线性模型第一课

import random
import torch
import matplotlib as pl
#生成样本，特征和标签
def synthetic_data(w,b,num_examples):
    x=torch.normal(0,1,(num_examples,len(w)))  #均值为0方差为1,w列
    y=torch.matmul(x,w)+b  #x*w+b
    y+=torch.normal(0,0.01,y.shape) #均值为0，方差为0.01的随机噪音
    return x,y.reshape((-1,1))
true_w=torch.tensor([2,-3.4])
true_b=4.2
features,lables=synthetic_data(true_w,true_b,1000)

#定义函数，接受批量大小，特征矩阵和标签向量作为输入，生成大小为batch_size的小批量
def data_iter(batch_size,features,lables):
    num_examples=len(features)#多个样本
    indices=list(range(num_examples))#每个样本的index
    random.shuffle(indices)#打乱顺序
    for i in range(0,num_examples,batch_size):#从0开始，每次跳batch_size个大小
        batch_indics=torch.tensor(
            indices[i:min(i+batch_size,num_examples)]
        )#每次拿b个index。如果不够拿一个最小值
        yield features[batch_indics],lables[batch_indics]
batch_size=10
for x,y in data_iter(batch_size,features,lables):
    print(x,'\n',y)
    break
w=torch.normal(0,0.01,size=(2,1),requires_grad=True)
b=torch.zeros(1,requires_grad=True)
#定义线性模型
def linreg(x,w,b):
    return torch.matmul(x,w)+b
#定义损失函数
#1/2(y-y_hat)(y-y_hat)
def squared_loss(y_hat,y):
    return (y_hat-y.reshape(y_hat.shape))**2/2
#定义最优化算法
#给定所有参数，学习率和批量
def sgd(params,lr,batch_size):
    with torch.no_grad():
        for param in params:
            param-=lr*param.grad/batch_size
            param.grad.zero_()
lr=0.03
num_epochs=3#整个模型扫3遍
net=linreg#线性模型
loss=squared_loss
for epoch in range(num_epochs):
    for x,y in data_iter(batch_size,features,lables):
        l=loss(net(x,w,b),y)#求y_hat,再求y_hat和y的损失
        l.sum().backward()
        sgd([w,b],lr,batch_size)
    with torch.no_grad():
        train_1=loss(net(features,w,b),lables)
        print(f'epoch{epoch+1} ,loss{float(train_1.mean()):f}')