#144 Abstracting fast vs. normal dvr/fbr transformations

[Ulf Lorenz]

What and why

Some transformations, namely the FFT transformations, have a simple and fast, and a correct and slow transformation. One would be used in general, and one would be used by operators during propagation, where some reshuffling is applied to the operator in contrast.

These different kinds of transformations could be abstracted away to become part of the Grid interface.

Acceptance criteria

• Grids have a separate "fast" DVR<->FBR transformation that skips some steps.
  • Somehow, this needs to be done in a generic, comprehensible manner. Maybe introduce a transformation class that encapsulates such details?
  • We also need some way to go from the "normal" FBR representation to the "fast" one, although there is always the generic approach FBR -> DVR -> FastFBR
• FFTGrid implements this transformation differently (phase, FFTShift).
• Possibly, hollow out the grid classes, moving all stuff to the transformations
• All operators use the transformation, not any FFT transformation directly
• Check how much we would gain if we combined multiple 1D FFTs into a single ND FFT

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This required quite a lot of framework to implement. I introduced transformations between representations, which changes the term representation (tensor dimenions + a meaning of the coefficients), making it different from the class Representation. Requires followup work.

Also, renamed some classes (FFTGrid has no FFT inside anymore, so I called it PlaneWaveGrid) and added some initial states.