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 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.

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 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.

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
Partial column norm updating strategy modified by

  Z. Drmac and Z. Bujanovic, Dept. of Mathematics,

  University of Zagreb, Croatia.

  June 2006.
For more details see LAPACK Working Note 176.