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Gilles commented on MATH-1201:
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I also think that we should not have such defaults.
A default should be the "most obvious", or "most likely" or "most often used" value. None applies here.
Or it should be something that "does the job", even if not in the most efficient way. This could be a valid justification here (but then another value could do the job as well).
> Please clarify tolerance semantics of org.apache.commons.math3.analysis.solvers
> --------------------------------------------------------------------------------
>
> Key: MATH-1201
> URL: https://issues.apache.org/jira/browse/MATH-1201
> Project: Commons Math
> Issue Type: Improvement
> Reporter: Jason Sachs
> Priority: Minor
>
> The documentation for [BrentSolver|http://commons.apache.org/proper/commons-math/apidocs/org/apache/commons/math3/analysis/solvers/BrentSolver.html] is somewhat vague and doesn't seem to agree with the source code:
> {quote}The {{solve}} method returns a zero {{x}} of the function f in the given interval {{[a, b]}} to within a tolerance {{6 eps abs \(x\) + t}} where {{eps}} is the relative accuracy and {{t}} is the absolute accuracy. The given interval must bracket the root.{quote}
> A couple of issues:
> - the default tolerance values are not clearly specified. The documentation says "default accuracy (1e-6)" but does not state whether it's absolute, relative, or function value accuracy. If I dig into the [source code|https://git-wip-us.apache.org/repos/asf?p=commons-math.git;a=blob;f=src/main/java/org/apache/commons/math3/analysis/solvers/BrentSolver.java], it is the default absolute accuracy. It is unclear what the default values for relative and function value accuracy are. I have to dig into the class tree and find [BaseAbstractUnivariateSolver|https://git-wip-us.apache.org/repos/asf?p=commons-math.git;a=blob;f=src/main/java/org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.java] to find out that the default relative accuracy is 10^-14 and the default function value accuracy is 10^-15. These constants in the code are never mentioned in the documentation for [BaseAbstractUnivariateSolver|https://commons.apache.org/proper/commons-math/javadocs/api-3.1/org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html] but should be there.
> - the code appears not to use function value accuracy at all.
> - the [code for BrentSolver|https://git-wip-us.apache.org/repos/asf?p=commons-math.git;a=blob;f=src/main/java/org/apache/commons/math3/analysis/solvers/BrentSolver.java#l165] has the expression {{tol = 2*eps * abs(b) + t}}, not {{tol = 6*eps * abs(b) + t}} as would be implied by the documentation. Is this an error, or is there a magic feature of Brent's algorithm that effectively turns the 2 into a 6?
> ----
> Suggest you:
> - include the default relative and function value tolerances in the documentation for BaseAbstractUnivariateSolver
> - amend the documentation for [BaseUnivariateSolver|https://commons.apache.org/proper/commons-math/javadocs/api-3.1/org/apache/commons/math3/analysis/solvers/BaseUnivariateSolver.html] to expand upon the three tolerances: Are they always used by each of the solver implementations? (no they aren't) Do they add together, or is the minimum error of the three used? (it seems dependent on each of the solver algorithms; in BrentSolver the relative and absolute tolerances add)
> - amend the documentation for BrentSolver to state clearly that the default absolute accuracy is 10^-6 and the other default tolerances are defined in the documentation for BaseAbstractUnivariateSolver (with a link)
> - amend the documentation for BrentSolver to state that it does not use function value accuracy
> - address the discrepancy in the total tolerance formula between the documentation and the code: is the relevant constant 2 or 6?)
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