Projection and retraction slow on the Stiefel manifold

[Damiano Zeffiro]

Hello, I've noticed that the retraction and the projection function for the Stiefel manifold are rather slow. due to, I assume, their use of "multiprod", "multisym", etc. even when there is only a single factor (i.e. only the standard Stiefel manifold and not products of Stiefel manifolds). Is my assumption correct, and if so is there any quick way to speed up these functions without rewriting new functions for the special case of a single factor?

[Nicolas Boumal]

Dear Damiano,

Can you tell us which versions of Manopt and Matlab you are using?

Type "version" and "manopt_version" at the command prompt.

With Matlab R2020b and Manopt 7.0, calls to multiprod are converted into calls to pagemtimes, which is a Matlab built-in function: it's a lot more efficient than what we were using before.

I'm curious to know if the speed issue you noticed is resolved by upgrading, or if you already had the latest versions and in that case I'd be curious to see how you came to the conclusion that it's slower than it should be.

Best,

Nicolas