from scipy.optimize import linear_sum_assignment
...
# 匈牙利算法实现二分图匹配
class HungarianMatcher(nn.Module):
    """This class computes an assignment between the targets and the predictions of the network
    For efficiency reasons, the targets don't include the no_object. Because of this, in general,
    there are more predictions than targets. In this case, we do a 1-to-1 matching of the best predictions,
    while the others are un-matched (and thus treated as non-objects).
    """
    def __init__(self, cost_class: float = 1, cost_bbox: float = 1, cost_giou: float = 1):
        """Creates the matcher
        Params:
            cost_class: This is the relative weight of the classification error in the matching cost
            cost_bbox: This is the relative weight of the L1 error of the bounding box coordinates in the matching cost
            cost_giou: This is the relative weight of the giou loss of the bounding box in the matching cost
        """
        super().__init__()
        self.cost_class = cost_class
        self.cost_bbox = cost_bbox
        self.cost_giou = cost_giou
        assert cost_class != 0 or cost_bbox != 0 or cost_giou != 0, "all costs cant be 0"
    @torch.no_grad()
    def forward(self, outputs, targets):
        """ Performs the matching
        Params:
            outputs: This is a dict that contains at least these entries:
                 "pred_logits": Tensor of dim [batch_size, num_queries, num_classes] with the classification logits
                 "pred_boxes": Tensor of dim [batch_size, num_queries, 4] with the predicted box coordinates
            targets: This is a list of targets (len(targets) = batch_size), where each target is a dict containing:
                 "labels": Tensor of dim [num_target_boxes] (where num_target_boxes is the number of ground-truth
                           objects in the target) containing the class labels
                 "boxes": Tensor of dim [num_target_boxes, 4] containing the target box coordinates
        Returns:
            A list of size batch_size, containing tuples of (index_i, index_j) where:
                - index_i is the indices of the selected predictions (in order)
                - index_j is the indices of the corresponding selected targets (in order)
            For each batch element, it holds:
                len(index_i) = len(index_j) = min(num_queries, num_target_boxes)
        """
        bs, num_queries = outputs["pred_logits"].shape[:2]
        # We flatten to compute the cost matrices in a batch
        out_prob = outputs["pred_logits"].flatten(0, 1).softmax(-1)  # [batch_size * num_queries, num_classes]
        out_bbox = outputs["pred_boxes"].flatten(0, 1)  # [batch_size * num_queries, 4]
        # Also concat the target labels and boxes
        tgt_ids = torch.cat([v["labels"] for v in targets])
        tgt_bbox = torch.cat([v["boxes"] for v in targets])
        # Compute the classification cost. Contrary to the loss, we don't use the NLL,
        # but approximate it in 1 - proba[target class].
        # The 1 is a constant that doesn't change the matching, it can be ommitted.
        cost_class = -out_prob[:, tgt_ids]
        # Compute the L1 cost between boxes
        cost_bbox = torch.cdist(out_bbox, tgt_bbox, p=1)
        # Compute the giou cost betwen boxes
        cost_giou = -generalized_box_iou(box_cxcywh_to_xyxy(out_bbox), box_cxcywh_to_xyxy(tgt_bbox))
        # Final cost matrix
        C = self.cost_bbox * cost_bbox + self.cost_class * cost_class + self.cost_giou * cost_giou
        C = C.view(bs, num_queries, -1).cpu()
        sizes = [len(v["boxes"]) for v in targets]
        indices = [linear_sum_assignment(c[i]) for i, c in enumerate(C.split(sizes, -1))]
        return [(torch.as_tensor(i, dtype=torch.int64), torch.as_tensor(j, dtype=torch.int64)) for i, j in indices]
# 损失计算
class SetCriterion(nn.Module):
    """ This class computes the loss for DETR.
    The process happens in two steps:
        1) we compute hungarian assignment between ground truth boxes and the outputs of the model
        2) we supervise each pair of matched ground-truth / prediction (supervise class and box)
    """
    def __init__(self, num_classes, matcher, weight_dict, eos_coef, losses):
        """ Create the criterion.
        Parameters:
            num_classes: number of object categories, omitting the special no-object category
            matcher: module able to compute a matching between targets and proposals
            weight_dict: dict containing as key the names of the losses and as values their relative weight.
            eos_coef: relative classification weight applied to the no-object category
            losses: list of all the losses to be applied. See get_loss for list of available losses.
