问如何在python中校正过拟合的样条曲线

EN

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.interpolate import UnivariateSpline

fig, ax = plt.subplots()
fig.set_size_inches(13,7, forward=True)
        
width=1.0
       
#data=pd.read_excel("h:/projects/psc/output/data.xlsx")

data=pd.DataFrame({'x':\[-29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30\],
                   'y':\[0.002383790226460071, 0.002383790226460071, 0.005164878823996822, 0.004370282081843465, 0.005164878823996822, 0.002383790226460071, 0.003178386968613429, 0.005959475566150178, 0.005959475566150178, 0.006754072308303536, 0.007945967421533572, 0.003575685339690107, 0.001986491855383393, 0.003575685339690107, 0.003972983710766786, 0.00278108859753675, 0.005959475566150178, 0.007151370679380214, 0.004767580452920143, 0.005164878823996822, 0.003575685339690107, 0.004370282081843465, 0.007945967421533572, 0.01311084624553039, 0.01072705601907032, 0.01430274135876043, 0.01231624950337704, 0.01589193484306714, 0.02264600715137068, 0.09654350417163289, 0.05164878823996821, 0.0166865315852205, 0.01549463647199046, 0.01350814461660707, 0.01191895113230036, 0.01191895113230036, 0.00874056416368693, 0.01152165276122368, 0.007151370679380214, 0.009137862534763607, 0.006356773937226857, 0.007151370679380214, 0.00834326579261025, 0.006356773937226857, 0.005562177195073501, 0.006754072308303536, 0.005164878823996822, 0.005164878823996822, 0.005959475566150178, 0.004767580452920143, 0.00278108859753675, 0.007945967421533572, 0.001589193484306714, 0.00278108859753675, 0.003178386968613429, 0.003575685339690107, 0.003178386968613429, 0.004370282081843465, 0.005562177195073501, 0.004370282081843465\]})
       
plt.bar(data\['x'\],data\['y'\],width, color='r',  alpha=0.95)
          
x=data\['x'\]
y=data\['y'\]
x_new = np.linspace(x.min(),x.max(),300)
spl=UnivariateSpline(x,y)
spl.set_smoothing_factor(0.001)
y_smooth =spl(x_new)
plt.plot(x_new,y_smooth, color='b', alpha=0.95)][1]    

import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.optimize import differential_evolution
import warnings

xData = numpy.array([-29.0, -28.0, -27.0, -26.0, -25.0, -24.0, -23.0, -22.0, -21.0, -20.0, -19.0, -18.0, -17.0, -16.0, -15.0, -14.0, -13.0, -12.0, -11.0, -10.0, -9.0, -8.0, -7.0, -6.0, -5.0, -4.0, -3.0, -2.0, -1.0, 0.0, 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])
yData = numpy.array([0.002383790226460071, 0.002383790226460071, 0.005164878823996822, 0.004370282081843465, 0.005164878823996822, 0.002383790226460071, 0.003178386968613429, 0.005959475566150178, 0.005959475566150178, 0.006754072308303536, 0.007945967421533572, 0.003575685339690107, 0.001986491855383393, 0.003575685339690107, 0.003972983710766786, 0.00278108859753675, 0.005959475566150178, 0.007151370679380214, 0.004767580452920143, 0.005164878823996822, 0.003575685339690107, 0.004370282081843465, 0.007945967421533572, 0.01311084624553039, 0.01072705601907032, 0.01430274135876043, 0.01231624950337704, 0.01589193484306714, 0.02264600715137068, 0.09654350417163289, 0.05164878823996821, 0.0166865315852205, 0.01549463647199046, 0.01350814461660707, 0.01191895113230036, 0.01191895113230036, 0.00874056416368693, 0.01152165276122368, 0.007151370679380214, 0.009137862534763607, 0.006356773937226857, 0.007151370679380214, 0.00834326579261025, 0.006356773937226857, 0.005562177195073501, 0.006754072308303536, 0.005164878823996822, 0.005164878823996822, 0.005959475566150178, 0.004767580452920143, 0.00278108859753675, 0.007945967421533572, 0.001589193484306714, 0.00278108859753675, 0.003178386968613429, 0.003575685339690107, 0.003178386968613429, 0.004370282081843465, 0.005562177195073501, 0.004370282081843465])


def LorentzianPeakG_Offset(x_in, a, b, c, Offset): # from zunzun.com peak equation search
    temp = 0.0
    temp = a/ (1.0 + numpy.power((x_in-b)/c, 2.0))
    temp += Offset
    return temp

# function for genetic algorithm to minimize (sum of squared error)
def sumOfSquaredError(parameterTuple):
    warnings.filterwarnings("ignore") # do not print warnings by genetic algorithm
    val = LorentzianPeakG_Offset(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([minX, maxX]) # seach bounds for a
    parameterBounds.append([minX, maxX]) # seach bounds for b
    parameterBounds.append([minX, maxX]) # seach bounds for c
    parameterBounds.append([0.0, maxY]) # seach bounds for Offset

    # "seed" the numpy random number generator for repeatable results
    result = differential_evolution(sumOfSquaredError, parameterBounds, seed=3)
    return result.x

# generate initial parameter values
geneticParameters = generate_Initial_Parameters()

# curve fit the test data
fittedParameters, pcov = curve_fit(LorentzianPeakG_Offset, xData, yData, geneticParameters)

print('Parameters', fittedParameters)

modelPredictions = LorentzianPeakG_Offset(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('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), 250)
    yModel = LorentzianPeakG_Offset(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)