pytorch 有多种乘法运算，在这里做一次全面的总结。
元素一一相乘
该操作又称作 "哈达玛积", 简单来说就是 tensor 元素逐个相乘。这个操作，是通过 也就是常规的乘号操作符定义的操作结果。torch.mul 是等价的。
import torch
def element_by_element():
x = torch.tensor([1, 2, 3])
y = torch.tensor([4, 5, 6])
return x * y, torch.mul(x, y)
element_by_element()
(tensor([ 4, 10, 18]), tensor([ 4, 10, 18]))
这个操作是可以 broad cast 的。
def element_by_element_broadcast():
x = torch.tensor([1, 2, 3])
y = 2
return x * y
element_by_element_broadcast()
tensor([2, 4, 6])
向量点乘
torch.matmul: If both tensors are 1-dimensional, the dot product (scalar) is returned.
如果都是1维的，返回的就是 dot product 结果
def vec_dot_product():
x = torch.tensor([1, 2, 3])
y = torch.tensor([4, 5, 6])
return torch.matmul(x, y)
vec_dot_product()
tensor(32)
矩阵乘法
torch.matmul: If both arguments are 2-dimensional, the matrix-matrix product is returned.
如果都是2维，那么就是矩阵乘法的结果返回。与 torch.mm 是等价的，torch.mm 仅仅能处理的是矩阵乘法。
def matrix_multiple():
x = torch.tensor([
[1, 2, 3],
[4, 5, 6]
])
y = torch.tensor([
[7, 8],
[9, 10],
[11, 12]
])
return torch.matmul(x, y), torch.mm(x, y)
matrix_multiple()
(tensor([[ 58, 64],
[139, 154]]), tensor([[ 58, 64],
[139, 154]]))
vector 与 matrix 相乘
torch.matmul: 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.
如果第一个是 vector, 第二个是 matrix, 会在 vector 中增加一个维度。也就是 vector 变成了 与 matrix
相乘之后，变成
, 在结果中将
维 再去掉。
def vec_matrix():
x = torch.tensor([1, 2, 3])
y = torch.tensor([
[7, 8],
[9, 10],
[11, 12]
])
return torch.matmul(x, y)
vec_matrix()
tensor([58, 64])
matrix 与 vector 相乘
同样的道理， vector会被扩充一个维度。
def matrix_vec():
x = torch.tensor([
[1, 2, 3],
[4, 5, 6]
])
y = torch.tensor([
7, 8, 9
])
return torch.matmul(x, y)
matrix_vec()
tensor([ 50, 122])
带有batch_size 的 broad cast乘法
def batched_matrix_broadcasted_vector():
x = torch.tensor([
[
[1, 2], [3, 4]
],
[
[5, 6], [7, 8]
]
])
print(f"x shape: {x.size()} \n {x}")
y = torch.tensor([1, 3])
return torch.matmul(x, y)
batched_matrix_broadcasted_vector()
x shape: torch.Size([2, 2, 2])
tensor([[[1, 2],
[3, 4]],
[[5, 6],
[7, 8]]])
tensor([[ 7, 15],
[23, 31]])
batched matrix x batched matrix
def batched_matrix_batched_matrix():
x = torch.tensor([
[
[1, 2, 1], [3, 4, 4]
],
[
[5, 6, 2], [7, 8, 0]
]
])
y = torch.tensor([
[
[1, 2],
[3, 4],
[5, 6]
],
[
[7, 8],
[9, 10],
[1, 2]
]
])
print(f"x shape: {x.size()} \n y shape: {y.size()}")
return torch.matmul(x, y)
xy = batched_matrix_batched_matrix()
print(f"xy shape: {xy.size()} \n {xy}")
x shape: torch.Size([2, 2, 3])
y shape: torch.Size([2, 3, 2])
xy shape: torch.Size([2, 2, 2])
tensor([[[ 12, 16],
[ 35, 46]],
[[ 91, 104],
[121, 136]]])
上面的效果与 torch.bmm 是一样的。matmul 比 bmm 功能更加强大，但是 bmm 的语义非常明确， bmm 处理的只能是 3维的。
def batched_matrix_batched_matrix_bmm():
x = torch.tensor([
[
[1, 2, 1], [3, 4, 4]
],
[
[5, 6, 2], [7, 8, 0]
]
])
y = torch.tensor([
[
[1, 2],
[3, 4],
[5, 6]
],
[
[7, 8],
[9, 10],
[1, 2]
]
])
print(f"x shape: {x.size()} \n y shape: {y.size()}")
return torch.bmm(x, y)
xy = batched_matrix_batched_matrix()
print(f"xy shape: {xy.size()} \n {xy}")
x shape: torch.Size([2, 2, 3])
y shape: torch.Size([2, 3, 2])
xy shape: torch.Size([2, 2, 2])
tensor([[[ 12, 16],
[ 35, 46]],
[[ 91, 104],
[121, 136]]])
tensordot
这个函数还没有特别清楚。
def tesnordot():
x = torch.tensor([
[1, 2, 1],
[3, 4, 4]])
y = torch.tensor([
[7, 8],
[9, 10],
[1, 2]])
print(f"x shape: {x.size()}, y shape: {y.size()}")
return torch.tensordot(x, y, dims=([0], [1]))
tesnordot()
x shape: torch.Size([2, 3]), y shape: torch.Size([3, 2])
tensor([[31, 39, 7],
[46, 58, 10],
[39, 49, 9]])
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