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DSYRK(1)			 BLAS routine			      DSYRK(1)

NAME
       DSYRK  -	 performs  one	of  the	 symmetric  rank  k  operations	  C :=
       alpha*A*A' + beta*C,

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

	   DOUBLE					       PRECISION
							       ALPHA,BETA

	   INTEGER					       K,LDA,LDC,N

	   CHARACTER					       TRANS,UPLO

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

PURPOSE
       DSYRK  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.

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*A' + beta*C.

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

	      TRANS = 'C' or 'c'   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' or 'C' or 'c',  K  specifies	the  number of rows of
	      the matrix  A.  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.

       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 tri‐
	      angular  part   of the  symmetric 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   symmet‐
	      ric  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.

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.

BLAS routine			 November 2008			      DSYRK(1)
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