Faster fft with pyfftw

[ljgray]

This adds a basic class and api to do ffts using the fftw backend, which is implemented by pyfftw and is quite a bit faster than the backend used by numpy.fft and scipy.fft.

In particular, I found that fftw scales much better when multiple cores are available, but even single-threaded benchmarks show a speedup of around 3x.

The pyfftw api is a bit cumbersome to use, so I put this module together to try to abstract it a bit for some common fft functions with minimal overhead.

So far, I've just implemented a few functions which I've found useful. It's easy to expand as needed, but I want to keep this fairly minimal - as things get more complex, there's less of a reason to re-implement them.

[ketiltrout]

Other than that, I think this looks okay as an implementation.

Though, what do I gain by setting forward or backward to false in the initialiser? Is it just a runtime savings?

Some unit tests, even very rudimentary ones would be nice.

Also, making pyfftw a hard requirement, forces anyone wanting to install caput at all to also install the FFTW clib, even if they're not FFT-ing with caput. I would prefer it be optional (with the understanding that not installing it means this module won't work). As-is this is going to force us to install FFTW on, say, wind, just so we can access ch_ephem.

[ljgray]

Re. the forward and backward arguments - as you guessed, the idea was just for runtime savings, especially for small arrays

[ljgray]

I've added unit tests and made the pyfftw dependency optional. Note that I've also restricted this module to complex->complex transforms only for now - this is mostly due to laziness because of the extra overhead to manage differing array sizes for real->complex fft and complex->real ifft, and the fact that I don't really need it, but I guess we could implement it down the road if anyone want

[ketiltrout]

Very nice.

I guess we could implement it down the road if anyone want

Yeah, that definitely feels like something to leave until someone actually wants it for something.