code: def train(
      network_def,
      online_params,
      target_params,
      optimizer,
      optimizer_state,
      states,
      actions,
      next_states,
      rewards,
      terminals,
      num_tau_samples,
      num_tau_prime_samples,
      num_quantile_samples,
      cumulative_gamma,
      double_dqn,
      kappa,
      rng,
  ):
      """Run a training step."""
      batch_size = states.shape[0]
  
      def loss_fn(params, rng_input, target_quantile_vals):
          def online(state, key):
              return network_def.apply(
                  params, state, num_quantiles=num_tau_samples, rng=key
              )
  
          batched_rng = jnp.stack(
              jax.random.split(rng_input, num=batch_size)
          )
          model_output = jax.vmap(online)(states, batched_rng)
          quantile_values = model_output.quantile_values
          quantiles = model_output.quantiles
          chosen_action_quantile_values = jax.vmap(
              lambda x, y: x[:, y][:, None]
          )(quantile_values, actions)
          # Shape of bellman_erors and huber_loss:
          # batch_size x num_tau_prime_samples x num_tau_samples x 1.
          bellman_errors = (
              target_quantile_vals[:, :, None, :]
              - chosen_action_quantile_values[:, None, :, :]
          )
          # The huber loss (see Section 2.3 of the paper) is defined via two cases:
          # case_one: |bellman_errors| <= kappa
          # case_two: |bellman_errors| > kappa
          huber_loss_case_one = (
              (jnp.abs(bellman_errors) <= kappa).astype(jnp.float32)
              * 0.5
              * bellman_errors**2
          )
          huber_loss_case_two = (
              (jnp.abs(bellman_errors) > kappa).astype(jnp.float32)
              * kappa
              * (jnp.abs(bellman_errors) - 0.5 * kappa)
          )
          huber_loss = huber_loss_case_one + huber_loss_case_two
          # Tile by num_tau_prime_samples along a new dimension. Shape is now
          # batch_size x num_tau_prime_samples x num_tau_samples x 1.
          # These quantiles will be used for computation of the quantile huber loss
          # below (see section 2.3 of the paper).
          quantiles = jnp.tile(
              quantiles[:, None, :, :], [1, num_tau_prime_samples, 1, 1]
          ).astype(jnp.float32)
          # Shape: batch_size x num_tau_prime_samples x num_tau_samples x 1.
          quantile_huber_loss = (
              jnp.abs(
                  quantiles
                  - jax.lax.stop_gradient(
                      (bellman_errors < 0).astype(jnp.float32)
                  )
              )
              * huber_loss
          ) / kappa
          # Sum over current quantile value (num_tau_samples) dimension,
          # average over target quantile value (num_tau_prime_samples) dimension.
          # Shape: batch_size x num_tau_prime_samples x 1.
          loss = jnp.sum(quantile_huber_loss, axis=2)
          loss = jnp.mean(loss, axis=1)
          return jnp.mean(loss)
  
      rng, target_rng = jax.random.split(rng, num=2)
      batched_target_rng = jnp.stack(
          jax.random.split(target_rng, num=batch_size)
      )
      _, target_quantile_vals = target_quantile_values(
          network_def,
          online_params,
          target_params,
          next_states,
          rewards,
          terminals,
          num_tau_prime_samples,
          num_quantile_samples,
          cumulative_gamma,
          double_dqn,
          batched_target_rng,
      )
      grad_fn = jax.value_and_grad(loss_fn)
      rng, rng_input = jax.random.split(rng)
      loss, grad = grad_fn(
          online_params, rng_input, target_quantile_vals
      )
      updates, optimizer_state = optimizer.update(
          grad, optimizer_state, params=online_params
      )
      online_params = optax.apply_updates(online_params, updates)
      return rng, optimizer_state, online_params, 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
  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, num_tau_samples, num_tau_prime_samples, num_quantile_samples, cumulative_gamma, double_dqn, kappa, rng) and returns: rng,  optimizer_state,  online_params,  loss, jnp, network_def