matcond                package:adlift                R Documentation

_m_a_t_c_o_n_d

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

     Works out two alternative condition numbers for the transform
     associated to the prediction scheme given in the arguments to the
     function.

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

     matcond(x, f, Pred, neigh, int, clo, keep)

_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 the transform matrices to work out their norms
     and singular value decompositions.  Condition numbers are
     calculated by ||T_j ||*||T_j^{-1} || and
     'svd$d[1]/svd$d[nrow(T_j)]' respectively.

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

     cno: the condition numbers for the augmented transform matrices,
          calculated using the Frobenius norm (see condno).

       v: the condition numbers for the augmented transform matrices,
          calculated using the ratio between the largest to the
          smallest singular values in the singular value decomposition
          of the augmented matrices.

       a: the transform matrix information for the transform (output
          from transmatdual).

_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:

     'condno', 'transmatdual'

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

     x1<-runif(256)
     y1<-make.signal2("doppler",x=x1)
     #
     m<-matcond(x1,y1,AdaptNeigh,2,TRUE,TRUE,2)
     #
     m$cno
     #
     m$v
     # shows the two different condition number measures for the matrix associated
     # to the transform performed.
     #

