text: from .distributions import LinearChainCRF
  from .autoregressive import Autoregressive
  from .semirings import KMaxSemiring
  import torch
  from hypothesis import given, settings
  from hypothesis.strategies import integers, data, sampled_from
  
  smint = integers(min_value=2, max_value=4)
  tint = integers(min_value=1, max_value=2)
  lint = integers(min_value=2, max_value=10)
  
  
  @given(data(), integers(min_value=1, max_value=20))
  @settings(max_examples=50, deadline=None)
  def test_simple(data, seed):
  
      model = data.draw(sampled_from([LinearChainCRF]))
      struct = model.struct
      torch.manual_seed(seed)
      vals, (batch, N) = struct._rand()
      lengths = torch.tensor(
          [data.draw(integers(min_value=2, max_value=N)) for b in range(batch - 1)] + [N]
      )
      dist = model(vals, lengths)
      edges, enum_lengths = dist.enumerate_support()
      log_probs = dist.log_prob(edges)
      for b in range(lengths.shape[0]):
          log_probs[enum_lengths[b] :, b] = -1e9
      assert torch.isclose(log_probs.exp().sum(0), torch.tensor(1.0)).all()
      entropy = dist.entropy
      assert torch.isclose(entropy, -log_probs.exp().mul(log_probs).sum(0)).all()
  
      vals2 = torch.rand(*vals.shape)
      dist2 = model(vals2, lengths)
  
      cross_entropy = dist.cross_entropy(other=dist2)
      kl = dist.kl(other=dist2)
  
      edges2, enum_lengths2 = dist2.enumerate_support()
      log_probs2 = dist2.log_prob(edges2)
      for b in range(lengths.shape[0]):
          log_probs2[enum_lengths2[b] :, b] = -1e9
  
      assert torch.isclose(cross_entropy, -log_probs.exp().mul(log_probs2).sum(0)).all()
      assert torch.isclose(kl, -log_probs.exp().mul(log_probs2-log_probs).sum(0)).all()
  
      argmax = dist.argmax
      _, max_indices = log_probs.max(0)
  
      amax = edges[max_indices, torch.arange(batch)]
      print(argmax.nonzero())
      print((amax - argmax).nonzero(), lengths)
      assert (amax == argmax).all()
  
      samples = dist.sample((100,))
      marginals = dist.marginals
      assert ((samples.mean(0) - marginals).abs() < 0.2).all()
  
      dist.kmax(5)
      dist.count
  
  
  @given(data(), integers(min_value=1, max_value=20))
  @settings(max_examples=50, deadline=None)
  def test_autoregressive(data, seed):
      n_classes = 2
      n_length = 5
      batch = 3
      BATCH = 3
  
      values = torch.rand(batch, n_length, n_classes)
  
      values2 = values.unsqueeze(-1).expand(batch, n_length, n_classes, n_classes).clone()
      values2[:, 0, :, :] = -1e9
      values2[:, 0, torch.arange(n_classes), torch.arange(n_classes)] = values[:, 0]
  
      init = (torch.zeros(batch, 5).long(),)
  
      class Model(torch.nn.Module):
          def forward(self, inputs, state):
              if inputs.shape[1] == 1:
                  (state,) = state
                  in_batch, hidden = state.shape
                  t = state[0, 0]
                  batch = values.shape[0]
                  x = (
                      values[:, t, :]
                      .unsqueeze(0)
                      .expand(in_batch // batch, batch, n_classes)
                  )
                  state = (state + 1,)
                  return x.contiguous().view(in_batch, 1, n_classes), state
              else:
                  return (
                      torch.cat((values, torch.zeros(BATCH, 1, n_classes)), dim=1),
                      state,
                  )
  
      auto = Autoregressive(Model(), init, n_classes, n_length, normalize=False)
      v, _, _ = auto.greedy_max()
      batch, n, c = v.shape
      assert n == n_length
      assert c == n_classes
  
