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_SYMM(3F)							     _SYMM(3F)


NAME    [Toc]    [Back]

     dsymm, ssymm, zsymm, csymm	- BLAS level three   Symmetric Matrix Product


FORTRAN	77 SYNOPSIS
     subroutine	dsymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc )
	   character*1	      side,uplo
	   integer	      m, n, lda, ldb, ldc
	   double precision   alpha, beta
	   double precision   a( lda,*), b(ldb,*), c(ldc,*)

     subroutine	ssymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc )
	   character*1	      side,uplo
	   integer	      m, n, lda, ldb, ldc
	   real		      alpha, beta
	   real		      a( lda,*), b(ldb,*), c(ldc,*)

     subroutine	zsymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc )
	   character*1	      side,uplo
	   integer	      m, n, lda, ldb, ldc
	   double complex     alpha, beta
	   double complex     a( lda,*), b(ldb,*), c(ldc,*)

     subroutine	csymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc )
	   character*1	      side,uplo
	   integer	      m, n, lda, ldb, ldc
	   complex	      alpha, beta
	   complex	      a( lda,*), b(ldb,*), c(ldc,*)

C SYNOPSIS    [Toc]    [Back]

     void dsymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc )
	   OperationSide	 side;
	   MatrixTriangle	 uplo;
	   Integer		 m, n, lda, ldb, ldc;
	   double		 alpha,	beta;
	   double		 (*a)[lda*ka], (*b)[lda*n], (*c)[lda*n];

     void ssymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc )
	   OperationSide	 side;
	   MatrixTriangle	 uplo;
	   Integer		 m, n, lda, ldb, ldc;
	   float		 alpha,	beta;
	   float		 (*a)[lda*ka], (*b)[lda*n], (*c)[lda*n];

     void zsymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc )
	   OperationSide	 side;
	   MatrixTriangle	 uplo;
	   Integer		 m, n, lda, ldb, ldc;
	   Zomplex		 alpha,	beta;
	   Zomplex		 (*a)[lda*ka], (*b)[lda*n], (*c)[lda*n];




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_SYMM(3F)							     _SYMM(3F)



     void csymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc )
	   OperationSide	 side;
	   MatrixTriangle	 uplo;
	   Integer		 m, n, lda, ldb, ldc;
	   Complex		 alpha,	beta;
	   Complex		 (*a)[lda*ka], (*b)[lda*n], (*c)[lda*n];


DESCRIPTION    [Toc]    [Back]

     dsymm, ssymm, zsymm and csymm

     perform one of the	matrix-matrix operations

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

     where alpha and beta are scalars, A is a symmetric	matrix and B and C are
     m by n matrices.

PARAMETERS    [Toc]    [Back]

     side    On	entry, side specifies whether op( A ) multiplies B from	the
	     left or right as follows:


		  FORTRAN
		  side = 'L' or	'l'   B	:= alpha*op( A )*B.
		  side = 'R' or	'r'   B	:= alpha*B*op( A ).

		  C
		  side = LeftSide     B	:= alpha*op( A )*B.
		  side = RightSide    B	:= alpha*B*op( A ).

	     Unchanged on exit.

     uplo    On	entry, uplo specifies whether the matrix A is an upper or
	     lower triangular matrix as	follows:


		  FORTRAN
		  uplo = 'U' or	'u'   A	is an upper triangular matrix.
		  uplo = 'L' or	'l'   A	is a lower triangular matrix.

		  C
		  uplo = UpperTriangle	   A is	an upper triangular matrix.
		  uplo = LowerTriangle	   A is	a lower	triangular matrix.

	     Unchanged on exit.






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_SYMM(3F)							     _SYMM(3F)



     m	     On	entry, m specifies the number of rows of the matrix C. m must
	     be	at least zero.
	     Unchanged on exit.

     n	     On	entry, n specifies the number of columns of the	matrix C. n
	     must be at	least zero.
	     Unchanged on exit.

     alpha   On	entry, alpha specifies the scalar alpha. When alpha is zero
	     then a is not referenced and b need not be	set before entry.













































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_SYMM(3F)							     _SYMM(3F)



	     Unchanged on exit.

     a	     An	array containing the matrix A.

	     FORTRAN
	     Array of dimension	(lda, ka).

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

	     ka	is m when side = 'L' or	'l' or LeftSide	and is n otherwise.

	     Before entry  with	side = 'L' or 'l' or LeftSide, the array
	     elements corresponding to the m by	m part of the matrix A must
	     contain the symmetric matrix, such	that when:
	     uplo = 'U'	or 'u' or UpperTriangle, the array elements that
	     correspond	to the leading m by m upper triangular part of the
	     matrix A must contain the upper triangular	part of	the symmetric
	     matrix and	the corresponding strictly lower triangular part of A
	     is	not referenced,
	     and when uplo = 'L' or 'l'	or LowerTriangle, the array elements
	     that correspond to	the leading m by m lower triangular part of
	     the matrix	A must contain the lower triangular part of the
	     symmetric matrix and the corresponding strictly upper triangular
	     part of A is not referenced.

	     Before entry  with	side = 'R' or 'r' or RightSide,	the array
	     elements corresponding to the n by	n  part	of the matrix A	must
	     contain the symmetric matrix, such	that when:
	     uplo = 'U'	or 'u' or UpperTriangle, the array elements that
	     correspond	to the leading n by n upper triangular part of the
	     matrix A must contain the upper triangular	part of	the symmetric
	     matrix and	the corresponding strictly lower triangular part of A
	     is	not referenced,
	     and when uplo = 'L' or 'l'	or LowerTriangle, the array elements
	     that correspond to	the leading n by n lower triangular part of
	     the matrix	A must contain the lower triangular part of the
	     symmetric matrix and the corresponding strictly upper triangular
	     part of A is not referenced.

	     Unchanged on exit.

     lda     On	entry, lda specifies the first dimension of a as declared in
	     the calling (sub) program.	When side = 'L'	or 'l' or LeftSide,
	     then lda must be at least max( 1, m ), otherwise lda must be at
	     least max(	1, n ).
	     Unchanged on exit.

     b	     An	array containing the matrix B.

	     FORTRAN



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_SYMM(3F)							     _SYMM(3F)



	     An	array of dimension ( ldb, n ).

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

	     Before entry, the array elements corresponding to the leading m
	     by	n part of the matrix B must contain the	matrix B.
	     Unchanged on exit.

     ldb     On	entry, ldb specifies the first dimension of b as declared in
	     the calling (sub)program. ldb must	be at least max( 1, m ).
	     Unchanged on exit.

     beta    On	entry, beta specifies the scalar beta.	When beta is supplied
	     as	zero then c need not be	set on input.
	     Unchanged on exit.

     c	     An	array containing the matrix C.

	     FORTRAN
	     An	array of dimension ( ldc, n ).

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

	     Before entry, the elements	corresponding to the leading m by n
	     part of the matrix	C must contain the matrix C, except when beta
	     is	zero, in which case c need not be set on entry.
	     On	exit, the array	c is overwritten by the	m by n updated matrix

     ldc     On	entry, ldc specifies the first dimension of c as declared in
	     the calling (sub) program.	ldc must be at least max( 1, m ).
	     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.
	  Sven Hammarling, Numerical Algorithms	Group Ltd.




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_SYMM(3F)							     _SYMM(3F)


TUNING    [Toc]    [Back]

	  Optimized and	parallelized for SGI R3000, R4x00 and R8000 platforms.


									PPPPaaaaggggeeee 6666
[ Back ]
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