import numpy as np
import matplotlib.pyplot as plt
data=np.genfromtxt('artificial.txt', delimiter=',', skip_header=1) # Columns: x, y

def generate_poly_features(x, q):
    # Generate "design matrix" for the polynomial regression model
    #   y= θ_0 + θ_1*x + θ_1*x^2 + ... + θ_q*x^q
    # The matrix has(q + 1) columns where column i contains elements
    # of the vector x raised to the i-th power
    X=np.ones(shape=(x.shape[0],q+1))

    for i in range(0,q+1):
        X[:,i] = np.power(x,i)
    return X

def poly_fit(x, y, q):
    # Pre: x and y are 1-dimensional arrays
    theta = np.linalg.solve(X.T.dot(x), X.T.dot(y))
    return theta

def poly_predict(xtest, theta):
    ypred=xtest.dot(theta)

    return ypred

# Load data, predict and plot
x=data[:,0]
y=data[:,1]
deg = 3
X=generate_poly_features(x, deg)
theta = poly_fit(X,y,deg)
ypred = poly_predict(X, theta)
plt.plot(x,ypred, color="red")
plt.scatter(x,y)