Wendland               package:fields               R Documentation

_W_e_n_d_l_a_n_d _f_a_m_i_l_y _o_f _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:

     Computes the compactly supported, stationatry Wendland covariance
     function as a function ofdistance. This family is useful for
     creating sparse covariance matrices.

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

     Wendland(d, theta = 1, dimension, k,derivative=0, phi=1)

     Wendland2.2(d, theta=1)

     wendland.coef(d,k)

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

       d: Distances between locations. Or for wendland.coef the
          dimension of the locations.

   theta: Scale for distances. This is the same as the range parameter.

dimension: Dimension of the locations

       k: Order of covariance function.

derivative: Indicates derivative of covariance function

     phi: Scale factor to multiply the function. Equivalent to the
          marginal variance or sill if viewed as a covariance function.

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

     This is the basic function applied to distances and called by the
     'wendland.cov' function. It can also be used as the Covariance or 
     Taper specifications in the more general  stationary.cov and
     station.taper.cov functions. The Wendland covariance function is a
     polynomial on [0,theta] and zero beyond theta.  The parameter 'k'
     detemines the smoothness of the covariance at zero.  The
     polynomial coefficients are computed recursively based on the
     values of 'k' and 'dimension' in the function 'wendland.coef'. The
     polynomial is evaluated using 'fields.evlpoly'. 

     A specific example of the Wendland family is 'Wendland2.2' and
     this  is included mainly for testing.

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

     A vector of the covariances or its derivative.

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

     Doug Nychka

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

     wendland.cov, stationary.taper.cov

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

     DD<- seq( 0,1.5,, 200)

     y<- Wendland( DD, k=2, dimension=2)

     plot( DD, y, type="l")

     # should agree with 

     y.test<- Wendland2.2( DD)