        """
        super().__init__()
        self.num_classes = num_classes
        self.matcher = matcher
        self.weight_dict = weight_dict
        self.eos_coef = eos_coef
        self.losses = losses
        empty_weight = torch.ones(self.num_classes + 1)
        empty_weight[-1] = self.eos_coef
        self.register_buffer('empty_weight', empty_weight)
    def loss_labels(self, outputs, targets, indices, num_boxes, log=True):
        """Classification loss (NLL)
        targets dicts must contain the key "labels" containing a tensor of dim [nb_target_boxes]
        """
        assert 'pred_logits' in outputs
        src_logits = outputs['pred_logits']
        idx = self._get_src_permutation_idx(indices)
        target_classes_o = torch.cat([t["labels"][J] for t, (_, J) in zip(targets, indices)])
        target_classes = torch.full(src_logits.shape[:2], self.num_classes,
                                    dtype=torch.int64, device=src_logits.device)
        target_classes[idx] = target_classes_o
        loss_ce = F.cross_entropy(src_logits.transpose(1, 2), target_classes, self.empty_weight)
        losses = {'loss_ce': loss_ce}
        if log:
            # TODO this should probably be a separate loss, not hacked in this one here
            losses['class_error'] = 100 - accuracy(src_logits[idx], target_classes_o)[0]
        return losses
    @torch.no_grad()
    def loss_cardinality(self, outputs, targets, indices, num_boxes):
        """ Compute the cardinality error, ie the absolute error in the number of predicted non-empty boxes
        This is not really a loss, it is intended for logging purposes only. It doesn't propagate gradients
        """
        pred_logits = outputs['pred_logits']
        device = pred_logits.device
        tgt_lengths = torch.as_tensor([len(v["labels"]) for v in targets], device=device)
        # Count the number of predictions that are NOT "no-object" (which is the last class)
        card_pred = (pred_logits.argmax(-1) != pred_logits.shape[-1] - 1).sum(1)
        card_err = F.l1_loss(card_pred.float(), tgt_lengths.float())
        losses = {'cardinality_error': card_err}
        return losses
    def loss_boxes(self, outputs, targets, indices, num_boxes):
        """Compute the losses related to the bounding boxes, the L1 regression loss and the GIoU loss
           targets dicts must contain the key "boxes" containing a tensor of dim [nb_target_boxes, 4]
           The target boxes are expected in format (center_x, center_y, w, h), normalized by the image size.
        """
        assert 'pred_boxes' in outputs
        idx = self._get_src_permutation_idx(indices)
        src_boxes = outputs['pred_boxes'][idx]
        target_boxes = torch.cat([t['boxes'][i] for t, (_, i) in zip(targets, indices)], dim=0)
        loss_bbox = F.l1_loss(src_boxes, target_boxes, reduction='none')
        losses = {}
        losses['loss_bbox'] = loss_bbox.sum() / num_boxes
        loss_giou = 1 - torch.diag(box_ops.generalized_box_iou(
            box_ops.box_cxcywh_to_xyxy(src_boxes),
            box_ops.box_cxcywh_to_xyxy(target_boxes)))
        losses['loss_giou'] = loss_giou.sum() / num_boxes
        return losses
    def loss_masks(self, outputs, targets, indices, num_boxes):
        """Compute the losses related to the masks: the focal loss and the dice loss.
