在pytorch上实现VAE，完成对矩阵数据降噪的代码

好的，以下是在PyTorch上实现VAE，完成对矩阵数据降噪的代码：

import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils.data import DataLoader, TensorDataset

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

        self.input_dim = input_dim
        self.latent_dim = latent_dim

        # 编码器
        self.encoder = nn.Sequential(
            nn.Linear(input_dim, 256),
            nn.ReLU(),
            nn.Linear(256, 128),
            nn.ReLU(),
            nn.Linear(128, latent_dim * 2)
        )

        # 解码器
        self.decoder = nn.Sequential(
            nn.Linear(latent_dim, 128),
            nn.ReLU(),
            nn.Linear(128, 256),
            nn.ReLU(),
            nn.Linear(256, input_dim),
            nn.Sigmoid()
        )

    def encode(self, x):
        h = self.encoder(x)
        mu, logvar = torch.chunk(h, 2, dim=-1)
        std = torch.exp(0.5 * logvar)
        z = torch.randn_like(std) * std + mu
        return z, mu, logvar

    def decode(self, z):
        return self.decoder(z)

    def forward(self, x):
        z, mu, logvar = self.encode(x)
        x_recon = self.decode(z)
        return x_recon, mu, logvar

    def loss_function(self, x, x_recon, mu, logvar):
        # 计算重构误差
        recon_loss = F.binary_cross_entropy(x_recon, x, reduction='sum')
        # 计算KL散度
        kld_loss = -0.5 * torch.sum(1 + logvar - mu.pow(2) - logvar.exp())
        return recon_loss + kld_loss

# 加载数据
data = torch.load('data.pt')

# 划分训练集和测试集
train_size = int(0.8 * len(data))
test_size = len(data) - train_size
train_data, test_data = torch.utils.data.random_split(data, [train_size, test_size])

# 创建数据加载器
batch_size = 64
train_loader = DataLoader(train_data, batch_size=batch_size, shuffle=True)
test_loader = DataLoader(test_data, batch_size=batch_size, shuffle=True)

# 定义VAE模型和优化器
input_dim = data.size(-1)
latent_dim = 10
vae = VAE(input_dim, latent_dim)
optimizer = torch.optim.Adam(vae.parameters(), lr=1e-3)

# 训练VAE模型
epochs = 100
for epoch in range(epochs):
    vae.train()
    train_loss = 0
    for batch_idx, x in enumerate(train_loader):
        x = x.float()
        optimizer.zero_grad()
        x_recon, mu, logvar = vae(x)
        loss = vae.loss_function(x, x_recon, mu, logvar)
        loss.backward()
        train_loss += loss.item()
        optimizer.step()

    print('Epoch: {} Train Loss: {:.4f}'.format(epoch + 1, train_loss / len(train_loader.dataset)))

# 评估VAE模型
vae.eval()
test_loss = 0
with torch.no_grad():
    for batch_idx, x in enumerate(test_loader):
        x = x