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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 tri‐
	      angular  part   of the  hermitian matrix	and the strictly lower
	      triangular part of C is not referenced.  On exit, the upper tri‐
	      angular  part of the array  C is overwritten by the upper trian‐
	      gular 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   hermit‐
	      ian  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)
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