slasyf_rook.f(3)

NAME
slasyf_rook.f -

SYNOPSIS

  Functions/Subroutines

subroutine slasyf_rook (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
SLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method.

Function/Subroutine Documentation

  subroutine slasyf_rook (characterUPLO, integerN, integerNB, integerKB, real, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, real, dimension( ldw, * )W, integerLDW, integerINFO)

SLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method.

Purpose:

     SLASYF_ROOK computes a partial factorization of a real symmetric
     matrix A using the bounded Bunch-Kaufman ("rook") 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**T U22**T )

     A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  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.

     SLASYF_ROOK is an auxiliary routine called by SSYTRF_ROOK. 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
              symmetric 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 REAL array, dimension (LDA,N)
              On entry, the symmetric 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) < 0 and IPIV(k-1) < 0, then rows and
                 columns k and -IPIV(k) were interchanged and rows and
                 columns k-1 and -IPIV(k-1) were inerchaged,
                 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) < 0 and IPIV(k+1) < 0, then rows and
                 columns k and -IPIV(k) were interchanged and rows and
                 columns k+1 and -IPIV(k+1) were inerchaged,
                 D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

    W

              W is REAL 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

      September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                      School of Mathematics,
                      University of Manchester

Definition at line 184 of file slasyf_rook.f.

Author

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