Fitting to exponential functions using python

Question

I am trying to fit a data set on exponential funtion. To do this I have created this function to recreate exponential functions:

def exponential(x,a,b,c):
    return a*(b**x)+c

I am using the module scipy . Here the code to do the fit and print it:

def fit_exponential(x_data,y_data,file):
  params,paramscov= optimize.curve_fit(exponential, x_data, y_data,p0=[1,2,3])

  #Here we calculate the Coeficent of deternination (R²)
  #It is a statistical measure of how well the regression predictions approximate the real data points.
  residuals = y_data - exponential(x_data, *params)

  ss_res = np.sum(residuals**2)
  ss_tot = np.sum((y_data-np.mean(y_data))**2)
  r_squared = 1 - (ss_res / ss_tot)
  print('R²= ',r_squared)

  result = print_exponential(*params)
  print(result)

  #Compound the chart of data and the data with a little text of results
  plt.figure(figsize=(6, 4))
  plt.plot(x_data, exponential(x_data,*params),label='Fitted function',color='m')
  plt.scatter(x_data, y_data, label='Data',color='salmon')

  texto='R²= '+str(round(r_squared,5))+'\n'+result

  plt.text(x_data[-1]*0.55, y_data[-1]*0.15, texto,verticalalignment='center',bbox=dict(facecolor='m', alpha=0.3))

  plt.legend(loc='best')
  plt.xlabel('Size N')
  plt.ylabel('Steps')

  plt.savefig(file)

What I am obtaining is this chart:

As we see the data seems to be exponential but I cant fit a function to it. I have already see some posts, but I couldn't do it.

Can you include your import statements so we can run the code? — Nicolas Gervais
– Nicolas Gervais, Commented Nov 7, 2019 at 14:56

James Phillips · Accepted Answer · 2019-11-07 16:24:59Z

3

Here is a graphical Python fitter with your equation and data extracted from the scatterplot, you should re-fit using the actual data.

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

xData = numpy.array([1.408e-01, 8.169e-01, 1.915e+00, 3.183e+00, 3.972e+00, 4.986e+00, 5.972e+00, 6.986e+00, 7.972e+00, 8.873e+00, 9.915e+00, 1.087e+01, 1.192e+01, 1.299e+01, 1.386e+01, 1.496e+01, 1.594e+01, 1.792e+01, 1.682e+01, 1.890e+01, 1.992e+01]) 
yData = numpy.array([8.214e-01, 8.214e-01, 8.214e-01, 8.214e-01, 6.160e-01, 8.214e-01, 8.214e-01, 4.107e-01, 1.027e+00, 1.027e+00, 8.214e-01, 1.027e+00, 1.027e+00, 1.643e+00, 1.643e+00, 3.285e+00, 5.749e+00, 2.300e+01, 1.170e+01, 4.723e+01, 9.651e+01])


def func(x, a, b, c):
    return a*(b**x)+c


# these are the same as the scipy defaults
initialParameters = numpy.array([1.0, 1.0, 1.0])

# curve fit the test data
fittedParameters, pcov = curve_fit(func, xData, yData, initialParameters)

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('Parameters:', fittedParameters)
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)

answered Nov 7, 2019 at 16:24

James Phillips

4,6673 gold badges16 silver badges11 bronze badges

Sign up to request clarification or add additional context in comments.

3 Comments

Javier Jiménez de la Jara Over a year ago

Oh thanks you so much, that looks incredible. I am still thinking why it didnt work to me.

James Phillips Over a year ago

I got the same fitted parameters from your code as with my code. If you look at my plotting code, it has xModel and yModel to smoothly draw the fitted curve.

JeeyCi Over a year ago

sort xData first

Collectives™ on Stack Overflow

Fitting to exponential functions using python

1 Answer 1

3 Comments

Your Answer

Linked

Hot Network Questions

Collectives™ on Stack Overflow

1 Answer 1

3 Comments

Your Answer

Sign up or log in

Post as a guest

Linked

Related