      assert (v == LinearChainCRF(values2).argmax.sum(-1)).all()
      crf = LinearChainCRF(values2)
      v2 = auto.beam_topk(K=5)
  
      assert (v2.nonzero() == crf.topk(5).sum(-1).nonzero()).all()
      assert (v2[0] == LinearChainCRF(values2).argmax.sum(-1)).all()
  
      print(auto.log_prob(v.unsqueeze(0)))
      print(crf.struct().score(crf.argmax, values2))
      assert (
          auto.log_prob(v.unsqueeze(0)) == crf.struct().score(crf.argmax, values2)
      ).all()
      assert auto.sample((7,)).shape == (7, batch, n_length, n_classes)
  
      assert auto.sample_without_replacement((7,)).shape == (
          7,
          batch,
          n_length,
          n_classes,
      )
  
  
  def test_ar2():
      batch, N, C, H = 3, 5, 2, 5
      layer = 1
  
      def t(a):
          return tuple((t.transpose(0, 1) for t in a))
  
      init = (torch.zeros(batch, layer, H),)
  
      class AR(torch.nn.Module):
          def __init__(self, sparse=True):
              super().__init__()
              self.sparse = sparse
              self.rnn = torch.nn.RNN(H, H, batch_first=True)
              self.proj = torch.nn.Linear(H, C)
              if sparse:
                  self.embed = torch.nn.Embedding(C, H)
              else:
                  self.embed = torch.nn.Linear(C, H)
  
          def forward(self, inputs, state):
              if not self.sparse and inputs.dim() == 2:
                  inputs = torch.nn.functional.one_hot(inputs, C).float()
              inputs = self.embed(inputs)
              out, state = self.rnn(inputs, t(state)[0])
              out = self.proj(out)
              return out, t((state,))
  
      dist2 = Autoregressive(AR(sparse=False), init, C, N, normalize=False)
      path, _, _ = dist2.greedy_tempmax(1)
  
      dist = Autoregressive(AR(), init, C, N, normalize=False)
  
      path, scores, _ = dist.greedy_max()
  
      assert torch.isclose(scores, dist.log_prob(path.unsqueeze(0))).all()
      scores = dist._beam_max(7)
      path = dist.beam_topk(7)
  
      a = torch.tensor([[1, 2, 5], [3, 4, 6]])
      print(KMaxSemiring(2).sparse_sum(a))
  
      import itertools
  
      for i in range(5):
          print(dist.log_prob(path)[i])
          print(scores[i])
          print(path[i, 0])
  
      print(path.shape, scores.shape)
      assert torch.isclose(scores, dist.log_prob(path)).all()
  
      v = torch.tensor(list(itertools.product([0, 1], repeat=N)))
  
      v = v.unsqueeze(1).expand(v.shape[0], batch, N)
      all_scores = dist.log_prob(v, sparse=True)
      best, ind = torch.max(all_scores, dim=0)
      assert (scores[0, 0] == best[0]).all()
  
      print(v[ind[0], 0].shape, path[0, 0].shape)
      assert (torch.nn.functional.one_hot(v[ind, 0], C) == path[0, 0].long()).all()
  
      dist = Autoregressive(AR(), init, C, N, normalize=True)
      path = dist.sample((7,))
  
      init = (torch.zeros(batch, layer, H), torch.zeros(batch, layer, H))
  
      class AR(torch.nn.Module):
          def __init__(self):
              super().__init__()
              self.rnn = torch.nn.LSTM(H, H, batch_first=True)
              self.proj = torch.nn.Linear(H, C)
              self.embed = torch.nn.Embedding(C, H)
  
          def forward(self, inputs, state):
              inputs = self.embed(inputs)
              out, state = self.rnn(inputs, t(state))
              out = self.proj(out)
              return out, t(state)
  
      dist = Autoregressive(AR(), init, C, N)
      dist.greedy_max()
      dist.beam_topk(5)
  