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