_HER2K(3F)							    _HER2K(3F)

NAME    [Toc]    [Back]

     zher2k, cher2k - BLAS level three	 Hermitian Rank	2K Update


FORTRAN	77 SYNOPSIS
     subroutine	zher2k(	uplo,trans,n,k,alpha,a,lda,b,ldb,beta,c,ldc )
	   character*1	      uplo, trans
	   integer	      n, k, lda, ldb, ldc
	   double complex     alpha, beta
	   double complex     a( lda,*), b( ldb,*), c(ldc,*)

     subroutine	cher2k(	uplo,trans,n,k,alpha,a,lda,b,ldb,beta,c,ldc )
	   character*1	      uplo, trans
	   integer	      n, k, lda, ldb, ldc
	   complex	      alpha, beta
	   complex	      a( lda,*), b( ldb,*), c(ldc,*)

C SYNOPSIS    [Toc]    [Back]

     subroutine	zher2k(	uplo,trans,n,k,alpha,a,lda,b,ldb,beta,c,ldc )
	   MatrixTriangle     uplo;
	   MatrixTranspose    trans;
	   Integer	      n, k, lda, ldb, ldc;
	   Zomplex	      alpha, beta;
	   Zomplex	      (*a)[lda*k], (*b)[lda*k],	(*c)[lda*n];

     void zher2k( uplo,trans,n,k,alpha,a,lda,b,ldb,beta,c,ldc )
	   MatrixTriangle     uplo;
	   MatrixTranspose    trans;
	   Integer	      n, k, lda, ldb, ldc;
	   Complex	      alpha, beta;
	   Complex	      (*a)[lda*k], (*b)[lda*k],	(*c)[lda*n];

DESCRIPTION    [Toc]    [Back]

     zher2k and	cher2k perform one of the hermitian rank 2k operations

	   C :=	alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C,

     or

	   C :=	alpha*conjg( A'	)*B + conjg( alpha )*conjg( B' )*A + beta*C,

     where alpha and beta are scalars with beta	real, C	is an n	by n hermitian
     matrix and	A and B	are n by k matrices in the first case and k by n
     matrices in the second case.








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_HER2K(3F)							    _HER2K(3F)



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

	     FORTRAN
	     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.

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

	     Unchanged on exit.

     trans   On	entry, trans specifies the operation to	be performed as
	     follows:

	     FORTRAN
	     trans = 'N' or 'n'		   C :=	alpha*A*conjg( B' )	     +
						conjg( alpha )*B*conjg(	A' ) +
						beta*C.
	     trans = 'C' or 'c'		   C :=	alpha*conjg( A'	)*B	     +
						conjg( alpha )*conjg( B' )*A +
						beta*C.

	     C
	     trans = NoTranspose	   C :=	alpha*A*conjg( B' )	     +
						conjg( alpha )*B*conjg(	A' ) +
						beta*C.
	     trans = ConjugateTranspose	   C :=	alpha*conjg( A'	)*B	     +
						conjg( alpha )*conjg( B' )*A +
						beta*C.

	     Unchanged on exit.

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

     k	     On	entry with, trans = 'N'	or 'n' or NoTranspose k	specifies the
	     number of columns of the matrices A and B,	and on entry with
	     trans = 'T' or 't'	or Transpose, k	specifies  the number of rows
	     of	the matries A and B.  K	must be	at least zero.
	     Unchanged on exit.

     alpha   specifies the scalar alpha.
	     Unchanged on exit.




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_HER2K(3F)							    _HER2K(3F)



     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 k when transa = 'N' or 'n' or NoTranspose and is n
	     otherwise.	 Before	entry with trans = 'N' or 'n' or NoTranspose,
	     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     On	entry, lda specifies the first dimension of a as declared in
	     the calling (sub) program.	When  transa = 'N' or 'n' or
	     NoTranspose, then lda must	be at least max( 1, n ), otherwise lda
	     must be at	least  max( 1, k ).
	     Unchanged on exit.

     b	     An	array containing the matrix B.

	     FORTRAN
	     Array of dimension	(lda, kb).

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

	     kb	is k when transa = 'N' or 'n' or NoTranspose and is n
	     otherwise.	 Before	entry with trans = 'N' or 'n' or NoTranspose,
	     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     On	entry, ldb specifies the first dimension of b as declared in
	     the calling (sub) program.	When  trans = 'N' or 'n' or
	     NoTranspose, then ldb must	be at least max( 1, n ), otherwise lda
	     must be at	least  max( 1, k ).
	     Unchanged on exit.

       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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_HER2K(3F)							    _HER2K(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 4444