
Type: Improvement

Status: Open

Priority: Minor

Resolution: Unresolved

Affects Version/s: None

Fix Version/s: 4.X

Labels:None
The documentation for BrentSolver 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 (1e6)" but does not state whether it's absolute, relative, or function value accuracy. If I dig into the source code, 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 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 but should be there.
 the code appears not to use function value accuracy at all.
 the code for BrentSolver 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 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?)