# Decomposition of a Field

### Description

This function computes global and local components (fields) on grid from an initial field.

### Usage

 1 mrafield.comp(grid, coeff, site, netlab, eta, field, density) 

### Arguments

 grid grid points of extrapolation sites in radian coeff coefficients of multi-scale SBF's site grid points of observation sites in radian netlab vector of labels representing sub-networks eta bandwidth parameters for Poisson kernel field extrapolation on grid density density of locations induced from an initial field

### Details

This function generates decomposition of a field,

T_1(x) = T_l(x) + D_{l-1}(x) + … + D_1(x), l = 2,…, L

where a global component T_{l+1}(x) \in V_{l+1} and a local component D_l(x) \in W_l. The corresponding space are nested as V_l \supset V_{l+1}, so that V_l = V_{l+1} + W_l.

### Value

 global matrix of successively smoothed data local matrix of difference of successively smoothed data density density of locations in global and local fields swcoeff spherical wavelet coefficients

### References

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.

sbf, swd, swthresh, swr