Improve performance of calculating the initial field distribution

[DanielKotik]

There is a huge Python bottleneck due to the high number of necessary function calls of the integrand function in psi_spherical. We use Cython to tackle this problem. According to a527d2d we start our journey from an average execution time of roughly one second:

In [1]: import beamprofile                                                        

In [2]: psi = beamprofile.main()                                                  
Using MPI version 3.1, 1 processes

In [3]: %timeit psi()                                                             
Calculating inital field configuration. This will take some time...
1 s ± 58.4 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

[DanielKotik]

At 2436587 we have now (same parameters as in #3 (comment)):

Pure Python implementation:

In [1]: import optbeam

Please consider compiling `optbeam.py` via Cython: `$ cythonize -3 -i optbeam.py`


In [2]: beamLGspherical, beamLGcartesian, r = optbeam.main()

In [3]: psi = beamLGspherical.profile

In [4]: %timeit psi(r)
Calculating inital field configuration. This will take some time...
79.9 ms ± 408 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

Cython implementation (without disabled checks):

In [1]: import optbeam

In [2]: beamLGspherical, beamLGcartesian, r = optbeam.main()

In [3]: psi = beamLGspherical.profile

In [4]: %timeit psi(r)
Calculating inital field configuration. This will take some time...
9.25 ms ± 74.2 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)