ZLAHEF(1) LAPACK routine (version 3.2) ZLAHEF(1)NAME
ZLAHEF - computes 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 factor‐
ization 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 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 = '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 contains details of the partial factor‐
ization.
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 routine (version 3.2) November 2008 ZLAHEF(1)
