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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Ch 10
Step2:  Define the RNN model
Step3:  Now, we'll train a series predictor. Let's say we have a sequence of numbers [a, b, c, d] that we want to transform into [a, a+b, b+c, c+d]. We'll give the RNN a couple examples in the training data. Let's see how well it learns this intended transformation
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Python Code:
import numpy as np
import tensorflow as tf
from tensorflow.contrib import rnn
Explanation: Ch 10: Concept 02
Recurrent Neural Network
Import the relevant libraries:
End of explanation
class SeriesPredictor:
    def __init__(self, input_dim, seq_size, hidden_dim=10):
        # Hyperparameters
        self.input_dim = input_dim
        self.seq_size = seq_size
        self.hidden_dim = hidden_dim
        # Weight variables and input placeholders
        self.W_out = tf.Variable(tf.random_normal([hidden_dim, 1]), name='W_out')
        self.b_out = tf.Variable(tf.random_normal([1]), name='b_out')
        self.x = tf.placeholder(tf.float32, [None, seq_size, input_dim])
        self.y = tf.placeholder(tf.float32, [None, seq_size])
        # Cost optimizer
        self.cost = tf.reduce_mean(tf.square(self.model() - self.y))
        self.train_op = tf.train.AdamOptimizer().minimize(self.cost)
        # Auxiliary ops
        self.saver = tf.train.Saver()
    def model(self):
        
        :param x: inputs of size [T, batch_size, input_size]
        :param W: matrix of fully-connected output layer weights
        :param b: vector of fully-connected output layer biases
        
        cell = rnn.BasicLSTMCell(self.hidden_dim, reuse=tf.get_variable_scope().reuse)
        outputs, states = tf.nn.dynamic_rnn(cell, self.x, dtype=tf.float32)
        num_examples = tf.shape(self.x)[0]
        W_repeated = tf.tile(tf.expand_dims(self.W_out, 0), [num_examples, 1, 1])
        out = tf.matmul(outputs, W_repeated) + self.b_out
        out = tf.squeeze(out)
        return out
    def train(self, train_x, train_y):
        with tf.Session() as sess:
            tf.get_variable_scope().reuse_variables()
            sess.run(tf.global_variables_initializer())
            for i in range(1000):
                _, mse = sess.run([self.train_op, self.cost], feed_dict={self.x: train_x, self.y: train_y})
                if i % 100 == 0:
                    print(i, mse)
            save_path = self.saver.save(sess, 'model.ckpt')
            print('Model saved to {}'.format(save_path))
    def test(self, test_x):
        with tf.Session() as sess:
            tf.get_variable_scope().reuse_variables()
            self.saver.restore(sess, './model.ckpt')
            output = sess.run(self.model(), feed_dict={self.x: test_x})
            return output
Explanation: Define the RNN model:
End of explanation
if __name__ == '__main__':
    predictor = SeriesPredictor(input_dim=1, seq_size=4, hidden_dim=10)
    train_x = [[[1], [2], [5], [6]],
               [[5], [7], [7], [8]],
               [[3], [4], [5], [7]]]
    train_y = [[1, 3, 7, 11],
               [5, 12, 14, 15],
               [3, 7, 9, 12]]
    predictor.train(train_x, train_y)
    test_x = [[[1], [2], [3], [4]],  # 1, 3, 5, 7
              [[4], [5], [6], [7]]]  # 4, 9, 11, 13
    actual_y = [[[1], [3], [5], [7]],
                [[4], [9], [11], [13]]]
    pred_y = predictor.test(test_x)
    
    print("\nLets run some tests!\n")
    
    for i, x in enumerate(test_x):
        print("When the input is {}".format(x))
        print("The ground truth output should be {}".format(actual_y[i]))
        print("And the model thinks it is {}\n".format(pred_y[i]))
Explanation: Now, we'll train a series predictor. Let's say we have a sequence of numbers [a, b, c, d] that we want to transform into [a, a+b, b+c, c+d]. We'll give the RNN a couple examples in the training data. Let's see how well it learns this intended transformation:
End of explanation
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