在新旧版的torch中的傅里叶变换函数在定义和用法上存在不同，记录一下。
1、旧版
fft = torch.rfft(input, 2, normalized=True, onesided=False) # input 为输入的图片或者向量，dtype=torch.float32，size比如为[1,3,64,64] # signal_ndim(int):The number of dimensions in each signal,can only be 1、2、3 # normalized(bool,optional):controls wheather to return normallized results. Default:False # onesided(bool,optional):controls whether to return half of results to avoid redundancy.Default:True
上面例子中图像中 singal_ndim = 2 ,是因为输入图像是2维的。
1.7之后的版本中，如果要用 oneside output，则改用torch.fft.rfft();如果要用two-side output，则改用torch.fft.fft()
input= torch.arange(4) fft = torch.rfft(input, 2, normalized=True, onesided=False)
2、新版
一维离散傅里叶变换
torch.fft.rfft(input,n=None,dim=-1,norm=None) --> Tensor
# input:Tensor
# n(int,optional):Output signal length. This determines the length of the
output signal.
# dim(int, optional): The dimension along which to take the one dimensional real IFFT.
# norm (str, optional): Normalization mode.
二维离散傅里叶变换
torch.fft.rfft2(input, s=None, dim=(-2, -1), norm=None, *, out=None) -> Tensor input (Tensor): the input tensor s (Tuple[int], optional): Signal size in the transformed dimensions. dim (Tuple[int], optional): Dimensions to be transformed. norm (str, optional): Normalization mode.
高维离散傅里叶变换
rfftn(input, s=None, dim=None, norm=None, *, out=None) -> Tensor input (Tensor): the input tensor s (Tuple[int], optional): Signal size in the transformed dimensions. dim (Tuple[int], optional): Dimensions to be transformed. norm (str, optional): Normalization mode. For the forward transform
3、新旧版对比
import torch input = torch.rand(1,3,32,32) # 旧版pytorch.rfft()函数 fft = torch.rfft(input, 2, normalized=True, onesided=False) # 新版 pytorch.fft.rfft2()函数 output = torch.fft.fft2(input, dim=(-2, -1)) output = torch.stack((output.real, output_new.imag), -1)
ffted = torch.rfft(input, 1, onesided=False) to ffted = torch.view_as_real(torch.fft.fft(input, dim=1)) and iffted = torch.irfft(time_step_as_inner, 1, onesided=False) to iffted = torch.fft.irfft(torch.view_as_complex(time_step_as_inner), n=time_step_as_inner.shape[1], dim=1)
补充：使用numpy模拟torch.fft.fft拯救paddle
import numpy as np
import torch
import paddle
def paddle_fft(x,dim=-1):
if dim==-1:
return paddle.to_tensor(np.fft.fft(x.numpy()))
else:
shape= [i for i in range(len(x.shape))]
shape[dim],shape[-1]=shape[-1],shape[dim]
x=np.transpose(np.fft.fft(np.transpose(x.numpy(), shape)),shape)
return paddle.to_tensor(x)
if __name__ == '__main__':
data=paddle.to_tensor(np.array([[[1, 4, 3], [1, 2, 3]], [[1, 2, 3], [1, 2, 3]]]))
paddle_f_d=paddle_fft(paddle_fft(data,-1),-2)
torch_f_d =paddle_fft(torch.fft.fft(torch.Tensor(data.numpy()),dim=-1),-2)
print(paddle_f_d.numpy())
print(torch_f_d.numpy())
总结
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