DLASYF man page on IRIX

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DLASYF(3F)							    DLASYF(3F)

NAME
     DLASYF - compute a partial factorization of a real symmetric matrix A
     using the Bunch-Kaufman diagonal pivoting method

SYNOPSIS
     SUBROUTINE DLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )

	 CHARACTER	UPLO

	 INTEGER	INFO, KB, LDA, LDW, N, NB

	 INTEGER	IPIV( * )

	 DOUBLE		PRECISION A( LDA, * ), W( LDW, * )

PURPOSE
     DLASYF 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.

     DLASYF is an auxiliary routine called by DSYTRF. 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.

									Page 1

DLASYF(3F)							    DLASYF(3F)

     A	     (input/output) 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     (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) DOUBLE PRECISION 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.

									Page 2

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