为什么会这样scipy.optimize.curve\u fit曲线拟合不符合数据？

如何解决为什么会这样scipy.optimize.curve\u fit曲线拟合不符合数据？

数值算法往往更好地工作时，没有饲料非常小（或 （大）数字。 在本例中，图表显示数据的x和y值非常小。如果 如果缩放它们，拟合效果会更好：

xData = np.load('xData.npy')*10**5
yData = np.load('yData.npy')*10**5

from __future__ import division

import os
os.chdir(os.path.expanduser('~/tmp'))

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

def func(x,a,b,c):
   return a*np.exp(-b*x)-c


xData = np.load('xData.npy')*10**5
yData = np.load('yData.npy')*10**5

print(xData.min(), xData.max())
print(yData.min(), yData.max())

trialX = np.linspace(xData[0], xData[-1], 1000)

# Fit a polynomial 
fitted = np.polyfit(xData, yData, 10)[::-1]
y = np.zeros(len(trialX))
for i in range(len(fitted)):
   y += fitted[i]*trialX**i

# Fit an exponential
popt, pcov = optimize.curve_fit(func, xData, yData)
print(popt)
yEXP = func(trialX, *popt)

plt.figure()
plt.plot(xData, yData, label='Data', marker='o')
plt.plot(trialX, yEXP, 'r-',ls='--', label="Exp Fit")
plt.plot(trialX, y, label = '10 Deg poly')
plt.legend()
plt.show()

Note that after rescaling xData and yData, the parameters returned bycurve_fit must also be rescaled. In this case, a, b and c each must be divided by 10**5 to obtain fitted parameters for the original data.

One objection you might have to the above is that the scaling has to be chosen rather “carefully”. (Read: Not every reasonable choice of scale works!)

You can improve the robustness of curve_fit by providing a reasonable initial guess for the parameters. Usually you have some a priori kNowledge about the data which can motivate ballpark / back-of-the envelope type guesses for reasonable parameter values.

For example, calling curve_fit with

guess = (-1, 0.1, 0)
popt, pcov = optimize.curve_fit(func, xData, yData, guess)

helps improve the range of scales on which curve_fit succeeds in this case.

解决方法

我试着用指数拟合一些数据已经有一段时间了scipy.optimize.curve\u fit曲线拟合但我真的有困难。我真的看不见有什么理由不起作用，但它只是产生了一条海峡线，不知道
为什么？
任何帮助都将不胜感激

from __future__ import division
import numpy
from scipy.optimize import curve_fit
import matplotlib.pyplot as pyplot

def func(x,a,b,c):
   return a*numpy.exp(-b*x)-c


yData = numpy.load('yData.npy')
xData = numpy.load('xData.npy')

trialX = numpy.linspace(xData[0],xData[-1],1000)

# Fit a polynomial 
fitted = numpy.polyfit(xData,yData,10)[::-1]
y = numpy.zeros(len(trailX))
for i in range(len(fitted)):
   y += fitted[i]*trialX**i

# Fit an exponential
popt,pcov = curve_fit(func,xData,yData)
yEXP = func(trialX,*popt)

pyplot.figure()
pyplot.plot(xData,label='Data',marker='o')
pyplot.plot(trialX,yEXP,'r-',ls='--',label="Exp Fit")
pyplot.plot(trialX,y,label = '10 Deg Poly')
pyplot.legend()
pyplot.show()






xData = [1e-06,2e-06,3e-06,4e-06,5e-06,6e-06,7e-06,8e-06,9e-06,1e-05,2e-05,3e-05,4e-05,5e-05,6e-05,7e-05,8e-05,9e-05,0.0001,0.0002,0.0003,0.0004,0.0005,0.0006,0.0007,0.0008,0.0009,0.001,0.002,0.003,0.004,0.005,0.006,0.007,0.008,0.009,0.01]

yData = 
[6.37420666067e-09,1.13082012115e-08,1.52835756975e-08,2.19214493931e-08,2.71258852882e-08,3.38556130078e-08,3.55765277358e-08,4.13818145846e-08,4.72543475372e-08,4.85834751151e-08,9.53876562077e-08,1.45110636413e-07,1.83066627931e-07,2.10138415308e-07,2.43503982686e-07,2.72107045549e-07,3.02911771395e-07,3.26499455951e-07,3.48319349445e-07,5.13187669283e-07,5.98480176303e-07,6.57028222701e-07,6.98347073045e-07,7.28699930335e-07,7.50686502279e-07,7.7015576866e-07,7.87147246927e-07,7.99607141001e-07,8.61398763228e-07,8.84272900407e-07,8.96463883243e-07,9.04105135329e-07,9.08443443149e-07,9.12391264185e-07,9.150842683e-07,9.16878548643e-07,9.18389990067e-07]