在jupyter notebook中 请帮我编代码实现VAE

以下是一个简单的VAE实现，用于MNIST数据集：

import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt
from tensorflow.examples.tutorials.mnist import input_data

# 加载MNIST数据集
mnist = input_data.read_data_sets('MNIST_data')

# 定义VAE模型
class VAE:
    def __init__(self, input_dim, hidden_dim, latent_dim):
        self.input_dim = input_dim
        self.hidden_dim = hidden_dim
        self.latent_dim = latent_dim
        self.build()

    def build(self):
        # 定义编码器
        self.x = tf.placeholder(tf.float32, [None, self.input_dim])
        self.encoder_hidden_layer = tf.layers.dense(inputs=self.x, units=self.hidden_dim, activation=tf.nn.relu)
        self.mu = tf.layers.dense(inputs=self.encoder_hidden_layer, units=self.latent_dim)
        self.log_var = tf.layers.dense(inputs=self.encoder_hidden_layer, units=self.latent_dim)

        # 定义潜在变量z
        self.epsilon = tf.random_normal(tf.shape(self.log_var), dtype=tf.float32)
        self.z = self.mu + tf.sqrt(tf.exp(self.log_var)) * self.epsilon

        # 定义解码器
        self.decoder_hidden_layer = tf.layers.dense(inputs=self.z, units=self.hidden_dim, activation=tf.nn.relu)
        self.logits = tf.layers.dense(inputs=self.decoder_hidden_layer, units=self.input_dim)
        self.x_hat = tf.nn.sigmoid(self.logits)

        # 定义损失函数
        self.reconstruction_loss = tf.reduce_sum(tf.nn.sigmoid_cross_entropy_with_logits(labels=self.x, logits=self.logits), axis=1)
        self.kl_divergence = 0.5 * tf.reduce_sum(tf.exp(self.log_var) + self.mu**2 - 1 - self.log_var, axis=1)
        self.loss = tf.reduce_mean(self.reconstruction_loss + self.kl_divergence)

        # 定义优化器
        self.optimizer = tf.train.AdamOptimizer(learning_rate=0.001).minimize(self.loss)

    def train(self, num_epochs, batch_size):
        with tf.Session() as sess:
            sess.run(tf.global_variables_initializer())
            for epoch in range(num_epochs):
                num_batches = mnist.train.num_examples // batch_size
                for i in range(num_batches):
                    batch_x, _ = mnist.train.next_batch(batch_size)
                    _, loss = sess.run([self.optimizer, self.loss], feed_dict={self.x: batch_x})
                print('Epoch %d, Loss: %.2f' % (epoch+1, loss))

            # 生成新的图像
            num_samples = 10
            z = np.random.normal(size=[num_samples, self.latent_dim])
            samples = sess.run(self.x_hat, feed_dict={self.z: z})
            fig, axs = plt.subplots(1, num_samples, figsize=(num_samples, 1))
            for i in range(num_samples):
                axs[i].imshow(samples[i].reshape(28, 28), cmap='gray')
                axs[i].axis('off')
            plt.show()

# 定义模型参数
input_dim = 784
hidden_dim = 512
latent_dim = 2

# 训练模型
vae = VAE(input_dim, hidden_dim, latent_dim)
vae.train(num_epochs=20, batch_size=128)

该代码会训练一个VAE模型，并生成10个新的MNIST图像。您可以根据需要更改模型参数和训练参数