| integrateSphereStroud11 {SphericalCubature} | R Documentation |
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 |
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.
Value
A single number, the approximation to the integral.
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
f2 <- function( x ) { return(x[1]^2) }
integrateSphereStroud11( f2, n=3 )