CSYRK(3)							   BLAS routine 							  CSYRK(3)

NAME

       CSYRK - perform one of the symmetric rank k operations	C := alpha*A*A' + beta*C,

SYNOPSIS

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

	   CHARACTER*1	UPLO, TRANS

	   INTEGER	N, K, LDA, LDC

	   COMPLEX	ALPHA, BETA

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

PURPOSE

       CSYRK  performs one of the symmetric rank k operations

       or

	  C := alpha*A'*A + beta*C,

       where  alpha and beta  are scalars,  C is an  n by n symmetric 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*A' + beta*C.

	      TRANS = 'T' or 't'   C := alpha*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  =
	      'T' or 't',  K  specifies  the number of rows of the matrix A.  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.

       BETA   - COMPLEX 	.
	      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  symmetric 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   symmetric  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.

       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							  CSYRK(3)