I think the documentation is correct. U, a.k.a. "the code" or "the
activations" has shape (n_samples, n_components) and V a.k.a. "the
dictionary" or "the components" has shape (n_components, n_features) in
both case.

We could use n_components uniformly instead of n_atoms for consistency's
sake (and just make sure that the "components" is a synonym for "dictionary
atoms" in the literature).

I think V_k is fine because the dimension with size n_components is the
first dimension of V.
​
If you spot issues or other things that are unclear or incomplete in the
doc, please feel free to open an issue on github. You can also directly
submit a pull request if you are familiar with git. The website is built
from the docs that live in the "doc/" subfolder of the repo.

-- 
Olivier
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