fft2在numpy和matlab中的结果不同

Question

I was trying to port one code from python to matlab, but I encounter one inconsistence between numpy fft2 and matlab fft2:

peak = 
4.377491037053e-223  3.029446976068e-216 ...
1.271610790463e-209  3.237410810582e-203 ...

(Large data can't be list directly, it can be accessed here: https://drive.google.com/file/d/0Bz1-hopez9CGTFdzU0t3RDAyaHc/edit?usp=sharing )

Matlab:

fft2(peak)               --(sample result)
12.5663706143590    -12.4458341615690
-12.4458341615690   12.3264538927637

Python:

np.fft.fft2(peak)        --(sample result)
12.56637061 +0.00000000e+00j -12.44583416 +3.42948517e-15j
-12.44583416 +3.35525358e-15j  12.32645389 -6.78073635e-15j

Please help me to explain why, and give suggestion on how to fix it.

Answer 1

The Fourier transform of a real, even function is real and even ( ref ). Therefore, it appears that your FFT should be real? Numpy is probably just struggling with the numerics while MATLAB may outright check for symmetry and force the solution to be real.

MATLAB uses FFTW3 while my research indicates Numpy uses a library called FFTPack. FFTW is one of the standards for FFT performance and uses a number of tricks to work quickly and perform calculations to the best precision possible. You can incredibly tiny numbers and this offers a number of numerical challenges that any library will be hard pressed to resolve.

You might consider executing the Python code against an FFTW3 wrapper like pyFFTW3 and see if you get similar results.

It appears that your input data is gaussian real and even, in which case we do expect the FFT2 of the signal to be real and even. If all your inputs are this way you could just take the real part. Or round to a certain precision. I would trust MATLAB's FFTW code over the Python code.

Or you could just ignore it. The differences are quite small and a value of 3e-15i is effectively zero for most applications. If you have automated the comparison, consider calling them equivalent if the mean square error of all the entries is less than some threshold (say 1e-8 or 1e-15 or 1e-20).