a * b，要求两个矩阵维度完全一致，即两个矩阵对应元素相乘，输出的维度也和原矩阵维度相同：
import torch
a = torch.randn(2,3)
b = torch.randn(2,3)
print(a)
print(b)
c = a * b
print(c.size())
print(c)
结果：
tensor([[-0.6309, -1.4365, -0.8549],
[ 1.1856, 0.8986, 1.6343]])
tensor([[-0.2452, -1.0548, 0.9490],
[-1.7368, 1.2816, -0.2548]])
(2, 3)
tensor([[ 0.1547, 1.5153, -0.8113],
[-2.0591, 1.1516, -0.4163]])
torch.mm(a,b)，要求两个矩阵维度是（n×m）和（m×p），即普通二维矩阵乘法
import torch
a = torch.randn(2,3)
b = torch.randn(3,2)
print(a)
print(b)
c = torch.mm(a,b)
print(c.size())
print(c)
结果：
tensor([[ 1.0326, -0.8577, 0.9282],
[-0.1615, 2.2162, 1.1355]])
tensor([[-0.2482, -0.7289],
[-1.4625, 0.9330],
[-0.6411, -1.5660]])
(2, 2)
tensor([[ 0.4031, -3.0065],
[-3.9292, 0.4072]])
torch.matul(a,b)，matmul可以进行张量乘法，输入可以是高维，当输入是多维时，把多出的一维作为batch提出来，其他部分做矩阵乘法
import torch
a = torch.randn(5,3,4)
b = torch.randn(4,2)
print(a)
print(b)
c = torch.matmul(a,b)
print(c.size())
print(c)
结果：
tensor([[[-0.6082, -0.4990, 0.5180, 0.4803],
[ 0.4278, -1.4530, 0.7533, 2.0362],
[-0.7447, -0.4938, 0.9194, 0.7219]],
[[-0.9034, 3.1070, -0.0789, -0.1922],
[-0.7752, -0.0700, -1.2752, -0.1430],
[-0.1135, 0.4542, 1.5085, -0.8310]],
[[-0.4306, -0.7926, 0.0455, -1.4027],
[ 1.8869, -1.3122, -0.1038, 1.8231],
[-0.6760, -0.4332, -0.9828, -1.0844]],
[[-0.9391, 0.0992, -0.3816, 1.7813],
[ 0.4111, -1.3645, -1.2178, 0.9432],
[ 1.4839, 0.6080, -0.3512, -0.9438]],
[[-0.8659, -0.4728, -0.6430, 0.7306],
[ 2.1543, -0.0352, 0.3309, -0.8087],
[ 2.3823, 0.4962, -0.0237, -0.0065]]])
tensor([[ 0.2750, 0.5015],
[-0.5091, -0.2192],
[-0.1881, -0.3595],
[-1.0113, -0.1662]])
(5, 3, 2)
tensor([[[-0.4963, -0.4617],
[-1.3434, -0.0761],
[-0.8563, -0.7157]],
[[-1.6210, -1.0739],
[ 0.2070, 0.1088],
[ 0.2941, -0.5607]],
[[ 1.6951, 0.1746],
[-0.6372, 0.9683],
[ 1.3162, 0.2895]],
[[-2.0383, -0.6516],
[ 0.0830, 0.7864],
[ 1.1189, 0.8940]],
[[-0.6152, -0.2209],
[ 1.3658, 1.1036],
[ 0.4134, 1.0956]]])
import torch
a = torch.randn(2,5,3)
b = torch.randn(1,3,4)
print(a)
print(b)
c = torch.matmul(a,b)
print(c.size())
print(c)
结果：
tensor([[[ 1.3973, -0.6357, -1.1457],
[-1.0271, -0.0732, 0.8141],
[ 0.0373, 0.2833, 0.1024],
[-0.0090, -1.4797, 0.1669],
[ 1.2712, -0.0930, 1.0184]],
[[-2.2818, -0.6199, 0.5868],
[ 0.8801, 0.7427, 1.1135],
[ 0.7952, -0.1778, 1.2183],
[ 0.8849, -0.2708, -0.2155],
[-0.1221, 0.5816, 3.0285]]])
tensor([[[ 0.0745, -0.6830, -0.6044, 0.0647],
[-1.5686, 0.3620, 0.8491, 1.0607],
[ 1.3519, 0.7895, 1.4727, 0.8019]]])
(2, 5, 4)
tensor([[[-0.4477, -2.0890, -3.0716, -1.5026],
[ 1.1389, 1.3178, 1.7576, 0.5088],
[-0.3032, 0.1579, 0.3689, 0.3851],
[ 2.5459, -0.3977, -1.0052, -1.4362],
[ 1.6174, -0.0979, 0.6526, 0.8003]],
[[ 1.5957, 1.7975, 1.7169, -0.3346],
[ 0.4058, 0.5468, 1.7386, 1.7377],
[ 1.9851, 0.3543, 1.1625, 0.8398],
[ 0.1993, -0.8726, -1.0822, -0.4028],
[ 3.1728, 2.6848, 5.0278, 3.0376]]])
总结：
1. a * b 要求两个矩阵输入维度一致，即矩阵对应元素相乘
2. 当输入是二维矩阵时，torch.mm(a,b)和torch.matul(a,b)是一样的
3. torch.matul(a,b)可计算高维矩阵相乘，此时，把多出的一维作为batch提出来，其他部分做矩阵乘法
