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


SYNOPSIS

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

           REAL         ALPHA, BETA

           INTEGER      INCX, INCY, LDA, N

           CHARACTER*1  UPLO

           REAL         A( LDA, * ), X( * ), Y( * )


PURPOSE

       SSYMV  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  - REAL            .
              On   entry,   ALPHA  specifies  the  scalar  alpha.
              Unchanged on exit.

       A      - REAL             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 con­
              tain 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

              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      - REAL             array of dimension at least
              (  1  + ( n - 1 )*abs( INCX ) ).  Before entry, the
              incremented array X must contain the n element vec­
              tor x.  Unchanged on exit.

       INCX   - INTEGER.
              On entry, INCX specifies the increment for the ele­
              ments of X. INCX must not be  zero.   Unchanged  on
              exit.

       BETA   - REAL            .
              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      - REAL             array of dimension at least
              (  1  + ( n - 1 )*abs( INCY ) ).  Before entry, the
              incremented array Y must contain the n element vec­
              tor  y.  On  exit,  Y is overwritten by the updated
              vector y.

       INCY   - INTEGER.
              On entry, INCY specifies the increment for the ele­
              ments  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.


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