Python 使用 fsolve 找到解决方案
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using fsolve to find the solution
提问by dustin
import numpy as np
from scipy.optimize import fsolve
musun = 132712000000
T = 365.25 * 86400 * 2 / 3
e = 581.2392124070273
def f(x):
return ((T * musun ** 2 / (2 * np.pi)) ** (1 / 3) * np.sqrt(1 - x ** 2)
- np.sqrt(.5 * musun ** 2 / e * (1 - x ** 2)))
x = fsolve(f, 0.01)
f(x)
print x
What is wrong with this code? It seems to not work.
这段代码有什么问题？它似乎不起作用。
采纳答案by Simon
fsolve()returns the roots of f(x) = 0(see here).
fsolve()返回f(x) = 0(see here)的根。
When I plotted the values of f(x)for xin the range -1 to 1, I found that there are roots at x = -1and x = 1. However, if x > 1or x < -1, both of the sqrt()functions will be passed a negative argument, which causes the error invalid value encountered in sqrt.
当我在 -1 到 1 的范围内绘制f(x)for的值时x，我发现在x = -1和处有根x = 1。但是，如果x > 1或x < -1，这两个sqrt()函数都将传递一个负参数，这会导致错误invalid value encountered in sqrt。
It doesn't surprise me that fsolve()fails to find roots that are at the very ends of the valid range for the function.
fsolve()无法找到位于函数有效范围末端的根，这并不令我感到惊讶。
I find that it is always a good idea to plot the graph of a function before trying to find its roots, as that can indicate how likely (or in this case, unlikely) it is that the roots will be found by any root-finding algorithm.
我发现在试图找到它的根之前绘制一个函数的图形总是一个好主意，因为这可以表明任何寻根找到根的可能性（或在这种情况下，不太可能）算法。
回答by HYRY
Because sqrtreturns NaN for nagative argument, you function f(x) is not calculatable for all real x. I change your function to use numpy.emath.sqrt()which can output complex values when the argument < 0, and returns the absolute value of the expression.
因为sqrt为否定参数返回 NaN，所以函数 f(x) 无法计算所有实数 x。我将您的函数更改为使用numpy.emath.sqrt()它可以在参数 < 0 时输出复数值，并返回表达式的绝对值。
import numpy as np
from scipy.optimize import fsolve
sqrt = np.emath.sqrt
musun = 132712000000
T = 365.25 * 86400 * 2 / 3
e = 581.2392124070273
def f(x):
return np.abs((T * musun ** 2 / (2 * np.pi)) ** (1 / 3) * sqrt(1 - x ** 2)
- sqrt(.5 * musun ** 2 / e * (1 - x ** 2)))
x = fsolve(f, 0.01)
x, f(x)
Then you can get the right result:
然后你可以得到正确的结果：
(array([ 1.]), array([ 121341.22302275]))
the solution is very close to the true root, but f(x) is still very large, because f(x) has a very large factor: musun.
解非常接近真根，但 f(x) 仍然非常大，因为 f(x) 有一个非常大的因子：musun。
