You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
380 lines
12 KiB
380 lines
12 KiB
*> \brief \b ZUNGTSQR_ROW
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download ZUNGTSQR_ROW + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunrgtsqr_row.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zunrgtsqr_row.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunrgtsqr_row.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE ZUNGTSQR_ROW( M, N, MB, NB, A, LDA, T, LDT, WORK,
|
|
* $ LWORK, INFO )
|
|
* IMPLICIT NONE
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER INFO, LDA, LDT, LWORK, M, N, MB, NB
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * )
|
|
* ..
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> ZUNGTSQR_ROW generates an M-by-N complex matrix Q_out with
|
|
*> orthonormal columns from the output of ZLATSQR. 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 ZLATSQR 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 ZLATSQR 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 ZLARFB_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 ZLATSQR generates the output blocks.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] M
|
|
*> \verbatim
|
|
*> M is INTEGER
|
|
*> The number of rows of the matrix A. M >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> The number of columns of the matrix A. M >= N >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] MB
|
|
*> \verbatim
|
|
*> MB is INTEGER
|
|
*> The row block size used by ZLATSQR 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).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] NB
|
|
*> \verbatim
|
|
*> NB is INTEGER
|
|
*> The column block size used by ZLATSQR 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).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] A
|
|
*> \verbatim
|
|
*> A is COMPLEX*16 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 ZLATSQR
|
|
*> that defines the input matrices Q_in(k) (ones on the
|
|
*> diagonal are not stored). See ZLATSQR 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.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> The leading dimension of the array A. LDA >= max(1,M).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] T
|
|
*> \verbatim
|
|
*> T is COMPLEX*16 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 ZLATSQR for more details on the format
|
|
*> of T.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDT
|
|
*> \verbatim
|
|
*> LDT is INTEGER
|
|
*> The leading dimension of the array T.
|
|
*> LDT >= max(1,min(NB,N)).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
|
|
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LWORK
|
|
*> \verbatim
|
|
*> 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.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] INFO
|
|
*> \verbatim
|
|
*> INFO is INTEGER
|
|
*> = 0: successful exit
|
|
*> < 0: if INFO = -i, the i-th argument had an illegal value
|
|
*> \endverbatim
|
|
*>
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \ingroup complex16OTHERcomputational
|
|
*
|
|
*> \par Contributors:
|
|
* ==================
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> November 2020, Igor Kozachenko,
|
|
*> Computer Science Division,
|
|
*> University of California, Berkeley
|
|
*>
|
|
*> \endverbatim
|
|
*>
|
|
* =====================================================================
|
|
SUBROUTINE ZUNGTSQR_ROW( M, N, MB, NB, A, LDA, T, LDT, WORK,
|
|
$ LWORK, INFO )
|
|
IMPLICIT NONE
|
|
*
|
|
* -- LAPACK computational routine --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER INFO, LDA, LDT, LWORK, M, N, MB, NB
|
|
* ..
|
|
* .. Array Arguments ..
|
|
COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
COMPLEX*16 CONE, CZERO
|
|
PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
|
|
$ CZERO = ( 0.0D+0, 0.0D+0 ) )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL LQUERY
|
|
INTEGER NBLOCAL, MB2, M_PLUS_ONE, ITMP, IB_BOTTOM,
|
|
$ LWORKOPT, NUM_ALL_ROW_BLOCKS, JB_T, IB, IMB,
|
|
$ KB, KB_LAST, KNB, MB1
|
|
* ..
|
|
* .. Local Arrays ..
|
|
COMPLEX*16 DUMMY( 1, 1 )
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL ZLARFB_GETT, ZLASET, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC DCMPLX, MAX, MIN
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Test the input parameters
|
|
*
|
|
INFO = 0
|
|
LQUERY = LWORK.EQ.-1
|
|
IF( M.LT.0 ) THEN
|
|
INFO = -1
|
|
ELSE IF( N.LT.0 .OR. M.LT.N ) THEN
|
|
INFO = -2
|
|
ELSE IF( MB.LE.N ) THEN
|
|
INFO = -3
|
|
ELSE IF( NB.LT.1 ) THEN
|
|
INFO = -4
|
|
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
|
INFO = -6
|
|
ELSE IF( LDT.LT.MAX( 1, MIN( NB, N ) ) ) THEN
|
|
INFO = -8
|
|
ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
|
|
INFO = -10
|
|
END IF
|
|
*
|
|
NBLOCAL = MIN( NB, N )
|
|
*
|
|
* Determine the workspace size.
|
|
*
|
|
IF( INFO.EQ.0 ) THEN
|
|
LWORKOPT = NBLOCAL * MAX( NBLOCAL, ( N - NBLOCAL ) )
|
|
END IF
|
|
*
|
|
* Handle error in the input parameters and handle the workspace query.
