CGETSQRHRT 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 CGEQRT
 (Q is in blocked compact WY-representation). See the documentation
 of CGEQRT 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 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 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

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Univ. of California Berkeley

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NAG Ltd.

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