<commit_before># Copyright (c) MONAI Consortium
# 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.

import warnings
from typing import Callable, List, Optional, Sequence, Union

import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.nn.modules.loss import _Loss

from monai.losses.focal_loss import FocalLoss
from monai.losses.spatial_mask import MaskedLoss
from monai.networks import one_hot
from monai.utils import DiceCEReduction, LossReduction, Weight, look_up_option


class DiceLoss(_Loss):
    """
    Compute average Dice loss between two tensors. It can support both multi-classes and multi-labels tasks.
    The data `input` (BNHW[D] where N is number of classes) is compared with ground truth `target` (BNHW[D]).

    Note that axis N of `input` is expected to be logits or probabilities for each class, if passing logits as input,
    must set `sigmoid=True` or `softmax=True`, or specifying `other_act`. And the same axis of `target`
    can be 1 or N (one-hot format).

    The `smooth_nr` and `smooth_dr` parameters are values added to the intersection and union components of
    the inter-over-union calculation to smooth results respectively, these values should be small.

    The original paper: <NAME>. et. al. (2016) V-Net: Fully Convolutional Neural Networks forVolumetric
    Medical Image Segmentation, 3DV, 2016.

    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Optional[Callable] = None,
        squared_pred: bool = False,
        jaccard: bool = False,
        reduction: Union[LossReduction, str] = LossReduction.MEAN,
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
    ) -> None:
        """
        Args:
            include_background: if False, channel index 0 (background category) is excluded from the calculation.
                if the non-background segmentations are small compared to the total image size they can get overwhelmed
                by the signal from the background so excluding it in such cases helps convergence.
            to_onehot_y: whether to convert `y` into the one-hot format. Defaults to False.
            sigmoid: if True, apply a sigmoid function to the prediction.
            softmax: if True, apply a softmax function to the prediction.
            other_act: if don't want to use `sigmoid` or `softmax`, use other callable function to execute
                other activation layers, Defaults to ``None``. for example:
                `other_act = torch.tanh`.
            squared_pred: use squared versions of targets and predictions in the denominator or not.
            jaccard: compute Jaccard Index (soft IoU) instead of dice or not.
            reduction: {``"none"``, ``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``.

                - ``"none"``: no reduction will be applied.
                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.

            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.
            batch: whether to sum the intersection and union areas over the batch dimension before the dividing.
                Defaults to False, a Dice loss value is computed independently from each item in the batch
                before any `reduction`.

        Raises:
            TypeError: When ``other_act`` is not an ``Optional[Callable]``.
            ValueError: When more than 1 of [``sigmoid=True``, ``softmax=True``, ``other_act is not None``].
                Incompatible values.

        """
        super().__init__(reduction=LossReduction(reduction).value)
        if other_act is not None and not callable(other_act):
            raise TypeError(f"other_act must be None or callable but is {type(other_act).__name__}.")
        if int(sigmoid) + int(softmax) + int(other_act is not None) > 1:
            raise ValueError("Incompatible values: more than 1 of [sigmoid=True, softmax=True, other_act is not None].")
        self.include_background = include_background
        self.to_onehot_y = to_onehot_y
        self.sigmoid = sigmoid
        self.softmax = softmax
        self.other_act = other_act
        self.squared_pred = squared_pred
        self.jaccard = jaccard
        self.smooth_nr = float(smooth_nr)
        self.smooth_dr = float(smooth_dr)
        self.batch = batch

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD], where N is the number of classes.
            target: the shape should be BNH[WD] or B1H[WD], where N is the number of classes.

        Raises:
            AssertionError: When input and target (after one hot transform if set)
                have different shapes.
            ValueError: When ``self.reduction`` is not one of ["mean", "sum", "none"].

        Example:
            >>> from monai.losses.dice import *  # NOQA
            >>> import torch
            >>> from monai.losses.dice import DiceLoss
            >>> B, C, H, W = 7, 5, 3, 2
            >>> input = torch.rand(B, C, H, W)
            >>> target_idx = torch.randint(low=0, high=C - 1, size=(B, H, W)).long()
            >>> target = one_hot(target_idx[:, None, ...], num_classes=C)
            >>> self = DiceLoss(reduction='none')
            >>> loss = self(input, target)
            >>> assert np.broadcast_shapes(loss.shape, input.shape) == input.shape
        """
        if self.sigmoid:
            input = torch.sigmoid(input)

        n_pred_ch = input.shape[1]
        if self.softmax:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `softmax=True` ignored.")
            else:
                input = torch.softmax(input, 1)

        if self.other_act is not None:
            input = self.other_act(input)

        if self.to_onehot_y:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `to_onehot_y=True` ignored.")
            else:
                target = one_hot(target, num_classes=n_pred_ch)

        if not self.include_background:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `include_background=False` ignored.")
            else:
                # if skipping background, removing first channel
                target = target[:, 1:]
                input = input[:, 1:]

        if target.shape != input.shape:
            raise AssertionError(f"ground truth has different shape ({target.shape}) from input ({input.shape})")

        # reducing only spatial dimensions (not batch nor channels)
        reduce_axis: List[int] = torch.arange(2, len(input.shape)).tolist()
        if self.batch:
            # reducing spatial dimensions and batch
            reduce_axis = [0] + reduce_axis

        intersection = torch.sum(target * input, dim=reduce_axis)

        if self.squared_pred:
            target = torch.pow(target, 2)
            input = torch.pow(input, 2)

        ground_o = torch.sum(target, dim=reduce_axis)
        pred_o = torch.sum(input, dim=reduce_axis)

        denominator = ground_o + pred_o

        if self.jaccard:
            denominator = 2.0 * (denominator - intersection)

        f: torch.Tensor = 1.0 - (2.0 * intersection + self.smooth_nr) / (denominator + self.smooth_dr)

        if self.reduction == LossReduction.MEAN.value:
            f = torch.mean(f)  # the batch and channel average
        elif self.reduction == LossReduction.SUM.value:
            f = torch.sum(f)  # sum over the batch and channel dims
        elif self.reduction == LossReduction.NONE.value:
            # If we are not computing voxelwise loss components at least
            # make sure a none reduction maintains a broadcastable shape
            broadcast_shape = list(f.shape[0:2]) + [1] * (len(input.shape) - 2)
            f = f.view(broadcast_shape)
        else:
            raise ValueError(f'Unsupported reduction: {self.reduction}, available options are ["mean", "sum", "none"].')

        return f


class MaskedDiceLoss(DiceLoss):
    """
    Add an additional `masking` process before `DiceLoss`, accept a binary mask ([0, 1]) indicating a region,
    `input` and `target` will be masked by the region: region with mask `1` will keep the original value,
    region with `0` mask will be converted to `0`. Then feed `input` and `target` to normal `DiceLoss` computation.
    This has the effect of ensuring only the masked region contributes to the loss computation and
    hence gradient calculation.

    """

    def __init__(self, *args, **kwargs) -> None:
        """
        Args follow :py:class:`monai.losses.DiceLoss`.
        """
        super().__init__(*args, **kwargs)
        self.spatial_weighted = MaskedLoss(loss=super().forward)

    def forward(self, input: torch.Tensor, target: torch.Tensor, mask: Optional[torch.Tensor] = None):
        """
        Args:
            input: the shape should be BNH[WD].
            target: the shape should be BNH[WD].
            mask: the shape should B1H[WD] or 11H[WD].
        """
        return self.spatial_weighted(input=input, target=target, mask=mask)


class GeneralizedDiceLoss(_Loss):
    """
    Compute the generalised Dice loss defined in:

        Sudre, C. et. al. (2017) Generalised Dice overlap as a deep learning
        loss function for highly unbalanced segmentations. DLMIA 2017.

