_SYR,_HER(3F)							 _SYR,_HER(3F)

NAME    [Toc]    [Back]

     dsyr, ssyr, zher, cher - BLAS Level Two   (Symmetric/Hermitian)Matrix
     Rank 1 Update


FORTRAN	77 SYNOPSIS
     subroutine	dsyr( uplo, n, alpha, x, incx, a, lda )
	   character*1	      uplo
	   integer	      n, incx, lda
	   double precision   alpha
	   double precision   a( lda,*), x(*)

     subroutine	ssyr( uplo, n, alpha, x, incx, a, lda )
	   character*1	      uplo
	   integer	      n, incx, lda
	   real		      alpha
	   real		      a( lda,*), x(*)

     subroutine	zher( uplo, n, alpha, x, incx, a, lda )
	   character*1	      uplo
	   integer	      n, incx, lda
	   complex*16	      alpha
	   complex*16	      a( lda,*), x(*)

     subroutine	cher( uplo, n, alpha, x, incx, a, lda )
	   character*1	      uplo
	   integer	      n, incx, lda
	   complex	      alpha
	   complex	      a( lda,*), x(*)

C SYNOPSIS    [Toc]    [Back]

     void dsyr(	uplo, n, alpha,	x, incx, a, lda	)
	   MatrixTriangle     uplo;
	   Integer	      n, incx, lda;
	   double	      alpha;
	   double	      (*a)[lda*n], (*x)[ n ];

     void ssyr(	uplo, n, alpha,	x, incx, a, lda	)
	   MatrixTriangle     uplo;
	   Integer	      n, incx, lda;
	   float	      alpha;
	   float	      (*a)[lda*n], (*x)[ n ];

     void zher(	uplo, n, alpha,	x, incx, a, lda	)
	   MatrixTriangle     uplo;
	   Integer	      n, incx, lda;
	   Zomplex	      alpha;
	   Zomplex	      (*a)[lda*n], (*x)[ n ];

     void cher(	uplo, n, alpha,	x, incx, a, lda	)



									Page 1






_SYR,_HER(3F)							 _SYR,_HER(3F)



	   MatrixTriangle     uplo;
	   Integer	      n, incx, lda;
	   Complex	      alpha;
	   Complex	      (*a)[lda*n], (*x)[ n ]

DESCRIPTION    [Toc]    [Back]

     dsyr and ssyr perform the symmetric rank 1	operation

	   A :=	alpha*x*x' + A,

     zher and cher perform the hermitian rank 1	operation

	   A :=	alpha*x*conjg( x' ) + A,

     where alpha is a real/complex scalar, x is	an n element vector and	A is
     an	n by n symmetric/hermitian matrix.

PARAMETERS    [Toc]    [Back]

     uplo    On	entry, uplo specifies whether the upper	or lower triangular
	     part of the array A is to be referenced a follows:



	     FORTRAN
	     uplo = 'U'	or 'u'	 Only the upper	triangular part	of A
				 is to be referenced.
	     uplo = 'L'	or 'l'	 Only the lower	triangular part	of A
				 is to be referenced.

	     C
	     uplo = UpperTriangle     Only the lower triangular	part of	A
				      is to be referenced.
	     uplo = LowerTriangle     Only the lower triangular	part of	A
				      is to be referenced.

	     Unchanged on exit.

     n	     On	entry, n specifies the the order of the	matrix A.  n must be
	     at	least zero.
	     Unchanged on exit.

     alpha   specifies the scalar alpha.
	     Unchanged on exit.

     x	     Array of size at least ( 1	+ ( n -	1 )*abs( incx )	). Before
	     entry, the	incremented array x must contain the n element vector
	     x.
	     Unchanged on exit.




									Page 2






_SYR,_HER(3F)							 _SYR,_HER(3F)



     incx    On	entry, incx specifies the increment for	the elements of	x.
	     incx must not be zero.
	     Unchanged on exit.

     a	     An	array containing the matrix A.

	     FORTRAN
	     Array of dimension	( lda, n ).

	     C
	     A pointer to an array of size lda*n.
	     See note below about array	storage	convention for C.

	     Before entry with uplo = 'U' or 'u' or , the array	elements
	     corresponding to the leading n by n upper triangular part of the
	     matrix A must contain the uppertriangular part of the
	     symmetric/hermitian matrix	and the	corresponding strictly lower
	     triangular	part of	A is not referenced. On	exit, the array
	     elements corresponding to the upper triangular part of the	matrix
	     A is overwritten by the upper triangular part of the updated
	     matrix.

	     Before entry with uplo = 'L' or 'l' or , the array	elements
	     corresponding to the leading n by n lower triangular part of the
	     matrix A must contain the lower triangular	part of	the
	     symmetric/hermitian matrix	and the	corresponding strictly upper
	     triangular	part of	A is not referenced. On	exit, the array
	     elements corresponding to the lower triangular part of the	matrix
	     A is overwritten by the lower triangular part of the updated
	     matrix.

	     Note that the imaginary parts of the diagonal elements need not
	     be	set and	are assumed to be zero.

     lda     On	entry, lda specifies the first dimension of A as declared in
	     the calling (sub) program.	lda must be at least ( k + 1 ).
	     Unchanged on exit.


C ARRAY	STORAGE	CONVENTION
       The matrices  are assumed  to be	stored in a  one dimensional C array
       in an analogous fashion as a Fortran array (column major). Therefore,
       the element  A(i+1,j)  of matrix	A  is stored  immediately  after the
       element	A(i,j),	while  A(i,j+1)	is lda	elements apart from  A(i,j).
       The element A(i,j) of the matrix	can be accessed	directly by reference
       to  a[ (j-1)*lda	+ (i-1)	].

AUTHORS    [Toc]    [Back]

	  Jack Dongarra, Argonne National Laboratory.
	  Iain Duff, AERE Harwell.
	  Jeremy Du Croz, Numerical Algorithms Group Ltd.



									Page 3






_SYR,_HER(3F)							 _SYR,_HER(3F)



	  Sven Hammarling, Numerical Algorithms	Group Ltd.


									PPPPaaaaggggeeee 4444