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performance of adaptIntegrate vs. integrate
2 messages · Ravi Varadhan, 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