Operations allowed on `Tangent`

[mcabbott]

Why is scaling a Tangent by an array allowed?

julia> Tangent{Any}(a=5, b=0) * [1 2; 3 4]
Tangent{Any}(a = [5 10; 15 20], b = [0 0; 0 0])

Scaling by a number I understand. But shouldn't - also work?

julia> (a=10, b=20) + 0.1 * Tangent{NamedTuple}(a=5, b=0)
(a = 10.5, b = 20.0)

julia> (a=10, b=20) - 0.1 * Tangent{NamedTuple}(a=5, b=0)
ERROR: MethodError: no method matching -(::NamedTuple{(:a, :b), Tuple{Int64, Int64}}, ::Tangent{NamedTuple, NamedTuple{(:a, :b), Tuple{Float64, Float64}}})

julia> -Tangent{Any}(a=5, b=0)
ERROR: MethodError: no method matching -(::Tangent{Any, NamedTuple{(:a, :b), Tuple{Int64, Int64}}})

Even better would be to fuse these updates -- if I understand right, 0.1 * Tangent will allocate a new copy of any arrays inside. But ideally something like this would be one pass over everything:

julia> (a=10, b=20) .+ 0.1 .* Tangent{NamedTuple}(a=5, b=0)
ERROR: ArgumentError: broadcasting over dictionaries and `NamedTuple`s is reserved

[willtebbutt]

Why is scaling a Tangent by an array allowed?

This also seems really weird to me. I'm not even sure how it ought to be defined in general...

But shouldn't - also work?

Probably should. I'd be happy to review a PR that added it.

[oxinabox]

Why is scaling a Tangent by an array allowed?

This is not a feature.
It's a coincidence, from implementation.
We can, and arguably should make it an error.
A (nonsquare?) array is not a field as it doesn't define one

[mcabbott]

The above weird behaviours are now fixed.

The documentation says this:

Tangents support a number of operations. Most importantly: + and *, which let them act as mathematical objects.

(at https://juliadiff.org/ChainRulesCore.jl/dev/rule_author/tangents.html)

but I think it means to say that they form a vector space -- they should always allow multiplication by a scalar not another tangent, and addition.

I think it should also say that they always support addition to the primal, x + dx. If that is indeed required.