Visible to Intel only — GUID: GUID-8F15B861-04EB-4C96-A346-2B336E318210
Visible to Intel only — GUID: GUID-8F15B861-04EB-4C96-A346-2B336E318210
?latsqr
Computes a blocked Tall-Skinny QR matrix factorization.
call slatsqr(m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
call dlatsqr(m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
call clatsqr(m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
call zlatsqr(m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
Description
?latsqr computes a blocked Tall-Skinny QR (TSQR) factorization of an m-by-n matrix A, where m≥n: A = Q*R.
TSQR performs QR 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 subdiagonal entries of a block of mb rows of A:
Q(1) zeros out the subdiagonal entries of rows 1:MB of A,
Q(2) zeros out the bottom mb - n rows of rows [1:n, mb + 1:2*mb - n] of A,
Q(3) zeros out the bottom mb - n rows of rows [1:n, 2*mb - n + 1:3*mb - 2*n] of A . . . .
Q(1) is computed by geqrt, 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 geqrt.
Q(i) for i > 1 is computed by tpqrt, which represents Q(i) by Householder vectors stored in rows [(i - 1)*(mb - n) + n + 1:i*(mb - n) + n] of a, and by upper triangular block reflectors, stored in array t(1:ldt, (i - 1)*n + 1:i*n). The last Q(k) may use fewer rows. For more information, see tpqrt. 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. m≥n≥ 0.
- mb
-
INTEGER. The row block size to be used in the blocked QR. mb > n.
- nb
-
INTEGER. The column block size to be used in the blocked QR. n≥nb≥ 1.
- a
-
REAL for slatsqr
DOUBLE PRECISION for dlatsqr
COMPLEX for clatsqr
COMPLEX*16 for zlatsqr
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≥nb.
- lwork
-
INTEGER. The dimension of the array work. lwork≥nb*n. 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 above the diagonal of the array contain the n-by-n upper triangular matrix R and the elements below the diagonal represent Q by the columns of blocked V.
- t
-
REAL for slatsqr
DOUBLE PRECISION for dlatsqr
COMPLEX for clatsqr
COMPLEX*16 for zlatsqr
Array of size (ldt, n * Number_of_row_blocks) where Number_of_row_blocks = ceiling((m - n)/(mb - n)) The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks.
- work
-
REAL for slatsqr
DOUBLE PRECISION for dlatsqr
COMPLEX for clatsqr
COMPLEX*16 for zlatsqr
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.