# 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:

        >>> 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)