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*
* Definition:
* ===========
*
* SUBROUTINE SGEMLQ( 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 ..
* REAL A( LDA, * ), T( * ), C(LDC, * ), WORK( * )
* ..
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SGEMLQ overwrites the general real M-by-N matrix C with
*>
*> SIDE = 'L' SIDE = 'R'
*> TRANS = 'N': Q * C C * Q
*> TRANS = 'T': Q**T * C C * Q**T
*> where Q is a real orthogonal matrix defined as the product
*> of blocked elementary reflectors computed by short wide LQ
*> factorization (SGELQ)
*>
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is CHARACTER*1
*> = 'L': apply Q or Q**T from the Left;
*> = 'R': apply Q or Q**T from the Right.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> = 'N': No transpose, apply Q;
*> = 'T': Transpose, apply Q**T.
*> \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 REAL array, dimension
*> (LDA,M) if SIDE = 'L',
*> (LDA,N) if SIDE = 'R'
*> Part of the data structure to represent Q as returned by DGELQ.
*> \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 REAL array, dimension (MAX(5,TSIZE)).
*> Part of the data structure to represent Q as returned by SGELQ.
*> \endverbatim
*>
*> \param[in] TSIZE
*> \verbatim
*> TSIZE is INTEGER
*> The dimension of the array T. TSIZE >= 5.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is REAL array, dimension (LDC,N)
*> On entry, the M-by-N matrix C.
*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T 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) REAL 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 unlikely not
*> 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
*> SLASWLQ or SGELQT
*>
*> Depending on the matrix dimensions M and N, and row and column
*> block sizes MB and NB returned by ILAENV, SGELQ will use either
*> SLASWLQ (if the matrix is wide-and-short) or SGELQT to compute
*> the LQ factorization.
*> This version of SGEMLQ will use either SLAMSWLQ or SGEMLQT to
*> multiply matrix Q by another matrix.
*> Further Details in SLAMSWLQ or SGEMLQT.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE SGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
$ C, LDC, WORK, LWORK, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2016
*
* .. Scalar Arguments ..
CHARACTER SIDE, TRANS
INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
* ..
* .. Array Arguments ..
REAL 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 SLAMSWLQ, SGEMLQT, 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, 'T' )
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( 'SGEMLQ', -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 SGEMLQT( SIDE, TRANS, M, N, K, MB, A, LDA,
$ T( 6 ), MB, C, LDC, WORK, INFO )
ELSE
CALL SLAMSWLQ( 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 SGEMLQ
*
END
|
