NAME

       DSYMV - perform the matrix-vector operation   y := alpha*A*x + beta*y,

SYNOPSIS

       SUBROUTINE DSYMV ( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )

           DOUBLE       PRECISION ALPHA, BETA

           INTEGER      INCX, INCY, LDA, N

           CHARACTER*1  UPLO

           DOUBLE       PRECISION A( LDA, * ), X( * ), Y( * )

PURPOSE

       DSYMV  performs the matrix-vector  operation

       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.