打印曲线拟合功能答案

【问题标题】：Printing Curve Fit Function打印曲线拟合功能
【发布时间】：2018-10-09 03:13:46
【问题描述】：

我一直在努力寻找一种方法来为下面的曲线拟合函数打印确定的参数。该图与我的数据正确匹配，但我不知道如何得到它产生的方程。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='--')

【问题讨论】：

您已经在fitFunc 中实现了等式。元组popt 包含(a, b, c, d)。
把fitFunc中的“print(a, b, c, d)”去掉，在curve_fit调用后加上“print(popt)”。

标签： python numpy printing curve-fitting trigonometry

【解决方案1】：

这是一个使用您的数据的图形示例，请注意方程式。此示例使用从数据散点图中手动估计的初始参数估计值，默认的 curve_fit 估计值默认均为 1.0，在这种情况下效果不佳。

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)

【讨论】：