code: def test_sequential_gaussian_filter_sample(
      sample_shape, batch_shape, state_dim, num_steps
  ):
      init = random_gaussian(batch_shape, state_dim, requires_grad=True)
      trans = random_gaussian(
          batch_shape + (num_steps,),
          state_dim + state_dim,
          requires_grad=True,
      )
      duration = 1 + num_steps
  
      # Check shape.
      sample = sequential_gaussian_filter_sample(
          init, trans, sample_shape
      )
      assert sample.shape == sample_shape + batch_shape + (
          duration,
          state_dim,
      )
  
      # Check gradients.
      assert sample.requires_grad
      loss = (torch.randn_like(sample) * sample).sum()
      params = [
          init.info_vec,
          init.precision,
          trans.info_vec,
          trans.precision,
      ]
      torch.autograd.grad(loss, params)
  
imports: import math
  from collections import OrderedDict
  import pytest
  import torch
  from torch.distributions import constraints, transform_to
  from torch.nn.functional import pad
  import pyro.distributions
  from pyro.distributions.util import broadcast_shape
  from pyro.ops.gaussian import AffineNormal, Gaussian, gaussian_tensordot, matrix_and_gaussian_to_gaussian, matrix_and_mvn_to_gaussian, mvn_to_gaussian, sequential_gaussian_filter_sample, sequential_gaussian_tensordot
  from tests.common import assert_close
  from tests.ops.gaussian import assert_close_gaussian, random_gaussian, random_mvn
label_desc: Use image node_id 20 for calling a global function with example usage: test_sequential_gaussian_filter_sample(sample_shape, batch_shape, state_dim, num_steps) without return types