Code analysis of Numpy's broadcast principle in python

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In order to understand this principle, let's first look at a set of examples:

# 数组直接对一个数进行加减乘除，产生的结果是数组中的每个元素都会加减乘除这个数。
In [12]: import numpy as np
In [13]: a = np.arange(1,13).reshape((4, 3))
In [14]: a * 2
Out[14]: array([[ 2, 4, 6],
                [ 8, 10, 12],
                [14, 16, 18],
                [20, 22, 24]])
# 接下来我们看一下数组与数组之间的计算
In [17]: b = np.arange(12,24).reshape((4,3))
In [18]: b
Out[18]: array([[12, 13, 14],
                [15, 16, 17],
                [18, 19, 20],
                [21, 22, 23]])
In [19]: a + b
Out[19]: array([[13, 15, 17],
                [19, 21, 23],
                [25, 27, 29],
                [31, 33, 35]])
In [20]: c = np.array([1,2,3])
In [21]: a+c
Out[21]: array([[ 2, 4, 6],
                [ 5, 7, 9],
                [ 8, 10, 12],
                [11, 13, 15]])
In [22]: d = np.arange(10,14).reshape((4,1))
In [23]: d
Out[23]: array([[10],
                [11],
                [12],
                [13]])
In [24]: a + d
Out[24]: array([[11, 12, 13],
                [15, 16, 17],
                [19, 20, 21],
                [23, 24, 25]])
# 从上面可以看出，和线性代数中不同的是，m*n列的m行的一维数组或者n列的一维数组也是可以计算的。

Why is this? The broadcasting principle of numpy should be mentioned here:

If the trailing edge dimensions of the two arrays (dimensions starting from the end) ’s axis lengths match or where If the length of one side is 1, they are considered broadcast compatible. Broadcasting will occur on missing dimensions and/or dimensions with axis length 1.

In the above code, the dimension of a is (4, 3), the dimension of c is (1, 3); the dimension of d is (4, 1). So suppose there are two arrays. The first one has dimensions (x_1, y_1, z_1), and the other array has dimensions (x_2, y_2, z_2). To determine whether these two arrays can be calculated, you can use the following method To judge:

if z_1 == z_2 or z_1 == 1 or z_2 == 1:
    if y_1 == y_2 or y_1 == 1 or y_2 == 1:
        if x_1 == x_2 or x_1 == 1 or x_2 == 1:
            可以运算
        else:
            不可以运算
    else:
        不可以运算
else:
    不可以运算

It should be noted here: (3, 3, 2) and (3, 2) can be operated, because the two-dimensional array (3, 2) can also be expressed as (1, 3 , 2), it is completely applicable to apply the above rules. In the same way: (4, 2, 5, 4) and (2, 1, 4) can also be operated.

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