SLASYF (3lapack)

compute 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' U22' )

  A  =  ( L11  0 ) (  D   0  ) ( L11' L21' )  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.