Complex numbers in ifft(fft(x))

Hi, i want to realize a convolution through fft and i also want to compare the time required for this process between gpu and cpu. Here is the code:

len=100000;
x=randi(50,1,len);
y=randi(50,1,len);
tic
l=gpuArray([x zeros(1,len-1)]);                       
m=gpuArray([y zeros(1,len-1)]);                      
c_1_temp=ifft(fft(l).*fft(m));                             
toc                                                        
c_1=gather(c_1_temp);
tic
l_1=[x zeros(1,len-1)];                                
m_1=[y zeros(1,len-1)];                              
c_2=ifft(fft(l_1,2*len-1).*fft(m_1,2*len-1));                    
toc

But strangely i've found this result:

c_1= 559,999999985352 - 4,88283691418457e-09i  1655,00000000398 - 1,39078548907368e-08i  3569,99999999371 + 7,06640683828822e-09i  5104,99999999144 + 2,13079904230657e-08i  6494,99999999661 - 1,24666866807290e-08i  7888,00000000453 - 3,32333192044652e-08i  8864,99999998867 - 4,37161194092030e-09i  8850,99999999144 - 1,35629723232990e-08i  8513,99999995740 - 1,81275757497787e-08i  8608,99999998969 + 3,02029185265248e-08i  8493,99999997188 - 1,37329756956340e-08i

and

c_2= 559,999999995117  1655,00000000488  3569,99999998047  5105  6494,99999998047  7888,00000001587  8864,99999998657  8850,99999997559  8513,99999997314  8609,00000001221  8494,00000000122

The same operation for gpu gives complex value which is approximately real.

WHY?

Answer 1

[Joss Knight]

I'm not sure but I assume it's because the GPU FFT computation is non-deterministic. The order of operations is not preserved between FFT and IFFT and so round-off creeps in, whereas on the CPU everything cancels out perfectly. You can enforce symmetricity in the IFFT using the 'symmetric' option.

[Damiano Capocci]

Yes absolutely. Thank you.

ps: with the option symmetric is all ok but is slower.

Answer 2

[Edric Ellis]

The gpuArray implementation of the fft family of functions always returns complex results. This is described in the help text, accessed via help gpuArray/fft. The reason for this is that the output of the fft operation might need to be complex, and to be efficient, the implementation chooses always to return complex data. (The alternative is to perform the fft and then delete the imaginary part if it turns out to be all-zero - the gpuArray methods differ from built-in MATLAB methods in that they never do this).

[Damiano Capocci]

Ok perfect, thank you