# Copyright The PyTorch Lightning team.
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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#     http://www.apache.org/licenses/LICENSE-2.0
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from typing import Any

import torch
from torch import Tensor, tensor

from torchmetrics.functional.regression.r2 import _r2_score_compute, _r2_score_update
from torchmetrics.metric import Metric


class R2Score(Metric):
    r"""Computes r2 score also known as `R2 Score_Coefficient Determination`_:

    .. math:: R^2 = 1 - \frac{SS_{res}}{SS_{tot}}

    where :math:`SS_{res}=\sum_i (y_i - f(x_i))^2` is the sum of residual squares, and
    :math:`SS_{tot}=\sum_i (y_i - \bar{y})^2` is total sum of squares. Can also calculate
    adjusted r2 score given by

    .. math:: R^2_{adj} = 1 - \frac{(1-R^2)(n-1)}{n-k-1}

    where the parameter :math:`k` (the number of independent regressors) should be provided as the `adjusted` argument.
    The score is only proper defined when :math:`SS_{tot}\neq 0`, which can happen for near constant targets. In this
    case a score of 0 is returned. By definition the score is bounded between 0 and 1, where 1 corresponds to the
    predictions exactly matching the targets.

    As input to ``forward`` and ``update`` the metric accepts the following input:

    - ``preds`` (:class:`~torch.Tensor`): Predictions from model in float tensor with shape ``(N,)``
      or ``(N, M)`` (multioutput)
    - ``target`` (:class:`~torch.Tensor`): Ground truth values in float tensor with shape ``(N,)``
      or ``(N, M)`` (multioutput)

    As output of ``forward`` and ``compute`` the metric returns the following output:

    - ``r2score`` (:class:`~torch.Tensor`): A tensor with the r2 score(s)

    In the case of multioutput, as default the variances will be uniformly averaged over the additional dimensions.
    Please see argument ``multioutput`` for changing this behavior.

    Args:
        num_outputs: Number of outputs in multioutput setting
        adjusted: number of independent regressors for calculating adjusted r2 score.
        multioutput: Defines aggregation in the case of multiple output scores. Can be one of the following strings:

            * ``'raw_values'`` returns full set of scores
            * ``'uniform_average'`` scores are uniformly averaged
            * ``'variance_weighted'`` scores are weighted by their individual variances
        kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.

    Raises:
        ValueError:
            If ``adjusted`` parameter is not an integer larger or equal to 0.
        ValueError:
            If ``multioutput`` is not one of ``"raw_values"``, ``"uniform_average"`` or ``"variance_weighted"``.

    Example:
        >>> from torchmetrics import R2Score
        >>> target = torch.tensor([3, -0.5, 2, 7])
        >>> preds = torch.tensor([2.5, 0.0, 2, 8])
        >>> r2score = R2Score()
        >>> r2score(preds, target)
        tensor(0.9486)

        >>> target = torch.tensor([[0.5, 1], [-1, 1], [7, -6]])
        >>> preds = torch.tensor([[0, 2], [-1, 2], [8, -5]])
        >>> r2score = R2Score(num_outputs=2, multioutput='raw_values')
        >>> r2score(preds, target)
        tensor([0.9654, 0.9082])
    """
    is_differentiable: bool = True
    higher_is_better: bool = True
    full_state_update: bool = False
    sum_squared_error: Tensor
    sum_error: Tensor
    residual: Tensor
    total: Tensor

    def __init__(
        self,
        num_outputs: int = 1,
        adjusted: int = 0,
        multioutput: str = "uniform_average",
        **kwargs: Any,
    ) -> None:
        super().__init__(**kwargs)

        self.num_outputs = num_outputs

        if adjusted < 0 or not isinstance(adjusted, int):
            raise ValueError("`adjusted` parameter should be an integer larger or equal to 0.")
        self.adjusted = adjusted

        allowed_multioutput = ("raw_values", "uniform_average", "variance_weighted")
        if multioutput not in allowed_multioutput:
            raise ValueError(
                f"Invalid input to argument `multioutput`. Choose one of the following: {allowed_multioutput}"
            )
        self.multioutput = multioutput

        self.add_state("sum_squared_error", default=torch.zeros(self.num_outputs), dist_reduce_fx="sum")
        self.add_state("sum_error", default=torch.zeros(self.num_outputs), dist_reduce_fx="sum")
        self.add_state("residual", default=torch.zeros(self.num_outputs), dist_reduce_fx="sum")
        self.add_state("total", default=tensor(0), dist_reduce_fx="sum")

    def update(self, preds: Tensor, target: Tensor) -> None:
        """Update state with predictions and targets."""
        sum_squared_error, sum_error, residual, total = _r2_score_update(preds, target)

        self.sum_squared_error += sum_squared_error
        self.sum_error += sum_error
        self.residual += residual
        self.total += total

    def compute(self) -> Tensor:
        """Computes r2 score over the metric states."""
        return _r2_score_compute(
            self.sum_squared_error, self.sum_error, self.residual, self.total, self.adjusted, self.multioutput
        )