Implement arbitrary penalties for SNLLS & Pathway amplitudes contstraint

[luisfabib]

Description

This is a major upgrade to snlls.py and fitmodel.py. It improves snlls.py to be able to handle arbitrary penalties defined by outer functions or scripts. This allows us to implement a penalty in fitmodel.py that constrains the pathway amplitudes and makes the separation of the Lam0 and V0 parameters identifiable, strongly improving the fit accuracy and suppressing most uncertainty in fits of multi-pathway models such as 5-pulse DEER, etc.

Changelog:

snlls.py

• Implement an option to pass arbitrary penalty function residuals to be included in the SNLLS algorithm.
• Remove double smoothness penalization in the residual (snnls: double addition of regularization term #103).
• Return the uncertainty quantification of linear and nonlinear parts as separate objects.
• Improve uncertainty analysis by including correlations between linear and non-linear parameters.
• Major code refactoring.
• Improved behavior of scale determination.

fitmodel.py

• Implement constraint Lam0+sum(lam)<=1 to ensure identifiability of Lam0 and V0 during SNLLS optimization (Scale invariability of pathway amplitudes and redundancy with V0 #76).
• Refactor the uncertainty handling code to adapt to the new changes in snlls.py.

Related Issues:

Closes #103
Closes #76

[luisfabib]

The new keyword argument in snlls.py to pass custom penalties is called custom_penalty. We might want to change this, as it was the quick name I chose during development.

Another notation issue might be the difference between the built-in smoothness penalty (needed to ensure the linear problem is correctly computed) and any custom penalty passed by the user. A way to refer to them would be linear-penalty (for the smoothness penalty applied to the linear problem) and non-linear penalty (the user-defined penalty applied to the non-linear problem).

We need to adjust this before merging.