SRC/zgetsqrhrt.f(3)        Library Functions Manual        SRC/zgetsqrhrt.f(3)

NAME
       SRC/zgetsqrhrt.f

SYNOPSIS
   Functions/Subroutines
       subroutine zgetsqrhrt (m, n, mb1, nb1, nb2, a, lda, t, ldt, work,
           lwork, info)
           ZGETSQRHRT

Function/Subroutine Documentation
   subroutine zgetsqrhrt (integer m, integer n, integer mb1, integer nb1,
       integer nb2, complex*16, dimension( lda, * ) a, integer lda,
       complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension(
       * ) work, integer lwork, integer info)
       ZGETSQRHRT

       Purpose:


            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.

       Parameters
           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

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:


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

       Definition at line 177 of file zgetsqrhrt.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0             SRC/zgetsqrhrt.f(3)