    Adapted from:
        https://github.com/NifTK/NiftyNet/blob/v0.6.0/niftynet/layer/loss_segmentation.py#L279
    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Optional[Callable] = None,
        w_type: Union[Weight, str] = Weight.SQUARE,
        reduction: Union[LossReduction, str] = LossReduction.MEAN,
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
    ) -> None:
        """
        Args:
            include_background: If False channel index 0 (background category) is excluded from the calculation.
            to_onehot_y: whether to convert `y` into the one-hot format. Defaults to False.
            sigmoid: If True, apply a sigmoid function to the prediction.
            softmax: If True, apply a softmax function to the prediction.
            other_act: if don't want to use `sigmoid` or `softmax`, use other callable function to execute
                other activation layers, Defaults to ``None``. for example:
                `other_act = torch.tanh`.
            w_type: {``"square"``, ``"simple"``, ``"uniform"``}
                Type of function to transform ground truth volume to a weight factor. Defaults to ``"square"``.
            reduction: {``"none"``, ``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``.

                - ``"none"``: no reduction will be applied.
                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.
            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.
            batch: whether to sum the intersection and union areas over the batch dimension before the dividing.
                Defaults to False, intersection over union is computed from each item in the batch.

        Raises:
            TypeError: When ``other_act`` is not an ``Optional[Callable]``.
            ValueError: When more than 1 of [``sigmoid=True``, ``softmax=True``, ``other_act is not None``].
                Incompatible values.

        """
        super().__init__(reduction=LossReduction(reduction).value)
        if other_act is not None and not callable(other_act):
            raise TypeError(f"other_act must be None or callable but is {type(other_act).__name__}.")
        if int(sigmoid) + int(softmax) + int(other_act is not None) > 1:
            raise ValueError("Incompatible values: more than 1 of [sigmoid=True, softmax=True, other_act is not None].")

        self.include_background = include_background
        self.to_onehot_y = to_onehot_y
        self.sigmoid = sigmoid
        self.softmax = softmax
        self.other_act = other_act

        self.w_type = look_up_option(w_type, Weight)

        self.smooth_nr = float(smooth_nr)
        self.smooth_dr = float(smooth_dr)
        self.batch = batch

    def w_func(self, grnd):
        if self.w_type == Weight.SIMPLE:
            return torch.reciprocal(grnd)
        if self.w_type == Weight.SQUARE:
            return torch.reciprocal(grnd * grnd)
        return torch.ones_like(grnd)

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD].
            target: the shape should be BNH[WD].

        Raises:
            ValueError: When ``self.reduction`` is not one of ["mean", "sum", "none"].

        """
        if self.sigmoid:
            input = torch.sigmoid(input)
        n_pred_ch = input.shape[1]
        if self.softmax:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `softmax=True` ignored.")
            else:
                input = torch.softmax(input, 1)

        if self.other_act is not None:
            input = self.other_act(input)

        if self.to_onehot_y:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `to_onehot_y=True` ignored.")
            else:
                target = one_hot(target, num_classes=n_pred_ch)

        if not self.include_background:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `include_background=False` ignored.")
            else:
                # if skipping background, removing first channel
                target = target[:, 1:]
                input = input[:, 1:]

        if target.shape != input.shape:
            raise AssertionError(f"ground truth has differing shape ({target.shape}) from input ({input.shape})")

        # reducing only spatial dimensions (not batch nor channels)
        reduce_axis: List[int] = torch.arange(2, len(input.shape)).tolist()
        if self.batch:
            reduce_axis = [0] + reduce_axis
        intersection = torch.sum(target * input, reduce_axis)

        ground_o = torch.sum(target, reduce_axis)
        pred_o = torch.sum(input, reduce_axis)

        denominator = ground_o + pred_o

        w = self.w_func(ground_o.float())
        infs = torch.isinf(w)
        if self.batch:
            w[infs] = 0.0
            w = w + infs * torch.max(w)
        else:
            w[infs] = 0.0
            max_values = torch.max(w, dim=1)[0].unsqueeze(dim=1)
            w = w + infs * max_values

        final_reduce_dim = 0 if self.batch else 1
        numer = 2.0 * (intersection * w).sum(final_reduce_dim, keepdim=True) + self.smooth_nr
        denom = (denominator * w).sum(final_reduce_dim, keepdim=True) + self.smooth_dr
        f: torch.Tensor = 1.0 - (numer / denom)

        if self.reduction == LossReduction.MEAN.value:
            f = torch.mean(f)  # the batch and channel average
        elif self.reduction == LossReduction.SUM.value:
            f = torch.sum(f)  # sum over the batch and channel dims
        elif self.reduction == LossReduction.NONE.value:
            # If we are not computing voxelwise loss components at least
            # make sure a none reduction maintains a broadcastable shape
            broadcast_shape = list(f.shape[0:2]) + [1] * (len(input.shape) - 2)
            f = f.view(broadcast_shape)
        else:
            raise ValueError(f'Unsupported reduction: {self.reduction}, available options are ["mean", "sum", "none"].')

        return f


class GeneralizedWassersteinDiceLoss(_Loss):
    """
    Compute the generalized Wasserstein Dice Loss defined in:

        <NAME>. et al. (2017) Generalised Wasserstein Dice Score for Imbalanced Multi-class
        Segmentation using Holistic Convolutional Networks. BrainLes 2017.

    Or its variant (use the option weighting_mode="GDL") defined in the Appendix of:

        <NAME>. et al. (2020) Comparative study of deep learning methods for the automatic
        segmentation of lung, lesion and lesion type in CT scans of COVID-19 patients.
        arXiv preprint arXiv:2007.15546

    Adapted from:
        https://github.com/LucasFidon/GeneralizedWassersteinDiceLoss
    """

    def __init__(
        self,
        dist_matrix: Union[np.ndarray, torch.Tensor],
        weighting_mode: str = "default",
        reduction: Union[LossReduction, str] = LossReduction.MEAN,
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
    ) -> None:
        """
        Args:
            dist_matrix: 2d tensor or 2d numpy array; matrix of distances between the classes.
            It must have dimension C x C where C is the number of classes.
            weighting_mode: {``"default"``, ``"GDL"``}
                Specifies how to weight the class-specific sum of errors.
                Default to ``"default"``.

                - ``"default"``: (recommended) use the original weighting method as in:
                    <NAME>. et al. (2017) Generalised Wasserstein Dice Score for Imbalanced Multi-class
                    Segmentation using Holistic Convolutional Networks. BrainLes 2017.
                - ``"GDL"``: use a GDL-like weighting method as in the Appendix of:
                    Tilborghs, S. et al. (2020) Comparative study of deep learning methods for the automatic
                    segmentation of lung, lesion and lesion type in CT scans of COVID-19 patients.
                    arXiv preprint arXiv:2007.15546
            reduction: {``"none"``, ``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``.

                - ``"none"``: no reduction will be applied.
                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.
            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.

        Raises:
            ValueError: When ``dist_matrix`` is not a square matrix.

        Example:
            .. code-block:: python

                import torch
                import numpy as np
                from monai.losses import GeneralizedWassersteinDiceLoss

                # Example with 3 classes (including the background: label 0).
                # The distance between the background class (label 0) and the other classes is the maximum, equal to 1.
                # The distance between class 1 and class 2 is 0.5.
                dist_mat = np.array([[0.0, 1.0, 1.0], [1.0, 0.0, 0.5], [1.0, 0.5, 0.0]], dtype=np.float32)
                wass_loss = GeneralizedWassersteinDiceLoss(dist_matrix=dist_mat)

                pred_score = torch.tensor([[1000, 0, 0], [0, 1000, 0], [0, 0, 1000]], dtype=torch.float32)
                grnd = torch.tensor([0, 1, 2], dtype=torch.int64)
                wass_loss(pred_score, grnd)  # 0

        """
        super().__init__(reduction=LossReduction(reduction).value)

        if dist_matrix.shape[0] != dist_matrix.shape[1]:
            raise ValueError(f"dist_matrix must be C x C, got {dist_matrix.shape[0]} x {dist_matrix.shape[1]}.")

        if weighting_mode not in ["default", "GDL"]:
            raise ValueError("weighting_mode must be either 'default' or 'GDL, got %s." % weighting_mode)

        self.m = dist_matrix
        if isinstance(self.m, np.ndarray):
            self.m = torch.from_numpy(self.m)
        if torch.max(self.m) != 1:
            self.m = self.m / torch.max(self.m)
        self.alpha_mode = weighting_mode
        self.num_classes = self.m.size(0)
        self.smooth_nr = float(smooth_nr)
        self.smooth_dr = float(smooth_dr)

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD].
            target: the shape should be BNH[WD].

