDZ >= 1, and if
    *          JOBZ = 'V', LDZ >= max(1,N).
    *
    *  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) INTEGER
    *          The length of the array WORK.  LWORK >= 1, when N <= 1;
    *          otherwise 2*N.
    *          For optimal efficiency, LWORK >= (NB+1)*N,
    *          where NB is the max of the blocksize for CHETRD and for
    *          CUNMTR as returned by ILAENV.
    *
    *          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 (7*N)
    *
    *  IWORK   (workspace) INTEGER array, dimension (5*N)
    *
    *  IFAIL   (output) INTEGER array, dimension (N)
    *          If JOBZ = 'V', then if INFO = 0, the first M elements of
    *          IFAIL are zero.  If INFO > 0, then IFAIL contains the
    *          indices of the eigenvectors that failed to converge.
    *          If JOBZ = 'N', then IFAIL is not referenced.
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *          > 0:  if INFO = i, then i eigenvectors failed to converge.
    *                Their indices are stored in array IFAIL.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ZERO, ONE
          PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
          COMPLEX            CONE
          PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ) )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG,
         $                   WANTZ
          CHARACTER          ORDER
          INTEGER            I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
         $                   INDISP, INDIWK, INDRWK, INDTAU, INDWRK, ISCALE,
         $                   ITMP1, J, JJ, LLWORK, LWKMIN, LWKOPT, NB,
         $                   NSPLIT
          REAL               ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
         $                   SIGMA, SMLNUM, TMP1, VLL, VUU
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          REAL               CLANHE, SLAMCH
          EXTERNAL           LSAME, ILAENV, CLANHE, SLAMCH
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CHETRD, CLACPY, CSSCAL, CSTEIN, CSTEQR, CSWAP,
         $                   CUNGTR, CUNMTR, SCOPY, SSCAL, SSTEBZ, SSTERF,
         $                   XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN, REAL, SQRT
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          LOWER = LSAME( UPLO, 'L' )
          WANTZ = LSAME( JOBZ, 'V' )
          ALLEIG = LSAME( RANGE, 'A' )
          VALEIG = LSAME( RANGE, 'V' )
          INDEIG = LSAME( RANGE, 'I' )
          LQUERY = ( LWORK.EQ.-1 )
    *
          INFO = 0
          IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
             INFO = -1
          ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
             INFO = -2
          ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
             INFO = -3
          ELSE IF( N.LT.0 ) THEN
             INFO = -4
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -6
          ELSE
             IF( VALEIG ) THEN
                IF( N.GT.0 .AND. VU.LE.VL )
         $         INFO = -8
             ELSE IF( INDEIG ) THEN
                IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
                   INFO = -9
                ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
                   INFO = -10
                END IF
             END IF
          END IF
          IF( INFO.EQ.0 ) THEN
             IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
                INFO = -15
             END IF
          END IF
    *
          IF( INFO.EQ.0 ) THEN
             IF( N.LE.1 ) THEN
                LWKMIN = 1
                WORK( 1 ) = LWKMIN
             ELSE
                LWKMIN = 2*N
                NB = ILAENV( 1, 'CHETRD', UPLO, N, -1, -1, -1 )
                NB = MAX( NB, ILAENV( 1, 'CUNMTR', UPLO, N, -1, -1, -1 ) )
                LWKOPT = MAX( 1, ( NB + 1 )*N )
                WORK( 1 ) = LWKOPT
             END IF
    *
             IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY )
         $      INFO = -17
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'CHEEVX', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          M = 0
          IF( N.EQ.0 ) THEN
             RETURN
          END IF
    *
          IF( N.EQ.1 ) THEN
             IF( ALLEIG .OR. INDEIG ) THEN
                M = 1
                W( 1 ) = A( 1, 1 )
             ELSE IF( VALEIG ) THEN
                IF( VL.LT.REAL( A( 1, 1 ) ) .AND. VU.GE.REAL( A( 1, 1 ) ) )
         $           THEN
                   M = 1
                   W( 1 ) = A( 1, 1 )
                END IF
             END IF
             IF( WANTZ )
         $      Z( 1, 1 ) = CONE
             RETURN
          END IF
    *
    *     Get machine constants.
    *
          SAFMIN = SLAMCH( 'Safe minimum' )
          EPS = SLAMCH( 'Precision' )
          SMLNUM = SAFMIN / EPS
          BIGNUM = ONE / SMLNUM
          RMIN = SQRT( SMLNUM )
          RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
    *
    *     Scale matrix to allowable range, if necessary.
