slaswlq.f(3)

NAME
slaswlq.f

SYNOPSIS

  Functions/Subroutines
subroutine slaswlq (M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK, INFO)

Function/Subroutine Documentation

  subroutine slaswlq (integer M, integer N, integer MB, integer NB, real, dimension( lda, * ) A, integer LDA, real, dimension( ldt, *) T, integer LDT, real, dimension( * ) WORK, integer LWORK, integer INFO)

Purpose:

SLASWLQ computes a blocked Short-Wide LQ factorization of a M-by-N matrix A, where N >= M: A = L * Q

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 > M.

    A

              A is REAL 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 REAL 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) REAL array, dimension (MAX(1,LWORK))

    LWORK

              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 152 of file slaswlq.f.

Author

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