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


SYNOPSIS

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

           CHARACTER     UPLO

           INTEGER       INCX, INCY, LDA, N

           COMPLEX*16    ALPHA, BETA

           COMPLEX*16    A( LDA, * ), X( * ), Y( * )


PURPOSE

       ZSYMV  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.


ARGUMENTS

       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  - COMPLEX*16
              On  entry,  ALPHA  specifies  the   scalar   alpha.
              Unchanged on exit.

       A      - COMPLEX*16 array, 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 tri­
              angular  part of A is not referenced.  Unchanged on


       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      - COMPLEX*16 array, 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 ele­
              ments  of  X.  INCX must not be zero.  Unchanged on
              exit.

       BETA   - COMPLEX*16
              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      - COMPLEX*16 array, 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.


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