image.png

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

class LinearRegression2(torch.nn.Module):
    def __init__(self):
        # y = a*x + b
        super(LinearRegression2, self).__init__()
        self.a = torch.rand(1, requires_grad=True)  # 参数a
        self.b = torch.rand(1, requires_grad=True)  # 参数b
        self.__parameters = dict(a=self.a, b=self.b)  # 参数字典

    def forward(self, inputs):
        # 这里根据公式y[...]=ax[...]+b forward拟合
        return self.a * inputs + self.b

    def parameters(self):
        # 全部输出参数字典
        for name, param in self.__parameters.items():
            yield param

def pltDraw(x, a, b):
    # plt.clf()  # 清除图像
    plt.plot(x.data.numpy(), a * x.data.numpy() + b, "r",alpha=0.1)  # f(x)的图像
    plt.title('y=%s*x+%s' % (a, b))
    plt.xlabel("X")
    plt.ylabel("Y")
    plt.pause(0.5)

# 生成 x 与 y模拟数据，其中加入1-25随机噪声
x = np.arange(50)
y = np.array([2 * x[i] + 30 + random.randint(1, 25) for i in range(len(x))])
x = torch.from_numpy(x.astype(np.float32))
y = torch.from_numpy(y.astype(np.float32))
plt.scatter(x, y) # 数据散点图

plt.ion() #打开plt交互模式

#线性回归正式开始
net = LinearRegression2() #初始化网络
learningRate = 0.001 #设定学习率
optimizer = torch.optim.Adam(net.parameters(), lr=learningRate, weight_decay=0.005)
loss_op = torch.nn.MSELoss(reduction='sum')

for i in range(1, 200001):  # 20万次拟合
    out = net.forward(x) # 向前传播
    loss = loss_op(y, out) # 计算out矩阵与y矩阵 损失
    optimizer.zero_grad()  # 清空梯度
    loss.backward()  # 向后传播，计算梯度∇f
    optimizer.step()  # 更新参数
    loss_numpy = loss.cpu().detach().numpy()  # 得到损失的numpy值

    if i % 5000 == 0:  # 每5000次打印一下损失
        print(i, loss_numpy)
        a = net.a.cpu().detach().numpy()
        b = net.b.cpu().detach().numpy()
        print(a, b)
        pltDraw(x, a, b)

plt.ioff()
print(a,b)
plt.show()

下面是每500次画一条alpha=0.05 线的拟合过程

image.png