code: def test_nca_loss(self):
      softmax_scale = 10
      loss_func = NCALoss(softmax_scale=softmax_scale)
  
      for dtype in TEST_DTYPES:
          embedding_angles = [0, 20, 40, 60, 80]
          embeddings = torch.tensor(
              [angle_to_coord(a) for a in embedding_angles],
              requires_grad=True,
              dtype=dtype,
          ).to(
              TEST_DEVICE
          )  # 2D embeddings
          labels = torch.LongTensor([0, 0, 1, 1, 2])
  
          loss = loss_func(embeddings, labels)
          loss.backward()
  
          pos_pairs = [(0, 1), (1, 0), (2, 3), (3, 2)]
          neg_pairs = [
              (0, 2),
              (0, 3),
              (0, 4),
              (1, 2),
              (1, 3),
              (1, 4),
              (2, 0),
              (2, 1),
              (2, 4),
              (3, 0),
              (3, 1),
              (3, 4),
              (4, 0),
              (4, 1),
              (4, 2),
              (4, 3),
          ]
  
          embeddings = torch.nn.functional.normalize(embeddings)
          correct_total = 0
          for a1, p in pos_pairs:
              anchor1, positive = embeddings[a1], embeddings[p]
              ap_dist = torch.sum((anchor1 - positive) ** 2)
              numerator = torch.exp(-ap_dist * softmax_scale)
              denominator = numerator.clone()
              for a2, n in neg_pairs:
                  if a2 == a1:
                      anchor2, negative = embeddings[a2], embeddings[n]
                      an_dist = torch.sum((anchor2 - negative) ** 2)
                      denominator += torch.exp(-an_dist * softmax_scale)
  
              correct_total += -torch.log(numerator / denominator)
  
          correct_total /= len(pos_pairs)
          rtol = 1e-2 if dtype == torch.float16 else 1e-5
          self.assertTrue(torch.isclose(loss, correct_total, rtol=rtol))
  
file_path: pytorch-metric-learning/tests/losses/test_nca_loss.py
imports: import unittest
  import torch
  from pytorch_metric_learning.losses import NCALoss
  from ..None import TEST_DEVICE, TEST_DTYPES
  from ..zzz_testing_utils.testing_utils import angle_to_coord
label_desc: Use image node_id 1 for calling the TestNCALoss obj's underlying member method code with example usage: obj.test_nca_loss() without return types