SRC/zlamswlq.f(3) Library Functions Manual SRC/zlamswlq.f(3) NAME SRC/zlamswlq.f SYNOPSIS Functions/Subroutines subroutine zlamswlq (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info) ZLAMSWLQ 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) ZLAMSWLQ Purpose: !> !> ZLAMSWLQ overwrites the general complex 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 complex unitary 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 >= 0. !> 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 LQ. !> M >= MB >= 1 !> NB !> NB is INTEGER !> The column block size to be used in the blocked LQ. !> NB > 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. LDA >= MAX(1,K). !> 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)) !> On exit, if INFO = 0, WORK(1) returns the minimal LWORK. !> LWORK !> LWORK is INTEGER !> The dimension of the array WORK. !> If MIN(M,N,K) = 0, LWORK >= 1. !> 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 minimal 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 !> Author 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 unitary transformations, !> representing Q as a product of other unitary 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 TPLQT. !> !> 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 198 of file zlamswlq.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 SRC/zlamswlq.f(3)