dot()函数处理一维数组、二维数组的计算方式。
处理一维数组
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| a = np.arange(5)
b = np.arange(5,10)
c = np.arange(10,14)
print(a, "# a")
print('-'*30)
print(b, "# b")
print('-'*30)
print(c, "# c")
print('-'*30)
print(np.dot(a, b))
print('-'*30)
print(np.dot(a, c))
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| [0 1 2 3 4] # a
------------------------------
[5 6 7 8 9] # b
------------------------------
[10 11 12 13] # c
------------------------------
80
------------------------------
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-58-f134be7edf61> in <module>
15 print('-'*30)
16
---> 17 print(np.dot(a, c))
<__array_function__ internals> in dot(*args, **kwargs)
ValueError: shapes (5,) and (4,) not aligned: 5 (dim 0) != 4 (dim 0)
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- 两个向量必须同维度，否则会报错；
- 计算过程：$$05+16+27+38+4*9 = 80$$
- 向量的内积公示：$$a=(x_{1},y_{1}),b=(x_{2},y_{2})$$，内积表示为：$$a*b = x_{1}x_{2}+y_{1}x_{2}$$
处理二维数组
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| x = np.matrix([[1,2], [3,4]])
print(x, "# x")
print('-'*30)
y = np.matrix("5,6;7,8")
print(y, "# y")
print('-'*30)
print(np.dot(x, y))
print('-'*30)
print(np.dot(y, x))
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| [[1 2]
[3 4]] # x
------------------------------
[[5 6]
[7 8]] # y
------------------------------
[[19 22]
[43 50]]
------------------------------
[[23 34]
[31 46]]
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矩阵积计算不遵循交换律，np.dot(a,b) 和 np.dot(b,a) 得到的结果是不一样。