      SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
     $                   LIWORK, INFO )
*
*  -- LAPACK driver routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, UPLO
      INTEGER            INFO, LDA, LIWORK, LWORK, N
*     ..
*     .. Array Arguments ..
      INTEGER            IWORK( * )
      DOUBLE PRECISION   A( LDA, * ), W( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  DSYEVD computes all eigenvalues and, optionally, eigenvectors of a
*  real symmetric 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.
*
*  Because of large use of BLAS of level 3, DSYEVD needs N**2 more
*  workspace than DSYEVX.
*
*  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.
*
*  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
*          On entry, the symmetric 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, if JOBZ = 'V', then if INFO = 0, A contains the
*          orthonormal eigenvectors of the matrix A.
*          If JOBZ = 'N', then 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).
*
*  W       (output) DOUBLE PRECISION array, dimension (N)
*          If INFO = 0, the eigenvalues in ascending order.
*
*  WORK    (workspace/output) DOUBLE PRECISION array,
*                                         dimension (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 2*N+1.
*          If JOBZ = 'V' and N > 1, LWORK must be at least
*                                                1 + 6*N + 2*N**2.
*
*          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.
*
*  IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
*          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
*
*  LIWORK  (input) INTEGER
*          The dimension of the array IWORK.
*          If N <= 1,                LIWORK must be at least 1.
*          If JOBZ  = 'N' and 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 size of the IWORK array,
*          returns this value as the first entry of the IWORK array, and
*          no error message related to 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.
*
*  Further Details
*  ===============
*
*  Based on contributions by
*     Jeff Rutter, Computer Science Division, University of California
*     at Berkeley, USA
*  Modified by Francoise Tisseur, University of Tennessee.
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
*
      LOGICAL            LOWER, LQUERY, WANTZ
      INTEGER            IINFO, INDE, INDTAU, INDWK2, INDWRK, ISCALE,
     $                   LIOPT, LIWMIN, LLWORK, LLWRK2, LOPT, LWMIN
      DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
     $                   SMLNUM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLAMCH, DLANSY
      EXTERNAL           LSAME, DLAMCH, DLANSY
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLACPY, DLASCL, DORMTR, DSCAL, DSTEDC, DSTERF,
     $                   DSYTRD, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      WANTZ = LSAME( JOBZ, 'V' )
      LOWER = LSAME( UPLO, 'L' )
      LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
*
      INFO = 0
      IF( N.LE.1 ) THEN
         LIWMIN = 1
         LWMIN = 1
         LOPT = LWMIN
         LIOPT = LIWMIN
      ELSE
         IF( WANTZ ) THEN
            LIWMIN = 3 + 5*N
            LWMIN = 1 + 6*N + 2*N**2
         ELSE
            LIWMIN = 1
            LWMIN = 2*N + 1
         END IF
         LOPT = LWMIN
         LIOPT = LIWMIN
      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( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
         INFO = -8
      ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
         INFO = -10
      END IF
*
      IF( INFO.EQ.0 ) THEN
         WORK( 1 ) = LOPT
         IWORK( 1 ) = LIOPT
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DSYEVD', -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 ) = A( 1, 1 )
         IF( WANTZ )
     $      A( 1, 1 ) = ONE
         RETURN
      END IF
*
*     Get machine constants.
*
      SAFMIN = DLAMCH( 'Safe minimum' )
      EPS = DLAMCH( 'Precision' )
      SMLNUM = SAFMIN / EPS
      BIGNUM = ONE / SMLNUM
      RMIN = SQRT( SMLNUM )
      RMAX = SQRT( BIGNUM )
*
*     Scale matrix to allowable range, if necessary.
*
      ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK )
      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 )
     $   CALL DLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
*
*     Call DSYTRD to reduce symmetric matrix to tridiagonal form.
*
      INDE = 1
      INDTAU = INDE + N
      INDWRK = INDTAU + N
      LLWORK = LWORK - INDWRK + 1
      INDWK2 = INDWRK + N*N
      LLWRK2 = LWORK - INDWK2 + 1
*
      CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ),
     $             WORK( INDWRK ), LLWORK, IINFO )
      LOPT = 2*N + WORK( INDWRK )
*
*     For eigenvalues only, call DSTERF.  For eigenvectors, first call
*     DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
*     tridiagonal matrix, then call DORMTR to multiply it by the
*     Householder transformations stored in A.
*
      IF( .NOT.WANTZ ) THEN
         CALL DSTERF( N, W, WORK( INDE ), INFO )
      ELSE
         CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,
     $                WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO )
         CALL DORMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ),
     $                WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO )
         CALL DLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA )
         LOPT = MAX( LOPT, 1+6*N+2*N**2 )
      END IF
*
*     If matrix was scaled, then rescale eigenvalues appropriately.
*
      IF( ISCALE.EQ.1 )
     $   CALL DSCAL( N, ONE / SIGMA, W, 1 )
*
      WORK( 1 ) = LOPT
      IWORK( 1 ) = LIOPT
*
      RETURN
*
*     End of DSYEVD
*
      END
