NAME

       CHER2  - perform the hermitian rank 2 operation   A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' )
       + A,

SYNOPSIS

       SUBROUTINE CHER2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )

           COMPLEX      ALPHA

           INTEGER      INCX, INCY, LDA, N

           CHARACTER*1  UPLO

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

PURPOSE

       CHER2  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         .
              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       X      - COMPLEX          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          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          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.