Special linear group?

[Alvaro Almeida Gomez]

So, I am trying to use Manopt, in my problem I use the special linear group (https://en.wikipedia.org/wiki/Special_linear_group). However, I see that this manifold is not avalaible on the set list. How can I add this manifold to Manopt?

[Nicolas Boumal]

Dear Alvaro,

Indeed, we do not have a factory for that Lie group.

To add support for SL(n) to Manopt, you need to create a factory file. As an example, you can check out the spherefactory, and read more about how factories work on the tutorial page:

https://www.manopt.org/tutorial.html#manifolds

There, you can find a table explaining the different functions that need to be implemented to manipulate points and tangent vectors, compute inner products, retractions, projections to tangent spaces, etc.

You can also read more about these in my book:

http://www.nicolasboumal.net/book

Don't hesitate to come back with questions about how to put this all together.

Best,

Nicolas