# 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,
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import torch
from torch import Tensor

from torchmetrics.functional.regression.pearson import _pearson_corrcoef_compute, _pearson_corrcoef_update


def _concordance_corrcoef_compute(
    mean_x: Tensor,
    mean_y: Tensor,
    var_x: Tensor,
    var_y: Tensor,
    corr_xy: Tensor,
    nb: Tensor,
) -> Tensor:
    """Computes the final concordance correlation coefficient based on accumulated statistics."""
    pearson = _pearson_corrcoef_compute(var_x, var_y, corr_xy, nb)
    return 2.0 * pearson * var_x.sqrt() * var_y.sqrt() / (var_x + var_y + (mean_x - mean_y) ** 2)


def concordance_corrcoef(preds: Tensor, target: Tensor) -> Tensor:
    r"""Computes concordance correlation coefficient that measures the agreement between two variables. It is
    defined as.

    .. math::
        \rho_c = \frac{2 \rho \sigma_x \sigma_y}{\sigma_x^2 + \sigma_y^2 + (\mu_x - \mu_y)^2}

    where :math:`\mu_x, \mu_y` is the means for the two variables, :math:`\sigma_x^2, \sigma_y^2` are the corresponding
    variances and \rho is the pearson correlation coefficient between the two variables.

    Args:
        preds: estimated scores
        target: ground truth scores

    Example (single output regression):
        >>> from torchmetrics.functional import concordance_corrcoef
        >>> target = torch.tensor([3, -0.5, 2, 7])
        >>> preds = torch.tensor([2.5, 0.0, 2, 8])
        >>> concordance_corrcoef(preds, target)
        tensor([0.9777])

    Example (multi output regression):
        >>> from torchmetrics.functional import concordance_corrcoef
        >>> target = torch.tensor([[3, -0.5], [2, 7]])
        >>> preds = torch.tensor([[2.5, 0.0], [2, 8]])
        >>> concordance_corrcoef(preds, target)
        tensor([0.7273, 0.9887])
    """
    d = preds.shape[1] if preds.ndim == 2 else 1
    _temp = torch.zeros(d, dtype=preds.dtype, device=preds.device)
    mean_x, mean_y, var_x = _temp.clone(), _temp.clone(), _temp.clone()
    var_y, corr_xy, nb = _temp.clone(), _temp.clone(), _temp.clone()
    mean_x, mean_y, var_x, var_y, corr_xy, nb = _pearson_corrcoef_update(
        preds, target, mean_x, mean_y, var_x, var_y, corr_xy, nb, num_outputs=1 if preds.ndim == 1 else preds.shape[-1]
    )
    return _concordance_corrcoef_compute(mean_x, mean_y, var_x, var_y, corr_xy, nb)