code: def enumerate_hsmm(
      semiring,
      init_z_1,
      transition_z_to_z,
      transition_z_to_l,
      emission_n_l_z,
  ):
      ssize = semiring.size()
      batch, N, K, C = emission_n_l_z.shape
  
      if init_z_1.dim() == 1:
          init_z_1 = init_z_1.unsqueeze(0).expand(batch, C)  # batch, C
      transition_z_to_z = transition_z_to_z.unsqueeze(0).expand(
          batch, C, C
      )
      transition_z_to_l = transition_z_to_l.unsqueeze(0).expand(
          batch, C, K
      )
  
      init_z_1 = semiring.convert(init_z_1)  # ssize, batch, C
      transition_z_to_z = semiring.convert(
          transition_z_to_z
      )  # ssize, batch, C, C
      transition_z_to_l = semiring.convert(
          transition_z_to_l
      )  # ssize, batch, C, K
      emission_n_l_z = semiring.convert(
          emission_n_l_z
      )  # ssize, batch, N, K, C
  
      def score_chain(chain):
          score = semiring.fill(
              torch.zeros(ssize, batch),
              torch.tensor(True),
              semiring.one,
          )
          state_0, _ = chain[0]
          # P(z_{-1})
          score = semiring.mul(score, init_z_1[:, :, state_0])
          prev_state = state_0
          n = 0
          for t in range(len(chain) - 1):
              state, k = chain[t + 1]
              # P(z_t | z_{t-1})
              score = semiring.mul(
                  score, transition_z_to_z[:, :, prev_state, state]
              )
              # P(l_t | z_t)
              score = semiring.mul(
                  score, transition_z_to_l[:, :, state, k]
              )
              # P(x_{n:n+l_t} | z_t, l_t)
              score = semiring.mul(
                  score, emission_n_l_z[:, :, n, k, state]
              )
              prev_state = state
              n += k
          return score
  
      chains = {}
      chains[0] = [[(c, 0)] for c in range(C)]
  
      for n in range(1, N + 1):
          chains[n] = []
          for k in range(1, K):
              if n - k not in chains:
                  continue
              for chain in chains[n - k]:
                  for c in range(C):
                      chains[n].append(chain + [(c, k)])
      ls = [score_chain(chain) for chain in chains[N]]
      return (
          semiring.unconvert(
              semiring.sum(torch.stack(ls, dim=1), dim=1)
          ),
          ls,
      )
  
imports: import torch_struct
  import torch
  from torch_struct import LogSemiring
  import itertools
  from hypothesis.strategies import integers, composite, floats
  from hypothesis.extra.numpy import arrays
  import numpy
label_desc: Use image node_id 3 for calling the SemiMarkovTest obj's underlying member method code with example usage: obj.enumerate_hsmm(semiring, init_z_1, transition_z_to_z, transition_z_to_l, emission_n_l_z) and returns: semiring,  ls, score