        """
        # Aggregate spatial dimensions
        flat_input = input.reshape(input.size(0), input.size(1), -1)
        flat_target = target.reshape(target.size(0), -1).long()

        # Apply the softmax to the input scores map
        probs = F.softmax(flat_input, dim=1)

        # Compute the Wasserstein distance map
        wass_dist_map = self.wasserstein_distance_map(probs, flat_target)

        # Compute the values of alpha to use
        alpha = self._compute_alpha_generalized_true_positives(flat_target)

        # Compute the numerator and denominator of the generalized Wasserstein Dice loss
        if self.alpha_mode == "GDL":
            # use GDL-style alpha weights (i.e. normalize by the volume of each class)
            # contrary to the original definition we also use alpha in the "generalized all error".
            true_pos = self._compute_generalized_true_positive(alpha, flat_target, wass_dist_map)
            denom = self._compute_denominator(alpha, flat_target, wass_dist_map)
        else:  # default: as in the original paper
            # (i.e. alpha=1 for all foreground classes and 0 for the background).
            # Compute the generalised number of true positives
            true_pos = self._compute_generalized_true_positive(alpha, flat_target, wass_dist_map)
            all_error = torch.sum(wass_dist_map, dim=1)
            denom = 2 * true_pos + all_error

        # Compute the final loss
        wass_dice: torch.Tensor = (2.0 * true_pos + self.smooth_nr) / (denom + self.smooth_dr)
        wass_dice_loss: torch.Tensor = 1.0 - wass_dice

        if self.reduction == LossReduction.MEAN.value:
            wass_dice_loss = torch.mean(wass_dice_loss)  # the batch and channel average
        elif self.reduction == LossReduction.SUM.value:
            wass_dice_loss = torch.sum(wass_dice_loss)  # sum over the batch and channel dims
        elif self.reduction == LossReduction.NONE.value:
            # If we are not computing voxelwise loss components at least
            # make sure a none reduction maintains a broadcastable shape
            broadcast_shape = input.shape[0:2] + (1,) * (len(input.shape) - 2)
            wass_dice_loss = wass_dice_loss.view(broadcast_shape)
        else:
            raise ValueError(f'Unsupported reduction: {self.reduction}, available options are ["mean", "sum", "none"].')

        return wass_dice_loss

    def wasserstein_distance_map(self, flat_proba: torch.Tensor, flat_target: torch.Tensor) -> torch.Tensor:
        """
        Compute the voxel-wise Wasserstein distance between the
        flattened prediction and the flattened labels (ground_truth) with respect
        to the distance matrix on the label space M.
        This corresponds to eq. 6 in:

            <NAME>. et al. (2017) Generalised Wasserstein Dice Score for Imbalanced Multi-class
            Segmentation using Holistic Convolutional Networks. BrainLes 2017.

        Args:
            flat_proba: the probabilities of input(predicted) tensor.
            flat_target: the target tensor.
        """
        # Turn the distance matrix to a map of identical matrix
        m = torch.clone(torch.as_tensor(self.m)).to(flat_proba.device)
        m_extended = torch.unsqueeze(m, dim=0)
        m_extended = torch.unsqueeze(m_extended, dim=3)
        m_extended = m_extended.expand((flat_proba.size(0), m_extended.size(1), m_extended.size(2), flat_proba.size(2)))

        # Expand the feature dimensions of the target
        flat_target_extended = torch.unsqueeze(flat_target, dim=1)
        flat_target_extended = flat_target_extended.expand(
            (flat_target.size(0), m_extended.size(1), flat_target.size(1))
        )
        flat_target_extended = torch.unsqueeze(flat_target_extended, dim=1)

        # Extract the vector of class distances for the ground-truth label at each voxel
        m_extended = torch.gather(m_extended, dim=1, index=flat_target_extended)
        m_extended = torch.squeeze(m_extended, dim=1)

        # Compute the wasserstein distance map
        wasserstein_map = m_extended * flat_proba

        # Sum over the classes
        wasserstein_map = torch.sum(wasserstein_map, dim=1)
        return wasserstein_map

    def _compute_generalized_true_positive(
        self, alpha: torch.Tensor, flat_target: torch.Tensor, wasserstein_distance_map: torch.Tensor
    ) -> torch.Tensor:
        """
        Args:
            alpha: generalised number of true positives of target class.
            flat_target: the target tensor.
            wasserstein_distance_map: the map obtained from the above function.
        """
        # Extend alpha to a map and select value at each voxel according to flat_target
        alpha_extended = torch.unsqueeze(alpha, dim=2)
        alpha_extended = alpha_extended.expand((flat_target.size(0), self.num_classes, flat_target.size(1)))
        flat_target_extended = torch.unsqueeze(flat_target, dim=1)
        alpha_extended = torch.gather(alpha_extended, index=flat_target_extended, dim=1)

        return torch.sum(alpha_extended * (1.0 - wasserstein_distance_map), dim=[1, 2])

    def _compute_denominator(
        self, alpha: torch.Tensor, flat_target: torch.Tensor, wasserstein_distance_map: torch.Tensor
    ) -> torch.Tensor:
        """
        Args:
            alpha: generalised number of true positives of target class.
            flat_target: the target tensor.
            wasserstein_distance_map: the map obtained from the above function.
        """
        # Extend alpha to a map and select value at each voxel according to flat_target
        alpha_extended = torch.unsqueeze(alpha, dim=2)
        alpha_extended = alpha_extended.expand((flat_target.size(0), self.num_classes, flat_target.size(1)))
        flat_target_extended = torch.unsqueeze(flat_target, dim=1)
        alpha_extended = torch.gather(alpha_extended, index=flat_target_extended, dim=1)

        return torch.sum(alpha_extended * (2.0 - wasserstein_distance_map), dim=[1, 2])

    def _compute_alpha_generalized_true_positives(self, flat_target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            flat_target: the target tensor.
        """
        alpha: torch.Tensor = torch.ones((flat_target.size(0), self.num_classes)).float().to(flat_target.device)
        if self.alpha_mode == "GDL":  # GDL style
            # Define alpha like in the generalized dice loss
            # i.e. the inverse of the volume of each class.
            one_hot_f = F.one_hot(flat_target, num_classes=self.num_classes).permute(0, 2, 1).float()
            volumes = torch.sum(one_hot_f, dim=2)
            alpha = 1.0 / (volumes + 1.0)
        else:  # default, i.e. like in the original paper
            # alpha weights are 0 for the background and 1 the other classes
            alpha[:, 0] = 0.0
        return alpha


class DiceCELoss(_Loss):
    """
    Compute both Dice loss and Cross Entropy Loss, and return the weighted sum of these two losses.
    The details of Dice loss is shown in ``monai.losses.DiceLoss``.
    The details of Cross Entropy Loss is shown in ``torch.nn.CrossEntropyLoss``. In this implementation,
    two deprecated parameters ``size_average`` and ``reduce``, and the parameter ``ignore_index`` are
    not supported.

