_HERK(3F)							     _HERK(3F)

NAME    [Toc]    [Back]

     zherk, cherk - BLAS level three   Hermitian Rank K	Update


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

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

C SYNOPSIS    [Toc]    [Back]

     void zherk(uplo,trans,n,k,alpha,a,lda,beta,c,ldc)
	   MatrixTriangle     uplo;
	   MatrixTranspose    trans;
	   Integer	      n, k, lda, ldc;
	   Zomplex	      alpha, beta;
	   Zomplex	     (*a)[lda*k], (*c)[lda*n];

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

DESCRIPTION    [Toc]    [Back]

     zherk and cherk perform one of the	matrix-matrix operations

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

     or

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

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







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_HERK(3F)							     _HERK(3F)

PARAMETERS    [Toc]    [Back]

     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   specifies the operation to	be performed as	follows:

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

	     C
	     trans = NoTranspose      C	:= alpha*A*conjg( A' ) + beta*C.
	     trans = ConjugateTranspose	   C :=	alpha*conjg( A'	)*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 matrix A,	and on entry with trans	= 'T'
	     or	't' or Transpose, k specifies  the number of rows of the
	     matrix A.	K must be at least zero.
	     Unchanged on exit.

     alpha   specifies the scalar alpha.
	     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.




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_HERK(3F)							     _HERK(3F)



	     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.

     beta    On	entry, beta specifies the scalar beta.
	     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  with	uplo = 'U' or 'u' or UpperTraingle, the
	     leading  n	by n triangular	part  of the  symmetric	matrix	and
	     the strictly lower	triangular part	of C is	not referenced.	 On
	     exit, the upper triangular	part of	the array  C is	overwritten by
	     the upper triangular 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  symmetric 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     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.



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



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_HERK(3F)							     _HERK(3F)



       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.

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


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