from IPython.display import clear_output

f_true = lambda x: 2*x*np.sin(5*x) + x**2 - 1 # this is the true function

# We need this to make the plot of f_true:
x_grid = np.linspace(-2,5,100) # 100 linearly spaced numbers
x_grid_enl = np.hstack((x_grid.reshape((100,1))**j for j in range(6)))
y_grid = f_true(x_grid)

A = np.dot(x_grid_enl.T, x_grid_enl)
B = np.dot((x_grid_enl).T, y_grid)

for i in range(200):
    x_new = np.random.uniform(-2, 5)
    y_new = f_true(x_new) + 2*np.random.randn()
    p = [x_new**j for j in range(6)]
    for l in range(len(A)):
        for j in range(len(A)):
            A[j,l] += p[l] * p[j]
    for l in range(len(B)):
        B[l] += p[l] * y_new

    koeff = np.dot(np.linalg.inv(A), B)
    # the rest of code is just bells and whistles
    if (i+1)%5==0:
        clear_output(True)
        plt.plot(x_grid,y_grid, color='blue', label='true f')
        plt.scatter(x_new, y_new, color='red')

        y_pred = [koeff[0] + koeff[1] * (i) + koeff[2] * (i**2) + koeff[3] * (i**3) +
                  koeff[4] * (i**4) + koeff[5] * (i**5) for i in x_grid]

        plt.scatter(x_grid, y_pred, color='orange', linewidth=5, label='predicted f')

        plt.legend(loc='upper left')
        plt.show()