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From "Jason Sachs (JIRA)" <j...@apache.org>
Subject [jira] [Created] (MATH-1201) Please clarify tolerance semantics of org.apache.commons.math3.analysis.solvers
Date Tue, 03 Feb 2015 21:08:34 GMT
Jason Sachs created MATH-1201:
---------------------------------

             Summary: 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:

>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.

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, or is the minimum error used? (it seems dependent on each of
the solver algorithms
- 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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