numpy dot() 和 inner() 的区别 [英] difference between numpy dot() and inner()

问题描述

有什么区别

将 numpy 导入为 npnp.dot(a,b)

和

将 numpy 导入为 npnp.inner(a,b)

我尝试的所有示例都返回了相同的结果.维基百科 两者都有相同的文章?！在描述中inner() 它说，它的行为在更高维度上是不同的，但我无法产生任何不同的输出.我应该使用哪一种?

解决方案

numpy.dot:

<块引用>

对于二维数组，它相当于矩阵乘法，对于一维数组，它相当于向量的内积(没有复共轭).对于 N 维，它是 a 的最后一个轴和 b 的倒数第二个的和积:

numpy.inner::><块引用>

一维数组的向量的普通内积(没有复杂的共轭)，在更高维度上是最后一个轴上的和积.

(强调我的.)

以二维数组为例:

<预><代码>>>>a=np.array([[1,2],[3,4]])>>>b=np.array([[11,12],[13,14]])>>>np.dot(a,b)数组([[37, 40],[85, 92]])>>>np.inner(a,b)数组([[35, 41],[81, 95]])

因此，您应该使用能够为您的应用程序提供正确行为的那个.

<小时>

性能测试

(请注意，我仅测试一维情况，因为这是 .dot 和 .inner 给出相同结果的唯一情况.)

<预><代码>>>>导入时间>>>setup = '将 numpy 导入为 np;a=np.random.random(1000);b = np.random.random(1000)'>>>[timeit.timeit('np.dot(a,b)',setup,number=1000000) for _ in range(3)][2.6920320987701416, 2.676928997039795, 2.633111000061035]>>>[timeit.timeit('np.inner(a,b)',setup,number=1000000) for _ in range(3)][2.588860034942627, 2.5845699310302734, 2.6556360721588135]

所以也许 .inner 更快，但我的机器目前负载相当大，所以时间不一致，也不一定非常准确.

What is the difference between

import numpy as np
np.dot(a,b)

and

import numpy as np
np.inner(a,b)

all examples I tried returned the same result. Wikipedia has the same article for both?! In the description of inner() it says, that its behavior is different in higher dimensions, but I couldn't produce any different output. Which one should I use?

解决方案

numpy.dot:

For 2-D arrays it is equivalent to matrix multiplication, and for 1-D arrays to inner product of vectors (without complex conjugation). For N dimensions it is a sum product over the last axis of a and the second-to-last of b:

numpy.inner:

Ordinary inner product of vectors for 1-D arrays (without complex conjugation), in higher dimensions a sum product over the last axes.

(Emphasis mine.)

As an example, consider this example with 2D arrays:

>>> a=np.array([[1,2],[3,4]])
>>> b=np.array([[11,12],[13,14]])
>>> np.dot(a,b)
array([[37, 40],
       [85, 92]])
>>> np.inner(a,b)
array([[35, 41],
       [81, 95]])

Thus, the one you should use is the one that gives the correct behaviour for your application.

---

Performance testing

(Note that I am testing only the 1D case, since that is the only situation where .dot and .inner give the same result.)

>>> import timeit
>>> setup = 'import numpy as np; a=np.random.random(1000); b = np.random.random(1000)'

>>> [timeit.timeit('np.dot(a,b)',setup,number=1000000) for _ in range(3)]
[2.6920320987701416, 2.676928997039795, 2.633111000061035]

>>> [timeit.timeit('np.inner(a,b)',setup,number=1000000) for _ in range(3)]
[2.588860034942627, 2.5845699310302734, 2.6556360721588135]

So maybe .inner is faster, but my machine is fairly loaded at the moment, so the timings are not consistent nor are they necessarily very accurate.

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