sorgtsqr_row.f(3)

NAME
sorgtsqr_row.f

SYNOPSIS

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

Function/Subroutine Documentation

  subroutine sorgtsqr_row (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)

SORGTSQR_ROW

Purpose:

     SORGTSQR_ROW generates an M-by-N real matrix Q_out with
     orthonormal columns from the output of SLATSQR. These N orthonormal
     columns are the first N columns of a product of complex unitary
     matrices Q(k)_in of order M, which are returned by SLATSQR in
     a special format.
          Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
     The input matrices Q(k)_in are stored in row and column blocks in A.
     See the documentation of SLATSQR for more details on the format of
     Q(k)_in, where each Q(k)_in is represented by block Householder
     transformations. This routine calls an auxiliary routine SLARFB_GETT,
     where the computation is performed on each individual block. The
     algorithm first sweeps NB-sized column blocks from the right to left
     starting in the bottom row block and continues to the top row block
     (hence _ROW in the routine name). This sweep is in reverse order of
     the order in which SLATSQR generates the output blocks.

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 used by SLATSQR to return
              arrays A and T. MB > N.
              (Note that if MB > M, then M is used instead of MB
              as the row block size).

    NB

              NB is INTEGER
              The column block size used by SLATSQR to return
              arrays A and T. NB >= 1.
              (Note that if NB > N, then N is used instead of NB
              as the column block size).

    A

              A is REAL array, dimension (LDA,N)
              On entry:
                 The elements on and above the diagonal are not used as
                 input. The elements below the diagonal represent the unit
                 lower-trapezoidal blocked matrix V computed by SLATSQR
                 that defines the input matrices Q_in(k) (ones on the
                 diagonal are not stored). See SLATSQR for more details.
              On exit:
                 The array A contains an M-by-N orthonormal matrix Q_out,
                 i.e the columns of A are orthogonal unit vectors.

    LDA

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

    T

              T is REAL array,
              dimension (LDT, N * NIRB)
              where NIRB = Number_of_input_row_blocks
                         = MAX( 1, CEIL((M-N)/(MB-N)) )
              Let NICB = Number_of_input_col_blocks
                       = CEIL(N/NB)
              The upper-triangular block reflectors used to define the
              input matrices Q_in(k), k=(1:NIRB*NICB). The block
              reflectors are stored in compact form in NIRB block
              reflector sequences. Each of the NIRB block reflector
              sequences is stored in a larger NB-by-N column block of T
              and consists of NICB smaller NB-by-NB upper-triangular
              column blocks. See SLATSQR for more details on the format
              of T.

    LDT

              LDT is INTEGER
              The leading dimension of the array T.
              LDT >= max(1,min(NB,N)).

    WORK

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

    LWORK

              The dimension of the array WORK.
              LWORK >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)),
              where NBLOCAL=MIN(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.

Contributors:

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

Definition at line 186 of file sorgtsqr_row.f.

Author

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