*> \brief \b DORMHR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORMHR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, * LDC, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DORMHR 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 of order nq, with nq = m if *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of *> IHI-ILO elementary reflectors, as returned by DGEHRD: *> *> Q = H(ilo) H(ilo+1) . . . H(ihi-1). *> \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 C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[in] IHI *> \verbatim *> IHI is INTEGER *> *> ILO and IHI must have the same values as in the previous call *> of DGEHRD. Q is equal to the unit matrix except in the *> submatrix Q(ilo+1:ihi,ilo+1:ihi). *> If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and *> ILO = 1 and IHI = 0, if M = 0; *> if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and *> ILO = 1 and IHI = 0, if N = 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension *> (LDA,M) if SIDE = 'L' *> (LDA,N) if SIDE = 'R' *> The vectors which define the elementary reflectors, as *> returned by DGEHRD. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension *> (M-1) if SIDE = 'L' *> (N-1) if SIDE = 'R' *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by DGEHRD. *> \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 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 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> If SIDE = 'L', LWORK >= max(1,N); *> if SIDE = 'R', LWORK >= max(1,M). *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. *> *> 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. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, 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..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL LEFT, LQUERY INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NH, NI, NQ, NW * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL DORMQR, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 NH = IHI - ILO LEFT = LSAME( SIDE, 'L' ) LQUERY = ( LWORK.EQ.-1 ) * * NQ is the order of Q and NW is the minimum dimension of WORK * IF( LEFT ) THEN NQ = M NW = N ELSE NQ = N NW = M END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) ) \$ THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, NQ ) ) THEN INFO = -5 ELSE IF( IHI.LT.MIN( ILO, NQ ) .OR. IHI.GT.NQ ) THEN INFO = -6 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -8 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -11 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN INFO = -13 END IF * IF( INFO.EQ.0 ) THEN IF( LEFT ) THEN NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, NH, N, NH, -1 ) ELSE NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, NH, NH, -1 ) END IF LWKOPT = MAX( 1, NW )*NB WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORMHR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. NH.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * IF( LEFT ) THEN MI = NH NI = N I1 = ILO + 1 I2 = 1 ELSE MI = M NI = NH I1 = 1 I2 = ILO + 1 END IF * CALL DORMQR( SIDE, TRANS, MI, NI, NH, A( ILO+1, ILO ), LDA, \$ TAU( ILO ), C( I1, I2 ), LDC, WORK, LWORK, IINFO ) * WORK( 1 ) = LWKOPT RETURN * * End of DORMHR * END