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RedHat 9 (Linux i386) - man page for zlahef (redhat section l)

ZLAHEF(l)					)					ZLAHEF(l)

NAME
       ZLAHEF  - compute a partial factorization of a complex Hermitian matrix A using the Bunch-
       Kaufman diagonal pivoting method

SYNOPSIS
       SUBROUTINE ZLAHEF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KB, LDA, LDW, N, NB

	   INTEGER	  IPIV( * )

	   COMPLEX*16	  A( LDA, * ), W( LDW, * )

PURPOSE
       ZLAHEF computes a partial factorization of a complex Hermitian matrix A using  the  Bunch-
       Kaufman diagonal pivoting method. The partial factorization has the form:

       A  =  ( I  U12 ) ( A11  0  ) (  I    0	)  if UPLO = 'U', or:
	     ( 0  U22 ) (  0   D  ) ( U12' U22' )

       A  =  ( L11  0 ) (  D   0  ) ( L11' L21' )  if UPLO = 'L'
	     ( L21  I ) (  0  A22 ) (  0    I	)

       where  the  order of D is at most NB. The actual order is returned in the argument KB, and
       is either NB or NB-1, or N if N <= NB.  Note that U' denotes the conjugate transpose of U.

       ZLAHEF is an auxiliary routine called by ZHETRF. It uses blocked  code  (calling  Level	3
       BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L').

ARGUMENTS
       UPLO    (input) CHARACTER*1
	       Specifies  whether the upper or lower triangular part of the Hermitian matrix A is
	       stored:
	       = 'U':  Upper triangular
	       = 'L':  Lower triangular

       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       NB      (input) INTEGER
	       The maximum number of columns of the matrix A that should be factored.  NB  should
	       be at least 2 to allow for 2-by-2 pivot blocks.

       KB      (output) INTEGER
	       The  number of columns of A that were actually factored.  KB is either NB-1 or NB,
	       or N if N <= NB.

       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
	       On entry, the Hermitian matrix A.  If UPLO = 'U', the leading n-by-n upper  trian-
	       gular  part  of	A  contains  the  upper  triangular part of the matrix A, and the
	       strictly lower triangular part of A is not referenced.  If UPLO = 'L', the leading
	       n-by-n lower triangular part of A contains the lower triangular part of the matrix
	       A, and the strictly upper triangular part of A is not referenced.  On exit, A con-
	       tains details of the partial factorization.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,N).

       IPIV    (output) INTEGER array, dimension (N)
	       Details of the interchanges and the block structure of D.  If UPLO = 'U', only the
	       last KB elements of IPIV are set; if UPLO = 'L', only the first	KB  elements  are
	       set.

	       If  IPIV(k)  > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k)
	       is a 1-by-1 diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then  rows
	       and  columns  k-1  and  -IPIV(k)  were interchanged and D(k-1:k,k-1:k) is a 2-by-2
	       diagonal block.	If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and  columns
	       k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

       W       (workspace) COMPLEX*16 array, dimension (LDW,NB)

       LDW     (input) INTEGER
	       The leading dimension of the array W.  LDW >= max(1,N).

       INFO    (output) INTEGER
	       = 0: successful exit
	       >  0:  if INFO = k, D(k,k) is exactly zero.  The factorization has been completed,
	       but the block diagonal matrix D is exactly singular.

LAPACK version 3.0			   15 June 2000 				ZLAHEF(l)


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