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## zhetrf_aa_2stage()

subroutine zhetrf_aa_2stage | ( | character | uplo,
|  | integer | n,
|  | complex*16, dimension( lda, * ) | a,
|  | integer | lda,
|  | complex*16, dimension( * ) | tb,
|  | integer | ltb,
|  | integer, dimension( * ) | ipiv,
|  | integer, dimension( * ) | ipiv2,
|  | complex*16, dimension( * ) | work,
|  | integer | lwork,
|  | integer | info )

ZHETRF_AA_2STAGE

Download ZHETRF_AA_2STAGE + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> ZHETRF_AA_2STAGE computes the factorization of a double hermitian matrix A
      !> using the Aasen's algorithm.  The form of the factorization is
      !>
      !>    A = U**H*T*U  or  A = L*T*L**H
      !>
      !> where U (or L) is a product of permutation and unit upper (lower)
      !> triangular matrices, and T is a hermitian band matrix with the
      !> bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
      !> LU factorized with partial pivoting).
      !>
      !> This is the blocked version of the algorithm, calling Level 3 BLAS.
      !>

Parameters

  [in]

  UPLO

      !>          UPLO is CHARACTER*1
      !>          = 'U':  Upper triangle of A is stored;
      !>          = 'L':  Lower triangle of A is stored.
      !>

  [in]

  N

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

  [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, L is stored below (or above) the subdiagonal blocks,
      !>          when UPLO  is 'L' (or 'U').
      !>

  [in]

  LDA

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

  [out]

  TB

      !>          TB is COMPLEX*16 array, dimension (MAX(1,LTB))
      !>          On exit, details of the LU factorization of the band matrix.
      !>

  [in]

  LTB

      !>          LTB is INTEGER
      !>          The size of the array TB. LTB >= MAX(1,4*N), internally
      !>          used to select NB such that LTB >= (3*NB+1)*N.
      !>
      !>          If LTB = -1, then a workspace query is assumed; the
      !>          routine only calculates the optimal size of LTB,
      !>          returns this value as the first entry of TB, and
      !>          no error message related to LTB is issued by XERBLA.
      !>

  [out]

  IPIV

      !>          IPIV is INTEGER array, dimension (N)
      !>          On exit, it contains the details of the interchanges, i.e.,
      !>          the row and column k of A were interchanged with the
      !>          row and column IPIV(k).
      !>

  [out]

  IPIV2

      !>          IPIV2 is INTEGER array, dimension (N)
      !>          On exit, it contains the details of the interchanges, i.e.,
      !>          the row and column k of T were interchanged with the
      !>          row and column IPIV(k).
      !>

  [out]

  WORK

      !>          WORK is COMPLEX*16 workspace of size (MAX(1,LWORK))
      !>

  [in]

  LWORK

      !>          LWORK is INTEGER
      !>          The size of WORK. LWORK >= MAX(1,N), internally used to
      !>          select NB such that LWORK >= N*NB.
      !>
      !>          If LWORK = -1, then a workspace query is assumed; the
      !>          routine only calculates the optimal size of the WORK array,
      !>          returns this value as the first entry of the WORK array, and
      !>          no error message related to LWORK is issued by XERBLA.
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0:  successful exit
      !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
      !>          > 0:  if INFO = i, band LU factorization failed on i-th column
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.