periodic               package:assist               R Documentation

_C_a_l_c_u_l_a_t_e _R_e_p_r_o_d_u_c_i_n_g _K_e_r_n_e_l_s _f_o_r _P_e_r_i_o_d_i_c _P_o_l_y_n_o_m_i_a_l _S_p_l_i_n_e_s _w_i_t_h _P_e_r_i_o_d _1

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

     Return a matrix evaluating reproducing kernels for periodic
     polynomial splines at observed points.

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

     periodic(s, t=s, order=2)

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

       s: a numeric vector.

       t: an optional vector. Default is the same as s.

   order: an optional integer sepcifying the order of the polynomial
          spline. Default is 2 for the  periodic cubic spline.

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

     The general formula of the reproducing kernel is sum of an
     infinite series, which is approximated by taking the first 50
     terms. For the case of order=2, the close form is available and
     used.

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

     a matrix with the numbers of row and column equal to the lengths
     of s and t respectively. The [i, j] element is the reproducing
     kernel evaluated at (s[i], t[j]).

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

     'cubic', 'lspline'

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

     x<- seq(0, 1, len=100)
     periodic(x, order=3)

