为什么scipy.optimize.curve_fit不正确地适合数据? [英] Why does scipy.optimize.curve_fit not fit correctly to the data?

问题描述

一段时间以来，我一直在尝试使用scipy.optimize.curve_fit将函数拟合到某些数据，但我确实遇到了困难.我真的看不到为什么这行不通.

I've been trying to fit a function to some data for a while using scipy.optimize.curve_fit but I have real difficulty. I really can't see any reason why this wouldn't work.

# encoding: utf-8
from __future__ import (print_function,
                        division,
                        unicode_literals,
                        absolute_import,
                        with_statement)
import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as mpl

x, y, e_y = np.loadtxt('data.txt', unpack=True)

def f(x, a, k):
    return (1/(np.sqrt(1 + a*((k-x)**2))))

popt, pcov = curve_fit(f, x, y, maxfev = 100000000)

mpl.plot(x, f(x, *popt), 'r-', label='Fit')
mpl.plot(x, y, 'rx', label='Original')
mpl.legend(loc='best')
mpl.savefig('curve.pdf')
print(popt)

# correct values which should be calculated
# a=0.003097
# k=35.4

这是由上层代码生成的绘图图像:

Here is the plot-image which is produced by upper code:

data.txt:
#x      y       e_y
4.4     0.79    0.13
19.7    4.9     0.8
23.5    7.3     1.2
29.7    17      2.79
30.7    21.5    3.52
34      81      13.28
34.6    145     23.77
35.4    610     100
36.3    115     18.85
38.1    38      6.23
43.7    14      2.3
56.2    6.2     1.02
64.7    4.6     0.75
79.9    3.2     0.52
210     0.98    0.16

推荐答案

首先尝试不要将maxfev增大得太大，通常这表明其他问题出在哪里！玩耍时，我可以通过以下补充锻炼身体:

Firstly try not to increase maxfev so large, this is usually a sign something else is going wrong! Playing around I can get a fit by the following addition:

def f(x, b, a, k):
    return (b/(np.sqrt(1 + a*((k-x)**2))))

popt, pcov = curve_fit(f, x, y, p0=[20, 600.0, 35.0])

首先，给定您提供的拟合函数的最大值为1，因为数据中的峰值为600，所以它将永远无法拟合.因此，我添加了一个总体因数b.其次，尝试帮助较差的旧curve_fit.如果用肉眼可以看到它在x~35达到峰值，然后通过p0告诉它.这需要对函数的工作方式有一些直觉，但是如果您要使用曲线拟合函数，则非常重要.

Firstly give the fitting function you have given has a maximum of 1, since the peak in your data is 600, it will never fit. So I added an overall factor b. Secondly , try to help poor old curve_fit out. If by eye you can see it peaks at x~35 then tell it through the p0. This requires some intuition as to how the function works but is very important if your going to use a curve fitting function.

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