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https://issues.apache.org/jira/browse/MATH-631?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13080608#comment-13080608
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Gilles commented on MATH-631:
-----------------------------
> (which is difficult to see as you also change other things in the same commit)
Sorry, but I didn't hit the solution right away, i.e. before changing those two
additional little things to make the code clearer (for me)...
The only actual change is that the {{REGULA_FALSI}} enum was not used (i.e.
with the {{switch}} little change, the corresponding {{case}} would have been
empty) whereas now it contains the update of x0 to avoid an infinite loop.
The other (cosmetic) change was to take these two statements
{code}
x1 = x;
f1 = fx;
{code}
out of the previous {{if}} and {{else}} blocks, as they were duplicated there
(which made me wonder whether it was a bug that they were _not_ different).
You say
> [...] convergence is guaranteed [...]
> [...] it converges very slowly for certain problems, [...]
> [...] The limited convergence of the algorithm is a property of the
> algorithm, [...]
All the above imply that one expects that the algorithm _can_ find the solution.
However, in this implementation, it _can't_.
Therefore there is a bug, somewhere.
I agree that it is a limitation of double precision. But, IMHO, leaving the
code as-is is not a good idea because because it leads to the impression that
the "Regula Falsi" mathematical algorithm can fail to converge, which is not
correct (IIUC).
Therefore, we could add a comment stating that the _implementation_ with
limited precision can fail to converge but that would be akin to saying to
users: "Here is a code, but don't use it."
Personally, I would prefer to say: "Because of limited precision, the
implementation can fail to converge. In those cases, we slightly modified the
original algorithm in order to avoid failure."
> "RegulaFalsiSolver" failure
> ---------------------------
>
> Key: MATH-631
> URL: https://issues.apache.org/jira/browse/MATH-631
> Project: Commons Math
> Issue Type: Bug
> Reporter: Gilles
> Fix For: 3.0
>
>
> The following unit test:
> {code}
> @Test
> public void testBug() {
> final UnivariateRealFunction f = new UnivariateRealFunction() {
> @Override
> public double value(double x) {
> return Math.exp(x) - Math.pow(Math.PI, 3.0);
> }
> };
> UnivariateRealSolver solver = new RegulaFalsiSolver();
> double root = solver.solve(100, f, 1, 10);
> }
> {code}
> fails with
> {noformat}
> illegal state: maximal count (100) exceeded: evaluations
> {noformat}
> Using "PegasusSolver", the answer is found after 17 evaluations.
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