NAME

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

SYNOPSIS

       SUBROUTINE ZHERK ( UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC )

           CHARACTER*1  UPLO, TRANS

           INTEGER      N, K, LDA, LDC

           DOUBLE       PRECISION ALPHA, BETA

           COMPLEX*16   A( LDA, * ), C( LDC, * )

PURPOSE

       ZHERK  performs one of the hermitian rank k operations

       or

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

       where   alpha  and  beta   are   real  scalars,   C is an  n by n  hermitian matrix and  A  is an  n by k
       matrix in the  first case and a  k by n matrix 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( A' ) + beta*C.

              TRANS = 'C' or 'c'   C := alpha*conjg( A' )*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   matrix   A,
              and  on   entry   with TRANS = 'C' or 'c',  K  specifies  the number of rows of the matrix  A.   K
              must be at least zero.  Unchanged on exit.

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

       A      - COMPLEX*16       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.

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

       C      - COMPLEX*16       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.

BLAS routine                                     16 October 1992                                        ZHERK(3)