Error handling 使用scipy.odr拟合曲线
我试图通过一个fit函数来拟合一组数据点,该函数依赖于两个变量,让我们调用这些扩展数据和sdata。问题是我的曲线相当平坦,我希望它或多或少地“跟随点” 我尝试使用scipy.odr来拟合曲线,效果相当不错,只是曲线太平了:Error handling 使用scipy.odr拟合曲线,error-handling,scipy,curve-fitting,one-definition-rule,Error Handling,Scipy,Curve Fitting,One Definition Rule,我试图通过一个fit函数来拟合一组数据点,该函数依赖于两个变量,让我们调用这些扩展数据和sdata。问题是我的曲线相当平坦,我希望它或多或少地“跟随点” 我尝试使用scipy.odr来拟合曲线,效果相当不错,只是曲线太平了: import numpy as np from math import pi from math import sqrt from math import log from scipy import optimize import scipy.optimize import
import numpy as np
from math import pi
from math import sqrt
from math import log
from scipy import optimize
import scipy.optimize
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.odr import *
mudr=np.array([ 57.43708609, 46.26119205, 55.60688742, 33.21615894,
28.27072848, 22.54649007, 21.80662252, 11.21483444, 5.80211921])
#xdata points
dme=array([ 128662.54890776, 105265.32915726, 128652.56835434,
77968.67019573, 66273.56542068, 58464.58559543,
54570.66624991, 27286.90038703, 19480.92689266]) #xdata error
dmss22=np.array([ 4.90050000e+17, 4.90050000e+17, 4.90050000e+17,
4.90050000e+17, 4.90050000e+17, 4.90050000e+17,
4.90050000e+17, 4.90050000e+17, 4.90050000e+17]) #sdata points
dmse=np.array([ 1.09777592e+21, 1.11512117e+21, 1.13381702e+21,
1.15033267e+21, 1.14883089e+21, 1.27076265e+21,
1.22637165e+21, 1.19237598e+21, 1.64539205e+21]) # sdata error
F=np.array([ 115.01944248, 110.24354867, 112.77812389, 104.81830088,
104.35746903, 101.32016814, 100.54513274, 96.94226549,
93.00424779]) #ydata points
dF=np.array([ 72710.75386699, 72590.6256987 , 176539.40403673,
130555.27503081, 124299.52080164, 176426.64340597,
143013.52848306, 122117.93022746, 157547.78395513])#ydata error
def Ffitsso(p,X,B=2.58,Fc=92.2,mu=770,Za=0.9468): #fitfunction
temp1 = (2*B*X[0])/(4*pi*Fc)**2
temp2 = temp1*(afij[0]+afij[1]*np.log((2*B*X[0])/mu**2))
temp3 = temp1**2*(afij[2]+afij[3]*np.log((2*B*X[0])/mu**2)+\
afij[4]*(np.log((2*B*X[0])/mu**2))**2)
temp4 = temp1**3*(afij[5]+afij[6]*np.log((2*B*X[0])/mu**2)+\
afij[7]*(np.log((2*B*X[0])/mu**2))**2+\
afij[8]*(np.log((2*B*X[0])/mu**2))**3)
return Fc/Za*(1+p[0]*X[1])*(1+temp2+temp3+temp4)+p[1]
#fitting using scipy.odr
xtot=np.row_stack( (mudr, dmss22) )
etot=np.row_stack( (Ze, dmss22e) )
fitting = Model(Ffitsso)
mydata = RealData(xtot, F, sx=etot2, sy=dF)
myodr = ODR(mydata, fitting, beta0=[0, 100])
myoutput = myodr.run()
myoutput.pprint()
bet=myoutput.beta
plt.plot(mudr,F,"b^")
plt.plot(mudr,Ffitsso(bet,[mudr,dmss22]))
fit函数中的p[0]*X[0]应该比1小,但使用fit时,p[0]的值为e-18,而dmss22的值为e-17,这不够小
更糟糕的是,它是负的,这意味着函数减少了,这是不应该发生的,它应该像绘制的数据点一样增加
编辑:我修正了,不知道它对初始beta值如此敏感,把beta[0]=1.5*10(-15)放进去就行了** 这是一个图形拟合工具,同时具有曲线拟合和ODR拟合工具,使用scipy的差分进化(DE)遗传算法为非线性解算器提供初始参数估计。DE的scipy实现使用拉丁超立方体算法来确保对参数空间的彻底搜索,这需要在其中搜索参数边界——在本例中,这些边界取自数据的最大值和最小值。注意,给出初始参数估计的界限要比给出单个特定值容易得多
import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
import scipy.odr
from scipy.optimize import differential_evolution
