.TH CLAHEF 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
CLAHEF - a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
.SH SYNOPSIS
.TP 19
SUBROUTINE CLAHEF(
UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
.TP 19
.ti +4
CHARACTER
UPLO
.TP 19
.ti +4
INTEGER
INFO, KB, LDA, LDW, N, NB
.TP 19
.ti +4
INTEGER
IPIV( * )
.TP 19
.ti +4
COMPLEX
A( LDA, * ), W( LDW, * )
.SH 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:
.br
A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = \(aqU\(aq, or:
( 0 U22 ) ( 0 D ) ( U12\(aq U22\(aq )
.br
A = ( L11 0 ) ( D 0 ) ( L11\(aq L21\(aq ) if UPLO = \(aqL\(aq
( L21 I ) ( 0 A22 ) ( 0 I )
.br
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\(aq denotes the conjugate transpose of U.
.br
CLAHEF is an auxiliary routine called by CHETRF. It uses blocked code
(calling Level 3 BLAS) to update the submatrix A11 (if UPLO = \(aqU\(aq) or
A22 (if UPLO = \(aqL\(aq).
.br
.SH ARGUMENTS
.TP 8
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
.br
= \(aqU\(aq: Upper triangular
.br
= \(aqL\(aq: Lower triangular
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0.
.TP 8
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.
.TP 8
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.
.TP 8
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = \(aqU\(aq, the leading
n-by-n upper triangular 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 = \(aqL\(aq, 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 contains details of the partial factorization.
.TP 8
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
.TP 8
IPIV (output) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D.
If UPLO = \(aqU\(aq, only the last KB elements of IPIV are set;
if UPLO = \(aqL\(aq, 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 = \(aqU\(aq 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 = \(aqL\(aq 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.
.TP 8
W (workspace) COMPLEX array, dimension (LDW,NB)
.TP 8
LDW (input) INTEGER
The leading dimension of the array W. LDW >= max(1,N).
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
> 0: if INFO = k, D(k,k) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular.