[R] Fwd: Numerical integration

Hans W Borchers hwborchers at googlemail.com
Thu Nov 18 07:06:23 CET 2010

Eduardo de Oliveira Horta <eduardo.oliveirahorta <at> gmail.com> writes:

> ---------- Forwarded message ----------
> From: Eduardo de Oliveira Horta <eduardo.oliveirahorta <at> gmail.com>
> Date: Wed, Nov 17, 2010 at 3:59 PM
> Subject: Re: [R] Numerical integration
> To: David Winsemius <dwinsemius <at> comcast.net>
> It works, however is not very efficient for the problem I'm working with,
> since it is the same as vectorizing the integrand before applying
> "integrate".
> Any other thoughts? Efficiency would be highly welcome!
> Thanks again,
> Eduardo Horta

'adaptIntegrate' in package "cubature" does not require pre-vectorized 
functions. But I doubt it is more efficient as every integration needs
to perform a lot of function calls.

And with 'adaptIntegrate' you have to do the reduction of an infinite
interval to a finite one yourself. E. g., with a given function f define

    g <- function(x) f(1/x) / x^2
    adaptIntegrate(g, 0, 1/a)      # instead of integrate(f, a, Inf)

You have not given the slightest indication why your function integration
would be so slow. So it's difficult to give more focussed advice.

Hans Werner

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