import warnings
xData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.0, 6.6, 7.7, 0.0])
yData = numpy.array([1.1, 20.2, 30.3, 40.4, 50.0, 60.6, 70.7, 0.1])
def func(x, a, b, c, d, offset): # curve fitting function for curve_fit()
return a*numpy.exp(-(x-b)**2/(2*c**2)+d) + offset
def func_wrapper_for_ODR(parameters, x): # parameter order for ODR
return func(x, *parameters)
# 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)
parameterBounds = []
parameterBounds.append([minY, maxY]) # search bounds for a
parameterBounds.append([minX, maxX]) # search bounds for b
parameterBounds.append([minX, maxX]) # search bounds for c
parameterBounds.append([minY, maxY]) # search bounds for d
parameterBounds.append([0.0, maxY]) # search bounds for Offset
# "seed" the numpy random number generator for repeatable results
result = differential_evolution(sumOfSquaredError, parameterBounds, seed=3)
return result.x
geneticParameters = generate_Initial_Parameters()
##########################
# curve_fit section
##########################
fittedParameters_curvefit, pcov = curve_fit(func, xData, yData, geneticParameters)
print('Fitted parameters curve_fit:', fittedParameters_curvefit)
print()
modelPredictions_curvefit = func(xData, *fittedParameters_curvefit)
absError_curvefit = modelPredictions_curvefit - yData
SE_curvefit = numpy.square(absError_curvefit) # squared errors
MSE_curvefit = numpy.mean(SE_curvefit) # mean squared errors
RMSE_curvefit = numpy.sqrt(MSE_curvefit) # Root Mean Squared Error, RMSE
Rsquared_curvefit = 1.0 - (numpy.var(absError_curvefit) / numpy.var(yData))
print()
print('RMSE curve_fit:', RMSE_curvefit)
print('R-squared curve_fit:', Rsquared_curvefit)
print()
##########################
# ODR section
##########################
data = scipy.odr.odrpack.Data(xData,yData)
model = scipy.odr.odrpack.Model(func_wrapper_for_ODR)
odr = scipy.odr.odrpack.ODR(data, model, beta0=geneticParameters)
# Run the regression.
odr_out = odr.run()
print('Fitted parameters ODR:', odr_out.beta)
print()
modelPredictions_odr = func(xData, *odr_out.beta)
absError_odr = modelPredictions_odr - yData
SE_odr = numpy.square(absError_odr) # squared errors
MSE_odr = numpy.mean(SE_odr) # mean squared errors
RMSE_odr = numpy.sqrt(MSE_odr) # Root Mean Squared Error, RMSE
Rsquared_odr = 1.0 - (numpy.var(absError_odr) / numpy.var(yData))
print()
print('RMSE ODR:', RMSE_odr)
print('R-squared ODR:', Rsquared_odr)
print()
##########################################################
# graphics output section
def ModelsAndScatterPlot(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 plots
xModel = numpy.linspace(min(xData), max(xData))
yModel_curvefit = func(xModel, *fittedParameters_curvefit)
yModel_odr = func(xModel, *odr_out.beta)
# now the models as line plots
axes.plot(xModel, yModel_curvefit)
axes.plot(xModel, yModel_odr)
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
ModelsAndScatterPlot(graphWidth, graphHeight)