text: from typing import List
  
  import numpy as np
  import torch
  
  
  def point_form(boxes: torch.Tensor) -> torch.Tensor:
      """Convert prior_boxes to (x_min, y_min, x_max, y_max) representation for comparison to point form ground truth data.
  
      Args:
          boxes: center-size default boxes from priorbox layers.
      Return:
          boxes: Converted x_min, y_min, x_max, y_max form of boxes.
      """
      return torch.cat((boxes[:, :2] - boxes[:, 2:] / 2, boxes[:, :2] + boxes[:, 2:] / 2), dim=1)
  
  
  def center_size(boxes: torch.Tensor) -> torch.Tensor:
      """Convert prior_boxes to (cx, cy, w, h) representation for comparison to center-size form ground truth data.
      Args:
          boxes: point_form boxes
      Return:
          boxes: Converted x_min, y_min, x_max, y_max form of boxes.
      """
      return torch.cat(((boxes[:, 2:] + boxes[:, :2]) / 2, boxes[:, 2:] - boxes[:, :2]), dim=1)
  
  
  def intersect(box_a: torch.Tensor, box_b: torch.Tensor) -> torch.Tensor:
      """ We resize both tensors to [A,B,2] without new malloc:
      [A, 2] -> [A, 1, 2] -> [A, B, 2]
      [B, 2] -> [1, B, 2] -> [A, B, 2]
      Then we compute the area of intersect between box_a and box_b.
      Args:
        box_a: bounding boxes, Shape: [A, 4].
        box_b: bounding boxes, Shape: [B, 4].
      Return:
        intersection area, Shape: [A, B].
      """
      A = box_a.size(0)
      B = box_b.size(0)
      max_xy = torch.min(box_a[:, 2:].unsqueeze(1).expand(A, B, 2), box_b[:, 2:].unsqueeze(0).expand(A, B, 2))
      min_xy = torch.max(box_a[:, :2].unsqueeze(1).expand(A, B, 2), box_b[:, :2].unsqueeze(0).expand(A, B, 2))
      inter = torch.clamp((max_xy - min_xy), min=0)
      return inter[:, :, 0] * inter[:, :, 1]
  
  
  def jaccard(box_a: torch.Tensor, box_b: torch.Tensor) -> torch.Tensor:
      """Compute the jaccard overlap of two sets of boxes. The jaccard overlap is simply the intersection over
      union of two boxes.  Here we operate on ground truth boxes and default boxes.
      E.g.:
          A ∩ B / A ∪ B = A ∩ B / (area(A) + area(B) - A ∩ B)
      Args:
          box_a: Ground truth bounding boxes, Shape: [num_objects,4]
          box_b: Prior boxes from priorbox layers, Shape: [num_priors,4]
      Return:
          jaccard overlap: Shape: [box_a.size(0), box_b.size(0)]
      """
      inter = intersect(box_a, box_b)
      area_a = ((box_a[:, 2] - box_a[:, 0]) * (box_a[:, 3] - box_a[:, 1])).unsqueeze(1).expand_as(inter)  # [A,B]
      area_b = ((box_b[:, 2] - box_b[:, 0]) * (box_b[:, 3] - box_b[:, 1])).unsqueeze(0).expand_as(inter)  # [A,B]
      union = area_a + area_b - inter
      return inter / union
  
  
  def matrix_iof(a: np.ndarray, b: np.ndarray) -> np.ndarray:
      """
      return iof of a and b, numpy version for data augmentation
      """
      lt = np.maximum(a[:, np.newaxis, :2], b[:, :2])
      rb = np.minimum(a[:, np.newaxis, 2:], b[:, 2:])
  
      area_i = np.prod(rb - lt, axis=2) * (lt < rb).all(axis=2)
      area_a = np.prod(a[:, 2:] - a[:, :2], axis=1)
      return area_i / np.maximum(area_a[:, np.newaxis], 1)
  
  
  def match(
      threshold: float,
      box_gt: torch.Tensor,
      priors: torch.Tensor,
      variances: List[float],
      labels_gt: torch.Tensor,
      landmarks_gt: torch.Tensor,
      box_t: torch.Tensor,
      label_t: torch.Tensor,
      landmarks_t: torch.Tensor,
      batch_id: int,
  ) -> None:
      """Match each prior box with the ground truth box of the highest jaccard overlap, encode the bounding
      boxes, then return the matched indices corresponding to both confidence and location preds.
  
