Loading...
Searching...
No Matches

## zlahef()

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).

Download ZLAHEF + dependencies [TGZ] [ZIP] [TXT]

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

  [in]

  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
      !>

  [in]

  N

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

  [in]

  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.
      !>

  [out]

  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.
      !>

  [in,out]

  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.
      !>

  [in]

  LDA

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

  [out]

  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.
      !>

  [out]

  W

      !>          W is COMPLEX*16 array, dimension (LDW,NB)
      !>

  [in]

  LDW

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

  [out]

  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
      !>