SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, 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, LDA, LWORK, N
!     ..
!     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), W( * ), WORK( * )
!     ..
!
!  Purpose
!  =======
!
!  DSYEV computes all eigenvalues and, optionally, eigenvectors of a
!  real symmetric matrix A.
!
!  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 (MAX(1,LWORK))
!          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!
!  LWORK   (input) INTEGER
!          The length of the array WORK.  LWORK >= max(1,3*N-1).
!          For optimal efficiency, LWORK >= (NB+2)*N,
!          where NB is the blocksize for DSYTRD 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.
!
!  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 ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
!     ..
!     .. Local Scalars ..
      LOGICAL            LOWER, LQUERY, WANTZ
      INTEGER            IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE, &
                         LLWORK, LWKOPT, NB
      DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, &
                         SMLNUM
!     ..
!     .. External Functions ..
!     LOGICAL            LSAME
!     INTEGER            ILAENV
!     DOUBLE PRECISION   DLAMCH, DLANSY
!     EXTERNAL           LSAME
!     EXTERNAL           ILAENV, DLAMCH, DLANSY
!     ..
!     .. External Subroutines ..
!     EXTERNAL           DLASCL, DORGTR, DSCAL, DSTEQR, 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 )
!
      INFO = 0
      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
      END IF
!
      IF( INFO.EQ.0 ) THEN
         NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
         LWKOPT = MAX( 1, ( NB+2 )*N )
         WORK( 1 ) = LWKOPT
!
         IF( LWORK.LT.MAX( 1, 3*N-1 ) .AND. .NOT.LQUERY ) &
            INFO = -8
      END IF
!
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DSYEV ', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
!
!     Quick return if possible
!
      IF( N.EQ.0 ) THEN
         RETURN
      END IF
!
      IF( N.EQ.1 ) THEN
         W( 1 ) = A( 1, 1 )
         WORK( 1 ) = 2
         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
      CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ), &
                   WORK( INDWRK ), LLWORK, IINFO )
!
!     For eigenvalues only, call DSTERF.  For eigenvectors, first call
!     DORGTR to generate the orthogonal matrix, then call DSTEQR.
!
      IF( .NOT.WANTZ ) THEN
         CALL DSTERF( N, W, WORK( INDE ), INFO )
      ELSE
         CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ), &
                      LLWORK, IINFO )
         CALL DSTEQR( JOBZ, N, W, WORK( INDE ), A, LDA, WORK( INDTAU ), &
                      INFO )
      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 DSCAL( IMAX, ONE / SIGMA, W, 1 )
      END IF
!
!     Set WORK(1) to optimal workspace size.
!
      WORK( 1 ) = LWKOPT
!
      RETURN
!
!     End of DSYEV
!
      END SUBROUTINE DSYEV