Speed-up options for pipeflow and timeseries calculation

[dlohmeier]

This discussion is moved from issue #88:

This discussion should be a short overview of possible measures to decrease the calculation time of the pipeflow in general or in the case of a timeseries calculation.

We should address the following aspects for timeseries calculations:

• Initialization of state variables based on user input or previous results (see issue Setting initial values for pipeflow #86 ).
• Recycle options to take over internal variables from previous calculations, in analogy to pandapower. So, it should be possible to just take over the pit, to just update the jacobi matrix (cf. PR Speedup of timeseries calculation through additional option #87 ) and to reuse lookups.

Just concerning the internals of pipeflow, I see the following possible improvements:

• Vectorize the derivative calculation of components that are based on the same code. This is rather urgent, as currently a pipeflow calculation for a grid with pipes and valves takes much longer than for a grid with only pipes, although the derivative calculation does exactly the same and could be summarized for both components.
• The result extraction of different components should be checked to make sure that it is as efficient as possible. It should as much as possible be based on numpy code, pandas calls like loc should be avoided where possible.
• Eliminate equations from the system matrix that can be simplified (e.g. at a node with just two branch elements the mass flow balance might be left out and calculated afterwards).

The list should be extended and I think it would make sense to create an action item list with milestones from it.