redhat man page for dsyr2k

DSYR2K(l)							   BLAS routine 							 DSYR2K(l)

NAME
       DSYR2K - perform one of the symmetric rank 2k operations   C := alpha*A*B' + alpha*B*A' + beta*C,

SYNOPSIS
       SUBROUTINE DSYR2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC )

	   CHARACTER*1	  UPLO, TRANS

	   INTEGER	  N, K, LDA, LDB, LDC

	   DOUBLE	  PRECISION ALPHA, BETA

	   DOUBLE	  PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )

PURPOSE
       DSYR2K  performs one of the symmetric rank 2k operations

       or

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

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

	      TRANS = 'T' or 't'   C := alpha*A'*B + alpha*B'*A + beta*C.

	      TRANS = 'C' or 'c'   C := alpha*A'*B + alpha*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  =
	      'T'  or  't'  or	'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  - DOUBLE PRECISION.
	      On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       A      - DOUBLE PRECISION 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      - DOUBLE PRECISION 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   - DOUBLE PRECISION.
	      On entry, BETA specifies the scalar beta.  Unchanged on exit.

       C      - DOUBLE PRECISION 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							 DSYR2K(l)