code: def log_multivariate_normal_density(X, means, covars, covariance_type='diag'):
      
      log_multivariate_normal_density_dict = {
          'spherical': _log_multivariate_normal_density_spherical,
          'tied': _log_multivariate_normal_density_tied,
          'diag': _log_multivariate_normal_density_diag,
          'full': _log_multivariate_normal_density_full}
      return log_multivariate_normal_density_dict[covariance_type](
          X, means, covars
      )
docs: Compute the log probability under a multivariate Gaussian distribution.
      Parameters
      ----------
      X : array_like, shape (n_samples, n_features)
          List of n_features-dimensional data points. Each row corresponds to a
          single data point.
      means : array_like, shape (n_components, n_features)
          List of n_features-dimensional mean vectors for n_components Gaussians.
          Each row corresponds to a single mean vector.
      covars : array_like
          List of n_components covariance parameters for each Gaussian. The shape
          depends on `covariance_type`:
              (n_components, n_features)      if 'spherical',
              (n_features, n_features)    if 'tied',
              (n_components, n_features)    if 'diag',
              (n_components, n_features, n_features) if 'full'
      covariance_type : string
          Type of the covariance parameters.  Must be one of
          'spherical', 'tied', 'diag', 'full'.  Defaults to 'diag'.
      Returns
      -------
      lpr : array_like, shape (n_samples, n_components)
          Array containing the log probabilities of each data point in
          X under each of the n_components multivariate Gaussian distributions.