.TH SLAQPS 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) "
.SH NAME
SLAQPS - a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3
.SH SYNOPSIS
.TP 19
SUBROUTINE SLAQPS(
M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
VN2, AUXV, F, LDF )
.TP 19
.ti +4
INTEGER
KB, LDA, LDF, M, N, NB, OFFSET
.TP 19
.ti +4
INTEGER
JPVT( * )
.TP 19
.ti +4
REAL
A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ),
VN1( * ), VN2( * )
.SH 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.
.br
In some cases, due to catastrophic cancellations, it cannot
factorize NB columns. Hence, the actual number of factorized
columns is returned in KB.
.br
Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
.SH ARGUMENTS
.TP 8
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
.TP 8
N (input) INTEGER
The number of columns of the matrix A. N >= 0
.TP 8
OFFSET (input) INTEGER
The number of rows of A that have been factorized in
previous steps.
.TP 8
NB (input) INTEGER
The number of columns to factorize.
.TP 8
KB (output) INTEGER
The number of columns actually factorized.
.TP 8
A (input/output) REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, block A(OFFSET+1:M,1:KB) is the triangular
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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.
.TP 8
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
.TP 8
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.
.TP 8
TAU (output) REAL array, dimension (KB)
The scalar factors of the elementary reflectors.
.TP 8
VN1 (input/output) REAL array, dimension (N)
The vector with the partial column norms.
.TP 8
VN2 (input/output) REAL array, dimension (N)
The vector with the exact column norms.
.TP 8
AUXV (input/output) REAL array, dimension (NB)
Auxiliar vector.
.TP 8
F (input/output) REAL array, dimension (LDF,NB)
Matrix F\(aq = L*Y\(aq*A.
.TP 8
LDF (input) INTEGER
The leading dimension of the array F. LDF >= max(1,N).
.SH FURTHER DETAILS
Based on contributions by
.br
G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
X. Sun, Computer Science Dept., Duke University, USA
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Partial column norm updating strategy modified by
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Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
.br
University of Zagreb, Croatia.
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June 2006.
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For more details see LAPACK Working Note 176.
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