    *
          ISCALE = 0
          ABSTLL = ABSTOL
          IF( VALEIG ) THEN
             VLL = VL
             VUU = VU
          END IF
          ANRM = CLANHE( 'M', UPLO, N, A, LDA, RWORK )
          IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
             ISCALE = 1
             SIGMA = RMIN / ANRM
          ELSE IF( ANRM.GT.RMAX ) THEN
             ISCALE = 1
             SIGMA = RMAX / ANRM
          END IF
          IF( ISCALE.EQ.1 ) THEN
             IF( LOWER ) THEN
                DO 10 J = 1, N
                   CALL CSSCAL( N-J+1, SIGMA, A( J, J ), 1 )
       10       CONTINUE
             ELSE
                DO 20 J = 1, N
                   CALL CSSCAL( J, SIGMA, A( 1, J ), 1 )
       20       CONTINUE
             END IF
             IF( ABSTOL.GT.0 )
         $      ABSTLL = ABSTOL*SIGMA
             IF( VALEIG ) THEN
                VLL = VL*SIGMA
                VUU = VU*SIGMA
             END IF
          END IF
    *
    *     Call CHETRD to reduce Hermitian matrix to tridiagonal form.
    *
          INDD = 1
          INDE = INDD + N
          INDRWK = INDE + N
          INDTAU = 1
          INDWRK = INDTAU + N
          LLWORK = LWORK - INDWRK + 1
          CALL CHETRD( UPLO, N, A, LDA, RWORK( INDD ), RWORK( INDE ),
         $             WORK( INDTAU ), WORK( INDWRK ), LLWORK, IINFO )
    *
    *     If all eigenvalues are desired and ABSTOL is less than or equal to
    *     zero, then call SSTERF or CUNGTR and CSTEQR.  If this fails for
    *     some eigenvalue, then try SSTEBZ.
    *
          TEST = .FALSE.
          IF( INDEIG ) THEN
             IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
                TEST = .TRUE.
             END IF
          END IF
          IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN
             CALL SCOPY( N, RWORK( INDD ), 1, W, 1 )
             INDEE = INDRWK + 2*N
             IF( .NOT.WANTZ ) THEN
                CALL SCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
                CALL SSTERF( N, W, RWORK( INDEE ), INFO )
             ELSE
                CALL CLACPY( 'A', N, N, A, LDA, Z, LDZ )
                CALL CUNGTR( UPLO, N, Z, LDZ, WORK( INDTAU ),
         $                   WORK( INDWRK ), LLWORK, IINFO )
                CALL SCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
                CALL CSTEQR( JOBZ, N, W, RWORK( INDEE ), Z, LDZ,
         $                   RWORK( INDRWK ), INFO )
                IF( INFO.EQ.0 ) THEN
                   DO 30 I = 1, N
                      IFAIL( I ) = 0
       30          CONTINUE
                END IF
             END IF
             IF( INFO.EQ.0 ) THEN
                M = N
                GO TO 40
             END IF
             INFO = 0
          END IF
    *
    *     Otherwise, call SSTEBZ and, if eigenvectors are desired, CSTEIN.
    *
          IF( WANTZ ) THEN
             ORDER = 'B'
          ELSE
             ORDER = 'E'
          END IF
          INDIBL = 1
          INDISP = INDIBL + N
          INDIWK = INDISP + N
          CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
         $             RWORK( INDD ), RWORK( INDE ), M, NSPLIT, W,
         $             IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ),
         $             IWORK( INDIWK ), INFO )
    *
          IF( WANTZ ) THEN
             CALL CSTEIN( N, RWORK( INDD ), RWORK( INDE ), M, W,
         $                IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
         $                RWORK( INDRWK ), IWORK( INDIWK ), IFAIL, INFO )
    *
    *        Apply unitary matrix used in reduction to tridiagonal
    *        form to eigenvectors returned by CSTEIN.
    *
             CALL CUNMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z,
         $                LDZ, WORK( INDWRK ), LLWORK, IINFO )
          END IF
    *
    *     If matrix was scaled, then rescale eigenvalues appropriately.
    *
       40 CONTINUE
          IF( ISCALE.EQ.1 ) THEN
             IF( INFO.EQ.0 ) THEN
                IMAX = M
             ELSE
                IMAX = INFO - 1
             END IF
             CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
          END IF
    *
    *     If eigenvalues are not in order, then sort them, along with
    *     eigenvectors.
    *
          IF( WANTZ ) THEN
             DO 60 J = 1, M - 1
                I = 0
                TMP1 = W( J )
                DO 50 JJ = J + 1, M
                   IF( W( JJ ).LT.TMP1 ) THEN
                      I = JJ
                      TMP1 = W( JJ )
                   END IF
       50       CONTINUE
    *
                IF( I.NE.0 ) THEN
                   ITMP1 = IWORK( INDIBL+I-1 )
                   W( I ) = W( J )
                   IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
                   W( J ) = TMP1
                   IWORK( INDIBL+J-1 ) = ITMP1
                   CALL CSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
                   IF( INFO.NE.0 ) THEN
                      ITMP1 = IFAIL( I )
                      IFAIL( I ) = IFAIL( J )
                      IFAIL( J ) = ITMP1
                   END IF
                END IF
       60    CONTINUE
          END IF
    *
    *     Set WORK(1) to optimal complex workspace size.
    *
          WORK( 1 ) = LWKOPT
    *
          RETURN
    *
    *     End of CHEEVX
    *
          END