text: import jax
  import jax.numpy as jnp
  import copy
  import gym
  import numpy as np
  
  class MBRL():
      def __init__(self, env, agent, lr = 1e-3, batch_size = 32):
          self.env = env
          self.agent = agent
          self.lr = lr
          self.batch_size = batch_size
          self.f_grad = jax.value_and_grad(self.roll_out,argnums=2)
          self.value_loss_grad = jax.value_and_grad(self.loss_value,argnums=3)
          self.model_loss_grad = jax.value_and_grad(self.loss_hybrid_model,argnums=3)
  
          self.trajectory_prev_state_buffer = jnp.zeros(env.state_size)
          self.trajectory_action_buffer = jnp.zeros(env.action_size)
          self.trajectory_reward_buffer = jnp.zeros(1)
          self.trajectory_next_state_buffer = jnp.zeros(env.state_size)
  
      def step(self, context, x):
          env, agent, params = context
          # env, agent, policy_params, rnn_params = context
          # control = agent(env.state, (policy_params, rnn_params))
          control = agent.sample_action(env.state, params)
          # control = control + 10 * np.random.uniform()
          prev_state = copy.deepcopy(env.state)
          _, reward, done, _ = env.step(env.state,control)
          # next_state, reward, done, _ = self.cartpole_gym_env(control)
          # env.state =  next_state
  
          return (env, agent), reward, done
  
      def roll_out(self, env, agent, params, horizon):
          policy_params, value_params =  params
          # policy_params, rnn_params = params
          # policy_params =  params
          gamma = 0.99
          total_return = 0.0
          for i in range(horizon):
          # for i in range(T):
              (env, agent), r, done= self.step((env, agent, policy_params), i)
              # (env, agent), r, done= self.step((env, agent, policy_params, rnn_params), i)
              # total_return = total_return * gamma + r 
              total_return = total_return + (gamma ** i)* r
              if done:
                  # total_return -= 1000
                  print("end this episode because out of threshhold in policy update")
                  env.past_reward = 0
                  break
          # total_return += agent.value(env.state,value_params) * gamma 
          total_return += agent.value(env.state,value_params) * gamma ** horizon
          # total_return += agent.value(env.state,value_params)
          losses = -total_return       
          return losses
  
      def loss_value(self, state, next_state, reward, value_params, agent):
          gamma = 0.99
          # td = reward + gamma * agent.value(next_state, value_params) - agent.value(state, value_params)
          td = reward + agent.value(next_state, value_params) - agent.value(state, value_params)
          value_loss = 0.5 * (td ** 2).mean()
          return value_loss
  
      def step_for_render(self, context, x):
          env, hybrid_env, agent, params = context
          # policy_params, rnn_params = params
  
          if(env.render_flag==True):
              # env.osim_render()
              env.render()
              # env.ddpg_render()
          control = agent.sample_action(env.state, params)
          # control = agent(env.state, (policy_params, rnn_params))
          # control = jnp.array([0.0])
          prev_state = copy.deepcopy(env.state)
          next_state, reward, done, _ = env.step(env.state,control)  
          
          # #update hybrid model
          # model_loss, model_grads = self.model_loss_grad(prev_state,control,next_state,hybrid_env.model_params, hybrid_env)
          # # print("model_loss",model_loss)
          # hybrid_env.model_losses.append(model_loss)
          # hybrid_env.model_params = agent.update(model_grads,hybrid_env.model_params,hybrid_env.model_lr)
  
