NAME

       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
              contain 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  triangular  part  of  A  is not referenced.  Note that 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
              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   - 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
              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.

BLAS routine                                     16 October 1992                                        ZHEMV(3)