- 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( * )
PURPOSESLAQPS 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.
- 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.
- 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) 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 DETAILSBased 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.