我有一個數(shù)據(jù)集，我知道它適合以下形式的曲線：y = a x2我想提取a.在 Python（使用 scipy 等）中解決這個問題的最佳方法是什么？
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慕的地6264312
TA貢獻1817條經(jīng)驗 獲得超6個贊
這是使用 scipy 的 curve_fit() 的圖形擬合器示例：
import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
xData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.0, 6.6, 7.7])
yData = numpy.array([1.1, 20.2, 30.3, 60.4, 50.0, 60.6, 70.7])
def func(x, a):
return (a * numpy.square(x))
# same as the scipy default
initialParameters = numpy.array([1.0])
# curve fit the test data
fittedParameters, pcov = curve_fit(func, xData, yData, initialParameters)
modelPredictions = func(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('Parameters:', fittedParameters)
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 = func(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)
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