Merge pull request #76 from Ethan-Chen-plus/master

update ch03

codes/ch03/3.2.py

@@ -0,0 +1,126 @@
+# ------------------------------
+#用代码验证电阻为$30 \Omega$的电流与电压的计算公式
+# ------------------------------
+
+import torch
+import random
+
+import numpy as np
+from d2l import torch as d2l
+# 生成数据
+x = torch.randn(100, 1)
+y = 30 * x
+
+# 定义模型
+model = torch.nn.Linear(1, 1)
+
+# 定义损失函数和优化器
+criterion = torch.nn.MSELoss()
+optimizer = torch.optim.SGD(model.parameters(), lr=0.01)
+
+# 训练模型
+for epoch in range(500):
+    # 前向传播
+    y_pred = model(x)
+
+    # 计算损失
+    loss = criterion(y_pred, y)
+
+    # 反向传播
+    optimizer.zero_grad()
+    loss.backward()
+    optimizer.step()
+
+print(model.weight)
+print(model.bias)
+
+# ------------------------------
+#torch求导
+# ------------------------------
+
+
+x = torch.randn((2), requires_grad=True)
+y = x ** 3
+# 一阶导数
+dy = torch.autograd.grad(y, x, grad_outputs=torch.ones(x.shape), 
+                         retain_graph=True, create_graph=True)
+
+# 二阶导数
+dy2 = torch.autograd.grad(dy, x, grad_outputs=torch.ones(x.shape))
+dy[0] == 3 * x**2
+dy2[0] == 6 * x
+
+# ------------------------------
+# 尝试使用不同的学习率，观察损失函数值下降的快慢。
+# ------------------------------
+
+
+
+# 生成数据集
+def synthetic_data(w, b, num_examples):  #@save
+    """生成y=Xw+b+噪声"""
+    X = torch.normal(0, 1, (num_examples, len(w)))
+    y = torch.matmul(X, w) + b
+    y += torch.normal(0, 0.01, y.shape)
+    return X, y.reshape((-1, 1))
+
+true_w = torch.tensor([2, -3.4])
+true_b = 4.2
+features, labels = synthetic_data(true_w, true_b, 1000)
+
+# 读取数据集
+def data_iter(batch_size, features, labels):
+    num_examples = len(features)
+    indices = list(range(num_examples))
+    # 这些样本是随机读取的，没有特定的顺序
+    random.shuffle(indices)
+    for i in range(0, num_examples, batch_size):
+        batch_indices = torch.tensor(
+            indices[i: min(i + batch_size, num_examples)])
+        yield features[batch_indices], labels[batch_indices]
+
+# 初始化参数
+w = torch.normal(0, 0.01, size=(2,1), requires_grad=True)
+b = torch.zeros(1, requires_grad=True)
+
+def linreg(X, w, b):  #@save
+    """线性回归模型"""
+    return torch.matmul(X, w) + b
+
+def squared_loss(y_hat, y):  #@save
+    """均方损失"""
+    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2
+
+def sgd(params, lr, batch_size):  #@save
+    """小批量随机梯度下降"""
+    with torch.no_grad():
+        for param in params:
+            param -= lr * param.grad / batch_size
+            param.grad.zero_()
+
+lrs = [0.5, 0.3, 0.1, 0.01]
+num_epochs = 10
+net = linreg
+loss = squared_loss
+
+batch_size = 10
+
+all_lrs = []
+for lr in lrs:
+    train_lrs = []
+    for epoch in range(num_epochs):
+        for X, y in data_iter(batch_size, features, labels):
+            l = loss(net(X, w, b), y)  # X和y的小批量损失
+            # 因为l形状是(batch_size,1)，而不是一个标量。l中的所有元素被加到一起，
+            # 并以此计算关于[w,b]的梯度
+            l.sum().backward()
+            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)
+            train_lrs.append(float(train_l.mean()))
+    all_lrs.append(train_lrs)
+
+epochs = np.arange(1, num_epochs+1)
+d2l.plot(epochs, all_lrs, xlabel='epoch num', ylabel='loss', 
+         legend=[f'learn rate {lr}' for lr in lrs],
+         figsize=(6, 4))

codes/ch03/3.3.py

@@ -0,0 +1,53 @@
+# ------------------------------
+#使用其他不常见的损失函数
+# ------------------------------
+import numpy as np
+import torch
+from torch.utils import data
+from d2l import torch as d2l
+
+# 生成数据集
+true_w = torch.tensor([2, -3.4])
+true_b = 4.2
+features, labels = d2l.synthetic_data(true_w, true_b, 1000)
+
+# 读取数据集
+def load_array(data_arrays, batch_size, is_train=True):  #@save
+    """构造一个PyTorch数据迭代器"""
+    dataset = data.TensorDataset(*data_arrays)
+    return data.DataLoader(dataset, batch_size, shuffle=is_train)
+
+batch_size = 10
+data_iter = load_array((features, labels), batch_size)
+
+
+net = nn.Sequential(nn.Linear(2, 1))
+
+# 使用Huber损失函数
+loss = nn.HuberLoss()
+
+trainer = torch.optim.SGD(net.parameters(), lr=0.03)
+
+num_epochs = 3
+for epoch in range(num_epochs):
+    for X, y in data_iter:
+        l = loss(net(X) ,y)
+        trainer.zero_grad()
+        l.backward()
+        trainer.step()
+    l = loss(net(features), labels)
+    print(f'epoch {epoch + 1}, loss {l:f}')
+
+w = net[0].weight.data
+print('w的估计误差：', true_w - w.reshape(true_w.shape))
+b = net[0].bias.data
+print('b的估计误差：', true_b - b)
+
+# ------------------------------
+# 如何访问线性回归的梯度：
+# ------------------------------
+
+w_grad = net[0].weight.grad
+print('w的梯度：', w_grad)
+b_grad = net[0].bias.grad
+print('b的梯度：', b_grad)

codes/ch03/3.6.py

@@ -0,0 +1,13 @@
+# ------------------------------
+# 自定义softmax函数
+# ------------------------------
+
+def softmax(X):
+    X_exp = np.exp(X)
+    partition = X_exp.sum(1, keepdims=True)
+    return X_exp / partition  # 这里应用了广播机制
+
+try:
+    softmax(np.array([[50]]))
+except Exception as e:
+    print(e)