Exponential, Matern, Radial Basis   package:fields   R Documentation

_C_o_v_a_r_i_a_n_c_e _f_u_n_c_t_i_o_n_s

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

     Functional form of covariance function assuming the argument is a
     distance between locations.

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

     Exponential(d, range = 1, alpha = 1/range, phi = 1)
     Matern (d , scale = 1, range = 1,alpha=1/range,
          smoothness = 0.5, nu= smoothness, phi=scale) 
     RadialBasis(d,M,dimension)

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

       d: Vector of distances 

   range: Range parameter default is one. Note  that the scale can also
          be specified  through the "theta"  scaling argument  used in
          fields covariance functions) 

   alpha: 1/range 

   scale: Same as phi 

     phi: Marginal variance.

smoothness: Smoothness parameter in Matern. Controls the number of
          derivatives in the process. Default is 1/2 corresponding to
          an exponential  covariance.

      nu: Same as smoothness

       M: Interpreted as a spline M is the order of the derivatives in
          the penalty.

dimension: Dimension of function

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

     Exponential: 

     phi* exp( -d/range)

     Matern:

     phi*con*(d\^nu) * besselK(d , nu )

     Matern covariance function transcribed from Stein's book page 31
     nu==smoothness, alpha ==  1/range

     GeoR parameters map to kappa==smoothness and phi == range check
     for negative distances

     'con' is a constant that normalizes the expression to be 1.0  when
     phi=1.0 and d=0. 

     Radial basis functions:

     C.m,d  d\^(2m-dim)        dim- odd

     C.m,d  d\^(2m-dim)ln( d)  dim-even

     where C.m.d is a constant based on spline theory. See
     'radbas.constant'.

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

     A vector of covariances.

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

     Doug Nychka

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

     Stein's book

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

     stationary.cov, stationary.image.cov,
     Wendland,stationary.taper.cov rad.cov

