Alter the contract of UnivariateRealSolverUtils.bracket() to handle piecewise
constant functions
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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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