SLAQPS(1) LAPACK auxiliary routine (version 3.2) SLAQPS(1)NAME
SLAQPS - computes a step of QR factorization with column pivoting of a
real M-by-N matrix A by using Blas-3
SYNOPSIS
SUBROUTINE SLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2,
AUXV, F, LDF )
INTEGER KB, LDA, LDF, M, N, NB, OFFSET
INTEGER JPVT( * )
REAL A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ), VN1(
* ), VN2( * )
PURPOSE
SLAQPS 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) REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A. On exit, block A(OFF‐
SET+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(OFFSET+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 per‐
muted into position I in AP.
TAU (output) REAL array, dimension (KB)
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.
AUXV (input/output) REAL array, dimension (NB)
Auxiliar vector.
F (input/output) REAL 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
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.
LAPACK auxiliary routine (versioNovember 2008 SLAQPS(1)
