380 lines
12 KiB
Fortran
380 lines
12 KiB
Fortran
*> \brief \b SORGTSQR_ROW
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SORGTSQR_ROW + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sorgtsqr_row.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sorgtsqr_row.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorgtsqr_row.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SORGTSQR_ROW( M, N, MB, NB, A, LDA, T, LDT, WORK,
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* $ LWORK, INFO )
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* IMPLICIT NONE
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDT, LWORK, M, N, MB, NB
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), T( LDT, * ), WORK( * )
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* ..
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SORGTSQR_ROW generates an M-by-N real matrix Q_out with
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*> orthonormal columns from the output of SLATSQR. These N orthonormal
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*> columns are the first N columns of a product of complex unitary
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*> matrices Q(k)_in of order M, which are returned by SLATSQR in
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*> a special format.
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*>
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*> Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
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*>
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*> The input matrices Q(k)_in are stored in row and column blocks in A.
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*> See the documentation of SLATSQR for more details on the format of
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*> Q(k)_in, where each Q(k)_in is represented by block Householder
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*> transformations. This routine calls an auxiliary routine SLARFB_GETT,
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*> where the computation is performed on each individual block. The
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*> algorithm first sweeps NB-sized column blocks from the right to left
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*> starting in the bottom row block and continues to the top row block
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*> (hence _ROW in the routine name). This sweep is in reverse order of
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*> the order in which SLATSQR generates the output blocks.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix A. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the matrix A. M >= N >= 0.
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*> \endverbatim
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*>
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*> \param[in] MB
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*> \verbatim
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*> MB is INTEGER
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*> The row block size used by SLATSQR to return
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*> arrays A and T. MB > N.
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*> (Note that if MB > M, then M is used instead of MB
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*> as the row block size).
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*> \endverbatim
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*>
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*> \param[in] NB
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*> \verbatim
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*> NB is INTEGER
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*> The column block size used by SLATSQR to return
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*> arrays A and T. NB >= 1.
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*> (Note that if NB > N, then N is used instead of NB
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*> as the column block size).
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*>
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*> On entry:
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*>
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*> The elements on and above the diagonal are not used as
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*> input. The elements below the diagonal represent the unit
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*> lower-trapezoidal blocked matrix V computed by SLATSQR
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*> that defines the input matrices Q_in(k) (ones on the
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*> diagonal are not stored). See SLATSQR for more details.
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*>
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*> On exit:
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*>
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*> The array A contains an M-by-N orthonormal matrix Q_out,
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*> i.e the columns of A are orthogonal unit vectors.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,M).
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*> \endverbatim
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*>
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*> \param[in] T
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*> \verbatim
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*> T is REAL array,
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*> dimension (LDT, N * NIRB)
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*> where NIRB = Number_of_input_row_blocks
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*> = MAX( 1, CEIL((M-N)/(MB-N)) )
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*> Let NICB = Number_of_input_col_blocks
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*> = CEIL(N/NB)
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*>
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*> The upper-triangular block reflectors used to define the
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*> input matrices Q_in(k), k=(1:NIRB*NICB). The block
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*> reflectors are stored in compact form in NIRB block
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*> reflector sequences. Each of the NIRB block reflector
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*> sequences is stored in a larger NB-by-N column block of T
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*> and consists of NICB smaller NB-by-NB upper-triangular
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*> column blocks. See SLATSQR for more details on the format
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*> of T.
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*> \endverbatim
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*>
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*> \param[in] LDT
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*> \verbatim
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*> LDT is INTEGER
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*> The leading dimension of the array T.
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*> LDT >= max(1,min(NB,N)).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> (workspace) REAL array, dimension (MAX(1,LWORK))
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> The dimension of the array WORK.
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*> LWORK >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)),
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*> where NBLOCAL=MIN(NB,N).
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*> If LWORK = -1, then a workspace query is assumed.
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*> The routine only calculates the optimal size of the WORK
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*> array, returns this value as the first entry of the WORK
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*> array, and no error message related to LWORK is issued
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*> by XERBLA.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> \endverbatim
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*>
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup sigleOTHERcomputational
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*
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*> \par Contributors:
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* ==================
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*>
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*> \verbatim
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*>
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*> November 2020, Igor Kozachenko,
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*> Computer Science Division,
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*> University of California, Berkeley
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*>
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE SORGTSQR_ROW( M, N, MB, NB, A, LDA, T, LDT, WORK,
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$ LWORK, INFO )
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IMPLICIT NONE
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, LDT, LWORK, M, N, MB, NB
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), T( LDT, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY
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INTEGER NBLOCAL, MB2, M_PLUS_ONE, ITMP, IB_BOTTOM,
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$ LWORKOPT, NUM_ALL_ROW_BLOCKS, JB_T, IB, IMB,
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$ KB, KB_LAST, KNB, MB1
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* ..
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* .. Local Arrays ..
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REAL DUMMY( 1, 1 )
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* ..
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* .. External Subroutines ..
