
NAMEclamtsqr.fSYNOPSISFunctions/Subroutinessubroutine clamtsqr (SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO) CLAMTSQR Function/Subroutine Documentationsubroutine clamtsqr (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)CLAMTSQRPurpose: CLAMTSQR overwrites the general complex MbyN 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 tall skinny QR factorization (CLATSQR) 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 A. M >=0. N N is INTEGER The number of columns of the matrix C. M >= N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0; MB MB is INTEGER The block size to be used in the blocked QR. MB > N. (must be the same as DLATSQR) 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,K) The ith column must contain the vector which defines the blockedelementary reflector H(i), for i = 1,2,...,k, as returned by DLATSQR in the first k columns 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 ( N * Number of blocks(CEIL(MK/MBK)), 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 >= NB. 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,N)*NB; if SIDE = 'R', LWORK >= max(1,MB)*NB. 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: TallSkinny 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 MBN rows of rows [1:N,MB+1:2*MBN] of A Q(3) zeros out the bottom MBN rows of rows [1:N,2*MBN+1:3*MB2*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 [(i1)*(MBN)+N+1:i*(MBN)+N] of A, and by upper triangular block reflectors, stored in array T(1:LDT,(i1)*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] “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 196 of file clamtsqr.f. AuthorGenerated automatically by Doxygen for LAPACK from the source code.
Visit the GSP FreeBSD Man Page Interface. 