fourierpen                package:fda                R Documentation

_F_o_u_r_i_e_r _P_e_n_a_l_t_y _M_a_t_r_i_x

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

     Computes the matrix defining the roughness penalty for functions
     expressed in terms of a Fourier basis.

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

     fourierpen(basisobj, Lfdobj=2)

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

basisobj : A Fourier basis object. 

 Lfdobj : Either a nonnegative integer or a linear differential
          operator object. 

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

     A roughness penalty for a function x(t) is defined by integrating
     the square of either the derivative of x(t) or, more generally,
     the result of applying a linear differential operator L to it. The
     most common roughness penalty is the integral of the square of the
     second derivative D2x(t), and this is the default. To apply this
     roughness penalty, the matrix of inner products of the basis
     functions (possibly after applying the linear differential
     operator to them) defining this function is necessary. This
     function just calls the roughness penalty evaluation function
     specific to the basis involved.

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

     A symmetric matrix of order equal to the number of basis functions
     defined by the Fourier basis object. Each element is the inner
     product of two Fourier basis functions after applying the
     derivative or linear differential operator defined by Lfdobj.

_N_o_t_e:

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

_R_e_f_e_r_e_n_c_e_s:

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

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

