<p>这是一个使用数据和公式的图形拟合器。此示例代码使用scipy的差分进化遗传算法来确定curve_fit()的初始参数估计。这个scipy模块使用拉丁超立方体算法来确保对参数空间的彻底搜索,这需要搜索范围。找到参数的范围要比单个值容易得多,在这里,我尝试了不同的边界,直到拟合看起来对我来说还可以。你应该检查一下我使用的界限,看看它们是否合理。在</p>
<p><a href="https://i.stack.imgur.com/JTzPQ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/JTzPQ.png" alt="plot"/></a></p>
<pre><code>import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.optimize import differential_evolution
import warnings
xData = numpy.array([7128.67, 6814, 6490, 6135.67, 5951.67,
5753.67, 5350, 4929.33, 4499.33,4068.67, 3641.33,
3225.33, 2827.33, 2451, 2104.67, 1788, 1503, 1251.33,
1032.33, 434.199, 271.707, 134.532, 75.7034, 40.9144, 21.7112, 14.9206, 9.29772])
yData = numpy.array([0.1, 0.1426, 0.2034, 0.29, 0.4135, 0.5897, 0.8409, 1.199,
1.71, 2.438, 3.477, 4.959, 7.071, 10.08, 14.38, 20.5,
29.24, 41.7, 59.46, 135.438, 279.707, 772.93,
1709.91, 3734.32, 8082.32, 12665.8, 22353.3])
def carreaulaw(x, eta_0, lam, n, a):
return eta_0 * (1.0+(lam*x)**a)**((n-1.0)/a)
# function for genetic algorithm to minimize (sum of squared error)
def sumOfSquaredError(parameterTuple):
warnings.filterwarnings("ignore") # do not print warnings by genetic algorithm
val = carreaulaw(xData, *parameterTuple)
return numpy.sum((yData - val) ** 2.0)
def generate_Initial_Parameters():
parameterBounds = []
parameterBounds.append([0.0, 50.0]) # search bounds for eta_0
parameterBounds.append([0.0, 1.0]) # search bounds for lam
parameterBounds.append([-1.0, 0.0]) # search bounds for n
parameterBounds.append([-200.0, 0.0]) # search bounds for a
# "seed" the numpy random number generator for repeatable results
result = differential_evolution(sumOfSquaredError, parameterBounds, seed=3)
return result.x
# by default, differential_evolution completes by calling curve_fit() using parameter bounds
geneticParameters = generate_Initial_Parameters()
# now call curve_fit without passing bounds from the genetic algorithm,
# just in case the best fit parameters are aoutside those bounds
fittedParameters, pcov = curve_fit(carreaulaw, xData, yData, geneticParameters)
print('Fitted parameters:', fittedParameters)
print()
modelPredictions = carreaulaw(xData, *fittedParameters)
absError = modelPredictions - yData
SE = numpy.square(absError) # squared errors
MSE = numpy.mean(SE) # mean squared errors
RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (numpy.var(absError) / numpy.var(yData))
print()
print('RMSE:', RMSE)
print('R-squared:', Rsquared)
print()
##########################################################
# graphics output section
def ModelAndScatterPlot(graphWidth, graphHeight):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
axes = f.add_subplot(111)
# first the raw data as a scatter plot
axes.plot(xData, yData, 'D')
# create data for the fitted equation plot
xModel = numpy.linspace(min(xData), max(xData))
yModel = carreaulaw(xModel, *fittedParameters)
# now the model as a line plot
axes.plot(xModel, yModel)
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
plt.show()
plt.close('all') # clean up after using pyplot
graphWidth = 800
graphHeight = 600
ModelAndScatterPlot(graphWidth, graphHeight)
</code></pre>