градиентный спуск

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

#--- Gradient descent\

# polynomial degree
pol_deg = 2

# a0 - a5
A = np.zeros(pol_deg+1)

A = np.array([random.random() for i in range(pol_deg+1)])

# h(x) = a0 + a1*x + a2*x**2 + ... + am*x**m,  where (m = pol_deg) and (ai = A[i])

# It's important to find proper alfa
# if it's too big convergion won't be able
# if too small convergion takes many time
alfa = 0.1

X = np.array([0, -1, 1, 2])
Y = np.array([0, 0, 2, 1])

def h(X_arr = X):
    return np.array(sum([A[i]*X_arr**i for i in range(len(A))]))


def derivative():
    h_val = h()
    comm = h_val - Y
    # Array of derrivatives for all ai in A
    return np.array([sum(comm*X**i) * alfa**i for i in range(len(A))]) * (1 / (len(X)))
    # Yes, alfa**i don't have any realtions with derivation but only this way the programm works (\_/)
    #                                                                                            (-_-)

def J():
    h_val = h()
    # Error for current model. Dispertion or something like that, i'm bad in Spanish songs
    return sum((h_val-Y)**2)/(2*len(h_val))

for i in range(10000):

    # The heart of gradient descent
    # Operating with array of ai and array of derivatives J(ai)
    A -= derivative() * alfa

    print("--\nITERATION ", i)
    print("A = ", A)
    print("ERROR = ", J())

    if (i % 500 == 0):
        plt.clf()

        plt.suptitle("iter = " + str(i) + str(A),               fontsize=14, fontweight='bold')

        plt.scatter(X, Y)
        x_ap = np.linspace(0, 10, 50)
        y_ap = h(x_ap)
        plt.plot(x_ap, y_ap)
        plt.xlabel(i)
        plt.text(5, 15, 'iter: ' + str(i),
            verticalalignment='bottom', horizontalalignment='left',
            color='green', fontsize=10)
        plt.pause(0.01)

plt.show()