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From S├ębastien Brisard (JIRA) <j...@apache.org>
Subject [jira] [Commented] (MATH-797) Single step integrators
Date Wed, 27 Jun 2012 11:33:44 GMT

    [ https://issues.apache.org/jira/browse/MATH-797?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13402148#comment-13402148
] 

S├ębastien Brisard commented on MATH-797:
----------------------------------------

Yes, that's much better than what I had in mind. I thought of something like {{GaussIntegrator}}
as a mother class, with various impls: {{GaussLegendreIntegrator extends GaussIntegrator}},
{{GaussChebyshevIntegrator extends GaussIntegrator}}, and so on. That's why I was saying that
{{GaussIntegrator}} was a bad name for {{GaussLegendreIntegrator}}.

But I like your way of seeing things very much. Plus it would be fairly easy to start with
a basic implementation, only legendre, limited order, and build on this later on.

I think that {{GaussIntegrator}} should not implement {{UnivariateIntegrator}}, because the
implicit weighting function would otherwise be misleading. What do you think?
                
> 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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