[pytorch] 通过一个例子分析torch.matmul矩阵与向量相乘的维度

我就是我 2023-10-05 08:14 7阅读 0赞

## pytorch文档中关于[torch.matmul()][torch.matmul]的维度说明如下： ##

>  *  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).

最后一项可能光看文档难以理解，下面举个例子：

1.  `>>a = torch.arange(0,18).view(2,3,3)`
2.  `>>b = torch.ones(3,dtype=torch.long)`
3.  `>>c = torch.matmul(a,b)`
4.  `>>d = torch.matmul(b,a)`
5.  `>>a.size()`
6.  `torch.Size([2, 3, 3])`
7.  `>>b.size()`
8.  `torch.Size([3])`
9.  `>>c.size()`
10. `torch.Size([2, 3])`
11. `>>d.size()`
12. `torch.Size([2, 3])`
13. `>>a[0]`
14. `tensor([[0, 1, 2],`
15. `[3, 4, 5],`
16. `[6, 7, 8]])`
17. `>>a[1]`
18. `tensor([[ 9, 10, 11],`
19. `[12, 13, 14],`
20. `[15, 16, 17]])`
21. `>>c`
22. `tensor([[ 3, 12, 21],`
23. `[30, 39, 48]])`
24. `>>d`
25. `tensor([[ 9, 12, 15],`
26. `[36, 39, 42]])`

通过分析上面的结果我们可以发现，c = torch.matmul(a,b)等价于将a\[0\]和a\[1\]这两个(3,3)维的矩阵与b这个3维向量相乘：a\[0\]×b和a\[1\]×b，而d = torch.matmul(b,a)只是相乘顺序相反：b×a\[0\]和b×a\[1\].

来源:[https://blog.csdn.net/CVAIDL/article/details/107752697][https_blog.csdn.net_CVAIDL_article_details_107752697]

[torch.matmul]: https://links.jianshu.com/go?to=%255Bhttps%3A%2F%2Fpytorch.org%2Fdocs%2Fstable%2Ftorch.html%3Fhighlight%3Dmatmul%23torch.matmul%255D%28https%3A%2F%2Fpytorch.org%2Fdocs%2Fstable%2Ftorch.html%3Fhighlight%3Dmatmul%23torch.matmul%29
[broadcasted]: https://links.jianshu.com/go?to=https%3A%2F%2Fpytorch.org%2Fdocs%2Fstable%2Fnotes%2Fbroadcasting.html%23broadcasting-semantics
[https_blog.csdn.net_CVAIDL_article_details_107752697]: https://blog.csdn.net/CVAIDL/article/details/107752697