coefmatrix             package:SpherWave             R Documentation

_C_o_m_p_u_t_a_t_i_o_n _o_f _C_o_e_f_f_i_c_i_e_n_t_s _o_f _S_B_F _a_n_d _S_W

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

     This function generates several coefficients such as coefficients
     of SBF in spherical wavelets (SW),  coefficients of SBF after
     removing subnet l, and coefficients of SW for subnet l.

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

     coefmatrix(beta1, fullcov, netlab, l)

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

   beta1: coefficients of SBF from previous SBF representation

 fullcov: covariance matrix of all observation sites

  netlab: vector of labels representing sub-networks

       l: resolution level

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

     The multiresolution analysis based on SBF is derived from the
     problem of characterizing the loss in an SBF representation  as
     the number of observations are more larger. This function provides
     the coefficients of basis functions of multiresolution levels. 
     For details, see references below.

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

   wcoef: coefficients of SBF in SW

   beta2: coefficients of SBF after removing sub-network l

  gamma1: coefficients of SW for sub-network l

  alpha1: detailed coefficients of SBF for sub-network l

    norm: norms of SW for sub-network l

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

     Oh, H-S. (1999)  Spherical wavelets and their statistical analysis
     with applications to meteorological data. Ph.D. Thesis, 
     Department of Statistics, Texas A&M University, College Station.

     Li, T-H. (1999) Multiscale representation and analysis of
     spherical data by spherical wavelets.  _SIAM Journal on Scientific
     Computing_, *21*, 924-953.

     Oh, H-S. and Li, T-H. (2004) Estimation of global temperature
     fields from scattered observations by  a spherical-wavelet-based
     spatially adaptive method. _Journal of the Royal Statistical
     Society Ser._ B, *66*, 221-238.

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

     'mracoef.comp'

