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.
283 lines
7.7 KiB
283 lines
7.7 KiB
*> \brief \b CGEMLQ
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T,
|
|
* $ TSIZE, C, LDC, WORK, LWORK, INFO )
|
|
*
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER SIDE, TRANS
|
|
* INTEGER INFO, LDA, M, N, K, LDT, TSIZE, LWORK, LDC
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* COMPLEX A( LDA, * ), T( * ), C(LDC, * ), WORK( * )
|
|
* ..
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CGEMLQ overwrites the general real M-by-N matrix C with
|
|
*>
|
|
*> SIDE = 'L' SIDE = 'R'
|
|
*> TRANS = 'N': Q * C C * Q
|
|
*> TRANS = 'C': Q**H * C C * Q**H
|
|
*> where Q is a complex unitary matrix defined as the product
|
|
*> of blocked elementary reflectors computed by short wide
|
|
*> LQ factorization (CGELQ)
|
|
*>
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] SIDE
|
|
*> \verbatim
|
|
*> SIDE is CHARACTER*1
|
|
*> = 'L': apply Q or Q**H from the Left;
|
|
*> = 'R': apply Q or Q**H from the Right.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] TRANS
|
|
*> \verbatim
|
|
*> TRANS is CHARACTER*1
|
|
*> = 'N': No transpose, apply Q;
|
|
*> = 'C': Conjugate transpose, apply Q**H.
|
|
*> \endverbatim
|
|
*>
|
|
*> \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 C. N >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] K
|
|
*> \verbatim
|
|
*> K is INTEGER
|
|
*> The number of elementary reflectors whose product defines
|
|
*> the matrix Q.
|
|
*> If SIDE = 'L', M >= K >= 0;
|
|
*> if SIDE = 'R', N >= K >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] A
|
|
*> \verbatim
|
|
*> A is COMPLEX array, dimension
|
|
*> (LDA,M) if SIDE = 'L',
|
|
*> (LDA,N) if SIDE = 'R'
|
|
*> Part of the data structure to represent Q as returned by CGELQ.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> The leading dimension of the array A. LDA >= max(1,K).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] T
|
|
*> \verbatim
|
|
*> T is COMPLEX array, dimension (MAX(5,TSIZE)).
|
|
*> Part of the data structure to represent Q as returned by CGELQ.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] TSIZE
|
|
*> \verbatim
|
|
*> TSIZE is INTEGER
|
|
*> The dimension of the array T. TSIZE >= 5.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] C
|
|
*> \verbatim
|
|
*> C is COMPLEX array, dimension (LDC,N)
|
|
*> On entry, the M-by-N matrix C.
|
|
*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDC
|
|
*> \verbatim
|
|
*> LDC is INTEGER
|
|
*> The leading dimension of the array C. LDC >= max(1,M).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> (workspace) COMPLEX array, dimension (MAX(1,LWORK))
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LWORK
|
|
*> \verbatim
|
|
*> LWORK is INTEGER
|
|
*> The dimension of the array WORK.
|
|
*> If LWORK = -1, then a workspace query is assumed. The routine
|
|
*> only calculates the size of the WORK array, returns this
|
|
*> value as WORK(1), and no error message related to WORK
|
|
*> 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.
|
|
*
|
|
*> \par Further Details
|
|
* ====================
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> These details are particular for this LAPACK implementation. Users should not
|
|
*> take them for granted. These details may change in the future, and are not likely
|
|
*> true for another LAPACK implementation. These details are relevant if one wants
|
|
*> to try to understand the code. They are not part of the interface.
|
|
*>
|
|
*> In this version,
|
|
*>
|
|
*> T(2): row block size (MB)
|
|
*> T(3): column block size (NB)
|
|
*> T(6:TSIZE): data structure needed for Q, computed by
|
|
*> CLASWQR or CGELQT
|
|
*>
|
|
*> Depending on the matrix dimensions M and N, and row and column
|
|
*> block sizes MB and NB returned by ILAENV, CGELQ will use either
|
|
*> CLASWLQ (if the matrix is wide-and-short) or CGELQT to compute
|
|
*> the LQ factorization.
