Implement a check_retraction function.

[kellertuer]

Manopt/Matlab has a nice function to numerically check retractions

https://github.com/NicolasBoumal/manopt/blob/master/manopt/tools/checkretraction.m

which requires that the exponential map is implemented. I think it should even be possible to check two retractions – since both are linear approximations of exp, they should also be of linear error when comparing them directly. So if you trust one retraction you could check another one.

And maybe one could even extend this to inverse retractions (or maybe even to vector transports?) The overall scheme to implement (maybe even with a bit of code duplication from there) is very similar to the numerical check for gradients and Hessians over in Manopt.jl, see https://manoptjl.org/stable/helpers/checks/