[英]RuntimeError: using curve_fit in Python
我是Python的新手,我正在嘗試使用一個小的數據框進行繪制。 但是我也想使用curve_fit來獲取某些參數的值。
######Fitting Using Data Frame######
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit
# Data into a dictionary
data = {'keV':[22.16,32.19,8.05,17.48,13.39,44.47,5],'ToT':[31.68,39.87,10.67,26.38,21.4,53.56,0]}
# Create dataframe and get only the values of arrays
df = pd.DataFrame(data)
xdata = df['keV'].values
ydata = df['ToT'].values
# Main function for the mathematical method
def main_test(x, a, b,c,t):
return a*x +b - c/(x-t)
# Guess of the fit values
guess = [1,1,100,150]
n = len(xdata)
# Empty np array that will get these values
y = np.empty(n)
# Repeat in all these times
c, cov = curve_fit(main_test,xdata,ydata)
# THE MOST IMPORTANT PART OF THE CODE. TO GET THE PARAMETERS VALUES.
print(c)
for sample in range(n):
# Populating y with guess numbers = Prediction
y[sample] = main_test(xdata[sample],a[0],b[1],c[2],t[3])
plt.figure(figsize=(6,4))
plt.scatter(xdata,ydata)
plt.plot(xdata, y,'r.')
plt.show()
RuntimeError:找不到最佳參數:函數調用的數量已達到maxfev = 1000。
這是找到良好的啟動參數的問題。 這是一個使用您的數據和方程式的圖形化求解器,其中scipy的differential_evolution遺傳算法模塊用於確定curve_fit()的初始參數估計。 該scipy模塊使用Latin Hypercube算法來確保對參數空間進行徹底搜索,從而需要在搜索范圍內進行搜索。 由於搜索范圍可能很寬泛,因此我首先嘗試對所有參數進行+/- 100.0的搜索范圍,並且該方法有效。
import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.optimize import differential_evolution
import warnings
keV = [22.16,32.19,8.05,17.48,13.39,44.47,5]
ToT = [31.68,39.87,10.67,26.38,21.4,53.56,0]
# rename data to re-use previous example code
xData = numpy.array(keV)
yData = numpy.array(ToT)
# mathematical model
def func(x, a, b,c,t):
return a*x +b - c/(x-t)
# 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():
parameterBounds = []
parameterBounds.append([-100.0, 100.0]) # search bounds for a
parameterBounds.append([-100.0, 100.0]) # search bounds for b
parameterBounds.append([-100.0, 100.0]) # search bounds for c
parameterBounds.append([-100.0, 100.0]) # search bounds for t
# "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('keV') # X axis data label
axes.set_ylabel('ToT') # 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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