SRC/dlaswlq.f(3)           Library Functions Manual           SRC/dlaswlq.f(3)

NAME
       SRC/dlaswlq.f

SYNOPSIS
   Functions/Subroutines
       subroutine dlaswlq (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
           DLASWLQ

Function/Subroutine Documentation
   subroutine dlaswlq (integer m, integer n, integer mb, integer nb, double
       precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( ldt, *) t, integer ldt, double precision, dimension( * )
       work, integer lwork, integer info)
       DLASWLQ

       Purpose:


            DLASWLQ computes a blocked Tall-Skinny LQ factorization of
            a real M-by-N matrix A for M <= N:

               A = ( L 0 ) *  Q,

            where:

               Q is a n-by-N orthogonal matrix, stored on exit in an implicit
               form in the elements above the diagonal of the array A and in
               the elements of the array T;
               L is a lower-triangular M-by-M matrix stored on exit in
               the elements on and below the diagonal of the array A.
               0 is a M-by-(N-M) zero matrix, if M < N, and is not stored.

       Parameters
           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 A.  N >= M >= 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 > 0.

           A

                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit, the elements on and below the diagonal
                     of the array contain the N-by-N lower triangular matrix L;
                     the elements above the diagonal represent Q by the rows
                     of blocked V (see Further Details).

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           T

                     T is DOUBLE PRECISION array,
                     dimension (LDT, N * Number_of_row_blocks)
                     where Number_of_row_blocks = CEIL((N-M)/(NB-M))
                     The blocked upper triangular block reflectors stored in compact form
                     as a sequence of upper triangular blocks.
                     See Further Details below.

           LDT

                     LDT is INTEGER
                     The leading dimension of the array T.  LDT >= MB.

           WORK

                    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.  LWORK >= MB*M.
                     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 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 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 TPQRT.

            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 165 of file dlaswlq.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                SRC/dlaswlq.f(3)