Complex derivative of real-to-real function

autograd
1

Hello, can anyone please point out what I do wrong in the computation of the following two functions? Both f1 and f2 should be identical and real-to-real functions and therefore should give the same derivative. However, they give a different output :frowning: Thanks a lot.

import torch

def f1(x):
    return torch.view_as_complex(torch.Tensor([x, 0])).unsqueeze(0).abs()

def f2(x):
    return torch.Tensor(x).abs()

x = torch.Tensor([1])
print(torch.autograd.functional.jacobian(f1, x))
print(torch.autograd.functional.jacobian(f2, x))

outputs

tensor([[0.]])
tensor([[1.]])
2

Problem solved by replacing f1 by

def f1(x):
    return torch.view_as_complex(torch.hstack((x,torch.zeros_like(x)))).unsqueeze(0).abs()