SRC/zungtsqr_row.f(3)      Library Functions Manual      SRC/zungtsqr_row.f(3)

NAME
       SRC/zungtsqr_row.f

SYNOPSIS
   Functions/Subroutines
       subroutine zungtsqr_row (m, n, mb, nb, a, lda, t, ldt, work, lwork,
           info)
           ZUNGTSQR_ROW

Function/Subroutine Documentation
   subroutine zungtsqr_row (integer m, integer n, integer mb, integer nb,
       complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
       ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer
       lwork, integer info)
       ZUNGTSQR_ROW

       Purpose:


            ZUNGTSQR_ROW generates an M-by-N complex matrix Q_out with
            orthonormal columns from the output of ZLATSQR. 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 ZLATSQR 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 ZLATSQR 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 ZLARFB_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 ZLATSQR 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 ZLATSQR 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 ZLATSQR 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 COMPLEX*16 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 ZLATSQR
                        that defines the input matrices Q_in(k) (ones on the
                        diagonal are not stored). See ZLATSQR 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 COMPLEX*16 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 ZLATSQR 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) COMPLEX*16 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 zungtsqr_row.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0           SRC/zungtsqr_row.f(3)