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CHERK(l)			 BLAS routine			      CHERK(l)

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	 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.

	      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			      CHERK(l)
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