我一直在努力寻找一种方法来获取确定的参数以供下面的曲线拟合函数打印。该图正确地匹配了我的数据，但我不知道如何获得它生成的方程式。任何帮助，将不胜感激！
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit
x_data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]
y_data = [.99, 1, .98, .93, .85, .77, .67, .56, .46, .36, .27, .19, .12, .07, .03, .01, 0, .01, .05, .09, .16, .24, .33, .44, .55, .65, .76, .85, .93, .98, 1]
x_val = np.array(x_data)
y_val = np.array(y_data)
def fitFunc(x, a, b, c, d):
return a * np.sin((2* np.pi / b) * x - c) + d
print(a, b, c, d)
plt.plot(x_val, y_val, marker='.', markersize=0, linewidth='0.5', color='green')
popt, pcov = curve_fit(fitFunc, x_val, y_val)
plt.plot(x_val, fitFunc(x_val, *popt), color='orange', linestyle='--')参考方案
这是一个使用数据的图形示例，请注意公式。本示例使用从数据散点图手动估算的初始参数估算值，默认情况下默认的curve_fit估算值均为1.0，在这种情况下不能很好地工作。
import numpy as np
import scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
xData = np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 25.0, 26.0, 27.0, 28.0, 29.0, 30.0, 31.0])
yData = np.array([.99, 1.0, 0.98, 0.93, 0.85, 0.77, 0.67, 0.56, 0.46, 0.36, 0.27, 0.19, 0.12, 0.07, 0.03, 0.01, 0, 0.01, 0.05, 0.09, 0.16, 0.24, 0.33, 0.44, 0.55, 0.65, 0.76, 0.85, 0.93, 0.98, 1.0])
def fitFunc(x, amplitude, center, width, offset):
return amplitude * np.sin(np.pi * (x - center) / width) + offset
# these are the curve_fit default parameter estimates, and
# do not work well for this data and equation - manually estimate below
#initialParameters = np.array([1.0, 1.0, 1.0, 1.0])
# eyeball the scatterplot for some better, simple, initial parameter estimates
initialParameters = np.array([0.5, 1.0, 16.0, 0.5])
# curve fit the test data using initial parameters
fittedParameters, pcov = curve_fit(fitFunc, xData, yData, initialParameters)
print(fittedParameters)
modelPredictions = fitFunc(xData, *fittedParameters)
absError = modelPredictions - yData
SE = np.square(absError) # squared errors
MSE = np.mean(SE) # mean squared errors
RMSE = np.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (np.var(absError) / np.var(yData))
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 = np.linspace(min(xData), max(xData))
yModel = fitFunc(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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