!>
!>      ZLAMTSQR overwrites the general complex M-by-N matrix C with
!>
!>
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      Q * C          C * Q
!> TRANS = 'C':      Q**H * C       C * Q**H
!>      where Q is a complex unitary matrix defined as the product
!>      of blocked elementary reflectors computed by tall skinny
!>      QR factorization (ZLATSQR)
!> 

SIDE

!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**H from the Left;
!>          = 'R': apply Q or Q**H from the Right.
!> 

TRANS

!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  Conjugate Transpose, apply Q**H.
!> 

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 C. N >= 0.
!> 

K

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q. M >= K >= 0;
!>
!> 

MB

!>          MB is INTEGER
!>          The block size to be used in the blocked QR.
!>          MB > N. (must be the same as ZLATSQR)
!> 

NB

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

A

!>          A is COMPLEX*16 array, dimension (LDA,K)
!>          The i-th column must contain the vector which defines the
!>          blockedelementary reflector H(i), for i = 1,2,...,k, as
!>          returned by ZLATSQR in the first k columns of
!>          its array argument A.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.
!>          If SIDE = 'L', LDA >= max(1,M);
!>          if SIDE = 'R', LDA >= max(1,N).
!> 

T

!>          T is COMPLEX*16 array, dimension
!>          ( N * Number of blocks(CEIL(M-K/MB-K)),
!>          The blocked upper triangular block reflectors stored in compact form
!>          as a sequence of upper triangular blocks.  See below
!>          for further details.
!> 

LDT

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

C

!>          C is COMPLEX*16 array, dimension (LDC,N)
!>          On entry, the M-by-N matrix C.
!>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
!> 

LDC

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

WORK

!>         (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
!>
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>
!>          If SIDE = 'L', LWORK >= max(1,N)*NB;
!>          if SIDE = 'R', LWORK >= max(1,MB)*NB.
!>          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

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NAG Ltd.

!> Tall-Skinny QR (TSQR) performs QR by a sequence of unitary transformations,
!> representing Q as a product of other unitary matrices
!>   Q = Q(1) * Q(2) * . . . * Q(k)
!> where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:
!>   Q(1) zeros out the subdiagonal entries of rows 1:MB of A
!>   Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
!>   Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
!>   . . .
!>
!> Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors
!> stored under the diagonal of rows 1:MB of A, and by upper triangular
!> block reflectors, stored in array T(1:LDT,1:N).
!> For more information see Further Details in GEQRT.
!>
!> Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors
!> stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular
!> block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).
!> The last Q(k) may use fewer rows.
!> For more information see Further Details in TPQRT.
!>
!> For more details of the overall algorithm, see the description of
!> Sequential TSQR in Section 2.2 of [1].
!>
!> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
!>     J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
!>     SIAM J. Sci. Comput, vol. 34, no. 1, 2012
!>