[英]Using scipy curve_fit to fit exponential curve (fitted curve does match real curve)
我正在嘗試使用curve_fit (scipy.optimize)
擬合指數曲線,但擬合曲線看起來與真實曲線完全不同。 現在我正在使用以下代碼:
X=[0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0]
Y=[0.090316199, -0.078157925, -0.350137315, -0.695193468, -1.106773689, -1.60467115, -2.196169408]
#plot Y against X
fig = plt.figure(num=None, figsize=(9, 7),facecolor='w', edgecolor='k')
ax=fig.add_subplot(111)
ax.scatter(X,Y)
#fit using curve_fit
popt, pcov = curve_fit(func, X, Y,maxfev=10000)
#compute Y_estiamted using fitted parameters
Y_estimated=[popt[0]*np.exp(i+popt[1])+popt[2] for i in X]
#plot Y_estiamted against X
ax.scatter(X,Y_estimated, c='r')
def func(x,a,b,c):
return a*(np.exp(x+b))+c
藍色曲線是真實曲線,紅色曲線是擬合曲線。
如您所見,擬合的紅色曲線與真正的藍色曲線完全不匹配。 任何幫助,將不勝感激!
我認為問題在於模型功能。 如果您將其更改為如下函數:
def func(x, a, b, c, d):
return a * (np.exp(d*(x + b))) + c
我在代碼中更改了一些內容:
def func(x, a, b, c, d):
return a * (np.exp(d*(x + b))) + c
X = [0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0]
Y = [0.090316199, -0.078157925, -0.350137315, -0.695193468, -1.106773689, -1.60467115, -2.196169408]
# plot Y against X
fig = plt.figure(num=None, figsize=(9, 7), facecolor='w', edgecolor='k')
ax = fig.add_subplot(111)
ax.scatter(X, Y)
# fit using curve_fit
popt, pcov = curve_fit(func, X, Y, maxfev=10000)
# compute Y_estiamted using fitted parameters
x = np.linspace(min(X), max(X), 100)
Y_estimated = func(x, *popt)
# plot Y_estiamted against X
ax.plot(x, Y_estimated, c='r')
我非常適合具有單個形狀參數和小偏移量的漸近指數類型的方程,“1.0 - pow(a, x) + b”。 這是一個圖形化的 Python 擬合器,使用這個方程和你的數據。
import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
# ignore warnings within curve_fit() routine
import warnings
warnings.filterwarnings("ignore")
X=[0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0]
Y=[0.090316199, -0.078157925, -0.350137315, -0.695193468, -1.106773689, -1.60467115, -2.196169408]
# alias data to match previous example
xData = numpy.array(X, dtype=float)
yData = numpy.array(Y, dtype=float)
def func(x, a, b): # Asymptotic Exponential A equation with offset from zunzun.com
return 1.0 - numpy.power(a, x) + b
# these are the same as the scipy defaults
initialParameters = numpy.array([1.0, 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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