text: # Copyright The PyTorch Lightning team.
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #     http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  from typing import Tuple
  
  import torch
  
  from pytorch_lightning.metrics.utils import _stable_1d_sort
  
  
  def _auc_update(x: torch.Tensor, y: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
      if x.ndim > 1 or y.ndim > 1:
          raise ValueError(
              f'Expected both `x` and `y` tensor to be 1d, but got'
              f' tensors with dimention {x.ndim} and {y.ndim}'
          )
      if x.numel() != y.numel():
          raise ValueError(
              f'Expected the same number of elements in `x` and `y`'
              f' tensor but received {x.numel()} and {y.numel()}'
          )
      return x, y
  
  
  def _auc_compute(x: torch.Tensor, y: torch.Tensor, reorder: bool = False) -> torch.Tensor:
      if reorder:
          x, x_idx = _stable_1d_sort(x)
          y = y[x_idx]
  
      dx = x[1:] - x[:-1]
      if (dx < 0).any():
          if (dx <= 0).all():
              direction = -1.
          else:
              raise ValueError(
                  "The `x` tensor is neither increasing or decreasing."
                  " Try setting the reorder argument to `True`."
              )
      else:
          direction = 1.
      return direction * torch.trapz(y, x)
  
  
  def auc(x: torch.Tensor, y: torch.Tensor, reorder: bool = False) -> torch.Tensor:
      """
      Computes Area Under the Curve (AUC) using the trapezoidal rule
  
      Args:
          x: x-coordinates
          y: y-coordinates
          reorder: if True, will reorder the arrays
  
      Return:
          Tensor containing AUC score (float)
  
      Example:
          >>> from pytorch_lightning.metrics.functional import auc
          >>> x = torch.tensor([0, 1, 2, 3])
          >>> y = torch.tensor([0, 1, 2, 2])
          >>> auc(x, y)
          tensor(4.)
      """
      x, y = _auc_update(x, y)
      return _auc_compute(x, y, reorder=reorder)
  