广播规则：从最右侧开始广播。

 Broadcasting — NumPy v1.25 Manual 截图

下面给出一些样例：

三维矩阵广播

a = np.array([[[0,0],
               [0,0]],
              [[0, 0],
               [0, 0]]
              ])

print('-'*10, 'a', '-'*10)
print(a.shape)
print(a)

b = np.array([[[1]],
              [[2]]])
print('-'*10, 'b', '-'*10)
print(b.shape)
print(b)

c = b - a
print('-'*10, 'a-b', '-'*10)
print(c.shape)
print(c)

运行结果： 

---------- a ----------
(2, 2, 2)
[[[0 0]
  [0 0]]
 [[0 0]
  [0 0]]]
---------- b ----------
(2, 1, 1)
[[[1]]
 [[2]]]
---------- a-b ----------
(2, 2, 2)
[[[1 1]
  [1 1]]
 [[2 2]
  [2 2]]]

三维矩阵向四维矩阵广播

a = np.array([[[[0,0],
               [0,0]],
              [[0, 0],
               [0, 0]]],
             [[[0,0],
               [0,0]],
              [[0, 0],
               [0, 0]]]
              ])

print('-'*10, 'a', '-'*10)
print(a.shape)
print(a)

b = np.array([[[1]],
              [[2]]])
print('-'*10, 'b', '-'*10)
print(b.shape)
print(b)

c = b - a
print('-'*10, 'a-b', '-'*10)
print(c.shape)
print(c)

运行结果：

---------- a ----------
(2, 2, 2, 2)
[[[[0 0]
   [0 0]]
  [[0 0]
   [0 0]]]
 [[[0 0]
   [0 0]]
  [[0 0]
   [0 0]]]]
---------- b ----------
(2, 1, 1)
[[[1]]
 [[2]]]
---------- a-b ----------
(2, 2, 2, 2)
[[[[1 1]
   [1 1]]
  [[2 2]
   [2 2]]]
 [[[1 1]
   [1 1]]
  [[2 2]
   [2 2]]]]

四维矩阵广播

a = np.array([[[[0,0],
               [0,0]],
              [[0, 0],
               [0, 0]]],
             [[[0,0],
               [0,0]],
              [[0, 0],
               [0, 0]]]
              ])

print('-'*10, 'a', '-'*10)
print(a.shape)
print(a)

b = np.array([[[[1]]],
              [[[2]]]])
print('-'*10, 'b', '-'*10)
print(b.shape)
print(b)

c = b - a
print('-'*10, 'a-b', '-'*10)
print(c.shape)
print(c)

运行结果： 

---------- a ----------
(2, 2, 2, 2)
[[[[0 0]
   [0 0]]
  [[0 0]
   [0 0]]]
 [[[0 0]
   [0 0]]
  [[0 0]
   [0 0]]]]
---------- b ----------
(2, 1, 1, 1)
[[[[1]]]
 [[[2]]]]
---------- a-b ----------
(2, 2, 2, 2)
[[[[1 1]
   [1 1]]
  [[1 1]
   [1 1]]]
 [[[2 2]
   [2 2]]
  [[2 2]
   [2 2]]]]