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.
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