Use Cython instead of f2py

[certik]

The f2py wrappers seem to have some overhead. In my experience, one can get the best performance when using Cython, and making sure everything is compiled with all optimizations on. I have done that in this PR.

Now the Cython Fortran version is about 10% faster than Numba on my machine, here is how the executed notebook looks like for me now: http://nbviewer.jupyter.org/gist/certik/4dec819b75ef49488fb223918b148fae:

In [15]: numba_time.best / fortran_time2.best
Out[15]: 1.1155824066253082

I used gfortran 5.4.0 on Ubuntu 16.04.

I also converted the Fortran subroutine to modern Fortran:

subroutine abc_model(a, b, c, inflow, outflow)
real(dp), intent(in) :: a, b, c, inflow(:)
real(dp), intent(out) :: outflow(:)
real(dp) :: state_in, state_out
integer :: t
state_in = 0
do t = 1, size(inflow)
    state_out = (1 - c) * state_in + a * inflow(t)
    outflow(t) = (1 - a - b) * inflow(t) + c * state_in
    state_in = state_out
end do
end subroutine

That does not affect performance, but the function is much cleaner and shorter, more in line with the Python version.

[kratzert]

As said in in the other pull request, I'm on travel till sunday and won't find much time until I'm home to try and merge this. But I already had a look at the nb. Thanks for the effort you put into this. I'm not so experienced with fortran so I really appreaciate your suggestions

[certik]

@kratzert no problem, take your time. I did it, since benchmark comparisons should be fair, and numba is probably using the most optimized LLVM together with the most efficient wrappers, and so it wasn't fair to compare against not fully optimized Fortran build together with less efficient Python wrappers. This PR fixes it, so now the benchmark is fair, as far as I can tell.

[kratzert]

I share your opinion that all implementations should be implemented (and compiled) as best as possible for a speed comparision. I did it to my best knowledge but I wasn't aware of the different compile possibilities. Thanks for the correction And I think this PR even shows another advantage of numba (compile complexity) which seems to come with a minor speed trade off.

[certik]

Regarding the compile complexity, for actual projects I just use cmake and have written tools that generate the Cython and C header files from Fortran code (https://github.com/certik/dftatom/blob/4c435a30feb8f075b7d62fd5788970e4d100678d/utils/fparser), similarly how f2py works, just without the speed overhead. I should probably make it a standalone library and integrate with the jupyter notebook, so that it's as painless as f2py.

[kratzert]

@certik I think many people would appreciate having your code as a maybe documented pardon to the f2py library since there is a serious speed gain. So maybe you should go for it :)

[certik]

@kratzert Yes, I should do that, I put it on my TODO list.