code: def train(
      network_def,
      online_params,
      target_params,
      optimizer,
      optimizer_state,
      states,
      actions,
      next_states,
      rewards,
      terminals,
      same_traj_mask,
      loss_weights,
      support,
      cumulative_gamma,
      double_dqn,
      distributional,
      rng,
      spr_weight,
  ):
      """Run a training step."""
  
      current_state = states[:, 0]
      # Split the current rng into 2 for updating the rng after this call
      rng, rng1, rng2 = jax.random.split(rng, num=3)
      use_spr = spr_weight > 0
  
      def q_online(state, key, actions=None, do_rollout=False):
          return network_def.apply(
              online_params,
              state,
              actions=actions,
              do_rollout=do_rollout,
              key=key,
              support=support,
              mutable=["batch_stats"],
          )
  
      def q_target(state, key):
          return network_def.apply(
              target_params,
              state,
              key=key,
              support=support,
              mutable=["batch_stats"],
          )
  
      def encode_project(state, key):
          latent, _ = network_def.apply(
              target_params,
              state,
              method=network_def.encode,
              mutable=["batch_stats"],
          )
          latent = latent.reshape(-1)
          return network_def.apply(
              target_params,
              latent,
              key=key,
              eval_mode=True,
              method=network_def.project,
          )
  
      def loss_fn(params, target, spr_targets, loss_multipliers):
          """Computes the distributional loss for C51 or huber loss for DQN."""
  
          def q_online(state, key, actions=None, do_rollout=False):
              return network_def.apply(
                  params,
                  state,
                  actions=actions,
                  do_rollout=do_rollout,
                  key=key,
                  support=support,
                  mutable=["batch_stats"],
              )
  
          if distributional:
              (logits, spr_predictions) = get_logits(
                  q_online, current_state, actions[:, :-1], use_spr, rng
              )
              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[:, 0]
              )
              dqn_loss = jax.vmap(
                  losses.softmax_cross_entropy_loss_with_logits
              )(target, chosen_action_logits)
          else:
              q_values, spr_predictions = get_q_values(
                  q_online, current_state, actions[:, :-1], use_spr, rng
              )
              q_values = jnp.squeeze(q_values)
              replay_chosen_q = jax.vmap(lambda x, y: x[y])(
                  q_values, actions[:, 0]
              )
              dqn_loss = jax.vmap(losses.huber_loss)(
                  target, replay_chosen_q
              )
  
          if use_spr:
              # transpose to move from (time, batch, latent_dim) to
              # (batch, time, latent_dim) to match targets
              spr_predictions = spr_predictions.transpose(1, 0, 2)
  
              # Calculate SPR loss (normalized L2)
              spr_predictions = spr_predictions / jnp.linalg.norm(
                  spr_predictions, 2, -1, keepdims=True
              )
              spr_targets = spr_targets / jnp.linalg.norm(
                  spr_targets, 2, -1, keepdims=True
              )
  
              spr_loss = jnp.power(
                  spr_predictions - spr_targets, 2
              ).sum(-1)
  
              # Zero out loss for predictions that cross into the next episode
              spr_loss = (
                  spr_loss * same_traj_mask.transpose(1, 0)
              ).mean(0)
          else:
              spr_loss = 0
  
          loss = dqn_loss + spr_weight * spr_loss
  
          mean_loss = jnp.mean(loss_multipliers * loss)
          return mean_loss, (loss, dqn_loss, spr_loss)
  
      # Use the weighted mean loss for gradient computation.
      grad_fn = jax.value_and_grad(loss_fn, has_aux=True)
      target = target_output(
          q_online,
          q_target,
          next_states,
          rewards,
          terminals,
          support,
          cumulative_gamma,
          double_dqn,
          distributional,
          rng1,
      )
  
      if use_spr:
          future_states = states[:, 1:]
          spr_targets = get_spr_targets(
              encode_project,
              future_states.reshape(-1, *future_states.shape[2:]),
              rng1,
          )
          spr_targets = spr_targets.reshape(
              *future_states.shape[:2], *spr_targets.shape[1:]
          ).transpose(1, 0, 2)
      else:
          spr_targets = None
  
      # Get the unweighted loss without taking its mean for updating priorities.
      (mean_loss, (_, dqn_loss, spr_loss)), grad = grad_fn(
          online_params, target, spr_targets, loss_weights
      )
      updates, optimizer_state = optimizer.update(grad, optimizer_state)
      online_params = optax.apply_updates(online_params, updates)
      return (
          optimizer_state,
          online_params,
          mean_loss,
          dqn_loss,
          spr_loss,
          rng2,
      )
  
imports: import collections
  import copy
  import functools
  import time
  from absl import logging
  from dopamine.jax import losses
  from dopamine.jax.agents.dqn import dqn_agent
  from dopamine.jax.agents.rainbow import rainbow_agent
  from dopamine.labs.atari_100k import atari_100k_rainbow_agent
  from dopamine.labs.atari_100k.replay_memory import subsequence_replay_buffer
  from dopamine.labs.atari_100k.spr_networks import SPRNetwork
  import gin
  import jax
  import jax.numpy
  import optax
  import tensorflow
label_desc: Use image node_id 4 for calling a global function with example usage: train(network_def, online_params, target_params, optimizer, optimizer_state, states, actions, next_states, rewards, terminals, same_traj_mask, loss_weights, support, cumulative_gamma, double_dqn, distributional, rng, spr_weight) and returns: optimizer_state,  online_params,  mean_loss,  dqn_loss,  spr_loss,  rng2, network_def, network_def, network_def, mean_loss,  loss,  dqn_loss,  spr_loss, network_def