似乎無法讓 Scipy curve_fit Sigmoid 在 Python 中工作

Question

有一些關於這個的帖子，通常答案是有一個很好的初步猜測和界限。 我已經玩了一段時間，找不到產生任何曲線的配置。

import numpy as np
array1 = np.array(column1).astype(float)
array2 = np.array(column2).astype(float)
print(array1)
print(array2)

Output: [18.7327 9.3784 6.6293 20.8361 11.2603 19.3706 5.4302 10.1293 13.7516 8.0567 16.8688 4.969 3.94 19.4793 11.7527 13.2811 13.338 0.5944 7.4406 11.2338 6.2283 3.4818 10.1056 16.2689 22.442 18.7345 5.2605 5.6405 12.7186 18.2497 5.4315 14.2651 16.7544 12.9192 13.5955 10.9256 5.7798 8.4485 8.5229 11.879 6.5271 10.3376 7.781 31.4558 8.0236 2.3527 10.8926 16.1995 11.1924 25.8071 13.9692 20.7791 10.3045 12.2833 7.4066 15.9807 11.4462 15.1504 5.9021 19.1184]

[83.85 52.45 41.2 92.59 62.65 86.77 30.63 53.78 73.34 48.55 82.53 28.3 23.87 90.99 62.95 68.82 71.06 20.74 45.25 60.65 39.07 21.93 53.35 79.61 93.27 85.88 28.95 32.73 65.89 83.51 30.74 75.22 79.8 67.43 71.12 58.41 35.83 49.61 50.72 63.49 40.67 55.75 46.49 96.22 47.62 21.8 56.23 76.97 59.07 94.67 74.9 92.52 55.61 63.51 41.34 76.8 62.81 75.99 36.34 85.96]

import pylab
from scipy.optimize import curve_fit

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

popt, pcov = curve_fit(sigmoid, array1, array2, p0 = [5,20], method='dogbox', bounds=([0, 20],[40, 100]))
print(popt)

x = np.linspace(0, 35, 50)
y = sigmoid(x, *popt)

pylab.plot(array1, array2, 'o', label='data')
pylab.plot(x,y, label='fit')
pylab.ylim(0, 100)
pylab.legend(loc='best')
pylab.show()

輸出：圖表

如您所見，它根本沒有做任何事情。 非常感謝任何幫助以獲得粗略的 sigmoid 曲線。 不需要非常准確。

非常感謝。

Answer 1

在您的情況下，問題不是一個好的初始猜測，而是一個不合適的模型。 請注意您的 sigmoid 如何不能大於 1，但您的數據在 ~10 - 100 的范圍內。

xs = np.linspace(0, 15)
as_ = np.linspace(0, 5, num=10)
bs_ = np.linspace(0, 5, num=10)
for a in as_:
    for b in bs_:
        plt.plot(xs, sigmoid(xs, a, b))

因此，您要么必須修改模型以接受縮放參數，要么將數據縮小到模型可以適應的范圍。 這是兩個解決方案：

前言

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

array1 = np.array([18.7327,9.3784,6.6293,20.8361,11.2603,19.3706,5.4302,10.1293,13.7516,8.0567,16.8688,4.969,3.94,19.4793,11.7527,13.2811,13.338,0.5944,7.4406,11.2338,6.2283,3.4818,10.1056,16.2689,22.442,18.7345,5.2605,5.6405,12.7186,18.2497,5.4315,14.2651,16.7544,12.9192,13.5955,10.9256,5.7798,8.4485,8.5229,11.879,6.5271,10.3376,7.781,31.4558,8.0236,2.3527,10.8926,16.1995,11.1924,25.8071,13.9692,20.7791,10.3045,12.2833,7.4066,15.9807,11.4462,15.1504,5.9021,19.1184])
array2 = np.array([83.85,52.45,41.2,92.59,62.65,86.77,30.63,53.78,73.34,48.55,82.53,28.3,23.87,90.99,62.95,68.82,71.06,20.74,45.25,60.65,39.07,21.93,53.35,79.61,93.27,85.88,28.95,32.73,65.89,83.51,30.74,75.22,79.8,67.43,71.12,58.41,35.83,49.61,50.72,63.49,40.67,55.75,46.49,96.22,47.62,21.8,56.23,76.97,59.07,94.67,74.9,92.52,55.61,63.51,41.34,76.8,62.81,75.99,36.34,85.96])
df = pd.DataFrame({'x':array1, 'y':array2})
df = df.sort_values('x')

縮放數據以匹配參數

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

popt, pcov = curve_fit(sigmoid, df['x'], df['y'] / df['y'].max(), p0 = [5,20], method='dogbox', bounds=([0, 0],[40, 100]))

plt.plot(df['x'], df['y'] / df['y'].max(), label='data')
plt.plot(df['x'], sigmoid(df['x'], *popt))

流行音樂是 [ popt [8.56754823 0.20609918]

向函數添加新參數

def sigmoid2(x, a, b, scale):
    y = scale / (1 + np.exp(-b*(x-a)))
    return y

popt, pcov = curve_fit(sigmoid2, df['x'], df['y'], p0 = [5,20, 100], method='dogbox', bounds=([0, 0, 0],[40, 100, 1E5]))

plt.plot(df['x'], df['y'], label='data')
plt.plot(df['x'], sigmoid2(df['x'], *popt))

popt是array([ 8.81708442, 0.19749557, 98.357044 ])