解隐函数

Question

我有一个隐函数要解：

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因此，我尝试了从scipy.optimize中查找根的函数：

- fsolve : RuntimeWarning: The iteration is not making good progress, as 
  measured by the improvement from the last ten iterations.
- excitingmixing : NoConvergence
-brent:  RuntimeWarning: invalid value encountered in double_scalars (but 
  without a chance to set constraints)

我不得不承认，我不确定正确的解决办法。有人能帮忙吗？

最小工作实例：

from scipy.optimize import fsolve, newton, brent, excitingmixing
import numpy as np

def func_zeta(zeta):
    k= 1.2
    Re = 5000.
    d = 0.03
    return (2.51 /Re/np.sqrt(zeta)+k/d/3.71) + 10**(0.5/ np.sqrt(zeta))
zeta = fsolve(func_zeta, 64/Re)

Answer 1

你的公式翻译有问题。它不是应该是下面的return语句吗？

return 2.51 / (Re * np.sqrt(zeta)) + k / (d * 3.71) - 10 ** (-0.5 / np.sqrt(zeta))

但即使如此，我们还是得到了一个RuntimeWarning。让我们再试一次，代替zeta

from scipy.optimize import fsolve
import numpy as np

def zeta_in_disguise(x):
    global k, d, Re
    return x + 2 * np.log10(2.51 * x / Re + k / (d * 3.71))

k = 1.2
Re = 5000
d = 0.03
#x = 1 / np.sqrt(zeta)
x = fsolve(zeta_in_disguise, 0)
print(x)
#let's test, if x is really the solution to the equation
print(-2 * np.log10(2.51 * x / Re + k / d / 3.71))

啊，现在它收敛了，产生了下面的输出

-2.06528864

这就是我们的问题--当我们只考虑浮点数的时候，你的给定参数没有解，至少没有。