DLAQPS(l)								 )								 DLAQPS(l)

NAME

       DLAQPS - compute a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3

SYNOPSIS

       SUBROUTINE DLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF )

	   INTEGER	  KB, LDA, LDF, M, N, NB, OFFSET

	   INTEGER	  JPVT( * )

	   DOUBLE	  PRECISION A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ), VN1( * ), VN2( * )

PURPOSE

       DLAQPS computes a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3. It tries to factorize NB columns
       from A starting from the row OFFSET+1, and updates all of the matrix with Blas-3 xGEMM.

       In some cases, due to catastrophic cancellations, it cannot factorize NB columns.  Hence,  the  actual  number  of  factorized  columns	is
       returned in KB.

       Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.

ARGUMENTS

       M       (input) INTEGER
	       The number of rows of the matrix A. M >= 0.

       N       (input) INTEGER
	       The number of columns of the matrix A. N >= 0

       OFFSET  (input) INTEGER
	       The number of rows of A that have been factorized in previous steps.

       NB      (input) INTEGER
	       The number of columns to factorize.

       KB      (output) INTEGER
	       The number of columns actually factorized.

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	       On entry, the M-by-N matrix A.  On exit, block A(OFFSET+1:M,1:KB) is the triangular
	       factor  obtained  and  block A(1:OFFSET,1:N) has been accordingly pivoted, but no factorized.  The rest of the matrix, block A(OFF-
	       SET+1:M,KB+1:N) has been updated.

       LDA     (input) INTEGER
	       The leading dimension of the array A. LDA >= max(1,M).

       JPVT    (input/output) INTEGER array, dimension (N)
	       JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP.

       TAU     (output) DOUBLE PRECISION array, dimension (KB)
	       The scalar factors of the elementary reflectors.

       VN1     (input/output) DOUBLE PRECISION array, dimension (N)
	       The vector with the partial column norms.

       VN2     (input/output) DOUBLE PRECISION array, dimension (N)
	       The vector with the exact column norms.

       AUXV    (input/output) DOUBLE PRECISION array, dimension (NB)
	       Auxiliar vector.

       F       (input/output) DOUBLE PRECISION array, dimension (LDF,NB)
	       Matrix F' = L*Y'*A.

       LDF     (input) INTEGER
	       The leading dimension of the array F. LDF >= max(1,N).

FURTHER DETAILS

       Based on contributions by
	 G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
	 X. Sun, Computer Science Dept., Duke University, USA

LAPACK version 3.0						   15 June 2000 							 DLAQPS(l)