          return (env, hybrid_env, agent), prev_state, control, reward, next_state, done
  
      def roll_out_for_render(self, env, hybrid_env, agent, params, T):
          # trajectory_state_buffer.append(env.state)
          gamma = 0.99
          rewards = 0.0
          for i in range(T):
              (env, hybrid_env, agent), prev_state, control, reward, next_state, done= self.step_for_render((env, hybrid_env, agent,params), i)
              # if (i == 0):
              #     trajectory_prev_state_buffer = prev_state
              #     trajectory_action_buffer = control
              #     trajectory_reward_buffer = reward
              #     trajectory_next_state_buffer = next_state
              # else:
              #     trajectory_prev_state_buffer = jnp.vstack((trajectory_prev_state_buffer,prev_state))
              #     trajectory_action_buffer = jnp.vstack((trajectory_action_buffer,control))
              #     trajectory_reward_buffer = jnp.vstack((trajectory_reward_buffer,reward))
              #     trajectory_next_state_buffer = jnp.vstack((trajectory_next_state_buffer,next_state))
              self.trajectory_prev_state_buffer = jnp.vstack((self.trajectory_prev_state_buffer,prev_state))
              self.trajectory_action_buffer = jnp.vstack((self.trajectory_action_buffer,control))
              self.trajectory_reward_buffer = jnp.vstack((self.trajectory_reward_buffer,reward))
              self.trajectory_next_state_buffer = jnp.vstack((self.trajectory_next_state_buffer,next_state))
                  
              # rewards = rewards * gamma + r 
              rewards = rewards + reward
              # trajectory_state_buffer.append(env.state)
              if done:
                  print("end this episode because out of threshhold in model update")
                  env.past_reward = 0
                  break
          
          # buffer =  [trajectory_prev_state_buffer, trajectory_action_buffer, trajectory_reward_buffer, trajectory_next_state_buffer]
          #update value function
          prev_state_batch, action_batch, reward_batch, next_state_batch = self.sample_batch()
          # value_loss, value_grads =  self.value_loss_grad(trajectory_prev_state_buffer,trajectory_next_state_buffer,trajectory_reward_buffer,agent.value_params, agent)
          value_loss, value_grads =  self.value_loss_grad(prev_state_batch, next_state_batch, reward_batch, agent.value_params, agent)
          agent.value_losses.append(value_loss)
          agent.value_params = self.update(value_grads,agent.value_params, self.lr)            
          return rewards, prev_state_batch
  
      def loss_hybrid_model(self, prev_state, control, true_next_state, model_params, hybrid_env):
          next_state = hybrid_env.forward(prev_state, control, model_params)
          model_loss = jnp.sum((next_state - true_next_state)**2)
          # model_loss = jnp.linalg.norm(next_state - true_next_state)
          # print("model loss",model_loss)
          # print("model_loss.value",model_loss[0])
          # model_losses.append(model_loss)
          return model_loss
  
      def update(self, grads, params, lr):
          """
          Description: update weights
          """
          #get norm square
          total_norm_sqr = 0                
          for (dw,db) in grads:
              # print("previous dw",dw)
              # dw = normalize(dw)
              # db = normalize(db[:,np.newaxis],axis =0).ravel()
              total_norm_sqr += np.linalg.norm(dw) ** 2
              total_norm_sqr += np.linalg.norm(db) ** 2
          # print("grads",grads)
  
          #scale the gradient
          # print("gradient total_norm_sqr",total_norm_sqr)
          gradient_clip = 0.2
          scale = min(
              1.0, gradient_clip / (total_norm_sqr**0.5 + 1e-4))
  
          params = [(w - lr * dw, b - lr * db)
                  for (w, b), (dw, db) in zip(params, grads)]
  
          return params        
  
      def sample_batch(self):
          if self.trajectory_prev_state_buffer.shape[0] < self.batch_size:
              batch_size = self.trajectory_prev_state_buffer.shape[0] - 1
          else:
              batch_size = self.batch_size
          idxs = np.random.choice(np.arange(1,self.trajectory_prev_state_buffer.shape[0]), batch_size, replace=False)
          prev_state_batch = self.trajectory_prev_state_buffer[idxs,:]
          action_batch = self.trajectory_action_buffer[idxs,:]
          reward_batch = self.trajectory_reward_buffer[idxs,:]
          next_state_batch = self.trajectory_next_state_buffer[idxs,:]
          return prev_state_batch, action_batch, reward_batch, next_state_batch