NumPy科学计算库学习_010_NumPy数组的广播机制

NumPy数组广播机制的说明

当两个数组形状不同时，可以通过扩展数组的方式实现计算操作。这种机制就叫做广播机制。

1维NumPy数组的广播机制

\[加法： \begin{bmatrix} {0}&{0}&{0}\\ {1}&{1}&{1}\\ {2}&{2}&{2}\\ {3}&{3}&{3}\\ \end{bmatrix} + \begin{bmatrix} \color{red}{1}&\color{red}{2}&\color{red}{3}\\ \color{lightgrey}{1}&\color{lightgrey}{2}&\color{lightgrey}{3}\\ \color{lightgrey}{1}&\color{lightgrey}{2}&\color{lightgrey}{3}\\ \color{lightgrey}{1}&\color{lightgrey}{2}&\color{lightgrey}{3}\\ \end{bmatrix} = \begin{bmatrix} {1}&{2}&{3}\\ {2}&{3}&{4}\\ {3}&{4}&{5}\\ {4}&{5}&{6}\\ \end{bmatrix} \]

\[减法： \begin{bmatrix} {0}&{0}&{0}\\ {1}&{1}&{1}\\ {2}&{2}&{2}\\ {3}&{3}&{3}\\ \end{bmatrix} - \begin{bmatrix} \color{red}{1}&\color{red}{2}&\color{red}{3}\\ \color{lightgrey}{1}&\color{lightgrey}{2}&\color{lightgrey}{3}\\ \color{lightgrey}{1}&\color{lightgrey}{2}&\color{lightgrey}{3}\\ \color{lightgrey}{1}&\color{lightgrey}{2}&\color{lightgrey}{3}\\ \end{bmatrix} = \begin{bmatrix} {-1}&{-2}&{-3}\\ {0}&{1}&{2}\\ {2}&{0}&{-1}\\ {2}&{1}&{0}\\ \end{bmatrix} \]

\[乘，除，取余，取模等操作同上。 \]

arr1 = np.array([[0,0,0],[1,1,1],[2,2,2],[3,3,3]])
print("【arr1】\n",arr1,"形状:",arr1.shape,"\n")

arr2 = np.array([1,2,3]) # 1维度
print("【arr2】\n",arr2,"形状:",arr2.shape,"\n")

arr3 = arr1 + arr2
arr4 = arr1 - arr2
arr5 = arr1 * arr2
arr6 = arr1 / arr2

print("【arr3 = arr1 + arr2】\n",arr3,"形状:",arr3.shape,"\n")
print("【arr4 = arr1 - arr2】\n",arr4,"形状:",arr4.shape,"\n")
print("【arr5 = arr1 * arr2】\n",arr5,"形状:",arr5.shape,"\n")
print("【arr6 = arr1 / arr2】\n",arr6,"形状:",arr6.shape)

【arr1】
 [[0 0 0]
 [1 1 1]
 [2 2 2]
 [3 3 3]] 形状: (4, 3) 

【arr2】
 [1 2 3] 形状: (3,) 

【arr3 = arr1 + arr2】
 [[1 2 3]
 [2 3 4]
 [3 4 5]
 [4 5 6]] 形状: (4, 3) 

【arr4 = arr1 - arr2】
 [[-1 -2 -3]
 [ 0 -1 -2]
 [ 1  0 -1]
 [ 2  1  0]] 形状: (4, 3) 

【arr5 = arr1 * arr2】
 [[0 0 0]
 [1 2 3]
 [2 4 6]
 [3 6 9]] 形状: (4, 3) 

【arr6 = arr1 / arr2】
 [[0.         0.         0.        ]
 [1.         0.5        0.33333333]
 [2.         1.         0.66666667]
 [3.         1.5        1.        ]] 形状: (4, 3)

2维NumPy数组的广播机制

\[加法： \begin{bmatrix} {0}&{0}&{0}\\ {1}&{1}&{1}\\ {2}&{2}&{2}\\ {3}&{3}&{3}\\ \end{bmatrix} + \begin{bmatrix} \color{red}{1}&\color{lightgrey}{1}&\color{lightgrey}{1}\\ \color{red}{2}&\color{lightgrey}{2}&\color{lightgrey}{2}\\ \color{red}{3}&\color{lightgrey}{3}&\color{lightgrey}{3}\\ \color{red}{4}&\color{lightgrey}{4}&\color{lightgrey}{4}\\ \end{bmatrix} = \begin{bmatrix} {1}&{1}&{1}\\ {3}&{3}&{3}\\ {5}&{5}&{5}\\ {7}&{7}&{7}\\ \end{bmatrix} \]

