subroutine clamswlq (SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
Purpose:
CLAMQRTS overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**H * C C * Q**H where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (CLASWLQ)
Parameters:
SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right.
TRANS
TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Transpose, apply Q**H.
M
M is INTEGER The number of rows of the matrix C. M >=0.
N
N is INTEGER The number of columns of the matrix C. N >= M.
K
K is INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0;
MB
MB is INTEGER The row block size to be used in the blocked QR. M >= MB >= 1
NB
NB is INTEGER The column block size to be used in the blocked QR. NB > M.
NB
NB is INTEGER The block size to be used in the blocked QR. MB > M.
A
A is COMPLEX array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must contain the vector which defines the blocked elementary reflector H(i), for i = 1,2,...,k, as returned by CLASWLQ in the first k rows of its array argument A.
LDA
LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N).
T
T is COMPLEX array, dimension ( M * Number of blocks(CEIL(N-K/NB-K)), The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.
LDT
LDT is INTEGER The leading dimension of the array T. LDT >= MB.
C
C is COMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
LDC
LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).
WORK
(workspace) COMPLEX array, dimension (MAX(1,LWORK))
LWORK
LWORK is INTEGER The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,NB) * MB; if SIDE = 'R', LWORK >= max(1,M) * MB. 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.
INFO
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Q(1) is computed by GELQT, 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 Further Details in 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 Further Details in TPQRT.
For more details of the overall algorithm, see the description of Sequential TSQR in Section 2.2 of [1].
[1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,” J. Demmel, L. Grigori, M. Hoemmen, J. Langou, SIAM J. Sci. Comput, vol. 34, no. 1, 2012
Definition at line 204 of file clamswlq.f.
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