Python code for fitting a linear and cubic polynomial for the Cp data & Plotting the curves along with the raw data points

Problem Statement: Matlab code for fitting a linear and cubic polynomial for the Cp data & Plotting the curves along with the raw data points.

Given Data:'data' file (which contain actual temperature & cp value)

Program:

# Step 1
# Importing necessary library for this program
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit
import math

#---------------------------------------------------------------------------------------------------------------------

# Step 2
# Defining the linear function
def linear(t,a,b):
	return a*t+b

#---------------------------------------------------------------------------------------------------------------------

# Step 3
# Defining the cubic function
def cubic(t,a,b,c,d):
	return a*pow(t,3)+b*pow(t,2)+c*t+d

#---------------------------------------------------------------------------------------------------------------------

# Step 4
# Reading the data file & extracting actual value of temperature & cp
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]

#---------------------------------------------------------------------------------------------------------------------

# Step 5
# Writing the function of calculate the mean of array
def mean(numbers):
    return float(sum(numbers)) / max(len(numbers), 1)

#---------------------------------------------------------------------------------------------------------------------

# Step 6
# Writing the function to calculate the value of cp by dividing the temperature array in N of group by using linear curve fitting 
def lineardivide(cp,temperature,no_of_division):
	
	div=int(len(cp)/no_of_division)
	fit_cp=[]

	a=0
	for i in range(0,no_of_division):
		
	    temperature_div=[]
	    cp_div=[]
	    for ct in range(a,a+(div)):
	        temperature_div.append(temperature[ct])
	        cp_div.append(cp[ct])
	    popt,pcov=curve_fit(linear,temperature_div,cp_div)
	    fit_cp_div=linear(np.array(temperature_div),*popt)
	    c=0
	    for b in range(c,c+(div)):
	        fit_cp.append(fit_cp_div[b])
	    a=a+div
	return fit_cp

#-------------------------------------------------------------------------------------------------------------------------------------

# Step 7
# Writing the function to calculate the value of cp by dividing the temperature array in N of group by using cubic curve fitting 
def cubicdivide(cp,temperature,no_of_division):
	
	div=int(len(cp)/no_of_division)
	fit_cp=[]

	a=0
	for i in range(0,no_of_division):
		
	    temperature_div=[]
	    cp_div=[]
	    for ct in range(a,a+(div)):
	        temperature_div.append(temperature[ct])
	        cp_div.append(cp[ct])
	    popt,pcov=curve_fit(cubic,temperature_div,cp_div)
	    fit_cp_div=cubic(np.array(temperature_div),*popt)
	    c=0
	    for b in range(c,c+(div)):
	        fit_cp.append(fit_cp_div[b])
	    a=a+div

	return fit_cp

#---------------------------------------------------------------------------------------------------------------------

# Step 8
# Writing function to plot the results
def plot(cp,fit_cp,div_fit_cp,i):
	plt.figure(i)
	plt.plot(temperature,cp,,linewidth=3)
	plt.plot(temperature, fit_cp,,linewidth=2)
	plt.plot(temperature, div_fit_cp,color="green",linewidth=1)
	plt.legend(['Actual data','Simple Curve fit','best fit'])
	plt.xlabel('Temperature[K]')
	plt.ylabel('cp')

#---------------------------------------------------------------------------------------------------------------------

# Step 9
# Writing the function to calculate the choleretics of new cp values
def best_fit(cp,cp_fit):

	error=np.array(cp_fit)-np.array(cp)
	# Calculation of sum of squared error
	SSE = sum(error*error)
 
	# Calculation of sum of squares of regression
	b=mean(cp)
	d=[]
	for i in range(0,len(cp)):
		c=fit_cp[i]-b
		d.append(c*c)

	SSR = sum(d)

	# Calculation of R_square
	SST = SSR + SSE
	R1_square = SSR/SST
	
	
	if R1_square>0.95:
		print('Fitness Characteristics: Best Fit (R^2 =',R1_square,')')
	else:
		print('Fitness Characteristics: Not Best Fit (R^2 =',R1_square,')')
    
#---------------------------------------------------------------------------------------------------------------------

# Step 10
# Main Program
# Writing the main program & extracting the value of cp & temperature

temperature,cp=read_file()

