在pytorch上构建卷积神经网络实现VAE，并完成对矩阵数据集500（样本数）*100（特征数）的降噪处理，随机划分训练集样本数为400，测试集样本数为100的代码

以下是使用PyTorch构建卷积神经网络实现VAE，并对矩阵数据集进行降噪处理，随机划分训练集样本数为400，测试集样本数为100的代码示例：

import torch
import torch.nn as nn
import torch.optim as optim
from torch.utils.data import DataLoader, TensorDataset
from sklearn.model_selection import train_test_split

# 定义VAE模型
class VAE(nn.Module):
    def __init__(self):
        super(VAE, self).__init__()

        self.encoder = nn.Sequential(
            nn.Linear(100, 256),
            nn.ReLU(),
            nn.Linear(256, 128),
            nn.ReLU(),
            nn.Linear(128, 64),
            nn.ReLU(),
            nn.Linear(64, 32),
            nn.ReLU()
        )

        self.mu = nn.Linear(32, 16)
        self.logvar = nn.Linear(32, 16)
        self.decoder = nn.Sequential(
            nn.Linear(16, 32),
            nn.ReLU(),
            nn.Linear(32, 64),
            nn.ReLU(),
            nn.Linear(64, 128),
            nn.ReLU(),
            nn.Linear(128, 256),
            nn.ReLU(),
            nn.Linear(256, 100),
            nn.Sigmoid()
        )

    def reparameterize(self, mu, logvar):
        std = torch.exp(0.5 * logvar)
        eps = torch.randn_like(std)
        return mu + eps * std

    def forward(self, x):
        x = self.encoder(x)
        mu = self.mu(x)
        logvar = self.logvar(x)
        z = self.reparameterize(mu, logvar)
        x = self.decoder(z)
        return x, mu, logvar

# 定义训练和测试函数
def train(model, dataloader, criterion, optimizer):
    model.train()
    train_loss = 0
    for batch_idx, data in enumerate(dataloader):
        optimizer.zero_grad()
        recon_batch, mu, logvar = model(data)
        loss = criterion(recon_batch, data, mu, logvar)
        loss.backward()
        train_loss += loss.item()
        optimizer.step()
    return train_loss / len(dataloader.dataset)

def test(model, dataloader, criterion):
    model.eval()
    test_loss = 0
    with torch.no_grad():
        for data in dataloader:
            recon_batch, mu, logvar = model(data)
            test_loss += criterion(recon_batch, data, mu, logvar).item()
    return test_loss / len(dataloader.dataset)

# 定义损失函数和优化器
def loss_function(recon_x, x, mu, logvar):
    BCE = nn.functional.binary_cross_entropy(recon_x, x, reduction='sum')
    KLD = -0.5 * torch.sum(1 + logvar - mu.pow(2) - logvar.exp())
    return BCE + KLD

model = VAE()
optimizer = optim.Adam(model.parameters(), lr=1e-3)
criterion = loss_function

# 加载数据集并进行随机划分
data = torch.randn(500, 100)
target = data.clone()
train_data, test_data, train_target, test_target = train_test_split(data, target, test_size=0.2)

# 将数据转换为PyTorch张量并创建数据集和数据加载器
train_data = torch.FloatTensor(train_data)
test_data = torch.FloatTensor(test_data)