[R] performance of adaptIntegrate vs. integrate

[baptiste auguie]

Dear Ravi,

Thank you for your answer.

The integrand I proposed was a dummy example for demonstration
purposes. I experienced a similar slowdown in a real problem, where
knowing in advance the shape of the integrand would not be so easy.

Your advice is sound; I would have to study the underlying code of the
two implementations to know where the difference lies. Delving into
the source code and the algorithms gets quite technical though, so I
was hoping someone already familiar with integrate's internals might
shed some light.

Thanks,

baptiste



On 12 November 2011 03:55, Ravi Varadhan <rvaradhan at jhmi.edu> wrote:
> The integrand is highly peaked.  It is approximately an impulse function
> where much of the mass is concentrated at a very small interval.  Plot the
> function and see for yourself.  This is the likely cause of the problem.
>
>
>
> Other types of integrands where you could experience problems are:
> integrands with singularity at either limit and slowly decaying oscillatory
> integrands.  As to why integrate performs better than adaptIntegrate in this
> situation, I don’t know.  You have to study the two implementations.
>  Wynn’s epsilon algorithm is an extrapolation method for improving the
> convergence of a sequence.  This could be an explanation for the better
> performance, but I cannot say for sure.
>
>
>
> Hope this is helpful,
>
> Ravi
>
> -------------------------------------------------------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor,
>
> Division of Geriatric Medicine and Gerontology School of Medicine Johns
> Hopkins University
>
>
>
> Ph. (410) 502-2619
>
> email: rvaradhan at jhmi.edu
>
>