`is_point` too optimistic for (co)tangent bundles

[SteffenPL]

The following code surprised me

using Manifolds

M = Euclidean(2)
TM = TangentBundle(M)
coTM = CotangentBundle(M)

pt = [1.0,1]
nopt = [1.0, 1.0, 1.0]
v = [1.0,0.0]
nov = [1.0, 0.0, 0.0]

is_point(M, pt)           # true
is_point(M, nopt)         # false
# is_point(M, nothing)    # throws size error

is_point(TM, (pt, v))    # true   (correct)
is_point(TM, (nopt, v))  # true
is_point(TM, (pt, nov))  # true
is_point(TM, nothing)    # true

It seems that is_point isn't checking anything for (co)tangentbundles.

(I am traveling now, but happy to also draft a PR to get into manifolds; posted also here https://discourse.julialang.org/t/tangent-cotangent-bundles-in-manifolds-jl/137801/3)

[kellertuer]

Thanks for reporting this. Yes, is_point is usually optimistic.

A bit of technical background: since you can “ask” is_point to make “less of a fuzz” about errors, see https://github.com/JuliaManifolds/ManifoldsBase.jl/blob/e36b1a089c282c821437cdc37d294b501a025c56/src/ManifoldsBase.jl#L846-L851

It internally passes to check_point first. That method is optimistic in the sense that it

• returns (but does not throw) an error (usually a DomainError)
• returns nothing if there is no error – or in other words “all is fine and the point is correct”

check_point on the other hand has an optimistic default:

https://github.com/JuliaManifolds/ManifoldsBase.jl/blob/e36b1a089c282c821437cdc37d294b501a025c56/src/ManifoldsBase.jl#L324

The simple reason for this is ease of use. If you implement a manifold “from scratch” and do not yet think about verification, you do not get hit by too many direct errors. But sure we could change such a default.

On the other hand I would consider the current state of co tangent vectors in Manifolds.jl quite experimental. I had a few moments where colleagues asked whether they could be used and we usually found out, that using flat/sharp – even in theory before not in coding – and phrasing things in tangent vectors was much easier. I am happy to help making that better, but I would be careful with that to get it correct then.

edit: For the case with is_point(M, nothing) though – I am not sure we should “capture” all cases where functions are used wrongly, since that would raise the question where to stop.

So yes a PR to improve things is always welcome :)

Gute Reise!