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.

See Also

sbf, swd, swthresh, swr

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