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https://issues.apache.org/jira/browse/MATH-464?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12981731#action_12981731
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Phil Steitz commented on MATH-464:
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I am now thinking that this is not a bug, but a consequence of the fact that
the integrand in the example is not at all well-approximated by a polynomial.
With a small-enough stepsize, the algorithm does converge, but requiring the
large number of function evaluations above. Here are some stepsize values for
the example and the associated absolute error:
n 8 error 0.05738431110184819
n 28 error 0.027423287634332688
n 100 error 8.62162720248888E-5
n 249 error 5.308122631570711E-4
n 650 error 4.3582615516528367E-4
n 1641 error 2.519984967931377E-4
n 3829 error 5.838605030586419E-5
...
n 1102593 error 6.71416523906343E-8
The last entry is from the last (26th) iteration. I haven't verified the
rationale for the updating formula for n above, but it does appear warranted in
this case to increase n quickly as large n (= small stepsize) is required to
get a decent estimate of the integral using Gaussian quadrature.
> LegendreGaussIntegrator ignores defaultMaximalIterationCount and does 38
> million iterations
> -------------------------------------------------------------------------------------------
>
> Key: MATH-464
> URL: https://issues.apache.org/jira/browse/MATH-464
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.1
> Reporter: Michael Borcherds
> Priority: Critical
> Fix For: 2.2
>
> Original Estimate: 3h
> Remaining Estimate: 3h
>
> The following code results in count = 37801710 which is effectively an
> infinite loop for typical functions we are using
> (in GeoGebra)
> The argument defaultMaximalIterationCount = 100 is being ignored
> This is the version we are using:
> http://www.geogebra.org/trac/browser/trunk/geogebra/org/apache/commons/math/analysis/integration/LegendreGaussIntegrator.java
> LegendreGaussIntegrator gauss = new LegendreGaussIntegrator(5, 100);
>
> try {
> double result = gauss.integrate(new testFun(), -10,
> 0.32462367623786328);
> } catch (Exception ee) {
> ee.printStackTrace();
> }
> class testFun implements UnivariateRealFunction {
> public double value(double x) throws FunctionEvaluationException {
> count ++;
> if (x>=0 && x<=5) return 0.2; else return 0;
> }
> }
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