Introduce Eigen-style transpose() for Tangent-types

[markusgft]

Dear all,
what do you think of introducing an Eigen-style transpose() call for manif tangent types?
The context of the question is the same as in #137.
So far, I helped myself with introducing the following public method to my personal clone of manifs tangent_base.h:

auto transpose() const {return coeffs().transpose();} 

Note that it in fact returns the transpose of the underlying data type, i.e. the transpose of an Eigen-matrix.
I would like to hear your opinion regarding such a feature, and like to suggest that this could also be helpful for other users?
Best!

[joansola]

Just for clarification. I suppose you are aware that all our tangent types are Cartesian vectors, that is Matrix<T, size, 1>, and that we do not expose normally the true Lie algebra types. Does this affect your comment / request in some way?

[markusgft]

No, I don't think that affects the principal idea. Maybe an application example: what I would like to achieve is that one can evaluate quadratic forms like the following ...

manif::SE3Tangentd t = /* ... some init. */; 
Eigen::Matrix M (6,6);
M = /* ... some init. */;

// We should be able to do this..:
Eigen::MatrixXd res = t.transpose() * M * t;

... while using pure Eigen-syntax! Does that clarify the idea?

[joansola]

Yes it does! Thanks. I'm mostly concerned with the math of the library. Jeremie is the one involved in the design / development of the library. Let us see what he says.

[artivis]

Hi all,
looks like this request, just like #143, if about bringing some of Eigen's vector API to the tangent classes. I'm wondering if it would make sense for the TangentBase class to 'simply' directly inherit from Eigen::Matrix<T, size, 1>. This would bring a lot to the API space but since the tangent types are Cartesian vectors maybe it make sense. We would also benefit from some Eigen optimizations here and there...
@joansola thoughts?

[joansola]

Yes, it makes perfect sense and you save a lot of work.

I think the base API from Eigen can be exposed partially also, should some parts of it become irrelevant or dangerous for any reason, using the using and delete keywords or similar, but you know better than me about these things.

[markusgft]

Inheriting from Eigen::Matrix seems like a good idea, I did not have that on my radar, but it probably makes sense for the Tangent class!

[markusgft]

Dear @artivis @joansola
I wanted to use the opportunity to follow up and further energize the idea of deriving the Tangent classes from Eigen::Matrix. I think that would be a fantastic feature, which would help a lot of people to run advanced linear algebra routines in the tangent space with ease.
If you are considering implementing it, it would be very helpful if you quickly comment on potential timelines, as to simplify our own planning of feature development for the control toolbox.
Best, and thanks a lot in advance!

[artivis]

Hi @markusgft,
I am quite sold to the idea of the Tangent class inheriting from Matrix (MatrixBase most likely) however I anticipate this not to be simple and fairly time consuming. So that you know, I develop manif on my free time, therefore it is not always easy to find large blocks of hours to properly focus.
I will have a look at this over the weekend to get a better idea of the implications and hopefully provide you with an estimated time of landing.
Cheers.

[markusgft]

No worries, I fully understand (it's the same for me and the control toolbox) and I certainly did not want to appear too demanding!
Let me know if there's anything I can contribute to the effort.
Cheers.

[joansola]

From my side there's not much I can do. But I'd like to see this evolving since I believe this would be a powerful upgrade of the library.

[artivis]

Hi guyz,
a quick update to let you know that I looked at the inheritance thingy over the weekend and as I expected it won't be simple. Actually I don't even know how to deal with it atm. The problem is the following: manif design, much like Eigen's, separates the interface (Base classes) from the actual memory allocation (say e.g. final SE2 class). This scheme allows for instance to easily specialize Eigen::Map for manif object through inheritance (a Map<SE2> inherits from SE2Base). If TangentBase (or any intermediate base for that matter) was to inherit directly from eigen::Matrix this separation of concern would be broken (a Map<SE2> object would allocate to underlying vector even if it doesn't use it...). I gave a quick shot at inheriting from MatrixBase but that raises all kind of issues on Eigen's side (traits that are not specialized for manif objects etc). I'm not sure how to get around this, maybe any of you know of a Eigen super expert? I'll also ask for guidance on Eigen's forum asap.
Depending on how urgent is the API extension, we may implement it directly in manif for now while resolving the inheritance difficulty.

Thoughts?