Week 5 - Curve fitting

1)What does popt and pcov mean?

popt- An array of values for the parameters which minimizes the polynomials and gives out residual values

Pcov -An array of Estimated covarience of popt perameters.

2. What does np.array(temperature) do?

it gives out a array of numbers which we feed inside.

3.What does the * in *popt mean?

It passes the values of all constants and co.effs of a polynomial defined inside a function as agruments.

4-a)program code for linear polynomials:

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

#def fun1(t,a,b,c,d):
	#return (a*t*t*t)+(b*t*t)+(c*t)+d

def fun2(t,a,b):
	return (a*t)+b

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]

temperature,cp=read_file()
popt,pcov=curve_fit(fun2,temperature,cp)
fit_cp=fun2(np.array(temperature),*popt)
plt.plot(temperature,cp,color='b',linewidth=3)
plt.plot(temperature,fit_cp,color='r',linewidth=3)
plt.xlabel("Temperature")
plt.ylabel("Cp")
plt.show()

output plot- linear polynomial curve fit:

4-b)program code for cubic polynomials:

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

def fun1(t,a,b,c,d):
	return (a*t*t*t)+(b*t*t)+(c*t)+d

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]

temperature,cp=read_file()
popt,pcov=curve_fit(fun1,temperature,cp)
fit_cp=fun1(np.array(temperature),*popt)
plt.plot(temperature,cp,color='b',linewidth=3)
plt.plot(temperature,fit_cp,color='r',linewidth=3)
plt.xlabel("Temperature")
plt.ylabel("Cp")
plt.show()

output plot- cubic polynomial curve fit:

5. What needs to be done in order to make the curve fit perfect?

1)Adjust the co.eff values to get perfect fits.

2)Optomize through error function.