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Gilles commented on MATH-797:
-----------------------------
Actually, I filed this issue on behalf of another team within the project I work for.
They indeed are currently using a stripped-down (single step) version of the "LegendreGaussIntegrator".
Their problem is mainly an efficiency one because for their use-case, they know in advance
that a single iteration is enough.
So, your proposal is quite fine (i.e. focus only on Gauss-like integrators and make them
more flexible). Thanks!
> 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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