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From "Gilles (JIRA)" <>
Subject [jira] [Commented] (MATH-797) Single step integrators
Date Tue, 26 Jun 2012 14:41:44 GMT


Gilles commented on MATH-797:

I'm not familiar _at all_ with those algorithms, so I wouldn't be able to comment much.

However, I'm indeed eager to propose something quite soon (because time for code changes starts
to run out for some teams in the project I work for). If not, they will keep their "fork"
from the current CM code (and we run the risk of implementing something that nobody will actually

Thus, what I would propose is to create a code that performs what is requested, using a stripped-down
version of your code (i.e. no interface, minimum number of accessors, ...), maybe hiding everything
in a "SingleStepGaussLegendreIntegrator" class. This will enable to quickly assess correctness
(e.g. comparing with the current CM code) and performance (the reason for the reporter's request).
Then we can gradually add more flexibility/refinements ("public" factories, etc.) as we agree
on their API.

How does that sound?

> Single step integrators
> -----------------------
>                 Key: MATH-797
>                 URL:
>             Project: Commons Math
>          Issue Type: Wish
>    Affects Versions: 3.0
>            Reporter: Gilles
>            Assignee: Gilles
>            Priority: Trivial
>             Fix For: 3.1
> CM assumes that the user wants to integrate a complex function on a large interval, so
the large interval has to be subdivided into many subintervals. CM does the partition, and
performs convergence checks, using an iterative approach.
> However, if the function is smooth enough, no subdivision of the integration interval
is required. Those use-cases could benefit from the efficiency gain of not performing a convergence
> The proposal is to provide a new interface "UnivariateSingleStepIntegrator":
> {code}
> interface SingleIntervalIntegrator {
>     /**
>      * Method for implementing a single interval integration.
>      * There is no convergence checks because it is not iterative.
>      *
>      * @param f Function to integrate.
>      * @param lower Lower bound of the interval over which to integrate.
>      * @param upper Upper bound of the interval over which to integrate.
>      * @return the integrated value.
>      */
>     double integrate(UnivariateFunction f,
>                      double lower,
>                      double upper);
> }
> {code}
> In effect, the implementation of the above "integrate" method of a new "LegendreGaussIntegratorSingleStepIntegrator"
would the equivalent of "stage(1)" in the current "LegendreGaussIntegrator".

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