      Args:
          threshold: The overlap threshold used when matching boxes.
          box_gt: Ground truth boxes, Shape: [num_obj, 4].
          priors: Prior boxes from priorbox layers, Shape: [n_priors, 4].
          variances: Variances corresponding to each prior coord, Shape: [num_priors, 4].
          labels_gt: All the class labels for the image, Shape: [num_obj, 2].
          landmarks_gt: Ground truth landms, Shape [num_obj, 10].
          box_t: Tensor to be filled w/ endcoded location targets.
          label_t: Tensor to be filled w/ matched indices for labels predictions.
          landmarks_t: Tensor to be filled w/ endcoded landmarks targets.
          batch_id: current batch index
      Return:
          The matched indices corresponding to 1)location 2)confidence 3)landmarks preds.
      """
      # Compute iou between gt and priors
      overlaps = jaccard(box_gt, point_form(priors))
      # (Bipartite Matching)
      # [1, num_objects] best prior for each ground truth
      best_prior_overlap, best_prior_idx = overlaps.max(1, keepdim=True)
  
      # ignore hard gt
      valid_gt_idx = best_prior_overlap[:, 0] >= 0.2
      best_prior_idx_filter = best_prior_idx[valid_gt_idx, :]
      if best_prior_idx_filter.shape[0] <= 0:
          box_t[batch_id] = 0
          label_t[batch_id] = 0
          return
  
      # [1, num_priors] best ground truth for each prior
      best_truth_overlap, best_truth_idx = overlaps.max(0, keepdim=True)
      best_truth_idx.squeeze_(0)
      best_truth_overlap.squeeze_(0)
      best_prior_idx.squeeze_(1)
      best_prior_idx_filter.squeeze_(1)
      best_prior_overlap.squeeze_(1)
      best_truth_overlap.index_fill_(0, best_prior_idx_filter, 2)  # ensure best prior
      # TODO refactor: index  best_prior_idx with long tensor
      # ensure every gt matches with its prior of max overlap
      for j in range(best_prior_idx.size(0)):  # 判别此anchor是预测哪一个boxes
          best_truth_idx[best_prior_idx[j]] = j
  
      matches = box_gt[best_truth_idx]  # Shape: [num_priors, 4] 此处为每一个anchor对应的bbox取出来
      labels = labels_gt[best_truth_idx]  # Shape: [num_priors]      此处为每一个anchor对应的label取出来
      labels[best_truth_overlap < threshold] = 0  # label as background   overlap<0.35的全部作为负样本
      loc = encode(matches, priors, variances)
  
      matches_landm = landmarks_gt[best_truth_idx]
      landmarks_gt = encode_landm(matches_landm, priors, variances)
      box_t[batch_id] = loc  # [num_priors, 4] encoded offsets to learn
      label_t[batch_id] = labels  # [num_priors] top class label for each prior
      landmarks_t[batch_id] = landmarks_gt
  
  
  def encode(matched, priors, variances):
      """Encode the variances from the priorbox layers into the ground truth boxes
      we have matched (based on jaccard overlap) with the prior boxes.
      Args:
          matched: (tensor) Coords of ground truth for each prior in point-form
              Shape: [num_priors, 4].
          priors: (tensor) Prior boxes in center-offset form
              Shape: [num_priors,4].
          variances: (list[float]) Variances of priorboxes
      Return:
          encoded boxes (tensor), Shape: [num_priors, 4]
      """
  