#---------------------------------------------------------------------------------------------------------------------

# Step 11
# Calculate the value of cp with respect temperature by linear curve fitting method
print('***************************************************************************')
print('Linear Curve Fitting')
print('***************************************************************************')

#---------------------------------------------------------------------------------------------------------------------

# Step 12
# Calculating the value of cp with respect temperature by simple linear curve fitting method
fit_cp=lineardivide(cp,temperature,1)
print('Fitness Characteristics of curve by Simple Linear Curve Fitting')

#---------------------------------------------------------------------------------------------------------------------

# Step 13
# Calculating the fitting characteristics of curve
best_fit(cp,fit_cp)
print('----------------------------------------------------------------------------')

#---------------------------------------------------------------------------------------------------------------------

# Step 14
# Calculating the value of cp with respect temperature by divide linear curve fitting method
no_of_division=4
div_fit_cp=lineardivide(cp,temperature,no_of_division)
print('Fitness Characteristics of curve by Divide Linear Curve Fitting')

#---------------------------------------------------------------------------------------------------------------------

# Step 15
# Calculating the fitting characteristics of curve
best_fit(cp,div_fit_cp)
print('----------------------------------------------------------------------------')

#---------------------------------------------------------------------------------------------------------------------

# Step 16
# Plotting the curve
plot(cp,fit_cp,div_fit_cp,1)
plt.title('Linear Curve Fit')
plt.show()

#---------------------------------------------------------------------------------------------------------------------

# Step 17
# Calculate the value of cp with respect temperature by cubic curve fitting method
print('\n***************************************************************************')
print('Cubic Curve Fitting')
print('***************************************************************************')

#---------------------------------------------------------------------------------------------------------------------

# Step 18
# Calculating the value of cp with respect temperature by simple cubic curve fitting method
fit_cp=cubicdivide(cp,temperature,1)
print('Fitness Characteristics of curve by Simple Cubic Curve Fitting')

#---------------------------------------------------------------------------------------------------------------------

# Step 19
# Calculating the fitting characteristics of curve
best_fit(cp,fit_cp)
print('----------------------------------------------------------------------------')

#---------------------------------------------------------------------------------------------------------------------

# Step 20
# Calculating the value of cp with respect temperature by divide cubic curve fitting method
no_of_division=2
div_fit_cp=cubicdivide(cp,temperature,no_of_division)
print('Fitness Characteristics of curve by Divide Cubic Curve Fitting')

#---------------------------------------------------------------------------------------------------------------------

# Step 21
# Calculating the fitting characteristics of curve 
best_fit(cp,div_fit_cp)
print('----------------------------------------------------------------------------')
plot(cp,fit_cp,div_fit_cp,2)
plt.title('Cubic Curve Fit')
plt.show()

#--------------------------------------------------------END-----------------------------------------------------------

Step Wise explanation:

Step 1: Importing necessary library for this program

Step 2: Defining the linear function

Step 3: Defining the cubic function

Step 4: Reading the data file & extracting actual value of temperature & cp

Step 5: Writing the function of calculate the mean of array

Step 6: Writing the function to calculate the value of cp by dividing the temperature array in N of group by using linear curve fitting

Step 7: Writing the function to calculate the value of cp by dividing the temperature array in N of group by using cubic curve fitting

Step 8: Writing function to plot the results

Step 9: Writing the function to calculate the choleretics of new cp values

Step 10: Writing the main program & extracting the value of cp & temperature

Step 11: Calculate the value of cp with respect temperature by linear curve fitting method

Step 12: Calculating the value of cp with respect temperature by simple linear curve fitting method

Step 13: Calculating the fitting characteristics of curve

Step 14: Calculating the value of cp with respect temperature by divide linear curve fitting method

Step 15: Calculating the fitting characteristics of curve

Step 16: Plotting the curve

Step 17: Calculate the value of cp with respect temperature by cubic curve fitting method

Step 18: Calculating the value of cp with respect temperature by simple cubic curve fitting method

Step 19: Calculating the fitting characteristics of curve

Step 20: Calculating the value of cp with respect temperature by divide cubic curve fitting method

Step 21: Calculating the fitting characteristics of curve

Results:

Error & Solution:

I didn't get any specific error for this program, only errors regarding format has been arised in this program.