!>
!> SORGTSQR generates an M-by-N real matrix Q_out with orthonormal columns,
!> which are the first N columns of a product of real orthogonal
!> matrices of order M which are returned by SLATSQR
!>
!>      Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
!>
!> See the documentation for SLATSQR.
!> 

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 accessed.
!>             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) (same format as the output A
!>             below the diagonal in SLATSQR).
!>
!>          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 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.
!>          (same format as the output T in SLATSQR).
!> 

LDT

!>          LDT is INTEGER
!>          The leading dimension of the array T.
!>          LDT >= max(1,min(NB1,N)).
!> 

WORK

!>          (workspace) REAL array, dimension (MAX(2,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.  LWORK >= (M+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 2019, Igor Kozachenko,
!>                Computer Science Division,
!>                University of California, Berkeley
!>
!>