code: def error_relative_global_dimensionless_synthesis(
      preds: Tensor,
      target: Tensor,
      ratio: float = 4,
      reduction: Literal[
          "elementwise_mean", "sum", "none", None
      ] = "elementwise_mean",
  ) -> Tensor:
      """Erreur Relative Globale Adimensionnelle de Synthèse.
  
      Args:
          preds: estimated image
          target: ground truth image
          ratio: ratio of high resolution to low resolution
          reduction: a method to reduce metric score over labels.
  
              - ``'elementwise_mean'``: takes the mean (default)
              - ``'sum'``: takes the sum
              - ``'none'`` or ``None``: no reduction will be applied
  
      Return:
          Tensor with RelativeG score
  
      Raises:
          TypeError:
              If ``preds`` and ``target`` don't have the same data type.
          ValueError:
              If ``preds`` and ``target`` don't have ``BxCxHxW shape``.
  
      Example:
          >>> from torchmetrics.functional.image import error_relative_global_dimensionless_synthesis
          >>> gen = torch.manual_seed(42)
          >>> preds = torch.rand([16, 1, 16, 16], generator=gen)
          >>> target = preds * 0.75
          >>> ergds = error_relative_global_dimensionless_synthesis(preds, target)
          >>> torch.round(ergds)
          tensor(154.)
  
      References:
          [1] Qian Du; Nicholas H. Younan; Roger King; Vijay P. Shah, "On the Performance Evaluation of
          Pan-Sharpening Techniques" in IEEE Geoscience and Remote Sensing Letters, vol. 4, no. 4, pp. 518-522,
          15 October 2007, doi: 10.1109/LGRS.2007.896328.
  
      """
      preds, target = _ergas_update(preds, target)
      return _ergas_compute(preds, target, ratio, reduction)
  
file_path: torchmetrics/src/torchmetrics/functional/image/ergas.py
imports: from typing import Tuple
  import torch
  from torch import Tensor
  from typing_extensions import Literal
  from torchmetrics.utilities.checks import _check_same_shape
  from torchmetrics.utilities.distributed import reduce
label_desc: Use image node_id 3 for calling a global function with example usage: error_relative_global_dimensionless_synthesis(preds, target, ratio, reduction) and returns: _ergas_compute