请你扮演一个程序员，利用pytorch，比较用同一个vgg16模型、同一个epoch=200训练轮数、同一个Adam优化器下，比较不同学习率更新方法下的ROC曲线。请写出实际代码。

好的，以下是实现代码：

import torch
import torch.nn as nn
import torch.optim as optim
from torchvision import datasets, transforms
from torch.utils.data import DataLoader
from sklearn.metrics import roc_curve, auc
import matplotlib.pyplot as plt

# 定义设备
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")

# 加载数据集
transform = transforms.Compose([
    transforms.Resize((224, 224)),
    transforms.ToTensor(),
    transforms.Normalize((0.5,), (0.5,))
])

train_dataset = datasets.CIFAR10(root='./data', train=True, download=True, transform=transform)
test_dataset = datasets.CIFAR10(root='./data', train=False, download=True, transform=transform)

train_loader = DataLoader(train_dataset, batch_size=64, shuffle=True, num_workers=4)
test_loader = DataLoader(test_dataset, batch_size=64, shuffle=False, num_workers=4)

# 定义模型
class VGG16(nn.Module):
    def __init__(self):
        super(VGG16, self).__init__()
        self.features = nn.Sequential(
            nn.Conv2d(3, 64, kernel_size=3, padding=1),
            nn.ReLU(inplace=True),
            nn.Conv2d(64, 64, kernel_size=3, padding=1),
            nn.ReLU(inplace=True),
            nn.MaxPool2d(kernel_size=2, stride=2),
            nn.Conv2d(64, 128, kernel_size=3, padding=1),
            nn.ReLU(inplace=True),
            nn.Conv2d(128, 128, kernel_size=3, padding=1),
            nn.ReLU(inplace=True),
            nn.MaxPool2d(kernel_size=2, stride=2),
            nn.Conv2d(128, 256, kernel_size=3, padding=1),
            nn.ReLU(inplace=True),
            nn.Conv2d(256, 256, kernel_size=3, padding=1),
            nn.ReLU(inplace=True),
            nn.Conv2d(256, 256, kernel_size=3, padding=1),
            nn.ReLU(inplace=True),
            nn.MaxPool2d(kernel_size=2, stride=2),
            nn.Conv2d(256, 512, kernel_size=3, padding=1),
            nn.ReLU(inplace=True),
            nn.Conv2d(512, 512, kernel_size=3, padding=1),
            nn.ReLU(inplace=True),
            nn.Conv2d(512, 512, kernel_size=3, padding=1),
            nn.ReLU(inplace=True),
            nn.MaxPool2d(kernel_size=2, stride=2),
            nn.Conv2d(512, 512, kernel_size=3, padding=1),
            nn.ReLU(inplace=True),
            nn.Conv2d(512, 512, kernel_size=3, padding=1),
            nn.ReLU(inplace=True),
            nn.Conv2d(512, 512, kernel_size=3, padding=1),
            nn.ReLU(inplace=True),
            nn.MaxPool2d(kernel_size=2, stride=2),
        )
        self.avgpool = nn.AdaptiveAvgPool2d((7, 7))
        self.classifier = nn.Sequential(
            nn.Linear(512 * 7 * 7, 4096),
            nn.ReLU(inplace=True),
            nn.Dropout(),
            nn.Linear(4096, 4096),
            nn.ReLU(inplace=True),
            nn.Dropout(),
            nn.Linear(4096, 10),
        )

    def forward(self, x):
        x = self.features(x)
        x = self.avgpool(x)
        x = torch.flatten(x, 1)
        x = self.classifier(x)
        return x

# 定义训练参数
model = VGG16().to(device)
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(model.parameters(), lr=0.001)

# 定义学习率更新方法
scheduler1 = optim.lr_scheduler.StepLR(optimizer, step_size=50, gamma=0.1)
scheduler2 = optim.lr_scheduler.ExponentialLR(optimizer, gamma=0.9)
scheduler3 = optim.lr_scheduler.CosineAnnealingLR(optimizer, T_max=200)

# 训练模型
def train(model, device, train_loader, criterion, optimizer, epoch):
    model.train()
    for batch_idx, (data, target) in enumerate(train_loader):
        data, target = data.to(device), target.to(device)
        optimizer.zero_grad()
        output = model(data)
        loss = criterion(output, target)
        loss.backward()
        optimizer.step()
        if batch_idx % 100 == 0:
            print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                epoch, batch_idx * len(data), len(train_loader.dataset),
                100. * batch_idx / len(train_loader), loss.item()))

# 测试模型
def test(model, device, test_loader):
    model.eval()
    test_loss = 0
    correct = 0
    y_score = []
    y_true = []
    with torch.no_grad():
        for data, target in test_loader:
            data, target = data.to(device), target.to(device)
            output = model(data)
            test_loss += criterion(output, target).item() * len(target)
            pred = output.argmax(dim=1, keepdim=True)
            correct += pred.eq(target.view_as(pred)).sum().item()
            y_score.extend(output.cpu().numpy())
            y_true.extend(target.cpu().numpy())

    test_loss /= len(test_loader.dataset)
    print('\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format(
        test_loss, correct, len(test_loader.dataset),
        100. * correct / len(test_loader.dataset)))
    
    # 计算ROC曲线
    fpr, tpr, _ = roc_curve(y_true, y_score, pos_label=1)
    roc_auc = auc(fpr, tpr)
    plt.figure()
    lw = 2
    plt.plot(fpr, tpr, color='darkorange',
             lw=lw, label='ROC curve (area = %0.2f)' % roc_auc)
    plt.plot([0, 1], [0, 1], color='navy', lw=lw, linestyle='--')
    plt.xlim([0.0, 1.0])
    plt.ylim([0.0, 1.05])
    plt.xlabel('False Positive Rate')
    plt.ylabel('True Positive Rate')
    plt.title('Receiver operating characteristic example')
    plt.legend(loc="lower right")
    plt.show()

# 开始训练和测试
for epoch in range(1, 201):
    scheduler1.step()
    train(model, device, train_loader, criterion, optimizer, epoch)
    test(model, device, test_loader)

for epoch in range(1, 201):
    scheduler2.step()
    train(model, device, train_loader, criterion, optimizer, epoch)
    test(model, device, test_loader)

for epoch in range(1, 201):
    scheduler3.step()
    train(model, device, train_loader, criterion, optimizer, epoch)
    test(model, device, test_loader)

这段代码会输出每一个epoch的训练和测试结果，并且在每一个测试中会计算ROC曲线。此外，我们定义了三种不同的学习率更新方法，分别是StepLR、ExponentialLR和CosineAnnealingLR，分别用来比较它们对于模型训练的影响。