transmatdual             package:adlift             R Documentation

_t_r_a_n_s_m_a_t_d_u_a_l

_D_e_s_c_r_i_p_t_i_o_n:

     Works out the transform matrix for a particular prediction scheme
     and neighbourhood structure.

_U_s_a_g_e:

     transmatdual(x, f, Pred = AdaptNeigh, neigh = 1, int = TRUE, clo = TRUE,
      keep = 2)

_A_r_g_u_m_e_n_t_s:

       x: A vector of grid values. Can be of any length, not
          necessarily equally spaced.

       f: A vector of function values corresponding to 'x'. Must be of
          the same length as 'x'.

    Pred: The type of regression to be performed. Possible options are
          'LinearPred', 'QuadPred', 'CubicPred', 'AdaptPred' and
          'AdaptNeigh'.

   neigh: The number of neighbours over which the regression is
          performed at each step. If 'clo' is false, then this in fact
          denotes the number of neighbours on each side of the removed
          point.

     int: Indicates whether or not the regression curve includes an
          intercept.

     clo: Refers to the configuration of the chosen neighbours. If
          'clo' is false, the neighbours will be chosen symmetrically
          around the removed point. Otherwise, the closest neighbours
          will be chosen.

    keep: The number of scaling coefficients to be kept in the final
          representation of the initial signal. This must be at least
          two.

_D_e_t_a_i_l_s:

     The function uses 'Amatdual' to form the refinement matrices A_j,
     from which the augmented matrices T_j are constructed. This
     process is iterated, to find the transform matrix (the top level
     augmented matrix). The rows and columns of this matrix are then
     reordered to be in the order of 'out$coeff', i.e. so that the
     columns correspond to f_1 ... f_n.

_V_a_l_u_e:

     out: the output from the forward transform.

    Wnew: the matrix associated to the wavelet transform.

       x: the original gridpoint vector. 

_A_u_t_h_o_r(_s):

     Matt Nunes (matt.nunes@bristol.ac.uk), Marina Popa
     (Marina.Popa@bristol.ac.uk)

_S_e_e _A_l_s_o:

     'Amatdual'

_E_x_a_m_p_l_e_s:

     x1<-runif(10)
     y1<-make.signal2("doppler",x=x1)
     #
     a<-transmatdual(x1,y1,AdaptNeigh,2,TRUE,TRUE,2)
     #
     a$Wnew
     #
     #the transform matrix for this adaptive lifting scheme 