\[减法： \begin{bmatrix} {0}&{0}&{0}\\ {1}&{1}&{1}\\ {2}&{2}&{2}\\ {3}&{3}&{3}\\ \end{bmatrix} - \begin{bmatrix} \color{red}{1}&\color{lightgrey}{1}&\color{lightgrey}{1}\\ \color{red}{2}&\color{lightgrey}{2}&\color{lightgrey}{2}\\ \color{red}{3}&\color{lightgrey}{3}&\color{lightgrey}{3}\\ \color{red}{4}&\color{lightgrey}{4}&\color{lightgrey}{4}\\ \end{bmatrix} = \begin{bmatrix} {-1}&{-1}&{-1}\\ {-1}&{-1}&{-1}\\ {-1}&{-1}&{-1}\\ {-1}&{-1}&{-1}\\ \end{bmatrix} \]

\[乘，除，取余，取模等操作同上。 \]

arr1 = np.array([[0,0,0],[1,1,1],[2,2,2],[3,3,3]])
print("【arr1】\n",arr1,"形状:",arr1.shape,"\n")

arr2 = np.array([[1],[2],[3],[4]]) # 2维度
print("【arr2】\n",arr2,"形状:",arr2.shape,"\n")

arr3 = arr1 + arr2
arr4 = arr1 - arr2
arr5 = arr1 * arr2
arr6 = arr1 / arr2

print("【arr3 = arr1 + arr2】\n",arr3,"形状:",arr3.shape,"\n")
print("【arr4 = arr1 - arr2】\n",arr4,"形状:",arr4.shape,"\n")
print("【arr5 = arr1 * arr2】\n",arr5,"形状:",arr5.shape,"\n")
print("【arr6 = arr1 / arr2】\n",arr6,"形状:",arr6.shape)

【arr1】
 [[0 0 0]
 [1 1 1]
 [2 2 2]
 [3 3 3]] 形状: (4, 3) 

【arr2】
 [[1]
 [2]
 [3]
 [4]] 形状: (4, 1) 

【arr3 = arr1 + arr2】
 [[1 1 1]
 [3 3 3]
 [5 5 5]
 [7 7 7]] 形状: (4, 3) 

【arr4 = arr1 - arr2】
 [[-1 -1 -1]
 [-1 -1 -1]
 [-1 -1 -1]
 [-1 -1 -1]] 形状: (4, 3) 

【arr5 = arr1 * arr2】
 [[ 0  0  0]
 [ 2  2  2]
 [ 6  6  6]
 [12 12 12]] 形状: (4, 3) 

【arr6 = arr1 / arr2】
 [[0.         0.         0.        ]
 [0.5        0.5        0.5       ]
 [0.66666667 0.66666667 0.66666667]
 [0.75       0.75       0.75      ]] 形状: (4, 3)

3维NumPy数组的广播机制

arr1 = np.array([0,1,2,3,4,5,6,7]*3).reshape(3,4,2)
print("【arr1】\n",arr1)
arr2 = np.array([0,1,2,3,4,5,6,7]).reshape(4,2)
print("【arr2】\n",arr2)

arr3 = arr1 + arr2
arr4 = arr1 - arr2
arr5 = arr1 * arr2

print("【arr3 = arr1 + arr2】\n",arr3,"形状:",arr3.shape,"\n")
print("【arr4 = arr1 - arr2】\n",arr4,"形状:",arr4.shape,"\n")
print("【arr5 = arr1 * arr2】\n",arr5,"形状:",arr5.shape,"\n")

【arr1】
 [[[0 1]
  [2 3]
  [4 5]
  [6 7]]

 [[0 1]
  [2 3]
  [4 5]
  [6 7]]

 [[0 1]
  [2 3]
  [4 5]
  [6 7]]]
【arr2】
 [[0 1]
 [2 3]
 [4 5]
 [6 7]]
【arr3 = arr1 + arr2】
 [[[ 0  2]
  [ 4  6]
  [ 8 10]
  [12 14]]

 [[ 0  2]
  [ 4  6]
  [ 8 10]
  [12 14]]

 [[ 0  2]
  [ 4  6]
  [ 8 10]
  [12 14]]] 形状: (3, 4, 2) 

【arr4 = arr1 - arr2】
 [[[0 0]
  [0 0]
  [0 0]
  [0 0]]

 [[0 0]
  [0 0]
  [0 0]
  [0 0]]

 [[0 0]
  [0 0]
  [0 0]
  [0 0]]] 形状: (3, 4, 2) 

【arr5 = arr1 * arr2】
 [[[ 0  1]
  [ 4  9]
  [16 25]
  [36 49]]

 [[ 0  1]
  [ 4  9]
  [16 25]
  [36 49]]

 [[ 0  1]
  [ 4  9]
  [16 25]
  [36 49]]] 形状: (3, 4, 2)