    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Optional[Callable] = None,
        squared_pred: bool = False,
        jaccard: bool = False,
        reduction: str = "mean",
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
        ce_weight: Optional[torch.Tensor] = None,
        lambda_dice: float = 1.0,
        lambda_ce: float = 1.0,
    ) -> None:
        """
        Args:
            ``ce_weight`` and ``lambda_ce`` are only used for cross entropy loss.
            ``reduction`` is used for both losses and other parameters are only used for dice loss.

            include_background: if False channel index 0 (background category) is excluded from the calculation.
            to_onehot_y: whether to convert `y` into the one-hot format. Defaults to False.
            sigmoid: if True, apply a sigmoid function to the prediction, only used by the `DiceLoss`,
                don't need to specify activation function for `CrossEntropyLoss`.
            softmax: if True, apply a softmax function to the prediction, only used by the `DiceLoss`,
                don't need to specify activation function for `CrossEntropyLoss`.
            other_act: if don't want to use `sigmoid` or `softmax`, use other callable function to execute
                other activation layers, Defaults to ``None``. for example: `other_act = torch.tanh`.
                only used by the `DiceLoss`, don't need to specify activation function for `CrossEntropyLoss`.
            squared_pred: use squared versions of targets and predictions in the denominator or not.
            jaccard: compute Jaccard Index (soft IoU) instead of dice or not.
            reduction: {``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``. The dice loss should
                as least reduce the spatial dimensions, which is different from cross entropy loss, thus here
                the ``none`` option cannot be used.

                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.

            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.
            batch: whether to sum the intersection and union areas over the batch dimension before the dividing.
                Defaults to False, a Dice loss value is computed independently from each item in the batch
                before any `reduction`.
            ce_weight: a rescaling weight given to each class for cross entropy loss.
                See ``torch.nn.CrossEntropyLoss()`` for more information.
            lambda_dice: the trade-off weight value for dice loss. The value should be no less than 0.0.
                Defaults to 1.0.
            lambda_ce: the trade-off weight value for cross entropy loss. The value should be no less than 0.0.
                Defaults to 1.0.

        """
        super().__init__()
        reduction = look_up_option(reduction, DiceCEReduction).value
        self.dice = DiceLoss(
            include_background=include_background,
            to_onehot_y=to_onehot_y,
            sigmoid=sigmoid,
            softmax=softmax,
            other_act=other_act,
            squared_pred=squared_pred,
            jaccard=jaccard,
            reduction=reduction,
            smooth_nr=smooth_nr,
            smooth_dr=smooth_dr,
            batch=batch,
        )
        self.cross_entropy = nn.CrossEntropyLoss(weight=ce_weight, reduction=reduction)
        if lambda_dice < 0.0:
            raise ValueError("lambda_dice should be no less than 0.0.")
        if lambda_ce < 0.0:
            raise ValueError("lambda_ce should be no less than 0.0.")
        self.lambda_dice = lambda_dice
        self.lambda_ce = lambda_ce

    def ce(self, input: torch.Tensor, target: torch.Tensor):
        """
        Compute CrossEntropy loss for the input and target.
        Will remove the channel dim according to PyTorch CrossEntropyLoss:
        https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html?#torch.nn.CrossEntropyLoss.

        """
        n_pred_ch, n_target_ch = input.shape[1], target.shape[1]
        if n_pred_ch == n_target_ch:
            # target is in the one-hot format, convert to BH[WD] format to calculate ce loss
            target = torch.argmax(target, dim=1)
        else:
            target = torch.squeeze(target, dim=1)
        target = target.long()
        return self.cross_entropy(input, target)

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD].
            target: the shape should be BNH[WD] or B1H[WD].

        Raises:
            ValueError: When number of dimensions for input and target are different.
            ValueError: When number of channels for target is neither 1 nor the same as input.

        """
        if len(input.shape) != len(target.shape):
            raise ValueError("the number of dimensions for input and target should be the same.")

        dice_loss = self.dice(input, target)
        ce_loss = self.ce(input, target)
        total_loss: torch.Tensor = self.lambda_dice * dice_loss + self.lambda_ce * ce_loss

        return total_loss


class DiceFocalLoss(_Loss):
    """
    Compute both Dice loss and Focal Loss, and return the weighted sum of these two losses.
    The details of Dice loss is shown in ``monai.losses.DiceLoss``.
    The details of Focal Loss is shown in ``monai.losses.FocalLoss``.

    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Optional[Callable] = None,
        squared_pred: bool = False,
        jaccard: bool = False,
        reduction: str = "mean",
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
        gamma: float = 2.0,
        focal_weight: Optional[Union[Sequence[float], float, int, torch.Tensor]] = None,
        lambda_dice: float = 1.0,
        lambda_focal: float = 1.0,
    ) -> None:
        """
        Args:
            ``gamma``, ``focal_weight`` and ``lambda_focal`` are only used for focal loss.
            ``include_background``, ``to_onehot_y``and ``reduction`` are used for both losses
            and other parameters are only used for dice loss.
            include_background: if False channel index 0 (background category) is excluded from the calculation.
            to_onehot_y: whether to convert `y` into the one-hot format. Defaults to False.
            sigmoid: if True, apply a sigmoid function to the prediction, only used by the `DiceLoss`,
                don't need to specify activation function for `FocalLoss`.
            softmax: if True, apply a softmax function to the prediction, only used by the `DiceLoss`,
                don't need to specify activation function for `FocalLoss`.
            other_act: if don't want to use `sigmoid` or `softmax`, use other callable function to execute
                other activation layers, Defaults to ``None``. for example: `other_act = torch.tanh`.
                only used by the `DiceLoss`, don't need to specify activation function for `FocalLoss`.
            squared_pred: use squared versions of targets and predictions in the denominator or not.
            jaccard: compute Jaccard Index (soft IoU) instead of dice or not.
            reduction: {``"none"``, ``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``.

                - ``"none"``: no reduction will be applied.
                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.

            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.
            batch: whether to sum the intersection and union areas over the batch dimension before the dividing.
                Defaults to False, a Dice loss value is computed independently from each item in the batch
                before any `reduction`.
            gamma: value of the exponent gamma in the definition of the Focal loss.
            focal_weight: weights to apply to the voxels of each class. If None no weights are applied.
                The input can be a single value (same weight for all classes), a sequence of values (the length
                of the sequence should be the same as the number of classes).
            lambda_dice: the trade-off weight value for dice loss. The value should be no less than 0.0.
                Defaults to 1.0.
            lambda_focal: the trade-off weight value for focal loss. The value should be no less than 0.0.
                Defaults to 1.0.

        """
        super().__init__()
        self.dice = DiceLoss(
            include_background=include_background,
            to_onehot_y=to_onehot_y,
            sigmoid=sigmoid,
            softmax=softmax,
            other_act=other_act,
            squared_pred=squared_pred,
            jaccard=jaccard,
            reduction=reduction,
            smooth_nr=smooth_nr,
            smooth_dr=smooth_dr,
            batch=batch,
        )
        self.focal = FocalLoss(
            include_background=include_background,
            to_onehot_y=to_onehot_y,
            gamma=gamma,
            weight=focal_weight,
            reduction=reduction,
        )
        if lambda_dice < 0.0:
            raise ValueError("lambda_dice should be no less than 0.0.")
        if lambda_focal < 0.0:
            raise ValueError("lambda_focal should be no less than 0.0.")
        self.lambda_dice = lambda_dice
        self.lambda_focal = lambda_focal

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD]. The input should be the original logits
                due to the restriction of ``monai.losses.FocalLoss``.
            target: the shape should be BNH[WD] or B1H[WD].

        Raises:
            ValueError: When number of dimensions for input and target are different.
            ValueError: When number of channels for target is neither 1 nor the same as input.

