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From Sébastien Brisard (JIRA) <j...@apache.org>
Subject [jira] [Commented] (MATH-797) Single step integrators
Date Tue, 26 Jun 2012 15:03:44 GMT

    [ https://issues.apache.org/jira/browse/MATH-797?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13401444#comment-13401444
] 

Sébastien Brisard commented on MATH-797:
----------------------------------------

Fine by me. Only, I would not call it a {{SingleStepLegendreGaussIntegrator}}, as Gauss integrators
_are_ single-step by nature (of course, you can use refined Gauss-like integrators, like Gauss-Kronrod,
but that's another story). It's a shame that the name {{LegendreGaussIntegrator}} should already
be taken, by a class that is not that useful...

What we could do is create {{SingleStepLegendreGaussIntegrator}} for the time being in 3.1.
Then, I think the best we could do is get rid in 4.0 of the existing {{LegendreGaussIntegrator}},
rename {{SingleStepLegendreGaussIntegrator}} and include it in a hierarchy of Gauss-like integrators.

What do you think?

Sébastien
                
> Single step integrators
> -----------------------
>
>                 Key: MATH-797
>                 URL: https://issues.apache.org/jira/browse/MATH-797
>             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
check.
> 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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