CLAHEF(3)      LAPACK routine of NEC Numeric Library Collection      CLAHEF(3)



NAME
       CLAHEF

SYNOPSIS
       SUBROUTINE CLAHEF (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)



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').




ARGUMENTS
           UPLO      (input)
                     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         (input)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

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

           IPIV      (output)
                     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         (output)
                     W is COMPLEX array, dimension (LDW,NB)

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

           INFO      (output)
                     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.



LAPACK routine                  31 October 2017                      CLAHEF(3)