code: def test_appnp():
      x = torch.randn(4, 16)
      edge_index = torch.tensor(
          [[0, 0, 0, 1, 2, 3], [1, 2, 3, 0, 0, 0]]
      )
      adj1 = to_torch_csc_tensor(edge_index, size=(4, 4))
  
      conv = APPNP(K=3, alpha=0.1, cached=True)
      assert str(conv) == "APPNP(K=3, alpha=0.1)"
      out = conv(x, edge_index)
      assert out.size() == (4, 16)
      assert torch.allclose(conv(x, adj1.t()), out)
      if torch_geometric.typing.WITH_TORCH_SPARSE:
          adj2 = SparseTensor.from_edge_index(
              edge_index, sparse_sizes=(4, 4)
          )
          assert torch.allclose(conv(x, adj2.t()), out)
  
      # Run again to test the cached functionality:
      assert conv._cached_edge_index is not None
      assert torch.allclose(conv(x, edge_index), conv(x, adj1.t()))
      if torch_geometric.typing.WITH_TORCH_SPARSE:
          assert conv._cached_adj_t is not None
          assert torch.allclose(conv(x, edge_index), conv(x, adj2.t()))
  
      conv.reset_parameters()
      assert conv._cached_edge_index is None
      assert conv._cached_adj_t is None
  
      if is_full_test():
          jit = torch.jit.script(conv)
          assert torch.allclose(jit(x, edge_index), out)
  
          if torch_geometric.typing.WITH_TORCH_SPARSE:
              assert torch.allclose(jit(x, adj2.t()), out)
  
imports: import torch
  import torch_geometric.typing
  from torch_geometric.nn import APPNP
  from torch_geometric.testing import is_full_test
  from torch_geometric.typing import SparseTensor
  from torch_geometric.utils import to_torch_csc_tensor
label_desc: Use image node_id 1 for calling a global function with example usage: test_appnp() without return types