# 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 Optional, Tuple, Union

import torch
from torch import Tensor
from typing_extensions import Literal

from torchmetrics.functional.classification.confusion_matrix import (
    _binary_confusion_matrix_format,
    _binary_confusion_matrix_tensor_validation,
    _multiclass_confusion_matrix_format,
    _multiclass_confusion_matrix_tensor_validation,
)


def _binning_bucketize(
    confidences: Tensor, accuracies: Tensor, bin_boundaries: Tensor
) -> Tuple[Tensor, Tensor, Tensor]:
    """Compute calibration bins using ``torch.bucketize``. Use for pytorch >= 1.6.

    Args:
        confidences: The confidence (i.e. predicted prob) of the top1 prediction.
        accuracies: 1.0 if the top-1 prediction was correct, 0.0 otherwise.
        bin_boundaries: Bin boundaries separating the ``linspace`` from 0 to 1.

    Returns:
        tuple with binned accuracy, binned confidence and binned probabilities
    """
    accuracies = accuracies.to(dtype=confidences.dtype)
    acc_bin = torch.zeros(len(bin_boundaries) - 1, device=confidences.device, dtype=confidences.dtype)
    conf_bin = torch.zeros(len(bin_boundaries) - 1, device=confidences.device, dtype=confidences.dtype)
    count_bin = torch.zeros(len(bin_boundaries) - 1, device=confidences.device, dtype=confidences.dtype)

    indices = torch.bucketize(confidences, bin_boundaries) - 1

    count_bin.scatter_add_(dim=0, index=indices, src=torch.ones_like(confidences))

    conf_bin.scatter_add_(dim=0, index=indices, src=confidences)
    conf_bin = torch.nan_to_num(conf_bin / count_bin)

    acc_bin.scatter_add_(dim=0, index=indices, src=accuracies)
    acc_bin = torch.nan_to_num(acc_bin / count_bin)

    prop_bin = count_bin / count_bin.sum()
    return acc_bin, conf_bin, prop_bin


def _ce_compute(
    confidences: Tensor,
    accuracies: Tensor,
    bin_boundaries: Union[Tensor, int],
    norm: str = "l1",
    debias: bool = False,
) -> Tensor:
    """Computes the calibration error given the provided bin boundaries and norm.

    Args:
        confidences: The confidence (i.e. predicted prob) of the top1 prediction.
        accuracies: 1.0 if the top-1 prediction was correct, 0.0 otherwise.
        bin_boundaries: Bin boundaries separating the ``linspace`` from 0 to 1.
        norm: Norm function to use when computing calibration error. Defaults to "l1".
        debias: Apply debiasing to L2 norm computation as in
            `Verified Uncertainty Calibration`_. Defaults to False.

    Raises:
        ValueError: If an unsupported norm function is provided.

    Returns:
        Tensor: Calibration error scalar.
    """
    if isinstance(bin_boundaries, int):
        bin_boundaries = torch.linspace(0, 1, bin_boundaries + 1, dtype=torch.float, device=confidences.device)

    if norm not in {"l1", "l2", "max"}:
        raise ValueError(f"Norm {norm} is not supported. Please select from l1, l2, or max. ")

    with torch.no_grad():
        acc_bin, conf_bin, prop_bin = _binning_bucketize(confidences, accuracies, bin_boundaries)

    if norm == "l1":
        ce = torch.sum(torch.abs(acc_bin - conf_bin) * prop_bin)
    elif norm == "max":
        ce = torch.max(torch.abs(acc_bin - conf_bin))
    elif norm == "l2":
        ce = torch.sum(torch.pow(acc_bin - conf_bin, 2) * prop_bin)
        # NOTE: debiasing is disabled in the wrapper functions. This implementation differs from that in sklearn.
        if debias:
            # the order here (acc_bin - 1 ) vs (1 - acc_bin) is flipped from
            # the equation in Verified Uncertainty Prediction (Kumar et al 2019)/
            debias_bins = (acc_bin * (acc_bin - 1) * prop_bin) / (prop_bin * accuracies.size()[0] - 1)
            ce += torch.sum(torch.nan_to_num(debias_bins))  # replace nans with zeros if nothing appeared in a bin
        ce = torch.sqrt(ce) if ce > 0 else torch.tensor(0)
    return ce


