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Scipy ifft gives different results with seemingly identical input

Why would xcorr and xcorr2 be quite different here? M1 and M2 are numpy matrices. M1.shape[0] = M2.shape[0]. xcorr is what I would expect with this operation, but xcorr2 is something totally different and has imaginary numbers. xcorr does not have imaginary numbers.

from scipy.fft import fft, ifft

xcorr = np.zeros((M1.shape[0],M1.shape[1],M2.shape[1]))  
xcorr2 = xcorr.copy()

N = M1.shape[1]
for i in range(N):
    V = M1[:,i][:,None]
    xcorr[:,:,i] = ifft(fft(M2,axis = 0) * fft(np.flipud(V), axis = 0) ,axis = 0)

for i in range(N):
    V = M1[:,i][:,None]
    xcorr2[:,:,i] = fft(M2,axis = 0) * fft(np.flipud(V), axis = 0)        
xcorr2 = ifft(xcorr2, axis = 0)

Answer

Try giving xcorr and xcorr2 dtype=complex.

xcorr = np.zeros((M1.shape[0],M1.shape[1],M2.shape[1]), dtype=complex)  
xcorr2 = xcorr.copy()

According to scipy docs, the output from both fft and ifft is a complex ndarray.

You create xcorr and xcorr2 with np.zeros(), so it’ll have a default dtype of float64.

Putting the output from fft into the xcorr2 will result in a cast of complex to float64, that results in the imaginary part being discarded.

When you feed xcorr2 into ifft() it has no imaginary part, so you get a different result.

The cast is also why you don’t see the imaginary part in xcorr.