Curve fitting code

Approximation by linear function:

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

# Curve fit function for linear approx.

def func(t,a,b,):
	return a*t + b


# reading thermodynamic data file 

def read_file():
	temperature = []
	cp = []
	for line in open(\'data\',\'r\'):
		values = line.split(\',\')
		temperature.append(float(values[0]))
		cp.append(float(values[1]))

	return [temperature , cp]


# Main program 

temperature , cp = read_file()	
popt, pcov = curve_fit(func,temperature,cp)
fit_cp = func(np.array(temperature), *popt)


plt.plot(temperature, cp, color=\'blue\',linewidth=3)
plt.plot(temperature, fit_cp, color=\'red\',linewidth=3)
plt.legend([\'Actual data\',\'Curve fit\'])
plt.xlabel(\'Temperature [K]\')
plt.ylabel(\'Cp\')
plt.show()

Approximatiom by cubic polynomial :

The only change in the code above is the change of the function :

# Curve fit function by cubic polynomial

def func(t,a,b,c,d,):
	return a*pow(t,3) + b*pow(t,2) + c*t + d

The higher polynomial by degree the better approximation of the data.

Description:

popt that is an array with optimized values of parameters [ a,b,c,d]

pcov that represent 2d array of the estimated covariance of popt

np.array that creates an array in this case temperature values ada stores it in numpy array