sbf.comp: Calculation of Field and Density with Multi-sale SBF's

Description

This function calculates field and density with Multi-sale SBF's.

Usage

sbf.comp(point1, point2, site1, site2, coef, netlab, eta, p0)

Arguments

point1

latitude of extrapolation sites in radian

point2

longitude of extrapolation sites in radian

site1

latitude of observation sites in radian

site2

longitude of observation sites in radian

coef

coefficients of multi-scale SBF's

netlab

vector of labels representing sub-networks

eta

bandwidth parameters for Poisson kernel

specifies starting level for extrapolation. Among resolution levels $1, \ldots, L$, resolution levels $p0+1, \ldots, L$ will be included for extrapolation.

Value

aa: a multiscale SBF field on observation's locations
bb: density on observation's locations

Details

For a given field, this function provides a multiscale SBF representation $$ T(x)=\sum_{l}\sum_{j}\beta_{l,j}G_{l}(x \cdot x_j), $$ where $G_{l}()$ denotes a SBF with bandwidth $h_l$ at multiresolution level $l$.

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.