SLAQPS - compute 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 can
not 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 fac
torized.
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(OFFSET+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.
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. Quintana-Orti, Depto. de Informatica, Universidad
Jaime I, Spain
X. Sun, Computer Science Dept., Duke University, USA
Man(1) output converted with
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