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clatsqr.f(3) | LAPACK | clatsqr.f(3) |
NAME¶
clatsqr.f -SYNOPSIS¶
Functions/Subroutines¶
subroutine clatsqr (M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK, INFO)
Function/Subroutine Documentation¶
subroutine clatsqr (integerM, integerN, integerMB, integerNB, complex, dimension( lda, * )A, integerLDA, complex, dimension(ldt, *)T, integerLDT, complex, 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. M >= N >= 0.MB
MB is INTEGER The row block size to be used in the blocked QR. MB > N.NB
NB is INTEGER The column block size to be used in the blocked QR. N >= NB >= 1.A
A is COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the N-by-N upper triangular matrix R; the elements below the diagonal represent Q by the columns of blocked V (see Further Details).LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).T
T is COMPLEX array, dimension (LDT, N * Number_of_row_blocks) where Number_of_row_blocks = CEIL((M-N)/(MB-N)) 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 >= NB.WORK
(workspace) COMPLEX array, dimension (MAX(1,LWORK))LWORK
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.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:
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 Further
Details in 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 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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