subroutine dsymv ( uplo, n, alpha, a, lda, x, incx,
     $                   beta, y, incy )
*     .. scalar arguments ..
      double precision   alpha, beta
      integer            incx, incy, lda, n
      character*1        uplo
*     .. array arguments ..
      double precision   a( lda, * ), x( * ), y( * )
*     ..
*
*  purpose
*  =======
*
*  dsymv  performs the matrix-vector  operation
*
*     y := alpha*a*x + beta*y,
*
*  where alpha and beta are scalars, x and y are n element vectors and
*  a is an n by n symmetric matrix.
*
*  parameters
*  ==========
*
*  uplo   - character*1.
*           on entry, uplo specifies whether the upper or lower
*           triangular part of the array a is to be referenced as
*           follows:
*
*              uplo = 'u' or 'u'   only the upper triangular part of a
*                                  is to be referenced.
*
*              uplo = 'l' or 'l'   only the lower triangular part of a
*                                  is to be referenced.
*
*           unchanged on exit.
*
*  n      - integer.
*           on entry, n specifies the order of the matrix a.
*           n must be at least zero.
*           unchanged on exit.
*
*  alpha  - double precision.
*           on entry, alpha specifies the scalar alpha.
*           unchanged on exit.
*
*  a      - double precision array of dimension ( lda, n ).
*           before entry with  uplo = 'u' or 'u', the leading n by n
*           upper triangular part of the array a must contain the upper
*           triangular part of the symmetric matrix and the strictly
*           lower triangular part of a is not referenced.
*           before entry with uplo = 'l' or 'l', the leading n by n
*           lower triangular part of the array a must contain the lower
*           triangular part of the symmetric matrix and the strictly
*           upper triangular part of a is not referenced.
*           unchanged on exit.
*
*  lda    - integer.
*           on entry, lda specifies the first dimension of a as declared
*           in the calling (sub) program. lda must be at least
*           max( 1, n ).
*           unchanged on exit.
*
*  x      - double precision array of dimension at least
*           ( 1 + ( n - 1 )*abs( incx ) ).
*           before entry, the incremented array x must contain the n
*           element vector x.
*           unchanged on exit.
*
*  incx   - integer.
*           on entry, incx specifies the increment for the elements of
*           x. incx must not be zero.
*           unchanged on exit.
*
*  beta   - double precision.
*           on entry, beta specifies the scalar beta. when beta is
*           supplied as zero then y need not be set on input.
*           unchanged on exit.
*
*  y      - double precision array of dimension at least
*           ( 1 + ( n - 1 )*abs( incy ) ).
*           before entry, the incremented array y must contain the n
*           element vector y. on exit, y is overwritten by the updated
*           vector y.
*
*  incy   - integer.
*           on entry, incy specifies the increment for the elements of
*           y. incy must not be zero.
*           unchanged on exit.
*
*
*  level 2 blas routine.
*
*  -- written on 22-october-1986.
*     jack dongarra, argonne national lab.
*     jeremy du croz, nag central office.
*     sven hammarling, nag central office.
*     richard hanson, sandia national labs.
*