Message-ID: <CANLFJPqs26S72Ms0L014dQ-dGUzT8ndpPu15HkVqxCyhDTTq5g@mail.gmail.com>
Date: 2011-11-11T21:50:39Z
From: Baptiste Auguie
Subject: performance of adaptIntegrate vs. integrate
In-Reply-To: <2F9EA67EF9AE1C48A147CB41BE2E15C30B6BEB@DOM-EB-MAIL2.win.ad.jhu.edu>
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
>
>