Visible to Intel only — GUID: GUID-0A2F5A80-FC3A-404D-90EC-6EF9CCB11BD9
Visible to Intel only — GUID: GUID-0A2F5A80-FC3A-404D-90EC-6EF9CCB11BD9
?lamtsqr
Multiplies a general matrix by the product of blocked elementary reflectors computed by tall skinny QR factorization (?latsqr)
call slamtsqr(side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
call dlamtsqr(side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
call clamtsqr(side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
call zlamtsqr(side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
Description
?lamtsqr overwrites the general real or complexm-by-n matrix C with
side = 'L' | side = 'R' | |
---|---|---|
trans = 'N' | Q*C | C*Q |
trans = 'T' | QT*C | C*QT |
trans = 'C' | QH*C | C*QH |
where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by tall skinny QR factorization (?latsqr). Tall-Skinny QR (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
- side
-
CHARACTER*1.
If side = 'L': apply op(Q) from the left;
if side = 'R': apply op(Q) from the right.
- trans
-
CHARACTER*1.
If trans = 'N': No transpose, op(Q) = Q;
if trans = 'T': Transpose, op(Q) = QT;
if trans = 'C': Transpose, op(Q) = QH.
- m
-
INTEGER. The number of rows of the matrix C. m≥0.
- n
-
INTEGER. The number of columns of the matrix C. m≥n≥ 0.
- k
-
INTEGER. The number of elementary reflectors whose product defines the matrix Q. n≥k≥ 0;
- mb
-
INTEGER. The block size to be used in the blocked QR. mb > n. (Must be the same as in ?latsqr)
- nb
-
INTEGER. The column block size to be used in the blocked QR. n≥nb≥ 1.
- a
-
REAL for slamtsqr
DOUBLE PRECISION for dlamtsqr
COMPLEX for clamtsqr
COMPLEX*16 for zlamtsqr
Array of size (lda, k). The i-th column must contain the vector which defines the blocked elementary reflector H(i), for i = 1,2,...,k, as returned by ?latsqr in the first k columns of its array argument a.
- lda
-
INTEGER. The leading dimension of the array a.
If side = 'L', lda≥ max(1, m);
if side = 'R', lda≥ max(1, n).
- t
-
REAL for slamtsqr
DOUBLE PRECISION for dlamtsqr
COMPLEX for clamtsqr
COMPLEX*16 for zlamtsqr
Array of size (n * Number of blocks(ceiling(m-k/mb-k))). The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks, as described previously.
- ldt
-
INTEGER. The leading dimension of the array t. ldt≥nb.
- c
-
REAL for slamtsqr
DOUBLE PRECISION for dlamtsqr
COMPLEX for clamtsqr
COMPLEX*16 for zlamtsqr
Array of size (ldc,n). On entry, the m-by-n matrix C.
- ldc
-
INTEGER. The leading dimension of the array c. ldc≥ max(1, m).
- lwork
-
INTEGER. The dimension of the array work. If side = 'L', lwork≥ max(1, n)*nb; if side = 'R', lwork≥ max(1, mb)*nb. 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
- c
-
On exit, c is overwritten by op(Q)*C or C*op(Q).
- work
-
REAL for slamtsqr
DOUBLE PRECISION for dlamtsqr
COMPLEX for clamtsqr
COMPLEX*16 for zlamtsqr
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.