def _binary_calibration_error_arg_validation(
    n_bins: int,
    norm: Literal["l1", "l2", "max"] = "l1",
    ignore_index: Optional[int] = None,
) -> None:
    if not isinstance(n_bins, int) or n_bins < 1:
        raise ValueError(f"Expected argument `n_bins` to be an integer larger than 0, but got {n_bins}")
    allowed_norm = ("l1", "l2", "max")
    if norm not in allowed_norm:
        raise ValueError(f"Expected argument `norm` to be one of {allowed_norm}, but got {norm}.")
    if ignore_index is not None and not isinstance(ignore_index, int):
        raise ValueError(f"Expected argument `ignore_index` to either be `None` or an integer, but got {ignore_index}")


def _binary_calibration_error_tensor_validation(
    preds: Tensor, target: Tensor, ignore_index: Optional[int] = None
) -> None:
    _binary_confusion_matrix_tensor_validation(preds, target, ignore_index)
    if not preds.is_floating_point():
        raise ValueError(
            "Expected argument `preds` to be floating tensor with probabilities/logits"
            f" but got tensor with dtype {preds.dtype}"
        )


def _binary_calibration_error_update(preds: Tensor, target: Tensor) -> Tensor:
    confidences, accuracies = preds, target
    return confidences, accuracies


def binary_calibration_error(
    preds: Tensor,
    target: Tensor,
    n_bins: int = 15,
    norm: Literal["l1", "l2", "max"] = "l1",
    ignore_index: Optional[int] = None,
    validate_args: bool = True,
) -> Tensor:
    r"""`Top-label Calibration Error`_ for binary tasks. The expected calibration error can be used to quantify how
    well a given model is calibrated e.g. how well the predicted output probabilities of the model matches the
    actual probabilities of the ground truth distribution.

    Three different norms are implemented, each corresponding to variations on the calibration error metric.

    .. math::
        \text{ECE} = \sum_i^N b_i \|(p_i - c_i)\|, \text{L1 norm (Expected Calibration Error)}

    .. math::
        \text{MCE} =  \max_{i} (p_i - c_i), \text{Infinity norm (Maximum Calibration Error)}

    .. math::
        \text{RMSCE} = \sqrt{\sum_i^N b_i(p_i - c_i)^2}, \text{L2 norm (Root Mean Square Calibration Error)}

    Where :math:`p_i` is the top-1 prediction accuracy in bin :math:`i`, :math:`c_i` is the average confidence of
    predictions in bin :math:`i`, and :math:`b_i` is the fraction of data points in bin :math:`i`. Bins are constructed
    in an uniform way in the [0,1] range.

    Accepts the following input tensors:

    - ``preds`` (float tensor): ``(N, ...)``. Preds should be a tensor containing probabilities or logits for each
      observation. If preds has values outside [0,1] range we consider the input to be logits and will auto apply
      sigmoid per element.
    - ``target`` (int tensor): ``(N, ...)``. Target should be a tensor containing ground truth labels, and therefore
      only contain {0,1} values (except if `ignore_index` is specified). The value 1 always encodes the positive class.

    Additional dimension ``...`` will be flattened into the batch dimension.

    Args:
        preds: Tensor with predictions
        target: Tensor with true labels
        n_bins: Number of bins to use when computing the metric.
        norm: Norm used to compare empirical and expected probability bins.
        ignore_index:
            Specifies a target value that is ignored and does not contribute to the metric calculation
        validate_args: bool indicating if input arguments and tensors should be validated for correctness.
            Set to ``False`` for faster computations.

