man dlaqp2 (Fonctions bibliothèques) - compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)

NAME

DLAQP2 - compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)

SYNOPSIS

SUBROUTINE DLAQP2(
M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK )
INTEGER LDA, M, N, OFFSET
INTEGER JPVT( * )
DOUBLE PRECISION A( LDA, * ), TAU( * ), VN1( * ), VN2( * ), WORK( * )

PURPOSE

DLAQP2 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (min(M,N))
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.
WORK (workspace) DOUBLE PRECISION 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