code: def train(
      network_def,
      online_params,
      target_params,
      optimizer,
      optimizer_state,
      states,
      actions,
      next_states,
      rewards,
      terminals,
      kappa,
      num_atoms,
      cumulative_gamma,
  ):
      """Run a training step."""
  
      def loss_fn(params, target):
          def q_online(state):
              return network_def.apply(params, state)
  
          logits = jax.vmap(q_online)(states).logits
          logits = jnp.squeeze(logits)
          # Fetch the logits for its selected action. We use vmap to perform this
          # indexing across the batch.
          chosen_action_logits = jax.vmap(lambda x, y: x[y])(
              logits, actions
          )
          bellman_errors = (
              target[:, None, :] - chosen_action_logits[:, :, None]
          )  # Input `u' of Eq. 9.
          # Eq. 9 of paper.
          huber_loss = (jnp.abs(bellman_errors) <= kappa).astype(
              jnp.float32
          ) * 0.5 * bellman_errors**2 + (
              jnp.abs(bellman_errors) > kappa
          ).astype(
              jnp.float32
          ) * kappa * (
              jnp.abs(bellman_errors) - 0.5 * kappa
          )
  
          tau_hat = (
              jnp.arange(num_atoms, dtype=jnp.float32) + 0.5
          ) / num_atoms  # Quantile midpoints.  See Lemma 2 of paper.
          # Eq. 10 of paper.
          tau_bellman_diff = jnp.abs(
              tau_hat[None, :, None]
              - (bellman_errors < 0).astype(jnp.float32)
          )
          quantile_huber_loss = tau_bellman_diff * huber_loss
          # Sum over tau dimension, average over target value dimension.
          loss = jnp.sum(jnp.mean(quantile_huber_loss, 2), 1)
          return jnp.mean(loss), loss
  
      def q_target(state):
          return network_def.apply(target_params, state)
  
      grad_fn = jax.value_and_grad(loss_fn, has_aux=True)
      target = target_distribution(
          q_target, next_states, rewards, terminals, cumulative_gamma
      )
      (mean_loss, loss), grad = grad_fn(online_params, target)
      updates, optimizer_state = optimizer.update(
          grad, optimizer_state, params=online_params
      )
      online_params = optax.apply_updates(online_params, updates)
      return optimizer_state, online_params, loss, mean_loss
  
imports: from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  import functools
  from dopamine.jax import networks
  from dopamine.jax.agents.dqn import dqn_agent
  from dopamine.metrics import statistics_instance
  from dopamine.replay_memory import prioritized_replay_buffer
  import gin
  import jax
  import jax.numpy
  import numpy
  import optax
  import tensorflow
label_desc: Use image node_id 2 for calling a global function with example usage: train(network_def, online_params, target_params, optimizer, optimizer_state, states, actions, next_states, rewards, terminals, kappa, num_atoms, cumulative_gamma) and returns: optimizer_state,  online_params,  loss,  mean_loss, jnp,  loss, network_def, network_def