ssWavelets-package: Wavelet Functionality for Package 'sampSurf'
In ssWavelets: Wavelet Functionality for Package 'sampSurf'

Description Details Classes For Use In ssWavelets... Object Constructors Summary and Plotting Methods Other Functions Data Sets Author(s) References See Also

This package adds several classes, generics and associated methods as well as a few various functions to help with wavelet decomposition of sampling surfaces generated using sampSurf. As such, it can be thought of as an extension to sampSurf for wavelet analysis.

At present, the maximal overlap discrete wavelet transform (MODWT) as implemented in the R package waveslim is currently supported. Because objects of class “sampSurf” primarily contain results that are simply raster images, the two-dimensional routines from waveslim are used exclusively (though the 2-D pyramid algorithm employs the 1-D routines behind the scenes). Also, because one is interested in working with the full image rather than compression, methods such as the discrete wavelet transform (DWT) seem to make little sense on these data. However, other wavelet filters may prove useful in the future, and the package has been designed for easy extension to other methods.

Much of the package is geared towards decomposition of the sample variance; that is, the total variance of the sampSurf raster object. The idea is to decompose the sample (sampSurf) variance by scale (distance) to see how sampling methods compare at different scales. This distance-based decomposition gives an idea of the variation at scales that is unavailable in the overall sampSurf variance.

The “raw” wavelet decomposition is available in the objects, but its use seems limited in the simulated sampling context at this point. Plotting methods are available for both, but analysis functions are geared towards variance decomposition.

A rudimentary S4 class structure has been established for extending the current classes should one desire to do so.

Package:	ssWavelets
Type:	Package
Version:	0.1-2
Date:	29-Aug-2017
License:	GPL (>= 3)
LazyData:	TRUE

A list of the main resources are described in the following sections. Please refer to the links below for more information. The package vignette provides further details and examples on how to use this package.

The following S4 classes are available.

The “ssWavelet” class...

Objects of the non-virtual classes below can be created using constructor functions of the same name, see the Object Constructors section for details.

`ssWavelet`	Virtual base class for the following
`ssMODWT`	A class for MODWT decomposition
`ssCovMODWT`	A class for covariance decomposition

For each of the non-virtual classes defined in the table above, we must be able to create objects that can be used in R. This is done using class-specific “constructor” methods that take the drudgery away from creating what can often be somewhat complicated (with all the graphical components) new object instances. Eventually, there may be more than one constructor for a given class of object, and these are differentiated by the method signature; see the links provided below for more details.

“ssWavelet” class constructors...

`ssMODWT`	Constructor for individual `ssMODWT` objects
`ssCovMODWT`	Constructor for individual `ssCovMODWT` objects

The objects created above have graphical content made possible by using classes from the sp or raster packages. Therefore, functions have been developed to allow for graphical display of these objects to show different aspects of the wavelet decomposition (i.e., raw coefficients, variance, covariance).

In addition, summary and show methods are also available (sometimes producing the same result) for printing information within the object...

`plotMODWT2D`	Plots the MODWT object at a given level and anisotropic decomposition
`plotLevel2D`	Plots the set of MODWT object decompositions at chosen level
`show`	To succinctly print one of the package objects
`summary`	To summarize one of the package objects

Note that plot3D is used to plot “raster” and “sampSurf” objects using package rgl. However, it can also be used for “ssWavelet” object images by first ‘casting’ the desired matrix representation to an object of class “RasterLayer”. Casting is necessary as there is no method written specifically for objects of class “ssWavelets”, since the number of possible images in these objects is large. Examples of this procedure are given in the vignette.

A few other functions that will not normally be required listed below. These include some plotting methods in addition to those listed above...

`covMODWT`	Much like the R stats routine cov, but for wavelets
`hfsMODWT`	For comparing different sampling methods by scale
`hfsPlot`	Plots the results of `hfsMODWT`: An H. F. Smith plot
`varPlot`	A variance plot using results from `hfsMODWT`
`palMODWT`	A nice palette function for display
`ssEnergy`	Average “energy” for a “sampSurf” object
`ssToroid`	Returns the toroidal boundary correction object
`ssReflect`	Returns the reflection (periodization) boundary correction object