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From "Gilles (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MATH-797) Single step integrators
Date Wed, 27 Jun 2012 23:02:44 GMT

    [ https://issues.apache.org/jira/browse/MATH-797?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13402643#comment-13402643
] 

Gilles commented on MATH-797:
-----------------------------

bq. I think that GaussIntegrator should not implement UnivariateIntegrator, because the implicit
weighting function would otherwise be misleading.

If I refer to your nice ASCII equation, it indeed seems that {{UnivariateIntegrator}} and
{{GaussIntegrator}} are different concept that happen to intersect at the "Legendre point".
:-)
Anyways, it will be easier to start by not trying to make the concepts depend on each other
or otherwise overlap. Maybe "adapters" can be added later on.

So, are we set to go?

                
> 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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