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https://issues.apache.org/jira/browse/MATH-700?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13141066#comment-13141066
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Luc Maisonobe commented on MATH-700:
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I don't agree with this change.
It implies that user cannot provide an interval that ends exactly at a root,
they must enlarge their interval and then wait for the algorithm to reduce it
back. When a root is at the boundary of a function definition interval (think
about finding the root for sqrt(x)), enlarging the interval is not only
cumbersome, it triggers an error.
> Alter the contract of UnivariateRealSolverUtils.bracket() to handle piecewise
> 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: Sébastien Brisard
> Priority: Minor
>
> The current contract of
> {{o.a.c.m.analysis.solvers.UnivariateRealSolverUtils.bracket(UnivariateRealFunction
> function, double initial, double lowerBound, double upperBound, int
> maximumIterations)}} states that
> {quote}
> This method attempts to find two values a and b satisfying
> * {{lowerBound <= a < initial < b <= upperBound}}
> * {{f(a) * f(b) <= 0}}
> If f is continuous on [a,b], this means that a and b bracket a root of f.
> {quote}
> I don't think there is any problem with the current implementation. However,
> if f is constant, equal to zero on a whole interval, this implementation does
> not guarantee that the whole interval is bracketed. I therefore propose that
> the contract is changed to
> * {{f(a) * f(b) < 0}}
> This entails only a minor correction to the {{bracket()}} method: line 267 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 >= 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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