# CentOS 7.0 - man page for clahef (centos section 3)

```clahef.f(3)							      LAPACK							       clahef.f(3)

NAME
clahef.f -

SYNOPSIS
Functions/Subroutines
subroutine clahef (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix, using the diagonal pivoting method.

Function/Subroutine Documentation
subroutine clahef (characterUPLO, integerN, integerNB, integerKB, complex, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV,
complex, dimension( ldw, * )W, integerLDW, integerINFO)
CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix, using the diagonal pivoting method.

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**H U22**H )

A  =  ( L11  0 ) (	D   0  ) ( L11**H L21**H )  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**H 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').

Parameters:
UPLO

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

N

N is INTEGER
The order of the matrix A.  N >= 0.

NB

NB is 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

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

A

A is COMPLEX 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 factorization.

LDA

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

IPIV

IPIV is 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

W is COMPLEX array, dimension (LDW,NB)

LDW

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

INFO

INFO is 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.

Author:
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:
September 2012

Definition at line 158 of file clahef.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       clahef.f(3)```