
SLAQPS(l) ) SLAQPS(l)
NAME
SLAQPS  compute a step of QR factorization with column pivoting of a real MbyN matrix A
by using Blas3
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 MbyN matrix A
by using Blas3. It tries to factorize NB columns from A starting from the row OFFSET+1,
and updates all of the matrix with Blas3 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 MbyN matrix A. On exit, block A(OFFSET+1:M,1:KB) is the triangu
lar
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 permuted 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. QuintanaOrti, Depto. de Informatica, Universidad Jaime I, Spain
X. Sun, Computer Science Dept., Duke University, USA
LAPACK version 3.0 15 June 2000 SLAQPS(l) 
