Introduce absstep to specify the stepsize to use close to zero #55
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rename epsilon_factor to relstep.
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Coverage 58.02% 58.02%
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Files 6 6
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Hits 170 170
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| returntype::Type{T2}=eltype(x), | ||
| f_x::Union{Nothing,T}=nothing; | ||
| relstep=default_relstep(fdtype, T), | ||
| absstep=relstep) where {T<:Number,T1,T2} |
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why does this default make sense? Does it recover the previous behavior?
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Does it recover the previous behavior?
Yes, it's to match the current behavior.
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and rename epsilon_factor to relstep. Since we just introduced the
epsilon_factorargument, I haven't deprecated it.Setting the step size around zero can be important in applications and indeed I'm working on a project where the current default isn't a good choice.
The current version of this PR should have almost unchanged behavior for the current uses of the library. However, we might want to consider using a smaller absolute step size. This is effectively what https://cran.r-project.org/web/packages/numDeriv/numDeriv.pdf does and this can also be motivated by computing derivatives of
logandabs2around zero, seeWhere "new" uses the square of the relative step size for the absolute step size. However, Pareto improvements only exist in books so some functions can lose on such a change.
though I'm not sure if new error is really worrying.