Mateusz Baran

There is quite a lot to digest in that paper, though I'd assume that ideally one would for example just AD through the `geodesic` function and apply `egrad2rgrad` to the...

I was thinking a bit about AD and correct me if I'm wrong but I think at least in two simple cases we can use standard AD here: derivative of...

> > > > Given f: R -> M and a point t (in R), where we want to get the (covariant) deriative at as well as a step size...

Well, I do not need the derivative of log per se, $d/dh \log(f(t), f(t+h))$ at $h=0$ is a perfectly fine function for standard AD. To be clear, I think this...

Hmm... there might be a small semantic issue. For a function f: M -> R some places define the gradient of f at p \in M as an element of...

BTW, Exp/log could also be replaced with retraction and inverse retraction. Correct behavior up to first order should be enough. I'm not quite sure how to turn it into some...

If all you have is a hammer, everything looks like a nail and here I have the boring Euclidean AD...

> I would avoid using project here, since only tangent vectors are allowed for the last argumentof the exp (or retraction, you're right) anyways. Projection is required exactly because only...

> I don't feel well with this approach, since you can enter that computation with anything (i.e. nontangents) and would neither notice that nor whether the computation is errornous. Projection...

Well, I just noticed that my method of calculating gradients is just an application of the definition of the directional derivative over the whole basis of the tangent space at...