text: from typing import Tuple
  
  import torch
  
  from ignite.contrib.metrics.regression._base import _BaseRegression
  from ignite.exceptions import NotComputableError
  from ignite.metrics.metric import reinit__is_reduced, sync_all_reduce
  
  
  class GeometricMeanAbsoluteError(_BaseRegression):
      r"""Calculates the Geometric Mean Absolute Error.
  
      .. math::
          \text{GMAE} = \exp(\frac{1}{n}\sum_{j=1}^n\ln(|A_j - P_j|))
  
      where, :math:`A_j` is the ground truth and :math:`P_j` is the predicted value.
  
      More details can be found in `Botchkarev 2018`__.
  
      - ``update`` must receive output of the form ``(y_pred, y)`` or ``{'y_pred': y_pred, 'y': y}``.
      - `y` and `y_pred` must be of same shape `(N, )` or `(N, 1)`.
  
      __ https://arxiv.org/abs/1809.03006
  
      Parameters are inherited from ``Metric.__init__``.
  
      Args:
          output_transform: a callable that is used to transform the
              :class:`~ignite.engine.engine.Engine`'s ``process_function``'s output into the
              form expected by the metric. This can be useful if, for example, you have a multi-output model and
              you want to compute the metric with respect to one of the outputs.
              By default, metrics require the output as ``(y_pred, y)`` or ``{'y_pred': y_pred, 'y': y}``.
          device: specifies which device updates are accumulated on. Setting the
              metric's device to be the same as your ``update`` arguments ensures the ``update`` method is
              non-blocking. By default, CPU.
  
      Examples:
          To use with ``Engine`` and ``process_function``, simply attach the metric instance to the engine.
          The output of the engine's ``process_function`` needs to be in format of
          ``(y_pred, y)`` or ``{'y_pred': y_pred, 'y': y, ...}``.
  
          .. include:: defaults.rst
              :start-after: :orphan:
  
          .. testcode::
  
                  metric = GeometricMeanAbsoluteError()
                  metric.attach(default_evaluator, 'gmae')
                  y_pred = torch.Tensor([[3.8], [9.9], [-5.4], [2.1]])
                  y_true = y_pred * 1.5
                  state = default_evaluator.run([[y_pred, y_true]])
                  print(state.metrics['gmae'])
  
          .. testoutput::
  
                  2.2723...
  
      .. versionchanged:: 0.4.5
          - Works with DDP.
      """
  
      @reinit__is_reduced
      def reset(self) -> None:
          self._sum_of_errors = torch.tensor(0.0, device=self._device)
          self._num_examples = 0
  
      def _update(self, output: Tuple[torch.Tensor, torch.Tensor]) -> None:
          y_pred, y = output[0].detach(), output[1].detach()
          errors = torch.log(torch.abs(y.view_as(y_pred) - y_pred))
          self._sum_of_errors += torch.sum(errors).to(self._device)
          self._num_examples += y.shape[0]
  
      @sync_all_reduce("_sum_of_errors", "_num_examples")
      def compute(self) -> float:
          if self._num_examples == 0:
              raise NotComputableError(
                  "GeometricMeanAbsoluteError must have at least one example before it can be computed."
              )
          return torch.exp((self._sum_of_errors) / self._num_examples).item()
  