1/3是复数

I cannot understand the following output. I would expect Numpy to return -10 (or an approximation). Why is it a complex number?

我看不懂下面的输出。我期望Numpy返回-10(或近似)。为什么是复数?

print((-1000)**(1/3.))

Numpy answer

Numpy回答

(5+8.660254037844384j)

Numpy official tutorial says the answer is nan. You can find it in the middle of this tutorial.

Numpy官方教程说答案是nan。您可以在本教程的中间找到它。

1 个解决方案

#1

You are exponentiating a regular Python scalar rather than a numpy array.

您是在取一个普通的Python标量，而不是一个numpy数组。

Try this:

试试这个:

import numpy as np

print(np.array(-1000) ** (1. / 3))
# nan

The difference is that numpy does not automatically promote the result to a complex type, whereas a Python 3 scalar gets promoted to a complex value (in Python 2.7 you would just get a ValueError).

不同之处在于numpy不自动将结果提升为复杂类型，而Python 3标量提升为复杂值(在Python 2.7中，您只会得到ValueError)。

As explained in the link @jonrsharpe gave above, negative numbers have multiple cube roots. To get the root you are looking for, you could do something like this:

正如上面@jonrsharpe给出的链接所解释的，负数有多个立方根。要得到你想要的根，你可以这样做:

x = -1000
print(np.copysign(np.abs(x) ** (1. / 3), x))
# -10.0

---

Update 1

Mark Dickinson is absolutely right about the underlying cause of the problem - 1. / 3 is not exactly the same as a third because of rounding error, so x ** (1. / 3) is not quite the same thing as the cube root of x.

马克·迪金森对问题的根本原因是绝对正确的- 1。/ 3由于舍入误差不等于1 / 3，所以x * (1)/ 3)和√x不完全一样。

A better solution would be to use scipy.special.cbrt, which computes the 'exact' cube root rather than x ** (1./3):

更好的解决办法是使用剪刀。cbrt计算“准确”的立方根，而不是x ** * (1./3):

from scipy.special import cbrt

print(cbrt(-1000))
# -10.0

Update 2

It's also worth noting that versions of numpy >= 0.10.0 will have a new np.cbrt function based on the C99 cbrt function.

同样值得注意的是，numpy >= 0.10.0的版本将有一个新的np。基于C99 cbrt函数的cbrt函数。