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CHER2K(l)			 BLAS routine			     CHER2K(l)

NAME
       CHER2K  -  perform  one	of  the	 hermitian  rank  2k operations	  C :=
       alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C,

SYNOPSIS
       SUBROUTINE CHER2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB,  BETA,  C,
			  LDC )

	   CHARACTER*1	  UPLO, TRANS

	   INTEGER	  N, K, LDA, LDB, LDC

	   REAL		  BETA

	   COMPLEX	  ALPHA

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

PURPOSE
       CHER2K  performs one of the hermitian rank 2k operations

       or

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

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

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

       ALPHA  - COMPLEX		.
	      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.

       B      - COMPLEX		 array of DIMENSION ( LDB, kb ), where kb 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	 B  must contain the matrix  B,	 otherwise the leading
	      k by n  part of the  array   B   must  contain   the  matrix  B.
	      Unchanged on exit.

       LDB    - INTEGER.
	      On  entry, LDB specifies the first dimension of B as declared in
	      the  calling  (sub)  program.   When  TRANS = 'N'	 or  'n'  then
	      LDB  must	 be  at	 least	max( 1, n ), otherwise	LDB 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			     CHER2K(l)
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