ESMF_DORMBR Subroutine

subroutine ESMF_DORMBR(VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)

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

\verbatim

If VECT = ‘Q’, ESMF_DORMBR 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

If VECT = ‘P’, ESMF_DORMBR overwrites the general real M-by-N matrix C with SIDE = ‘L’ SIDE = ‘R’ TRANS = ‘N’: P * C C * P TRANS = ‘T’: PT * C C * PT

Here Q and PT are the orthogonal matrices determined by ESMF_DGEBRD when reducing a real matrix A to bidiagonal form: A = Q * B * PT. Q and P**T are defined as products of elementary reflectors H(i) and G(i) respectively.

Let nq = m if SIDE = ‘L’ and nq = n if SIDE = ‘R’. Thus nq is the order of the orthogonal matrix Q or P**T that is applied.

If VECT = ‘Q’, A is assumed to have been an NQ-by-K matrix: if nq >= k, Q = H(1) H(2) . . . H(k); if nq < k, Q = H(1) H(2) . . . H(nq-1).

If VECT = ‘P’, A is assumed to have been a K-by-NQ matrix: if k < nq, P = G(1) G(2) . . . G(k); if k >= nq, P = G(1) G(2) . . . G(nq-1). \endverbatim \param[in] VECT \verbatim VECT is CHARACTER1 = ‘Q’: apply Q or QT; = ‘P’: apply P or P*T. \endverbatim

\param[in] SIDE \verbatim SIDE is CHARACTER1 = ‘L’: apply Q, QT, P or PT from the Left; = ‘R’: apply Q, QT, P or P*T from the Right. \endverbatim

\param[in] TRANS \verbatim TRANS is CHARACTER1 = ‘N’: No transpose, apply Q or P; = ‘T’: Transpose, apply QT or P*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 If VECT = ‘Q’, the number of columns in the original matrix reduced by ESMF_DGEBRD. If VECT = ‘P’, the number of rows in the original matrix reduced by ESMF_DGEBRD. K >= 0. \endverbatim

\param[in] A \verbatim A is DOUBLE PRECISION array, dimension (LDA,min(nq,K)) if VECT = ‘Q’ (LDA,nq) if VECT = ‘P’ The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by ESMF_DGEBRD. \endverbatim

\param[in] LDA \verbatim LDA is INTEGER The leading dimension of the array A. If VECT = ‘Q’, LDA >= max(1,nq); if VECT = ‘P’, LDA >= max(1,min(nq,K)). \endverbatim

\param[in] TAU \verbatim TAU is DOUBLE PRECISION array, dimension (min(nq,K)) TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by ESMF_DGEBRD in the array argument TAUQ or TAUP. \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 or PC or PTC or CP or CP**T. \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 November 2011 \ingroup doubleOTHERcomputational

Arguments