
NAMEclamswlq.fSYNOPSISFunctions/Subroutinessubroutine clamswlq (SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO) CLAMSWLQ Function/Subroutine Documentationsubroutine clamswlq (character SIDE, character TRANS, integer M, integer N, integer K, integer MB, integer NB, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldt, * ) T, integer LDT, complex, dimension(ldc, * ) C, integer LDC, complex, dimension( * ) WORK, integer LWORK, integer INFO)CLAMSWLQPurpose: CLAMQRTS overwrites the general real MbyN 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
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. A A is COMPLEX array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The ith 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(NK/NBK)), 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 MbyN 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 ith argument had an illegal value Author Univ. of Tennessee
Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Further Details: ShortWide 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 MBN rows of rows [1:M,NB+1:2*NBM] of A Q(3) zeros out the bottom MBN rows of rows [1:M,2*NBM+1:3*NB2*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 [(i1)*(NBM)+M+1:i*(NBM)+M] of A, and by upper triangular block reflectors, stored in array T(1:LDT,(i1)*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] “CommunicationOptimal 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 195 of file clamswlq.f. AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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