#!/usr/bin/env python
# -*- encoding: utf-8 -*-
'''
@file     :linear01.py
@author   :cat
@version  :1.0
'''

import numpy as np
import matplotlib.pyplot as plt



"""
    为了能够很好地模拟真实样本的观测误差，我们给模型添加误差自变量𝜖，它采样自均值为 0，标准差为 1 的高斯分布
    𝑦 = 1.477𝑥 + 0.089 + 𝜖, 𝜖 ∼ 𝒩(0 , 1)
    :return:
"""


def make_data():
    data = []
    for _ in range(200):
        x = np.random.uniform(-10,10)
        y = 1.4777 * x + 0.089 + np.random.normal(0,0.1)
        data.append([x,y])

    # 可视化一下数据
    # plt.scatter([i[0] for i in data],[j[1] for j in data])
    # plt.show()

    data = np.array(data)
    # print(data.shape) # (200,2)
    return data

# 计算误差
def mse_error(w,b,data):
    total_error = 0.0
    for i in range(len(data)):
        x = data[i,0]
        y = data[i,1]
        error = (y - (x * w + b)) ** 2
        total_error += error
    return total_error / float(len(data))


# 计算梯度
def step_gradient(w_current,b_current,data,lr):
    b_gradient = 0
    w_gradient = 0
    for i in range(0,len(data)):
        x = data[i,0]
        y = data[i,1]
        b_gradient += 2 * ((w_current * x + b_current) - y) * 0.01
        w_gradient += 2 * x * ((w_current * x + b_current) - y) * 0.01

    new_b = b_current - (lr * b_gradient)
    new_w = w_current - (lr * w_gradient)

    return new_b,new_w

# 更新梯度
def gradient_descent(data, starting_b, starting_w, learning_rate, num_iterations):
    """
    在计算出误差函数在𝑤和𝑏处的梯度后，我们可以根据式(2.1)来更新𝑤和𝑏的值。
    我们把 对数据集的所有样本训练一次称为一个 Epoch，共循环迭代 num_iterations 个 Epoch
    :param data:
    :param starting_b:
    :param starting_w:
    :param learning_rate:
    :param num_iterations:
    :return:
    """
    b  =starting_b
    w = starting_w

    for step in range(num_iterations):
        b,w = step_gradient(w,b,np.array(data),learning_rate)
        loss = mse_error(b,w,data)
        print(f'iteration:{step + 1},loss:{loss}')

    return b,w



def main():
    lr = 1e-2
    initial_b = 0
    initial_w = 0


    num_iterations = 1000

    data = make_data()
    # 训练优化 1000 次，返回最优 w*,b*和训练 Loss 的下降过程
    [b, w] = gradient_descent(data, initial_b, initial_w, lr, num_iterations)
    loss = mse_error(b, w, data)  # 计算最优数值解 w,b 上的均方差
    print(f'Final loss:{loss}, w:{w}, b:{b}')

    # 绘制一下最终的图像
    plt.scatter([i[0] for i in data],[j[1] for j in data],c='r',alpha=.5)
    x_data = data[:,0]
    y_data = w * x_data + b
    plt.plot(x_data,y_data)
    plt.show()


if __name__ == "__main__":
    main()
# Final loss:64.66513807777812, w:1.4766844022375065, b:0.09135514886298757