    Example:
        >>> from torchmetrics.functional.classification import binary_calibration_error
        >>> preds = torch.tensor([0.25, 0.25, 0.55, 0.75, 0.75])
        >>> target = torch.tensor([0, 0, 1, 1, 1])
        >>> binary_calibration_error(preds, target, n_bins=2, norm='l1')
        tensor(0.2900)
        >>> binary_calibration_error(preds, target, n_bins=2, norm='l2')
        tensor(0.2918)
        >>> binary_calibration_error(preds, target, n_bins=2, norm='max')
        tensor(0.3167)
    """
    if validate_args:
        _binary_calibration_error_arg_validation(n_bins, norm, ignore_index)
        _binary_calibration_error_tensor_validation(preds, target, ignore_index)
    preds, target = _binary_confusion_matrix_format(
        preds, target, threshold=0.0, ignore_index=ignore_index, convert_to_labels=False
    )
    confidences, accuracies = _binary_calibration_error_update(preds, target)
    return _ce_compute(confidences, accuracies, n_bins, norm)


def _multiclass_calibration_error_arg_validation(
    num_classes: int,
    n_bins: int,
    norm: Literal["l1", "l2", "max"] = "l1",
    ignore_index: Optional[int] = None,
) -> None:
    if not isinstance(num_classes, int) or num_classes < 2:
        raise ValueError(f"Expected argument `num_classes` to be an integer larger than 1, but got {num_classes}")
    if not isinstance(n_bins, int) or n_bins < 1:
        raise ValueError(f"Expected argument `n_bins` to be an integer larger than 0, but got {n_bins}")
    allowed_norm = ("l1", "l2", "max")
    if norm not in allowed_norm:
        raise ValueError(f"Expected argument `norm` to be one of {allowed_norm}, but got {norm}.")
    if ignore_index is not None and not isinstance(ignore_index, int):
        raise ValueError(f"Expected argument `ignore_index` to either be `None` or an integer, but got {ignore_index}")


def _multiclass_calibration_error_tensor_validation(
    preds: Tensor, target: Tensor, num_classes: int, ignore_index: Optional[int] = None
) -> None:
    _multiclass_confusion_matrix_tensor_validation(preds, target, num_classes, ignore_index)
    if not preds.is_floating_point():
        raise ValueError(
            "Expected argument `preds` to be floating tensor with probabilities/logits"
            f" but got tensor with dtype {preds.dtype}"
        )


def _multiclass_calibration_error_update(
    preds: Tensor,
    target: Tensor,
) -> Tensor:
    if not torch.all((0 <= preds) * (preds <= 1)):
        preds = preds.softmax(1)
    confidences, predictions = preds.max(dim=1)
    accuracies = predictions.eq(target)
    return confidences.float(), accuracies.float()


def multiclass_calibration_error(
    preds: Tensor,
    target: Tensor,
    num_classes: int,
    n_bins: int = 15,
    norm: Literal["l1", "l2", "max"] = "l1",
    ignore_index: Optional[int] = None,
    validate_args: bool = True,
) -> Tensor:
    r"""`Top-label Calibration Error`_ for multiclass tasks. The expected calibration error can be used to quantify
    how well a given model is calibrated e.g. how well the predicted output probabilities of the model matches the
    actual probabilities of the ground truth distribution.

    Three different norms are implemented, each corresponding to variations on the calibration error metric.

    .. math::
        \text{ECE} = \sum_i^N b_i \|(p_i - c_i)\|, \text{L1 norm (Expected Calibration Error)}

    .. math::
        \text{MCE} =  \max_{i} (p_i - c_i), \text{Infinity norm (Maximum Calibration Error)}

    .. math::
        \text{RMSCE} = \sqrt{\sum_i^N b_i(p_i - c_i)^2}, \text{L2 norm (Root Mean Square Calibration Error)}

    Where :math:`p_i` is the top-1 prediction accuracy in bin :math:`i`, :math:`c_i` is the average confidence of
    predictions in bin :math:`i`, and :math:`b_i` is the fraction of data points in bin :math:`i`. Bins are constructed
    in an uniform way in the [0,1] range.

    Accepts the following input tensors:

    - ``preds`` (float tensor): ``(N, C, ...)``. Preds should be a tensor containing probabilities or logits for each
      observation. If preds has values outside [0,1] range we consider the input to be logits and will auto apply
      softmax per sample.
    - ``target`` (int tensor): ``(N, ...)``. Target should be a tensor containing ground truth labels, and therefore
      only contain values in the [0, n_classes-1] range (except if `ignore_index` is specified).

