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cherk

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

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

          CHARACTER*1  UPLO, TRANS

          INTEGER      N, K, LDA, LDC

          REAL         ALPHA, BETA

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

 PURPOSE
      CHERK  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 per-
             formed 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  - REAL            .
             On entry, ALPHA specifies the scalar alpha.
             Unchanged on exit.

 ka is
      A      -
              COMPLEX          array of DIMENSION ( LDA, ka ), where
             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   - 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 con-
             tain 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 tri-
             angular 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 refer-
             enced.  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.