generalisation of S(Q,w) and F(Q,t) calculations

[franzlang]

This discussion board's purpose is to better define the desired mid- to long-term state of the MDMC code regarding dynamics structure factor calculations and the determination of related quantities.
The equations relating the dynamic structure factor S(Q,w), the intermediate scattering function F(Q,t) and the resolution function R(Q,w) are:
,
where F[f(Q,w)] and F^{-1}[f(Q,t)] refer to the Fourier and inverse Fourier transform, respectively.
The following diagram tries to capture both the mathematical relations between the different functions, as well as which of those relations and other methods have been implemented in MDMC or should/could be implemented:

Functionality already implemented (red arrows):

• factory pattern for creating SQw objects from different file formats: https://github.com/MDMCproject/MDMCv0.2_pilot/blob/master/MDMC/readers/observables/LAMPSQw.py, https://github.com/MDMCproject/MDMCv0.2_pilot/blob/master/MDMC/readers/observables/MantidSQw.py and https://github.com/MDMCproject/MDMCv0.2_pilot/blob/master/MDMC/readers/observables/xml_SQw.py
• factory pattern for Resolution object from different formats (file, gaussian, lorentzian):
  https://github.com/MDMCproject/MDMCv0.2_pilot/blob/06755753541975609fd24f836d9d08baf6320fa9/MDMC/resolution/resolution.py
• method to calculate FQt objects from an MD Trajectory:
  https://github.com/MDMCproject/MDMCv0.2_pilot/blob/06755753541975609fd24f836d9d08baf6320fa9/MDMC/trajectory_analysis/observables/fqt.py#L136
• method to apply a Resolution to an FQt object:
  https://github.com/MDMCproject/MDMCv0.2_pilot/blob/06755753541975609fd24f836d9d08baf6320fa9/MDMC/trajectory_analysis/observables/fqt.py#L498
• method to calculate SQw objects from an MD Trajectory via an FQt.calculate_SQw method (application of a Resolution being optional):
  https://github.com/MDMCproject/MDMCv0.2_pilot/blob/06755753541975609fd24f836d9d08baf6320fa9/MDMC/trajectory_analysis/observables/fqt.py#L430
  https://github.com/MDMCproject/MDMCv0.2_pilot/blob/06755753541975609fd24f836d9d08baf6320fa9/MDMC/trajectory_analysis/observables/sqw.py#L314

Functionality that has not been implemented yet has green arrows and the black dashed arrows denote mathematical operations that we need to double-check if they are feasible/possible.

[franzlang]

After discussion we agreed that the following functionality would be desirable:

• applying an inverse Fourier transform via a new SQw.calculate_FQt method to transform SQw to FQt
• convolving SQw with a Resolution via SQw.apply_resolution