# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.

import torch
from torch.nn import functional as F


def sigmoid_focal_loss(
    inputs: torch.Tensor,
    targets: torch.Tensor,
    alpha: float = -1,
    gamma: float = 2,
    reduction: str = "none",
) -> torch.Tensor:
    """
    Loss used in RetinaNet for dense detection: https://arxiv.org/abs/1708.02002.
    Args:
        inputs: A float tensor of arbitrary shape.
                The predictions for each example.
        targets: A float tensor with the same shape as inputs. Stores the binary
                 classification label for each element in inputs
                (0 for the negative class and 1 for the positive class).
        alpha: (optional) Weighting factor in range (0,1) to balance
                positive vs negative examples. Default = -1 (no weighting).
        gamma: Exponent of the modulating factor (1 - p_t) to
               balance easy vs hard examples.
        reduction: 'none' | 'mean' | 'sum'
                 'none': No reduction will be applied to the output.
                 'mean': The output will be averaged.
                 'sum': The output will be summed.
    Returns:
        Loss tensor with the reduction option applied.
    """
    inputs = inputs.float()
    targets = targets.float()
    p = torch.sigmoid(inputs)
    ce_loss = F.binary_cross_entropy_with_logits(inputs, targets, reduction="none")
    p_t = p * targets + (1 - p) * (1 - targets)
    loss = ce_loss * ((1 - p_t) ** gamma)

    if alpha >= 0:
        alpha_t = alpha * targets + (1 - alpha) * (1 - targets)
        loss = alpha_t * loss

    if reduction == "mean":
        loss = loss.mean()
    elif reduction == "sum":
        loss = loss.sum()

    return loss


sigmoid_focal_loss_jit: "torch.jit.ScriptModule" = torch.jit.script(sigmoid_focal_loss)


def sigmoid_focal_loss_star(
    inputs: torch.Tensor,
    targets: torch.Tensor,
    alpha: float = -1,
    gamma: float = 1,
    reduction: str = "none",
) -> torch.Tensor:
    """
    FL* described in RetinaNet paper Appendix: https://arxiv.org/abs/1708.02002.
    Args:
        inputs: A float tensor of arbitrary shape.
                The predictions for each example.
        targets: A float tensor with the same shape as inputs. Stores the binary
                 classification label for each element in inputs
                (0 for the negative class and 1 for the positive class).
        alpha: (optional) Weighting factor in range (0,1) to balance
                positive vs negative examples. Default = -1 (no weighting).
        gamma: Gamma parameter described in FL*. Default = 1 (no weighting).
        reduction: 'none' | 'mean' | 'sum'
                 'none': No reduction will be applied to the output.
                 'mean': The output will be averaged.
                 'sum': The output will be summed.
    Returns:
        Loss tensor with the reduction option applied.
    """
    inputs = inputs.float()
    targets = targets.float()
    shifted_inputs = gamma * (inputs * (2 * targets - 1))
    loss = -(F.logsigmoid(shifted_inputs)) / gamma

    if alpha >= 0:
        alpha_t = alpha * targets + (1 - alpha) * (1 - targets)
        loss *= alpha_t

    if reduction == "mean":
        loss = loss.mean()
    elif reduction == "sum":
        loss = loss.sum()

    return loss


sigmoid_focal_loss_star_jit: "torch.jit.ScriptModule" = torch.jit.script(
    sigmoid_focal_loss_star
)