curve-fitting example

curve.py

"""
The code is implementation of techniques in this lecture: https://www.essie.ufl.edu/~kgurl/Classes/Lect3421/Fall_01/NM5_curve_f01.pdf

"""
import matplotlib.pyplot as plt
import numpy as np

def curve(X, Y, order):
	sigma_x=[]
	for i in range(2*order + 1):
		if i==0:
			ans=len(X)
		else:
			ans=0
			for x in X:
				ans += x ** i
		sigma_x.append(ans)
	print(sigma_x)

	sigma_xy=[]
	for i in range(order + 1):
		ans = 0
		for index in range(len(Y)):
			x = X[index]
			y = Y[index]
			ans += (x ** i)*y
		sigma_xy.append(ans)
	print(sigma_xy)

	A=[]
	for i in range(order + 1):
		A.append(sigma_x[i:(i + order + 1)])

	numA = np.array(A)
	print(numA)
	numB = np.array(sigma_xy)
	coeff = np.dot(np.linalg.inv(numA),numB)
	print(coeff)

	## coeff matrix is our answer - creating sample data to plot the function for the polynomial below:
	sample_x = np.linspace(0,6,20)
	x_arr = []
	for sample in sample_x:
		pol = []
		for i in range(order + 1):
			pol.append(sample ** i)
		x_arr.append(pol)
	numSampleX = np.array(x_arr)
	sample_y = np.dot(numSampleX, coeff)
	print(sample_x)
	print(sample_y)

	plt.plot(sample_x, sample_y)
	
if __name__ == '__main__':
	size = 4
	def generate_data(size):
    		x = np.array(np.random.rand(size,))
    		y = 8 * (x**2) + 8*x + 5
    		return x,y
    
	X,Y = generate_data(size)
	
	order=2

	plt.plot(X, Y, 'ro')
	
	for i in range(1,order+1):	
		curve(X, Y, i)
	plt.show()	

Fitting to Order 1 polinomial:

Fitting to Order 2 polinomial: