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 BunchKaufman 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 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 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 contains 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.