Visible to Intel only — GUID: GUID-27F22B56-756E-407C-83CE-C569C4AFDD20
Visible to Intel only — GUID: GUID-27F22B56-756E-407C-83CE-C569C4AFDD20
?laqps
Computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.
Syntax
call slaqps( m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf )
call dlaqps( m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf )
call claqps( m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf )
call zlaqps( m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf )
Include Files
- mkl.fi
Description
The routine computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. The routine tries to factorize NB columns from A starting from the row offset+1, and updates all of the matrix with BLAS level 3 routine ?gemm.
In some cases, due to catastrophic cancellations, ?laqps 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.
Input Parameters
- m
-
INTEGER. The number of rows of the matrix A. m≥ 0.
- n
-
INTEGER. The number of columns of the matrix A. n≥ 0.
- offset
-
INTEGER. The number of rows of A that have been factorized in previous steps.
- nb
-
INTEGER. The number of columns to factorize.
- a
-
REAL for slaqps
DOUBLE PRECISION for dlaqps
COMPLEX for claqps
DOUBLE COMPLEX for zlaqps
Array, DIMENSION (lda,n).
On entry, the m-by-n matrix A.
- lda
-
INTEGER. The leading dimension of the array a.
lda≥ max(1,m).
- jpvt
-
INTEGER. Array, DIMENSION (n).
If jpvt(I) = k then column k of the full matrix A has been permuted into position i in AP.
- vn1, vn2
-
REAL for slaqps/claqps
DOUBLE PRECISION for dlaqps/zlaqps
Arrays, DIMENSION (n) each. Contain the vectors with the partial and exact column norms, respectively.
- auxv
-
REAL for slaqps
DOUBLE PRECISION for dlaqps
COMPLEX for claqps
DOUBLE COMPLEX for zlaqps
Array, DIMENSION (nb). Auxiliary vector.
- f
-
REAL for slaqps
DOUBLE PRECISION for dlaqps
COMPLEX for claqps
DOUBLE COMPLEX for zlaqps
Array, DIMENSION (ldf,nb). For real flavors, matrix FT = L*YT*A. For complex flavors, matrix FH = L*YH*A.
- ldf
-
INTEGER. The leading dimension of the array f.
ldf≥ max(1,n).
Output Parameters
- kb
-
INTEGER. The number of columns actually factorized.
- 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.
- jpvt
-
INTEGER array, DIMENSION (n). If jpvt(I) = k then column k of the full matrix A has been permuted into position i in AP.
- tau
-
REAL for slaqps
DOUBLE PRECISION for dlaqps
COMPLEX for claqps
DOUBLE COMPLEX for zlaqps
Array, DIMENSION (kb). The scalar factors of the elementary reflectors.
- vn1, vn2
-
The vectors with the partial and exact column norms, respectively.
- auxv
-
Auxiliary vector.
- f
-
Matrix F' = L*Y'*A.