mrafield.comp: Decomposition of a Field

Description

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

Usage

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

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

Details

This function generates decomposition of a field, $$ T_1(x)=T_l(x)+D_{l-1}(x)+\ldots+D_1(x), \qquad l=2,\ldots,L $$ 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 $V_l = V_{l+1} + W_l$.

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.