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_HEMM(3F)							     _HEMM(3F)


NAME    [Toc]    [Back]

     zhemm, chemm - BLAS level three   Hermitian Matrix	Product


FORTRAN	77 SYNOPSIS
     subroutine	zhemm( 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	chemm( 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 zhemm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc )
	   OperationSide	 side;
	   MatrixTriangle	 uplo;
	   Integer		 m, n, lda, ldb, ldc;
	   Zomplex		 (*a)[lda*ka], (*b)[lda*n], (*c)[lda*kb];

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

DESCRIPTION    [Toc]    [Back]

     zhemm and chemm 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 an hermitian matrix	and B and C
     are m by n	matrices.

PARAMETERS    [Toc]    [Back]

     side    specifies whether the hermitian matrix A appears on the left or
	     right in the operation as follows:


		  FORTRAN
		  side = 'L' or	'l'	   C :=	alpha*A*B + beta*C
		  side = 'R' or	'r'	   C :=	alpha*B*A + beta*C




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_HEMM(3F)							     _HEMM(3F)



		 C
		  side = LeftSide	   C :=	alpha*A*B + beta*C
		  side = RightSide	   C :=	alpha*B*A + beta*C

	     Unchanged on exit.

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


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

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

	     Unchanged on exit.

     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.






















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_HEMM(3F)							     _HEMM(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 when side =
	     'R' or 'r'	or RightSide.

	     Before entry with uplo = 'L' or 'l' or LowerTriangle , the
	     elements of the array a corresponding to the m by m matrix	A must
	     contain the hermitian matrix, such	that when uplo = 'U' or	'u' or
	     UpperTriangle , the elements of the array a corresponding to the
	     leading m by m upper triangular part of the matrix	A must contain
	     the upper triangular part of the hermitian	matrix and the
	     elements corresponding to the strictly lower triangular part of A
	     are not referenced. When uplo = 'L' or 'l'	or LowerTriangle , the
	     elements of the array a corresponding to the leading m by m lower
	     triangular	part of	the matrix A must contain the lower triangular
	     part of the hermitian matrix and the elements corresponding to
	     the strictly upper	triangular part	of A are not referenced.

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

	     Note that the imaginary parts corresponding to the	diagonal
	     elements need not be set, they are	assumed	to be zero.

	     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 ). When side =	'R' or 'r' or
	     RightSide,	then lda must be at least max( 1, n ).
	     Unchanged on exit.





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_HEMM(3F)							     _HEMM(3F)



     B	     An	array containing the matrix B.

	     FORTRAN
	     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 elements	of b that correspond to	the leading m
	     by	n part of the matrix B should contain the elements
	     corresponding to the m by n 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 leading m by n part of the array	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)	].




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_HEMM(3F)							     _HEMM(3F)


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.

TUNING    [Toc]    [Back]

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


									PPPPaaaaggggeeee 5555
[ Back ]
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