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 Bunch-
           Kaufman 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 Bunch-Kaufman
       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 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

                     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

       Definition at line 177 of file slasyf.f.

Author

       Generated automatically by Doxygen for LAPACK from the source code.