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274 lines
7.2 KiB
274 lines
7.2 KiB
2 years ago
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*> \brief \b SGEMLQT
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SGEMLQT( SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT,
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* C, LDC, WORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER SIDE, TRANS
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* INTEGER INFO, K, LDV, LDC, M, N, MB, LDT
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* ..
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* .. Array Arguments ..
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* REAL V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
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* ..
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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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*> DGEMLQT overwrites the general real M-by-N matrix C with
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*>
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*> SIDE = 'L' SIDE = 'R'
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*> TRANS = 'N': Q C C Q
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*> TRANS = 'T': Q**T C C Q**T
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*>
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*> where Q is a real orthogonal matrix defined as the product of K
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*> elementary reflectors:
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*>
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*> Q = H(1) H(2) . . . H(K) = I - V T V**T
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*>
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*> generated using the compact WY representation as returned by SGELQT.
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*>
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*> Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
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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] SIDE
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*> \verbatim
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*> SIDE is CHARACTER*1
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*> = 'L': apply Q or Q**T from the Left;
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*> = 'R': apply Q or Q**T from the Right.
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*> \endverbatim
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*>
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> = 'N': No transpose, apply Q;
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*> = 'C': Transpose, apply Q**T.
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*> \endverbatim
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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 C. 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 C. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is INTEGER
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*> The number of elementary reflectors whose product defines
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*> the matrix Q.
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*> If SIDE = 'L', M >= K >= 0;
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*> if SIDE = 'R', N >= K >= 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 block size used for the storage of T. K >= MB >= 1.
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*> This must be the same value of MB used to generate T
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*> in SGELQT.
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*> \endverbatim
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*>
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*> \param[in] V
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*> \verbatim
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*> V is REAL array, dimension
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*> (LDV,M) if SIDE = 'L',
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*> (LDV,N) if SIDE = 'R'
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*> The i-th row must contain the vector which defines the
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*> elementary reflector H(i), for i = 1,2,...,k, as returned by
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*> SGELQT in the first K rows of its array argument A.
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*> \endverbatim
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*>
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*> \param[in] LDV
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*> \verbatim
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*> LDV is INTEGER
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*> The leading dimension of the array V. LDV >= max(1,K).
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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, dimension (LDT,K)
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*> The upper triangular factors of the block reflectors
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*> as returned by SGELQT, stored as a MB-by-K matrix.
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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. LDT >= MB.
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*> \endverbatim
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*>
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*> \param[in,out] C
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*> \verbatim
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*> C is REAL array, dimension (LDC,N)
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*> On entry, the M-by-N matrix C.
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*> On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q.
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*> \endverbatim
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*>
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*> \param[in] LDC
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*> \verbatim
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*> LDC is INTEGER
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*> The leading dimension of the array C. LDC >= max(1,M).
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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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*> WORK is REAL array. The dimension of
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*> WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
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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 doubleGEcomputational
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*
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* =====================================================================
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SUBROUTINE SGEMLQT( SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT,
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$ C, LDC, WORK, INFO )
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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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CHARACTER SIDE, TRANS
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INTEGER INFO, K, LDV, LDC, M, N, MB, LDT
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* ..
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* .. Array Arguments ..
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REAL V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* ..
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* .. Local Scalars ..
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LOGICAL LEFT, RIGHT, TRAN, NOTRAN
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INTEGER I, IB, LDWORK, KF, Q
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, SLARFB
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* .. Test the input arguments ..
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*
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INFO = 0
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LEFT = LSAME( SIDE, 'L' )
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RIGHT = LSAME( SIDE, 'R' )
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TRAN = LSAME( TRANS, 'T' )
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NOTRAN = LSAME( TRANS, 'N' )
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*
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IF( LEFT ) THEN
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LDWORK = MAX( 1, N )
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Q = M
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ELSE IF ( RIGHT ) THEN
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LDWORK = MAX( 1, M )
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Q = N
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END IF
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IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
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INFO = -1
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ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
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INFO = -2
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ELSE IF( M.LT.0 ) THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( K.LT.0 .OR. K.GT.Q ) THEN
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INFO = -5
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ELSE IF( MB.LT.1 .OR. (MB.GT.K .AND. K.GT.0)) THEN
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INFO = -6
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ELSE IF( LDV.LT.MAX( 1, K ) ) THEN
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INFO = -8
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ELSE IF( LDT.LT.MB ) THEN
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INFO = -10
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ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
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INFO = -12
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SGEMLQT', -INFO )
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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( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) RETURN
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*
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IF( LEFT .AND. NOTRAN ) THEN
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*
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DO I = 1, K, MB
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IB = MIN( MB, K-I+1 )
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CALL SLARFB( 'L', 'T', 'F', 'R', M-I+1, N, IB,
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$ V( I, I ), LDV, T( 1, I ), LDT,
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$ C( I, 1 ), LDC, WORK, LDWORK )
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END DO
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*
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ELSE IF( RIGHT .AND. TRAN ) THEN
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*
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DO I = 1, K, MB
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IB = MIN( MB, K-I+1 )
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CALL SLARFB( 'R', 'N', 'F', 'R', M, N-I+1, IB,
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$ V( I, I ), LDV, T( 1, I ), LDT,
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$ C( 1, I ), LDC, WORK, LDWORK )
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END DO
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*
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ELSE IF( LEFT .AND. TRAN ) THEN
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*
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KF = ((K-1)/MB)*MB+1
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DO I = KF, 1, -MB
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IB = MIN( MB, K-I+1 )
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CALL SLARFB( 'L', 'N', 'F', 'R', M-I+1, N, IB,
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$ V( I, I ), LDV, T( 1, I ), LDT,
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$ C( I, 1 ), LDC, WORK, LDWORK )
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END DO
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*
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ELSE IF( RIGHT .AND. NOTRAN ) THEN
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*
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KF = ((K-1)/MB)*MB+1
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DO I = KF, 1, -MB
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IB = MIN( MB, K-I+1 )
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CALL SLARFB( 'R', 'T', 'F', 'R', M, N-I+1, IB,
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$ V( I, I ), LDV, T( 1, I ), LDT,
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$ C( 1, I ), LDC, WORK, LDWORK )
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END DO
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*
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END IF
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*
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RETURN
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*
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* End of SGEMLQT
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*
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END
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