A PyTorch wrapper for CUDA FFTs

pip install pytorch-fft==0.15


A PyTorch wrapper for CUDA FFTs License

A package that provides a PyTorch C extension for performing batches of 2D CuFFT transformations, by Eric Wong


This package is on PyPi. Install with pip install pytorch-fft.


  • From the pytorch_fft.fft module, you can use the following to do foward and backward FFT transformations (complex to complex)
    • fft and ifft for 1D transformations
    • fft2 and ifft2 for 2D transformations
    • fft3 and ifft3 for 3D transformations
  • From the same module, you can also use the following for real to complex / complex to real FFT transformations
    • rfft and irfft for 1D transformations
    • rfft2 and irfft2 for 2D transformations
    • rfft3 and irfft3 for 3D transformations
  • For an d-D transformation, the input tensors are required to have >= (d+1) dimensions (n1 x ... x nk x m1 x ... x md) where n1 x ... x nk is the batch of FFT transformations, and m1 x ... x md are the dimensions of the d-D transformation. d must be a number from 1 to 3.
  • Finally, the module contains the following helper functions you may find useful
    • reverse(X, group_size=1) reverses the elements of a tensor and returns the result in a new tensor. Note that PyTorch does not current support negative slicing, see this issue. If a group size is supplied, the elements will be reversed in groups of that size.
    • expand(X, imag=False, odd=True) takes a tensor output of a real 2D or 3D FFT and expands it with its redundant entries to match the output of a complex FFT.
  • For autograd support, use the following functions in the pytorch_fft.fft.autograd module:
    • Fft and Ifft for 1D transformations
    • Fft2d and Ifft2d for 2D transformations
    • Fft3d and Ifft3d for 3D transformations
# Example that does a batch of three 2D transformations of size 4 by 5. 
import torch
import pytorch_fft.fft as fft

A_real, A_imag = torch.randn(3,4,5).cuda(), torch.zeros(3,4,5).cuda()
B_real, B_imag = fft.fft2(A_real, A_imag)
fft.ifft2(B_real, B_imag) # equals (A, zeros)

B_real, B_imag = fft.rfft2(A) # is a truncated version which omits
                                   # redundant entries

reverse(torch.arange(0,6)) # outputs [5,4,3,2,1,0]
reverse(torch.arange(0,6), 2) # outputs [4,5,2,3,0,1]

expand(B_real) # is equivalent to  fft.fft2(A, zeros)[0]
expand(B_imag, imag=True) # is equivalent to  fft.fft2(A, zeros)[1]
# Example that uses the autograd for 2D fft:
import torch
from torch.autograd import Variable
import pytorch_fft.fft.autograd as fft
import numpy as np

f = fft.Fft2d()
invf= fft.Ifft2d()

fx, fy = (Variable(torch.arange(0,100).view((1,1,10,10)).cuda(), requires_grad=True), 
          Variable(torch.zeros(1, 1, 10, 10).cuda(),requires_grad=True))
k1,k2 = f(fx,fy)
z = k1.sum() + k2.sum()
print(fx.grad, fy.grad)


  • This follows NumPy semantics and behavior, so ifft2(fft2(x)) = x. Note that CuFFT semantics for inverse FFT only flip the sign of the transform, but it is not a true inverse.
  • Similarly, the real to complex / complex to real variants also follow NumPy semantics and behavior. In the 1D case, this means that for an input of size N, it returns an output of size N//2+1 (it omits redundant entries, see the Numpy docs)
  • The functions in the pytorch_fft.fft module do not implement the PyTorch autograd Function, and are semantically and functionally like their numpy equivalents.
  • Autograd functionality is in the pytorch_fft.fft.autograd module.

Repository contents

  • pytorch_fft/src: C source code
  • pytorch_fft/fft: Python convenience wrapper
  • build.py: compilation file
  • test.py: tests against NumPy FFTs and Autograd checks

Issues and Contributions

If you have any issues or feature requests, file an issue or send in a PR.