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'ZUNGTSQR_ROW', -INFO )
|
|
RETURN
|
|
ELSE IF ( LQUERY ) THEN
|
|
WORK( 1 ) = DCMPLX( LWORKOPT )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( MIN( M, N ).EQ.0 ) THEN
|
|
WORK( 1 ) = DCMPLX( LWORKOPT )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* (0) Set the upper-triangular part of the matrix A to zero and
|
|
* its diagonal elements to one.
|
|
*
|
|
CALL ZLASET('U', M, N, CZERO, CONE, A, LDA )
|
|
*
|
|
* KB_LAST is the column index of the last column block reflector
|
|
* in the matrices T and V.
|
|
*
|
|
KB_LAST = ( ( N-1 ) / NBLOCAL ) * NBLOCAL + 1
|
|
*
|
|
*
|
|
* (1) Bottom-up loop over row blocks of A, except the top row block.
|
|
* NOTE: If MB>=M, then the loop is never executed.
|
|
*
|
|
IF ( MB.LT.M ) THEN
|
|
*
|
|
* MB2 is the row blocking size for the row blocks before the
|
|
* first top row block in the matrix A. IB is the row index for
|
|
* the row blocks in the matrix A before the first top row block.
|
|
* IB_BOTTOM is the row index for the last bottom row block
|
|
* in the matrix A. JB_T is the column index of the corresponding
|
|
* column block in the matrix T.
|
|
*
|
|
* Initialize variables.
|
|
*
|
|
* NUM_ALL_ROW_BLOCKS is the number of row blocks in the matrix A
|
|
* including the first row block.
|
|
*
|
|
MB2 = MB - N
|
|
M_PLUS_ONE = M + 1
|
|
ITMP = ( M - MB - 1 ) / MB2
|
|
IB_BOTTOM = ITMP * MB2 + MB + 1
|
|
NUM_ALL_ROW_BLOCKS = ITMP + 2
|
|
JB_T = NUM_ALL_ROW_BLOCKS * N + 1
|
|
*
|
|
DO IB = IB_BOTTOM, MB+1, -MB2
|
|
*
|
|
* Determine the block size IMB for the current row block
|
|
* in the matrix A.
|
|
*
|
|
IMB = MIN( M_PLUS_ONE - IB, MB2 )
|
|
*
|
|
* Determine the column index JB_T for the current column block
|
|
* in the matrix T.
|
|
*
|
|
JB_T = JB_T - N
|
|
*
|
|
* Apply column blocks of H in the row block from right to left.
|
|
*
|
|
* KB is the column index of the current column block reflector
|
|
* in the matrices T and V.
|
|
*
|
|
DO KB = KB_LAST, 1, -NBLOCAL
|
|
*
|
|
* Determine the size of the current column block KNB in
|
|
* the matrices T and V.
|
|
*
|
|
KNB = MIN( NBLOCAL, N - KB + 1 )
|
|
*
|
|
CALL ZLARFB_GETT( 'I', IMB, N-KB+1, KNB,
|
|
$ T( 1, JB_T+KB-1 ), LDT, A( KB, KB ), LDA,
|
|
$ A( IB, KB ), LDA, WORK, KNB )
|
|
*
|
|
END DO
|
|
*
|
|
END DO
|
|
*
|
|
END IF
|
|
*
|
|
* (2) Top row block of A.
|
|
* NOTE: If MB>=M, then we have only one row block of A of size M
|
|
* and we work on the entire matrix A.
|
|
*
|
|
MB1 = MIN( MB, M )
|
|
*
|
|
* Apply column blocks of H in the top row block from right to left.
|
|
*
|
|
* KB is the column index of the current block reflector in
|
|
* the matrices T and V.
|
|
*
|
|
DO KB = KB_LAST, 1, -NBLOCAL
|
|
*
|
|
* Determine the size of the current column block KNB in
|
|
* the matrices T and V.
|
|
*
|
|
KNB = MIN( NBLOCAL, N - KB + 1 )
|
|
*
|
|
IF( MB1-KB-KNB+1.EQ.0 ) THEN
|
|
*
|
|
* In SLARFB_GETT parameters, when M=0, then the matrix B
|
|
* does not exist, hence we need to pass a dummy array
|
|
* reference DUMMY(1,1) to B with LDDUMMY=1.
|
|
*
|
|
CALL ZLARFB_GETT( 'N', 0, N-KB+1, KNB,
|
|
$ T( 1, KB ), LDT, A( KB, KB ), LDA,
|
|
$ DUMMY( 1, 1 ), 1, WORK, KNB )
|
|
ELSE
|
|
CALL ZLARFB_GETT( 'N', MB1-KB-KNB+1, N-KB+1, KNB,
|
|
$ T( 1, KB ), LDT, A( KB, KB ), LDA,
|
|
$ A( KB+KNB, KB), LDA, WORK, KNB )
|
|
|
|
END IF
|
|
*
|
|
END DO
|
|
*
|
|
WORK( 1 ) = DCMPLX( LWORKOPT )
|
|
RETURN
|
|
*
|
|
* End of ZUNGTSQR_ROW
|
|
*
|
|
END
|
|
|