The following methods for cubature (numerical integration) over polygonal domains are currently implemented: the two-dimensional midpoint rule as a simple wrapper around as.im.function() from package spatstat (Baddeley and Turner, 2005), the product Gauss cubature by Sommariva and Vianello (2007), an adaptive cubature for isotropic functions via line integrate() along the boundary (Meyer and Held, 2014), and quasi-exact methods specific to the integration of the bivariate Gaussian density over polygonal and circular domains (based on formulae from the Abramowitz and Stegun (1972) handbook). For cubature over simple hypercubes, the packages "cubature" and "R2Cuba" are more appropriate.
|Author||Sebastian Meyer [aut, cre, trl], Leonhard Held [ths], Michael Hoehle [ths]|
|Date of publication||2016-04-19 08:59:43|
|Maintainer||Sebastian Meyer <Sebastian.Meyer@ifspm.uzh.ch>|
checkintrfr: Check the Integral of r f_r(r)
circleCub.Gauss: Integration of the Isotropic Gaussian Density over Circular...
coerce-gpc-methods: Conversion between polygonal '"owin"' and '"gpc.poly"'
coerce-sp-methods: Coerce '"SpatialPolygons"' to '"owin"'
dotprod: Dot/Scalar Product of Two Vectors
gpclibPermit: 'gpclib' Licence Acceptance
isClosed: Check if Polygon is Closed
isScalar: Checks if Argument is Scalar
makegrid: Constructs Equally-Spaced Grid
plotpolyf: Plot Polygonal Domain on Image of Bivariate Function
plot_polyregion: Plots a Polygonal Domain (of Various Classes)
polyCub: Wrapper Function for the Various Cubature Methods
polyCub.exact.Gauss: Quasi-Exact Cubature of the Bivariate Normal Density
polyCub.iso: Cubature of Isotropic Functions over Polygonal Domains
polyCub.midpoint: Two-Dimensional Midpoint Rule
polyCub-package: Cubature over Polygonal Domains
polyCub.SV: Product Gauss Cubature over Polygonal Domains
polygauss: Calculate 2D Nodes and Weights of the Product Gauss Cubature
vecnorm: Euclidean Vector Norm (Length)
xylist: Convert Various Polygon Classes to a Simple List of Vertices