sphere                package:assist                R Documentation

_C_a_l_c_u_l_a_t_e _P_s_e_u_d_o _R_e_p_r_o_d_u_c_i_n_g _K_e_r_n_e_l_s _f_o_r _S_p_h_e_r_i_c_a_l _S_p_l_i_n_e_s

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

     Return a matrix evaluating reproducing kernels for splines on a
     sphere.

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

     sphere(x, y=x, order=2)

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

       x: a matrix of two columns or a list of two components,
          representing observed  latitude and longitude respectively. 

       y: a matrix of two columns or a list of two components,
          representing  latitude and longitude respectively. Default is
          the same as x. 

   order: an optional integer sepcifying the order of the spherical
          spline. Available are 2, 3, 4, 5 and 6, with a default 2. 

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

     The kernel for sperical splines is a series inconvenient to
     compute. This pseudo kernel is based on a topological equivalence
     as described in Wahba (1981), for which cases the closed form can
     be derived.

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

     a matrix with the numbers of row and column equal to the lengths
     of x and y respectively. The [i, j] element is the reproducing
     kernel evaluated at (x[i,], y[j,])  (or ((x[[1]][i], x[[2]][i]),
     (y[[1]][j], y[[2]][j])) for lists).

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

     Chunlei Ke chunlei_ke@pstat.ucsb.edu and Yuedong Wang
     yuedong@pstat.ucsb.edu

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

     Wahba, G. (1981). Spline Interprolation and Smoothing on the
     Sphere. SIAM J. Sci. Stat.Comput., Vol. 2, No. 1, March 1981.

     Wahba, G. (1990). Spline Models for Observational Data. SIAM, Vol.
     59.

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

     'periodic'

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

     x<- seq(0, 2*pi, len=10)
     y<- seq(-pi/2, pi/2, len=10)
     s.ker<- sphere(cbind(x, y), order=3)

