What is the difference between numpy.fft and scipy.fftpack?

Question

Is the later just a synonym of the former, or are they two different implementations of FFT? Which one is better?

Answer 1

Looking at the github respositories for each, scipy is not just importing numpy's version and renaming it (although it does borrow some functionality). You'll have to dig into the code if you want to discern the difference in implementations since the documentation doesn't make a direct comparison.

https://github.com/numpy/numpy/tree/master/numpy/fft

https://github.com/scipy/scipy/tree/master/scipy/fftpack

Answer 2

I found that numpy's 2D fft was significantly faster than scipy's, but FFTW was faster than both (using the PyFFTW bindings). Performance tests are here: code.google.com/p/agpy/source/browse/trunk/tests/test_ffts.py

And the results (for n x n arrays):

           n                sp               np             fftw
           8:         0.010189         0.005077         0.028378
          16:         0.010795         0.008069         0.028716
          32:         0.014351         0.008566         0.031076
          64:         0.028796         0.019308         0.036931
         128:         0.093085         0.074986         0.088365
         256:         0.459137         0.317680         0.170934
         512:         2.652487         1.811646         0.571402
        1024:        10.722885         7.796856         3.509452

Answer 3

SciPy does more:

• http://docs.scipy.org/doc/numpy/reference/routines.fft.html
• http://docs.scipy.org/doc/scipy/reference/fftpack.html#

In addition, SciPy exports some of the NumPy features through its own interface, for example if you execute scipy.fftpack.helper.fftfreq and numpy.fft.helper.fftfreq you're actually running the same code.

However, SciPy has its own implementations of much functionality. The source has performance benchmarks that compare the original NumPy and new SciPy versions. My archaic laptop shows something like this:

                 Fast Fourier Transform
=================================================
      |    real input     |   complex input    
-------------------------------------------------
 size |  scipy  |  numpy  |  scipy  |  numpy 
-------------------------------------------------
  100 |    0.07 |    0.06 |    0.06 |    0.07  (secs for 7000 calls)
 1000 |    0.06 |    0.09 |    0.09 |    0.09  (secs for 2000 calls)
  256 |    0.11 |    0.11 |    0.12 |    0.11  (secs for 10000 calls)
  512 |    0.16 |    0.21 |    0.20 |    0.21  (secs for 10000 calls)
 1024 |    0.03 |    0.04 |    0.04 |    0.04  (secs for 1000 calls)
 2048 |    0.05 |    0.09 |    0.08 |    0.08  (secs for 1000 calls)
 4096 |    0.05 |    0.08 |    0.07 |    0.09  (secs for 500 calls)
 8192 |    0.10 |    0.20 |    0.19 |    0.21  (secs for 500 calls)

It does seem that SciPy runs significantly faster as the array increases in size, though these are just contrived examples and it would be worth experimenting with both for your particular project.

It's worth checking out the source code http://www.scipy.org/Download#head-312ad78cdf85a9ca6fa17a266752069d23f785d1 . Yes those .f files really are Fortran! :-D