向现有np数组中添加维度

Question

我试图用经典的线性代数把数字数组中的维数和矩阵的维数联系起来。假设以下内容：

In [1]  import numpy as np
In [2]  rand = np.random.RandomState(42)
In [3]  a = rand.rand(3,2)
In [4]  a
Out[4]:
array([[0.61185289, 0.13949386],
       [0.29214465, 0.36636184],
       [0.45606998, 0.78517596]])
In [5]: a[np.newaxis,:,:]
Out[5]:
array([[[0.61185289, 0.13949386],
        [0.29214465, 0.36636184],
        [0.45606998, 0.78517596]]])
In [6]: a[:,np.newaxis,:]
Out[6]:
array([[[0.61185289, 0.13949386]],

       [[0.29214465, 0.36636184]],

       [[0.45606998, 0.78517596]]])

In [7]: a[:,:,np.newaxis]
Out[7]:
array([[[0.61185289],
        [0.13949386]],

       [[0.29214465],
        [0.36636184]],

       [[0.45606998],
        [0.78517596]]])

我的问题如下：

1. 说a的尺寸是3X2是正确的吗？换句话说，一个3X2矩阵？
2. a[np.newaxis,:,:]的尺寸是1×3×2，这是正确的吗？换句话说，包含3X2矩阵的矩阵？
3. a[:,np.newaxis,:]的尺寸是3×1×2，这是正确的吗？换句话说，包含31X2矩阵的矩阵？
4. a[:,:,np.newaxis]的尺寸是3×2 X1，这是正确的吗？换句话说，一个矩阵包含3个矩阵，每个矩阵包含21X1矩阵？

Answer 1

1. 是
2. 是
3. 是
4. 三个2x1矩阵，每个矩阵包含一个大小为1的向量

只要找到使用.shape的方法

import numpy as np

rand = np.random.RandomState(42)

# 1.
a = rand.rand(3, 2)
print(a.shape, a, sep='\n', end='\n\n')

# 2.
b = a[np.newaxis, :, :]
print(b.shape, b, sep='\n', end='\n\n')

# 3.
c = a[:, np.newaxis, :]
print(c.shape, c, sep='\n', end='\n\n')

# 4.a
d = a[:, :, np.newaxis]
print(d.shape, d, sep='\n', end='\n\n')

# 4.b
print(d[0].shape, d[0], sep='\n', end='\n\n')
print(d[0, 0].shape, d[0, 0])

产出：

(3, 2)
[[0.37454012 0.95071431]
 [0.73199394 0.59865848]
 [0.15601864 0.15599452]]

(1, 3, 2)
[[[0.37454012 0.95071431]
  [0.73199394 0.59865848]
  [0.15601864 0.15599452]]]

(3, 1, 2)
[[[0.37454012 0.95071431]]

 [[0.73199394 0.59865848]]

 [[0.15601864 0.15599452]]]

(3, 2, 1)
[[[0.37454012]
  [0.95071431]]

 [[0.73199394]
  [0.59865848]]

 [[0.15601864]
  [0.15599452]]]

(2, 1)
[[0.37454012]
 [0.95071431]]

(1,) [0.37454012]