code: def train_step(
      model: models.NerfModel,
      rng_key: Callable[[int], jnp.ndarray],
      state,
      batch: Dict[str, Any],
      scalar_params: ScalarParams,
      use_elastic_loss: bool = False,
      elastic_reduce_method: str = "median",
      elastic_loss_type: str = "log_svals",
      use_background_loss: bool = False,
      use_warp_reg_loss: bool = False,
  ):
      """One optimization step.
  
      Args:
        model: the model module to evaluate.
        rng_key: The random number generator.
        state: model_utils.TrainState, state of model and optimizer.
        batch: dict. A mini-batch of data for training.
        scalar_params: scalar-valued parameters.
        use_elastic_loss: is True use the elastic regularization loss.
        elastic_reduce_method: which method to use to reduce the samples for the
          elastic loss. 'median' selects the median depth point sample while
          'weight' computes a weighted sum using the density weights.
        elastic_loss_type: which method to use for the elastic loss.
        use_background_loss: if True use the background regularization loss.
        use_warp_reg_loss: if True use the warp regularization loss.
  
      Returns:
        new_state: model_utils.TrainState, new training state.
        stats: list. [(loss, psnr), (loss_coarse, psnr_coarse)].
      """
      rng_key, fine_key, coarse_key, reg_key = random.split(rng_key, 4)
  
      # pylint: disable=unused-argument
      def _compute_loss_and_stats(
          params, model_out, use_elastic_loss=False
      ):
          rgb_loss = (
              (model_out["rgb"] - batch["rgb"][..., :3]) ** 2
          ).mean()
          stats = {
              "loss/rgb": rgb_loss,
          }
          loss = rgb_loss
          if use_elastic_loss:
              elastic_fn = functools.partial(
                  compute_elastic_loss, loss_type=elastic_loss_type
              )
              v_elastic_fn = jax.jit(vmap(vmap(jax.jit(elastic_fn))))
              weights = lax.stop_gradient(model_out["weights"])
              jacobian = model_out["warp_jacobian"]
              # Pick the median point Jacobian.
              if elastic_reduce_method == "median":
                  depth_indices = model_utils.compute_depth_index(
                      weights
                  )
                  jacobian = jnp.take_along_axis(
                      # Unsqueeze axes: sample axis, Jacobian row, Jacobian col.
                      jacobian,
                      depth_indices[..., None, None, None],
                      axis=-3,
                  )
              # Compute loss using Jacobian.
              elastic_loss, elastic_residual = v_elastic_fn(jacobian)
              # Multiply weight if weighting by density.
              if elastic_reduce_method == "weight":
                  elastic_loss = weights * elastic_loss
              elastic_loss = elastic_loss.sum(axis=-1).mean()
              stats["loss/elastic"] = elastic_loss
              stats["residual/elastic"] = jnp.mean(elastic_residual)
              loss += scalar_params.elastic_loss_weight * elastic_loss
  
          if use_warp_reg_loss:
              weights = lax.stop_gradient(model_out["weights"])
              depth_indices = model_utils.compute_depth_index(weights)
              warp_mag = (
                  (model_out["points"] - model_out["warped_points"])
                  ** 2
              ).sum(axis=-1)
              warp_reg_residual = jnp.take_along_axis(
                  warp_mag, depth_indices[..., None], axis=-1
              )
              warp_reg_loss = utils.general_loss_with_squared_residual(
                  warp_reg_residual,
                  alpha=scalar_params.warp_reg_loss_alpha,
                  scale=scalar_params.warp_reg_loss_scale,
              ).mean()
              stats["loss/warp_reg"] = warp_reg_loss
              stats["residual/warp_reg"] = jnp.mean(
                  jnp.sqrt(warp_reg_residual)
              )
              loss += scalar_params.warp_reg_loss_weight * warp_reg_loss
  
          if "warp_jacobian" in model_out:
              jacobian = model_out["warp_jacobian"]
              jacobian_det = jnp.linalg.det(jacobian)
              jacobian_div = utils.jacobian_to_div(jacobian)
              jacobian_curl = utils.jacobian_to_curl(jacobian)
              stats["metric/jacobian_det"] = jnp.mean(jacobian_det)
              stats["metric/jacobian_div"] = jnp.mean(jacobian_div)
              stats["metric/jacobian_curl"] = jnp.mean(
                  jnp.linalg.norm(jacobian_curl, axis=-1)
              )
  
          stats["loss/total"] = loss
          stats["metric/psnr"] = utils.compute_psnr(rgb_loss)
          return loss, stats
  
      def _loss_fn(params):
          ret = model.apply(
              {"params": params["model"]},
              batch,
              warp_extra=state.warp_extra,
              return_points=use_warp_reg_loss,
              return_weights=(use_warp_reg_loss or use_elastic_loss),
              rngs={"fine": fine_key, "coarse": coarse_key},
          )
  
          losses = {}
          stats = {}
          if "fine" in ret:
              losses["fine"], stats["fine"] = _compute_loss_and_stats(
                  params, ret["fine"]
              )
          if "coarse" in ret:
              (
                  losses["coarse"],
                  stats["coarse"],
              ) = _compute_loss_and_stats(
                  params,
                  ret["coarse"],
                  use_elastic_loss=use_elastic_loss,
              )
  
          if use_background_loss:
              background_loss = compute_background_loss(
                  model,
                  state=state,
                  params=params["model"],
                  key=reg_key,
                  points=batch["background_points"],
                  noise_std=scalar_params.background_noise_std,
              )
              background_loss = background_loss.mean()
              losses["background"] = (
                  scalar_params.background_loss_weight * background_loss
              )
              stats["background_loss"] = background_loss
  
          return sum(losses.values()), stats
  
      optimizer = state.optimizer
      grad_fn = jax.value_and_grad(_loss_fn, has_aux=True)
      (_, stats), grad = grad_fn(optimizer.target)
      grad = jax.lax.pmean(grad, axis_name="batch")
      stats = jax.lax.pmean(stats, axis_name="batch")
      new_optimizer = optimizer.apply_gradient(
          grad, learning_rate=scalar_params.learning_rate
      )
      new_state = state.replace(optimizer=new_optimizer)
      return new_state, stats, rng_key
  
imports: import functools
  from typing import Any
  from typing import Callable
  from typing import Dict
  from absl import logging
  from flax import struct
  from flax.training import checkpoints
  import jax
  from jax import lax
  from jax import numpy
  from jax import random
  from jax import vmap
  from nerfies import model_utils
  from nerfies import models
  from nerfies import utils
label_desc: Use image node_id 5 for calling a global function with example usage: train_step(model, rng_key, state, batch, scalar_params, use_elastic_loss, elastic_reduce_method, elastic_loss_type, use_background_loss, use_warp_reg_loss) and returns: new_state,  stats,  rng_key, loss,  stats, sum,  stats