|
|
*> This version of CGEMLQ will use either CLAMSWLQ or CGEMLQT to
|
|
*> multiply matrix Q by another matrix.
|
|
*> Further Details in CLAMSWLQ or CGEMLQT.
|
|
*> \endverbatim
|
|
*>
|
|
* =====================================================================
|
|
SUBROUTINE CGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
|
|
$ C, LDC, WORK, LWORK, INFO )
|
|
*
|
|
* -- 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 ..
|
|
CHARACTER SIDE, TRANS
|
|
INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
|
|
* ..
|
|
* .. Array Arguments ..
|
|
COMPLEX A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
|
|
INTEGER MB, NB, LW, NBLCKS, MN
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
EXTERNAL LSAME
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CLAMSWLQ, CGEMLQT, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC INT, MAX, MIN, MOD
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Test the input arguments
|
|
*
|
|
LQUERY = LWORK.EQ.-1
|
|
NOTRAN = LSAME( TRANS, 'N' )
|
|
TRAN = LSAME( TRANS, 'C' )
|
|
LEFT = LSAME( SIDE, 'L' )
|
|
RIGHT = LSAME( SIDE, 'R' )
|
|
*
|
|
MB = INT( T( 2 ) )
|
|
NB = INT( T( 3 ) )
|
|
IF( LEFT ) THEN
|
|
LW = N * MB
|
|
MN = M
|
|
ELSE
|
|
LW = M * MB
|
|
MN = N
|
|
END IF
|
|
*
|
|
IF( ( NB.GT.K ) .AND. ( MN.GT.K ) ) THEN
|
|
IF( MOD( MN - K, NB - K ) .EQ. 0 ) THEN
|
|
NBLCKS = ( MN - K ) / ( NB - K )
|
|
ELSE
|
|
NBLCKS = ( MN - K ) / ( NB - K ) + 1
|
|
END IF
|
|
ELSE
|
|
NBLCKS = 1
|
|
END IF
|
|
*
|
|
INFO = 0
|
|
IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
|
|
INFO = -1
|
|
ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
|
|
INFO = -2
|
|
ELSE IF( M.LT.0 ) THEN
|
|
INFO = -3
|
|
ELSE IF( N.LT.0 ) THEN
|
|
INFO = -4
|
|
ELSE IF( K.LT.0 .OR. K.GT.MN ) THEN
|
|
INFO = -5
|
|
ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
|
|
INFO = -7
|
|
ELSE IF( TSIZE.LT.5 ) THEN
|
|
INFO = -9
|
|
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
|
|
INFO = -11
|
|
ELSE IF( ( LWORK.LT.MAX( 1, LW ) ) .AND. ( .NOT.LQUERY ) ) THEN
|
|
INFO = -13
|
|
END IF
|
|
*
|
|
IF( INFO.EQ.0 ) THEN
|
|
WORK( 1 ) = REAL( LW )
|
|
END IF
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'CGEMLQ', -INFO )
|
|
RETURN
|
|
ELSE IF( LQUERY ) THEN
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( MIN( M, N, K ).EQ.0 ) THEN
|
|
RETURN
|
|
END IF
|
|
*
|
|
IF( ( LEFT .AND. M.LE.K ) .OR. ( RIGHT .AND. N.LE.K )
|
|
$ .OR. ( NB.LE.K ) .OR. ( NB.GE.MAX( M, N, K ) ) ) THEN
|
|
CALL CGEMLQT( SIDE, TRANS, M, N, K, MB, A, LDA,
|
|
$ T( 6 ), MB, C, LDC, WORK, INFO )
|
|
ELSE
|
|
CALL CLAMSWLQ( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T( 6 ),
|
|
$ MB, C, LDC, WORK, LWORK, INFO )
|
|
END IF
|
|
*
|
|
WORK( 1 ) = REAL( LW )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CGEMLQ
|
|
*
|
|
END
|
|
|