!>
!> 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.
!> 

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
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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