import torch


def dice_loss_withlogits(logits, true, eps=1e-7):
    """Computes the Sørensen–Dice loss.
    Note that PyTorch optimizers minimize a loss. In this
    case, we would like to maximize the dice loss so we
    return the negated dice loss.
    Args:
        true: a tensor of shape [B, 1, H, W].
        logits: a tensor of shape [B, C, H, W]. Corresponds to
            the raw output or logits of the model.
        eps: added to the denominator for numerical stability.
    Returns:
        dice_loss: the Sørensen–Dice loss.
    """

    num_classes = logits.shape[1]
    true_1_hot = torch.eye(num_classes + 1)[true.type(torch.int64).squeeze(1)]
    true_1_hot = true_1_hot.permute(0, 3, 1, 2).float()
    true_1_hot_f = true_1_hot[:, 0:1, :, :]
    true_1_hot_s = true_1_hot[:, 1:2, :, :]
    true_1_hot = torch.cat([true_1_hot_s, true_1_hot_f], dim=1)
    pos_prob = torch.sigmoid(logits)
    neg_prob = 1 - pos_prob
    probas = torch.cat([pos_prob, neg_prob], dim=1)
    
    true_1_hot = true_1_hot.type(logits.type())
    dims = (0,) + tuple(range(2, true.ndimension()))
    intersection = torch.sum(probas * true_1_hot, dims)
    cardinality = torch.sum(probas + true_1_hot, dims)
    dice_loss = (2. * intersection / (cardinality + eps)).mean()
    return 1 - dice_loss