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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.