Why not store the dynamic modulus in complex form?

[akabla]

I am wondering why we store the complete modulus split into its real and imaginary parts. Wouldn't it be better to work with the complex expressions? They are a bit simpler to write/read, and possibly more effective to compute too. Often the norm and phase are important too, and a complex representation may be more suitable. But maybe @moustachio-belvedere @Ab2425 you have good reasons to prefer the real/imag parts as separate functions?

[moustachio-belvedere]

Related to #35 perhaps both could be solved at the same time.

I think we decided that most people get their experimental data in that format. Also made it convenient for having the multi-objective cost function so elastic/viscous components can be weighted in a sensible way. This could also be done by splitting modulus/arg, or some other wrapper to split real/imaginary, but I think some careful evaluation is required on real-world data to see how it affects fitting. Computation efficiency, fitting accuracy, fitting flexibility probably all need evaluation.

[akabla]

I'd say that the loading of the experimental data is fairly independent of the internal storage and processing afterwards. We could easily convert one into the other when the files are loaded.

The expressions for G' and G'' are more complicated that the expressions for G as a complex variable, since that gets rid of many sin and cos in the expressions. Usually, we need both G' and G'' for fitting purposes. In this case, I suspect that it would be better to calculate the whole expression as a complex variable and extract the real and imag axes later on, for instance for the cost function. We may as well want to build a cost function based on the log modulus of G and the phase difference, maybe?

Another benefit of the complex variable is that they are more directly related to the diff equation and Laplace transform.

Let's do some tests at some point then, and keep this issue open as a reminder.

[moustachio-belvedere]

To add though, I realised I did not mention enough the positive aspect of this. I think the complex form approach has a lot of potential, it could well yield excellent computational + readability + modulus definition benefits.