Python scipy fsolve 工作不正确

Question

我有方程式：

import numpy as np
from scipy import optimize

def wealth_evolution(price, wealth=10, rate=0.01, q=1, realEstate=0.1, prev_price=56):
    sum_wantedEstate = 100
    for delta in range(1,4):
        z = rate - ((price-prev_price) / (price + q / rate))
        k = delta * np.divide(1.0, float(np.maximum(0.0, z)))
        wantedEstate = (wealth / (price + q / rate)) * np.minimum(k, 1) - realEstate
        sum_wantedEstate += wantedEstate
    return sum_wantedEstate

所以我找到了这个方程的解：

sol = optimize.fsolve(wealth_evolution, 200)

但如果我将sol 代入等式，我将不会得到0 (welth_evolution(sol))。为什么会发生？ fsolve 找到 f(x)=0 的根。

更新： full_output 给出：

(array([ 2585200.]), {'qtf': array([-99.70002298]), 'nfev': 14, 'fjac': array([[-1.]]), 'r': array([  3.45456519e-11]), 'fvec': array([ 99.7000116])}, 5, 'The iteration is not making good progress, as measured by the \n  improvement from the last ten iterations.')

Answer 1

你尝试过绘制你的函数吗？

import numpy as np
from scipy import optimize
from matplotlib import pyplot as plt
small = 1e-30
def wealth_evolution(price, wealth=10, rate=0.01, q=1, realEstate=0.1, prev_price=56):
    sum_wantedEstate = 100
    for delta in range(1,4):
        z = rate - ((price-prev_price) / (price + q / rate))
        k = delta * np.divide(1.0, float(np.maximum(small, z)))
        wantedEstate = (wealth / (price + q / rate)) * np.minimum(k, 1) - realEstate
        sum_wantedEstate += wantedEstate
    return sum_wantedEstate




price_range = np.linspace(0,10000,10000)
we = [wealth_evolution(p) for p in price_range]

plt.plot(price_range,we)
plt.xlabel('price')
plt.ylabel('wealth_evolution(price)')
plt.show()

至少对于您指定的参数，它没有根，这是fsolve 试图找到的。如果你想最小化一个函数，你可以试试fmin。对于这个函数，这将无济于事，因为它似乎只是渐近衰减到 99.7 左右。所以最小化会导致无限的价格。

所以要么你必须忍受这个或想出一个不同的功能来优化或限制你的搜索范围（在这种情况下你不必搜索，因为它只是最大值......）。