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


SYNOPSIS

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

           COMPLEX*16   ALPHA, BETA

           INTEGER      INCX, INCY, LDA, N

           CHARACTER*1  UPLO

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


PURPOSE

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

       A      - COMPLEX*16       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  hermitian
              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  hermitian  matrix  and  the strictly upper

              the  imaginary  parts of the diagonal elements need
              not be set and are assumed to be  zero.   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      - COMPLEX*16       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   - 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 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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