[DL] introduction and understanding of tensor

1. Preface

In deep learning , We are sure to encounter a noun ： tensor （tensor）. For one dimension 、 Two dimensional is easy for us to understand , But three-dimensional 、 4 d 、…、n dimension , How do we understand ？ Now we will pytorch Take the deep learning framework as an example to introduce in detail .

2. A one-dimensional

import torch #  edition ：1.8.0+cpu
a = torch.tensor([1,2,3,4])
print(a)
print(a.shape)

Output ：

tensor([1, 2, 3, 4])
torch.Size([4])

The output has only one dimension , So it's one-dimensional .

3. A two-dimensional

import torch #  edition ：1.8.0+cpu
a = torch.tensor([[1,2,3,4]])
print(a)
print(a.shape)

Output ：

tensor([[1, 2, 3, 4]])
torch.Size([1, 4])

The output above has rows and columns , So it's a two-dimensional tensor , It's actually a two-dimensional matrix .

4. The three dimensional

import torch #  edition ：1.8.0+cpu
a = torch.ones(1,3,3)
print(a)
print(a.shape)

Output ：

tensor([[[1., 1., 1.],
         [1., 1., 1.],
         [1., 1., 1.]]])
torch.Size([1, 3, 3])

From the output results, we can see that this tensor has three dimensions , There is one more dimension ahead 1. But I can't see this intuitively 1 Where is it reflected . Now let's look at a tensor , Intuitively feel where the front dimension is reflected ：

import torch #  edition ：1.8.0+cpu
a = torch.ones(3,4,5)
print(a)
print(a.shape)

Output ：

tensor([[[1., 1., 1., 1., 1.],
         [1., 1., 1., 1., 1.],
         [1., 1., 1., 1., 1.],
         [1., 1., 1., 1., 1.]],

        [[1., 1., 1., 1., 1.],
         [1., 1., 1., 1., 1.],
         [1., 1., 1., 1., 1.],
         [1., 1., 1., 1., 1.]],

        [[1., 1., 1., 1., 1.],
         [1., 1., 1., 1., 1.],
         [1., 1., 1., 1., 1.],
         [1., 1., 1., 1., 1.]]])
torch.Size([3, 4, 5])

Output the results from above , You can intuitively feel the front dimension （ Numbers 3） The embodiment of ;
The first number 3： Divide into 3 Big row
The second number 4： Each line is divided into 4 Xiaoxing
The third number 5： Each line is divided into 5 Small column
So the dimension of data is 3×4×5, The last number represents the dimension of the column ; We can also understand it as 3 individual 4 That's ok 5 Columns of data .

If we compare the above tensor to a RGB Image , Numbers 3 Express 3 Channels , The size of each channel is 4 That's ok 5 Column .

5. 4 d

import torch #  edition ：1.8.0+cpu
a = torch.ones(2,3,4,5)
print(a)
print(a.shape)

Output ：

tensor([[[[1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.]],

         [[1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.]],

         [[1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.]]],


        [[[1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.]],

         [[1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.]],

         [[1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.],
          [1., 1., 1., 1., 1.]]]])
torch.Size([2, 3, 4, 5])

We separate the above output with a split line ：

The upper part of the red line is a “ dimension ”, Here is another “ dimension ”, So there are two dimensions .
Let's be a little bit more straightforward , Tensor a, Yes 2 Big row , Each line is divided again 3 Xiaoxing , Each line is divided again 4 That's ok , And then it was divided 5 Column .

tensor a It can be understood in the daily image data set ：
The first number 2： In fact, that is batchsize, It is equivalent to that this tensor is input 2 Zhang image
The second number 3： The number of channels per image is 3
The third number 4： The image is high 4
The fourth number 5： The width of the image is 5

Reference resources ：
https://mp.weixin.qq.com/s/9gdoufWGE8xOvwPvAcVEGw
https://blog.csdn.net/z240626191s/article/details/124204965

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