dlatsqr.f(3)

NAME
dlatsqr.f

SYNOPSIS

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

Function/Subroutine Documentation

  subroutine dlatsqr (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)

Purpose:@verbatim

DLATSQR computes a blocked Tall-Skinny QR factorization of an M-by-N matrix A, where M >= N: A = Q * R .

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. M >= N >= 0.

    MB

              MB is INTEGER
              The row block size to be used in the blocked QR.
              MB > N.

    NB

              NB is INTEGER
              The column block size to be used in the blocked QR.
              N >= NB >= 1.

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the elements on and above the diagonal
              of the array contain the N-by-N upper triangular matrix R;
              the elements below the diagonal represent Q by the columns
              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((M-N)/(MB-N))
              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 >= NB.

    WORK

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

    LWORK

              The dimension of the array WORK.  LWORK >= NB*N.
              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:@verbatim
    Tall-Skinny QR (TSQR) performs QR 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 subdiagonal entries of a block of MB rows of A: Q(1) zeros out the subdiagonal entries of rows 1:MB of A Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A . . .

Q(1) is computed by GEQRT, 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 GEQRT.

Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N). 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 151 of file dlatsqr.f.

Author

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