Iterated and inverse functions syntax

[jariji]

Using the syntax idea from JuliaLang/julia#39042, I wonder what you think about this syntax for iterated functions. This style is used in array languages.

using InverseFunctions, Test
struct IteratedFunction{F}
    f::F
    n::Int
end
((;f,n)::IteratedFunction)(x) =
    if n == 0
        x
    elseif n > 0
        foldl((y,f)->f(y), [f for _ in 1:n]; init=x);
    else # if n < 0
        (inverse(f) ∘̂ (-n))(x)
    end

f ∘̂ n = IteratedFunction(f,n)

@test (exp∘̂0)(3) == 3
@test (exp∘̂1)(1) ≈ 2.718281828459045
@test (exp∘̂2)(1) ≈ 15.154262241479262
@test (exp∘̂3)(1) ≈ 3.814279104760214e6
@test (exp∘̂(-1))(ℯ) ≈ 1.0
@test (exp∘̂(-2))(ℯ) ≈ 0

[oschulz]

@jariji, I have support for iterated function in FunctionChains, and FunctionChains supports InverseFunctions (and ChangesOfVariables as well):

julia> using FunctionChains, InverseFunctions, FillArrays

julia> f = setinverse(x -> x + 1, x -> x - 1)

julia> g = fchain(Fill(f, 10))

julia> g(3)
13

julia> inverse(g)(13)
3

It would certainly make sense to add a shortcut/equivalent for fchain(Fill(f, 10)) to FunctionChains (ideally without depending on FillArrays, which is rather heavy) - would you like to move this issue there?

About using f ∘̂ n is the operator - hm maybe, @devmotion, what do you think?

Supporting f ∘̂ -n in a type-stable fashion could get tricky though.

[devmotion]

I'm sorry, it's not clear to me how this syntax request is related to InverseFunctions.

Generally, I like the operator proposal - but since it's taken from the Julia PR I think (similar to other proposals in base Julia) if desired it should be tried in a separate dedicated package (similar to the tensor syntax in e.g. https://github.com/JuliaMath/TensorCore.jl) and not in InverseFunctions (InverseFunctions could then eg define inverse in an extension for such a package).

[oschulz]

I'm sorry, it's not clear to me how this syntax request is related to InverseFunctions.

Indeed, it should (for example) go into FunctionChains (see above). I was just wondering about the choice of operator - sorry, that was a bit off-topic given my remarks before.

I'll comment on the Julia PR.

[jariji]

It would certainly make sense to add a shortcut/equivalent for fchain(Fill(f, 10)) to FunctionChains (ideally without depending on FillArrays, which is rather heavy) - would you like to move this issue there?

Yes please.

[oschulz]

Ok, I'll get on that in FunctionChains then @jariji .

[oschulz]

Using Iterators.repeated should make this fairly easy without needing FillArrays.

[oschulz]

Closing this here in favor of oschulz/FunctionChains.jl#13 .