NAME

       CHER2K  -  perform  one  of  the  hermitian  rank 2k operations   C := alpha*A*conjg( B' ) + conjg( alpha
       )*B*conjg( A' ) + beta*C,

SYNOPSIS

       SUBROUTINE CHER2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC )

           CHARACTER*1    UPLO, TRANS

           INTEGER        N, K, LDA, LDB, LDC

           REAL           BETA

           COMPLEX        ALPHA

           COMPLEX        A( LDA, * ), B( LDB, * ), C( LDC, * )

PURPOSE

       CHER2K  performs one of the hermitian rank 2k operations

       or

          C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C,

       where  alpha and beta  are scalars with  beta  real,  C is an  n by n hermitian matrix and  A and B   are
       n by k matrices in the first case and  k by n  matrices in the second case.

PARAMETERS

       UPLO   - CHARACTER*1.
              On   entry,    UPLO   specifies  whether  the  upper  or  lower triangular  part  of the  array  C
              is to be  referenced  as follows:

              UPLO = 'U' or 'u'   Only the  upper triangular part of  C is to be referenced.

              UPLO = 'L' or 'l'   Only the  lower triangular part of  C is to be referenced.

              Unchanged on exit.

       TRANS  - CHARACTER*1.
              On entry,  TRANS  specifies the operation to be performed as follows:

              TRANS = 'N' or 'n'    C := alpha*A*conjg( B' )          + conjg( alpha )*B*conjg( A' ) + beta*C.

              TRANS = 'C' or 'c'    C := alpha*conjg( A' )*B          + conjg( alpha )*conjg( B' )*A + beta*C.

              Unchanged on exit.

       N      - INTEGER.
              On entry,  N specifies the order of the matrix C.  N must be at least zero.  Unchanged on exit.

       K      - INTEGER.
              On entry with  TRANS = 'N' or 'n',  K  specifies  the number of  columns  of the  matrices  A  and
              B,   and  on  entry  with TRANS = 'C' or 'c',  K  specifies  the number of rows of the matrices  A
              and B.  K must be at least zero.  Unchanged on exit.

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

       A      - COMPLEX          array of DIMENSION ( LDA, ka ), where ka is
              k  when  TRANS = 'N' or 'n',  and is  n  otherwise.  Before entry with  TRANS = 'N' or  'n',   the
              leading   n  by k part of the array  A  must contain the matrix  A,  otherwise the leading  k by n
              part of the array  A  must contain  the matrix A.  Unchanged on exit.

       LDA    - INTEGER.
              On entry, LDA specifies the first dimension of A as declared in   the   calling   (sub)   program.
              When   TRANS = 'N' or 'n' then  LDA must be at least  max( 1, n ), otherwise  LDA must be at least
              max( 1, k ).  Unchanged on exit.

       B      - COMPLEX          array of DIMENSION ( LDB, kb ), where kb is
              k  when  TRANS = 'N' or 'n',  and is  n  otherwise.  Before entry with  TRANS = 'N' or  'n',   the
              leading   n  by k part of the array  B  must contain the matrix  B,  otherwise the leading  k by n
              part of the array  B  must contain  the matrix B.  Unchanged on exit.

       LDB    - INTEGER.
              On entry, LDB specifies the first dimension of B as declared in   the   calling   (sub)   program.
              When   TRANS = 'N' or 'n' then  LDB must be at least  max( 1, n ), otherwise  LDB must be at least
              max( 1, k ).  Unchanged on exit.

       BETA   - REAL            .
              On entry, BETA specifies the scalar beta.  Unchanged on exit.

       C      - COMPLEX          array of DIMENSION ( LDC, n ).
              Before entry  with  UPLO = 'U' or 'u',  the leading  n by n upper triangular part of the  array  C
              must  contain  the  upper  triangular  part   of  the   hermitian  matrix   and the strictly lower
              triangular part of C is not referenced.  On exit, the upper triangular part of  the  array   C  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 C must contain the  lower  triangular
              part  of the  hermitian matrix  and the strictly upper triangular part of C is not referenced.  On
              exit, the lower triangular part of the array  C 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.

       LDC    - INTEGER.
              On entry, LDC specifies the first dimension of C as declared in   the   calling   (sub)   program.
              LDC  must  be  at  least max( 1, n ).  Unchanged on exit.

              Level 3 Blas routine.

              --  Written  on  8-February-1989.   Jack  Dongarra,  Argonne National Laboratory.  Iain Duff, AERE
              Harwell.  Jeremy Du Croz, Numerical Algorithms Group Ltd.  Sven Hammarling,  Numerical  Algorithms
              Group Ltd.