```      SUBROUTINE CHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
\$                   LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
*
*  -- LAPACK driver routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          JOBZ, UPLO
INTEGER            INFO, KD, LDAB, LDZ, LIWORK, LRWORK, LWORK, N
*     ..
*     .. Array Arguments ..
INTEGER            IWORK( * )
REAL               RWORK( * ), W( * )
COMPLEX            AB( LDAB, * ), WORK( * ), Z( LDZ, * )
*     ..
*
*  Purpose
*  =======
*
*  CHBEVD computes all the eigenvalues and, optionally, eigenvectors of
*  a complex Hermitian band matrix A.  If eigenvectors are desired, it
*  uses a divide and conquer algorithm.
*
*  The divide and conquer algorithm makes very mild assumptions about
*  floating point arithmetic. It will work on machines with a guard
*  digit in add/subtract, or on those binary machines without guard
*  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*  Cray-2. It could conceivably fail on hexadecimal or decimal machines
*  without guard digits, but we know of none.
*
*  Arguments
*  =========
*
*  JOBZ    (input) CHARACTER*1
*          = 'N':  Compute eigenvalues only;
*          = 'V':  Compute eigenvalues and eigenvectors.
*
*  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.
*
*  KD      (input) INTEGER
*          The number of superdiagonals of the matrix A if UPLO = 'U',
*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
*
*  AB      (input/output) COMPLEX array, dimension (LDAB, N)
*          On entry, the upper or lower triangle of the Hermitian band
*          matrix A, stored in the first KD+1 rows of the array.  The
*          j-th column of A is stored in the j-th column of the array AB
*          as follows:
*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
*
*          On exit, AB is overwritten by values generated during the
*          reduction to tridiagonal form.  If UPLO = 'U', the first
*          superdiagonal and the diagonal of the tridiagonal matrix T
*          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
*          the diagonal and first subdiagonal of T are returned in the
*          first two rows of AB.
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array AB.  LDAB >= KD + 1.
*
*  W       (output) REAL array, dimension (N)
*          If INFO = 0, the eigenvalues in ascending order.
*
*  Z       (output) COMPLEX array, dimension (LDZ, N)
*          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
*          eigenvectors of the matrix A, with the i-th column of Z
*          holding the eigenvector associated with W(i).
*          If JOBZ = 'N', then Z is not referenced.
*
*  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 dimension of the array WORK.
*          If N <= 1,               LWORK must be at least 1.
*          If JOBZ = 'N' and N > 1, LWORK must be at least N.
*          If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal sizes of the WORK, RWORK and
*          IWORK arrays, returns these values as the first entries of
*          the WORK, RWORK and IWORK arrays, and no error message
*          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
*
*  RWORK   (workspace/output) REAL array,
*                                         dimension (LRWORK)
*          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
*
*  LRWORK  (input) INTEGER
*          The dimension of array RWORK.
*          If N <= 1,               LRWORK must be at least 1.
*          If JOBZ = 'N' and N > 1, LRWORK must be at least N.
*          If JOBZ = 'V' and N > 1, LRWORK must be at least
*                        1 + 5*N + 2*N**2.
*
*          If LRWORK = -1, then a workspace query is assumed; the
*          routine only calculates the optimal sizes of the WORK, RWORK
*          and IWORK arrays, returns these values as the first entries
*          of the WORK, RWORK and IWORK arrays, and no error message
*          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
*
*  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
*          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
*
*  LIWORK  (input) INTEGER
*          The dimension of array IWORK.
*          If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
*          If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N .
*
*          If LIWORK = -1, then a workspace query is assumed; the
*          routine only calculates the optimal sizes of the WORK, RWORK
*          and IWORK arrays, returns these values as the first entries
*          of the WORK, RWORK and IWORK arrays, and no error message
*          related to LWORK or LRWORK or LIWORK 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 algorithm failed to converge; i
*                off-diagonal elements of an intermediate tridiagonal
*                form did not converge to zero.
*
*  =====================================================================
*
*     .. Parameters ..
REAL               ZERO, ONE
PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
COMPLEX            CZERO, CONE
PARAMETER          ( CZERO = ( 0.0E0, 0.0E0 ),
\$                   CONE = ( 1.0E0, 0.0E0 ) )
*     ..
*     .. Local Scalars ..
LOGICAL            LOWER, LQUERY, WANTZ
INTEGER            IINFO, IMAX, INDE, INDWK2, INDWRK, ISCALE,
\$                   LIWMIN, LLRWK, LLWK2, LRWMIN, LWMIN
REAL               ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
\$                   SMLNUM
*     ..
*     .. External Functions ..
LOGICAL            LSAME
REAL               CLANHB, SLAMCH
EXTERNAL           LSAME, CLANHB, SLAMCH
*     ..
*     .. External Subroutines ..
EXTERNAL           CGEMM, CHBTRD, CLACPY, CLASCL, CSTEDC, SSCAL,
\$                   SSTERF, XERBLA
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
WANTZ = LSAME( JOBZ, 'V' )
LOWER = LSAME( UPLO, 'L' )
LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 .OR. LRWORK.EQ.-1 )
*
INFO = 0
IF( N.LE.1 ) THEN
LWMIN = 1
LRWMIN = 1
LIWMIN = 1
ELSE
IF( WANTZ ) THEN
LWMIN = 2*N**2
LRWMIN = 1 + 5*N + 2*N**2
LIWMIN = 3 + 5*N
ELSE
LWMIN = N
LRWMIN = N
LIWMIN = 1
END IF
END IF
IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( KD.LT.0 ) THEN
INFO = -4
ELSE IF( LDAB.LT.KD+1 ) THEN
INFO = -6
ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
INFO = -9
END IF
*
IF( INFO.EQ.0 ) THEN
WORK( 1 ) = LWMIN
RWORK( 1 ) = LRWMIN
IWORK( 1 ) = LIWMIN
*
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -11
ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
INFO = -13
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
INFO = -15
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CHBEVD', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 )
\$   RETURN
*
IF( N.EQ.1 ) THEN
W( 1 ) = AB( 1, 1 )
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 = SQRT( BIGNUM )
*
*     Scale matrix to allowable range, if necessary.
*
ANRM = CLANHB( 'M', UPLO, N, KD, AB, LDAB, RWORK )
ISCALE = 0
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
CALL CLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
ELSE
CALL CLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
END IF
END IF
*
*     Call CHBTRD to reduce Hermitian band matrix to tridiagonal form.
*
INDE = 1
INDWRK = INDE + N
INDWK2 = 1 + N*N
LLWK2 = LWORK - INDWK2 + 1
LLRWK = LRWORK - INDWRK + 1
CALL CHBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, RWORK( INDE ), Z,
\$             LDZ, WORK, IINFO )
*
*     For eigenvalues only, call SSTERF.  For eigenvectors, call CSTEDC.
*
IF( .NOT.WANTZ ) THEN
CALL SSTERF( N, W, RWORK( INDE ), INFO )
ELSE
CALL CSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ),
\$                LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK,
\$                INFO )
CALL CGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO,
\$               WORK( INDWK2 ), N )
CALL CLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
END IF
*
*     If matrix was scaled, then rescale eigenvalues appropriately.
*
IF( ISCALE.EQ.1 ) THEN
IF( INFO.EQ.0 ) THEN
IMAX = N
ELSE
IMAX = INFO - 1
END IF
CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
END IF
*
WORK( 1 ) = LWMIN
RWORK( 1 ) = LRWMIN
IWORK( 1 ) = LIWMIN
RETURN
*
*     End of CHBEVD
*
END

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