        """
        if len(input.shape) != len(target.shape):
            raise ValueError("the number of dimensions for input and target should be the same.")

        dice_loss = self.dice(input, target)<commit_msg>Update dice.py (#4234)<commit_after># Copyright (c) MONAI Consortium
# 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.

import warnings
from typing import Callable, List, Optional, Sequence, Union

import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.nn.modules.loss import _Loss

from monai.losses.focal_loss import FocalLoss
from monai.losses.spatial_mask import MaskedLoss
from monai.networks import one_hot
from monai.utils import DiceCEReduction, LossReduction, Weight, look_up_option


class DiceLoss(_Loss):
    """
    Compute average Dice loss between two tensors. It can support both multi-classes and multi-labels tasks.
    The data `input` (BNHW[D] where N is number of classes) is compared with ground truth `target` (BNHW[D]).

    Note that axis N of `input` is expected to be logits or probabilities for each class, if passing logits as input,
    must set `sigmoid=True` or `softmax=True`, or specifying `other_act`. And the same axis of `target`
    can be 1 or N (one-hot format).

    The `smooth_nr` and `smooth_dr` parameters are values added to the intersection and union components of
    the inter-over-union calculation to smooth results respectively, these values should be small.

    The original paper: <NAME>. (2016) V-Net: Fully Convolutional Neural Networks forVolumetric
    Medical Image Segmentation, 3DV, 2016.

    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Optional[Callable] = None,
        squared_pred: bool = False,
        jaccard: bool = False,
        reduction: Union[LossReduction, str] = LossReduction.MEAN,
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
    ) -> None:
        """
        Args:
            include_background: if False, channel index 0 (background category) is excluded from the calculation.
                if the non-background segmentations are small compared to the total image size they can get overwhelmed
                by the signal from the background so excluding it in such cases helps convergence.
            to_onehot_y: whether to convert `y` into the one-hot format. Defaults to False.
            sigmoid: if True, apply a sigmoid function to the prediction.
            softmax: if True, apply a softmax function to the prediction.
            other_act: if don't want to use `sigmoid` or `softmax`, use other callable function to execute
                other activation layers, Defaults to ``None``. for example:
                `other_act = torch.tanh`.
            squared_pred: use squared versions of targets and predictions in the denominator or not.
            jaccard: compute Jaccard Index (soft IoU) instead of dice or not.
            reduction: {``"none"``, ``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``.

                - ``"none"``: no reduction will be applied.
                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.

            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.
            batch: whether to sum the intersection and union areas over the batch dimension before the dividing.
                Defaults to False, a Dice loss value is computed independently from each item in the batch
                before any `reduction`.

        Raises:
            TypeError: When ``other_act`` is not an ``Optional[Callable]``.
            ValueError: When more than 1 of [``sigmoid=True``, ``softmax=True``, ``other_act is not None``].
                Incompatible values.

        """
        super().__init__(reduction=LossReduction(reduction).value)
        if other_act is not None and not callable(other_act):
            raise TypeError(f"other_act must be None or callable but is {type(other_act).__name__}.")
        if int(sigmoid) + int(softmax) + int(other_act is not None) > 1:
            raise ValueError("Incompatible values: more than 1 of [sigmoid=True, softmax=True, other_act is not None].")
        self.include_background = include_background
        self.to_onehot_y = to_onehot_y
        self.sigmoid = sigmoid
        self.softmax = softmax
        self.other_act = other_act
        self.squared_pred = squared_pred
        self.jaccard = jaccard
        self.smooth_nr = float(smooth_nr)
        self.smooth_dr = float(smooth_dr)
        self.batch = batch

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD], where N is the number of classes.
            target: the shape should be BNH[WD] or B1H[WD], where N is the number of classes.

        Raises:
            AssertionError: When input and target (after one hot transform if set)
                have different shapes.
            ValueError: When ``self.reduction`` is not one of ["mean", "sum", "none"].

        Example:
            >>> from monai.losses.dice import *  # NOQA
            >>> import torch
            >>> from monai.losses.dice import DiceLoss
            >>> B, C, H, W = 7, 5, 3, 2
            >>> input = torch.rand(B, C, H, W)
            >>> target_idx = torch.randint(low=0, high=C - 1, size=(B, H, W)).long()
            >>> target = one_hot(target_idx[:, None, ...], num_classes=C)
            >>> self = DiceLoss(reduction='none')
            >>> loss = self(input, target)
            >>> assert np.broadcast_shapes(loss.shape, input.shape) == input.shape
        """
        if self.sigmoid:
            input = torch.sigmoid(input)

        n_pred_ch = input.shape[1]
        if self.softmax:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `softmax=True` ignored.")
            else:
                input = torch.softmax(input, 1)

        if self.other_act is not None:
            input = self.other_act(input)

        if self.to_onehot_y:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `to_onehot_y=True` ignored.")
            else:
                target = one_hot(target, num_classes=n_pred_ch)

        if not self.include_background:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `include_background=False` ignored.")
            else:
                # if skipping background, removing first channel
                target = target[:, 1:]
                input = input[:, 1:]

        if target.shape != input.shape:
            raise AssertionError(f"ground truth has different shape ({target.shape}) from input ({input.shape})")

        # reducing only spatial dimensions (not batch nor channels)
        reduce_axis: List[int] = torch.arange(2, len(input.shape)).tolist()
        if self.batch:
            # reducing spatial dimensions and batch
            reduce_axis = [0] + reduce_axis

        intersection = torch.sum(target * input, dim=reduce_axis)

        if self.squared_pred:
            target = torch.pow(target, 2)
            input = torch.pow(input, 2)

        ground_o = torch.sum(target, dim=reduce_axis)
        pred_o = torch.sum(input, dim=reduce_axis)

        denominator = ground_o + pred_o

        if self.jaccard:
            denominator = 2.0 * (denominator - intersection)

        f: torch.Tensor = 1.0 - (2.0 * intersection + self.smooth_nr) / (denominator + self.smooth_dr)

        if self.reduction == LossReduction.MEAN.value:
            f = torch.mean(f)  # the batch and channel average
        elif self.reduction == LossReduction.SUM.value:
            f = torch.sum(f)  # sum over the batch and channel dims
        elif self.reduction == LossReduction.NONE.value:
            # If we are not computing voxelwise loss components at least
            # make sure a none reduction maintains a broadcastable shape
            broadcast_shape = list(f.shape[0:2]) + [1] * (len(input.shape) - 2)
            f = f.view(broadcast_shape)
        else:
            raise ValueError(f'Unsupported reduction: {self.reduction}, available options are ["mean", "sum", "none"].')

        return f


class MaskedDiceLoss(DiceLoss):
    """
    Add an additional `masking` process before `DiceLoss`, accept a binary mask ([0, 1]) indicating a region,
    `input` and `target` will be masked by the region: region with mask `1` will keep the original value,
    region with `0` mask will be converted to `0`. Then feed `input` and `target` to normal `DiceLoss` computation.
    This has the effect of ensuring only the masked region contributes to the loss computation and
    hence gradient calculation.

    """

    def __init__(self, *args, **kwargs) -> None:
        """
        Args follow :py:class:`monai.losses.DiceLoss`.
        """
        super().__init__(*args, **kwargs)
        self.spatial_weighted = MaskedLoss(loss=super().forward)

    def forward(self, input: torch.Tensor, target: torch.Tensor, mask: Optional[torch.Tensor] = None):
        """
        Args:
            input: the shape should be BNH[WD].
            target: the shape should be BNH[WD].
            mask: the shape should B1H[WD] or 11H[WD].
        """
        return self.spatial_weighted(input=input, target=target, mask=mask)


class GeneralizedDiceLoss(_Loss):
    """
    Compute the generalised Dice loss defined in:

        <NAME>. al. (2017) Generalised Dice overlap as a deep learning
        loss function for highly unbalanced segmentations. DLMIA 2017.

