SphericalCubature (version 1.5)

integrateSphereStroud11: Integrate a function over the sphere in n-dimensions.

Description

Approximate the integral of a function f(x)=f(x[1],...,x[n]) over the unit sphere in n-space using Stroud's method of degree 11.

Usage

integrateSphereStroud11(f, n, ...)

Arguments

f

function f(x)=f(x[1],...,x[n]) to integrate

n

dimension of the space, implemented for n in the range 3:16.

…

optional arguments passed to f( ). If these are specified, they should be labeled with a tag, e.g. param1=3.4

Value

A single number, the approximation to the integral.

Details

This method works if the integrand is smooth. If the function changes rapidly, adaptive integration can be tried as described in 'See Also' below.

References

Stroud integration and related functions, adapted from fortran code by John Burkhart found at http://people.sc.fsu.edu/~jburkardt/f77_src/stroud/stroud.html Based on the book by A. H. Stroud, Approximate Calculation of multiple integrals, 1971, page 296-297.

See Also

adaptIntegrateSpherePolar, adaptIntegrateBallPolar, adaptIntegrateSphereTri

Examples

# NOT RUN {
f2 <- function( x ) { return(x[1]^2) }
integrateSphereStroud11( f2, n=3 )
# }