slasyf.f(3)

NAME
slasyf.f -

SYNOPSIS

  Functions/Subroutines
subroutine slasyf (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
SLASYF computes a partial factorization of a real symmetric matrix, using the diagonal pivoting method.

Function/Subroutine Documentation

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

SLASYF computes a partial factorization of a real symmetric matrix, using the diagonal pivoting method.

Purpose:

     SLASYF computes a partial factorization of a real symmetric 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**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 is an auxiliary routine called by SSYTRF. 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 UPLO = 'L', only the first KB elements 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 UPLO = 'U' and 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' and 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 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:
    September 2012

Definition at line 157 of file slasyf.f.

Author

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