slasyf_rook.f - Man Page

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.

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.

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 182 of file slasyf_rook.f.