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dlasyf_rook.f(3)		    LAPACK		      dlasyf_rook.f(3)

NAME
       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.

Version 3.4.2			Sat Nov 16 2013		      dlasyf_rook.f(3)
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