NAME

       ZHER - perform the hermitian rank 1 operation   A := alpha*x*conjg( x' ) + A,

SYNOPSIS

       SUBROUTINE ZHER ( UPLO, N, ALPHA, X, INCX, A, LDA )

           DOUBLE      PRECISION ALPHA

           INTEGER     INCX, LDA, N

           CHARACTER*1 UPLO

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

PURPOSE

       ZHER   performs the hermitian rank 1 operation

       where  alpha  is  a  real  scalar,  x  is an n element vector 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  - DOUBLE PRECISION.
              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.

       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.