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dlarft examples
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Man Page Details
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NAME
       DLARFT  -  the triangular factor T of a real block reflector H of order
       n, which is defined as a product of k elementary reflectors

SYNOPSIS
       SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )

           CHARACTER      DIRECT, STOREV

           INTEGER        K, LDT, LDV, N

           DOUBLE         PRECISION T( LDT, * ), TAU( * ), V( LDV, * )

PURPOSE
       DLARFT 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'

       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 * V


ARGUMENTS
       DIRECT  (input) CHARACTER*1
               Specifies the order in which the elementary reflectors are mul-
               tiplied to form the block reflector:
               = 'F': H = H(1) H(2) . . . H(k) (Forward)
               = 'B': H = H(k) . . . H(2) H(1) (Backward)

       STOREV  (input) CHARACTER*1
               Specifies how the vectors which define the  elementary  reflec-
               tors are stored (see also Further Details):
               = 'R': rowwise

       N       (input) INTEGER
               The order of the block reflector H. N >= 0.

       K       (input) INTEGER
               The  order  of the triangular factor T (= the number of elemen-
               tary reflectors). K >= 1.

       V       (input/output) DOUBLE PRECISION array, dimension
               (LDV,K) if STOREV = 'C' (LDV,N) if STOREV = 'R' The  matrix  V.
               See further details.

       LDV     (input) INTEGER
               The  leading dimension of the array V.  If STOREV = 'C', LDV >=
               max(1,N); if STOREV = 'R', LDV >= K.

       TAU     (input) DOUBLE PRECISION array, dimension (K)
               TAU(i) must contain the scalar factor of the elementary reflec-
               tor H(i).

       T       (output) 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.

       LDT     (input) INTEGER
               The leading dimension of the array T. LDT >= K.

FURTHER DETAILS
       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 )

