ESMF_DORMHR Subroutine

subroutine ESMF_DORMHR(SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)

\brief \b ESMF_DORMHR \htmlonly Download ESMF_DORMHR + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

ESMF_DORMHR overwrites the general real M-by-N matrix C with

            SIDE = 'L'     SIDE = 'R'

TRANS = ‘N’: Q * C C * Q TRANS = ‘T’: QT * C C * QT

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 ESMF_DGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1). \endverbatim \param[in] SIDE \verbatim SIDE is CHARACTER1 = ‘L’: apply Q or QT from the Left; = ‘R’: apply Q or Q*T from the Right. \endverbatim

\param[in] TRANS \verbatim TRANS is CHARACTER1 = ‘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 ESMF_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 ESMF_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 ESMF_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 QC or QTC or CQT or CQ. \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 >= NNB if SIDE = ‘L’, and LWORK >= MNB 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 ESMF_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 \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date December 2016 \ingroup doubleOTHERcomputational

Arguments