ESMF_DLARFB Subroutine

subroutine ESMF_DLARFB(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)

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

\verbatim

ESMF_DLARFB applies a real block reflector H or its transpose HT to a real m by n matrix C, from either the left or the right. \endverbatim \param[in] SIDE \verbatim SIDE is CHARACTER*1 = ‘L’: apply H or HT from the Left = ‘R’: apply H or H**T from the Right \endverbatim

\param[in] TRANS \verbatim TRANS is CHARACTER1 = ‘N’: apply H (No transpose) = ‘T’: apply H*T (Transpose) \endverbatim

\param[in] DIRECT \verbatim DIRECT is CHARACTER*1 Indicates how H is formed from a product of elementary reflectors = ‘F’: H = H(1) H(2) . . . H(k) (Forward) = ‘B’: H = H(k) . . . H(2) H(1) (Backward) \endverbatim

\param[in] STOREV \verbatim STOREV is CHARACTER*1 Indicates how the vectors which define the elementary reflectors are stored: = ‘C’: Columnwise = ‘R’: Rowwise \endverbatim

\param[in] M \verbatim M is INTEGER The number of rows of the matrix C. \endverbatim

\param[in] N \verbatim N is INTEGER The number of columns of the matrix C. \endverbatim

\param[in] K \verbatim K is INTEGER The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector). \endverbatim

\param[in] V \verbatim V is DOUBLE PRECISION array, dimension (LDV,K) if STOREV = ‘C’ (LDV,M) if STOREV = ‘R’ and SIDE = ‘L’ (LDV,N) if STOREV = ‘R’ and SIDE = ‘R’ The matrix V. See Further Details. \endverbatim

\param[in] LDV \verbatim LDV is INTEGER The leading dimension of the array V. If STOREV = ‘C’ and SIDE = ‘L’, LDV >= max(1,M); if STOREV = ‘C’ and SIDE = ‘R’, LDV >= max(1,N); if STOREV = ‘R’, LDV >= K. \endverbatim

\param[in] T \verbatim T is DOUBLE PRECISION array, dimension (LDT,K) The triangular k by k matrix T in the representation of the block reflector. \endverbatim

\param[in] LDT \verbatim LDT is INTEGER The leading dimension of the array T. LDT >= K. \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 HC or HTC or CH or CH**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 (LDWORK,K) \endverbatim

\param[in] LDWORK \verbatim LDWORK is INTEGER The leading dimension of the array WORK. If SIDE = ‘L’, LDWORK >= max(1,N); if SIDE = ‘R’, LDWORK >= max(1,M). \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date November 2011 \ingroup doubleOTHERauxiliary \par Further Details:

\verbatim

The shape of the matrix V and the storage of the vectors which define the H(i) is best illustrated by the following example with n = 5 and k = 3. The elements equal to 1 are not stored; the corresponding array elements are modified but restored on exit. The rest of the array is not used.

DIRECT = ‘F’ and STOREV = ‘C’: DIRECT = ‘F’ and STOREV = ‘R’:

          V = (  1       )                 V = (  1 v1 v1 v1 v1 )
              ( v1  1    )                     (     1 v2 v2 v2 )
              ( v1 v2  1 )                     (        1 v3 v3 )
              ( v1 v2 v3 )
              ( v1 v2 v3 )

DIRECT = ‘B’ and STOREV = ‘C’: DIRECT = ‘B’ and STOREV = ‘R’:

          V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
              ( v1 v2 v3 )                     ( v2 v2 v2  1    )
              (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
              (     1 v3 )
              (        1 )

\endverbatim

Arguments