Numpy offers optimized outer operations for any RxR -> R function, like np.multiply.outer or np.subtract.outer, with the behaviour:
>>> np.subtract.outer([6, 5, 4], [3, 2, 1])
array([[3, 4, 5],
[2, 3, 4],
[1, 2, 3]])
Pytorch does not seem to offer such a feature (or I have missed it).
What is the best / usual / fastest / cleanest way to do so with torch tensors?
Per the documenation:
Many PyTorch operations support NumPy Broadcasting Semantics.
An outer subtraction is a broadcasted subtraction from a 2d array to a 1d array, so essentially you can reshape the first array to (3, 1) and then subtract the second array from it:
x = torch.Tensor([6, 5, 4])
y = torch.Tensor([3, 2, 1])
x.reshape(-1, 1) - y
#tensor([[3., 4., 5.],
# [2., 3., 4.],
# [1., 2., 3.]])