This is a sample code of exercise in https://esslab.jp/~ess/ja/teaching/2019/cgo/.

least_square_polynomial_1d.py

import pprint
import numpy as np
class PolynomialPredictor(object):
    def __init__(self,u,v,n=1,debug=True): 
        self.n = n
        u = np.array(u)
        A = np.array([u**i for i in range(self.n,-1,-1)]).T
        b = np.array([v]).T
        self.alpha = np.matmul(np.matmul( np.linalg.inv( np.matmul(A.T,A) ), A.T ), b )
        self.sum_of_se = np.sum((np.matmul(A,np.fliplr(self.alpha))-b)**2)

        if debug:
            pprint.pprint('n')
            pprint.pprint(n)  
            pprint.pprint('u')
            pprint.pprint(u)  
            pprint.pprint('A')
            pprint.pprint(A)
            pprint.pprint('b')
            pprint.pprint(b)
            pprint.pprint('alpha')
            pprint.pprint(self.alpha)   
            pprint.pprint('pred')
            pprint.pprint(np.matmul(A,np.fliplr(self.alpha)))
            pprint.pprint('GT')
            pprint.pprint(b)
            pprint.pprint('diff')
            pprint.pprint(np.matmul(A,np.fliplr(self.alpha))-b)
            pprint.pprint('self.sum_of_se')
            pprint.pprint(self.sum_of_se)
        
    def __call__(self,u):
        u = np.array(u)
        A = np.array([u**i for i in range(self.n,-1,-1)]).T
        return np.matmul(A,np.fliplr(self.alpha))

      
import matplotlib.pyplot as plt
u = [0,1,2,3]
v = [1,2,0,3]
pps  = dict([['pp'+str(n),PolynomialPredictor(u,v,n=n,debug=False)] for n in range(1,5)])
print('[sum of square errors]')
for k in pps.keys():
    print('  ',k,pps[k].sum_of_se)


plt.scatter(u,v)
u = np.linspace(0,3,100)
for k in pps.keys():
    plt.plot(u, pps[k](u),label=k)
plt.legend()
_ = plt.ylim(-1,4)