scipy fsolve在输入中输入的值很少，以及如何提高求解器的收敛性

Question

我使用scipy.optimize fsolve来查找两个方程的根。 fsolve适用于某些b值范围（0.1到0.6），但对于0.9或0.99等值则失败。

我已尝试移动到least_squares或最小化，但在提供初始条件时得到元组错误。

包括来自以下发现的编辑是自我：

from scipy.optimize import fsolve
import scipy.stats as st
from numpy import *
import numpy as np



def rod(var1, var2, mu, sigma):
    return (st.lognorm.ppf(var1, s = sigma, scale = np.exp(mu), loc = sigma))/(st.lognorm.ppf(var2, s = sigma, scale = np.exp(mu), loc = sigma))
def fs_spfs(var1, mu, sigma):
    return (st.lognorm.ppf(var1, s = sigma, scale = np.exp(mu), loc = sigma))


a = 44.0
b = 0.5  #fsolve works for 0.5, 0.9, 0.99 but not for 0.95, incidentally works for 0.950001
c = 1.26

def f(x):
    y = np.zeros(2)
    y[0] = ((fs_spfs((1-b), x[0], x[1]) - a))
    y[1] = (((fs_spfs(0.9, x[0], x[1])/fs_spfs(0.1, x[0], x[1]))   - c))
    print(y)
    return y


x0 = np.array([1., 0.01])
solution = fsolve(f, x0)
print( "(x, y) = (" + str(solution[0]) + ", " + str(solution[1]) + ")")

结果b = 0.5

b = 0.5

(x, y) = (3.7821340072441982, 0.09035467410258388)

fs_spfs((1-b), solution[0], solution[1]) # expected answer = 44.
43.99999999999982

rod(0.9, 0.1, solution[0], solution[1]) # exptected answer = 1.26
1.2599999999999958

结果b = 0.9

b = 0.9

(x, y) = (3.8979025451494755, 0.09033430819655046)

fs_spfs((1-b), solution[0], solution[1]) # expected answer = 44.
43.999999999989164


rod(0.9, 0.1, solution[0], solution[1]) # exptected answer = 1.26
1.2600000000001814

也适用于b = 0.99，但b = 0.95则失败。 顺便说一下，对于b = 0.950001

Answer 1

初始条件似乎适用于大多数常见情况：

x0 = np.array([0.000001, 0.0000001])

适用于0.999的值，仍然不能为0.9999。