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).
You can install polyCub from CRAN via:
To install the development version from the GitHub repository, use:
The basic usage is:
polyregion represents the integration domain as an object of class "owin" (from spatstat.geom), "gpc.poly" (from gpclib or rgeos), "SpatialPolygons" (from sp), or "(MULTI)POLYGON" (from sf), 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.
polyCub.SV(): General-purpose product Gauss cubature (Sommariva and Vianello, 2007, BIT Numerical Mathematics, https://doi.org/10.1007/s10543-007-0131-2)
polyCub.midpoint(): Simple two-dimensional midpoint rule based on spatstat.geom::as.im.function()
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)
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.
The polyCub package evolved from the need to integrate so-called spatial interaction functions (Gaussian or power-law kernels) over the observation region of a spatio-temporal point process. Such epidemic models are implemented in surveillance.
Contributions are welcome! Please submit suggestions or report bugs at https://github.com/bastistician/polyCub/issues or via e-mail to maintainer("polyCub").
The polyCub package is free and open source software, licensed under the GPLv2.