.TH "SRC/zlamswlq.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/zlamswlq.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBzlamswlq\fP (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)" .br .RI "\fBZLAMSWLQ\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "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)" .PP \fBZLAMSWLQ\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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) !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fISIDE\fP .PP .nf !> SIDE is CHARACTER*1 !> = 'L': apply Q or Q**H from the Left; !> = 'R': apply Q or Q**H from the Right\&. !> .fi .PP .br \fITRANS\fP .PP .nf !> TRANS is CHARACTER*1 !> = 'N': No transpose, apply Q; !> = 'C': Conjugate Transpose, apply Q**H\&. !> .fi .PP .br \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the matrix C\&. M >=0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the matrix C\&. N >= 0\&. !> .fi .PP .br \fIK\fP .PP .nf !> K is INTEGER !> The number of elementary reflectors whose product defines !> the matrix Q\&. !> M >= K >= 0; !> !> .fi .PP .br \fIMB\fP .PP .nf !> MB is INTEGER !> The row block size to be used in the blocked LQ\&. !> M >= MB >= 1 !> .fi .PP .br \fINB\fP .PP .nf !> NB is INTEGER !> The column block size to be used in the blocked LQ\&. !> NB > M\&. !> .fi .PP .br \fIA\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= MAX(1,K)\&. !> .fi .PP .br \fIT\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDT\fP .PP .nf !> LDT is INTEGER !> The leading dimension of the array T\&. LDT >= MB\&. !> .fi .PP .br \fIC\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDC\fP .PP .nf !> LDC is INTEGER !> The leading dimension of the array C\&. LDC >= max(1,M)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the minimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> 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\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf !> 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 !> .fi .PP .RE .PP .PP Definition at line \fB198\fP of file \fBzlamswlq\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.