code: def test_gamma_and_mvn_to_gamma_gaussian(
      sample_shape, batch_shape, dim
  ):
      gamma = random_gamma(batch_shape)
      mvn = random_mvn(batch_shape, dim)
      g = gamma_and_mvn_to_gamma_gaussian(gamma, mvn)
      value = mvn.sample(sample_shape)
      s = gamma.sample(sample_shape)
      actual_log_prob = g.log_density(value, s)
  
      s_log_prob = gamma.log_prob(s)
      scaled_prec = mvn.precision_matrix * s.unsqueeze(-1).unsqueeze(-1)
      mvn_log_prob = dist.MultivariateNormal(
          mvn.loc, precision_matrix=scaled_prec
      ).log_prob(value)
      expected_log_prob = s_log_prob + mvn_log_prob
      assert_close(actual_log_prob, expected_log_prob)
  
imports: import math
  import pytest
  import torch
  from torch.nn.functional import pad
  import pyro.distributions
  from pyro.distributions.util import broadcast_shape
  from pyro.ops.gamma_gaussian import GammaGaussian, gamma_and_mvn_to_gamma_gaussian, gamma_gaussian_tensordot, matrix_and_mvn_to_gamma_gaussian
  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_gamma_and_mvn_to_gamma_gaussian(sample_shape, batch_shape, dim) without return types