code: import torch
  
  
  def point_form(boxes):
      """ Convert prior_boxes to (xmin, ymin, xmax, ymax)
      representation for comparison to point form ground truth data.
      Args:
          boxes: (tensor) center-size default boxes from priorbox layers.
      Return:
          boxes: (tensor) Converted xmin, ymin, xmax, ymax form of boxes.
      """
      return torch.cat((boxes[:, :2] - boxes[:, 2:]/2,     # xmin, ymin
                       boxes[:, :2] + boxes[:, 2:]/2), 1)  # xmax, ymax
  
  
  def center_size(boxes):
      """ Convert prior_boxes to (cx, cy, w, h)
      representation for comparison to center-size form ground truth data.
      Args:
          boxes: (tensor) point_form boxes
      Return:
          boxes: (tensor) Converted xmin, ymin, xmax, ymax form of boxes.
      """
      return torch.cat((boxes[:, 2:] + boxes[:, :2])/2,  # cx, cy
                       boxes[:, 2:] - boxes[:, :2], 1)  # w, h
  
  
  def intersect(box_a, box_b):
      """ 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: (tensor) bounding boxes, Shape: [A,4].
        box_b: (tensor) bounding boxes, Shape: [B,4].
      Return:
        (tensor) 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, box_b):
      """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: (tensor) Ground truth bounding boxes, Shape: [num_objects,4]
          box_b: (tensor) Prior boxes from priorbox layers, Shape: [num_priors,4]
      Return:
          jaccard overlap: (tensor) 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  # [A,B]
  
  
  def match(threshold, truths, priors, variances, labels, loc_t, conf_t, idx):
      """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: (float) The overlap threshold used when mathing boxes.
          truths: (tensor) Ground truth boxes, Shape: [num_obj, num_priors].
          priors: (tensor) Prior boxes from priorbox layers, Shape: [n_priors,4].
          variances: (tensor) Variances corresponding to each prior coord,
              Shape: [num_priors, 4].
          labels: (tensor) All the class labels for the image, Shape: [num_obj].
          loc_t: (tensor) Tensor to be filled w/ endcoded location targets.
          conf_t: (tensor) Tensor to be filled w/ matched indices for conf preds.
          idx: (int) current batch index
      Return:
          The matched indices corresponding to 1)location and 2)confidence preds.
      """
      # jaccard index
      overlaps = jaccard(
          truths,
          point_form(priors)
      )
      # (Bipartite Matching)
      # [1,num_objects] best prior for each ground truth
      best_prior_overlap, best_prior_idx = overlaps.max(1)
      # [1,num_priors] best ground truth for each prior
      best_truth_overlap, best_truth_idx = overlaps.max(0)
      best_truth_idx.squeeze_(0)
      best_truth_overlap.squeeze_(0)
      best_prior_idx.squeeze_(1)
      best_prior_overlap.squeeze_(1)
      best_truth_overlap.index_fill_(0, best_prior_idx, 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)):
          best_truth_idx[best_prior_idx[j]] = j
      matches = truths[best_truth_idx]          # Shape: [num_priors,4]
      conf = labels[best_truth_idx] + 1         # Shape: [num_priors]
      conf[best_truth_overlap < threshold] = 0  # label as background
      loc = encode(matches, priors, variances)
      loc_t[idx] = loc    # [num_priors,4] encoded offsets to learn
      conf_t[idx] = conf  # [num_priors] top class label for each prior
  
  
  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]
  
  
  # Adapted from https://github.com/Hakuyume/chainer-ssd
  def decode(loc, priors, variances):
      """Decode locations from predictions using priors to undo
      the encoding we did for offset regression at train time.
      Args:
          loc (tensor): location predictions for loc layers,
              Shape: [num_priors,4]
          priors (tensor): Prior boxes in center-offset form.
              Shape: [num_priors,4].
          variances: (list[float]) 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 log_sum_exp(x):
      """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 (Variable(tensor)): conf_preds from conf layers
      """
      x_max = x.data.max()
      return torch.log(torch.sum(torch.exp(x-x_max), 1)) + x_max
  
  
  # Original author: Francisco Massa:
  # https://github.com/fmassa/object-detection.torch
  # Ported to PyTorch by Max deGroot (02/01/2017)
  def nms(boxes, scores, overlap=0.5, top_k=200):
      """Apply non-maximum suppression at test time to avoid detecting too many
      overlapping bounding boxes for a given object.
      Args:
          boxes: (tensor) The location preds for the img, Shape: [num_priors,4].
          scores: (tensor) The class predscores for the img, Shape:[num_priors].
          overlap: (float) The overlap thresh for suppressing unnecessary boxes.
          top_k: (int) The Maximum number of box preds to consider.
      Return:
          The indices of the kept boxes with respect to num_priors.
      """
  
      keep = scores.new(scores.size(0)).zero_().long()
      if boxes.numel() == 0:
          return keep
      x1 = boxes[:, 0]
      y1 = boxes[:, 1]
      x2 = boxes[:, 2]
      y2 = boxes[:, 3]
      area = torch.mul(x2 - x1, y2 - y1)
      v, idx = scores.sort(0)  # sort in ascending order
      # I = I[v >= 0.01]
      idx = idx[-top_k:]  # indices of the top-k largest vals
      xx1 = boxes.new()
      yy1 = boxes.new()
      xx2 = boxes.new()
      yy2 = boxes.new()
      w = boxes.new()
      h = boxes.new()
  
      # keep = torch.Tensor()
      count = 0
      while idx.numel() > 0:
          i = idx[-1]  # index of current largest val
          # keep.append(i)
          keep[count] = i
          count += 1
          if idx.size(0) == 1:
              break
          idx = idx[:-1]  # remove kept element from view
          # load bboxes of next highest vals
          torch.index_select(x1, 0, idx, out=xx1)
          torch.index_select(y1, 0, idx, out=yy1)
          torch.index_select(x2, 0, idx, out=xx2)
          torch.index_select(y2, 0, idx, out=yy2)
          # store element-wise max with next highest score
          xx1 = torch.clamp(xx1, min=x1[i])
          yy1 = torch.clamp(yy1, min=y1[i])
          xx2 = torch.clamp(xx2, max=x2[i])
          yy2 = torch.clamp(yy2, max=y2[i])
          w.resize_as_(xx2)
          h.resize_as_(yy2)
          w = xx2 - xx1
          h = yy2 - yy1
          # check sizes of xx1 and xx2.. after each iteration
          w = torch.clamp(w, min=0.0)
          h = torch.clamp(h, min=0.0)
          inter = w*h
          # IoU = i / (area(a) + area(b) - i)
          rem_areas = torch.index_select(area, 0, idx)  # load remaining areas)
          union = (rem_areas - inter) + area[i]
          IoU = inter/union  # store result in iou
          # keep only elements with an IoU <= overlap
          idx = idx[IoU.le(overlap)]
      return keep, count
  
apis: torch.exp torch.mul torch.log torch.index_select torch.cat torch.clamp