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*> \brief \b DGEMLQT
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DGEMQRT + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgemlqt.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgemlqt.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgemlqt.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DGEMLQT( SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT,
* C, LDC, WORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER SIDE, TRANS
* INTEGER INFO, K, LDV, LDC, M, N, MB, LDT
* ..
* .. Array Arguments ..
* DOUBLE PRECISION V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGEMQRT 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 K
*> elementary reflectors:
*>
*> Q = H(1) H(2) . . . H(K) = I - V T V**T
*>
*> generated using the compact WY representation as returned by DGELQT.
*>
*> Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
*> \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;
*> = 'C': Transpose, apply Q**T.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix C. 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] MB
*> \verbatim
*> MB is INTEGER
*> The block size used for the storage of T. K >= MB >= 1.
*> This must be the same value of MB used to generate T
*> in DGELQT.
*> \endverbatim
*>
*> \param[in] V
*> \verbatim
*> V is DOUBLE PRECISION array, dimension (LDV,K)
*> The i-th row must contain the vector which defines the
*> elementary reflector H(i), for i = 1,2,...,k, as returned by
*> DGELQT in the first K rows of its array argument A.
*> \endverbatim
*>
*> \param[in] LDV
*> \verbatim
*> LDV is INTEGER
*> The leading dimension of the array V.
*> If SIDE = 'L', LDA >= max(1,M);
*> if SIDE = 'R', LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] T
*> \verbatim
*> T is DOUBLE PRECISION array, dimension (LDT,K)
*> The upper triangular factors of the block reflectors
*> as returned by DGELQT, stored as a MB-by-M matrix.
*> \endverbatim
*>
*> \param[in] LDT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= MB.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is DOUBLE PRECISION array, dimension (LDC,N)
*> On entry, the M-by-N matrix C.
*> On exit, C is overwritten by Q C, Q**T C, 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
*> WORK is DOUBLE PRECISION array. The dimension of
*> WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
*> \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.
*
*> \date December 2016
*
*> \ingroup doubleGEcomputational
*
* =====================================================================
SUBROUTINE DGEMLQT( SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT,
$ C, LDC, WORK, 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..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER SIDE, TRANS
INTEGER INFO, K, LDV, LDC, M, N, MB, LDT
* ..
* .. Array Arguments ..
DOUBLE PRECISION V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
* ..
*
* =====================================================================
*
* ..
* .. Local Scalars ..
LOGICAL LEFT, RIGHT, TRAN, NOTRAN
INTEGER I, IB, LDWORK, KF, Q
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, DLARFB
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* .. Test the input arguments ..
*
INFO = 0
LEFT = LSAME( SIDE, 'L' )
RIGHT = LSAME( SIDE, 'R' )
TRAN = LSAME( TRANS, 'T' )
NOTRAN = LSAME( TRANS, 'N' )
*
IF( LEFT ) THEN
LDWORK = MAX( 1, N )
ELSE IF ( RIGHT ) THEN
LDWORK = MAX( 1, M )
END IF
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) THEN
INFO = -5
ELSE IF( MB.LT.1 .OR. (MB.GT.K .AND. K.GT.0)) THEN
INFO = -6
ELSE IF( LDV.LT.MAX( 1, K ) ) THEN
INFO = -8
ELSE IF( LDT.LT.MB ) THEN
INFO = -10
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
INFO = -12
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DGEMLQT', -INFO )
RETURN
END IF
*
* .. Quick return if possible ..
*
IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) RETURN
*
IF( LEFT .AND. NOTRAN ) THEN
*
DO I = 1, K, MB
IB = MIN( MB, K-I+1 )
CALL DLARFB( 'L', 'T', 'F', 'R', M-I+1, N, IB,
$ V( I, I ), LDV, T( 1, I ), LDT,
$ C( I, 1 ), LDC, WORK, LDWORK )
END DO
*
ELSE IF( RIGHT .AND. TRAN ) THEN
*
DO I = 1, K, MB
IB = MIN( MB, K-I+1 )
CALL DLARFB( 'R', 'N', 'F', 'R', M, N-I+1, IB,
$ V( I, I ), LDV, T( 1, I ), LDT,
$ C( 1, I ), LDC, WORK, LDWORK )
END DO
*
ELSE IF( LEFT .AND. TRAN ) THEN
*
KF = ((K-1)/MB)*MB+1
DO I = KF, 1, -MB
IB = MIN( MB, K-I+1 )
CALL DLARFB( 'L', 'N', 'F', 'R', M-I+1, N, IB,
$ V( I, I ), LDV, T( 1, I ), LDT,
$ C( I, 1 ), LDC, WORK, LDWORK )
END DO
*
ELSE IF( RIGHT .AND. NOTRAN ) THEN
*
KF = ((K-1)/MB)*MB+1
DO I = KF, 1, -MB
IB = MIN( MB, K-I+1 )
CALL DLARFB( 'R', 'T', 'F', 'R', M, N-I+1, IB,
$ V( I, I ), LDV, T( 1, I ), LDT,
$ C( 1, I ), LDC, WORK, LDWORK )
END DO
*
END IF
*
RETURN
*
* End of DGEMLQT
*
END
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