torch.fft.ihfft2

torch.fft.ihfft2(input, s=None, dim=(-2, -1), norm=None, *, out=None) → Tensor

Computes the 2-dimensional inverse discrete Fourier transform of real input. Equivalent to ihfftn() but transforms only the two last dimensions by default.

Note

Supports torch.half on CUDA with GPU Architecture SM53 or greater. However it only supports powers of 2 signal length in every transformed dimensions.

Parameters

• input (Tensor) – the input tensor

• s (Tuple[int], optional) – Signal size in the transformed dimensions. If given, each dimension dim[i] will either be zero-padded or trimmed to the length s[i] before computing the Hermitian IFFT. If a length -1 is specified, no padding is done in that dimension. Default: s = [input.size(d) for d in dim]

• dim (Tuple[int], optional) – Dimensions to be transformed. Default: last two dimensions.

• norm (str, optional) –

  Normalization mode. For the backward transform (ihfft2()), these correspond to:

  • "forward" - no normalization

  • "backward" - normalize by 1/n

  • "ortho" - normalize by 1/sqrt(n) (making the Hermitian IFFT orthonormal)

  Where n = prod(s) is the logical IFFT size. Calling the forward transform (hfft2()) with the same normalization mode will apply an overall normalization of 1/n between the two transforms. This is required to make ihfft2() the exact inverse.

  Default is "backward" (normalize by 1/n).

Keyword Arguments

out (Tensor, optional) – the output tensor.

Example

>>> T = torch.rand(10, 10)
>>> t = torch.fft.ihfft2(t)
>>> t.size()
torch.Size([10, 6])

Compared against the full output from ifft2(), the Hermitian time-space signal takes up only half the space.

>>> fftn = torch.fft.ifft2(t)
>>> torch.allclose(fftn[..., :6], rfftn)
True

The discrete Fourier transform is separable, so ihfft2() here is equivalent to a combination of ifft() and ihfft():

>>> two_ffts = torch.fft.ifft(torch.fft.ihfft(t, dim=1), dim=0)
>>> torch.allclose(t, two_ffts)
True