    Adapted from:
        https://github.com/NifTK/NiftyNet/blob/v0.6.0/niftynet/layer/loss_segmentation.py#L279
    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Optional[Callable] = None,
        w_type: Union[Weight, str] = Weight.SQUARE,
        reduction: Union[LossReduction, str] = LossReduction.MEAN,
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
    ) -> None:
        """
        Args:
            include_background: If False channel index 0 (background category) is excluded from the calculation.
            to_onehot_y: whether to convert `y` into the one-hot format. Defaults to False.
            sigmoid: If True, apply a sigmoid function to the prediction.
            softmax: If True, apply a softmax function to the prediction.
            other_act: if don't want to use `sigmoid` or `softmax`, use other callable function to execute
                other activation layers, Defaults to ``None``. for example:
                `other_act = torch.tanh`.
            w_type: {``"square"``, ``"simple"``, ``"uniform"``}
                Type of function to transform ground truth volume to a weight factor. Defaults to ``"square"``.
            reduction: {``"none"``, ``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``.

                - ``"none"``: no reduction will be applied.
                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.
            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.
            batch: whether to sum the intersection and union areas over the batch dimension before the dividing.
                Defaults to False, intersection over union is computed from each item in the batch.

        Raises:
            TypeError: When ``other_act`` is not an ``Optional[Callable]``.
            ValueError: When more than 1 of [``sigmoid=True``, ``softmax=True``, ``other_act is not None``].
                Incompatible values.

        """
        super().__init__(reduction=LossReduction(reduction).value)
        if other_act is not None and not callable(other_act):
            raise TypeError(f"other_act must be None or callable but is {type(other_act).__name__}.")
        if int(sigmoid) + int(softmax) + int(other_act is not None) > 1:
            raise ValueError("Incompatible values: more than 1 of [sigmoid=True, softmax=True, other_act is not None].")

        self.include_background = include_background
        self.to_onehot_y = to_onehot_y
        self.sigmoid = sigmoid
        self.softmax = softmax
        self.other_act = other_act

        self.w_type = look_up_option(w_type, Weight)

        self.smooth_nr = float(smooth_nr)
        self.smooth_dr = float(smooth_dr)
        self.batch = batch

    def w_func(self, grnd):
        if self.w_type == Weight.SIMPLE:
            return torch.reciprocal(grnd)
        if self.w_type == Weight.SQUARE:
            return torch.reciprocal(grnd * grnd)
        return torch.ones_like(grnd)

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD].
            target: the shape should be BNH[WD].

        Raises:
            ValueError: When ``self.reduction`` is not one of ["mean", "sum", "none"].

        """
        if self.sigmoid:
            input = torch.sigmoid(input)
        n_pred_ch = input.shape[1]
        if self.softmax:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `softmax=True` ignored.")
            else:
                input = torch.softmax(input, 1)

        if self.other_act is not None:
            input = self.other_act(input)

        if self.to_onehot_y:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `to_onehot_y=True` ignored.")
            else:
                target = one_hot(target, num_classes=n_pred_ch)

        if not self.include_background:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `include_background=False` ignored.")
            else:
                # if skipping background, removing first channel
                target = target[:, 1:]
                input = input[:, 1:]

        if target.shape != input.shape:
            raise AssertionError(f"ground truth has differing shape ({target.shape}) from input ({input.shape})")

        # reducing only spatial dimensions (not batch nor channels)
        reduce_axis: List[int] = torch.arange(2, len(input.shape)).tolist()
        if self.batch:
            reduce_axis = [0] + reduce_axis
        intersection = torch.sum(target * input, reduce_axis)

        ground_o = torch.sum(target, reduce_axis)
        pred_o = torch.sum(input, reduce_axis)

        denominator = ground_o + pred_o

        w = self.w_func(ground_o.float())
        infs = torch.isinf(w)
        if self.batch:
            w[infs] = 0.0
            w = w + infs * torch.max(w)
        else:
            w[infs] = 0.0
            max_values = torch.max(w, dim=1)[0].unsqueeze(dim=1)
            w = w + infs * max_values

        final_reduce_dim = 0 if self.batch else 1
        numer = 2.0 * (intersection * w).sum(final_reduce_dim, keepdim=True) + self.smooth_nr
        denom = (denominator * w).sum(final_reduce_dim, keepdim=True) + self.smooth_dr
        f: torch.Tensor = 1.0 - (numer / denom)

        if self.reduction == LossReduction.MEAN.value:
            f = torch.mean(f)  # the batch and channel average
        elif self.reduction == LossReduction.SUM.value:
            f = torch.sum(f)  # sum over the batch and channel dims
        elif self.reduction == LossReduction.NONE.value:
            # If we are not computing voxelwise loss components at least
            # make sure a none reduction maintains a broadcastable shape
            broadcast_shape = list(f.shape[0:2]) + [1] * (len(input.shape) - 2)
            f = f.view(broadcast_shape)
        else:
            raise ValueError(f'Unsupported reduction: {self.reduction}, available options are ["mean", "sum", "none"].')

        return f


class GeneralizedWassersteinDiceLoss(_Loss):
    """
    Compute the generalized Wasserstein Dice Loss defined in:

        <NAME>. et al. (2017) Generalised Wasserstein Dice Score for Imbalanced Multi-class
        Segmentation using Holistic Convolutional Networks. BrainLes 2017.

    Or its variant (use the option weighting_mode="GDL") defined in the Appendix of:

        <NAME>. et al. (2020) Comparative study of deep learning methods for the automatic
        segmentation of lung, lesion and lesion type in CT scans of COVID-19 patients.
        arXiv preprint arXiv:2007.15546

    Adapted from:
        https://github.com/LucasFidon/GeneralizedWassersteinDiceLoss
    """

    def __init__(
        self,
        dist_matrix: Union[np.ndarray, torch.Tensor],
        weighting_mode: str = "default",
        reduction: Union[LossReduction, str] = LossReduction.MEAN,
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
    ) -> None:
        """
        Args:
            dist_matrix: 2d tensor or 2d numpy array; matrix of distances between the classes.
            It must have dimension C x C where C is the number of classes.
            weighting_mode: {``"default"``, ``"GDL"``}
                Specifies how to weight the class-specific sum of errors.
                Default to ``"default"``.

                - ``"default"``: (recommended) use the original weighting method as in:
                    <NAME>. et al. (2017) Generalised Wasserstein Dice Score for Imbalanced Multi-class
                    Segmentation using Holistic Convolutional Networks. BrainLes 2017.
                - ``"GDL"``: use a GDL-like weighting method as in the Appendix of:
                    <NAME>. et al. (2020) Comparative study of deep learning methods for the automatic
                    segmentation of lung, lesion and lesion type in CT scans of COVID-19 patients.
                    arXiv preprint arXiv:2007.15546
            reduction: {``"none"``, ``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``.

                - ``"none"``: no reduction will be applied.
                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.
            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.

        Raises:
            ValueError: When ``dist_matrix`` is not a square matrix.

        Example:
            .. code-block:: python

                import torch
                import numpy as np
                from monai.losses import GeneralizedWassersteinDiceLoss

                # Example with 3 classes (including the background: label 0).
                # The distance between the background class (label 0) and the other classes is the maximum, equal to 1.
                # The distance between class 1 and class 2 is 0.5.
                dist_mat = np.array([[0.0, 1.0, 1.0], [1.0, 0.0, 0.5], [1.0, 0.5, 0.0]], dtype=np.float32)
                wass_loss = GeneralizedWassersteinDiceLoss(dist_matrix=dist_mat)

                pred_score = torch.tensor([[1000, 0, 0], [0, 1000, 0], [0, 0, 1000]], dtype=torch.float32)
                grnd = torch.tensor([0, 1, 2], dtype=torch.int64)
                wass_loss(pred_score, grnd)  # 0

        """
        super().__init__(reduction=LossReduction(reduction).value)

        if dist_matrix.shape[0] != dist_matrix.shape[1]:
            raise ValueError(f"dist_matrix must be C x C, got {dist_matrix.shape[0]} x {dist_matrix.shape[1]}.")

        if weighting_mode not in ["default", "GDL"]:
            raise ValueError("weighting_mode must be either 'default' or 'GDL, got %s." % weighting_mode)

        self.m = dist_matrix
        if isinstance(self.m, np.ndarray):
            self.m = torch.from_numpy(self.m)
        if torch.max(self.m) != 1:
            self.m = self.m / torch.max(self.m)
        self.alpha_mode = weighting_mode
        self.num_classes = self.m.size(0)
        self.smooth_nr = float(smooth_nr)
        self.smooth_dr = float(smooth_dr)

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD].
            target: the shape should be BNH[WD].

