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pytorch tensor内所有元素相乘实例

作者：某C姓工程师傅　　发布时间：2023-05-16 15:28:16　

标签：pytorch,tensor,元素相乘

tensor内所有元素相乘

a = torch.Tensor([1,2,3])
print(torch.prod(a))

输出

tensor(6.)

tensor乘法运算汇总与解析

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}")