SRC/zlahef.f(3)            Library Functions Manual            SRC/zlahef.f(3)

NAME
       SRC/zlahef.f

SYNOPSIS
   Functions/Subroutines
       subroutine zlahef (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
           ZLAHEF computes a partial factorization of a complex Hermitian
           indefinite matrix using the Bunch-Kaufman diagonal pivoting method
           (blocked algorithm, calling Level 3 BLAS).

Function/Subroutine Documentation
   subroutine zlahef (character uplo, integer n, integer nb, integer kb,
       complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * )
       ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)
       ZLAHEF computes a partial factorization of a complex Hermitian
       indefinite matrix using the Bunch-Kaufman diagonal pivoting method
       (blocked algorithm, calling Level 3 BLAS).

       Purpose:


           !>
           !> ZLAHEF 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.
           !>
           !> 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').
           !>

       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*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 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 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 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':
           !>             Only the first KB elements of IPIV 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 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*16 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.

       Contributors:


           !>
           !>  December 2016,  Igor Kozachenko,
           !>                  Computer Science Division,
           !>                  University of California, Berkeley
           !>

       Definition at line 176 of file zlahef.f.

Author
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LAPACK                          Version 3.12.0                 SRC/zlahef.f(3)