import math
import matplotlib.pyplot as plt
import random
#不懂
def sum_of_gradient(x, y, thetas):
    """計算梯度向量，引數分別是x和y軸點座標資料以及方程引數"""
    m = len(x);
    grad0 = 1.0 / m * sum([(thetas[0] + thetas[1] * x[i] - y[i]) for i in range(m)])#求誤差的期望
    grad1 = 1.0 / m * sum([(thetas[0] + thetas[1] * x[i] - y[i]) * x[i] for i in range(m)])
    return [grad0, grad1];
def step(thetas, direction, step_size):
    """move step_size in the direction from thetas"""
    # return [thetas[0]+step_size*direction[0],thetas[1]+step_size*direction[1]]#等價嗎？
    return [thetas_i + step_size * direction_i
            for thetas_i, direction_i in zip(thetas, direction)]
def distance(v, w):
    """兩點的距離"""
    return math.sqrt(squared_distance(v, w))
def squared_distance(v, w):
    vector_subtract = [v_i - w_i for v_i, w_i in zip(v, w)]
    return sum(vector_subtract_i * vector_subtract_i for vector_subtract_i, vector_subtract_i
               in zip(vector_subtract, vector_subtract))
def gradient_descent(stepSize, x, y, tolerance=0.000000001, max_iter=100000):
    """梯度下降"""
    iter = 0
    # initial theta
    thetas = [0, 0];
    # Iterate Loop
    while True:
        gradient = sum_of_gradient(x, y, thetas);
        next_thetas = step(thetas, gradient, stepSize)
        # print(next_thetas)
        if distance(next_thetas, thetas) < tolerance:  # stop if we're converging
            break
        thetas = next_thetas  # continue if we're not
        iter += 1  # update iter
        if iter == max_iter:
            print('Max iteractions exceeded!')
            break
    return thetas
x=[i for i in range(15)]
y=[x[i]+random.uniform(0,10) for i in range(len(x))]
stepSize = 0.001
t0, t1= gradient_descent(-stepSize, x, y)
print(t0, " ", t1)
plt.scatter(x,y)
plt.plot(x,[t1*x[i]+t0 for i in range(len(x))],'r')
plt.show()