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:
install.packages("polyCub")To install the development version from the GitHub repository, use:
## install.packages("remotes")
remotes::install_github("bastistician/polyCub")The basic usage is:
library("polyCub")
polyCub(polyregion, f)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.