        """
        # Aggregate spatial dimensions
        flat_input = input.reshape(input.size(0), input.size(1), -1)
        flat_target = target.reshape(target.size(0), -1).long()

        # Apply the softmax to the input scores map
        probs = F.softmax(flat_input, dim=1)

        # Compute the Wasserstein distance map
        wass_dist_map = self.wasserstein_distance_map(probs, flat_target)

        # Compute the values of alpha to use
        alpha = self._compute_alpha_generalized_true_positives(flat_target)

        # Compute the numerator and denominator of the generalized Wasserstein Dice loss
        if self.alpha_mode == "GDL":
            # use GDL-style alpha weights (i.e. normalize by the volume of each class)
            # contrary to the original definition we also use alpha in the "generalized all error".
            true_pos = self._compute_generalized_true_positive(alpha, flat_target, wass_dist_map)
            denom = self._compute_denominator(alpha, flat_target, wass_dist_map)
        else:  # default: as in the original paper
            # (i.e. alpha=1 for all foreground classes and 0 for the background).
            # Compute the generalised number of true positives
            true_pos = self._compute_generalized_true_positive(alpha, flat_target, wass_dist_map)
            all_error = torch.sum(wass_dist_map, dim=1)
            denom = 2 * true_pos + all_error

        # Compute the final loss
        wass_dice: torch.Tensor = (2.0 * true_pos + self.smooth_nr) / (denom + self.smooth_dr)
        wass_dice_loss: torch.Tensor = 1.0 - wass_dice

        if self.reduction == LossReduction.MEAN.value:
            wass_dice_loss = torch.mean(wass_dice_loss)  # the batch and channel average
        elif self.reduction == LossReduction.SUM.value:
            wass_dice_loss = torch.sum(wass_dice_loss)  # sum over the batch and channel dims
        elif self.reduction == LossReduction.NONE.value:
            # If we are not computing voxelwise loss components at least
            # make sure a none reduction maintains a broadcastable shape
            broadcast_shape = input.shape[0:2] + (1,) * (len(input.shape) - 2)
            wass_dice_loss = wass_dice_loss.view(broadcast_shape)
        else:
            raise ValueError(f'Unsupported reduction: {self.reduction}, available options are ["mean", "sum", "none"].')

        return wass_dice_loss

    def wasserstein_distance_map(self, flat_proba: torch.Tensor, flat_target: torch.Tensor) -> torch.Tensor:
        """
        Compute the voxel-wise Wasserstein distance between the
        flattened prediction and the flattened labels (ground_truth) with respect
        to the distance matrix on the label space M.
        This corresponds to eq. 6 in:

            <NAME>. (2017) Generalised Wasserstein Dice Score for Imbalanced Multi-class
            Segmentation using Holistic Convolutional Networks. BrainLes 2017.

        Args:
            flat_proba: the probabilities of input(predicted) tensor.
            flat_target: the target tensor.
        """
        # Turn the distance matrix to a map of identical matrix
        m = torch.clone(torch.as_tensor(self.m)).to(flat_proba.device)
        m_extended = torch.unsqueeze(m, dim=0)
        m_extended = torch.unsqueeze(m_extended, dim=3)
        m_extended = m_extended.expand((flat_proba.size(0), m_extended.size(1), m_extended.size(2), flat_proba.size(2)))

        # Expand the feature dimensions of the target
        flat_target_extended = torch.unsqueeze(flat_target, dim=1)
        flat_target_extended = flat_target_extended.expand(
            (flat_target.size(0), m_extended.size(1), flat_target.size(1))
        )
        flat_target_extended = torch.unsqueeze(flat_target_extended, dim=1)

        # Extract the vector of class distances for the ground-truth label at each voxel
        m_extended = torch.gather(m_extended, dim=1, index=flat_target_extended)
        m_extended = torch.squeeze(m_extended, dim=1)

        # Compute the wasserstein distance map
        wasserstein_map = m_extended * flat_proba

        # Sum over the classes
        wasserstein_map = torch.sum(wasserstein_map, dim=1)
        return wasserstein_map

    def _compute_generalized_true_positive(
        self, alpha: torch.Tensor, flat_target: torch.Tensor, wasserstein_distance_map: torch.Tensor
    ) -> torch.Tensor:
        """
        Args:
            alpha: generalised number of true positives of target class.
            flat_target: the target tensor.
            wasserstein_distance_map: the map obtained from the above function.
        """
        # Extend alpha to a map and select value at each voxel according to flat_target
        alpha_extended = torch.unsqueeze(alpha, dim=2)
        alpha_extended = alpha_extended.expand((flat_target.size(0), self.num_classes, flat_target.size(1)))
        flat_target_extended = torch.unsqueeze(flat_target, dim=1)
        alpha_extended = torch.gather(alpha_extended, index=flat_target_extended, dim=1)

        return torch.sum(alpha_extended * (1.0 - wasserstein_distance_map), dim=[1, 2])

    def _compute_denominator(
        self, alpha: torch.Tensor, flat_target: torch.Tensor, wasserstein_distance_map: torch.Tensor
    ) -> torch.Tensor:
        """
        Args:
            alpha: generalised number of true positives of target class.
            flat_target: the target tensor.
            wasserstein_distance_map: the map obtained from the above function.
        """
        # Extend alpha to a map and select value at each voxel according to flat_target
        alpha_extended = torch.unsqueeze(alpha, dim=2)
        alpha_extended = alpha_extended.expand((flat_target.size(0), self.num_classes, flat_target.size(1)))
        flat_target_extended = torch.unsqueeze(flat_target, dim=1)
        alpha_extended = torch.gather(alpha_extended, index=flat_target_extended, dim=1)

        return torch.sum(alpha_extended * (2.0 - wasserstein_distance_map), dim=[1, 2])

    def _compute_alpha_generalized_true_positives(self, flat_target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            flat_target: the target tensor.
        """
        alpha: torch.Tensor = torch.ones((flat_target.size(0), self.num_classes)).float().to(flat_target.device)
        if self.alpha_mode == "GDL":  # GDL style
            # Define alpha like in the generalized dice loss
            # i.e. the inverse of the volume of each class.
            one_hot_f = F.one_hot(flat_target, num_classes=self.num_classes).permute(0, 2, 1).float()
            volumes = torch.sum(one_hot_f, dim=2)
            alpha = 1.0 / (volumes + 1.0)
        else:  # default, i.e. like in the original paper
            # alpha weights are 0 for the background and 1 the other classes
            alpha[:, 0] = 0.0
        return alpha


class DiceCELoss(_Loss):
    """
    Compute both Dice loss and Cross Entropy Loss, and return the weighted sum of these two losses.
    The details of Dice loss is shown in ``monai.losses.DiceLoss``.
    The details of Cross Entropy Loss is shown in ``torch.nn.CrossEntropyLoss``. In this implementation,
    two deprecated parameters ``size_average`` and ``reduce``, and the parameter ``ignore_index`` are
    not supported.

