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.
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