CLAHEF (3) Linux Manual Page

NAME

clahef.f –

SYNOPSIS

Functions/Subroutines

subroutine clahef (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
CLAHEF 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 clahef (characterUPLO, integerN, integerNB, integerKB, complex, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, complex, dimension( ldw, * )W, integerLDW, integerINFO)

CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).

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').

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

          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 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 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

          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 is COMPLEX 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.

Date:

: November 2013

Contributors:

  November 2013,  Igor Kozachenko,
                  Computer Science Division,
                  University of California, Berkeley

Definition at line 178 of file clahef.f.

Author

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