    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Optional[Callable] = None,
        squared_pred: bool = False,
        jaccard: bool = False,
        reduction: str = "mean",
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
        ce_weight: Optional[torch.Tensor] = None,
        lambda_dice: float = 1.0,
        lambda_ce: float = 1.0,
    ) -> None:
        """
        Args:
            ``ce_weight`` and ``lambda_ce`` are only used for cross entropy loss.
            ``reduction`` is used for both losses and other parameters are only used for dice loss.

            include_background: if False channel index 0 (background category) is excluded from the calculation.
            to_onehot_y: whether to convert `y` into the one-hot format. Defaults to False.
            sigmoid: if True, apply a sigmoid function to the prediction, only used by the `DiceLoss`,
                don't need to specify activation function for `CrossEntropyLoss`.
            softmax: if True, apply a softmax function to the prediction, only used by the `DiceLoss`,
                don't need to specify activation function for `CrossEntropyLoss`.
            other_act: if don't want to use `sigmoid` or `softmax`, use other callable function to execute
                other activation layers, Defaults to ``None``. for example: `other_act = torch.tanh`.
                only used by the `DiceLoss`, don't need to specify activation function for `CrossEntropyLoss`.
            squared_pred: use squared versions of targets and predictions in the denominator or not.
            jaccard: compute Jaccard Index (soft IoU) instead of dice or not.
            reduction: {``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``. The dice loss should
                as least reduce the spatial dimensions, which is different from cross entropy loss, thus here
                the ``none`` option cannot be used.

                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.

            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.
            batch: whether to sum the intersection and union areas over the batch dimension before the dividing.
                Defaults to False, a Dice loss value is computed independently from each item in the batch
                before any `reduction`.
            ce_weight: a rescaling weight given to each class for cross entropy loss.
                See ``torch.nn.CrossEntropyLoss()`` for more information.
            lambda_dice: the trade-off weight value for dice loss. The value should be no less than 0.0.
                Defaults to 1.0.
            lambda_ce: the trade-off weight value for cross entropy loss. The value should be no less than 0.0.
                Defaults to 1.0.

        """
        super().__init__()
        reduction = look_up_option(reduction, DiceCEReduction).value
        self.dice = DiceLoss(
            include_background=include_background,
            to_onehot_y=to_onehot_y,
            sigmoid=sigmoid,
            softmax=softmax,
            other_act=other_act,
            squared_pred=squared_pred,
            jaccard=jaccard,
            reduction=reduction,
            smooth_nr=smooth_nr,
            smooth_dr=smooth_dr,
            batch=batch,
        )
        self.cross_entropy = nn.CrossEntropyLoss(weight=ce_weight, reduction=reduction)
        if lambda_dice < 0.0:
            raise ValueError("lambda_dice should be no less than 0.0.")
        if lambda_ce < 0.0:
            raise ValueError("lambda_ce should be no less than 0.0.")
        self.lambda_dice = lambda_dice
        self.lambda_ce = lambda_ce

    def ce(self, input: torch.Tensor, target: torch.Tensor):
        """
        Compute CrossEntropy loss for the input and target.
        Will remove the channel dim according to PyTorch CrossEntropyLoss:
        https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html?#torch.nn.CrossEntropyLoss.

        """
        n_pred_ch, n_target_ch = input.shape[1], target.shape[1]
        if n_pred_ch == n_target_ch:
            # target is in the one-hot format, convert to BH[WD] format to calculate ce loss
            target = torch.argmax(target, dim=1)
        else:
            target = torch.squeeze(target, dim=1)
        target = target.long()
        return self.cross_entropy(input, target)

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD].
            target: the shape should be BNH[WD] or B1H[WD].

        Raises:
            ValueError: When number of dimensions for input and target are different.
            ValueError: When number of channels for target is neither 1 nor the same as input.

        """
        if len(input.shape) != len(target.shape):
            raise ValueError("the number of dimensions for input and target should be the same.")

        dice_loss = self.dice(input, target)
        ce_loss = self.ce(input, target)
        total_loss: torch.Tensor = self.lambda_dice * dice_loss + self.lambda_ce * ce_loss

        return total_loss


class DiceFocalLoss(_Loss):
    """
    Compute both Dice loss and Focal Loss, and return the weighted sum of these two losses.
    The details of Dice loss is shown in ``monai.losses.DiceLoss``.
    The details of Focal Loss is shown in ``monai.losses.FocalLoss``.

    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Optional[Callable] = None,
        squared_pred: bool = False,
        jaccard: bool = False,
        reduction: str = "mean",
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
        gamma: float = 2.0,
        focal_weight: Optional[Union[Sequence[float], float, int, torch.Tensor]] = None,
        lambda_dice: float = 1.0,
        lambda_focal: float = 1.0,
    ) -> None:
        """
        Args:
            ``gamma``, ``focal_weight`` and ``lambda_focal`` are only used for focal loss.
            ``include_background``, ``to_onehot_y``and ``reduction`` are used for both losses
            and other parameters are only used for dice loss.
            include_background: if False channel index 0 (background category) is excluded from the calculation.
            to_onehot_y: whether to convert `y` into the one-hot format. Defaults to False.
            sigmoid: if True, apply a sigmoid function to the prediction, only used by the `DiceLoss`,
                don't need to specify activation function for `FocalLoss`.
            softmax: if True, apply a softmax function to the prediction, only used by the `DiceLoss`,
                don't need to specify activation function for `FocalLoss`.
            other_act: if don't want to use `sigmoid` or `softmax`, use other callable function to execute
                other activation layers, Defaults to ``None``. for example: `other_act = torch.tanh`.
                only used by the `DiceLoss`, don't need to specify activation function for `FocalLoss`.
            squared_pred: use squared versions of targets and predictions in the denominator or not.
            jaccard: compute Jaccard Index (soft IoU) instead of dice or not.
            reduction: {``"none"``, ``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``.

                - ``"none"``: no reduction will be applied.
                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.

            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.
            batch: whether to sum the intersection and union areas over the batch dimension before the dividing.
                Defaults to False, a Dice loss value is computed independently from each item in the batch
                before any `reduction`.
            gamma: value of the exponent gamma in the definition of the Focal loss.
            focal_weight: weights to apply to the voxels of each class. If None no weights are applied.
                The input can be a single value (same weight for all classes), a sequence of values (the length
                of the sequence should be the same as the number of classes).
            lambda_dice: the trade-off weight value for dice loss. The value should be no less than 0.0.
                Defaults to 1.0.
            lambda_focal: the trade-off weight value for focal loss. The value should be no less than 0.0.
                Defaults to 1.0.

        """
        super().__init__()
        self.dice = DiceLoss(
            sigmoid=sigmoid,
            softmax=softmax,
            other_act=other_act,
            squared_pred=squared_pred,
            jaccard=jaccard,
            reduction=reduction,
            smooth_nr=smooth_nr,
            smooth_dr=smooth_dr,
            batch=batch,
        )
        self.focal = FocalLoss(gamma=gamma, weight=focal_weight, reduction=reduction)
        if lambda_dice < 0.0:
            raise ValueError("lambda_dice should be no less than 0.0.")
        if lambda_focal < 0.0:
            raise ValueError("lambda_focal should be no less than 0.0.")
        self.lambda_dice = lambda_dice
        self.lambda_focal = lambda_focal
        self.to_onehot_y = to_onehot_y
        self.include_background = include_background

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD]. The input should be the original logits
                due to the restriction of ``monai.losses.FocalLoss``.
            target: the shape should be BNH[WD] or B1H[WD].

        Raises:
            ValueError: When number of dimensions for input and target are different.
            ValueError: When number of channels for target is neither 1 nor the same as input.

        """
        if len(input.shape) != len(target.shape):
            raise ValueError("the number of dimensions for input and target should be the same.")

        n_pred_ch = input.shape[1]

        if self.to_onehot_y:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `to_onehot_y=True` ignored.")
            else:
                target = one_hot(target, num_classes=n_pred_ch)

        if not self.include_background:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `include_background=False` ignored.")
            else:
                # if skipping background, removing first channel
                target = target[:, 1:]
                input = input[:, 1:]

        dice_loss = self.dice(input, target)
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