Visible to Intel only — GUID: GUID-B7D77A39-138F-433B-9910-BB8172BE57AC
Visible to Intel only — GUID: GUID-B7D77A39-138F-433B-9910-BB8172BE57AC
?laswlq
Computes blocked Short-Wide LQ matrix factorization.
call slaswlq(m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
call dlaswlq(m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
call claswlq(m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
call zlaswlq(m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
Description
?laswlq computes a blocked Short-Wide LQ (SWLQ) factorization of an m-by-n matrix A, where n≥m: A = L*Q.
SWLQ performs LQ by a sequence of orthogonal transformations, representing Q as a product of other orthogonal matrices
Q = Q(1) * Q(2) * . . . * Q(k)
where each Q(i) zeros out upper diagonal entries of a block of nb rows of A:
Q(1) zeros out the upper diagonal entries of rows 1:nb of A,
Q(2) zeros out the bottom mb - n rows of rows [1:m, nb + 1:2*nb - m] of A,
Q(3) zeros out the bottom mb - n rows of rows [1:m, 2*nb - m + 1:3*nb - 2*m] of A....
Q(1) is computed bygelqt, which represents Q(1) by Householder vectors stored under the diagonal of rows 1:mb of a, and by upper triangular block reflectors, stored in array t(1:ldt, 1:n). For more information, see gelqt.
Q(i) for i > 1 is computed by tplqt, which represents Q(i) by Householder vectors stored in columns [(i - 1)*(nb - m) + m + 1:i*(nb - m) + m] of a, and by upper triangular block reflectors, stored in array t(1:ldt, (i - 1)*m + 1:i*m). The last Q(k) may use fewer rows. For more information, see tplqt. For more details of the overall algorithm, see [DEMMEL12].
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≥m≥ 0.
- mb
-
INTEGER. The row block size to be used in the blocked QR. m≥mb≥ 1
- nb
-
INTEGER. The column block size to be used in the blocked QR. nb > m.
- a
-
REAL for slaswlq
DOUBLE PRECISION for dlaswlq
COMPLEX for claswlq
COMPLEX*16 for zlaswlq
Array of size (lda, n). On entry, the m-by-n matrix A.
- lda
-
INTEGER. The leading dimension of the array a. lda≥ max(1,m).
- ldt
-
INTEGER. The leading dimension of the array t. ldt≥mb.
- lwork
-
INTEGER. The dimension of the array work. lwork≥mb * m.
If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by XERBLA.
Output Parameters
- a
-
On exit, the elements on and below the diagonal of the array contain the n-by-n lower triangular matrix L; the elements above the diagonal represent Q by the rows of blocked V.
- t
-
REAL for slaswlq
DOUBLE PRECISION for dlaswlq
COMPLEX for claswlq
COMPLEX*16 for zlaswlq
Array of size (ldt, n * Number_of_row_blocks), where Number_of_row_blocks = ceiling((n - m)/(nb-m)). The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks.
- work
-
REAL for slaswlq
DOUBLE PRECISION for dlaswlq
COMPLEX for claswlq
COMPLEX*16 for zlaswlq
Workspace array of size (max(1, lwork)).
- info
-
INTEGER.
info = 0: successful exit.
info < 0: if info = -i, the i-th argument had an illegal value.