SRC/dgetsqrhrt.f(3)

NAME
SRC/dgetsqrhrt.f

SYNOPSIS

  Functions/Subroutines
subroutine dgetsqrhrt (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)
DGETSQRHRT

Function/Subroutine Documentation

  subroutine dgetsqrhrt (integer m, integer n, integer mb1, integer nb1, integer nb2, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer lwork, integer info)

DGETSQRHRT

Purpose:

     DGETSQRHRT computes a NB2-sized column blocked QR-factorization
     of a real M-by-N matrix A with M >= N,
        A = Q * R.
     The routine uses internally a NB1-sized column blocked and MB1-sized
     row blocked TSQR-factorization and perfors the reconstruction
     of the Householder vectors from the TSQR output. The routine also
     converts the R_tsqr factor from the TSQR-factorization output into
     the R factor that corresponds to the Householder QR-factorization,
        A = Q_tsqr * R_tsqr = Q * R.
     The output Q and R factors are stored in the same format as in DGEQRT
     (Q is in blocked compact WY-representation). See the documentation
     of DGEQRT for more details on the format.

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.

    MB1

              MB1 is INTEGER
              The row block size to be used in the blocked TSQR.
              MB1 > N.

    NB1

              NB1 is INTEGER
              The column block size to be used in the blocked TSQR.
              N >= NB1 >= 1.

    NB2

              NB2 is INTEGER
              The block size to be used in the blocked QR that is
              output. NB2 >= 1.

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
              On entry: an M-by-N matrix A.
              On exit:
               a) the elements on and above the diagonal
                  of the array contain the N-by-N upper-triangular
                  matrix R corresponding to the Householder QR;
               b) the elements below the diagonal represent Q by
                  the columns of blocked V (compact WY-representation).

    LDA

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

    T

              T is DOUBLE PRECISION array, dimension (LDT,N))
              The upper triangular block reflectors stored in compact form
              as a sequence of upper triangular blocks.

    LDT

              LDT is INTEGER
              The leading dimension of the array T.  LDT >= NB2.

    WORK

              (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              The dimension of the array WORK.
              LWORK >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ),
              where
                 NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)),
                 NB1LOCAL = MIN(NB1,N).
                 LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL,
                 LW1 = NB1LOCAL * N,
                 LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ),
              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.

Contributors:

     November 2020, Igor Kozachenko,
                    Computer Science Division,
                    University of California, Berkeley

Definition at line 177 of file dgetsqrhrt.f.

Author

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