NAME

       ZHER2  -  perform the hermitian rank 2 operation   A := alpha*x*conjg( y' ) + conjg( alpha
       )*y*conjg( x' ) + A,

SYNOPSIS

       SUBROUTINE ZHER2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )

           COMPLEX*16   ALPHA

           INTEGER      INCX, INCY, LDA, N

           CHARACTER*1  UPLO

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

PURPOSE

       ZHER2  performs the hermitian rank 2 operation

       where alpha is a scalar, 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.

       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.

       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.  Unchanged on exit.

       INCY   - INTEGER.
              On entry, INCY specifies the increment for the elements of  Y.  INCY  must  not  be
              zero.  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.  On  exit, the upper
              triangular part of the array A is overwritten by the upper triangular part  of  the
              updated  matrix.   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. On
              exit, the lower triangular part  of  the  array  A  is  overwritten  by  the  lower
              triangular  part  of  the  updated  matrix.   Note  that the imaginary parts of the
              diagonal elements need not be set, they are assumed to be zero, and  on  exit  they
              are set to zero.

       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.

              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.