ping @adrinjalali @jnothman @agramfort @lschwetlick

This looks good to me, thanks for fixing!

Thanks for checking @lschwetlick . If you have time / feel like it, it'd be great if you could check with your notebook if the results make sense now? (but no worries otherwise)

Well... not sure if this is maybe quite edge case-y but

b = np.ones((9, 6))
print("rank=", np.linalg.matrix_rank(b))
u2, s2, vh2 = np.linalg.svd(b, full_matrices=True)
ll = np.empty_like(s2)
ll[0] = -np.inf
for r in range(1,s2.shape[0]):
    ll[r] = (_assess_dimension(np.asarray(s2), r, 9))
print(ll)

-> [-inf nan -inf -inf -inf -inf]

but then funnily enough it gives the right number of dimensions (1) because apparently argmax treats nan>-inf. Its giving nan because if all subsequent values in the spectrum are 0 then in line 76 v is also 0...

I'm also still slightly confused to be honest: we dont test full rank because the method isn't defined for testing full rank. But what if the number of dimensions is full rank?

Thanks @lschwetlick , I fixed that and added a test (though indeed it's an unlikely case I think)

But what if the number of dimensions is full rank?

I guess users use mle when they want some dimensionality reduction, but just don't know by how much. So that's fine not to consider rank==n_features (we can't anyway). There's always the solution to directly provide n_components=n_features.

Alright cool, other than that my notebook and I are happy :)

thanks a lot @NicolasHug and @lschwetlick for the team work !