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))

           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 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 195 of file zlamswlq.f.

Author
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LAPACK                          Version 3.12.0               SRC/zlamswlq.f(3)