           targets dicts must contain the key "masks" containing a tensor of dim [nb_target_boxes, h, w]
        """
        assert "pred_masks" in outputs
        src_idx = self._get_src_permutation_idx(indices)
        tgt_idx = self._get_tgt_permutation_idx(indices)
        src_masks = outputs["pred_masks"]
        src_masks = src_masks[src_idx]
        masks = [t["masks"] for t in targets]
        # TODO use valid to mask invalid areas due to padding in loss
        target_masks, valid = nested_tensor_from_tensor_list(masks).decompose()
        target_masks = target_masks.to(src_masks)
        target_masks = target_masks[tgt_idx]
        # upsample predictions to the target size
        src_masks = interpolate(src_masks[:, None], size=target_masks.shape[-2:],
                                mode="bilinear", align_corners=False)
        src_masks = src_masks[:, 0].flatten(1)
        target_masks = target_masks.flatten(1)
        target_masks = target_masks.view(src_masks.shape)
        losses = {
            "loss_mask": sigmoid_focal_loss(src_masks, target_masks, num_boxes),
            "loss_dice": dice_loss(src_masks, target_masks, num_boxes),
        }
        return losses
    def _get_src_permutation_idx(self, indices):
        # permute predictions following indices
        batch_idx = torch.cat([torch.full_like(src, i) for i, (src, _) in enumerate(indices)])
        src_idx = torch.cat([src for (src, _) in indices])
        return batch_idx, src_idx
    def _get_tgt_permutation_idx(self, indices):
        # permute targets following indices
        batch_idx = torch.cat([torch.full_like(tgt, i) for i, (_, tgt) in enumerate(indices)])
        tgt_idx = torch.cat([tgt for (_, tgt) in indices])
        return batch_idx, tgt_idx
    def get_loss(self, loss, outputs, targets, indices, num_boxes, **kwargs):
        loss_map = {
            'labels': self.loss_labels,
            'cardinality': self.loss_cardinality,
            'boxes': self.loss_boxes,
            'masks': self.loss_masks
        }
        assert loss in loss_map, f'do you really want to compute {loss} loss?'
        return loss_map[loss](outputs, targets, indices, num_boxes, **kwargs)
    def forward(self, outputs, targets):
        """ This performs the loss computation.
        Parameters:
             outputs: dict of tensors, see the output specification of the model for the format
             targets: list of dicts, such that len(targets) == batch_size.
                      The expected keys in each dict depends on the losses applied, see each loss' doc
        """
        outputs_without_aux = {k: v for k, v in outputs.items() if k != 'aux_outputs'}
        # Retrieve the matching between the outputs of the last layer and the targets
        indices = self.matcher(outputs_without_aux, targets)
        # Compute the average number of target boxes accross all nodes, for normalization purposes
        num_boxes = sum(len(t["labels"]) for t in targets)
        num_boxes = torch.as_tensor([num_boxes], dtype=torch.float, device=next(iter(outputs.values())).device)
        if is_dist_avail_and_initialized():
            torch.distributed.all_reduce(num_boxes)
        num_boxes = torch.clamp(num_boxes / get_world_size(), min=1).item()
        # Compute all the requested losses
        losses = {}
        for loss in self.losses:
            losses.update(self.get_loss(loss, outputs, targets, indices, num_boxes))
        # In case of auxiliary losses, we repeat this process with the output of each intermediate layer.
        if 'aux_outputs' in outputs:
            for i, aux_outputs in enumerate(outputs['aux_outputs']):
                indices = self.matcher(aux_outputs, targets)
                for loss in self.losses:
                    if loss == 'masks':
                        # Intermediate masks losses are too costly to compute, we ignore them.
                        continue
                    kwargs = {}
                    if loss == 'labels':
                        # Logging is enabled only for the last layer
                        kwargs = {'log': False}
                    l_dict = self.get_loss(loss, aux_outputs, targets, indices, num_boxes, **kwargs)
                    l_dict = {k + f'_{i}': v for k, v in l_dict.items()}
                    losses.update(l_dict)
        return losses

from scipy.optimize import linear_sum_assignment
import numpy as np
cost_mat = np.array([[12, 7, 9, 7, 9],
                     [8, 9, 6, 6, 6],
                     [7, 17, 12, 14, 9],
                     [15, 14, 6, 6, 10],
                     [4, 10, 7, 10, 9]])
index, target = linear_sum_assignment(cost_mat)
# idnex： (array([0, 1, 2, 3, 4])
# target： array([1, 2, 4, 3, 0]))
cost_ass = cost_mat.copy()
cost_ass = cost_mat.copy()
for i, t in zip(index, target):
    cost_ass[i][t] = 0
print(cost_ass)
# 输出: 赋予0值的就是被宝可梦被赋予的工作
# array([[12,  0,  9,  7,  9],
#        [ 8,  9,  0,  6,  6],
#        [ 7, 17, 12, 14,  0],
#        [15, 14,  6,  0, 10],
#        [ 0, 10,  7, 10,  9]])
# 代价
cost_mat[index, target].sum()
# 输出: 32