Optimising for speed

[CarlAndersson]

Faster execution is always nice! The most relevant parts (for me) are: 1) the initialisation of cost functions, i.e. calculating the spatial derivatives; 2) the optimisation procedure, i.e. evaluating the cost functions; 3) visualising the field.

The solution to 1) and 2) would be to profile properly is different cases, check if the implementation can be improved, and possible use numba or cython to increase execution speed.

The solution to 3) can partly be as for 1) and 2), but in might also be to replace matplotlib with something else. I've noted that displaying the plots can sometimes be as expensive (or more) as calculating the result.

[CarlAndersson]

I've noticed that there are significant limitations in storing the spatial derivatives in dicts. The major reason for this is that loops are frequently required when working with more than one point.
A solution would be to store them in a normal numpy array in a defined way. For easy mapping from string form to index form a top level function or dict could be used to keep track of the correct indices.