Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  - computes a partial factorization of a real symmetric matrix A using the Bunch-
       Kaufman diagonal pivoting method

SYNOPSIS

       SUBROUTINE SLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, KB, LDA, LDW, N, NB

           INTEGER        IPIV( * )

           REAL           A( LDA, * ), W( LDW, * )

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').

ARGUMENTS

        UPLO    (input) CHARACTER*1
                Specifies whether the upper or lower triangular part of the
                symmetric matrix A is stored:
                = 'U':  Upper triangular
                = 'L':  Lower triangular

        N       (input) INTEGER
                The order of the matrix A.  N >= 0.

        NB      (input) 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      (output) INTEGER
                The number of columns of A that were actually factored.
                KB is either NB-1 or NB, or N if N <= NB.

        A       (input/output) 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     (input) INTEGER
                The leading dimension of the array A.  LDA >= max(1,N).

        IPIV    (output) 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       (workspace) REAL array, dimension (LDW,NB)

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

        INFO    (output) 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.

 LAPACK routine (version 3.3.1)             April 2011                            SLASYF(3lapack)