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Date: Tue, 1 Nov 2011 10:40:32 +0000 (UTC)
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Subject: [jira] [Commented] (MATH-700) Alter the contract of
 UnivariateRealSolverUtils.bracket() to handle piecewise constant functions
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    [ https://issues.apache.org/jira/browse/MATH-700?page=3Dcom.atlassian.j=
ira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=3D131410=
69#comment-13141069 ]=20

S=C3=A9bastien Brisard commented on MATH-700:
----------------------------------------

Thanks for this counter-example. This proposal actually comes from MATH-699=
. To solve this bug, I think I need to alter the default bracketing method.=
 I was just wondering if this alteration would be useful to other parts of =
CM. It it's not, then I can define a custom protected bracketing method wit=
hin {{AbstractDistribution}}.=20
               =20
> Alter the contract of UnivariateRealSolverUtils.bracket() to handle piece=
wise constant functions
> -------------------------------------------------------------------------=
-----------------------
>
>                 Key: MATH-700
>                 URL: https://issues.apache.org/jira/browse/MATH-700
>             Project: Commons Math
>          Issue Type: Improvement
>    Affects Versions: 3.0
>            Reporter: S=C3=A9bastien Brisard
>            Priority: Minor
>
> The current contract of {{o.a.c.m.analysis.solvers.UnivariateRealSolverUt=
ils.bracket(UnivariateRealFunction function, double initial, double lowerBo=
und, double upperBound, int maximumIterations)}} states that
> {quote}
> This method attempts to find two values a and b satisfying
> * {{lowerBound <=3D a < initial < b <=3D upperBound}}
> * {{f(a) * f(b) <=3D 0}}
> If f is continuous on [a,b], this means that a and b bracket a root of f.=
=20
> {quote}
> I don't think there is any problem with the current implementation. Howev=
er, if f is constant, equal to zero on a whole interval, this implementatio=
n does not guarantee that the whole interval is bracketed. I therefore prop=
ose that the contract is changed to
> * {{f(a) * f(b) < 0}}
> This entails only a minor correction to the {{bracket()}} method: line 26=
7 of UnivariateRealSolverUtils currently reads
> ...{{while ((fa * fb > 0.0) && (numIterations < maximumIterations)}}...
> I think it would be safe to replace this line with
> ...{{while ((fa * fb >=3D 0.0) && (numIterations < maximumIterations)}}..=
.
> Do you agree in principle? I'll run the current tests to check that this =
change is indeed safe.

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