写一个复杂的LSTM类

好的，下面是一个复杂的LSTM类的代码实现：

import numpy as np

class LSTM:
    def __init__(self, input_dim, hidden_dim, output_dim):
        self.input_dim = input_dim
        self.hidden_dim = hidden_dim
        self.output_dim = output_dim
        
        # 初始化权重和偏置
        self.Wf = np.random.randn(hidden_dim, input_dim + hidden_dim)
        self.Uf = np.random.randn(hidden_dim, hidden_dim)
        self.bf = np.zeros((hidden_dim, 1))
        
        self.Wi = np.random.randn(hidden_dim, input_dim + hidden_dim)
        self.Ui = np.random.randn(hidden_dim, hidden_dim)
        self.bi = np.zeros((hidden_dim, 1))
        
        self.Wc = np.random.randn(hidden_dim, input_dim + hidden_dim)
        self.Uc = np.random.randn(hidden_dim, hidden_dim)
        self.bc = np.zeros((hidden_dim, 1))
        
        self.Wo = np.random.randn(hidden_dim, input_dim + hidden_dim)
        self.Uo = np.random.randn(hidden_dim, hidden_dim)
        self.bo = np.zeros((hidden_dim, 1))
        
        self.Wy = np.random.randn(output_dim, hidden_dim)
        self.by = np.zeros((output_dim, 1))
        
    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))
    
    def tanh(self, x):
        return np.tanh(x)
    
    def forward(self, x, h_prev, c_prev):
        # 计算遗忘门
        f = self.sigmoid(np.dot(self.Wf, np.concatenate((x, h_prev), axis=0)) + np.dot(self.Uf, c_prev) + self.bf)
        
        # 计算输入门
        i = self.sigmoid(np.dot(self.Wi, np.concatenate((x, h_prev), axis=0)) + np.dot(self.Ui, c_prev) + self.bi)
        
        # 计算新的候选单元状态
        c_tilde = self.tanh(np.dot(self.Wc, np.concatenate((x, h_prev), axis=0)) + np.dot(self.Uc, c_prev) + self.bc)
        
        # 更新单元状态
        c = f * c_prev + i * c_tilde
        
        # 计算输出门
        o = self.sigmoid(np.dot(self.Wo, np.concatenate((x, h_prev), axis=0)) + np.dot(self.Uo, c) + self.bo)
        
        # 计算隐藏状态和输出
        h = o * self.tanh(c)
        y = np.dot(self.Wy, h) + self.by
        
        # 保存中间变量，供反向传播使用
        self.x = x
        self.h_prev = h_prev
        self.c_prev = c_prev
        self.f = f
        self.i = i
        self.c_tilde = c_tilde
        self.c = c
        self.o = o
        self.h = h
        
        return y
    
    def backward(self, dy, dh_next, dc_next):
        # 反向传播输出层
        dWy = np.dot(dy, self.h.T)
        dby = dy
        
        # 反向传播隐藏层
        dh = np.dot(self.Wy.T, dy) + dh_next
        do = dh * self.tanh(self.c)
        do = do * self.o * (1 - self.o)
        dUo = np.dot(do, self.c.T)
        dWo = np.dot(do, np.concatenate((self.x, self.h_prev), axis=0).T)
        dbo = do
        
        dc = dh * self.o * (1 - self.tanh(self.c) ** 2) + dc_next
        dc_tilde = dc * self.i
        dc_tilde = dc_tilde * (1 - self.c_tilde ** 2)
        dUc = np.dot(dc_tilde, self.c_prev.T)
        dWc = np.dot(dc_tilde, np.concatenate((self.x, self.h_prev), axis=0).T)
        dbc = dc_tilde
        
        di = dc * self.c_tilde
        di = di * self.i * (1 - self.i)
        dUi = np.dot(di, self.c_prev.T)
        dWi = np.dot(di, np.concatenate((self.x, self.h_prev), axis=0).T)
        dbi = di
        
        df = dc * self.c_prev
        df = df * self.f * (1 - self.f)
        dUf = np.dot(df, self.c_prev.T)
        dWf = np.dot(df, np.concatenate((self.x, self.h_prev), axis=0).T)
        dbf = df
        
        # 反向传播到上一层
        dx = np.dot(self.Wf.T[:, :self.input_dim], dWf) + \
             np.dot(self.Wi.T[:, :self.input_dim], dWi) + \
             np.dot(self.Wc.T[:, :self.input_dim], dWc) + \
             np.dot(self.Wo.T[:, :self.input_dim], dWo)
        dh_prev = np.dot(self.Wf.T[:, self.input_dim:], dWf) + \
                  np.dot(self.Wi.T[:, self.input_dim:], dWi) + \
                  np.dot(self.Wc.T[:, self.input_dim:], dWc) + \
                  np.dot(self.Wo.T[:, self.input_dim:], dWo)
        dc_prev = dc * self.f
        
        return dx, dh_prev, dc_prev, dWf, dUf, dbf, dWi, dUi, dbi, dWc, dUc, dbc, dWo, dUo, dbo, dWy, dby
    
    def update(self, dWf, dUf, dbf, dWi, dUi, dbi, dWc, dUc, dbc, dWo, dUo, dbo, dWy, dby, lr):
        # 更新权重和偏置
        self.Wf -= lr * dWf
        self.Uf -= lr * dUf
        self.bf -= lr * dbf
        
        self.Wi -= lr * dWi
        self.Ui -= lr * dUi
        self.bi -= lr * dbi
        
        self.Wc -= lr * dWc
        self.Uc -= lr * dUc
        self.bc -= lr * dbc
        
        self.Wo -= lr * dWo
        self.Uo -= lr * dUo
        self.bo -= lr * dbo
        
        self.Wy -= lr * dWy
        self.by -= lr * dby

这个LSTM类实现了前向传播、反向传播和权重更新。其中，前向传播计算了各个门和状态的值，反向传播则计算了各个门和状态对损失函数的梯度，权重更新则根据梯度和学习率来更新权重和偏置。