docstr: The goal of this test is to assess if the gradient of the loss function
  is correct by testing if we can train a one layer neural network
  to segment one image.
  We verify that the loss is decreasing in almost all SGD steps.
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code: def test_convergence(self):
      """
      The goal of this test is to assess if the gradient of the loss function
      is correct by testing if we can train a one layer neural network
      to segment one image.
      We verify that the loss is decreasing in almost all SGD steps.
      """
      learning_rate = 0.001
      max_iter = 50
  
      # define a simple 3d example
      target_seg = torch.tensor(
          [
              # raw 0
              [[0, 0, 0, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 0, 0, 0]],
              # raw 1
              [[0, 0, 0, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 0, 0, 0]],
              # raw 2
              [[0, 0, 0, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 0, 0, 0]],
          ]
      )
      target_seg = torch.unsqueeze(target_seg, dim=0)
      image = 12 * target_seg + 27  # dummy image to segment
      image = image.float()
      num_classes = 2
      num_voxels = 3 * 4 * 4
  
      # define a model with one layer
      class OnelayerNet(nn.Module):
          def __init__(self):
              super().__init__()
              self.layer = nn.Linear(
                  num_voxels, num_voxels * num_classes
              )
  
          def forward(self, x):
              x = x.view(-1, num_voxels)
              x = self.layer(x)
              x = x.view(-1, num_classes, 3, 4, 4)
              return x
  
      for w_mode in ["default", "GDL"]:
          # initialise the network
          net = OnelayerNet()
  
          # initialize the loss
          loss = GeneralizedWassersteinDiceLoss(
              dist_matrix=np.array([[0.0, 1.0], [1.0, 0.0]]),
              weighting_mode=w_mode,
          )
  
          # initialize an optimizer
          optimizer = optim.Adam(net.parameters(), lr=learning_rate)
  
          # initial difference between pred and target
          pred_start = torch.argmax(net(image), dim=1)
          diff_start = torch.norm(
              pred_start.float() - target_seg.float()
          )
  
          loss_history = []
          # train the network
          for _ in range(max_iter):
              # set the gradient to zero
              optimizer.zero_grad()
  
              # forward pass
              output = net(image)
              loss_val = loss(output, target_seg)
  
              # backward pass
              loss_val.backward()
              optimizer.step()
  
              # stats
              loss_history.append(loss_val.item())
  
          # difference between pred and target after training
          pred_end = torch.argmax(net(image), dim=1)
          diff_end = torch.norm(pred_end.float() - target_seg.float())
  
          # count the number of SGD steps in which the loss decreases
          num_decreasing_steps = 0
          for i in range(len(loss_history) - 1):
              if loss_history[i] > loss_history[i + 1]:
                  num_decreasing_steps += 1
          decreasing_steps_ratio = float(num_decreasing_steps) / (
              len(loss_history) - 1
          )
  
          # verify that the loss is decreasing for sufficiently many SGD steps
          self.assertTrue(decreasing_steps_ratio > 0.75)
  
          # check that the predicted segmentation has improved
          self.assertGreater(diff_start, diff_end)
  
file_path: MONAI/tests/test_generalized_wasserstein_dice_loss.py
imports: from __future__ import annotations
  import unittest
  import numpy
  import torch
  import torch.nn
  import torch.nn.functional
  import torch.optim
  from monai.losses import GeneralizedWassersteinDiceLoss
  from tests.utils import test_script_save
label_desc: Use image node_id 5 for calling the TestGeneralizedWassersteinDiceLoss obj's underlying member method code with example usage: obj.test_convergence() and returns: x