CLAQPS(1) LAPACK auxiliary routine (version 3.2) CLAQPS(1)NAME
CLAQPS - computes a step of QR factorization with column pivoting of a
complex M-by-N matrix A by using Blas-3
SUBROUTINE CLAQPS( 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 VN1( * ), VN2( * )
COMPLEX A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * )
CLAQPS computes a step of QR factorization with column pivoting of a
complex M-by-N matrix A by using Blas-3. It tries to factorize NB col‐
umns 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
Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
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
NB (input) INTEGER
The number of columns to factorize.
KB (output) INTEGER
The number of columns actually factorized.
A (input/output) COMPLEX 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) COMPLEX 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) COMPLEX array, dimension (NB)
F (input/output) COMPLEX array, dimension (LDF,NB)
Matrix F' = L*Y'*A.
LDF (input) INTEGER
The leading dimension of the array F. LDF >= max(1,N).
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.
For more details see LAPACK Working Note 176.
LAPACK auxiliary routine (versioNovember 2008 CLAQPS(1)