powerpen                 package:fda                 R Documentation

_P_o_w_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 power basis.

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

     powerpen(basisobj, Lfd=2)

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

basisobj: A power basis object. 

     Lfd: 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 produced by this
     function is necessary.

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

     A symmetric matrix of order equal to the number of basis functions
     defined by the power basis object. Each element is the inner
     product of two power 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:

