Curve Fitting

popt:- popt gives the optimum value of constant(a,b,c,d... which depend upon the order of approximation if it linear then 2 constant ,quadratic then 3 constant, cubic then there are 4 constant) the values obtained are such that sum of squared error are minimized

pcov:-It gives covariance 2D array of the parameter of popt and used to calculate standard deviation error of popt parameter

np.array(temperature):-It will form the temperature array using numpy

#curve fitting project
#by Abhishek Parmar
import math
import matplotlib.pyplot as plt 
from scipy.optimize import curve_fit
import numpy as np
def fun1(t1,a,b):
	return a*t1 + b
def fun2(t2,a,b,c,d):
	return a*pow(t2,3) + b*pow(t2,2) + c*t2 + d 
def read_file():
	temperature=[]
	cp=[]
	for line in open(\'a\',\'r\') :
		values=line.split(\',\')
		temperature.append(float(values[0]))
		cp.append(float(values[1]))
	return(temperature,cp)
temperature,cp=read_file()
popt,pcov=curve_fit(fun1,temperature,cp)

fit_cp=fun1(np.array(temperature),*popt)
plt.figure(1)
plt.plot(temperature,cp,color=\'blue\',linewidth=3)
plt.plot(temperature,fit_cp,color=\'red\',linewidth=3)
plt.legend([\'Actual data\',\'Curve fit data\'])
plt.xlabel(\'Temperature\')
plt.ylabel(\'Cp\')
plt.show()
popt,pcov=curve_fit(fun2,temperature,cp)
fit_cp1=fun2(np.array(temperature),*popt)
plt.figure(2)
plt.plot(temperature,cp,color=\'blue\',linewidth=3)
plt.plot(temperature,fit_cp1,color=\'red\',linewidth=3)
plt.legend([\'Actual data\',\'Curve fit data\'])
plt.xlabel(\'Temperature\')
plt.ylabel(\'Cp\')
plt.show()

Seperate code for 4th and 5th order approximation is shown below

#curve fitting project 4th and 5th order approximation
#by Abhishek Parmar
import math
import matplotlib.pyplot as plt 
from scipy.optimize import curve_fit
import numpy as np
def fun1(t1,a,b,c,d,e):
	return a*pow(t1,4) + b*pow(t1,3) + c*pow(t1,2) + d*t1 + e
def fun2(t2,a,b,c,d,e,f):
	return a*pow(t2,5) + b*pow(t2,4) + c*pow(t2,3) + d*pow(t2,2) + e*t2 + f 
def read_file():
	temperature=[]
	cp=[]
	for line in open(\'a\',\'r\') :
		values=line.split(\',\')
		temperature.append(float(values[0]))
		cp.append(float(values[1]))
	return(temperature,cp)
temperature,cp=read_file()
popt,pcov=curve_fit(fun1,temperature,cp)

fit_cp=fun1(np.array(temperature),*popt)
plt.figure(1)
plt.title(\'4th order approximation of cp and temperature\')
plt.plot(temperature,cp,color=\'blue\',linewidth=3)
plt.plot(temperature,fit_cp,color=\'red\',linewidth=3)
plt.legend([\'Actual data\',\'Curve fit data\'])
plt.xlabel(\'Temperature\')
plt.ylabel(\'Cp\')
plt.show()
popt,pcov=curve_fit(fun2,temperature,cp)
fit_cp1=fun2(np.array(temperature),*popt)
plt.figure(2)
plt.title(\'5th order approximation of cp and temperature\')
plt.plot(temperature,cp,color=\'blue\',linewidth=3)
plt.plot(temperature,fit_cp1,color=\'red\',linewidth=3)
plt.legend([\'Actual data\',\'Curve fit data\'])
plt.xlabel(\'Temperature\')
plt.ylabel(\'Cp\')
plt.show()

Result are shown below

5th order approximation give better result as it exactly matches with original data