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

          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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 November 2020, Igor Kozachenko,


                Computer Science Division,


                University of California, Berkeley