pytorch的matmul怎么广播

1）如果是两个1维的，就向量内积；
2）如果两个都是2维的，就矩阵相乘
3）如果第一个是1维，第二个是2维；填充第一个使得能够和第二个参数相乘；如果第一个是2维，第二个是1维，就是矩阵和向量相乘；
例：

a = torch.zeros(7,)
b= torch.zeros(7,8)

>>> torch.matmul(a,b)
tensor([0., 0., 0., 0., 0., 0., 0., 0.])

如果a是5,8维，报错。

例子2：

a = torch.zeros(8,)
b= torch.zeros(7,8)

>>> torch.matmul(b,a)
tensor([0., 0., 0., 0., 0., 0., 0.])

如果a是5,7维，报错。

4) 高维情况

i）其中一个1维，另一个N维（N>2): 类似3），即需要靠近的那个维数相同，比如（7，）和（7,8,11），又比如（7,8,11）和（11，）

ii）都高于2维，那么除掉最后两个维度之外（两个数的维数满足矩阵乘法，即，(m,p)和(p,n)），剩下的纬度满足pytorch的广播机制。比如：

# can line up trailing dimensions
>>> x=torch.empty(5,3,4,1)
>>> y=torch.empty(  3,1,1)
# x and y are broadcastable.
# 1st trailing dimension: both have size 1
# 2nd trailing dimension: y has size 1
# 3rd trailing dimension: x size == y size
# 4th trailing dimension: y dimension doesn't exist

https://pytorch.org/docs/stable/notes/broadcasting.html#broadcasting-semantics

https://pytorch.org/docs/stable/torch.html?highlight=matmul#torch.matmul

torch.matmul(tensor1, tensor2, out=None) → Tensor：

# can line up trailing dimensions
>>> x=torch.empty(5,3,4,1)
>>> y=torch.empty(  3,1,1)
# x and y are broadcastable.
# 1st trailing dimension: both have size 1
# 2nd trailing dimension: y has size 1
# 3rd trailing dimension: x size == y size
# 4th trailing dimension: y dimension doesn't exist

###########################################################################需要除掉两个数的后两个维度，然后再看是否满足广播机制
torch.matmul(tensor1, tensor2, out=None) → Tensor

Matrix product of two tensors.

The behavior depends on the dimensionality of the tensors as follows:

• If both tensors are 1-dimensional, the dot product (scalar) is returned.

• If both arguments are 2-dimensional, the matrix-matrix product is returned.

• If the first argument is 1-dimensional and the second argument is 2-dimensional, a 1 is prepended to its dimension for the purpose of the matrix multiply. After the matrix multiply, the prepended dimension is removed.

• If the first argument is 2-dimensional and the second argument is 1-dimensional, the matrix-vector product is returned.

• If both arguments are at least 1-dimensional and at least one argument is N-dimensional (where N > 2), then a batched matrix multiply is returned. If the first argument is 1-dimensional, a 1 is prepended to its dimension for the purpose of the batched matrix multiply and removed after. If the second argument is 1-dimensional, a 1 is appended to its dimension for the purpose of the batched matrix multiple and removed after. The non-matrix (i.e. batch) dimensions are broadcasted (and thus must be broadcastable). For example, if tensor1 is a (j \times 1 \times n \times m)(j×1×n×m)tensor and tensor2 is a (k \times m \times p)(k×m×p) tensor, out will be an (j \times k \times n \times p)(j×k×n×p) tensor.