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polyCub (version 0.5-0)

polyCub.SV: Product Gauss Cubature over Polygonal Domains

Description

Product Gauss cubature over polygons as proposed by Sommariva and Vianello (2007).

Usage

polyCub.SV(polyregion, f, ..., nGQ = 20, alpha = NULL, rotation = FALSE,
  engine = "C", plot = FALSE)

Arguments

polyregion
a polygonal integration domain. The following classes are supported: "owin", "gpc.poly", "SpatialPolygon
f
two-dimensional function. As its first argument it must take a coordinate matrix, i.e. a numeric matrix with two columns.
...
further arguments for f.
nGQ
degree of the one-dimensional Gauss-Legendre quadrature rule (default: 20). See gauss.quad in package statmod. The nodes and weights up to degree 60 are cached in polyCub
plot
logical indicating if an illustrative plot of the numerical integration should be produced.
alpha
base-line of the (rotated) polygon at $x = \alpha$ (see Sommariva and Vianello (2007) for an explication). If NULL (default), the midpoint of the x-range of the polygon is chosen if no rotation is performed, and otherwise
rotation
logical (default: FALSE) or a list of points "P" and "Q" describing the preferred direction. If TRUE, the polygon is rotated according to the vertices "P" and "Q", which
engine
character string specifying the implementation to use. Up to polyCub version 0.4-3, the two-dimensional nodes and weights were computed by R functions and these are still available by setting engine = "R". The new C-implementation is

Value

  • The approximated value of the integral of f over polyregion.

References

Sommariva, A. and Vianello, M. (2007). Product Gauss cubature over polygons based on Green's integration formula. Bit Numerical Mathematics, 47 (2), 441-453.

See Also

Other polyCub.methods: .polyCub.iso, polyCub.iso; polyCub.exact.Gauss; polyCub.midpoint; polyCub

Examples

Run this code
# see example(polyCub)

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