cherk

CHERK(1)                         BLAS routine                         CHERK(1)



NAME
       CHERK - performs 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)

           REAL                                                ALPHA,BETA

           INTEGER                                             K,LDA,LDC,N

           CHARACTER                                           TRANS,UPLO

           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.


ARGUMENTS
       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  - REAL            .
              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.

       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.

FURTHER DETAILS
       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.

       -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1.
          Ed Anderson, Cray Research Inc.




BLAS routine                     November 2008                        CHERK(1)