关于作业可以直接看这篇博文:https://blog.csdn.net/JUNJUN_ZHAO/article/details/79409325

PS: 实现过程中，查看RNN反向的底层代码原理还是很重要的。底层在对应作业中另一文件下，不难理解。

另外关于LSTM可以避免梯度消失问题，可以捕获更长距离的依赖关系。

def rnn_step_forward(parameters, a_prev, x):
    
    Waa, Wax, Wya, by, b = parameters['Waa'], parameters['Wax'], parameters['Wya'], parameters['by'], parameters['b']
    a_next = np.tanh(np.dot(Wax, x) + np.dot(Waa, a_prev) + b) # hidden state
    p_t = softmax(np.dot(Wya, a_next) + by) # unnormalized log probabilities for next chars # probabilities for next chars 
    
    return a_next, p_t

def rnn_step_backward(dy, gradients, parameters, x, a, a_prev):
    
    gradients['dWya'] += np.dot(dy, a.T)
    gradients['dby'] += dy
    da = np.dot(parameters['Wya'].T, dy) + gradients['da_next'] # backprop into h
    daraw = (1 - a * a) * da # backprop through tanh nonlinearity
    gradients['db'] += daraw
    gradients['dWax'] += np.dot(daraw, x.T)
    gradients['dWaa'] += np.dot(daraw, a_prev.T)
    gradients['da_next'] = np.dot(parameters['Waa'].T, daraw)
    return gradients

def update_parameters(parameters, gradients, lr):

    parameters['Wax'] += -lr * gradients['dWax']
    parameters['Waa'] += -lr * gradients['dWaa']
    parameters['Wya'] += -lr * gradients['dWya']
    parameters['b']  += -lr * gradients['db']
    parameters['by']  += -lr * gradients['dby']
    return parameters

def rnn_forward(X, Y, a0, parameters, vocab_size = 27):
    
    # Initialize x, a and y_hat as empty dictionaries
    x, a, y_hat = {}, {}, {}
    
    a[-1] = np.copy(a0)
    
    # initialize your loss to 0
    loss = 0
    
    for t in range(len(X)):
        
        # Set x[t] to be the one-hot vector representation of the t'th character in X.
        # if X[t] == None, we just have x[t]=0. This is used to set the input for the first timestep to the zero vector. 
        x[t] = np.zeros((vocab_size,1)) 
        if (X[t] != None):
            x[t][X[t]] = 1
        
        # Run one step forward of the RNN
        a[t], y_hat[t] = rnn_step_forward(parameters, a[t-1], x[t])
        
        # Update the loss by substracting the cross-entropy term of this time-step from it.
        loss -= np.log(y_hat[t][Y[t],0])
        
    cache = (y_hat, a, x)
        
    return loss, cache

def rnn_backward(X, Y, parameters, cache):
    # Initialize gradients as an empty dictionary
    gradients = {}
    
    # Retrieve from cache and parameters
    (y_hat, a, x) = cache
    Waa, Wax, Wya, by, b = parameters['Waa'], parameters['Wax'], parameters['Wya'], parameters['by'], parameters['b']
    
    # each one should be initialized to zeros of the same dimension as its corresponding parameter
    gradients['dWax'], gradients['dWaa'], gradients['dWya'] = np.zeros_like(Wax), np.zeros_like(Waa), np.zeros_like(Wya)
    gradients['db'], gradients['dby'] = np.zeros_like(b), np.zeros_like(by)
    gradients['da_next'] = np.zeros_like(a[0])
    
    ### START CODE HERE ###
    # Backpropagate through time
    for t in reversed(range(len(X))):
        dy = np.copy(y_hat[t])
        dy[Y[t]] -= 1
        gradients = rnn_step_backward(dy, gradients, parameters, x[t], a[t], a[t-1])
    ### END CODE HERE ###
    
    return gradients, a