grnmol: Grundmann-Moller integration of a function over a simplex

In SimplicialCubature: Integration of Functions Over Simplices

Description

Computes an approximation to the integral of a function f(x) over a simplex S. This is an R translation of the matlab function grnmol.m which was written by Alan Genz.

Usage

grnmol(f,V,s) 

Arguments

f	a (real-valued) function f that can be evaluated at all points in V.
V	a single simplex, specified by an (n x (n+1)) matrix. The columns V[,1],...,V[,n+1] are the vertices of the simplex.
s	a positive integer specifying the order of the rule used

Details

The Grundmann-Moller algorithm approximates the integral of f(x) over the simplex V. When f(x) is a polynomial, and s is large enough, the integral is exact. This function is called by integrateSimplexPolynomial.

Value

Q	a vector of length s+1, with Q[i] the i-th degree approximate value of the integral
nv	number of function evaluations used

References

See reference by Grundmann and Moller in SimplicialCubature-package.

Examples

f <- function( x ) { x[1]^2*x[4]^5 }
grnmol( f, CanonicalSimplex(4), s=4 )

SimplicialCubature documentation built on Jan. 8, 2021, 5:40 p.m.