dorgtsqr_row()

subroutine dorgtsqr_row	(	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_ROW

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Purpose:

!>
!> DORGTSQR_ROW generates an M-by-N real matrix Q_out with
!> orthonormal columns from the output of DLATSQR. These N orthonormal
!> columns are the first N columns of a product of complex unitary
!> matrices Q(k)_in of order M, which are returned by DLATSQR in
!> a special format.
!>
!>      Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
!>
!> The input matrices Q(k)_in are stored in row and column blocks in A.
!> See the documentation of DLATSQR for more details on the format of
!> Q(k)_in, where each Q(k)_in is represented by block Householder
!> transformations. This routine calls an auxiliary routine DLARFB_GETT,
!> where the computation is performed on each individual block. The
!> algorithm first sweeps NB-sized column blocks from the right to left
!> starting in the bottom row block and continues to the top row block
!> (hence _ROW in the routine name). This sweep is in reverse order of
!> the order in which DLATSQR generates the output blocks.
!> 

Parameters

[in]	M	!> M is INTEGER !> The number of rows of the matrix A. M >= 0. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrix A. M >= N >= 0. !>
[in]	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). !>
[in]	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). !>
[in,out]	A	!> A is DOUBLE PRECISION array, dimension (LDA,N) !> !> On entry: !> !> The elements on and above the diagonal are not used as !> input. 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). See DLATSQR for more details. !> !> On exit: !> !> The array A contains an M-by-N orthonormal matrix Q_out, !> i.e the columns of A are orthogonal unit vectors. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>
[in]	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 the 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. See DLATSQR for more details on the format !> of T. !>
[in]	LDT	!> LDT is INTEGER !> The leading dimension of the array T. !> LDT >= max(1,min(NB,N)). !>
[out]	WORK	!> (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
[in]	LWORK	!> LWORK is INTEGER !> The dimension of the array WORK. !> LWORK >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)), !> where NBLOCAL=MIN(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. !>
[out]	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
!>
!>