[英]Data fitting with curve_fit not correct
我有一些实验数据需要拟合,因此我们可以为某些y值阐明x值。
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.interpolate import interp1d
#from xlrd import open_workbook
points = np.array([(0, -0.0142294), (20, 0.0308458785714286), (50,
0.1091054), (100
,0.2379176875), (200, 0.404354166666667)])
x = points[:,0]
y = points[:,1]
def func(x, p1,p2):
return p1*(1-np.e**(-p2*x))
popt, pcov = curve_fit(func, x, y)
p1 = popt[0]
p2 = popt[1]
curvex=np.linspace(0,200,1000)
fit = func(curvex, p1, p2)
plt.plot(x, y, 'yo', label='data')
f = interp1d(fit, curvex, kind = 'nearest')
print (f(100))
plt.plot(curvex,fit,'r', linewidth=1)
plt.plot(x,y,'x',label = 'Xsaved')
plt.show()
数据未正确安装。 帮助将不胜感激。
这是一个使用您的数据和方程式的图形拟合器示例,其中scipy的differential_evolution遗传算法用于提供初始参数估计值。 差分进化的科学实现是Latin Hypercube算法,以确保彻底搜索参数空间,这需要在搜索范围内进行。 在此示例中,我将数据的最大值和最小值用作搜索范围,在这种情况下,这似乎可行。 请注意,查找范围要比特定值容易得多。
import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.optimize import differential_evolution
import warnings
points = numpy.array([(0, -0.0142294), (20, 0.0308458785714286), (50, 0.1091054), (100 ,0.2379176875), (200, 0.404354166666667)])
x = points[:,0]
y = points[:,1]
# rename to match previous example code below
xData = x
yData = y
def func(x, p1,p2):
return p1*(1-numpy.exp(-p2*x))
# function for genetic algorithm to minimize (sum of squared error)
def sumOfSquaredError(parameterTuple):
warnings.filterwarnings("ignore") # do not print warnings by genetic algorithm
val = func(xData, *parameterTuple)
return numpy.sum((yData - val) ** 2.0)
def generate_Initial_Parameters():
# min and max used for bounds
maxX = max(xData)
minX = min(xData)
maxY = max(yData)
minY = min(yData)
minAllData = min(minX, minY)
maxAllData = min(maxX, maxY)
parameterBounds = []
parameterBounds.append([minAllData, maxAllData]) # search bounds for p1
parameterBounds.append([minAllData, maxAllData]) # search bounds for p2
# "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(func, xData, yData, geneticParameters)
print('Fitted parameters:', fittedParameters)
print()
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()
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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