# 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`