code: def _davie_foster_approximation(
      W, H, h, levy_area_approximation, get_noise
  ):
      if levy_area_approximation in (
          LEVY_AREA_APPROXIMATIONS.none,
          LEVY_AREA_APPROXIMATIONS.space_time,
      ):
          return None
      elif W.ndimension() in (0, 1):
          # If we have zero or one dimensions then treat the scalar / single dimension we have as batch, so that the
          # Brownian motion is one dimensional and the Levy area is zero.
          return torch.zeros_like(W)
      else:
          # Davie's approximation to the Levy area from space-time Levy area
          A = H.unsqueeze(-1) * W.unsqueeze(-2) - W.unsqueeze(
              -1
          ) * H.unsqueeze(-2)
          noise = get_noise()
          noise = noise - noise.transpose(
              -1, -2
          )  # noise is skew symmetric of variance 2
          if levy_area_approximation == LEVY_AREA_APPROXIMATIONS.foster:
              # Foster's additional correction to Davie's approximation
              tenth_h = 0.1 * h
              H_squared = H**2
              std = (
                  tenth_h
                  * (
                      tenth_h
                      + H_squared.unsqueeze(-1)
                      + H_squared.unsqueeze(-2)
                  )
              ).sqrt()
          else:  # davie approximation
              std = math.sqrt(_r12 * h**2)
          a_tilde = std * noise
          A += a_tilde
          return A
  
imports: import math
  import trampoline
  import warnings
  import numpy
  import torch
  from .None import brownian_base
  from ..settings import LEVY_AREA_APPROXIMATIONS
  from ..types import Scalar, Optional, Tuple, Union, Tensor
label_desc: Use image node_id 5 for calling a global function with example usage: _davie_foster_approximation(W, H, h, levy_area_approximation, get_noise) and returns: None, torch, A