
CLAHEF(l) ) CLAHEF(l)
NAME
CLAHEF  compute a partial factorization of a complex Hermitian matrix A using the Bunch
Kaufman diagonal pivoting method
SYNOPSIS
SUBROUTINE CLAHEF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
CHARACTER UPLO
INTEGER INFO, KB, LDA, LDW, N, NB
INTEGER IPIV( * )
COMPLEX A( LDA, * ), W( LDW, * )
PURPOSE
CLAHEF 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 NB1, or N if N <= NB. Note that U' denotes the conjugate transpose of U.
CLAHEF is an auxiliary routine called by CHETRF. 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 2by2 pivot blocks.
KB (output) INTEGER
The number of columns of A that were actually factored. KB is either NB1 or NB,
or N if N <= NB.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading nbyn 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
nbyn 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 1by1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k1) < 0, then rows
and columns k1 and IPIV(k) were interchanged and D(k1:k,k1:k) is a 2by2
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 2by2 diagonal block.
W (workspace) COMPLEX 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 CLAHEF(l) 
