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slamswlq.f(3) | LAPACK | slamswlq.f(3) |
NAME¶
slamswlq.f -SYNOPSIS¶
Functions/Subroutines¶
subroutine slamswlq (SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
Function/Subroutine Documentation¶
subroutine slamswlq (characterSIDE, characterTRANS, integerM, integerN, integerK, integerMB, integerNB, real, dimension( lda, * )A, integerLDA, real, dimension( ldt, * )T, integerLDT, real, dimension(ldc, * )C, integerLDC, real, dimension( * )WORK, integerLWORK, integerINFO)¶
Purpose:SIDE
Author:
SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.TRANS
TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T.M
M is INTEGER The number of rows of the matrix A. 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 >= 1NB
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 REAL array, dimension (LDA,K) The i-th row must contain the vector which defines the blocked elementary reflector H(i), for i = 1,2,...,k, as returned by DLASWLQ 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 REAL 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 REAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.LDC
LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).WORK
(workspace) REAL 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
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Short-Wide LQ (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 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
Author¶
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