广播语义

>>> x=torch.FloatTensor(5,7,3)
>>> y=torch.FloatTensor(5,7,3)
# 相同形状的质量可以被广播(上述规则总是成立的)

>>> x=torch.FloatTensor()
>>> y=torch.FloatTensor(2,2)
# can line up trailing dimensions
>>> x=torch.FloatTensor(5,3,4,1)
>>> y=torch.FloatTensor(  3,1,1)
# x 和 y 可以被广播
# 1st trailing dimension: both have size 1
# 2nd trailing dimension: y has size 1
# 3rd trailing dimension: x size == y size
# 但是:
>>> x=torch.FloatTensor(5,2,4,1)
>>> y=torch.FloatTensor(  3,1,1)
# x 和 y 不能被广播,因为在`3rd`中
# x and y are not broadcastable, because in the 3rd trailing dimension 2 != 3 

# 可以排列尾部维度,使阅读更容易
>>> x=torch.FloatTensor(5,1,4,1)
>>> y=torch.FloatTensor(  3,1,1)
>>> (x+y).size()
torch.Size([5, 3, 4, 1])

# 但不是必要的:
>>> x=torch.FloatTensor(1)
>>> y=torch.FloatTensor(3,1,7)
>>> (x+y).size()
torch.Size([3, 1, 7])

>>> x=torch.FloatTensor(5,2,4,1)
>>> y=torch.FloatTensor(3,1,1)
>>> (x+y).size()
RuntimeError: The size of tensor a (2) must match the size of tensor b (3) at non-singleton dimension 1 

>>> x=torch.FloatTensor(5,3,4,1)
>>> y=torch.FloatTensor(3,1,1)
>>> (x.add_(y)).size()
torch.Size([5, 3, 4, 1])

# but:
>>> x=torch.FloatTensor(1,3,1)
>>> y=torch.FloatTensor(3,1,7)
>>> (x.add_(y)).size()
RuntimeError: The expanded size of the tensor (1) must match the existing size (7) at non-singleton dimension 2. 

>>> torch.add(torch.ones(4,1), torch.randn(4)) 

>>> torch.utils.backcompat.broadcast_warning.enabled=True
>>> torch.add(torch.ones(4,1), torch.ones(4))
__main__:1: UserWarning: self and other do not have the same shape, but are broadcastable, and have the same number of elements.
Changing behavior in a backwards incompatible manner to broadcasting rather than viewing as 1-dimensional.