SRC/slatsqr.f(3)

NAME
SRC/slatsqr.f

SYNOPSIS

  Functions/Subroutines
subroutine slatsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
SLATSQR

Function/Subroutine Documentation

  subroutine slatsqr (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)

SLATSQR

Purpose:

    !>
    !> SLATSQR computes a blocked Tall-Skinny QR factorization of
    !> a real M-by-N matrix A for M >= N:
    !>
    !>    A = Q * ( R ),
    !>            ( 0 )
    !>
    !> where:
    !>
    !>    Q is a M-by-M orthogonal matrix, stored on exit in an implicit
    !>    form in the elements below the diagonal of the array A and in
    !>    the elements of the array T;
    !>
    !>    R is an upper-triangular N-by-N matrix, stored on exit in
    !>    the elements on and above the diagonal of the array A.
    !>
    !>    0 is a (M-N)-by-N zero matrix, 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. 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 REAL 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 REAL 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) REAL array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= NB*N, otherwise.
    !>
    !>          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.
    !>

    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:

    !> 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 170 of file slatsqr.f.

Author

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