ORGTSQR_ROW - 5.2 English - 68552

ORGTSQR_ROW generates an M-by-N real matrix Q_out with orthonormal columns from the output of LATSQR.

Purpose:

   ORGTSQR_ROW generates an M-by-N real matrix Q_out with
   orthonormal columns from the output of LATSQR. 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 – [in]

  M is INTEGER

  The number of rows of the matrix A. M >= 0.

• N – [in]

  N is INTEGER

  The number of columns of the matrix A. M >= N >= 0.

• MB – [in]

  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 – [in]

  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 – [inout]

  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 – [in]

  LDA is INTEGER

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

• T – [in]

  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 – [in]

  LDT is INTEGER

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

• WORK – [out]

  (workspace) REAL array, dimension (MAX(1,LWORK))

  On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

• LWORK – [in]

  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 – [out]

  INFO is INTEGER

  = 0: successful exit

  < 0: if INFO = -i, the i-th argument had an illegal value