code: def graphical_lasso_path(
      X,
      alphas,
      cov_init=None,
      X_test=None,
      mode="cd",
      tol=1e-4,
      enet_tol=1e-4,
      max_iter=100,
      verbose=False,
      eps=np.finfo(np.float64).eps,
  ):
      """l1-penalized covariance estimator along a path of decreasing alphas
  
      Read more in the :ref:`User Guide <sparse_inverse_covariance>`.
  
      Parameters
      ----------
      X : ndarray of shape (n_samples, n_features)
          Data from which to compute the covariance estimate.
  
      alphas : array-like of shape (n_alphas,)
          The list of regularization parameters, decreasing order.
  
      cov_init : array of shape (n_features, n_features), default=None
          The initial guess for the covariance.
  
      X_test : array of shape (n_test_samples, n_features), default=None
          Optional test matrix to measure generalisation error.
  
      mode : {'cd', 'lars'}, default='cd'
          The Lasso solver to use: coordinate descent or LARS. Use LARS for
          very sparse underlying graphs, where p > n. Elsewhere prefer cd
          which is more numerically stable.
  
      tol : float, default=1e-4
          The tolerance to declare convergence: if the dual gap goes below
          this value, iterations are stopped. The tolerance must be a positive
          number.
  
      enet_tol : float, default=1e-4
          The tolerance for the elastic net solver used to calculate the descent
          direction. This parameter controls the accuracy of the search direction
          for a given column update, not of the overall parameter estimate. Only
          used for mode='cd'. The tolerance must be a positive number.
  
      max_iter : int, default=100
          The maximum number of iterations. This parameter should be a strictly
          positive integer.
  
      verbose : int or bool, default=False
          The higher the verbosity flag, the more information is printed
          during the fitting.
  
      eps : float, default=eps
          The machine-precision regularization in the computation of the
          Cholesky diagonal factors. Increase this for very ill-conditioned
          systems. Default is `np.finfo(np.float64).eps`.
  
          .. versionadded:: 1.3
  
      Returns
      -------
      covariances_ : list of shape (n_alphas,) of ndarray of shape \
              (n_features, n_features)
          The estimated covariance matrices.
  
      precisions_ : list of shape (n_alphas,) of ndarray of shape \
              (n_features, n_features)
          The estimated (sparse) precision matrices.
  
      scores_ : list of shape (n_alphas,), dtype=float
          The generalisation error (log-likelihood) on the test data.
          Returned only if test data is passed.
      """
      inner_verbose = max(0, verbose - 1)
      emp_cov = empirical_covariance(X)
      if cov_init is None:
          covariance_ = emp_cov.copy()
      else:
          covariance_ = cov_init
      covariances_ = list()
      precisions_ = list()
      scores_ = list()
      if X_test is not None:
          test_emp_cov = empirical_covariance(X_test)
  
      for alpha in alphas:
          try:
              # Capture the errors, and move on
              covariance_, precision_, _, _ = _graphical_lasso(
                  emp_cov,
                  alpha=alpha,
                  cov_init=covariance_,
                  mode=mode,
                  tol=tol,
                  enet_tol=enet_tol,
                  max_iter=max_iter,
                  verbose=inner_verbose,
                  eps=eps,
              )
              covariances_.append(covariance_)
              precisions_.append(precision_)
              if X_test is not None:
                  this_score = log_likelihood(test_emp_cov, precision_)
          except FloatingPointError:
              this_score = -np.inf
              covariances_.append(np.nan)
              precisions_.append(np.nan)
          if X_test is not None:
              if not np.isfinite(this_score):
                  this_score = -np.inf
              scores_.append(this_score)
          if verbose == 1:
              sys.stderr.write(".")
          elif verbose > 1:
              if X_test is not None:
                  print(
                      "[graphical_lasso_path] alpha: %.2e, score: %.2e"
                      % (alpha, this_score)
                  )
              else:
                  print("[graphical_lasso_path] alpha: %.2e" % alpha)
      if X_test is not None:
          return covariances_, precisions_, scores_
      return covariances_, precisions_
  
imports: import operator
  import sys
  import time
  import warnings
  from numbers import Integral, Real
  import numpy
  from scipy import linalg
  from ..base import _fit_context
  from ..exceptions import ConvergenceWarning
  from ..linear_model import _cd_fast
  from ..linear_model import lars_path_gram
  from ..model_selection import check_cv, cross_val_score
  from ..utils._param_validation import Interval, StrOptions, validate_params
  from ..utils.metadata_routing import _RoutingNotSupportedMixin
  from ..utils.parallel import Parallel, delayed
  from ..utils.validation import _is_arraylike_not_scalar, check_random_state, check_scalar
  from .None import EmpiricalCovariance, empirical_covariance, log_likelihood
label_desc: Use image node_id 6 for calling a global function with example usage: graphical_lasso_path(X, alphas, cov_init, X_test, mode, tol, enet_tol, max_iter, verbose, eps) and returns: covariances_,  precisions_, covariances_,  precisions_,  scores_