polyCub

The R package polyCub implements cubature (numerical integration) over polygonal domains. It solves the problem of integrating a continuously differentiable function f(x,y) over simple closed polygons.

For the special case of a rectangular domain along the axes, the cubature package is more appropriate (cf. CRAN Task View: Numerical Mathematics).

Installation

You can install polyCub from CRAN via:

install.packages("polyCub")

To install the development version from the GitHub repository, use:

## install.packages("remotes")
remotes::install_github("bastistician/polyCub")

Usage

The basic usage is:

library("polyCub")
polyCub(polyregion, f)

• polyregion represents the integration domain as an object of class "owin" (from spatstat), "gpc.poly" (from gpclib or rgeos), or "SpatialPolygons" (from sp), or even as a plain list of lists of vertex coordinates ("xylist").

• f is the integrand and needs to take a two-column coordinate matrix as its first argument.

The polyCub() function by default calls polyCub.SV(), a C-implementation of product Gauss cubature. The various implemented cubature methods can also be called directly.

Implemented cubature methods

1. polyCub.SV(): General-purpose product Gauss cubature (Sommariva and Vianello, 2007, BIT Numerical Mathematics, https://doi.org/10.1007/s10543-007-0131-2)

2. polyCub.midpoint(): Simple two-dimensional midpoint rule based on spatstat::as.im.function()

3. polyCub.iso(): Adaptive cubature for radially symmetric functions via line integrate() along the polygon boundary (Meyer and Held, 2014, The Annals of Applied Statistics, https://doi.org/10.1214/14-AOAS743, Supplement B, Section 2.4)

4. polyCub.exact.Gauss(): Accurate (but slow) integration of the bivariate Gaussian density based on polygon triangulation and mvtnorm::pmvnorm()

For details and illustrations see the vignette("polyCub") in the installed package or on CRAN.

Applications

The polyCub package evolved from the need to integrate so-called spatial interaction functions (Gaussian or power-law kernels) over the observation region (an administrative shapefile) of a spatio-temporal point process. Such epidemic models are implemented in surveillance.

polyCub also powers phylogeographic analyses in rase.

Feedback

Contributions are welcome! Please submit suggestions or report bugs at https://github.com/bastistician/polyCub/issues or via e-mail to maintainer("polyCub"). Note that pull requests should only be submitted after discussion of the underlying issue.

License

The polyCub package is free and open source software, licensed under the GPLv2.