      # dist b/t match center and prior's center
      g_cxcy = (matched[:, :2] + matched[:, 2:]) / 2 - priors[:, :2]
      # encode variance
      g_cxcy /= variances[0] * priors[:, 2:]
      # match wh / prior wh
      g_wh = (matched[:, 2:] - matched[:, :2]) / priors[:, 2:]
      g_wh = torch.log(g_wh) / variances[1]
      # return target for smooth_l1_loss
      return torch.cat([g_cxcy, g_wh], 1)  # [num_priors,4]
  
  
  def encode_landm(matched: torch.Tensor, priors: torch.Tensor, variances: List[float]) -> torch.Tensor:
      """Encode the variances from the priorbox layers into the ground truth boxes we have matched
      (based on jaccard overlap) with the prior boxes.
      Args:
          matched: Coords of ground truth for each prior in point-form
              Shape: [num_priors, 10].
          priors: Prior boxes in center-offset form
              Shape: [num_priors,4].
          variances: Variances of priorboxes
      Return:
          encoded landmarks, Shape: [num_priors, 10]
      """
  
      # dist b/t match center and prior's center
      matched = torch.reshape(matched, (matched.size(0), 5, 2))
      priors_cx = priors[:, 0].unsqueeze(1).expand(matched.size(0), 5).unsqueeze(2)
      priors_cy = priors[:, 1].unsqueeze(1).expand(matched.size(0), 5).unsqueeze(2)
      priors_w = priors[:, 2].unsqueeze(1).expand(matched.size(0), 5).unsqueeze(2)
      priors_h = priors[:, 3].unsqueeze(1).expand(matched.size(0), 5).unsqueeze(2)
      priors = torch.cat([priors_cx, priors_cy, priors_w, priors_h], dim=2)
      g_cxcy = matched[:, :, :2] - priors[:, :, :2]
      # encode variance
      g_cxcy /= variances[0] * priors[:, :, 2:]
      # g_cxcy /= priors[:, :, 2:]
      g_cxcy = g_cxcy.reshape(g_cxcy.size(0), -1)
      # return target for smooth_l1_loss
      return g_cxcy
  
  
  # Adapted from https://github.com/Hakuyume/chainer-ssd
  def decode(loc: torch.Tensor, priors: torch.Tensor, variances: List[float]) -> torch.Tensor:
      """Decode locations from predictions using priors to undo the encoding we did for offset regression at train time.
      Args:
          loc: location predictions for loc layers,
              Shape: [num_priors, 4]
          priors: Prior boxes in center-offset form.
              Shape: [num_priors, 4].
          variances: Variances of priorboxes
      Return:
          decoded bounding box predictions
      """
  
      boxes = torch.cat(
          (
              priors[:, :2] + loc[:, :2] * variances[0] * priors[:, 2:],
              priors[:, 2:] * torch.exp(loc[:, 2:] * variances[1]),
          ),
          1,
      )
      boxes[:, :2] -= boxes[:, 2:] / 2
      boxes[:, 2:] += boxes[:, :2]
      return boxes
  
  
  def decode_landm(pre: torch.Tensor, priors: torch.Tensor, variances: List[float]) -> torch.Tensor:
      """Decode landmarks from predictions using priors to undo the encoding we did for offset regression at train time.
      Args:
          pre: landmark predictions for loc layers,
              Shape: [num_priors, 10]
          priors: Prior boxes in center-offset form.
              Shape: [num_priors, 4].
          variances: Variances of priorboxes
      Return:
          decoded landmark predictions
      """
      return torch.cat(
          (
              priors[:, :2] + pre[:, :2] * variances[0] * priors[:, 2:],
              priors[:, :2] + pre[:, 2:4] * variances[0] * priors[:, 2:],
              priors[:, :2] + pre[:, 4:6] * variances[0] * priors[:, 2:],
              priors[:, :2] + pre[:, 6:8] * variances[0] * priors[:, 2:],
              priors[:, :2] + pre[:, 8:10] * variances[0] * priors[:, 2:],
          ),
          dim=1,
      )
  
  
  def log_sum_exp(x: torch.Tensor) -> torch.Tensor:
      """Utility function for computing log_sum_exp while determining This will be used to determine unaveraged
      confidence loss across all examples in a batch.
      Args:
          x: conf_preds from conf layers
      """
      x_max = x.data.max()
      return torch.log(torch.sum(torch.exp(x - x_max), 1, keepdim=True)) + x_max
  