Week 5 - Curve fitting

curve fitting for temperature module

Quadratic Function Graph

The quadratic function is a second order polynomial function:

f(x) = ax² + bx + c

The solutions to the quadratic equation are the roots of the quadratic function, that are the intersection points of the quadratic function graph with the x-axis, when

f(x) = 0

When there are 2 intersection points of the graph with the x-axis, there are 2 solutions to the quadratic equation.

When there is 1 intersection point of the graph with the x-axis, there is 1 solution to the quadratic equation.

When there are no intersection points of the graph with the x-axis, we get not real solutions (or 2 complex solutions).

import numpy as np
import numpy
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
# file reading for input data files
# All files reading by using reading command

def read_file():
temprature =[]
cp =[]
for line in open('data','r'):
value = line.split(',')
temprature.append(float(value[0]))
cp.append(float(value[1]))
return [temprature,cp]

# function for cp using the input temprature 1st oder funtion
def func(t,a,b):
return a*t+b

# function cp for second 2 oder function
"""
def func(t,a,b,c):
return a*(t**2)+b*t+c
"""

# function cp for 3oder function

"""

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

"""

# function call given data analysing

temprature,cp = read_file()
popt, pcov = curve_fit(func,temprature,cp)
fit_cp=func(np.array(temprature),*popt)# ALL temperature array(np.array(temperature)) has to substitue and all optimum value to subtituted(*popt)

plt.plot(temprature,cp,color="red",linewidth=3)
plt.plot(temprature,fit_cp,color="blue",linewidth=3)
plt.legend(['Actual data', 'curve fit'])
plt.xlabel('temperature[K]')
plt.ylabel('cp')
plt.show()

#linear curve fit Anlysis process

length =len(temprature)
for i in range (length):
error= cp-fit_cp
sse=pow(error,2)
rmse_val=sse/6
rmse=pow(rmse_val,0.5)
mean=numpy.array(cp[i])-numpy.array(i)
ssr=pow(numpy.array(cp[i])-numpy.array(mean),2)
sst=ssr+sse
r_square=ssr/sst
print(r_square)

conclution

error value are going 0.99989665-0.99989629

that value are almost going to Zero that value fit good

Second order equation curve fit

2 nd order error 0.99996928-0.99996941

difference value almost going to zero so the fit good(perfect)

3rd order equation curve fit

3rd oder error 0.99998235-0.99998256

differnce value alomost to zero good fit