.TH CLAQP2 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME CLAQP2 - a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N) .SH SYNOPSIS .TP 19 SUBROUTINE CLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK ) .TP 19 .ti +4 INTEGER LDA, M, N, OFFSET .TP 19 .ti +4 INTEGER JPVT( * ) .TP 19 .ti +4 REAL VN1( * ), VN2( * ) .TP 19 .ti +4 COMPLEX A( LDA, * ), TAU( * ), WORK( * ) .SH PURPOSE CLAQP2 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. .SH ARGUMENTS .TP 8 M (input) INTEGER The number of rows of the matrix A. M >= 0. .TP 8 N (input) INTEGER The number of columns of the matrix A. N >= 0. .TP 8 OFFSET (input) INTEGER The number of rows of the matrix A that must be pivoted but no factorized. OFFSET >= 0. .TP 8 A (input/output) COMPLEX 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 elements 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. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). .TP 8 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 column 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. .TP 8 TAU (output) COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors. .TP 8 VN1 (input/output) REAL array, dimension (N) The vector with the partial column norms. .TP 8 VN2 (input/output) REAL array, dimension (N) The vector with the exact column norms. .TP 8 WORK (workspace) COMPLEX array, dimension (N) .SH FURTHER DETAILS Based on contributions by .br G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA .br Partial column norm updating strategy modified by .br Z. Drmac and Z. Bujanovic, Dept. of Mathematics, .br University of Zagreb, Croatia. .br June 2006. .br For more details see LAPACK Working Note 176. .br