code: def log_likelihood(emp_cov, precision):
      """Compute the sample mean of the log_likelihood under a covariance model.
  
      Computes the empirical expected log-likelihood, allowing for universal
      comparison (beyond this software package), and accounts for normalization
      terms and scaling.
  
      Parameters
      ----------
      emp_cov : ndarray of shape (n_features, n_features)
          Maximum Likelihood Estimator of covariance.
  
      precision : ndarray of shape (n_features, n_features)
          The precision matrix of the covariance model to be tested.
  
      Returns
      -------
      log_likelihood_ : float
          Sample mean of the log-likelihood.
      """
      p = precision.shape[0]
      log_likelihood_ = -np.sum(emp_cov * precision) + fast_logdet(
          precision
      )
      log_likelihood_ -= p * np.log(2 * np.pi)
      log_likelihood_ /= 2.0
      return log_likelihood_
  
file_path: catboost/contrib/python/scikit-learn/py3/sklearn/covariance/_empirical_covariance.py
imports: import warnings
  import numpy
  from scipy import linalg
  from ..None import config_context
  from ..base import BaseEstimator, _fit_context
  from ..metrics.pairwise import pairwise_distances
  from ..utils import check_array
  from ..utils._param_validation import validate_params
  from ..utils.extmath import fast_logdet
label_desc: Use image node_id 1 for calling a global function with example usage: log_likelihood(emp_cov, precision) and returns: log_likelihood_