DLAQPS
Purpose
DLAQPS 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 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.
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 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 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. |
| 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**T = L*Y**T*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
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.
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.