使用scipy.optimize.curve_fit来拟合分段函数

Question

我正在尝试编写一个程序，将.csv文件中的两组数据读入数组，然后将其与分段函数相匹配。对我来说最重要的是这些配合是同时完成的，因为它们具有相同的参数。这种分段功能是我尝试这样做的，尽管如果你知道一种更好的方法来同时适应它们，我也非常欣赏有关这方面的建议。

为避免上传csv文件，我已将数据直接添加到数组中。

import numpy
import csv
import matplotlib
from scipy import optimize

xdata = [2.0, 10.0, 30.0, 50.0, 70.0, 90.0, 110.0, 130.0, 150.0, 250.0, 400.0, 1002.0, 1010.0, 1030.0, 1050.0, 1070.0, 1090.0, 1110.0, 1130.0, 1150.0, 1250.0, 1400.0]
ydata = [0.013833958803215633, 0.024273268442992078, 0.08792766000711709, 0.23477725658012044, 0.31997367288103884, 0.3822895295625711, 0.46037063893452784, 0.5531831477605121, 0.559757863748663, 0.6443036770720387, 0.7344601382896991, 2.6773979205076136e-09, 9.297289736857164e-10, 0.10915332214935693, 0.1345307163724643, 0.1230161681870127, 0.11286094974672768, 0.09186485171688986, 0.06609131137369342, 0.052616358869021135, 0.034629686697483314, 0.03993853791147095]

前11个点我想要适合标记为＆＃39; SSdecay＆＃39;的功能，而第二个11点我想要适合标记为＆＃39; SUdecay＆＃39;的功能。我同时尝试这样做的尝试是将分段函数标记为“#fenfunciton＆＃39;。

#defines functions to be used in fitting

#to fit the first half of data
def SSdecay(x, lam1, lam2, norm, xoff):
    return norm*(1 + lam2/(lam1 - lam2)*numpy.exp(-lam1*(x - xoff)) -
        lam1/(lam1 - lam2)*numpy.exp(-lam2*(x - xoff)))

#to fit the second half of data
def SUdecay(x, lam1, lam2, norm, xoff):
    return norm*(lam1/(lam1 - lam2))*(-numpy.exp(-lam1*(x - xoff)) +
        numpy.exp(-lam2*(x - xoff)))

#piecewise function combining SS and SU functions to fit the whole data set
def fitfunction(x, lam1, lam2, norm, xoff):
    y = numpy.piecewise(x,[x < 1000, x >= 1000],[SSdecay(x, lam1, lam2, norm, xoff),SUdecay(x, lam1, lam2, norm, xoff)])
    return y

#fits the piecewise function with initial guesses for parameters
p0=[0.01,0.02,1,0]
popt, pcov = optimize.curve_fit(fitfunction, xdata, ydata, p0)

print(popt)
print(pcov)

运行此操作后，我收到错误：

ValueError: NumPy boolean array indexing assignment cannot assign 22 input values to the 11 output values where the mask is true

似乎curve_fit不喜欢我使用分段函数，但我不确定为什么或者它是否是一个可修复的问题。

Answer 1

以下是使用标准化数据单独拟合两个函数的结果。它们看起来不太可能作为单个分段方程运行，请参见下面的情节图像和源代码。对于这两个方程，我也有非常不同的拟合参数：

SS参数：[0.0110936,0.09560932,0.772929264,6.82520026]

SU参数：[3.46853883e-02,9.54208972e-03,1.99877873e-01,1.00465563e + 03]

import numpy
import matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

xdata = [2.0, 10.0, 30.0, 50.0, 70.0, 90.0, 110.0, 130.0, 150.0, 250.0, 400.0, 1002.0, 1010.0, 1030.0, 1050.0, 1070.0, 1090.0, 1110.0, 1130.0, 1150.0, 1250.0, 1400.0]
ydata = [0.013833958803215633, 0.024273268442992078, 0.08792766000711709, 0.23477725658012044, 0.31997367288103884, 0.3822895295625711, 0.46037063893452784, 0.5531831477605121, 0.559757863748663, 0.6443036770720387, 0.7344601382896991, 2.6773979205076136e-09, 9.297289736857164e-10, 0.10915332214935693, 0.1345307163724643, 0.1230161681870127, 0.11286094974672768, 0.09186485171688986, 0.06609131137369342, 0.052616358869021135, 0.034629686697483314, 0.03993853791147095]

#to fit the first half of data
def SSdecay(x, lam1, lam2, norm, xoff):
    return norm*(1 + lam2/(lam1 - lam2)*numpy.exp(-lam1*(x - xoff)) -
        lam1/(lam1 - lam2)*numpy.exp(-lam2*(x - xoff)))

#to fit the second half of data
def SUdecay(x, lam1, lam2, norm, xoff):
    return norm*(lam1/(lam1 - lam2))*(-numpy.exp(-lam1*(x - xoff)) +
        numpy.exp(-lam2*(x - xoff)))

# some initial parameter values
initialParameters_ss = numpy.array([0.01, 0.02, 1.0, 0.0])
initialParameters_su = initialParameters_ss # same values for this example

# curve fit the equations individually to their respective data
ssParameters, pcov = curve_fit(SSdecay, xdata[:11], ydata[:11], initialParameters_ss)
suParameters, pcov = curve_fit(SUdecay, xdata[11:], ydata[11:], initialParameters_su)

# values for display of fitted function
lam1_ss, lam2_ss, norm_ss, xoff_ss = ssParameters
lam1_su, lam2_su, norm_su, xoff_su = suParameters

# for plotting the fitting results
y_fit_ss = SSdecay(xdata[:11], lam1_ss, lam2_ss, norm_ss, xoff_ss) # first data set, first equation
y_fit_su = SUdecay(xdata[11:], lam1_su, lam2_su, norm_su, xoff_su) # second data set, second equation

plt.plot(xdata, ydata, 'D') # plot the raw data as a scatterplot
plt.plot(xdata[:11], y_fit_ss) # plot the SS equation using the fitted parameters
plt.plot(xdata[11:], y_fit_su) # plot the SU equation using the fitted parameters
plt.show()

print('SS parameters:', ssParameters)
print('SU parameters:', suParameters)