sorgtsqr_row.f - Man Page



subroutine sorgtsqr_row (M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK, INFO)

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 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.


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


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


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


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


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


          The dimension of the array WORK.
          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 is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.


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

Definition at line 186 of file sorgtsqr_row.f.


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Referenced By

The man page sorgtsqr_row(3) is an alias of sorgtsqr_row.f(3).

Thu Apr 1 2021 Version 3.9.1 LAPACK