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)-
polyregionrepresents the integration domain as an object of class"owin"(from spatstat.geom),"gpc.poly"(from gpclib),"SpatialPolygons"(from sp), or"(MULTI)POLYGON"(from sf), or even as a plain list of lists of vertex coordinates ("xylist"). -
fis the integrand and needs to take a two-column coordinate matrix as its first argument.
The polyCub() function wraps the implemented cubature methods and
by default calls polyCub.SV(), a C-implementation of product Gauss cubature.
Directly calling the desired cubature function is preferable,
see the list below.
-
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 lineintegrate()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)
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.