ESMF_DLARZT Subroutine

subroutine ESMF_DLARZT(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)

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

\verbatim

ESMF_DLARZT forms the triangular factor T of a real block reflector H of order > n, which is defined as a product of k elementary reflectors.

If DIRECT = ‘F’, H = H(1) H(2) . . . H(k) and T is upper triangular;

If DIRECT = ‘B’, H = H(k) . . . H(2) H(1) and T is lower triangular.

If STOREV = ‘C’, the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and

H = I - V * T * V**T

If STOREV = ‘R’, the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and

H = I - V**T * T * V

Currently, only STOREV = ‘R’ and DIRECT = ‘B’ are supported. \endverbatim \param[in] DIRECT \verbatim DIRECT is CHARACTER*1 Specifies the order in which the elementary reflectors are multiplied to form the block reflector: = ‘F’: H = H(1) H(2) . . . H(k) (Forward, not supported yet) = ‘B’: H = H(k) . . . H(2) H(1) (Backward) \endverbatim

\param[in] STOREV \verbatim STOREV is CHARACTER*1 Specifies how the vectors which define the elementary reflectors are stored (see also Further Details): = ‘C’: columnwise (not supported yet) = ‘R’: rowwise \endverbatim

\param[in] N \verbatim N is INTEGER The order of the block reflector H. N >= 0. \endverbatim

\param[in] K \verbatim K is INTEGER The order of the triangular factor T (= the number of elementary reflectors). K >= 1. \endverbatim

\param[in,out] V \verbatim V is DOUBLE PRECISION array, dimension (LDV,K) if STOREV = ‘C’ (LDV,N) if STOREV = ‘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’, LDV >= max(1,N); if STOREV = ‘R’, LDV >= K. \endverbatim

\param[in] TAU \verbatim TAU is DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i). \endverbatim

\param[out] T \verbatim T is DOUBLE PRECISION array, dimension (LDT,K) The k by k triangular factor T of the block reflector. If DIRECT = ‘F’, T is upper triangular; if DIRECT = ‘B’, T is lower triangular. The rest of the array is not used. \endverbatim

\param[in] LDT \verbatim LDT is INTEGER The leading dimension of the array T. LDT >= K. \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date November 2011 \ingroup doubleOTHERcomputational \par Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA \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_____
    ( v1 v2 v3 )                        /            !>         ( v1 v2 v3 )                      ( v1 v1 v1 v1 v1 . . . . 1 )
V = ( v1 v2 v3 )                      ( v2 v2 v2 v2 v2 . . . 1   )
    ( v1 v2 v3 )                      ( v3 v3 v3 v3 v3 . . 1     )
    ( v1 v2 v3 )
       .  .  .
       .  .  .
       1  .  .
          1  .
             1

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

                                                   ______V_____
       1                                          /            !>            .  1                           ( 1 . . . . v1 v1 v1 v1 v1 )
       .  .  1                        ( . 1 . . . v2 v2 v2 v2 v2 )
       .  .  .                        ( . . 1 . . v3 v3 v3 v3 v3 )
       .  .  .
    ( v1 v2 v3 )
    ( v1 v2 v3 )
V = ( v1 v2 v3 )
    ( v1 v2 v3 )
    ( v1 v2 v3 )

\endverbatim

Arguments