Numpy 第 n 个奇数根，包括负值 [英] Numpy n-th odd root including negative values

问题描述

我想在python中计算一些数字的第n个奇数根.Numpy 作为立方根函数.使用该函数我可以计算 x^(1/3).

I want to calculate the n-th odd root of some numbers in python. Numpy as a cube root function. Using that function I can compute x^(1/3).

x = np.linspace(-100,100,100)
np.cbrt(x)
>>> array([-4.64158883, -4.26859722, -3.81571414, -3.21829795, -2.23144317,
    2.23144317,  3.21829795,  3.81571414,  4.26859722,  4.64158883])

然而，如果我想以一种直接的方式为其他第 k 个奇数根计算同样的东西，我有点卡住了.我不能直接使用 np.power，甚至不能计算立方根:

However, if I want to compute the same thing for other k-th odd roots in a straightforward manner I'm somewhat stuck. I cannot use np.power directly, not even to compute the cube root:

np.power(x,1./3)
>>> array([       nan,        nan,        nan,        nan,        nan,
   2.23144317, 3.21829795, 3.81571414, 4.26859722, 4.64158883])

(-100.)**(1./3)
>>> ValueError: negative number cannot be raised to a fractional power

我可以计算 x 的绝对值的第 k 个奇数根，然后相应地更改 x 中负条目的符号，但我想知道是否有更直接的方法.这是我目前的解决方案:

I could compute the k-th odd root for the absolute values of x and then change the sign accordingly for the negative entries in x, but I am wondering if there is a more straightforward way. Here is my current solution:

def kth_root(x,k):
    if k % 2 != 0:
        res = np.power(np.abs(x),1./k)
        return res*np.sign(x)
    else:
        return np.power(np.abs(x),1./k)

kth_root(x,3)
>>> array([-4.64158883, -4.26859722, -3.81571414, -3.21829795, -2.23144317,
    2.23144317,  3.21829795,  3.81571414,  4.26859722,  4.64158883])

推荐答案

我将用我当前的解决方案来回答我自己的问题.这并不是说不存在更简单或更快的方法.

I'm going to respond to my own question with my current solution. This is not to say that there doesn't exist an easier or faster method.

def kth_root(x,k):
    if k % 2 != 0:
        res = np.power(np.abs(x),1./k)
        return res*np.sign(x)
    else:
        return np.power(np.abs(x),1./k)


x = np.linspace(-100,100,100)
kth_root(x,3)
>>> array([-4.64158883, -4.26859722, -3.81571414, -3.21829795, -2.23144317,
2.23144317,  3.21829795,  3.81571414,  4.26859722,  4.64158883])

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