问题描述

我正在尝试用S型曲线和三次多项式来拟合我的数据(成本与收入之比)，然后找出拐点/收益递减的点。

这是我到目前为止拥有的代码，适应性不是很好。任何建议都将是非常有用的，谢谢！

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

def sigmoid(x, a, b):
    y = 1 / (1 + np.exp(-b*(x-a)))
    return y

xdata = [ 404.91,  731.89,  804.23,    0.  ,  954.72,  954.72,  954.72, 744.54,  744.54,  498.5 ,  355.03,
         359.61,    0.  ,    0.  , 0.  ,  753.77, 1116.02,  557.07,  589.06,  761.86,  722.97, 162.69, 
         354.47,  474.  ,  306.83,  538.57,  134.26,  134.26, 134.26,  134.26,  134.26,  652.29, 1296.26,
         547.78,  845.22, 872.62,  881.59,  556.23,  500.2 ,  569.97,  679.46,  679.46, 623.08,  628.33,
         754.88, 2014.12, 1870.43, 1444.69,  826.05, 1071.03,  816.74]
ydata = [ 6986.97, 36591.27, 23702.95,  6380.01, 26873.68, 19398.27,24693.5 , 18435.52, 19066.1 ,  8534.14,  8534.14,  8534.14,
          2032.07,   567.26,  7544.64, 21051.07, 21051.07, 18592.84,18592.84, 18592.84, 19566.14,  4787.51,  7269.55,
         11596.66, 9083.43, 13260.51,  6280.95,  4112.17,  6004.46,  7613.15, 6436.83, 10726.22, 20430.67,  8265.88,
         15344.32, 30246.91,29928.96, 12215.02,  7776.27,  9714.94, 16642.3 , 29493.06,15496.04, 15496.04, 15496.04,
         33397.61, 33397.61, 33397.61, 22525.93, 22525.93, 48941.98]

#fit 3rd order polynomial
p = np.poly1d(np.polyfit(x, y, 3))
second_deriv = p.deriv(2)
inflection = -second_deriv[0]/second_deriv[1]
print("polynomial inflection point:", inflection)

#fitting a sigmoid curve
popt, pcov = curve_fit(sigmoid, xdata, ydata,  method='dogbox', p0=[1000, 0.6])
estimated_k, estimated_x0 = popt
print("sigmoid inflection point:", estimated_x0)

x = np.linspace(0, int(max(xdata)), len(ydata))
y = sigmoid(x, *popt)*max(ydata)

t = np.linspace(0, int(np.max(xdata)), int(np.max(xdata)))
plt.plot(xdata, ydata, 'o', label='data')
plt.plot(p(t), 'b-', label="polynomial")
plt.plot(x,y, label='sigmoid')
plt.legend(loc='best')
plt.show()

推荐答案

数据高度分散。根据所选的拟合标准(最小均方误差、最小均方相对误差或最小平均绝对误差等)，可获得一致的结果。另外，对于常用的迭代方法软件，猜测方便的参数初值可能是不确定的。

这篇关于拟合S型曲线(Python)的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持编程学习网！