code: def test_log_multivariate_gaussian():
      np.random.seed(0)
      x = np.random.random((2, 1, 1, 3))
      mu = np.random.random((3, 1, 3))
  
      V = positive_definite_matrix(3, M=4)
  
      res1 = log_multivariate_gaussian(x, mu, V)
      assert res1.shape == (2, 3, 4)
  
      res2 = np.zeros_like(res1)
      for i in range(2):
          for j in range(3):
              for k in range(4):
                  res2[i, j, k] = log_multivariate_gaussian(
                      x[i, 0, 0], mu[j, 0], V[k]
                  )
      assert_array_almost_equal(res1, res2)
  
file_path: astroML/astroML/utils/tests/test_utils.py
imports: import numpy
  from numpy.testing import assert_array_almost_equal, assert_allclose
  from astroML.utils import log_multivariate_gaussian, convert_2D_cov, completeness_contamination, split_samples
label_desc: Use image node_id 3 for calling a global function with example usage: test_log_multivariate_gaussian() without return types