dlasyf_rook.f man page

dlasyf_rook.f —

Synopsis

Functions/Subroutines

subroutine dlasyf_rook (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
DLASYF_ROOK *> DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method.

Function/Subroutine Documentation

subroutine dlasyf_rook (characterUPLO, integerN, integerNB, integerKB, double precision, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, double precision, dimension( ldw, * )W, integerLDW, integerINFO)

DLASYF_ROOK *> DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method.

Purpose:

DLASYF_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.

DLASYF_ROOK is an auxiliary routine called by DSYTRF_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 DOUBLE PRECISION 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 DOUBLE PRECISION 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

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                School of Mathematics,
                University of Manchester

Definition at line 184 of file dlasyf_rook.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

dlasyf_rook(3) is an alias of dlasyf_rook.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK