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dlaswlq.f(3) | LAPACK | dlaswlq.f(3) |
NAME¶
dlaswlq.f -SYNOPSIS¶
Functions/Subroutines¶
subroutine dlaswlq (M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK, INFO)
Function/Subroutine Documentation¶
subroutine dlaswlq (integerM, integerN, integerMB, integerNB, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldt, *)T, integerLDT, double precision, dimension( * )WORK, integerLWORK, integerINFO)¶
Purpose:M
Author:
M is INTEGER The number of rows of the matrix A. M >= 0.N
N is INTEGER The number of columns of the matrix A. N >= M >= 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.A
A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and bleow 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 (see Further Details).LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).T
T is DOUBLE PRECISION array, dimension (LDT, N * Number_of_row_blocks) where Number_of_row_blocks = CEIL((N-M)/(NB-M)) The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See Further Details below.LDT
LDT is INTEGER The leading dimension of the array T. LDT >= MB.WORK
(workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))LWORK
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.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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