Gilles created MATH-797:
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Summary: 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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