
DLAQPS(l) ) DLAQPS(l)
NAME
DLAQPS  compute a step of QR factorization with column pivoting of a real MbyN matrix A
by using Blas3
SYNOPSIS
SUBROUTINE DLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF )
INTEGER KB, LDA, LDF, M, N, NB, OFFSET
INTEGER JPVT( * )
DOUBLE PRECISION A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ), VN1( * ), VN2(
* )
PURPOSE
DLAQPS 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (KB)
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.
AUXV (input/output) DOUBLE PRECISION array, dimension (NB)
Auxiliar vector.
F (input/output) DOUBLE PRECISION 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 DLAQPS(l) 
