pytorch常用的乘法运算以及相关的运算符(@、*）

这里总结一下pytorch常用的乘法运算以及相关的运算符(@、*）。

总结放前面：

torch.mm : 用于两个矩阵（不包括向量）的乘法。如维度为(l,m)和(m,n)相乘

torch.bmm : 用于带batch的三维向量的乘法。如维度为(b,l,m)和(b,m,n)相乘

torch.mul : 用于两个同维度矩阵的逐像素点相乘（点乘）。如维度为(l,m)和(l,m)相乘

torch.mv : 用于矩阵和向量之间的乘法（矩阵在前，向量在后）。如维度为(l,m)和(m)相乘，结果的维度为(l)。

torch.matmul : 用于两个张量(后两维满足矩阵乘法的维度)相乘或者是矩阵与向量间的乘法，因为其具有广播机制(broadcasting，自动补充维度)。如维度为(b,l,m)和(b,m,n)；(l,m)和(b,m,n)；(b,c,l,m)和(b,c,m,n)；(l,m)和(m)相乘等。【其作用包含torch.mm、torch.bmm和torch.mv】

@运算符 : 其作用类似于torch.matmul。

*运算符 : 其作用类似于torch.mul。

1、torch.mm

import torch
a = torch.ones(1, 2)
print(a)
b = torch.ones(2, 3)
print(b)
output = torch.mm(a, b)
print(output)
print(output.size())
"""
tensor([[1., 1.]])
tensor([[1., 1., 1.],
        [1., 1., 1.]])
tensor([[2., 2., 2.]])
torch.Size([1, 3])
"""

2、torch.bmm

a = torch.randn(2, 1, 2)
print(a)
b = torch.randn(2, 2, 3)
print(b)
output = torch.bmm(a, b)
print(output)
print(output.size())
"""
tensor([[[-0.1187,  0.2110]],

        [[ 0.7463, -0.6136]]])
tensor([[[-0.1186,  1.5565,  1.3662],
         [ 1.0199,  2.4644,  1.1630]],

        [[-1.9483, -1.6258, -0.4654],
         [-0.1424,  1.3892,  0.7559]]])
tensor([[[ 0.2293,  0.3352,  0.0832]],

        [[-1.3666, -2.0657, -0.8111]]])
torch.Size([2, 1, 3])
"""

3、torch.mul

a = torch.ones(2, 3) * 2
print(a)
b = torch.randn(2, 3)
print(b)
output = torch.mul(a, b)
print(output)
print(output.size())
"""
tensor([[2., 2., 2.],
        [2., 2., 2.]])
tensor([[-0.1187,  0.2110,  0.7463],
        [-0.6136, -0.1186,  1.5565]])
tensor([[-0.2375,  0.4220,  1.4925],
        [-1.2271, -0.2371,  3.1130]])
torch.Size([2, 3])
"""

4、torch.mv

mat = torch.randn(3, 4)
print(mat)
vec = torch.randn(4)
print(vec)
output = torch.mv(mat, vec)
print(output)
print(output.size())
print(torch.mm(mat, vec.unsqueeze(1)).squeeze(1))
"""
tensor([[-0.1187,  0.2110,  0.7463, -0.6136],
        [-0.1186,  1.5565,  1.3662,  1.0199],
        [ 2.4644,  1.1630, -1.9483, -1.6258]])
tensor([-0.4654, -0.1424,  1.3892,  0.7559])
tensor([ 0.5982,  2.5024, -5.2481])
torch.Size([3])
tensor([ 0.5982,  2.5024, -5.2481])
"""

5、torch.matmul

# 其作用包含torch.mm、torch.bmm和torch.mv。其他类似，不一一举例。
a = torch.randn(2, 1, 2)
print(a)
b = torch.randn(2, 2, 3)
print(b)
output = torch.bmm(a, b)
print(output)
output1 = torch.matmul(a, b)
print(output1)
print(output1.size())
"""
tensor([[[-0.1187,  0.2110]],

        [[ 0.7463, -0.6136]]])
tensor([[[-0.1186,  1.5565,  1.3662],
         [ 1.0199,  2.4644,  1.1630]],

        [[-1.9483, -1.6258, -0.4654],
         [-0.1424,  1.3892,  0.7559]]])
tensor([[[ 0.2293,  0.3352,  0.0832]],

        [[-1.3666, -2.0657, -0.8111]]])
tensor([[[ 0.2293,  0.3352,  0.0832]],

        [[-1.3666, -2.0657, -0.8111]]])
torch.Size([2, 1, 3])
"""

# 维度为(b,l,m)和(b,m,n)；(l,m)和(b,m,n)；(b,c,l,m)和(b,c,m,n)；(l,m)和(m)等
a = torch.randn(2, 3, 4)
b = torch.randn(2, 4, 5)
print(torch.matmul(a, b).size())
a = torch.randn(3, 4)
b = torch.randn(2, 4, 5)
print(torch.matmul(a, b).size())
a = torch.randn(2, 3, 3, 4)
b = torch.randn(2, 3, 4, 5)
print(torch.matmul(a, b).size())
a = torch.randn(2, 3)
b = torch.randn(3)
print(torch.matmul(a, b).size())
"""
torch.Size([2, 3, 5])
torch.Size([2, 3, 5])
torch.Size([2, 3, 3, 5])
torch.Size([2])
"""

6、@运算符

# @运算符:其作用类似于torch.matmul
a = torch.randn(2, 3, 4)
b = torch.randn(2, 4, 5)
print(torch.matmul(a, b).size())
print((a @ b).size())
a = torch.randn(3, 4)
b = torch.randn(2, 4, 5)
print(torch.matmul(a, b).size())
print((a @ b).size())
a = torch.randn(2, 3, 3, 4)
b = torch.randn(2, 3, 4, 5)
print(torch.matmul(a, b).size())
print((a @ b).size())
a = torch.randn(2, 3)
b = torch.randn(3)
print(torch.matmul(a, b).size())
print((a @ b).size())
"""
torch.Size([2, 3, 5])
torch.Size([2, 3, 5])
torch.Size([2, 3, 5])
torch.Size([2, 3, 5])
torch.Size([2, 3, 3, 5])
torch.Size([2, 3, 3, 5])
torch.Size([2])
torch.Size([2])
"""

7、*运算符

# *运算符:其作用类似于torch.mul
a = torch.ones(2, 3) * 2
print(a)
b = torch.ones(2, 3) * 3
print(b)
output = torch.mul(a, b)
print(output)
print(output.size())
output1 = a * b
print(output1)
print(output1.size())
"""
tensor([[2., 2., 2.],
        [2., 2., 2.]])
tensor([[3., 3., 3.],
        [3., 3., 3.]])
tensor([[6., 6., 6.],
        [6., 6., 6.]])
torch.Size([2, 3])
tensor([[6., 6., 6.],
        [6., 6., 6.]])
torch.Size([2, 3])
"""