# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pylab as plt
from gradient_2d import numerical_gradient

def gradient_descent(f, init_x, lr = 0.01, step_num = 100):
    x = init_x
    x_history = []
    
    for i in range(step_num):
        x_history.append( x.copy() )
        
        grad = numerical_gradient(f, x)
        x -= lr * grad
        
    return x, np.array(x_history)

def function_2(x):
    return x[0] ** 2 + x[1] ** 2

init_x = np.array([-3.0, 4.0])

lr = 0.1
step_num = 20
x, x_history = gradient_descent(function_2, init_x, lr = lr, step_num = step_num)

plt.plot([-5, 5], [0, 0], '--b')
plt.plot([0, 0], [-5, 5], '--b')
plt.plot(x_history[:, 0], x_history[:, 1], 'o')

plt.xlim(-3.5, 3.5)
plt.ylim(-4.5, 4.5)
plt.xlabel("X0")
plt.ylabel("X1")
plt.show()