Question

我是python的新手，对代码感到困惑

X = np.array([2,3,4,4])
print(np.dot(X,X))

这有效

Y = np.array([[100],
        [200],
        [300],
        [400]])
print(np.dot(Y,Y))

不是。我了解这是由于与数组尺寸的关系。但我不明白如何。请解释。

Answer 1

X是一维数组（行向量不是正确的描述符）：

In [382]: X = np.array([2,3,4,4])
In [383]: X.shape
Out[383]: (4,)
In [384]: np.dot(X,X)     # docs for 1d arrays apply
Out[384]: 45

Y是2d数组。

In [385]: Y = X[:,None]
In [386]: Y
Out[386]: 
array([[2],
       [3],
       [4],
       [4]])
In [387]: Y.shape
Out[387]: (4, 1)
In [388]: np.dot(Y,Y)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-388-3a0bc5156893> in <module>()
----> 1 np.dot(Y,Y)

ValueError: shapes (4,1) and (4,1) not aligned: 1 (dim 1) != 4 (dim 0)

对于2d数组，第一个对的最后一个维度与第二个对的最后一个维度。

In [389]: np.dot(Y,Y.T)    # (4,1) pair with (1,4) to produce (4,4)
Out[389]: 
array([[ 4,  6,  8,  8],
       [ 6,  9, 12, 12],
       [ 8, 12, 16, 16],
       [ 8, 12, 16, 16]])
In [390]: np.dot(Y.T,Y)    # (1,4) pair with (4,1) to produce (1,1)
Out[390]: array([[45]])

Python中的矩阵点积

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