!>
!> ZGETSQRHRT computes a NB2-sized column blocked QR-factorization
!> of a complex M-by-N matrix A with M >= N,
!>
!>    A = Q * R.
!>
!> The routine uses internally a NB1-sized column blocked and MB1-sized
!> row blocked TSQR-factorization and perfors the reconstruction
!> of the Householder vectors from the TSQR output. The routine also
!> converts the R_tsqr factor from the TSQR-factorization output into
!> the R factor that corresponds to the Householder QR-factorization,
!>
!>    A = Q_tsqr * R_tsqr = Q * R.
!>
!> The output Q and R factors are stored in the same format as in ZGEQRT
!> (Q is in blocked compact WY-representation). See the documentation
!> of ZGEQRT for more details on the format.
!> 

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.
!> 

MB1

!>          MB1 is INTEGER
!>          The row block size to be used in the blocked TSQR.
!>          MB1 > N.
!> 

NB1

!>          NB1 is INTEGER
!>          The column block size to be used in the blocked TSQR.
!>          N >= NB1 >= 1.
!> 

NB2

!>          NB2 is INTEGER
!>          The block size to be used in the blocked QR that is
!>          output. NB2 >= 1.
!> 

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>
!>          On entry: an M-by-N matrix A.
!>
!>          On exit:
!>           a) the elements on and above the diagonal
!>              of the array contain the N-by-N upper-triangular
!>              matrix R corresponding to the Householder QR;
!>           b) the elements below the diagonal represent Q by
!>              the columns of blocked V (compact WY-representation).
!> 

LDA

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

T

!>          T is COMPLEX*16 array, dimension (LDT,N))
!>          The upper triangular block reflectors stored in compact form
!>          as a sequence of upper triangular blocks.
!> 

LDT

!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= NB2.
!> 

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 >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ),
!>          where
!>             NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)),
!>             NB1LOCAL = MIN(NB1,N).
!>             LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL,
!>             LW1 = NB1LOCAL * N,
!>             LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ),
!>          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
!>
!>