zlamswlq.f - Online Linux Manual PageSection : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEzlamswlq.f
SYNOPSIS
Functions/Subroutinessubroutine zlamswlq (SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
Function/Subroutine Documentation
subroutine zlamswlq (character SIDE, character TRANS, integer M, integer N, integer K, integer MB, integer NB, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldt, * ) T, integer LDT, complex*16, dimension(ldc, * ) C, integer LDC, complex*16, dimension( * ) WORK, integer LWORK, integer INFO)Purpose: ZLAMQRTS overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': 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 (ZLASWLQ) Parameters: SIDE 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': Conjugate 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*16 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
ZLASWLQ 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*16 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*16 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*16 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 valueAuthor: 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 Definition at line 204 of file zlamswlq.f.
AuthorGenerated automatically by Doxygen for LAPACK from the source code. 0
Johanes Gumabo
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