code: def test_gaussian_hmm_shape(
      diag,
      init_shape,
      trans_mat_shape,
      trans_mvn_shape,
      obs_mat_shape,
      obs_mvn_shape,
      hidden_dim,
      obs_dim,
  ):
      init_dist = random_mvn(init_shape, hidden_dim)
      trans_mat = torch.randn(
          trans_mat_shape + (hidden_dim, hidden_dim)
      )
      trans_dist = random_mvn(trans_mvn_shape, hidden_dim)
      obs_mat = torch.randn(obs_mat_shape + (hidden_dim, obs_dim))
      obs_dist = random_mvn(obs_mvn_shape, obs_dim)
      if diag:
          scale = obs_dist.scale_tril.diagonal(dim1=-2, dim2=-1)
          obs_dist = dist.Normal(obs_dist.loc, scale).to_event(1)
      d = dist.GaussianHMM(
          init_dist,
          trans_mat,
          trans_dist,
          obs_mat,
          obs_dist,
          duration=6,
      )
  
      shape = broadcast_shape(
          init_shape + (6,),
          trans_mat_shape,
          trans_mvn_shape,
          obs_mat_shape,
          obs_mvn_shape,
      )
      expected_batch_shape, time_shape = shape[:-1], shape[-1:]
      expected_event_shape = time_shape + (obs_dim,)
      assert d.batch_shape == expected_batch_shape
      assert d.event_shape == expected_event_shape
      assert d.support.event_dim == d.event_dim
  
      data = obs_dist.expand(shape).sample()
      assert data.shape == d.shape()
      actual = d.log_prob(data)
      assert actual.shape == expected_batch_shape
      check_expand(d, data)
      check_sample_shape(d)
  
      x = d.rsample()
      assert x.shape == d.shape()
      x = d.rsample((6,))
      assert x.shape == (6,) + d.shape()
      x = d.expand((6, 5)).rsample()
      assert x.shape == (6, 5) + d.event_shape
  
      likelihood = dist.Normal(data, 1).to_event(2)
      p, log_normalizer = d.conjugate_update(likelihood)
      assert p.batch_shape == d.batch_shape
      assert p.event_shape == d.event_shape
      x = p.rsample()
      assert x.shape == d.shape()
      x = p.rsample((6,))
      assert x.shape == (6,) + d.shape()
      x = p.expand((6, 5)).rsample()
      assert x.shape == (6, 5) + d.event_shape
  
      final = d.filter(data)
      assert isinstance(final, dist.MultivariateNormal)
      assert final.batch_shape == d.batch_shape
      assert final.event_shape == (hidden_dim,)
  
      z = d.rsample_posterior(data)
      assert z.shape == expected_batch_shape + time_shape + (
          hidden_dim,
      )
  
      for t in range(1, d.duration - 1):
          f = d.duration - t
          d2 = d.prefix_condition(data[..., :t, :])
          assert d2.batch_shape == d.batch_shape
          assert d2.event_shape == (f, obs_dim)
  
imports: import logging
  import operator
  from functools import reduce
  import opt_einsum
  import pytest
  import torch
  import pyro
  import pyro.distributions
  from pyro.distributions.hmm import _sequential_gamma_gaussian_tensordot, _sequential_logmatmulexp
  from pyro.distributions.util import broadcast_shape
  from pyro.infer import TraceEnum_ELBO, config_enumerate
  from pyro.ops.gamma_gaussian import gamma_and_mvn_to_gamma_gaussian, gamma_gaussian_tensordot, matrix_and_mvn_to_gamma_gaussian
  from pyro.ops.gaussian import gaussian_tensordot, matrix_and_mvn_to_gaussian, mvn_to_gaussian
  from pyro.ops.indexing import Vindex
  from tests.common import assert_close
  from tests.ops.gamma_gaussian import assert_close_gamma_gaussian, random_gamma, random_gamma_gaussian
  from tests.ops.gaussian import random_mvn
label_desc: Use image node_id 11 for calling a global function with example usage: test_gaussian_hmm_shape(diag, init_shape, trans_mat_shape, trans_mvn_shape, obs_mat_shape, obs_mvn_shape, hidden_dim, obs_dim) without return types