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EXTERNAL SLARFB_GETT, SLASET, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC REAL, MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters
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*
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INFO = 0
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LQUERY = LWORK.EQ.-1
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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.0 .OR. M.LT.N ) THEN
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INFO = -2
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ELSE IF( MB.LE.N ) THEN
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INFO = -3
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ELSE IF( NB.LT.1 ) THEN
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INFO = -4
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -6
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ELSE IF( LDT.LT.MAX( 1, MIN( NB, N ) ) ) THEN
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INFO = -8
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ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
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INFO = -10
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END IF
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*
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NBLOCAL = MIN( NB, N )
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*
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* Determine the workspace size.
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*
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IF( INFO.EQ.0 ) THEN
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LWORKOPT = NBLOCAL * MAX( NBLOCAL, ( N - NBLOCAL ) )
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END IF
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*
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* Handle error in the input parameters and handle the workspace query.
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SORGTSQR_ROW', -INFO )
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RETURN
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ELSE IF ( LQUERY ) THEN
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WORK( 1 ) = REAL( LWORKOPT )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( MIN( M, N ).EQ.0 ) THEN
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WORK( 1 ) = REAL( LWORKOPT )
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RETURN
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END IF
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*
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* (0) Set the upper-triangular part of the matrix A to zero and
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* its diagonal elements to one.
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*
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CALL SLASET('U', M, N, ZERO, ONE, A, LDA )
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*
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* KB_LAST is the column index of the last column block reflector
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* in the matrices T and V.
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*
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KB_LAST = ( ( N-1 ) / NBLOCAL ) * NBLOCAL + 1
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*
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*
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* (1) Bottom-up loop over row blocks of A, except the top row block.
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* NOTE: If MB>=M, then the loop is never executed.
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*
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IF ( MB.LT.M ) THEN
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*
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* MB2 is the row blocking size for the row blocks before the
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* first top row block in the matrix A. IB is the row index for
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* the row blocks in the matrix A before the first top row block.
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* IB_BOTTOM is the row index for the last bottom row block
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* in the matrix A. JB_T is the column index of the corresponding
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* column block in the matrix T.
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*
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* Initialize variables.
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*
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* NUM_ALL_ROW_BLOCKS is the number of row blocks in the matrix A
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* including the first row block.
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*
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MB2 = MB - N
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M_PLUS_ONE = M + 1
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ITMP = ( M - MB - 1 ) / MB2
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IB_BOTTOM = ITMP * MB2 + MB + 1
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NUM_ALL_ROW_BLOCKS = ITMP + 2
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JB_T = NUM_ALL_ROW_BLOCKS * N + 1
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*
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DO IB = IB_BOTTOM, MB+1, -MB2
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*
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* Determine the block size IMB for the current row block
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* in the matrix A.
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*
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IMB = MIN( M_PLUS_ONE - IB, MB2 )
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*
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* Determine the column index JB_T for the current column block
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* in the matrix T.
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*
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JB_T = JB_T - N
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*
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* Apply column blocks of H in the row block from right to left.
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*
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* KB is the column index of the current column block reflector
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* in the matrices T and V.
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*
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DO KB = KB_LAST, 1, -NBLOCAL
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*
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* Determine the size of the current column block KNB in
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* the matrices T and V.
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*
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KNB = MIN( NBLOCAL, N - KB + 1 )
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*
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CALL SLARFB_GETT( 'I', IMB, N-KB+1, KNB,
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$ T( 1, JB_T+KB-1 ), LDT, A( KB, KB ), LDA,
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$ A( IB, KB ), LDA, WORK, KNB )
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*
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END DO
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*
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END DO
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*
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END IF
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*
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* (2) Top row block of A.
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* NOTE: If MB>=M, then we have only one row block of A of size M
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* and we work on the entire matrix A.
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*
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MB1 = MIN( MB, M )
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*
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* Apply column blocks of H in the top row block from right to left.
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*
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* KB is the column index of the current block reflector in
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* the matrices T and V.
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*
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DO KB = KB_LAST, 1, -NBLOCAL
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*
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* Determine the size of the current column block KNB in
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* the matrices T and V.
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*
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KNB = MIN( NBLOCAL, N - KB + 1 )
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*
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IF( MB1-KB-KNB+1.EQ.0 ) THEN
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*
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* In SLARFB_GETT parameters, when M=0, then the matrix B
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* does not exist, hence we need to pass a dummy array
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* reference DUMMY(1,1) to B with LDDUMMY=1.
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*
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CALL SLARFB_GETT( 'N', 0, N-KB+1, KNB,
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$ T( 1, KB ), LDT, A( KB, KB ), LDA,
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$ DUMMY( 1, 1 ), 1, WORK, KNB )
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ELSE
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CALL SLARFB_GETT( 'N', MB1-KB-KNB+1, N-KB+1, KNB,
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$ T( 1, KB ), LDT, A( KB, KB ), LDA,
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$ A( KB+KNB, KB), LDA, WORK, KNB )
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END IF
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*
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END DO
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*
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WORK( 1 ) = REAL( LWORKOPT )
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RETURN
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*
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* End of SORGTSQR_ROW
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*
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END
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