Python scipy fsolve无法正常工作

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)

但是，如果我将sol代入方程式，则不会得到0 （ welth_evolution(sol) ）。 为什么会发生？ fsolve找到f(x)=0的根。

UPD： full_output提供：

(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

您是否尝试过绘制功能？

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试图找到的根。 如果要最小化功能，可以尝试fmin 。 对于此功能，这将无济于事，因为它似乎渐近地衰减到99.7左右。 因此，将其最小化将导致无限的价格 。

因此，要么您必须忍受这一点， 要么想出另一种功能来优化或限制搜索范围（在这种情况下，您不必搜索，因为它只是最大值...）。