SRC/dlamtsqr.f(3)

NAME
SRC/dlamtsqr.f

SYNOPSIS

  Functions/Subroutines
subroutine dlamtsqr (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
DLAMTSQR

Function/Subroutine Documentation

  subroutine dlamtsqr (character side, character trans, integer m, integer n, integer k, integer mb, integer nb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension(ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)

DLAMTSQR

Purpose:

          DLAMTSQR overwrites the general real M-by-N matrix C with
                     SIDE = 'L'     SIDE = 'R'
     TRANS = 'N':      Q * C          C * Q
     TRANS = 'T':      Q**T * C       C * Q**T
          where Q is a real orthogonal matrix defined as the product
          of blocked elementary reflectors computed by tall skinny
          QR factorization (DLATSQR)

Parameters
    SIDE

              SIDE is CHARACTER*1
              = 'L': apply Q or Q**T from the Left;
              = 'R': apply Q or Q**T from the Right.

    TRANS

              TRANS is CHARACTER*1
              = 'N':  No transpose, apply Q;
              = 'T':  Transpose, apply Q**T.

    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 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 block size to be used in the blocked QR.
              MB > N. (must be the same as DLATSQR)

    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,K)
              The i-th column must contain the vector which defines the
              blockedelementary reflector H(i), for i = 1,2,...,k, as
              returned by DLATSQR in the first k columns of
              its array argument A.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.
              If SIDE = 'L', LDA >= max(1,M);
              if SIDE = 'R', LDA >= max(1,N).

    T

              T is DOUBLE PRECISION array, dimension
              ( N * Number of blocks(CEIL(M-K/MB-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 >= NB.

    C

              C is DOUBLE PRECISION array, dimension (LDC,N)
              On entry, the M-by-N matrix C.
              On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

    LDC

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

    WORK

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

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If SIDE = 'L', LWORK >= max(1,N)*NB;
              if SIDE = 'R', LWORK >= max(1,MB)*NB.
              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:

     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 197 of file dlamtsqr.f.

Author

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