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

NAME
       SRC/dorgtsqr.f

SYNOPSIS
   Functions/Subroutines
       subroutine dorgtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
           DORGTSQR

Function/Subroutine Documentation
   subroutine dorgtsqr (integer m, integer n, integer mb, integer nb, double
       precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( ldt, * ) t, integer ldt, double precision, dimension( * )
       work, integer lwork, integer info)
       DORGTSQR

       Purpose:


            DORGTSQR 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 DLATSQR

                 Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).

            See the documentation for DLATSQR.

       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.

           MB

                     MB is INTEGER
                     The row block size used by DLATSQR 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 DLATSQR 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 DOUBLE PRECISION 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 DLATSQR
                        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 DLATSQR).

                     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 DOUBLE PRECISION 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 DLATSQR).

           LDT

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

           WORK

                     (workspace) DOUBLE PRECISION 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

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:


            November 2019, Igor Kozachenko,
                           Computer Science Division,
                           University of California, Berkeley

       Definition at line 174 of file dorgtsqr.f.

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

LAPACK                          Version 3.12.0               SRC/dorgtsqr.f(3)