梯度

实战

代码：

# %matplotlib inline
import random
import torch
import matplotlib.pyplot as plt
# from d21 import torch as d21

def synthetic_data(w, b, num_examples):
    """生成 Y = XW + b + 噪声。"""
    X = torch.normal(0, 1, (num_examples, len(w)))# 均值为0，方差为1的随机数，n个样本，列数为w的长度
    y = torch.matmul(X, w) + b # y = x * w + b
    y += torch.normal(0, 0.01, y.shape) # 加入随机噪音，均值为0.。形状与y的一样
    return X, y.reshape((-1, 1))# x， y做成列向量返回


true_w = torch.tensor([2, -3.4])
true_b = 4.2
features, labels = synthetic_data(true_w, true_b, 1000)
#读取小批量，输出batch_size的小批量，随机选取
def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))#转成list
    random.shuffle(indices)#打乱
    for i in range(0, num_examples, batch_size):#
        batch_indices = torch.tensor(indices[i:min(i + batch_size, num_examples)])#取
    yield features[batch_indices], labels[batch_indices]#不断返回



# #print(features)
# #print(labels)
#
#
batch_size = 10
#
# for x, y in data_iter(batch_size, features,labels):
#      print(x, '\n', y)
#      break
# # 提取第一列特征作为x轴，第二列特征作为y轴
# x = features[:, 1].detach().numpy() #将特征和标签转换为NumPy数组，以便能够在Matplotlib中使用。
# y = labels.detach().numpy()
#
# # 绘制散点图
# plt.scatter(x, y, 1)
# plt.xlabel('Feature 1')
# plt.ylabel('Feature 2')
# plt.title('Synthetic Data')
# plt.show()
#
# #定义初始化模型

w = torch.normal(0, 0.01, size=(2, 1), requires_grad=True)
b = torch.zeros(1, requires_grad = True)

def linreg(x, w, b):
    return torch.matmul(x, w) + b

#定义损失函数

def squared_loss(y_hat, y):
    return (y_hat - y.reshape(y_hat.shape))**2 / 2 #弄成一样的形状

# 定义优化算法
def sgd(params, lr, batch_size):
    """小批量随梯度下降"""
    with torch.no_grad():#节省内存和计算资源。
        for param in params:
            param -= lr * param.grad / batch_size
            param.grad.zero_()#用于清空张量param的梯度信息。

print("训练函数")

lr = 0.03 #学习率
num_ecopchs = 300 #数据扫描三遍
net = linreg #指定模型
loss = squared_loss #损失

for epoch in range(num_ecopchs):#扫描数据
    for x, y in data_iter(batch_size, features, labels): #拿出x, y
      l = loss(net(x, w, b), y)#求损失，预测net,真实y
      l.sum().backward()#算梯度
      sgd([w, b], lr, batch_size)#使用参数的梯度更新参数
    with torch.no_grad():
        train_l = loss(net(features, w, b), labels)
        print(f'epoch {epoch + 1},loss {float(train_l.mean()):f}')

运行效果：