SLAQP2(l)								 )								 SLAQP2(l)

NAME

       SLAQP2 - compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)

SYNOPSIS

       SUBROUTINE SLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK )

	   INTEGER	  LDA, M, N, OFFSET

	   INTEGER	  JPVT( * )

	   REAL 	  A( LDA, * ), TAU( * ), VN1( * ), VN2( * ), WORK( * )

PURPOSE

       SLAQP2  computes  a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N). The 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 the matrix A that must be pivoted but no factorized. OFFSET >= 0.

       A       (input/output) REAL array, dimension (LDA,N)
	       On entry, the M-by-N matrix A.  On exit, the upper triangle of block A(OFFSET+1:M,1:N) is the triangular factor obtained; the  ele-
	       ments in block A(OFFSET+1:M,1:N) below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of
	       elementary reflectors. Block A(1:OFFSET,1:N) has been accordingly pivoted, but no factorized.

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

       JPVT    (input/output) INTEGER array, dimension (N)
	       On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted to the front of A*P (a leading column); if JPVT(i) = 0, the i-th col-
	       umn of A is a free column.  On exit, if JPVT(i) = k, then the i-th column of A*P was the k-th column of A.

       TAU     (output) REAL array, dimension (min(M,N))
	       The scalar factors of the elementary reflectors.

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

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

       WORK    (workspace) REAL array, dimension (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 							 SLAQP2(l)