After some literature review, I believe the current naming convention for complex methods in xeofs (e.g., ComplexEOF, ComplexMCA etc.) is somewhat misleading. While there isn't a universally fixed naming standard, most textbooks I've consulted use the following convention:

• Complex Model: The input is a naturally complexified field, such as the $u$ and $v$ wind components combined into $z=u+iv$.
• Hilbert Model: The input is a real field that is complexified using the Hilbert transform.

Both models explore amplitude-phase relationships, but the difference lies in the input type. In xeofs, the methods currently labeled as "Complex" actually correspond to what are generally called "Hilbert Models." As a side note, xeofs can handle true complex models with the standard EOF class, but it lacks the functionality to easily access the amplitude and phase of components/scores.

I think xeofs would benefit from adopting this more commonly used naming convention. This would involve renaming all ComplexModel classes to HilbertModel and creating a new ComplexModel class that inherits from EOF and includes methods for amplitude and phase.

Although this is a small change, it would be a breaking one. We might consider bundling it with other potential breaking changes (#187 and #183) for a xeofs v3 release.