    Additional dimension ``...`` will be flattened into the batch dimension.

    Args:
        preds: Tensor with predictions
        target: Tensor with true labels
        num_classes: Integer specifing the number of classes
        n_bins: Number of bins to use when computing the metric.
        norm: Norm used to compare empirical and expected probability bins.
        ignore_index:
            Specifies a target value that is ignored and does not contribute to the metric calculation
        validate_args: bool indicating if input arguments and tensors should be validated for correctness.
            Set to ``False`` for faster computations.

    Example:
        >>> from torchmetrics.functional.classification import multiclass_calibration_error
        >>> preds = torch.tensor([[0.25, 0.20, 0.55],
        ...                       [0.55, 0.05, 0.40],
        ...                       [0.10, 0.30, 0.60],
        ...                       [0.90, 0.05, 0.05]])
        >>> target = torch.tensor([0, 1, 2, 0])
        >>> multiclass_calibration_error(preds, target, num_classes=3, n_bins=3, norm='l1')
        tensor(0.2000)
        >>> multiclass_calibration_error(preds, target, num_classes=3, n_bins=3, norm='l2')
        tensor(0.2082)
        >>> multiclass_calibration_error(preds, target, num_classes=3, n_bins=3, norm='max')
        tensor(0.2333)
    """
    if validate_args:
        _multiclass_calibration_error_arg_validation(num_classes, n_bins, norm, ignore_index)
        _multiclass_calibration_error_tensor_validation(preds, target, num_classes, ignore_index)
    preds, target = _multiclass_confusion_matrix_format(preds, target, ignore_index, convert_to_labels=False)
    confidences, accuracies = _multiclass_calibration_error_update(preds, target)
    return _ce_compute(confidences, accuracies, n_bins, norm)


def calibration_error(
    preds: Tensor,
    target: Tensor,
    task: Literal["binary", "multiclass"] = None,
    n_bins: int = 15,
    norm: Literal["l1", "l2", "max"] = "l1",
    num_classes: Optional[int] = None,
    ignore_index: Optional[int] = None,
    validate_args: bool = True,
) -> Tensor:
    r"""`Top-label Calibration Error`_. The expected calibration error can be used to quantify how well a given
    model is calibrated e.g. how well the predicted output probabilities of the model matches the actual
    probabilities of the ground truth distribution.

    Three different norms are implemented, each corresponding to variations on the calibration error metric.

    .. math::
        \text{ECE} = \sum_i^N b_i \|(p_i - c_i)\|, \text{L1 norm (Expected Calibration Error)}

    .. math::
        \text{MCE} =  \max_{i} (p_i - c_i), \text{Infinity norm (Maximum Calibration Error)}

    .. math::
        \text{RMSCE} = \sqrt{\sum_i^N b_i(p_i - c_i)^2}, \text{L2 norm (Root Mean Square Calibration Error)}

    Where :math:`p_i` is the top-1 prediction accuracy in bin :math:`i`, :math:`c_i` is the average confidence of
    predictions in bin :math:`i`, and :math:`b_i` is the fraction of data points in bin :math:`i`. Bins are constructed
    in an uniform way in the [0,1] range.

    This function is a simple wrapper to get the task specific versions of this metric, which is done by setting the
    ``task`` argument to either ``'binary'`` or ``'multiclass'``. See the documentation of
    :func:`binary_calibration_error` and :func:`multiclass_calibration_error` for the specific details of
    each argument influence and examples.
    """
    assert norm is not None
    if task == "binary":
        return binary_calibration_error(preds, target, n_bins, norm, ignore_index, validate_args)
    if task == "multiclass":
        assert isinstance(num_classes, int)
        return multiclass_calibration_error(preds, target, num_classes, n_bins, norm, ignore_index, validate_args)
    raise ValueError(f"Expected argument `task` to either be `'binary'` or `'multiclass'` but got {task}")