Open r0uv3n opened 5 days ago
sounds reasonable – especially since for Euclidean this is very easy (you even could consider just using DiffEq per se then). Do you feel you could do an PR for this as well (or in your PR you plan to do)?
If you are stuck somewhere we can help for sure (also with getting started with PRs and such).
Yes, support for local_metric
is somewhat incomplete at the moment. It should definitely also work with DefaultOrthonormalBasis
. Note though that DefaultOrthonormalBasis
is in general not designed to work well with local_metric
on all manifolds. Its main purpose is "I have a point, and I want to quickly transform tangent vectors into their coordinates and the other way around". As a result, not much attention is paid to the choice being continuous/differentiable/smooth between different points. For metric-related functions some level of smoothness is generally desirable and InducedBasis
was introduced as a way to (locally) guarantee it.
Okay I'll leave this to you
Currently,
local_metric
only works for manifolds of typeEuclidean
when using anInducedBasis
. For consistency I think it might be nice to have this return the same thing for theDefaultOrthonormalBasis
, which seems to be used by most internal methods by default, e.g.solve_exp_ode
.